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Spatio-temporal variability in Ebro river basin (NE Spain): Global SST as potential source of predictability on decadal time scales
Journal of Hydrology 409 (2011) 759–775
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Spatio-temporal variability in Ebro river basin (NE Spain): Global SST as potential source of predictability on decadal time scales S.R. Gámiz-Fortis ⇑, J.M. Hidalgo-Muñoz, D. Argüeso, M.J. Esteban-Parra, Y. Castro-Díez Applied Physics Department, University of Granada, Granada, Spain
a r t i c l e
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Article history: Received 8 March 2011 Received in revised form 20 August 2011 Accepted 12 September 2011 Available online 17 September 2011 This manuscript was handled by Konstantine P. Georgakakos, Editor-in-Chief, with the assistance of Ercan Kahya, Associate Editor Keywords: Ebro river basin Streamflow variability Decadal and interannual variability Global SST PDO ARMA modelling
s u m m a r y This paper investigates the spatial and temporal variability of streamflow in the Ebro river basin and its potential predictability. Principal Component Analysis applied to monthly streamflow series from 83 gauging stations distributed through the basin, reveals three homogeneous regions: Basque–Cantabrian, Pyrenees and Southern Mediterranean. Attending to this classification the main characteristic time scales of the maximum monthly streamflows are studied by Singular Spectral Analysis (SSA). Decadal variations in streamflow make particularly large contributions to year-to-year streamflow variance in stations placed in the Basque–Cantabrian and Southern Mediterranean regions, while for the Pyrenees flows the interannual contribution is more important. The predictability of the Ebro flow anomalies has been investigated using a combined methodology: at decadal time scales SST anomalies from several regions provide a significant source of predictability for the Ebro flow, while at interannual time scales autoregressive-moving-average modelling, applied to the time series previously filtered by SSA, is able to provide potential skill in forecasting. For gauging stations associated to the Basque–Cantabrian region significant correlations between the maximum monthly streamflow anomalies and a tripole-like pattern in the North Atlantic SSTs during the previous spring are found. This association is found maximum and stable for the tropical part of the pattern (approximately 0–20°N). For the gauging stations placed to the southeast of basin some influence from the Pacific Decadal Oscillation (PDO) is found. This method allows evaluating, independently, the decadal and interannual predictability of the streamflow series. In addition, the combination of both modelling techniques gives as result a methodology that has the capacity to provide basin-specific hydroclimatic predictions which vary (for the 1990–2003 validation period) between 62% for the Basque–Cantabrian region, 76% for the Southern Mediterranean and 81% for the Pyrenees. In summary, this work shows the existence of a valuable decadal and interannual predictability of the Ebro streamflow, a result which may be useful to water resources management. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Accurate simulation and forecasting of water availability is a key step in efficient planning, operation and management of water resources such as hydroelectric power production and agriculture crop yields. Developing reliable surface water flow forecasting methods for real-time operational water resources management becomes increasingly important. River flow variability plays an important role in water resources development and management in most of the world regions (IPCC, 2001; Gong et al., 2010). The hydrological system acts as spatial and temporal integrator of ⇑ Corresponding author. Address: Departamento de Física Aplicada, Facultad de Ciencias, Universidad de Granada, Campus Fuentenueva s/n, 18071 Granada, Spain. Tel.: +34 958 240026; fax: +34 958 243214. E-mail address: [email protected] (S.R. Gámiz-Fortis). 0022-1694/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jhydrol.2011.09.014
precipitation (rain and snow), temperature, and related evapotranspiration, also integrating land-surface processes such as vegetation and land cover changes, human uses or hydraulic infrastructures over a specific region. Seasonal variations of streamflows arise from variations in precipitation and temperature, which are controlled by large-scale fluctuations in atmospheric circulation patterns. Hence, streamflow records can serve as a pertinent index of hydroclimatic variability (Coulibaly and Burn, 2005). For this reason, the interest in seasonal predictability of river discharge variability has increased markedly during the last years (Trigo et al., 2004; Rimbu et al., 2004, 2005; Gámiz-Fortis et al., 2008a,b, 2010a; Ionita et al., 2008) in the context of climate predictability studies. The availability of water is mostly influenced by climate conditions that vary on seasonal, interannual and decadal time scales. On seasonal timescales, anomalous atmospheric conditions are
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often linked with seasonal variations in the rivers streamflow and reservoir storages, via variations in precipitation and temperature (Dettinger and Diaz, 2000; Cullen et al., 2002; Trigo et al., 2004; Karabörk et al., 2005; López-Moreno et al., 2007). The interannual climate and hydrologic fluctuations are modulated by, or superimposed upon, lower frequency variations with decadal and longer time scales. The sources of these lower frequency climate variations are uncertain but may have roots in the tropics (Barnett et al., 1992; Trenberth and Hoar, 1996), in the extratropical oceans (Pacific: Douglas et al., 1982; Trenberth, 1990; Latif and Barnett, 1994; Atlantic: Schlosser et al., 1991; Read and Gould, 1992; Deser and Blackmon, 1993; Tanimoto et al., 1993; Stocker and Broecker, 1994; Chen and Ghil, 1996; Houghton, 1996), or in some interplay of the two (e.g., Graham, 1994; Graham et al., 1994; Jacobs et al., 1994). Usually, the skill of the long-range forecasts is associated with the introduction of predictors that represent the slow varying components of the climate system such as sea ice, snow cover, soil moisture and sea surface temperatures (SST) (Koster et al., 2010). The oceans have a vast storage of energy that helps drive global climate variability, and SST is one manifestation of this energy storage. Given the oceanic mass and water’s large specific heat, the effect of SST on ocean–atmosphere heat and water vapour exchange can be on seasonal to annual time scales. Consequently, variability in SST can help provide predictive information about the hydroclimate in regions across the globe (Rimbu et al., 2005; Gámiz-Fortis et al., 2008b, 2010a; Ionita et al., 2008). Additionally, major oceanic and atmospheric circulation patterns such as the North Atlantic Oscillation (NAO) or Pacific Decadal Oscillation (PDO) can also improve the forecasts (Guetter and Georgakakos, 1996; López-Moreno et al., 2007; Trigo et al., 2004; Gámiz-Fortis et al., 2008a; Hamlet and Lettenmaier, 1999). The NAO index is computed as the difference of sea-level pressure between two stations situated close to the centres of Icelandic Low and Azores High (Hurrell, 1995), while the PDO index is calculated to be the first principal component of detrended SST anomalies northward of 20°N latitude in the Pacific Ocean (Mantua et al., 1997). There are two potential problems with using standard climate indices for hydroclimatic prediction. The first one is that the hydroclimate of a river basin may be more strongly correlated with an oceanic region’s SSTs, which is different from the predetermined regions that are used to calculate the standard indices (Namias, 1978; Kutzbach, 1970; Nicholls, 1980; Tootle and Piechota, 2006). The second problem is that matricial methods, such as PCA, used to obtaining these indices, might not preserve enough information from an original dataset (Switanek et al., 2009). In any case, the relationship between the climatic regimes and its hydrological response, through the streamflow, presents different grades of complexity according to the physical characteristics of the basin so it should be studied in detail. The Ebro River represents the Spanish most important catchment of the Iberian Peninsula, being a very representative example of large Mediterranean rivers. Floods during the cold season occur from October to March, sometimes until May, due mainly to an oceanic pluvial regime, whereas floods in spring are the result of melting snows in the Pyrenees (López-Moreno and García-Ruiz, 2004; Pedregal et al., 2009). Recent works have been conducted for the Ebro Basin, but for different purposes to that here considered, such as the study of the spatial and temporal variability of winter droughts for specific areas of the basin (Vicente-Serrano and López-Moreno, 2006), the hydrological characterisation of flow typologies (Bejarano et al., 2010), hydrological modelling of specific gauging stations at daily time scales (Pedregal et al., 2009) or the study of hydrological trends (López-Moreno et al., 2011). The novelty of this work is based mainly on three points: one is about characterisation of hydrological variability on the whole Ebro basin on different climatic timescales, which results in the
ability of separating the interannual and decadal predictability in different regions of the Basin. Other is about the identification of connections to climate forcings that could provide potential improvement for building hydrological models. On this point is important to emphasise the use of global SST as potential predictor variable. And another is on how different techniques are combined to produce an algorithm that generates reliable estimates of flow in different parts of the Ebro basin at seasonal time scales. In this sense, the results of the work reveal independent predictive models for different streamflows in the Basin. In summary, this paper presents a modelling scheme for Ebro streamflow anomalies based on the combination of different steps: (1) identification of homogeneous regions of Ebro streamflow variability, (2) analysis of the temporal structure of the series for each selected region in the Ebro basin, (3) detection of statistically significant linkage that exist between the streamflow series in the Ebro basin and large scale SST variability modes, and (4) separate modelling of high and low frequency variations through the use of autoregressive-moving-average (ARMA) models and stable teleconnections between oceanic SST anomalies and river flow, respectively. The paper is organised as follow: In Section 2 the study region and the data used are described. In Section 3 the different methodologies and the steps taken in building the prediction algorithm are presented. The spatio-temporal streamflow anomaly patterns are presented in Section 4, while in Section 5 we show the results of the streamflow modelling. A discussion and the main conclusions follow in Section 6.
2. Data The Ebro River (Fig. 1) presents the largest catchment in Spain, with an area of 85,530 km2 in the northeast of Spain. Ebro basin is a complex region from both the topographical and meteorological perspectives, with great physical heterogeneity, which is a deciding factor in the annual seasonality of flow. This region forms a broadly triangular morphological unite, which is a depression surrounded by high mountain ranges including, to the north, the Pyrenees and Basque–Cantabrian Mountains, to the east the Catalan Coastal Range, and from the northwest to southeast the Iberian Massif. The heterogeneous topography contrasts the influences of the Atlantic and Mediterranean as well as of different large-scale atmospheric patterns (Vicente-Serrano and López-Moreno, 2006). Some studies divide the Ebro basin into different climatic areas according to the precipitation regime (Batalla et al., 2004; Bejarano et al., 2010): the Cantabrian Mountains, with average annual precipitation of about 1100 mm, the eastern Pyreness (about 800 mm), the west-central Pyrenees (about 900 mm), the northwestern Iberian Massif (about 650 mm), the southern Iberian Massif (about 500 mm) and the centre of Ebro basin (about 350 mm). Monthly streamflow data were kindly provided by the Ebro Water Authority (Confederación Hidrográfica del Ebro – CHE –, http://www.chebro.es) and the National Water Research Centre (CEDEX, http://www.cedex.es). First, a study about the characterisation of hydrological sustained changes in gauging stations of basin was carried out, analysing information about the type of alteration, the period of alteration and the magnitude of the disturbance in the gauging station. Most of stations with medium, high or very high magnitude alterations were subsequently eliminated from the analysis. We selected a total of 83 streamflow series distributed in the basin that were intensively checked for inconsistencies, showing less than 10% of missing values during the period 1950–2006. Data gaps were filled using data from neighbouring stations with which there was a Pearson correlation coefficient of at least 0.8 (López-Moreno et al., 2011). Fig. 1 shows the spatial
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Fig. 1. Location of the Ebro river basin in the Iberian Peninsula (left) and spatial distribution of the gauging stations (right) used in this study in the basin. Topographical features of the Basin are expressed in m.
distribution of the gauging stations in the Ebro basin. We can see a reasonable although no homogeneous spatial coverage of the stations across the entire basin, where most of them are situated in the Cantabrian Mountains, Pyrenees and in the southern Mediterranean zone, while very few stations are placed in the centre of the basin. Hydrological series commonly do not follow a normal distribution, being highly biased, often requiring some preliminary transformation in order to adjust the records to an appropriate distribution. Also, the magnitude of the monthly streamflow values varies greatly among the stations, due to both the different climatic regions in Ebro basin and the different drainage basin characteristics associated with each streamflow station. Some studies have shown a good adjustment of the discharge series to the log-normal distribution (Zaidman et al., 2001; Kalayci and Kahya, 2006), while Vicente-Serrano (2006) and López-Moreno et al. (2009) found that the Pearson III distribution is more appropriate over some parts of the Iberian Peninsula. Using these considerations we tested three different theoretical distributions for modelling the monthly stream river flow: the Pearson III, the log-normal and the normal distribution. Furthermore, the goodness of fit was evaluated using three different tests, the Kolmogorov–Smirnov, the Anderson–Darling and the Chi-squared tests. We find that for the most of cases the Pearson III and the log-normal theoretical distributions present good results, but for the gauging stations placed in the southern Iberian Massif, the Pearson III is not an appropriate probability distribution. For this reason, and in order to facilitate the intercomparison between regions, the streamflow data were first subjected to logarithmic transformation to reduce the disparity in the magnitudes, from which monthly standardised streamflow anomalies were computed. The monthly standardised streamflow anomalies were constructed by subtracting the mean and dividing by the standard deviation for each month separately. The standardised streamflow for each station closely follows a normal distribution. The global SST data was taken from the HadISSTv1.1 data set (Rayner et al., 2003) derived from the Hadley Centre for Climate Prediction and Research (UK Meteorological Office). We generate the winter, spring, summer and autumn SST fields by averaging the monthly SST anomalies (using the mean and standard deviation for the period 1961–1990) for DJF, MAM, JJA and SON, respectively. SST data has a resolution of 1° 1° and the temporal length is 1871–2007. Also, the standardised PDO index derived as the leading PC of monthly SST anomalies in the North Pacific Ocean, poleward of
20°N from http://jisao.washington.edu/pdo/PDO.latest, that covers the period 1900–2010, has been used in this study (Zhang et al., 1997; Mantua et al., 1997).
3. Methodology In the present study, regionalisation of streamflow series in the Ebro basin was performed using rotated Principal Component Analysis (PCA). PCA has been applied in analysing the spatial variability of physical fields. In climatology and hydrology, the PCA is a tool to document the typical nature of streamflow and has been used in similar contexts of the present study (Widmann and Schär, 1997; Maurer et al., 2004; Kalayci and Kahya, 2006). PCA reduces a large number of interrelated variables to a few independent PCs that capture much of the variance of the original dataset (Wilks, 1995; Hannachi et al., 2007). It produces a few major spatial-variability patterns (or empirical orthogonal functions, EOFs), and the corresponding time series that represent the time evolution of the spatial-variation patterns. The North Rule based on the eigenvalue degeneration (North et al., 1982) was adopted here and the resulting significant EOFs varimax rotated to capture better the physically meaningful and simplified spatial patterns (Barnston and Livezey, 1987). This procedure allows extracting representative stations for each of the areas obtained in the regionalisation process. For the study of temporal variability a Singular Spectral Analysis (SSA) is applied to each streamflow time series representative of the regions previously identify by PCA. SSA is a powerful tool for time-series analysis that can identify intermittent oscillation spells, in short, noise time series (Vautard et al., 1992). SSA has been successfully applied to many geophysical and climatological time series to study and predict periodic activities (Ghil and Mo, 1991; Ghil and Vautard, 1991; Plaut and Vautard, 1994; GámizFortis et al., 2002, 2008a, 2010a,b; Paluš and Novotná, 2006). SSA solves eigenvalue problems stemming from the lag-autocovariance matrix of a single time series with a pre-defined window length (Vautard et al., 1992; Elsner and Tsonis, 1996). The PCs produced by SSA are called temporal PCs (T-PCs) and the empirical orthogonal functions are the time EOFs (T-EOFs) that describe the temporal oscillatory behaviour of the T-PCs. Eigenvalues are sorted in descending order, indicating the variance of each corresponding T-PC. When two consecutive eigenvalues are nearly equal, and the corresponding T-PCs are in quadrature, these two T-PCs form a pair and potentially represent an oscillation. The time evolution
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of each identified oscillation component is extracted based on the reconstruction technique developed by Plaut and Vautard (1994). Each reconstructed time series (RC) represents an isolated oscillation and the original series is exactly the sum of all the RCs. Additionally, the Maximum Entropy Method (MEM) has been used to evaluate the spectral contents of the T-PC time series, and the Monte Carlo (MC) technique was used for the significance study (see Gámiz-Fortis et al. (2002), for further details). The analysis of the temporal structure of the series allows us to model separately their variations at different time scales. To this end an independent analysis of the streamflow variability at low and high frequencies has been carried out. Standardised stremaflow anomalies were smoothed with a 7-year running mean filter to obtain the decadal component of the series (decadal_component hereinafter). This filter is designed to fall both near the low-frequency end of the spectrum associated with El Niño events and near the high-frequency end of the decadal climate variations of the Atlantic and North Pacific climate systems (Cayan et al., 1998; Dettinger et al., 2001), and has been used following other authors (Ionita et al., 2011) in order to exclude any cross-spectrum between Ebro River streamflow and El Niño. Note that in this filtering process, we lost 6 years, 3 at the beginning of the series and 3 at the end. Then, the dominant patterns of streamflow variability are related to global SST to identify potential large scale climate features that drive the variability at decadal time scales. Simple methods of statistical analysis were used in this study to describe the potential relationship between the streamflow series and the SST, both contemporary and of the preceding seasons in order to evaluate predictive ability. Linear correlation maps were constructed to identify regions of the global SST that exhibit teleconnections with streamflow at Ebro basin. Regions showing significant correlations are identified as potential predictors but only those identified as stable predictors will be used in a multiple linear regression model to simulate the Ebro river flow anomalies on decadal time scales (SST_model). Stable predictors are achieved through the analysis of the variability of the correlation between Ebro flow anomalies and SST anomalies from regions considered as potential predictors using a moving window of 15 years. Additional analysis using a window length of 20 years were carried out in order to examine the stability of the connections in time. Following the criterion of Ionita et al. (2008) the correlation is considered to be stable for those regions where streamflow and SST anomalies are significantly correlated at 90% level for more than 80% of the 15-year windows covering the total period and, furthermore, where the sign of the correlation does not change with time. SST regions verifying this criterion are considered as robust predictors for the decadal_component of the streamflow, and will be used in a multiple-linear-regression model that use the decadal components of the SST time series averaged over these regions as explanatory variables. The method of ordinary least squares was used to estimate the regression coefficients (Draper and Smith, 1998) by minimising the sum of squared errors (SSE), i.e. the unexplained variance part. The coefficient of multiple determination R2, which measures the fraction of variance in the response variable that can be explained by variations in the explanatory factors also is computed. Note that a high value of R2 does not imply that a particular model is appropriate. In fitting the model, the assumption is made that the unknown random effects are represented by ‘‘e’’, which is a vector of independent, normally distributed noise. The validity of this assumption should be checked. The remaining interannual variability of flows (for time scales less than 7 years) can be obtained by the difference between the raw flow and the decadal_component. This interannual_component is firstly modelled by the significant quasi-oscillatory modes (with periods <7 years) obtained from the previous SSA (interannual_SSA_filter hereinafter) and autoregressive-moving-average
(ARMA) models were fitted to the interannual_SSA_filter of streamflow. The SSA filter is able to partially remove background noise, retaining the leading statistically significant (and predictable) interannual components. For this reason the SSA filtering prior to obtaining the ARMA models considerably improves the forecasting skill of these ARMA models (Gámiz-Fortis et al., 2002, 2008a, 2010a). ARMA models can be regarded as a special case of general linear stochastic processes and provide a linear representative structure of the temporal evolution of the data. The order of the model is selected, in a preliminary approach, studying the autocorrelation function (ACF) and partial autocorrelation function (PACF). In physical terms, the best model has as few parameters as possible. We have used the Akaike information criterion (AIC) (Akaike, 1974) to select the final model among all the candidates. The AIC is based on information theory and represents a compromise between the goodness of the fit and the number of parameters of the model. A comprehensive review, explaining in detail how to fit ARMA models to datasets following the identification, estimation, and diagnostic check stages, can be found in Brockwell and Davis (1996) and Hipel and Mcleod (1994). Finally, the combination of both SST_models (for decadal time scales) and ARMA_models (for interannual time scales) is evaluated in a forecasting experiment. For reliable skill assessment, a fundamental aspect of this evaluation is the separation of calibration and validation periods (Wilks, 1995). We employ data until 1989 to calibrate the different modelling (decadal, interannual and combined), while data from 1990 to 2006 are used for validation purposes only. We would like also to apply cross-validation using development data set of size n 1 and verification data set containing the remainder single observation of the predictand, leading to n partitions of the dataset. The model is then calculated for each of these partitions, resulting in n similar forecast equations, each one computed without one of the observations of the predictand. Unfortunately, this procedure cannot be applied in our case for a number of reasons, namely because when fitting ARMA models, the temporal location of each data cares: i.e. the ‘‘history’’ of the series is very important. When removing one single data in the middle of the data set, the remaining data are not useful to fit the model, because the temporal structure of the data is then broken (Gámiz-Fortis et al., 2002). For model evaluation we employ appropriate skill measures commonly used, such as the mean absolute error (MAE) and the mean square error (MSE) as accuracy measures; the Pearson correlation coefficient, which is used to measure the relationship between the modelled/forecasted series and the original/expected series; the percentage of phase agreement, that is, the percentage of cases in which the modelled/forecasted values has the same sign as the original values; the Willmott agreement index (D) (Willmott, 1982), which is a dimensionless measure of relative error in model estimates which ranges from 0 (complete disagreement between estimated and observed values) to 1 (complete agreement); and the coefficient of multiple determination R2, which measures the fraction of variance in the response variable that can be explained by variations in the explanatory factors (Junge and Stephenson, 2003). The combined use of different methodologies has already been used by the authors in previous studies of predictability obtaining very useful results (Gámiz-Fortis et al., 2002, 2008a,b, 2010a,b).
4. Streamflow anomaly patterns The PCA of the monthly mean streamflow records at the 83 stations in the Ebro basin for the period 1950–2006 showed that most of the regional variations are attributable to relatively small number of basic anomaly patterns. Three significant spatial EOFs,
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Fig. 2. Loading factors for the first (a), second (b) and third (c) S-EOF resulting of the monthly streamflow PCA in the Ebro basin for the 1950–2006 period. (d) Location of the two specific gauging stations with the highest loading factors associated to the PC1 (red), PC2 (blue) and PC3 (green). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
accounting for 55.4% of the total variance, were found. Fig. 2 shows the corresponding spatial patterns by drawing the loading factors associated to each station. The leading mode (Fig. 2a) explains 23.4% of the total variance, and represents mainly the variability of streamflow in the Cantabrian Mountains. Additionally, the gauging station corresponding to Ebro in Zaragoza (EZ), sited in the middle of the basin, also shows high correlation coefficient with the PC1. Fig. 2b shows the spatial pattern associated with the second EOF, which explains 21.8% of the total variance, and is representative mainly of the variability over the Pyrenees area. Fig. 2c shows the pattern associated with the third EOF (10.2% of the total variance). This pattern is representative mainly of the variability of the southern mediterranean region in the basin. We have selected, for each one of these regions, two stations whose streamflow time series show the highest loading factors with the corresponding PC series, which can be considered like streamflow series representative of the region. Fig. 2d shows the
Table 1 List of individual gauging stations selected in the Ebro river basin, showing highest correlation coefficients with their associated PCs series. Code of the station from the CHE dataset, period data length and short name (hereinafter). Station name
Gauged code
Data length
Corr. coeff. (rPCi)
Short name
Ebro in Zaragoza Ebro in Mendavia Noguera Ribagorzana in Pont de Suer Esera in Grauss Martin in Alcaine Matarraña in Nonaspe
9011 9120 9137
1913–2006 1913–2006 1950–2006
rPC1 = 0.85 rPC1 = 0.82 rPC2 = 0.87
EZ_FLOW EM_FLOW NP_FLOW
9013 9127 9176
1950–2006 1950–2006 1950–2006
rPC2 = 0.85 rPC3 = 0.70 rPC3 = 0.70
EG_FLOW MA_FLOW MN_FLOW
location of these specific stations and Table 1 presents a description of them, including their short names. Fig. 3 presents the seasonal variability of the mean monthly flow for the six individual specific gauging stations of Table 1, along the entire period of available data. For the stations associated to the region represented by EOF1 (Fig. 3a) winter-time river flow account for the majority of runoff, being followed by a relatively long and dry summer period from July to September. This result corresponds with the flow type 4 of the classification done by Bejarano et al. (2010) about flow types in the Ebro basin. Flow type 4 of this classification corresponds with seasonal winter flow types and is located along the Basque–Cantabrian Mountains (Oro-Ibérica and Cantabro-Atlántica Subprovinces). For the stations associated to the region represented by EOF2 (Fig. 3b) a nivo-pluvial flow type, located in the Pyreness Mountains (Pirenaica Subprovince) (Bejarano et al., 2010) is presented, where snowmelt influence is very important. This area is characterised by a snowy winter, very rainy spring and rainy late summer an autumn (Bejarano et al., 2010). Finally, Fig. 3c shows the flows associated to the stations located in the southeast of the Ebro basin (Catalana-Valencia Subprovince) and were characterised by fairly low total annual precipitation and prolonged dry season. Taking into account the maximum streamflow values observed for the different flow types associated with the regions represented by the PCs, the study was limited to those months in which both discharge time series associated with a region are highest. That is, January for the river gauges associated to the PC1, June for those associated to the PC2 and May for those associated to the PC3. Fig. 4 shows these streamflow time series along with the associated PCs. Note from Fig. 3c that MN_FLOW time series shows an additional peak in December, which is even higher than in May. However, a detailed review (not shown) of the flow seasonality
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associated with this region of the basin shows that this MN_FLOW time series is the only one with this behaviour. The flows of the other series in this region all present the highest peak in May. For this reason, the study for the mediterranean region has been restricted to May month. 4.1. Temporal variations SSA is then applied to each of these streamflow series to further identify and extract the oscillation components. Different window lengths between M = 18 and M = 32 years and the Vautard and Ghil (1989) algorithm were used in SSA. Only the results obtained for EZ_FLOW in December, EG_FLOW in June and MN_FLOW in May are shown hereinafter (similar results are obtained for the related EM_FLOW, NP_FLOW and MA_FLOW stations, respectively). The oscillation pairs identified by SSA on streamflow series for the selected stations are summarised in Table 2. Because SSA cannot resolve periods longer than the window length, we identified the zero frequency as the non-linear trend, but it is important to note that this non-linear trend could be composed of quasi-oscillatory modes with periods longer than window length years. For the Basque–Cantabrian region, besides the non-significant zero-frequency mode (trend), the significant modes in the January streamflow anomaly of EZ_FLOW (9011 gauging station) were located at the frequencies (in cycles per year) 0.043, 0.45, 0.11, 0.23, 0.32 and 0.15 corresponding to periods around 23.3, 2.3, 9.1, 4.3, 3.1 and 6.6 years, respectively. Table 2 also shows the variance explained by each mode (see middle column). Note that about 31.3% of the variance of the raw series is associated to the
decadal or multi-decadal variability (periods longer than 7 years) while about the 32.6% is explained by quasi-oscillatory modes of high frequency (periodicities less than 7 years). For the Pyrenees region (EG_FLOW in June), along with a nonlinear trend, significant modes appeared at frequencies 0.232, between 0.454–0.370, and 0.105 cycles/year, corresponding to periods around 4.3, between 2.2–2.7 years and 9.5 years, respectively. In this case, the trend and the oscillatory mode with period around 9.5 years account with 22.6% of the total variability while the remainder of the oscillations represents around 50.6%. For the southern Mediterranean region of the basin (MN_FLOW in May), along with the non-linear trend, flow variability at decadal scales is given by a quasi-oscillatory mode with period around 15 years, representing around 35.2% of the variance explained. Additionally, at time scales lower than 7 years, significant quasioscillatory modes with periods around 2.5, 3.1, 3.6, 4.9 and 6.6 years are found, representing the 46.3% of the raw series variance. Note that for the three regions much of the variance is associated with time scales greater than 7 years (between 22% and 35% depending on the region), while the rest of the variance is determined by the interannual variability of the series at time scales lower than 7 years (between 30% and 50% depending on the region). Based on this distinction between time scales the three streamflow series selected representing the regions obtained in the previous PCA have been modelled in next section. For this end, the decadal variability of Ebro river basin and its connection with global SST is firstly analysed. Standardised streamflow anomalies
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a
4
b EZ_FLOW EM_FLOW PC1
3
3 NP_FLOW EG_FLOW PC2
2 standard deviation
2 standard deviation
4
1 0 -1
1 0 -1
-2
-2
-3
-3
-4 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
-4 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
c
4 3
MN_FLOW MA_FLOW PC3
standard deviation
2 1 0 -1 -2 -3 -4 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
Fig. 4. PC series and selected streamflow time series corresponding to (a) the Basque–Cantabrian region in January, (b) the Pyrenees region in June and (c) the southern mediterranean region in May.
Table 2 Oscillation pairs identified by SSA on streamflow gauging stations. The second column contains the peak period (in years), the pair order and the fraction of total variance (%) explained by the pair. An estimation of significance level using Monte Carlo SSA (MC-SSA) is also shown (last column). Streamflow series
Oscillation period (years), (rank order for the associated eigenvalues; explained variance)
Test: against red noise process (RN) and red noise + signal (RN + components)
EZ_FLOW (January)
Non-linear trend (7–8; 9.1%) 23.3 y (1–2; 12.7%) 2.3 y (3–4; 11.1%) 9.1 y (5–6; 9.5%) 4.3 y (9–10; 7.3%) 3.1 y (12–13 ; 7.3%) 6.6 y (14–15 ; 6.9%)
<90% >95% >95% >95% >95% >95% >95%
(RN + significant oscillations) (RN + 3–4) (RN) (RN + 3–4 + 1–2 + 9–10 + 12–13) (RN + 3–4 + 1–2) (RN + 3–4 + 1–2) (RN + 3–4 + 1–2 + 9–10 + 12–13)
EG_FLOW (June)
Non-linear trend (5–8; 12.5%) 4.3 y (1–2; 19.8%) 2.1 y (3–4; 18.3%) 2.7 y (6–7; 12.5%) 9.5 y (10–11; 10.1%)
<90% >95% <90% >95% >95%
(RN + 1–2 + 3–4) (RN) (RN + 1–2) (RN + 1–2 + 3–4) (RN + 1–2 + 3–4 + 6–7)
MN_FLOW (May)
Non-linear trend (7; 5%) 15 y (1–2; 30.2%) 2.5 y (3–4; 14.4%) 3.1 y (5–6; 8.9%) 3.6 y (9–10; 8.6%) 4.9 y (11–12; 7.5%) 6.6 y (13–14; 6.9%)
<90% >95% >95% >95% >95% >90% >90%
(RN + 1–2 + 3–4 + 7–8) (RN) (RN) (RN + 1–2 + 3–4 + 5–6) (RN + 1–2 + 3–4 + 5–6) (RN + 1–2 + 3–4 + 5–6) (RN + 1–2 + 3–4 + 5–6 + 9–10 + 11–12)
were smoothed with a 7-year running mean filter to obtain the decadal components of the series (decadal_component). The 7year running mean period has been already chosen by other authors in order to exclude the influence of El Niño events, whose periodicities oscillate between 2 and 7 years (Dettinger et al., 2000; Ionita et al., 2011). In this respect, similar results are found for the two streamflow gauging stations used to characterise each region previously selected in the Ebro basin. Again, only results for the gauging stations EZ_FLOW in January, EG_FLOW in June and MN_FLOW in May are shown. Fig. 5 shows the selected flows along
with the decadal component obtained by smoothing the series with a 7-year running mean.
5. Streamflow modelling 5.1. Basque–Cantabrian region (January) The spatial correlation maps between the decadal_component (7-year running mean filter) of January EZ_FLOW and the preced-
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b3
a3 EZ_FLOW EZ_FLOW_7year rm
2
standard deviation
standard deviation
2
1
0
-1
EG_FLOW EG_FLOW_7year rm
1 0 -1 -2
-2
-3
-3 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
-4 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
c3 MN_FLOW MN_FLOW_7year rm
standard deviation
2
1
0
-1
-2
-3 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
Fig. 5. Time series of monthly streamflow anomalies (solid lines) for (a) EZ_FLOW in January, (b) EG_FLOW in June, and (c) MN_FLOW in May. Dotted lines represent the decadal components obtained by smoothing the series with a 7-year running mean.
a
b
c
d
Fig. 6. Correlation maps between the decadal_component of January streamflow anomalies of EZ_FLOW and (a) previous spring SST anomalies, (b) previous summer SST anomalies, (c) previous autumn SST anomalies, and (d) previous December SST anomalies. Only significant values at the 95% confidence level are shown. Period of study is 1916–2003. The rectangle corresponds to the SST region finally considered for the decadal_component modelling.
ing seasons for SST data are shown in Fig. 6. For meaningful evaluation of the relationship between the SST and streamflow fields on decadal time scales, the linear trend components of all the data sets need to be removed. The fact of eliminating the trend when we
work with variables of different physical natures is necessary because otherwise trends could lead spurious correlations. Maximum statistically significant correlations were found with the previous SST in the Atlantic region. Particularly, we can identify
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positive correlations with the SST anomalies in the tropical North Atlantic and southern Greenland, with the tropical part of the SST pattern (approximately 0–20°N) playing the most important role. This pattern represents what is commonly called North Atlantic horseshoe pattern, described e.g. in Czaja and Frankignoul (2002). Correlations coefficients are maxima in previous spring, decreased in summer and autumn, and come back strongly in the tropical area in December. This spring SST pattern is shown to be related with the subsequent winter NAO (Rodwell and Folland, 2002). An additional region in the south Pacific also shows significant positive correlation during previous summer. Based on this correlation maps we define three SST indices by averaging the normalised SST anomalies over the regions showing maximum correlation values: SST1EZ (54°W–49°W; 9°N–12°N) and SST2EZ (44°W– 39°W; 54°N–56°N) in previous spring, and SST3EZ (99°W–96°W; 28°S–22°S) in previous summer. SST indices were smoothed with a 7-year running mean filter to obtain the decadal component of the series associated to these SST regions, and correlations between the January streamflow anomalies and the SST1EZ, SST2EZ and SST3EZ indices using a moving window of 15 years were computed. Stable positive correlations (not shown) during the period 1916–2003 are found only for the SST1EZ index, while the SST2EZ and SST3EZ indices fail the stability test and dismissed from the rest of the analysis. Using the significant and stable index SST1EZ as predictor for the January EZ_FLOW at decadal time scales we developed a model based on linear regression, using as calibration period 1916– 1989. The optimal model for explaining the decadal_component of this flow can be written as: previous spring
AR ¼ ðU1 ¼ 1:38 ;
-2
EZ_FLOW ARMA (7,6) ARMA (7,6) + SST_model
-3 1915
1925
1935
1945
1955
1965
1975
1985
b3 EZ_FLOW ARMA (7,6) ARMA (7,6) + SST_model
2
1
0
-1
2003
2002
2001
2000
1999
1998
1997
1996
-3
1995
Significance of the parameters was computed using approximate t-values, derived from the parameter standard errors. Parameters highlighted with ‘‘’’ are statistically significant at 5% significance level. The selected order model indicates a certain degree of persistence. Given the values of some of the parameters of the model and the ACF and PACF (not shown), the current interannual_component state is considerable dependent on its state up to 7 years earlier. This ARMA (7,6) model is able to explain around
-2
1993
h3 ¼ 0:23 ;
h4 ¼ 1:09 ; h5 ¼ 0:40 ; h6 ¼ 0:62 Þ
1994
h2 ¼ 1:24 ;
-1
1992
MA ¼ ðh1 ¼ 0:29 ;
0
1991
1
1990
U4 ¼ 1:25 ;
U2 ¼ 1:16 ; U3 ¼ 1:15 ; U5 ¼ 1:18 ; U6 ¼ 0:74 ; U7 ¼ 0:09Þ
standard deviation
2
This SST_modelEZ is able to explain around 56% of the variance of the streamflow decadal_component during the calibration period, showing around 84% agreement in the phase accordance between observed and modelled decadal_component. Regarding the modelling of the interannual variability (time scales less than 7 years) an additional analysis has been carried out using the quasi-oscillatory modes with periods lower than 7 years obtained from the previous SSA. Firstly, a SSA-filtered series, the interannual_SSA_filter, has been computed like the sum of the reconstructed components of these oscillatory modes, and then an ARMA_model is fitted to this SSA-filtered series. Using the sample Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) (not shown) we find that while the interannual_component behave like a white noise process, the interannual_SSA_filter series shows a strong autocorrelation pattern. This feature implies a higher predictability of the interannual_SSA_filter when compared to the unfiltered time series. Based on these analysis, we used the Akaike Information Criterion (AIC) to select an ARMA (7,6) model for the interannual_SSA_filter, containing the following parameters:
a3
standard deviation
SST modelEZ ¼ 2:07 SST1EZ
67% of the variance of the streamflow interannual_component during the calibration period, showing around 88% agreement in the phase accordance between observed and modelled interannual_component. Finally, the combination of SST_model (for decadal time scales) and ARMA_model (for interannual time scales) is evaluated. The observed and modelled January EZ_FLOW series are shown in Fig. 7 for calibration and validation periods. Results obtained reveal a considerable skill achieved by the combined [ARMA (7,6) + SST_model] model (see Table 3), with a good correlation coefficient between the raw series and the model for the calibration period (r = 0.81) and coefficient of multiple determination R2 (66%). Moreover the model presents a relatively low MSE = 0.35, MAE = 0.47 and a relatively high Willmott’s index (D = 0.86). Over the period 1990–2003, not used to fit the model, MSE is 0.73, MAE is 0.72 and Willmott’s index is 0.68. From Table 3 we can also see the contribution made by each of the modelling carried out (decadal and interannual) and can be seen as the overall quality of the combined model has increased significantly in both calibration and validation periods. For the validation period the correlation coefficient between the raw series and the combined model is 0.79 and the variance explained by this model rises to 62%. The combined [ARMA (7,6) + SST_model] modelling capacity can be appreciated in Fig. 7 with a clear improvement in relation to the ARMA model, particularly evident during the period 1960– 1993.
Fig. 7. (a) Observed (black circles) and modelled January EZ_FLOW anomalies during the calibration period (1916–1989) based on the interannual_component alone (red squares) and the combined modelling [ARMA (7,6) + SST_model] (blue triangles). (b) As in (a) but during the validation period (1990–2003). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Table 3 Statistical results of the modelling carried out for the January raw EZ_FLOW time series. Separate contributions from the decadal_component (SST_model) and the interannual_component (ARMA_model) to the raw series modelling, along with the combined modelling [ARMA (7,6) + SST_model] are shown. Results are displayed both for the calibration and validation periods. Values highlighted with ‘‘’’ are statistically significant at the 95% confidence level. Calibration period 1916–1989
MSE MAE Correlation coeft. Willmott index (D) % Phase accordance R2
Validation period 1990–2003
SST_model
ARMA (7,6)
ARMA (7,6) + SST_model
SST_model
ARMA (7,6)
ARMA (7,6) + SST_model
0.74 0.67 0.43 0.57 57% 18%
0.49 0.56 0.73 0.74 72% 53%
0.35 0.47 0.81 0.86 84% 66%
1.14 0.88 0.45 0.34 50% 20%
1.02 0.80 0.66 0.50 43% 44%
0.73 0.72 0.79 0.68 79% 62%
a
b
c
d
e
Fig. 8. Correlation maps between the decadal_component of June streamflow anomalies of EG_FLOW and (a) spring SST anomalies from the previous year, (b) previous summer SST anomalies, (c) previous autumn SST anomalies, (d) previous winter SST anomalies, and e) spring SST anomalies from the contemporary year. Only significant values at the 95% confidence level are shown. Period of study is 1953–2003. Rectangles correspond to the SST regions finally considered for the decadal_component modelling.
5.2. Pyrenees region (June) The spatial correlation maps between the decadal_component (7-year running mean filter) of June EG_FLOW and the preceding seasons for SST data are shown in Fig. 8. Statistically significant correlations with global SST are weaker than for the Basque–Cantabrian region, and appear fundamentally in the north Atlantic and in the Black Sea, being maxima during the spring of the previ-
ous year and in some regions of the Pacific for the previous summer. SST indices were computed and smoothed with a 7-year running mean filter similarly for the previous analysis. Stable correlations (not shown) during the period 1953–2003 are only found for the following defined indices: SST1EG = (30°E–40°E; 41°N– 46°N), corresponding to the Black Sea during the spring of the previous year, and SST2EG = (88°W–81°W; 25°S–20°S), associated to the south-eastern Pacific Ocean during the previous summer. From
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Table 4 Statistical results of the modelling carried out for the June raw EG_FLOW time series. Separate contributions from the decadal_component (SST_model) and the interannual_component (ARMA_model) to the raw series modelling, along with the combined modelling [ARMA (4,8) + SST_model] are shown. Results are displayed both for the calibration and validation periods. Values highlighted with ‘‘’’ are statistically significant at the 95% confidence level. Calibration period 1953–1989
MSE MAE Correlation coeft. Willmott index (D) % Phase accordance R2
Validation period 1990–2003
SST_model
ARMA (4,8)
ARMA (4,8) + SST_model
SST_model
ARMA (4,8)
ARMA (4,8) + SST_model
0.70 0.64 0.41 0.45 40% 17%
0.34 0.46 0.77 0.82 49% 59%
0.22 0.37 0.84 0.90 53% 71%
0.47 0.56 0.26 0.38 64% 6%
0.18 0.35 0.79 0.88 86% 62%
0.11 0.26 0.90 0.93 86% 81%
this result, the SST_model for June flow at decadal time scales computed using multiple linear regressions for the calibration period 1953–1989 is:
SST modelEG ¼ 0:068 þ 0:601 SST1EG þ 0:53 SST2EG
spring previous year
previous summer
This SST_modelEG is able to explain around 71% of the variance of the streamflow decadal_component, showing around 75% agreement in the phase accordance between observed and modelled decadal_component.
a
3 EG_FLOW ARMA (4,8) ARMA (4,8) + SST_model
standard deviation
2
1
0
-1
-2
b
1988
1986
1984
1980
1982
1976
1978
3
EG_FLOW ARMA (4,8) ARMA (4,8) + SST_model
2
standard deviation
1974
1972
1968
1970
1964
1966
1962
1960
1956
1958
1952
1954
1950
-3
1
0
-1
-2
Regards to the modelling of the interannual variability (time scales less than 7 years) a similar procedure to the Basque– Cantabrian region was carried out, finally selecting an ARMA (4,8) model for the interannual_SSA_filter, containing the following parameters:
AR ¼ ðU1 ¼ 1:2 ;
U2 ¼ 1:06 ;
MA ¼ ðh1 ¼ 0:26 ;
h2 ¼ 0:17 ;
h5 ¼ 0:14 ;
h6 ¼ 0:05;
U3 ¼ 1:1 ;
h3 ¼ 0:39 ;
h7 ¼ 0:22 ;
U4 ¼ 0:5 Þ
h4 ¼ 0:13 ;
h8 ¼ 0:74 Þ
Note from Table 1 that the interannual variability of this time series is determined by quasi-oscillatory modes with periods between 2 and 4 years. In this sense, again the selected order model indicates a certain degree of persistence. Given the values of some of the parameters of the model and the ACF and PACF (not shown), the current interannual_component state is considerable dependent on its state up to 4 years earlier. In this case, this ARMA (4,8) model is able to explain around 76% of the variance of the streamflow interannual_component, showing around 80% agreement in the phase accordance between observed and modelled interannual_component. The combination of SST_model (for decadal time scales) and ARMA_model (for interannual time scales) is evaluated in Table 4 and the observed and modelled June EG_FLOW series are shown in Fig. 9 for calibration and validation periods. Results obtained reveal a considerable skill achieved by the combined [ARMA (4,8) + SST_model] model (see Table 4), with a good correlation coefficient between the raw series and the model for the calibration period (r = 0.84) and coefficient of multiple determination R2 (71%). The model presents a relatively low MSE = 0.22, MAE = 0.37 and a high Willmott’s index (D = 0.90). Over the period 1990–2003, not used to fit the model, skill scores are even better (MSE is 0.11, MAE is 0.26 and Willmott’s index is 0.93). From Table 4 we can also see the contribution made by each of the modelling carried out (decadal and interannual) and can be seen as the overall quality of the combined model has increased significantly in both calibration and validation periods. For the validation period the correlation coefficient between the raw series and the combined model is 0.90 and the variance explained by this model rises to 81%. The combined [ARMA (4,8) + SST_model] modelling capacity can be appreciated in Fig. 9 with a clear improvement in relation to the ARMA model, particularly evident between 1987 and 1992. 5.3. Southern mediterranean region (May)
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
-3
Fig. 9. (a) Observed (black circles) and modelled June EG_FLOW anomalies during the calibration period (1953–1989) based on the interannual_component alone (red squares) and the combined modelling [ARMA (4,8) + SST_model ] (blue triangles). (b) As in (a) but during the validation period (1990–2003). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
The spatial correlation maps between the 7-year running mean filter of May MN_FLOW and the preceding seasons for SST data are shown in Fig. 10. Maximum statistically significant correlations were found with the previous SST fundamentally in the Pacific region. Particularly, we can identify correlations that resemble the negative pattern of the Pacific Decadal Oscillation during the
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a
b
c
d
e
Fig. 10. Correlation maps between the decadal_component of May streamflow anomalies of MN_FLOW and (a) spring SST anomalies from the previous year, (b) previous summer SST anomalies, (c) previous autumn SST anomalies, (d) previous winter SST anomalies, and e) spring (as March–April average) SST anomalies from the contemporary year. Only significant values at the 95% confidence level are shown. Period of study is 1953–2003. Rectangles correspond to the SST regions finally considered for the decadal_component modelling.
spring of the previous year. Correlations coefficients are maxima in spring of the previous year, decrease during the following seasons until intensify in the Atlantic Ocean after one year. Based on this correlation maps we define six SST indices by averaging the normalised SST anomalies over the regions showing maximum correlation values, indicated in Fig. 10: SST1MN (174°W–158°W; 29°N–33°N), SST2MN (158°W–154°W; 50°N– 55°N), SST3MN (76°W–72°W; 30°S–21°S), SST4MN (168°E–172°E; 21°S–18°S), SST5MN (14°W–9°W; 36°N–39°N) and SST6MN (4°W– 1°W; 64°N–66°N). Stable correlations (not shown) during the period 1953–2003 are found for all the indices except with the SST6MN, which fails the stability test and was dismissed from the rest of the analysis. Additionally, the stability of the correlation between the May streamflow and the spring PDO index of the previous year was also studied, finding negative stable correlation along the period. Using these SST indices and the PDO index as explanatory variables multiple linear regression models were fitted to the decadal_component of the streamflow. To avoid problems of collinearity among the variables, the backward stepwise procedure was applied, and the selected model is as follows:
SST modelMN ¼ 0:1 0:69 SST2MN
previous spring
0:79 SST3MN
previous summer
þ 1:22 SST4MN
previous summer
þ 0:26 PDOprevious
spring :
The fact that some SST indices do not play a role in the regression model, even though these present high correlation coefficients with the streamflow, is due to the high mutual correlation shown between them. This effect leads to that only some of the factors remain important in the combined regression model. This is the case of the SST1MN index which has a correlation with the PDO around 0.84. The SST5MN index, meanwhile, brings a small improvement for the model and has been removed. The obtained SST_modelMN is able to explain around 81% of the variance of the streamflow decadal_component, showing around 96% agreement in the phase accordance between observed and modelled decadal_component. For the modelling of the interannual variability (time scales less than 7 years) an ARMA (4,3) was selected model, containing the following parameters:
AR ¼ ðU1 ¼ 1:04 ;
U2 ¼ 0:78 ;
MA ¼ ðh1 ¼ 0:89 ;
h2 ¼ 0:96 ;
U3 ¼ 0:40 ;
U4 ¼ 0:37 Þ
h3 ¼ 0:93 Þ
In this case, this ARMA (4,3) model is able to explain around 64% of the variance of the streamflow interannual_component, showing around 87% agreement in the phase accordance between observed and modelled interannual_component. The combination of SST_model (for decadal time scales) and ARMA_model (for interannual time scales) is evaluated in Table 5
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Table 5 Statistical results of the modelling carried out for the May raw MN_FLOW time series. Separate contributions from the decadal_component (SST_model) and the interannual_component (ARMA_model) to the raw series modelling, along with the combined modelling [ARMA (4,3) + SST_model] are shown. Results are displayed both for the calibration and validation periods. Values highlighted with ‘‘’’ are statistically significant at the 95% confidence level. Calibration period 1953–1989
MSE MAE Correlation coeft. Willmott index (D) % Phase accordance R2
Validation period 1990–2003
SST_model
ARMA (4,3)
ARMA (4,3) + SST_model
SST_model
ARMA (4,3)
ARMA (4,3) + SST_model
0.59 0.64 0.56 0.59 73% 31%
0.33 0.46 0.76 0.73 82% 58%
0.14 0.32 0.90 0.88 79% 81%
0.89 0.78 0.60 0.64 79% 36%
0.80 0.79 0.72 0.83 79% 52%
0.45 0.59 0.87 0.94 79% 76%
and the observed and modelled May streamflow series are shown in Fig. 11 for calibration and validation periods. Results reveal a considerable skill achieved by the combined [ARMA (4,3) + SST_model] model (see Table 5), with a good correlation coefficient between the raw series and the model for the calibration period (r = 0.90) and coefficient of multiple determination R2 (81%). The model presents a relatively low MSE = 0.14, MAE = 0.32 and a high Willmott’s index (D = 0.88). Over the period 1990–2003, not used to fit the model, MSE and MAE are a little worse (0.45 and 0.59, respectively), but the Willmott’s index is better (D = 0.94). From Table 5 we can also see the contribution made by each of the modelling carried out (decadal and interannual) and
a
3 MN_FLOW ARMA (4,3) ARMA (4,3) + SST_model
standard deviation
2
1
0
-1
b
1988
1984
1986
1982
1978
1980
1974
1976
1972
1970
1966
1968
1964
1960
3 MN_FLOW ARMA (4,3) ARMA (4,3) + SST_model
2
standard deviation
1962
1958
1956
1952
1954
-3
1950
-2
1
0
-1
2003
2002
2001
1999
2000
1998
1997
1996
1995
1994
1993
1991
1992
-3
1990
-2
Fig. 11. (a) Observed (black circles) and modelled May MN_FLOW anomalies during the calibration period (1953–1989) based on the interannual_component alone (red squares) and the combined modelling [ARMA (4,3) + SST_model] (blue triangles). (b) As in (a) but during the validation period (1990–2003). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
can be seen as the overall quality of the combined model has increased significantly in both calibration and validation periods. For the validation period the correlation coefficient between the raw series and the combined model is 0.87 and the variance explained by this model rises to 76%. The combined [ARMA (4,3) + SST_model] modelling capacity can be appreciated in Fig. 11 with a clear improvement in relation to the ARMA model, particularly important for the peaks of streamflow. 6. Discussion and conclusions A dataset of monthly streamflow series from 83 sites around the Ebro basin has been analysed to characterise geographic differences in terms of the streamflow seasonality and some aspects of interannual and decadal variability. The space–time variability of the streamflow in the Ebro basin has been analysed by using, first, PCA, and then SSA. With respect to the spatial variability of streamflow, three significant spatial EOFs were found, associated with different regions in the basin. The first mode covers mainly the variability of gauging streamflows recorded at the Basque–Cantabrian Mountains. The second one is fundamentally representative of the variability over the Pyrenees area, and the third mode represents the variability of the southern mediterranean region. Streamflow seasonality varies regionally, depending on the timing of maximum precipitation, evapotranspiration, and contributions from snow and ice. Lags between peaks of precipitation and streamflow vary smoothly from long delays in mountainous regions to short delays in the warmest sectors (Dettinger and Diaz, 2000). Globally, at most gauges, both the timing and amplitude of streamflow seasonality depends on the local month of maximum precipitation and the extent to which precipitation is trapped in snow and ice. For the stations associated to the region represented by EOF1 winter-time river flow account for the majority of runoff, being followed by a relatively long and dry summer period. For the stations associated to the EOF2 a nivo-pluvial flow type is presented, where snowmelt influence is very important, with streamflow peaking in June. Finally, flows associated to the southern mediterranean region are characterised by low total annual streamflow and prolonged dry season, with streamflow peaking in May. This separation is in agreement with the classification developed by Bejarano et al. (2010) in the same basin, which separates Eurosiberian nival from Mediterranean pluvial flow types, although they show a much more detailed classification type flows based on the physical characteristics of the catchments. Attending to the classification found the main characteristic time scales of the maximum monthly streamflows are studied by SSA. The applied SSA algorithm to isolate the main characteristics of the streamflow series revealed a similar model structure for the three regions, including: (1) a non-linear trend dominated by multidecadal variability; (2) modulated amplitude oscillations with periods longer than 7 years (decadal periodicities are around 23 years, 9.5 years and 15 years for the Basque–Cantabrian,
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Pyrenees and southern mediterranean regions, respectively); (3) quasi-oscillatory modes in the bands 2–3, 4–5, and 6–7 year, depending of the region; and 4) a red noise process. Decadal variations in streamflow make particularly large contributions to yearto-year streamflow variance in stations placed in the Cantabrian Mountains and southern mediterranean region (31.3% and 35.2%, respectively), while for the Pyrenees flows the interannual contribution to the streamflow variations is more important (50.6%). From this point, the predictability of the Ebro flow anomalies has been investigated using a combined methodology: (1) for decadal and longer time scales (e.g., >7 years) we use as predictors in a multiple linear regression model the global sea surface temperatures from the preceding seasons (obtaining the SST_model); (2) for interannual time scales (e.g., <7 years) ARMA modelling were developed for the interannual_SSA-filtered streamflow series. It is expected that the potential relationships between the flow and the SST field will be intensified for those months showing maximum streamflow values, although similar SST patterns are obtained if different monthly, seasonal or annual streamflow time series are used because the SST study has been restricted to decadal time scales. However, variations for the interannual variability modelling could be achieved if other months, different to those showing maximum streamflow values, are also used, because both the study of quasi-oscillatory modes by SSA and the ARMA modelling could change depending on the season. The results of this analysis demonstrated the existence of strong influences of ocean conditions in the Ebro River at decadal time scales. For the gauging stations associated to the Basque–Cantabrian region we find positive significant correlations between the streamflow anomalies in January and the North Atlantic horseshoe pattern (Czaja and Frankignoul, 2002) during the previous spring. This association is found maximum and stable for the tropical part of the pattern (approximately 0–20°N) in previous spring, decreases in summer and autumn, and comes back strongly in December. This result is in agreement with other studies that suggest a link between spring conditions in the North Atlantic Ocean and atmospheric conditions over the same region the subsequent winter (Czaja and Frankignoul, 1999, 2002; Rodwell and Folland, 2002; Drevillon et al., 2003; Frankignoul and Kestenare, 2005; Iwi et al., 2006). Rodwell and Folland (2002) showed that the North Atlantic SST in May could be used as a predictor of the subsequent winter NAO. One hypothesis is that conditions present in the North Atlantic Ocean in spring persist through the summer to influence the atmosphere in the following autumn and winter. During summer the ocean anomalies may be capped by the shallow mixed layer, subsequently to emerge as the mixed layer deepens in early winter. This mechanism is known as re-emergence (Deser et al., 2003; Cassou et al., 2004). Sutton et al. (2001) showed that a tripole pattern of SST anomalies could induce a weak NAO-like atmospheric response, and further experiments indicated the important role played by the tropical part of the pattern (Terray and Cassou, 2002; Cassou et al., 2004; Peng et al., 2005). These results could provide information concerning the underlying physics of the teleconnection found for the streamflow and Atlantic SST, suggesting an important influence of the SLP as a main component in the SST/streamflow relationship; however, physical explanations for the connection between the SST and streamflow are not yet clear. Additionally, it is important to note that SLP patterns other than the NAO could also have a dominant role for determining streamflows. For the gauging stations associated to the Pyrenees region the correlations between the June streamflow and global SST, at decadal time scales, are weaker than for those of the Basque–Cantabrian region, and only stable connections are found in the Black Sea SST during the spring of the previous year and in the south-eastern of the Pacific Ocean during the previous summer. How this connec-
tion between the SST and the flow is produced is an issue that needs further research. Oguz et al. (2006) carried out an examination of a wide spectrum of hydro-meteorological records in the Black Sea. They found a robust climatic signature at interannual to interdecadal time scales in the Black Sea SST, with variations on the order of 15–30-year band superimposed to oscillations with the period of about 10 years. These variations appear to be governed by the North Atlantic Oscillation and East Atlantic-West Russia (EAWR) teleconnection patterns. For the gauging stations associated to the southeast of basin higher than average values of the Ebro river flow in May tend to be associated with cooler than average SST anomalies along the western coast of North America, and warmer than average SSTs in the central North Pacific during spring of the previous year. This Pacific SST pattern associated with the Ebro flow decadal variability bears some resemblance to the SST pattern characterising the negative phase of the Pacific Decadal Oscillation (PDO) (Mantua et al., 1997). Currently, there are several hypotheses concerning the causes of decadal variations in different geographical regions and the influence of PDO is one of these hypotheses (Baik and Paek, 1998; Tomita et al., 2001; Voskresenskaya, 2005). Other authors have also found teleconnections between the PDO and other rivers in Europe (Dettinger and Diaz, 2000; Rimbu et al., 2002; Bardin and Voskresenskaya, 2007; Labat, 2010). For example, Rimbu et al. (2002) found an opposite association between the streamflow of the Danube River and the PDO, while Bardin and Voskresenskaya (2007) state that the decadal variability of the NAO supported by the large-scale anomalies of the PDO can be regarded as the most important cause of the natural decadal oscillations of hydro-meteorological characteristics in the Atlantic-European region. These later authors find that the positive phase of the PDO corresponds to the intensification of the NAO, which is accompanied by the positive anomalies of sea level pressure in the tropical and subtropical Atlantic, over central and southern Europe, and over the Mediterranean Sea. Opposite conditions correspond to the negative phase of the PDO. The basic physical proposed scheme is that the climatic anomalies of the atmosphere–ocean interaction propagate from the Pacific Ocean toward the neighbouring continents and other oceans by means of stationary Rossby waves and synoptic atmospheric formations (Ambrizzi and Hoskins, 1997). Additionally, two more regions placed in the southeast and southwest of the Pacific Ocean, respectively, also show stable significant correlations with the decadal variability of the Ebro streamflows recorded in the southeast Basin. These southern regions in the Pacific are also shown in the Pacific multidecadal pattern obtained by Enfield and Mestas-Nuñez (1999) on their analysis of the global SST, which resembles the PDO pattern with somewhat weaker extension to the southeast, west of Chile. The SST teleconnection indices found, related to the hydrology of the Ebro Basin, have been incorporated into statistical streamflow forecasting models. Note that the Ebro basin is a complex region from both the topographical and meteorological perspectives, with great physical heterogeneity, which is a deciding factor in the variability of flow. There are several papers that assess this complex behaviour (Vicente-Serrano and López-Moreno, 2006; LópezBustins et al., 2008). Moreover, Ebro basin represents a transition zone between the Atlantic and Mediterranean influences. So it is reasonable to assume that different regions of the basin are being affected by different physical mechanisms, which can be translated to different SST teleconnection indices. Moreover, the way of coupling between local, atmospheric circulation and SST patterns, probably non-linear, could explain these different streamflow responses into the basin, an aspect that recently some authors have considered to need a further research, pointing out to possible nonlinear interactions between climate systems (Shaman and Tziperman, 2011; Switanek et al., 2009).
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Regarding the interannual variability and predictability of the Ebro streamflow series selected as representative of the three regions obtained by the application of PCA to the basin, this has been studied using the previous SSA and ARMA models. First, interannual_SSA_filters were constructed from the quasi-oscillatory modes with periodicities less than 7 years found by SSA. These resulting filters account for the 32.6%, 50.6% and 46.3% variance of the streamflow for the Basque–Cantabrian, Pyrenees and southern mediterranean regions, respectively. Then, an ARMA model was obtained for each interannual_SSA_filtered streamflow series and a forecasting experiment was conducted. The models were calibrated for the period 1916–1989 for the streamflow time series associated to the Basque–Cantabrian region, and for 1953–1989 for Pyrenees and southern mediterranean regions. The period 1990–2003 was used for validation in all the three cases. An ARMA (7,6) model, with constrained parameters, was fitted for the Basque–Cantabrian region, while ARMA (4,8) and ARMA (4,3) models were found, respectively, for the Pyrenees and mediterranean regions. The ARMA modelling applied to the interannual_SSA_filters is able to provide the interannual linearly predictable signal contained in the history of the time series which is not related to the decadal variability of the SST. Finally, the combination of SST_model (for decadal time scales) and ARMA_model (for interannual time scales) has been evaluated for each region. The combined modelling of Ebro anomalies based on our statistical scheme outperforms significantly the modelling based on ARMA models alone. Additionally, this methodology allows evaluating, independently, the decadal and interannual predictability of the streamflow series, which vary (for the validation period) between 20% and 44% for the Basque–Cantabrian region, between 6% and 62% for the Pyrenees region and between 36% and 52% for the mediterranean region, respectively. In summary, this work shows the existence of a valuable decadal and interannual predictability of the Ebro streamflow, a result that may be useful to water resources management. At decadal time scales SST anomalies from several regions provide a significant source of predictability for the Ebro flow, while at interannual time scales ARMA modelling, applied to the time series previously filtered by SSA, is able to provide potential skill in forecasting. The combination of both modelling gives as result a methodology that has the capacity to provide basin-specific hydroclimatic predictions. The work presented here raises several issues that require further analysis and can be improved in different ways. First, our results are encouraging since that only information contained in the global SST has been used to explain the Ebro streamflow variability. Statistical forecasting models that use multiple variables such as land surface temperature, precipitation or SLP as potential predictor variables can improve forecast skill by increasing the robustness of the methodology. Second, at interannual time scales the direct influence of SST variability on streamflow has not been considered. However, the periodicities associated to El Niño, which oscillate between 2 and 7 years, could be related in some way with the interannual quasi-oscillatory modes found in the Ebro streamflow. Although most studies suggest a weak but significant ENSO response over the North Atlantic-European sector (Ropelewski and Halpert, 1987; Fraedrich et al., 1992; Gouirand and Moron, 2003; Pozo-Vázquez et al., 2005; Vicente-Serrano, 2005; Mariotti et al., 2005; Brönnimann et al., 2004, 2007; Gámiz-Fortis et al., 2010a), uncertainties regarding the regional details must be studied in detail. In a recent paper, Shaman and Tziperman (2011) cited several papers that found relations between ENSO and Mediterranean climate during all season of the year, and established that it is difficult to determine whether the time and space discrepancies in these studies are due to different teleconnection processes or result from a single teleconnection mechanism that produces differ-
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ent seasonal and regional effects. Unfortunately, understanding of the dynamics of the ENSO–Mediterranean teleconnections has not advanced much since Ropelewski and Halpert (1987) stated that the ‘‘implied ENSO relationships in these regions are difficult to understand or attribute to any of the known ENSO related atmospheric circulation changes’’. On the other hand, these authors argue that the persistence of ENSO (or other SST patterns) is an important factor to take into account to explain these teleconnections. Similar considerations could be done for other SST indices obtained in this work. All the cited results support the findings of our analysis about the influence of SST in the streamflow behaviour; however, physical explanations for the connection between the SST and streamflow are not yet clear, especially the contribution of different latitudes and ocean basins is still highly controversial. This paper represents a contribution on this subject. In this sense, the methodology used here detects not only statistically significant relationship, but also stable on time. However, it is not able to give information about the physical foundation. Therefore, there is an obvious need for further research to elucidate the physical explanation of the relationships between the SST and the streamflow. For this end dynamical methods with reliable GCM simulations and downscaling techniques would become necessary. Acknowledgements The Spanish Ministry of Science and Innovation, with additional support from the European Community Funds (FEDER), Projects CGL2007-61151/CLI and CGL2010-21188/CLI, financed this study. S.R. Gámiz-Fortis is supported by the University of Granada under a postdoctoral contract. References Akaike, H., 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control 19, 716–7233. Ambrizzi, T., Hoskins, B., 1997. Stationary Rossby-wave propagation in a baroclinic atmosphere. Quarterly Journal of the Royal Meteorological Society 123 (540), 919–928. Baik, J.J., Paek, J.S., 1998. A climatology of sea surface temperature and the maximum intensity of western North Pacific tropical cyclones. Journal of Meteorolycal Society of Japan 76 (1), 129–137. Bardin, M.Y., Voskresenskaya, E.N., 2007. Pacific Decadal Oscillation and European climatic anomalies. Physical Oceanography 17 (4), 200–208. Barnett, T.P., Del Genio, A.D., Ruedy, R.A., 1992. Unforced decadal fluctuations in a coupled model of the atmosphere and ocean mixed layer. Journal of Geophysical Research 97, 7341–7354. Barnston, A.G., Livezey, R.E., 1987. Classification, seasonality, and persistence of low-frequency atmospheric circulation patterns. Monthly Weather Review 115, 1083–1126. Batalla, R.J., Gomez, C.M., Kondolf, G.M., 2004. Reservoir-induced hydrological changes in the Ebro river basin (NE Spain). Journal of Hydrology 290, 17–136. Bejarano, M.D., Marchamalo, M., García de Jalón, D., González del Tánago, M., 2010. Flow regime patterns and their controlling factors in the Ebro basin (Spain). Journal of Hydrology 385, 323–335. doi:10.1016/j.jhydrol.2010.03.001. Brockwell, P.J., Davis, R.A., 1996. Introduction to Time Series and Forecasting. Springer-Verlag, 420 pp. Brönnimann, S., Luterbacher, J., Staehelin, J., Svendby, T.M., Hansen, G., Svenøe, T., 2004. Extreme climate of the global troposphere and stratosphere 1940–1942 related to El Niño. Nature 431, 971–974. Brönnimann, S., Xoplaki, E., Casty, C., Pauling, A., Luterbacher, J., 2007. ENSO influence on Europe during the last centuries. Climate Dynamic 28, 181–197. Cassou, C., Deser, C., Terray, L., Hurrell, J.W., Drevillon, M., 2004. Summer sea surface temperature conditions in the North Atlantic and their impact upon the atmospheric circulation in early winter. Journal of Climate 17, 3349–3363. Cayan, D., Dettinger, M.D., Dias, H.F., Graham, N., 1998. Decadal variability of precipitation over western United States. Journal of Climate 12, 2881–2893. Chen, F., Ghil, M., 1996. Interdecadal variability in a hybrid coupled oceanatmosphere model. Journal of Physical Oceanography 26, 1561–1578. Coulibaly, P., Burn, D.H., 2005. Spatial and temporal variability of Canadian seasonal streamflows. Journal of Climate 18 (1), 191–210. Cullen, H.M., Kaplan, A., Arkin, P., DeMenocal, P.B., 2002. Impact of the North Atlantic Oscillation on Middle Eastern climate and streamflow. Climate Change 55, 315–338. Czaja, A., Frankignoul, C., 1999. Influence of the North Atlantic SST on the atmospheric circulation. Geophysical Research Letters 26 (19), 2969–2972.
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Journal of Hydrology journal homepage: www.elsevier.com/locate/jhydrol
Spatio-temporal variability in Ebro river basin (NE Spain): Global SST as potential source of predictability on decadal time scales S.R. Gámiz-Fortis ⇑, J.M. Hidalgo-Muñoz, D. Argüeso, M.J. Esteban-Parra, Y. Castro-Díez Applied Physics Department, University of Granada, Granada, Spain
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Article history: Received 8 March 2011 Received in revised form 20 August 2011 Accepted 12 September 2011 Available online 17 September 2011 This manuscript was handled by Konstantine P. Georgakakos, Editor-in-Chief, with the assistance of Ercan Kahya, Associate Editor Keywords: Ebro river basin Streamflow variability Decadal and interannual variability Global SST PDO ARMA modelling
s u m m a r y This paper investigates the spatial and temporal variability of streamflow in the Ebro river basin and its potential predictability. Principal Component Analysis applied to monthly streamflow series from 83 gauging stations distributed through the basin, reveals three homogeneous regions: Basque–Cantabrian, Pyrenees and Southern Mediterranean. Attending to this classification the main characteristic time scales of the maximum monthly streamflows are studied by Singular Spectral Analysis (SSA). Decadal variations in streamflow make particularly large contributions to year-to-year streamflow variance in stations placed in the Basque–Cantabrian and Southern Mediterranean regions, while for the Pyrenees flows the interannual contribution is more important. The predictability of the Ebro flow anomalies has been investigated using a combined methodology: at decadal time scales SST anomalies from several regions provide a significant source of predictability for the Ebro flow, while at interannual time scales autoregressive-moving-average modelling, applied to the time series previously filtered by SSA, is able to provide potential skill in forecasting. For gauging stations associated to the Basque–Cantabrian region significant correlations between the maximum monthly streamflow anomalies and a tripole-like pattern in the North Atlantic SSTs during the previous spring are found. This association is found maximum and stable for the tropical part of the pattern (approximately 0–20°N). For the gauging stations placed to the southeast of basin some influence from the Pacific Decadal Oscillation (PDO) is found. This method allows evaluating, independently, the decadal and interannual predictability of the streamflow series. In addition, the combination of both modelling techniques gives as result a methodology that has the capacity to provide basin-specific hydroclimatic predictions which vary (for the 1990–2003 validation period) between 62% for the Basque–Cantabrian region, 76% for the Southern Mediterranean and 81% for the Pyrenees. In summary, this work shows the existence of a valuable decadal and interannual predictability of the Ebro streamflow, a result which may be useful to water resources management. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Accurate simulation and forecasting of water availability is a key step in efficient planning, operation and management of water resources such as hydroelectric power production and agriculture crop yields. Developing reliable surface water flow forecasting methods for real-time operational water resources management becomes increasingly important. River flow variability plays an important role in water resources development and management in most of the world regions (IPCC, 2001; Gong et al., 2010). The hydrological system acts as spatial and temporal integrator of ⇑ Corresponding author. Address: Departamento de Física Aplicada, Facultad de Ciencias, Universidad de Granada, Campus Fuentenueva s/n, 18071 Granada, Spain. Tel.: +34 958 240026; fax: +34 958 243214. E-mail address: [email protected] (S.R. Gámiz-Fortis). 0022-1694/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jhydrol.2011.09.014
precipitation (rain and snow), temperature, and related evapotranspiration, also integrating land-surface processes such as vegetation and land cover changes, human uses or hydraulic infrastructures over a specific region. Seasonal variations of streamflows arise from variations in precipitation and temperature, which are controlled by large-scale fluctuations in atmospheric circulation patterns. Hence, streamflow records can serve as a pertinent index of hydroclimatic variability (Coulibaly and Burn, 2005). For this reason, the interest in seasonal predictability of river discharge variability has increased markedly during the last years (Trigo et al., 2004; Rimbu et al., 2004, 2005; Gámiz-Fortis et al., 2008a,b, 2010a; Ionita et al., 2008) in the context of climate predictability studies. The availability of water is mostly influenced by climate conditions that vary on seasonal, interannual and decadal time scales. On seasonal timescales, anomalous atmospheric conditions are
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often linked with seasonal variations in the rivers streamflow and reservoir storages, via variations in precipitation and temperature (Dettinger and Diaz, 2000; Cullen et al., 2002; Trigo et al., 2004; Karabörk et al., 2005; López-Moreno et al., 2007). The interannual climate and hydrologic fluctuations are modulated by, or superimposed upon, lower frequency variations with decadal and longer time scales. The sources of these lower frequency climate variations are uncertain but may have roots in the tropics (Barnett et al., 1992; Trenberth and Hoar, 1996), in the extratropical oceans (Pacific: Douglas et al., 1982; Trenberth, 1990; Latif and Barnett, 1994; Atlantic: Schlosser et al., 1991; Read and Gould, 1992; Deser and Blackmon, 1993; Tanimoto et al., 1993; Stocker and Broecker, 1994; Chen and Ghil, 1996; Houghton, 1996), or in some interplay of the two (e.g., Graham, 1994; Graham et al., 1994; Jacobs et al., 1994). Usually, the skill of the long-range forecasts is associated with the introduction of predictors that represent the slow varying components of the climate system such as sea ice, snow cover, soil moisture and sea surface temperatures (SST) (Koster et al., 2010). The oceans have a vast storage of energy that helps drive global climate variability, and SST is one manifestation of this energy storage. Given the oceanic mass and water’s large specific heat, the effect of SST on ocean–atmosphere heat and water vapour exchange can be on seasonal to annual time scales. Consequently, variability in SST can help provide predictive information about the hydroclimate in regions across the globe (Rimbu et al., 2005; Gámiz-Fortis et al., 2008b, 2010a; Ionita et al., 2008). Additionally, major oceanic and atmospheric circulation patterns such as the North Atlantic Oscillation (NAO) or Pacific Decadal Oscillation (PDO) can also improve the forecasts (Guetter and Georgakakos, 1996; López-Moreno et al., 2007; Trigo et al., 2004; Gámiz-Fortis et al., 2008a; Hamlet and Lettenmaier, 1999). The NAO index is computed as the difference of sea-level pressure between two stations situated close to the centres of Icelandic Low and Azores High (Hurrell, 1995), while the PDO index is calculated to be the first principal component of detrended SST anomalies northward of 20°N latitude in the Pacific Ocean (Mantua et al., 1997). There are two potential problems with using standard climate indices for hydroclimatic prediction. The first one is that the hydroclimate of a river basin may be more strongly correlated with an oceanic region’s SSTs, which is different from the predetermined regions that are used to calculate the standard indices (Namias, 1978; Kutzbach, 1970; Nicholls, 1980; Tootle and Piechota, 2006). The second problem is that matricial methods, such as PCA, used to obtaining these indices, might not preserve enough information from an original dataset (Switanek et al., 2009). In any case, the relationship between the climatic regimes and its hydrological response, through the streamflow, presents different grades of complexity according to the physical characteristics of the basin so it should be studied in detail. The Ebro River represents the Spanish most important catchment of the Iberian Peninsula, being a very representative example of large Mediterranean rivers. Floods during the cold season occur from October to March, sometimes until May, due mainly to an oceanic pluvial regime, whereas floods in spring are the result of melting snows in the Pyrenees (López-Moreno and García-Ruiz, 2004; Pedregal et al., 2009). Recent works have been conducted for the Ebro Basin, but for different purposes to that here considered, such as the study of the spatial and temporal variability of winter droughts for specific areas of the basin (Vicente-Serrano and López-Moreno, 2006), the hydrological characterisation of flow typologies (Bejarano et al., 2010), hydrological modelling of specific gauging stations at daily time scales (Pedregal et al., 2009) or the study of hydrological trends (López-Moreno et al., 2011). The novelty of this work is based mainly on three points: one is about characterisation of hydrological variability on the whole Ebro basin on different climatic timescales, which results in the
ability of separating the interannual and decadal predictability in different regions of the Basin. Other is about the identification of connections to climate forcings that could provide potential improvement for building hydrological models. On this point is important to emphasise the use of global SST as potential predictor variable. And another is on how different techniques are combined to produce an algorithm that generates reliable estimates of flow in different parts of the Ebro basin at seasonal time scales. In this sense, the results of the work reveal independent predictive models for different streamflows in the Basin. In summary, this paper presents a modelling scheme for Ebro streamflow anomalies based on the combination of different steps: (1) identification of homogeneous regions of Ebro streamflow variability, (2) analysis of the temporal structure of the series for each selected region in the Ebro basin, (3) detection of statistically significant linkage that exist between the streamflow series in the Ebro basin and large scale SST variability modes, and (4) separate modelling of high and low frequency variations through the use of autoregressive-moving-average (ARMA) models and stable teleconnections between oceanic SST anomalies and river flow, respectively. The paper is organised as follow: In Section 2 the study region and the data used are described. In Section 3 the different methodologies and the steps taken in building the prediction algorithm are presented. The spatio-temporal streamflow anomaly patterns are presented in Section 4, while in Section 5 we show the results of the streamflow modelling. A discussion and the main conclusions follow in Section 6.
2. Data The Ebro River (Fig. 1) presents the largest catchment in Spain, with an area of 85,530 km2 in the northeast of Spain. Ebro basin is a complex region from both the topographical and meteorological perspectives, with great physical heterogeneity, which is a deciding factor in the annual seasonality of flow. This region forms a broadly triangular morphological unite, which is a depression surrounded by high mountain ranges including, to the north, the Pyrenees and Basque–Cantabrian Mountains, to the east the Catalan Coastal Range, and from the northwest to southeast the Iberian Massif. The heterogeneous topography contrasts the influences of the Atlantic and Mediterranean as well as of different large-scale atmospheric patterns (Vicente-Serrano and López-Moreno, 2006). Some studies divide the Ebro basin into different climatic areas according to the precipitation regime (Batalla et al., 2004; Bejarano et al., 2010): the Cantabrian Mountains, with average annual precipitation of about 1100 mm, the eastern Pyreness (about 800 mm), the west-central Pyrenees (about 900 mm), the northwestern Iberian Massif (about 650 mm), the southern Iberian Massif (about 500 mm) and the centre of Ebro basin (about 350 mm). Monthly streamflow data were kindly provided by the Ebro Water Authority (Confederación Hidrográfica del Ebro – CHE –, http://www.chebro.es) and the National Water Research Centre (CEDEX, http://www.cedex.es). First, a study about the characterisation of hydrological sustained changes in gauging stations of basin was carried out, analysing information about the type of alteration, the period of alteration and the magnitude of the disturbance in the gauging station. Most of stations with medium, high or very high magnitude alterations were subsequently eliminated from the analysis. We selected a total of 83 streamflow series distributed in the basin that were intensively checked for inconsistencies, showing less than 10% of missing values during the period 1950–2006. Data gaps were filled using data from neighbouring stations with which there was a Pearson correlation coefficient of at least 0.8 (López-Moreno et al., 2011). Fig. 1 shows the spatial
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Fig. 1. Location of the Ebro river basin in the Iberian Peninsula (left) and spatial distribution of the gauging stations (right) used in this study in the basin. Topographical features of the Basin are expressed in m.
distribution of the gauging stations in the Ebro basin. We can see a reasonable although no homogeneous spatial coverage of the stations across the entire basin, where most of them are situated in the Cantabrian Mountains, Pyrenees and in the southern Mediterranean zone, while very few stations are placed in the centre of the basin. Hydrological series commonly do not follow a normal distribution, being highly biased, often requiring some preliminary transformation in order to adjust the records to an appropriate distribution. Also, the magnitude of the monthly streamflow values varies greatly among the stations, due to both the different climatic regions in Ebro basin and the different drainage basin characteristics associated with each streamflow station. Some studies have shown a good adjustment of the discharge series to the log-normal distribution (Zaidman et al., 2001; Kalayci and Kahya, 2006), while Vicente-Serrano (2006) and López-Moreno et al. (2009) found that the Pearson III distribution is more appropriate over some parts of the Iberian Peninsula. Using these considerations we tested three different theoretical distributions for modelling the monthly stream river flow: the Pearson III, the log-normal and the normal distribution. Furthermore, the goodness of fit was evaluated using three different tests, the Kolmogorov–Smirnov, the Anderson–Darling and the Chi-squared tests. We find that for the most of cases the Pearson III and the log-normal theoretical distributions present good results, but for the gauging stations placed in the southern Iberian Massif, the Pearson III is not an appropriate probability distribution. For this reason, and in order to facilitate the intercomparison between regions, the streamflow data were first subjected to logarithmic transformation to reduce the disparity in the magnitudes, from which monthly standardised streamflow anomalies were computed. The monthly standardised streamflow anomalies were constructed by subtracting the mean and dividing by the standard deviation for each month separately. The standardised streamflow for each station closely follows a normal distribution. The global SST data was taken from the HadISSTv1.1 data set (Rayner et al., 2003) derived from the Hadley Centre for Climate Prediction and Research (UK Meteorological Office). We generate the winter, spring, summer and autumn SST fields by averaging the monthly SST anomalies (using the mean and standard deviation for the period 1961–1990) for DJF, MAM, JJA and SON, respectively. SST data has a resolution of 1° 1° and the temporal length is 1871–2007. Also, the standardised PDO index derived as the leading PC of monthly SST anomalies in the North Pacific Ocean, poleward of
20°N from http://jisao.washington.edu/pdo/PDO.latest, that covers the period 1900–2010, has been used in this study (Zhang et al., 1997; Mantua et al., 1997).
3. Methodology In the present study, regionalisation of streamflow series in the Ebro basin was performed using rotated Principal Component Analysis (PCA). PCA has been applied in analysing the spatial variability of physical fields. In climatology and hydrology, the PCA is a tool to document the typical nature of streamflow and has been used in similar contexts of the present study (Widmann and Schär, 1997; Maurer et al., 2004; Kalayci and Kahya, 2006). PCA reduces a large number of interrelated variables to a few independent PCs that capture much of the variance of the original dataset (Wilks, 1995; Hannachi et al., 2007). It produces a few major spatial-variability patterns (or empirical orthogonal functions, EOFs), and the corresponding time series that represent the time evolution of the spatial-variation patterns. The North Rule based on the eigenvalue degeneration (North et al., 1982) was adopted here and the resulting significant EOFs varimax rotated to capture better the physically meaningful and simplified spatial patterns (Barnston and Livezey, 1987). This procedure allows extracting representative stations for each of the areas obtained in the regionalisation process. For the study of temporal variability a Singular Spectral Analysis (SSA) is applied to each streamflow time series representative of the regions previously identify by PCA. SSA is a powerful tool for time-series analysis that can identify intermittent oscillation spells, in short, noise time series (Vautard et al., 1992). SSA has been successfully applied to many geophysical and climatological time series to study and predict periodic activities (Ghil and Mo, 1991; Ghil and Vautard, 1991; Plaut and Vautard, 1994; GámizFortis et al., 2002, 2008a, 2010a,b; Paluš and Novotná, 2006). SSA solves eigenvalue problems stemming from the lag-autocovariance matrix of a single time series with a pre-defined window length (Vautard et al., 1992; Elsner and Tsonis, 1996). The PCs produced by SSA are called temporal PCs (T-PCs) and the empirical orthogonal functions are the time EOFs (T-EOFs) that describe the temporal oscillatory behaviour of the T-PCs. Eigenvalues are sorted in descending order, indicating the variance of each corresponding T-PC. When two consecutive eigenvalues are nearly equal, and the corresponding T-PCs are in quadrature, these two T-PCs form a pair and potentially represent an oscillation. The time evolution
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of each identified oscillation component is extracted based on the reconstruction technique developed by Plaut and Vautard (1994). Each reconstructed time series (RC) represents an isolated oscillation and the original series is exactly the sum of all the RCs. Additionally, the Maximum Entropy Method (MEM) has been used to evaluate the spectral contents of the T-PC time series, and the Monte Carlo (MC) technique was used for the significance study (see Gámiz-Fortis et al. (2002), for further details). The analysis of the temporal structure of the series allows us to model separately their variations at different time scales. To this end an independent analysis of the streamflow variability at low and high frequencies has been carried out. Standardised stremaflow anomalies were smoothed with a 7-year running mean filter to obtain the decadal component of the series (decadal_component hereinafter). This filter is designed to fall both near the low-frequency end of the spectrum associated with El Niño events and near the high-frequency end of the decadal climate variations of the Atlantic and North Pacific climate systems (Cayan et al., 1998; Dettinger et al., 2001), and has been used following other authors (Ionita et al., 2011) in order to exclude any cross-spectrum between Ebro River streamflow and El Niño. Note that in this filtering process, we lost 6 years, 3 at the beginning of the series and 3 at the end. Then, the dominant patterns of streamflow variability are related to global SST to identify potential large scale climate features that drive the variability at decadal time scales. Simple methods of statistical analysis were used in this study to describe the potential relationship between the streamflow series and the SST, both contemporary and of the preceding seasons in order to evaluate predictive ability. Linear correlation maps were constructed to identify regions of the global SST that exhibit teleconnections with streamflow at Ebro basin. Regions showing significant correlations are identified as potential predictors but only those identified as stable predictors will be used in a multiple linear regression model to simulate the Ebro river flow anomalies on decadal time scales (SST_model). Stable predictors are achieved through the analysis of the variability of the correlation between Ebro flow anomalies and SST anomalies from regions considered as potential predictors using a moving window of 15 years. Additional analysis using a window length of 20 years were carried out in order to examine the stability of the connections in time. Following the criterion of Ionita et al. (2008) the correlation is considered to be stable for those regions where streamflow and SST anomalies are significantly correlated at 90% level for more than 80% of the 15-year windows covering the total period and, furthermore, where the sign of the correlation does not change with time. SST regions verifying this criterion are considered as robust predictors for the decadal_component of the streamflow, and will be used in a multiple-linear-regression model that use the decadal components of the SST time series averaged over these regions as explanatory variables. The method of ordinary least squares was used to estimate the regression coefficients (Draper and Smith, 1998) by minimising the sum of squared errors (SSE), i.e. the unexplained variance part. The coefficient of multiple determination R2, which measures the fraction of variance in the response variable that can be explained by variations in the explanatory factors also is computed. Note that a high value of R2 does not imply that a particular model is appropriate. In fitting the model, the assumption is made that the unknown random effects are represented by ‘‘e’’, which is a vector of independent, normally distributed noise. The validity of this assumption should be checked. The remaining interannual variability of flows (for time scales less than 7 years) can be obtained by the difference between the raw flow and the decadal_component. This interannual_component is firstly modelled by the significant quasi-oscillatory modes (with periods <7 years) obtained from the previous SSA (interannual_SSA_filter hereinafter) and autoregressive-moving-average
(ARMA) models were fitted to the interannual_SSA_filter of streamflow. The SSA filter is able to partially remove background noise, retaining the leading statistically significant (and predictable) interannual components. For this reason the SSA filtering prior to obtaining the ARMA models considerably improves the forecasting skill of these ARMA models (Gámiz-Fortis et al., 2002, 2008a, 2010a). ARMA models can be regarded as a special case of general linear stochastic processes and provide a linear representative structure of the temporal evolution of the data. The order of the model is selected, in a preliminary approach, studying the autocorrelation function (ACF) and partial autocorrelation function (PACF). In physical terms, the best model has as few parameters as possible. We have used the Akaike information criterion (AIC) (Akaike, 1974) to select the final model among all the candidates. The AIC is based on information theory and represents a compromise between the goodness of the fit and the number of parameters of the model. A comprehensive review, explaining in detail how to fit ARMA models to datasets following the identification, estimation, and diagnostic check stages, can be found in Brockwell and Davis (1996) and Hipel and Mcleod (1994). Finally, the combination of both SST_models (for decadal time scales) and ARMA_models (for interannual time scales) is evaluated in a forecasting experiment. For reliable skill assessment, a fundamental aspect of this evaluation is the separation of calibration and validation periods (Wilks, 1995). We employ data until 1989 to calibrate the different modelling (decadal, interannual and combined), while data from 1990 to 2006 are used for validation purposes only. We would like also to apply cross-validation using development data set of size n 1 and verification data set containing the remainder single observation of the predictand, leading to n partitions of the dataset. The model is then calculated for each of these partitions, resulting in n similar forecast equations, each one computed without one of the observations of the predictand. Unfortunately, this procedure cannot be applied in our case for a number of reasons, namely because when fitting ARMA models, the temporal location of each data cares: i.e. the ‘‘history’’ of the series is very important. When removing one single data in the middle of the data set, the remaining data are not useful to fit the model, because the temporal structure of the data is then broken (Gámiz-Fortis et al., 2002). For model evaluation we employ appropriate skill measures commonly used, such as the mean absolute error (MAE) and the mean square error (MSE) as accuracy measures; the Pearson correlation coefficient, which is used to measure the relationship between the modelled/forecasted series and the original/expected series; the percentage of phase agreement, that is, the percentage of cases in which the modelled/forecasted values has the same sign as the original values; the Willmott agreement index (D) (Willmott, 1982), which is a dimensionless measure of relative error in model estimates which ranges from 0 (complete disagreement between estimated and observed values) to 1 (complete agreement); and the coefficient of multiple determination R2, which measures the fraction of variance in the response variable that can be explained by variations in the explanatory factors (Junge and Stephenson, 2003). The combined use of different methodologies has already been used by the authors in previous studies of predictability obtaining very useful results (Gámiz-Fortis et al., 2002, 2008a,b, 2010a,b).
4. Streamflow anomaly patterns The PCA of the monthly mean streamflow records at the 83 stations in the Ebro basin for the period 1950–2006 showed that most of the regional variations are attributable to relatively small number of basic anomaly patterns. Three significant spatial EOFs,
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Fig. 2. Loading factors for the first (a), second (b) and third (c) S-EOF resulting of the monthly streamflow PCA in the Ebro basin for the 1950–2006 period. (d) Location of the two specific gauging stations with the highest loading factors associated to the PC1 (red), PC2 (blue) and PC3 (green). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
accounting for 55.4% of the total variance, were found. Fig. 2 shows the corresponding spatial patterns by drawing the loading factors associated to each station. The leading mode (Fig. 2a) explains 23.4% of the total variance, and represents mainly the variability of streamflow in the Cantabrian Mountains. Additionally, the gauging station corresponding to Ebro in Zaragoza (EZ), sited in the middle of the basin, also shows high correlation coefficient with the PC1. Fig. 2b shows the spatial pattern associated with the second EOF, which explains 21.8% of the total variance, and is representative mainly of the variability over the Pyrenees area. Fig. 2c shows the pattern associated with the third EOF (10.2% of the total variance). This pattern is representative mainly of the variability of the southern mediterranean region in the basin. We have selected, for each one of these regions, two stations whose streamflow time series show the highest loading factors with the corresponding PC series, which can be considered like streamflow series representative of the region. Fig. 2d shows the
Table 1 List of individual gauging stations selected in the Ebro river basin, showing highest correlation coefficients with their associated PCs series. Code of the station from the CHE dataset, period data length and short name (hereinafter). Station name
Gauged code
Data length
Corr. coeff. (rPCi)
Short name
Ebro in Zaragoza Ebro in Mendavia Noguera Ribagorzana in Pont de Suer Esera in Grauss Martin in Alcaine Matarraña in Nonaspe
9011 9120 9137
1913–2006 1913–2006 1950–2006
rPC1 = 0.85 rPC1 = 0.82 rPC2 = 0.87
EZ_FLOW EM_FLOW NP_FLOW
9013 9127 9176
1950–2006 1950–2006 1950–2006
rPC2 = 0.85 rPC3 = 0.70 rPC3 = 0.70
EG_FLOW MA_FLOW MN_FLOW
location of these specific stations and Table 1 presents a description of them, including their short names. Fig. 3 presents the seasonal variability of the mean monthly flow for the six individual specific gauging stations of Table 1, along the entire period of available data. For the stations associated to the region represented by EOF1 (Fig. 3a) winter-time river flow account for the majority of runoff, being followed by a relatively long and dry summer period from July to September. This result corresponds with the flow type 4 of the classification done by Bejarano et al. (2010) about flow types in the Ebro basin. Flow type 4 of this classification corresponds with seasonal winter flow types and is located along the Basque–Cantabrian Mountains (Oro-Ibérica and Cantabro-Atlántica Subprovinces). For the stations associated to the region represented by EOF2 (Fig. 3b) a nivo-pluvial flow type, located in the Pyreness Mountains (Pirenaica Subprovince) (Bejarano et al., 2010) is presented, where snowmelt influence is very important. This area is characterised by a snowy winter, very rainy spring and rainy late summer an autumn (Bejarano et al., 2010). Finally, Fig. 3c shows the flows associated to the stations located in the southeast of the Ebro basin (Catalana-Valencia Subprovince) and were characterised by fairly low total annual precipitation and prolonged dry season. Taking into account the maximum streamflow values observed for the different flow types associated with the regions represented by the PCs, the study was limited to those months in which both discharge time series associated with a region are highest. That is, January for the river gauges associated to the PC1, June for those associated to the PC2 and May for those associated to the PC3. Fig. 4 shows these streamflow time series along with the associated PCs. Note from Fig. 3c that MN_FLOW time series shows an additional peak in December, which is even higher than in May. However, a detailed review (not shown) of the flow seasonality
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Fig. 3. Annual cycle of the variability of average monthly river flow for the specific gauging series associated to (a) PC1, (b) PC2 and (c) PC3.
associated with this region of the basin shows that this MN_FLOW time series is the only one with this behaviour. The flows of the other series in this region all present the highest peak in May. For this reason, the study for the mediterranean region has been restricted to May month. 4.1. Temporal variations SSA is then applied to each of these streamflow series to further identify and extract the oscillation components. Different window lengths between M = 18 and M = 32 years and the Vautard and Ghil (1989) algorithm were used in SSA. Only the results obtained for EZ_FLOW in December, EG_FLOW in June and MN_FLOW in May are shown hereinafter (similar results are obtained for the related EM_FLOW, NP_FLOW and MA_FLOW stations, respectively). The oscillation pairs identified by SSA on streamflow series for the selected stations are summarised in Table 2. Because SSA cannot resolve periods longer than the window length, we identified the zero frequency as the non-linear trend, but it is important to note that this non-linear trend could be composed of quasi-oscillatory modes with periods longer than window length years. For the Basque–Cantabrian region, besides the non-significant zero-frequency mode (trend), the significant modes in the January streamflow anomaly of EZ_FLOW (9011 gauging station) were located at the frequencies (in cycles per year) 0.043, 0.45, 0.11, 0.23, 0.32 and 0.15 corresponding to periods around 23.3, 2.3, 9.1, 4.3, 3.1 and 6.6 years, respectively. Table 2 also shows the variance explained by each mode (see middle column). Note that about 31.3% of the variance of the raw series is associated to the
decadal or multi-decadal variability (periods longer than 7 years) while about the 32.6% is explained by quasi-oscillatory modes of high frequency (periodicities less than 7 years). For the Pyrenees region (EG_FLOW in June), along with a nonlinear trend, significant modes appeared at frequencies 0.232, between 0.454–0.370, and 0.105 cycles/year, corresponding to periods around 4.3, between 2.2–2.7 years and 9.5 years, respectively. In this case, the trend and the oscillatory mode with period around 9.5 years account with 22.6% of the total variability while the remainder of the oscillations represents around 50.6%. For the southern Mediterranean region of the basin (MN_FLOW in May), along with the non-linear trend, flow variability at decadal scales is given by a quasi-oscillatory mode with period around 15 years, representing around 35.2% of the variance explained. Additionally, at time scales lower than 7 years, significant quasioscillatory modes with periods around 2.5, 3.1, 3.6, 4.9 and 6.6 years are found, representing the 46.3% of the raw series variance. Note that for the three regions much of the variance is associated with time scales greater than 7 years (between 22% and 35% depending on the region), while the rest of the variance is determined by the interannual variability of the series at time scales lower than 7 years (between 30% and 50% depending on the region). Based on this distinction between time scales the three streamflow series selected representing the regions obtained in the previous PCA have been modelled in next section. For this end, the decadal variability of Ebro river basin and its connection with global SST is firstly analysed. Standardised streamflow anomalies
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a
4
b EZ_FLOW EM_FLOW PC1
3
3 NP_FLOW EG_FLOW PC2
2 standard deviation
2 standard deviation
4
1 0 -1
1 0 -1
-2
-2
-3
-3
-4 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
-4 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
c
4 3
MN_FLOW MA_FLOW PC3
standard deviation
2 1 0 -1 -2 -3 -4 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
Fig. 4. PC series and selected streamflow time series corresponding to (a) the Basque–Cantabrian region in January, (b) the Pyrenees region in June and (c) the southern mediterranean region in May.
Table 2 Oscillation pairs identified by SSA on streamflow gauging stations. The second column contains the peak period (in years), the pair order and the fraction of total variance (%) explained by the pair. An estimation of significance level using Monte Carlo SSA (MC-SSA) is also shown (last column). Streamflow series
Oscillation period (years), (rank order for the associated eigenvalues; explained variance)
Test: against red noise process (RN) and red noise + signal (RN + components)
EZ_FLOW (January)
Non-linear trend (7–8; 9.1%) 23.3 y (1–2; 12.7%) 2.3 y (3–4; 11.1%) 9.1 y (5–6; 9.5%) 4.3 y (9–10; 7.3%) 3.1 y (12–13 ; 7.3%) 6.6 y (14–15 ; 6.9%)
<90% >95% >95% >95% >95% >95% >95%
(RN + significant oscillations) (RN + 3–4) (RN) (RN + 3–4 + 1–2 + 9–10 + 12–13) (RN + 3–4 + 1–2) (RN + 3–4 + 1–2) (RN + 3–4 + 1–2 + 9–10 + 12–13)
EG_FLOW (June)
Non-linear trend (5–8; 12.5%) 4.3 y (1–2; 19.8%) 2.1 y (3–4; 18.3%) 2.7 y (6–7; 12.5%) 9.5 y (10–11; 10.1%)
<90% >95% <90% >95% >95%
(RN + 1–2 + 3–4) (RN) (RN + 1–2) (RN + 1–2 + 3–4) (RN + 1–2 + 3–4 + 6–7)
MN_FLOW (May)
Non-linear trend (7; 5%) 15 y (1–2; 30.2%) 2.5 y (3–4; 14.4%) 3.1 y (5–6; 8.9%) 3.6 y (9–10; 8.6%) 4.9 y (11–12; 7.5%) 6.6 y (13–14; 6.9%)
<90% >95% >95% >95% >95% >90% >90%
(RN + 1–2 + 3–4 + 7–8) (RN) (RN) (RN + 1–2 + 3–4 + 5–6) (RN + 1–2 + 3–4 + 5–6) (RN + 1–2 + 3–4 + 5–6) (RN + 1–2 + 3–4 + 5–6 + 9–10 + 11–12)
were smoothed with a 7-year running mean filter to obtain the decadal components of the series (decadal_component). The 7year running mean period has been already chosen by other authors in order to exclude the influence of El Niño events, whose periodicities oscillate between 2 and 7 years (Dettinger et al., 2000; Ionita et al., 2011). In this respect, similar results are found for the two streamflow gauging stations used to characterise each region previously selected in the Ebro basin. Again, only results for the gauging stations EZ_FLOW in January, EG_FLOW in June and MN_FLOW in May are shown. Fig. 5 shows the selected flows along
with the decadal component obtained by smoothing the series with a 7-year running mean.
5. Streamflow modelling 5.1. Basque–Cantabrian region (January) The spatial correlation maps between the decadal_component (7-year running mean filter) of January EZ_FLOW and the preced-
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b3
a3 EZ_FLOW EZ_FLOW_7year rm
2
standard deviation
standard deviation
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1
0
-1
EG_FLOW EG_FLOW_7year rm
1 0 -1 -2
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-4 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
c3 MN_FLOW MN_FLOW_7year rm
standard deviation
2
1
0
-1
-2
-3 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
Fig. 5. Time series of monthly streamflow anomalies (solid lines) for (a) EZ_FLOW in January, (b) EG_FLOW in June, and (c) MN_FLOW in May. Dotted lines represent the decadal components obtained by smoothing the series with a 7-year running mean.
a
b
c
d
Fig. 6. Correlation maps between the decadal_component of January streamflow anomalies of EZ_FLOW and (a) previous spring SST anomalies, (b) previous summer SST anomalies, (c) previous autumn SST anomalies, and (d) previous December SST anomalies. Only significant values at the 95% confidence level are shown. Period of study is 1916–2003. The rectangle corresponds to the SST region finally considered for the decadal_component modelling.
ing seasons for SST data are shown in Fig. 6. For meaningful evaluation of the relationship between the SST and streamflow fields on decadal time scales, the linear trend components of all the data sets need to be removed. The fact of eliminating the trend when we
work with variables of different physical natures is necessary because otherwise trends could lead spurious correlations. Maximum statistically significant correlations were found with the previous SST in the Atlantic region. Particularly, we can identify
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positive correlations with the SST anomalies in the tropical North Atlantic and southern Greenland, with the tropical part of the SST pattern (approximately 0–20°N) playing the most important role. This pattern represents what is commonly called North Atlantic horseshoe pattern, described e.g. in Czaja and Frankignoul (2002). Correlations coefficients are maxima in previous spring, decreased in summer and autumn, and come back strongly in the tropical area in December. This spring SST pattern is shown to be related with the subsequent winter NAO (Rodwell and Folland, 2002). An additional region in the south Pacific also shows significant positive correlation during previous summer. Based on this correlation maps we define three SST indices by averaging the normalised SST anomalies over the regions showing maximum correlation values: SST1EZ (54°W–49°W; 9°N–12°N) and SST2EZ (44°W– 39°W; 54°N–56°N) in previous spring, and SST3EZ (99°W–96°W; 28°S–22°S) in previous summer. SST indices were smoothed with a 7-year running mean filter to obtain the decadal component of the series associated to these SST regions, and correlations between the January streamflow anomalies and the SST1EZ, SST2EZ and SST3EZ indices using a moving window of 15 years were computed. Stable positive correlations (not shown) during the period 1916–2003 are found only for the SST1EZ index, while the SST2EZ and SST3EZ indices fail the stability test and dismissed from the rest of the analysis. Using the significant and stable index SST1EZ as predictor for the January EZ_FLOW at decadal time scales we developed a model based on linear regression, using as calibration period 1916– 1989. The optimal model for explaining the decadal_component of this flow can be written as: previous spring
AR ¼ ðU1 ¼ 1:38 ;
-2
EZ_FLOW ARMA (7,6) ARMA (7,6) + SST_model
-3 1915
1925
1935
1945
1955
1965
1975
1985
b3 EZ_FLOW ARMA (7,6) ARMA (7,6) + SST_model
2
1
0
-1
2003
2002
2001
2000
1999
1998
1997
1996
-3
1995
Significance of the parameters was computed using approximate t-values, derived from the parameter standard errors. Parameters highlighted with ‘‘’’ are statistically significant at 5% significance level. The selected order model indicates a certain degree of persistence. Given the values of some of the parameters of the model and the ACF and PACF (not shown), the current interannual_component state is considerable dependent on its state up to 7 years earlier. This ARMA (7,6) model is able to explain around
-2
1993
h3 ¼ 0:23 ;
h4 ¼ 1:09 ; h5 ¼ 0:40 ; h6 ¼ 0:62 Þ
1994
h2 ¼ 1:24 ;
-1
1992
MA ¼ ðh1 ¼ 0:29 ;
0
1991
1
1990
U4 ¼ 1:25 ;
U2 ¼ 1:16 ; U3 ¼ 1:15 ; U5 ¼ 1:18 ; U6 ¼ 0:74 ; U7 ¼ 0:09Þ
standard deviation
2
This SST_modelEZ is able to explain around 56% of the variance of the streamflow decadal_component during the calibration period, showing around 84% agreement in the phase accordance between observed and modelled decadal_component. Regarding the modelling of the interannual variability (time scales less than 7 years) an additional analysis has been carried out using the quasi-oscillatory modes with periods lower than 7 years obtained from the previous SSA. Firstly, a SSA-filtered series, the interannual_SSA_filter, has been computed like the sum of the reconstructed components of these oscillatory modes, and then an ARMA_model is fitted to this SSA-filtered series. Using the sample Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) (not shown) we find that while the interannual_component behave like a white noise process, the interannual_SSA_filter series shows a strong autocorrelation pattern. This feature implies a higher predictability of the interannual_SSA_filter when compared to the unfiltered time series. Based on these analysis, we used the Akaike Information Criterion (AIC) to select an ARMA (7,6) model for the interannual_SSA_filter, containing the following parameters:
a3
standard deviation
SST modelEZ ¼ 2:07 SST1EZ
67% of the variance of the streamflow interannual_component during the calibration period, showing around 88% agreement in the phase accordance between observed and modelled interannual_component. Finally, the combination of SST_model (for decadal time scales) and ARMA_model (for interannual time scales) is evaluated. The observed and modelled January EZ_FLOW series are shown in Fig. 7 for calibration and validation periods. Results obtained reveal a considerable skill achieved by the combined [ARMA (7,6) + SST_model] model (see Table 3), with a good correlation coefficient between the raw series and the model for the calibration period (r = 0.81) and coefficient of multiple determination R2 (66%). Moreover the model presents a relatively low MSE = 0.35, MAE = 0.47 and a relatively high Willmott’s index (D = 0.86). Over the period 1990–2003, not used to fit the model, MSE is 0.73, MAE is 0.72 and Willmott’s index is 0.68. From Table 3 we can also see the contribution made by each of the modelling carried out (decadal and interannual) and can be seen as the overall quality of the combined model has increased significantly in both calibration and validation periods. For the validation period the correlation coefficient between the raw series and the combined model is 0.79 and the variance explained by this model rises to 62%. The combined [ARMA (7,6) + SST_model] modelling capacity can be appreciated in Fig. 7 with a clear improvement in relation to the ARMA model, particularly evident during the period 1960– 1993.
Fig. 7. (a) Observed (black circles) and modelled January EZ_FLOW anomalies during the calibration period (1916–1989) based on the interannual_component alone (red squares) and the combined modelling [ARMA (7,6) + SST_model] (blue triangles). (b) As in (a) but during the validation period (1990–2003). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Table 3 Statistical results of the modelling carried out for the January raw EZ_FLOW time series. Separate contributions from the decadal_component (SST_model) and the interannual_component (ARMA_model) to the raw series modelling, along with the combined modelling [ARMA (7,6) + SST_model] are shown. Results are displayed both for the calibration and validation periods. Values highlighted with ‘‘’’ are statistically significant at the 95% confidence level. Calibration period 1916–1989
MSE MAE Correlation coeft. Willmott index (D) % Phase accordance R2
Validation period 1990–2003
SST_model
ARMA (7,6)
ARMA (7,6) + SST_model
SST_model
ARMA (7,6)
ARMA (7,6) + SST_model
0.74 0.67 0.43 0.57 57% 18%
0.49 0.56 0.73 0.74 72% 53%
0.35 0.47 0.81 0.86 84% 66%
1.14 0.88 0.45 0.34 50% 20%
1.02 0.80 0.66 0.50 43% 44%
0.73 0.72 0.79 0.68 79% 62%
a
b
c
d
e
Fig. 8. Correlation maps between the decadal_component of June streamflow anomalies of EG_FLOW and (a) spring SST anomalies from the previous year, (b) previous summer SST anomalies, (c) previous autumn SST anomalies, (d) previous winter SST anomalies, and e) spring SST anomalies from the contemporary year. Only significant values at the 95% confidence level are shown. Period of study is 1953–2003. Rectangles correspond to the SST regions finally considered for the decadal_component modelling.
5.2. Pyrenees region (June) The spatial correlation maps between the decadal_component (7-year running mean filter) of June EG_FLOW and the preceding seasons for SST data are shown in Fig. 8. Statistically significant correlations with global SST are weaker than for the Basque–Cantabrian region, and appear fundamentally in the north Atlantic and in the Black Sea, being maxima during the spring of the previ-
ous year and in some regions of the Pacific for the previous summer. SST indices were computed and smoothed with a 7-year running mean filter similarly for the previous analysis. Stable correlations (not shown) during the period 1953–2003 are only found for the following defined indices: SST1EG = (30°E–40°E; 41°N– 46°N), corresponding to the Black Sea during the spring of the previous year, and SST2EG = (88°W–81°W; 25°S–20°S), associated to the south-eastern Pacific Ocean during the previous summer. From
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Table 4 Statistical results of the modelling carried out for the June raw EG_FLOW time series. Separate contributions from the decadal_component (SST_model) and the interannual_component (ARMA_model) to the raw series modelling, along with the combined modelling [ARMA (4,8) + SST_model] are shown. Results are displayed both for the calibration and validation periods. Values highlighted with ‘‘’’ are statistically significant at the 95% confidence level. Calibration period 1953–1989
MSE MAE Correlation coeft. Willmott index (D) % Phase accordance R2
Validation period 1990–2003
SST_model
ARMA (4,8)
ARMA (4,8) + SST_model
SST_model
ARMA (4,8)
ARMA (4,8) + SST_model
0.70 0.64 0.41 0.45 40% 17%
0.34 0.46 0.77 0.82 49% 59%
0.22 0.37 0.84 0.90 53% 71%
0.47 0.56 0.26 0.38 64% 6%
0.18 0.35 0.79 0.88 86% 62%
0.11 0.26 0.90 0.93 86% 81%
this result, the SST_model for June flow at decadal time scales computed using multiple linear regressions for the calibration period 1953–1989 is:
SST modelEG ¼ 0:068 þ 0:601 SST1EG þ 0:53 SST2EG
spring previous year
previous summer
This SST_modelEG is able to explain around 71% of the variance of the streamflow decadal_component, showing around 75% agreement in the phase accordance between observed and modelled decadal_component.
a
3 EG_FLOW ARMA (4,8) ARMA (4,8) + SST_model
standard deviation
2
1
0
-1
-2
b
1988
1986
1984
1980
1982
1976
1978
3
EG_FLOW ARMA (4,8) ARMA (4,8) + SST_model
2
standard deviation
1974
1972
1968
1970
1964
1966
1962
1960
1956
1958
1952
1954
1950
-3
1
0
-1
-2
Regards to the modelling of the interannual variability (time scales less than 7 years) a similar procedure to the Basque– Cantabrian region was carried out, finally selecting an ARMA (4,8) model for the interannual_SSA_filter, containing the following parameters:
AR ¼ ðU1 ¼ 1:2 ;
U2 ¼ 1:06 ;
MA ¼ ðh1 ¼ 0:26 ;
h2 ¼ 0:17 ;
h5 ¼ 0:14 ;
h6 ¼ 0:05;
U3 ¼ 1:1 ;
h3 ¼ 0:39 ;
h7 ¼ 0:22 ;
U4 ¼ 0:5 Þ
h4 ¼ 0:13 ;
h8 ¼ 0:74 Þ
Note from Table 1 that the interannual variability of this time series is determined by quasi-oscillatory modes with periods between 2 and 4 years. In this sense, again the selected order model indicates a certain degree of persistence. Given the values of some of the parameters of the model and the ACF and PACF (not shown), the current interannual_component state is considerable dependent on its state up to 4 years earlier. In this case, this ARMA (4,8) model is able to explain around 76% of the variance of the streamflow interannual_component, showing around 80% agreement in the phase accordance between observed and modelled interannual_component. The combination of SST_model (for decadal time scales) and ARMA_model (for interannual time scales) is evaluated in Table 4 and the observed and modelled June EG_FLOW series are shown in Fig. 9 for calibration and validation periods. Results obtained reveal a considerable skill achieved by the combined [ARMA (4,8) + SST_model] model (see Table 4), with a good correlation coefficient between the raw series and the model for the calibration period (r = 0.84) and coefficient of multiple determination R2 (71%). The model presents a relatively low MSE = 0.22, MAE = 0.37 and a high Willmott’s index (D = 0.90). Over the period 1990–2003, not used to fit the model, skill scores are even better (MSE is 0.11, MAE is 0.26 and Willmott’s index is 0.93). From Table 4 we can also see the contribution made by each of the modelling carried out (decadal and interannual) and can be seen as the overall quality of the combined model has increased significantly in both calibration and validation periods. For the validation period the correlation coefficient between the raw series and the combined model is 0.90 and the variance explained by this model rises to 81%. The combined [ARMA (4,8) + SST_model] modelling capacity can be appreciated in Fig. 9 with a clear improvement in relation to the ARMA model, particularly evident between 1987 and 1992. 5.3. Southern mediterranean region (May)
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
-3
Fig. 9. (a) Observed (black circles) and modelled June EG_FLOW anomalies during the calibration period (1953–1989) based on the interannual_component alone (red squares) and the combined modelling [ARMA (4,8) + SST_model ] (blue triangles). (b) As in (a) but during the validation period (1990–2003). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
The spatial correlation maps between the 7-year running mean filter of May MN_FLOW and the preceding seasons for SST data are shown in Fig. 10. Maximum statistically significant correlations were found with the previous SST fundamentally in the Pacific region. Particularly, we can identify correlations that resemble the negative pattern of the Pacific Decadal Oscillation during the
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a
b
c
d
e
Fig. 10. Correlation maps between the decadal_component of May streamflow anomalies of MN_FLOW and (a) spring SST anomalies from the previous year, (b) previous summer SST anomalies, (c) previous autumn SST anomalies, (d) previous winter SST anomalies, and e) spring (as March–April average) SST anomalies from the contemporary year. Only significant values at the 95% confidence level are shown. Period of study is 1953–2003. Rectangles correspond to the SST regions finally considered for the decadal_component modelling.
spring of the previous year. Correlations coefficients are maxima in spring of the previous year, decrease during the following seasons until intensify in the Atlantic Ocean after one year. Based on this correlation maps we define six SST indices by averaging the normalised SST anomalies over the regions showing maximum correlation values, indicated in Fig. 10: SST1MN (174°W–158°W; 29°N–33°N), SST2MN (158°W–154°W; 50°N– 55°N), SST3MN (76°W–72°W; 30°S–21°S), SST4MN (168°E–172°E; 21°S–18°S), SST5MN (14°W–9°W; 36°N–39°N) and SST6MN (4°W– 1°W; 64°N–66°N). Stable correlations (not shown) during the period 1953–2003 are found for all the indices except with the SST6MN, which fails the stability test and was dismissed from the rest of the analysis. Additionally, the stability of the correlation between the May streamflow and the spring PDO index of the previous year was also studied, finding negative stable correlation along the period. Using these SST indices and the PDO index as explanatory variables multiple linear regression models were fitted to the decadal_component of the streamflow. To avoid problems of collinearity among the variables, the backward stepwise procedure was applied, and the selected model is as follows:
SST modelMN ¼ 0:1 0:69 SST2MN
previous spring
0:79 SST3MN
previous summer
þ 1:22 SST4MN
previous summer
þ 0:26 PDOprevious
spring :
The fact that some SST indices do not play a role in the regression model, even though these present high correlation coefficients with the streamflow, is due to the high mutual correlation shown between them. This effect leads to that only some of the factors remain important in the combined regression model. This is the case of the SST1MN index which has a correlation with the PDO around 0.84. The SST5MN index, meanwhile, brings a small improvement for the model and has been removed. The obtained SST_modelMN is able to explain around 81% of the variance of the streamflow decadal_component, showing around 96% agreement in the phase accordance between observed and modelled decadal_component. For the modelling of the interannual variability (time scales less than 7 years) an ARMA (4,3) was selected model, containing the following parameters:
AR ¼ ðU1 ¼ 1:04 ;
U2 ¼ 0:78 ;
MA ¼ ðh1 ¼ 0:89 ;
h2 ¼ 0:96 ;
U3 ¼ 0:40 ;
U4 ¼ 0:37 Þ
h3 ¼ 0:93 Þ
In this case, this ARMA (4,3) model is able to explain around 64% of the variance of the streamflow interannual_component, showing around 87% agreement in the phase accordance between observed and modelled interannual_component. The combination of SST_model (for decadal time scales) and ARMA_model (for interannual time scales) is evaluated in Table 5
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Table 5 Statistical results of the modelling carried out for the May raw MN_FLOW time series. Separate contributions from the decadal_component (SST_model) and the interannual_component (ARMA_model) to the raw series modelling, along with the combined modelling [ARMA (4,3) + SST_model] are shown. Results are displayed both for the calibration and validation periods. Values highlighted with ‘‘’’ are statistically significant at the 95% confidence level. Calibration period 1953–1989
MSE MAE Correlation coeft. Willmott index (D) % Phase accordance R2
Validation period 1990–2003
SST_model
ARMA (4,3)
ARMA (4,3) + SST_model
SST_model
ARMA (4,3)
ARMA (4,3) + SST_model
0.59 0.64 0.56 0.59 73% 31%
0.33 0.46 0.76 0.73 82% 58%
0.14 0.32 0.90 0.88 79% 81%
0.89 0.78 0.60 0.64 79% 36%
0.80 0.79 0.72 0.83 79% 52%
0.45 0.59 0.87 0.94 79% 76%
and the observed and modelled May streamflow series are shown in Fig. 11 for calibration and validation periods. Results reveal a considerable skill achieved by the combined [ARMA (4,3) + SST_model] model (see Table 5), with a good correlation coefficient between the raw series and the model for the calibration period (r = 0.90) and coefficient of multiple determination R2 (81%). The model presents a relatively low MSE = 0.14, MAE = 0.32 and a high Willmott’s index (D = 0.88). Over the period 1990–2003, not used to fit the model, MSE and MAE are a little worse (0.45 and 0.59, respectively), but the Willmott’s index is better (D = 0.94). From Table 5 we can also see the contribution made by each of the modelling carried out (decadal and interannual) and
a
3 MN_FLOW ARMA (4,3) ARMA (4,3) + SST_model
standard deviation
2
1
0
-1
b
1988
1984
1986
1982
1978
1980
1974
1976
1972
1970
1966
1968
1964
1960
3 MN_FLOW ARMA (4,3) ARMA (4,3) + SST_model
2
standard deviation
1962
1958
1956
1952
1954
-3
1950
-2
1
0
-1
2003
2002
2001
1999
2000
1998
1997
1996
1995
1994
1993
1991
1992
-3
1990
-2
Fig. 11. (a) Observed (black circles) and modelled May MN_FLOW anomalies during the calibration period (1953–1989) based on the interannual_component alone (red squares) and the combined modelling [ARMA (4,3) + SST_model] (blue triangles). (b) As in (a) but during the validation period (1990–2003). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
can be seen as the overall quality of the combined model has increased significantly in both calibration and validation periods. For the validation period the correlation coefficient between the raw series and the combined model is 0.87 and the variance explained by this model rises to 76%. The combined [ARMA (4,3) + SST_model] modelling capacity can be appreciated in Fig. 11 with a clear improvement in relation to the ARMA model, particularly important for the peaks of streamflow. 6. Discussion and conclusions A dataset of monthly streamflow series from 83 sites around the Ebro basin has been analysed to characterise geographic differences in terms of the streamflow seasonality and some aspects of interannual and decadal variability. The space–time variability of the streamflow in the Ebro basin has been analysed by using, first, PCA, and then SSA. With respect to the spatial variability of streamflow, three significant spatial EOFs were found, associated with different regions in the basin. The first mode covers mainly the variability of gauging streamflows recorded at the Basque–Cantabrian Mountains. The second one is fundamentally representative of the variability over the Pyrenees area, and the third mode represents the variability of the southern mediterranean region. Streamflow seasonality varies regionally, depending on the timing of maximum precipitation, evapotranspiration, and contributions from snow and ice. Lags between peaks of precipitation and streamflow vary smoothly from long delays in mountainous regions to short delays in the warmest sectors (Dettinger and Diaz, 2000). Globally, at most gauges, both the timing and amplitude of streamflow seasonality depends on the local month of maximum precipitation and the extent to which precipitation is trapped in snow and ice. For the stations associated to the region represented by EOF1 winter-time river flow account for the majority of runoff, being followed by a relatively long and dry summer period. For the stations associated to the EOF2 a nivo-pluvial flow type is presented, where snowmelt influence is very important, with streamflow peaking in June. Finally, flows associated to the southern mediterranean region are characterised by low total annual streamflow and prolonged dry season, with streamflow peaking in May. This separation is in agreement with the classification developed by Bejarano et al. (2010) in the same basin, which separates Eurosiberian nival from Mediterranean pluvial flow types, although they show a much more detailed classification type flows based on the physical characteristics of the catchments. Attending to the classification found the main characteristic time scales of the maximum monthly streamflows are studied by SSA. The applied SSA algorithm to isolate the main characteristics of the streamflow series revealed a similar model structure for the three regions, including: (1) a non-linear trend dominated by multidecadal variability; (2) modulated amplitude oscillations with periods longer than 7 years (decadal periodicities are around 23 years, 9.5 years and 15 years for the Basque–Cantabrian,
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Pyrenees and southern mediterranean regions, respectively); (3) quasi-oscillatory modes in the bands 2–3, 4–5, and 6–7 year, depending of the region; and 4) a red noise process. Decadal variations in streamflow make particularly large contributions to yearto-year streamflow variance in stations placed in the Cantabrian Mountains and southern mediterranean region (31.3% and 35.2%, respectively), while for the Pyrenees flows the interannual contribution to the streamflow variations is more important (50.6%). From this point, the predictability of the Ebro flow anomalies has been investigated using a combined methodology: (1) for decadal and longer time scales (e.g., >7 years) we use as predictors in a multiple linear regression model the global sea surface temperatures from the preceding seasons (obtaining the SST_model); (2) for interannual time scales (e.g., <7 years) ARMA modelling were developed for the interannual_SSA-filtered streamflow series. It is expected that the potential relationships between the flow and the SST field will be intensified for those months showing maximum streamflow values, although similar SST patterns are obtained if different monthly, seasonal or annual streamflow time series are used because the SST study has been restricted to decadal time scales. However, variations for the interannual variability modelling could be achieved if other months, different to those showing maximum streamflow values, are also used, because both the study of quasi-oscillatory modes by SSA and the ARMA modelling could change depending on the season. The results of this analysis demonstrated the existence of strong influences of ocean conditions in the Ebro River at decadal time scales. For the gauging stations associated to the Basque–Cantabrian region we find positive significant correlations between the streamflow anomalies in January and the North Atlantic horseshoe pattern (Czaja and Frankignoul, 2002) during the previous spring. This association is found maximum and stable for the tropical part of the pattern (approximately 0–20°N) in previous spring, decreases in summer and autumn, and comes back strongly in December. This result is in agreement with other studies that suggest a link between spring conditions in the North Atlantic Ocean and atmospheric conditions over the same region the subsequent winter (Czaja and Frankignoul, 1999, 2002; Rodwell and Folland, 2002; Drevillon et al., 2003; Frankignoul and Kestenare, 2005; Iwi et al., 2006). Rodwell and Folland (2002) showed that the North Atlantic SST in May could be used as a predictor of the subsequent winter NAO. One hypothesis is that conditions present in the North Atlantic Ocean in spring persist through the summer to influence the atmosphere in the following autumn and winter. During summer the ocean anomalies may be capped by the shallow mixed layer, subsequently to emerge as the mixed layer deepens in early winter. This mechanism is known as re-emergence (Deser et al., 2003; Cassou et al., 2004). Sutton et al. (2001) showed that a tripole pattern of SST anomalies could induce a weak NAO-like atmospheric response, and further experiments indicated the important role played by the tropical part of the pattern (Terray and Cassou, 2002; Cassou et al., 2004; Peng et al., 2005). These results could provide information concerning the underlying physics of the teleconnection found for the streamflow and Atlantic SST, suggesting an important influence of the SLP as a main component in the SST/streamflow relationship; however, physical explanations for the connection between the SST and streamflow are not yet clear. Additionally, it is important to note that SLP patterns other than the NAO could also have a dominant role for determining streamflows. For the gauging stations associated to the Pyrenees region the correlations between the June streamflow and global SST, at decadal time scales, are weaker than for those of the Basque–Cantabrian region, and only stable connections are found in the Black Sea SST during the spring of the previous year and in the south-eastern of the Pacific Ocean during the previous summer. How this connec-
tion between the SST and the flow is produced is an issue that needs further research. Oguz et al. (2006) carried out an examination of a wide spectrum of hydro-meteorological records in the Black Sea. They found a robust climatic signature at interannual to interdecadal time scales in the Black Sea SST, with variations on the order of 15–30-year band superimposed to oscillations with the period of about 10 years. These variations appear to be governed by the North Atlantic Oscillation and East Atlantic-West Russia (EAWR) teleconnection patterns. For the gauging stations associated to the southeast of basin higher than average values of the Ebro river flow in May tend to be associated with cooler than average SST anomalies along the western coast of North America, and warmer than average SSTs in the central North Pacific during spring of the previous year. This Pacific SST pattern associated with the Ebro flow decadal variability bears some resemblance to the SST pattern characterising the negative phase of the Pacific Decadal Oscillation (PDO) (Mantua et al., 1997). Currently, there are several hypotheses concerning the causes of decadal variations in different geographical regions and the influence of PDO is one of these hypotheses (Baik and Paek, 1998; Tomita et al., 2001; Voskresenskaya, 2005). Other authors have also found teleconnections between the PDO and other rivers in Europe (Dettinger and Diaz, 2000; Rimbu et al., 2002; Bardin and Voskresenskaya, 2007; Labat, 2010). For example, Rimbu et al. (2002) found an opposite association between the streamflow of the Danube River and the PDO, while Bardin and Voskresenskaya (2007) state that the decadal variability of the NAO supported by the large-scale anomalies of the PDO can be regarded as the most important cause of the natural decadal oscillations of hydro-meteorological characteristics in the Atlantic-European region. These later authors find that the positive phase of the PDO corresponds to the intensification of the NAO, which is accompanied by the positive anomalies of sea level pressure in the tropical and subtropical Atlantic, over central and southern Europe, and over the Mediterranean Sea. Opposite conditions correspond to the negative phase of the PDO. The basic physical proposed scheme is that the climatic anomalies of the atmosphere–ocean interaction propagate from the Pacific Ocean toward the neighbouring continents and other oceans by means of stationary Rossby waves and synoptic atmospheric formations (Ambrizzi and Hoskins, 1997). Additionally, two more regions placed in the southeast and southwest of the Pacific Ocean, respectively, also show stable significant correlations with the decadal variability of the Ebro streamflows recorded in the southeast Basin. These southern regions in the Pacific are also shown in the Pacific multidecadal pattern obtained by Enfield and Mestas-Nuñez (1999) on their analysis of the global SST, which resembles the PDO pattern with somewhat weaker extension to the southeast, west of Chile. The SST teleconnection indices found, related to the hydrology of the Ebro Basin, have been incorporated into statistical streamflow forecasting models. Note that the Ebro basin is a complex region from both the topographical and meteorological perspectives, with great physical heterogeneity, which is a deciding factor in the variability of flow. There are several papers that assess this complex behaviour (Vicente-Serrano and López-Moreno, 2006; LópezBustins et al., 2008). Moreover, Ebro basin represents a transition zone between the Atlantic and Mediterranean influences. So it is reasonable to assume that different regions of the basin are being affected by different physical mechanisms, which can be translated to different SST teleconnection indices. Moreover, the way of coupling between local, atmospheric circulation and SST patterns, probably non-linear, could explain these different streamflow responses into the basin, an aspect that recently some authors have considered to need a further research, pointing out to possible nonlinear interactions between climate systems (Shaman and Tziperman, 2011; Switanek et al., 2009).
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Regarding the interannual variability and predictability of the Ebro streamflow series selected as representative of the three regions obtained by the application of PCA to the basin, this has been studied using the previous SSA and ARMA models. First, interannual_SSA_filters were constructed from the quasi-oscillatory modes with periodicities less than 7 years found by SSA. These resulting filters account for the 32.6%, 50.6% and 46.3% variance of the streamflow for the Basque–Cantabrian, Pyrenees and southern mediterranean regions, respectively. Then, an ARMA model was obtained for each interannual_SSA_filtered streamflow series and a forecasting experiment was conducted. The models were calibrated for the period 1916–1989 for the streamflow time series associated to the Basque–Cantabrian region, and for 1953–1989 for Pyrenees and southern mediterranean regions. The period 1990–2003 was used for validation in all the three cases. An ARMA (7,6) model, with constrained parameters, was fitted for the Basque–Cantabrian region, while ARMA (4,8) and ARMA (4,3) models were found, respectively, for the Pyrenees and mediterranean regions. The ARMA modelling applied to the interannual_SSA_filters is able to provide the interannual linearly predictable signal contained in the history of the time series which is not related to the decadal variability of the SST. Finally, the combination of SST_model (for decadal time scales) and ARMA_model (for interannual time scales) has been evaluated for each region. The combined modelling of Ebro anomalies based on our statistical scheme outperforms significantly the modelling based on ARMA models alone. Additionally, this methodology allows evaluating, independently, the decadal and interannual predictability of the streamflow series, which vary (for the validation period) between 20% and 44% for the Basque–Cantabrian region, between 6% and 62% for the Pyrenees region and between 36% and 52% for the mediterranean region, respectively. In summary, this work shows the existence of a valuable decadal and interannual predictability of the Ebro streamflow, a result that may be useful to water resources management. At decadal time scales SST anomalies from several regions provide a significant source of predictability for the Ebro flow, while at interannual time scales ARMA modelling, applied to the time series previously filtered by SSA, is able to provide potential skill in forecasting. The combination of both modelling gives as result a methodology that has the capacity to provide basin-specific hydroclimatic predictions. The work presented here raises several issues that require further analysis and can be improved in different ways. First, our results are encouraging since that only information contained in the global SST has been used to explain the Ebro streamflow variability. Statistical forecasting models that use multiple variables such as land surface temperature, precipitation or SLP as potential predictor variables can improve forecast skill by increasing the robustness of the methodology. Second, at interannual time scales the direct influence of SST variability on streamflow has not been considered. However, the periodicities associated to El Niño, which oscillate between 2 and 7 years, could be related in some way with the interannual quasi-oscillatory modes found in the Ebro streamflow. Although most studies suggest a weak but significant ENSO response over the North Atlantic-European sector (Ropelewski and Halpert, 1987; Fraedrich et al., 1992; Gouirand and Moron, 2003; Pozo-Vázquez et al., 2005; Vicente-Serrano, 2005; Mariotti et al., 2005; Brönnimann et al., 2004, 2007; Gámiz-Fortis et al., 2010a), uncertainties regarding the regional details must be studied in detail. In a recent paper, Shaman and Tziperman (2011) cited several papers that found relations between ENSO and Mediterranean climate during all season of the year, and established that it is difficult to determine whether the time and space discrepancies in these studies are due to different teleconnection processes or result from a single teleconnection mechanism that produces differ-
773
ent seasonal and regional effects. Unfortunately, understanding of the dynamics of the ENSO–Mediterranean teleconnections has not advanced much since Ropelewski and Halpert (1987) stated that the ‘‘implied ENSO relationships in these regions are difficult to understand or attribute to any of the known ENSO related atmospheric circulation changes’’. On the other hand, these authors argue that the persistence of ENSO (or other SST patterns) is an important factor to take into account to explain these teleconnections. Similar considerations could be done for other SST indices obtained in this work. All the cited results support the findings of our analysis about the influence of SST in the streamflow behaviour; however, physical explanations for the connection between the SST and streamflow are not yet clear, especially the contribution of different latitudes and ocean basins is still highly controversial. This paper represents a contribution on this subject. In this sense, the methodology used here detects not only statistically significant relationship, but also stable on time. However, it is not able to give information about the physical foundation. Therefore, there is an obvious need for further research to elucidate the physical explanation of the relationships between the SST and the streamflow. For this end dynamical methods with reliable GCM simulations and downscaling techniques would become necessary. Acknowledgements The Spanish Ministry of Science and Innovation, with additional support from the European Community Funds (FEDER), Projects CGL2007-61151/CLI and CGL2010-21188/CLI, financed this study. S.R. Gámiz-Fortis is supported by the University of Granada under a postdoctoral contract. References Akaike, H., 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control 19, 716–7233. Ambrizzi, T., Hoskins, B., 1997. Stationary Rossby-wave propagation in a baroclinic atmosphere. Quarterly Journal of the Royal Meteorological Society 123 (540), 919–928. Baik, J.J., Paek, J.S., 1998. A climatology of sea surface temperature and the maximum intensity of western North Pacific tropical cyclones. Journal of Meteorolycal Society of Japan 76 (1), 129–137. Bardin, M.Y., Voskresenskaya, E.N., 2007. Pacific Decadal Oscillation and European climatic anomalies. Physical Oceanography 17 (4), 200–208. Barnett, T.P., Del Genio, A.D., Ruedy, R.A., 1992. Unforced decadal fluctuations in a coupled model of the atmosphere and ocean mixed layer. Journal of Geophysical Research 97, 7341–7354. Barnston, A.G., Livezey, R.E., 1987. Classification, seasonality, and persistence of low-frequency atmospheric circulation patterns. Monthly Weather Review 115, 1083–1126. Batalla, R.J., Gomez, C.M., Kondolf, G.M., 2004. Reservoir-induced hydrological changes in the Ebro river basin (NE Spain). Journal of Hydrology 290, 17–136. Bejarano, M.D., Marchamalo, M., García de Jalón, D., González del Tánago, M., 2010. Flow regime patterns and their controlling factors in the Ebro basin (Spain). Journal of Hydrology 385, 323–335. doi:10.1016/j.jhydrol.2010.03.001. Brockwell, P.J., Davis, R.A., 1996. Introduction to Time Series and Forecasting. Springer-Verlag, 420 pp. Brönnimann, S., Luterbacher, J., Staehelin, J., Svendby, T.M., Hansen, G., Svenøe, T., 2004. Extreme climate of the global troposphere and stratosphere 1940–1942 related to El Niño. Nature 431, 971–974. Brönnimann, S., Xoplaki, E., Casty, C., Pauling, A., Luterbacher, J., 2007. ENSO influence on Europe during the last centuries. Climate Dynamic 28, 181–197. Cassou, C., Deser, C., Terray, L., Hurrell, J.W., Drevillon, M., 2004. Summer sea surface temperature conditions in the North Atlantic and their impact upon the atmospheric circulation in early winter. Journal of Climate 17, 3349–3363. Cayan, D., Dettinger, M.D., Dias, H.F., Graham, N., 1998. Decadal variability of precipitation over western United States. Journal of Climate 12, 2881–2893. Chen, F., Ghil, M., 1996. Interdecadal variability in a hybrid coupled oceanatmosphere model. Journal of Physical Oceanography 26, 1561–1578. Coulibaly, P., Burn, D.H., 2005. Spatial and temporal variability of Canadian seasonal streamflows. Journal of Climate 18 (1), 191–210. Cullen, H.M., Kaplan, A., Arkin, P., DeMenocal, P.B., 2002. Impact of the North Atlantic Oscillation on Middle Eastern climate and streamflow. Climate Change 55, 315–338. Czaja, A., Frankignoul, C., 1999. Influence of the North Atlantic SST on the atmospheric circulation. Geophysical Research Letters 26 (19), 2969–2972.
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