Seasonal streamflow prediction in Colombia using atmospheric and oceanic patterns

Accepted Manuscript Seasonal streamflow prediction in Colombia using atmospheric and oceanic patterns Samir Córdoba-Machado, Reiner Palomino-Lemus, Sonia Raquel GámizFortis, Yolanda Castro-Díez, María Jesús Esteban-Parra PII: DOI: Reference:

S0022-1694(16)30184-6 http://dx.doi.org/10.1016/j.jhydrol.2016.04.003 HYDROL 21173

To appear in:

Journal of Hydrology

Received Date: Revised Date: Accepted Date:

17 October 2015 2 March 2016 2 April 2016

Please cite this article as: Córdoba-Machado, S., Palomino-Lemus, R., Gámiz-Fortis, S.R., Castro-Díez, Y., EstebanParra, M.J., Seasonal streamflow prediction in Colombia using atmospheric and oceanic patterns, Journal of Hydrology (2016), doi: http://dx.doi.org/10.1016/j.jhydrol.2016.04.003

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Seasonal streamflow prediction in Colombia using atmospheric and oceanic patterns Samir Córdoba-Machado1,2, Reiner Palomino-Lemus1,2, Sonia Raquel Gámiz-Fortis1, Yolanda Castro-Díez1, María Jesús Esteban-Parra1,* 1

Applied Physics Department, University of Granada, Granada, Spain 2

Technological University of Chocó, Colombia

(*) Corresponding author address: María Jesús Esteban Parra Departamento de Física Aplicada Facultad de Ciencias Universidad de Granada Campus Fuentenueva s/n 18071-Granada. Spain. E-mail: [email protected] Phone: +34 958 240021 Fax: +34 958 243214

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ABSTRACT The predictability of the Magdalena River seasonal streamflow anomalies is evaluated using previous Sea Surface Temperature (SST), Precipitation (Pt) and Temperature over land (Tm) seasonal anomalies. Through a moving correlation analysis of 30 years, several regions that show stable significant teleconnections between the seasonal streamflow and SST, Pt and Tm from previous seasons have been identified during the period 1936-2009. For lags from one to four 3-month seasons (i.e. up to one year) for the SST and one to two seasons (i.e. up to six months) for Pt and Tm, the Magdalena River seasonal streamflow presents significant and stable correlations with the tropical Pacific SST (El Niño region), with Pt in South America and with Tm over the north of South America, mainly at lags of one and two seasons. The first PCs resulting from the significant and stable regions of the SST, Pt, and Tm fields are used in a forecast scheme to predict seasonal streamflow anomalies. The prediction based on this scheme shows an acceptable prediction skill and represents a relative improvement compared with the predictability of teleconnection indices associated with El Niño, which are traditionally used to predict streamflow in the country. This improvement is particularly more noticeable when lag between streamflow and predictors increases. Keywords: Seasonal streamflow prediction, Tropical Pacific SST, El Niño, Magdalena River, Hydro-climatology of Colombia. 1. Introduction Predictions

concerning

different

hydro-climatic

variables

(e.g.

precipitation,

streamflow, temperature, wind) are of great importance for planning, using, and managing natural resources of a country as well as for mitigating the impacts of natural 2

disasters caused by extreme phases of climatic variability. Good climate prediction can help palliate negative consequences for human populations (outbreaks of diseases, loss of human lives, etc.), and allows managers to take advantage of favorable conditions to manage resources more efficiently through proper planning. Water is a vital resource for human as well as the natural ecosystems. It has been established that changes in the cycling of water between the land, sea, and air can have significant impacts on the environment, economy, and society through their effects on the water resources and their management (Arnell, 1999; Arnell and Reynard, 1996). Anomalous oceanic-atmospheric conditions are often linked to seasonal variations in river streamflow via variations in precipitation, temperature, and soil moisture (Dettinger and Diaz, 2000; Cullen et al., 2002; Poveda et al., 2001). One of the most important phenomenon of ocean-atmosphere coupling is the El Niño Southern Oscillation (ENSO), which, during its El Niño phase, shows a pattern of positive sea surface temperature (SST) anomalies (anomalous warming) over the east tropical Pacific and negative SST anomalies (anomalous cooling) in the west (e.g. Rasmusson and Carpenter, 1982). Several studies have reported evidences of the strong relationship and the strong predictive ability of the tropical Pacific SST (ENSO) variability over the fluctuations of the river discharges (hydrologic variability) in different regions of the world: e.g. on South America (Hastenrath, 1990; Mechoso and Iribarren, 1992; Tootle et al., 2008; Marengo, 1995, 1992; Souza and Lall, 2003; Gutiérrez and Dracup, 2001), North America (Kalra et al., 2013; Maurer et al., 2004; Tootle et al., 2007; Abudu et al., 2010; Tootle and Piechota, 2006; Cayan and Webb, 1992), Australia (Simpson et al., 1993; Chiew et al., 1998; Piechota et al., 1998; Kuhnel et al., 1990; Kiem and Franks, 2001; Sahu et al., 2012), Africa (Molinier et al., 2009; Hirst and Hastenrath, 3

1983; Amarasekera et al., 1997; Jury., 2003; Labat et al., 2005; Abtew et al., 2009), Europe (Gámiz-Fortis et al., 2010; Ionita et al., 2008; Rimbu et al., 2004; Rimbu et al., 2005; Dettinger and Diaz, 2000; Hidalgo-Muñoz et al., 2015), and Asia (Zhang et al., 2007; Tong et al., 2006; Whitaker et al., 2001; Shrestha and Kostaschuk, 2005; Chandimala and Zubair, 2007; Cluis and Laberge, 2002). A notable study by Chiew and McMahon (2002) has investigated the global ENSO-streamflow teleconnection and its potential ability for forecasting streamflow by fitting a harmonic to 24-month El Niño streamflow composites from 581 catchments worldwide. These authors calculate the lag correlations between streamflows and two indicators of ENSO, revealing major relationships over many of the rivers studied. Similarly, Ward et al. (2010), quantifying the impact of ENSO over several rivers in the world, found that on average, ENSO exerts a greater impact on annual high-flows than on mean annual discharge. Several authors have analyzed the influence of the ENSO over the precipitation in Colombia and northern South America (Poveda and Mesa 1997; Poveda et al., 2005, 2011; Pabón 2002; Kayano et al. 2012; Tedeschi et al. 2013, Córdoba-Machado et al., 2015), showing that the variability associated with the ENSO is the major forcing mechanism of climatic and hydrological anomalies in Colombia (Poveda et al., 2001), having a direct influence on the environment, society, and economy of a country. So, for Colombia, these works concluded that during El Niño (/La Niña) the rainfall decreases (/increases), mainly in the center, north, and west of the country, while temperatures increase (/decrease) with the presence of this phenomenon. Moreover, the magnitude of the climate effect on Colombia caused by strong El Niño during the years 1997-1998, was considered to be of the highest intensity and spatial amplitude (IDEAM, 2002), considerably affecting the ecosystems, agriculture, hydropower 4

production, and other sectors of economic development of the country. Overall, the climatic conditions generated phenomena such as heat waves with historical maximum temperatures, droughts, numerous forest fires, increased the melting of mountain glaciers, and diminished stream flows in many regions that exceeded the minimum values for the last 50 years. Of 1160 districts, 100 presented extreme deficits, 861 deficits, 67 slight deficits and 42 normal, with droughts dominating about 90% of the country, forcing electricity rationing in several regions (IDEAM, 2002). All these anomalous conditions had a negative impact on the economy and the country's development. Recently, Córdoba-Machado et al. (2015a, 2015b) evaluated the response of the seasonal precipitation for different phases of El Niño and El Niño Modoki using singular value decomposition (SVD), in order to establish patterns of seasonal rainfall prediction based on the tropical Pacific SST variability associated with these phenomena (El Niño and El Niño Modoki). Given the important influence that the ENSO cycle has on the hydro-climatology of Colombia, some studies have explored its relation over the streamflow of several rivers in the country. Thus, Poveda et al. (2001) identified a pronounced seasonality in the influence of ENSO on the hydro-climatology of Colombia, using analyses of precipitation, river discharges, soil moisture and the Normalized Difference Vegetation Index (NDVI), demonstrating through a seasonal cross-correlation analysis that El Niño produces drier than normal and more prolonged seasonal dry periods in Colombia, while La Niña amplifies the wetness of wet seasons. These researchers also confirm that seasonal river discharge and rainfall are highly and simultaneously correlated with the Southern Oscillation Index (SOI, correlation values around 0.7 – 0.8) during DecemberJanuary-February, and conclude that the consideration of these high correlations of the 5

SOI in the two previous seasons with river discharge in the following winter can benefit the forecasts. Likewise, Gutiérrez and Dracup (2001) investigated the relationships between the ENSO events and the discharge of Colombian rivers and analyzed the possibility of using these relationships to forecast streamflows, showing through crosscorrelations (with several lags) that long-range streamflow forecasting for Colombia based on ENSO indicators is possible, and that the best ENSO indicators for predicting streamflows in Colombia are the Multivariate ENSO Index (MEI), the SOI, and the Niño 4 SST anomalies. On the other hand, Tootle et al. (2008) assessed the Pacific and Atlantic Ocean SST variability and Colombian streamflow variability, identifying a strong relationship between SST and streamflow of the country. Also, these authors concluded that the Singular Value Decomposition (SVD) temporal expansion series for Pacific Ocean SSTs associated with large oceanic regions may improve long lead-time forecasts of Colombian streamflow. Recently Poveda et al. (2011) have published a major review on the hydro-climatic variability of the Colombian Andes associated with ENSO, affirming that, in addition to ENSO, other macro-climatic phenomena affect the hydro-climatic variability of the tropical Andes. These include significant statistical correlations between the NAO and Colombia’s hydrology as well as with the PDO and SST over the tropical Atlantic (Poveda, 2004). This review also presents various physical hydrology-related mechanisms associated with El Niño in Colombia, showing significant seasonal lagged correlations between the MEI and river discharges throughout the country, indicating that ENSO indices constitute valuable tools to forecast many hydro-climatological variables in the region. In particular, in the relationship between ENSO and the hydrology of Colombia evidenced by the abovementioned authors, they show the important influence of the ENSO on the Magdalena 6

River streamflow, which presents strong decreases (or increases) with the occurrence of the El Niño (or La Niña) phenomenon (Poveda et al., 1997). Although these studies reveal significant correlations between ENSO and hydroclimatic variability of this country and confirm the notable predictive ability that this phenomenon has over the streamflow, they do not present a development of a forecasting model to predict the streamflow, nor has the stability of the relationships found been evaluated. Ionita et al. (2008) establish that one way to improve the seasonal forecast for streamflow is to use stable predictors. This paper describes a forecasting scheme for seasonal streamflow of Magdalena River (MR) based on stable lag-correlations with the SST, global precipitation (Pt) and mean temperature over land (Tm), exploring the forecast ability of these fields with several seasons in advance. In addition, the use of climate indices from stable regions that represent teleconnections configured as a whole is compared to the use of predefined teleconnection indices as predictors for the long-range forecasts over seasonal streamflow of MR. The MR is the most important fluvial artery in Colombia with the greatest socioeconomic importance on the country (Restrepo et al., 2012; Gutiérrez and Dracup, 2001). These aspects justifies the importance of the scheme prediction developed in this paper by himself. Also, it is noteworthy that the improvement in the streamflow prediction achieved by this scheme compared with the predictability of commonly used teleconnection indices, is capable of being applied to other basins.

7

The present study is structured as follows. In Section 2 datasets used are described. Section 3 describes the methodology. In Section 4 the main results are presented, and the main conclusions follow in Section 5. 2. Data The Magdalena River (MR) is considered the most important river of Colombia (Figure 1a), because its catchment area occupies 25% of Colombian territory, serving nearly 32 million inhabitants, and generates approximately 85% of gross national product (GNP). The MR crosses the country from south to north among the eastern and central branch of the Andes Mountains, with a total length of approximately 1600 km, from its source at 3685 m elevation in the south-western part of the country on the Páramo de las Papas (Colombian Massif), to its mouth on the Caribbean Sea (Velasco and Granados, 2006). The monthly streamflow time series used in this study were provided by Institute of Hydrology, Meteorology and Environmental Studies of Colombia (IDEAM). Initially three stations located on the main course of MR (Figure 1a) with continuous records of more than 35 years and without missing data in the series were selected. The stations 1 (74.7°W – 5.5°N) and 3 (73.97°W – 8.99°N) register data for the periods 19602010 and 19722010, respectively; while station 2 (74.4°W  6.5°N) covers the period 19362009. The homogeneity of the three streamflow series has been verified through the application of the non-parametric test of Pettitt (Pettitt, 1979), which has been widely used for detecting abrupt changes in hydrological series (Kundzewicz and Robson, 2000; Gao et al., 2010; Sahin and Cigizoglu, 2010; Hofstra et al., 2009; Toreti et al., 2011) and is considered a robust test in terms of changes in the form of the data 8

distribution (Kundzewicz and Robson, 2004). In addition, correlations between the monthly (/seasonal) streamflow series of station 2 and series of stations 1 and 3, during the common period (19722010), registered values greater than 0.8, indicating the strong relationship between the streamflows at these locations of the MR Basin. Considering this result and the longer streamflow time series, we selected station 2 as being a representative series of MR streamflow, and therefore this will be analyzed in detail in the remainder of the study. In addition, this station has been also used in the past by different authors to study the variability of the streamflow in the MR (Tootle et al. 2008; Poveda and Mesa, 1997; Poveda, 2004; Velasco and Granados, 2006; Gutiérrez and Dracup, 2001). Moreover, the correlations between station 2 and other 13 streamflow stations located on different basins in Colombia during the common period 1971- 2009 (Figure 1b), show significant values even for gauging stations located far away, and so, the analysis developed for this station could be useful for other ones in the country. The streamflow recorded at station 2 has a marked seasonal cycle, showing a bimodal behavior (Figure 1c). Maximum values appear for the months of April-May-June (AMJ) and October-November-December (OND), and minimum values in January-FebruaryMarch (JFM) and July-August-September (JAS), as result of double passage of the Intertropical Confluence Zone (ITCZ) on Colombia (Poveda, 2004). Taking into account that the average streamflow during these seasons reaches its highest value in OND (2890 m3/s) and its lowest value in JFM (1825 m3/s), we established the seasonal streamflow time series (Qs) for winter, spring, summer and autumn, by the average of the monthly series of JFM, AMJ, JAS, and OND, respectively.

9

The following monthly databases were used as predictor variables, using a seasonal scale analogous to the streamflow data, for the period 1936-2009: -

The sea surface temperature (SST), obtained from the Hadley Centre (HadISST, Rayner et al., 2003). This database has a resolution of 1° latitude x 1° longitude for the entire planet, covering the period 1870-2012. The domain used corresponds to 70°N  70°S and 179.5°E  179.5°W, thus eliminating the most extreme latitudes.

-

The global precipitation (Pt) from the Global Precipitation Climatology Center (GPCC) Version 6 - Total Full (Schneider et al., 2014.), with a resolution of 1° x 1° for the region corresponding to South America [100ºW-30ºW, 60ºS-18ºN], during the period 19012010.

-

The mean temperature over land (Tm), taken from the high resolution database of the Climatic Research Unit (CRU-TS.3.10, Harris et al., 2014), with a 0.5° x 0.5° spatial resolution during the period 1901-2009, for South America region [100ºW-30W, 60ºS-18ºN].

-

The teleconnection indices provided from various sources (Table 1), during the period 1950-2009.

For all databases, seasonal anomalies were calculated regarding the seasonal average during the period 19362009, standardized dividing by the respective seasonal standard deviation in the aforementioned period. Furthermore, prior to any further analysis, the linear trend of each series was subtracted to avoid spurious correlations. All levels of statistical significance were calculated using Student's two-tailed t-test. 3. Methodology 10

The methodology used is based on the development of a prediction scheme in which time lags between the predictor fields (SST, Pt and Tm) and the predictand field Qs are established. Because of the thermal inertia of SST, time lags of 1, 2, 3, and 4 seasons (Lag_1, Lag_2, Lag_3 and Lag_4, respectively) have been selected for this predictor variable, while for Pt and Tm only lags of 1 and 2 seasons are used. A lag of 1 season (Lag_1) indicates the prediction of Qs with a season in advance, and a lag of 4 seasons (Lag_4) refers to the prediction of Qs with a year in advance. Essentially, the prediction scheme uses the SST, Pt, and Tm anomalies, determined over regions, identified as significant and stable predictors from a correlation analysis (Lohmann et al., 2005). This methodology has been successfully applied to the prediction of the streamflow in different European rivers such as the Danube (Rimbu et al., 2005), Elbe (Ionita et al., 2008), Duero (Gámiz-Fortis et al., 2010), Ebro (Gámiz-Fortis et al., 2011) and Inland Catalan Basins (Hernández-Martínez, 2014). Following the method of Ionita et al. (2008) and Gámiz-Fortis et al. (2010, 2011), to determine the regions of the predictor variables that show stable teleconnections with the Qs, the correlations between streamflow seasonal anomalies and SST, Pt, and Tm global seasonal anomalies, for 44 moving windows of 30 years (starting in 1936) are calculated. The correlation is considered stable for those grid points where Qs anomalies and the predictor fields are significantly correlated at a level of 80% (r = 0.246), for more than 80% of all moving windows of 30-yr. In addition, only the regions that grouped a surface greater than or equal to 5° latitude x 5° longitude for the case of SST and Tm, and 2.5° latitude x 2.5° longitude for Pt, were selected, in order to remove very small regions that might include spurious relationships, considering the resolution of each database (Ionita et al., 2008; Hernández-Martínez et al., 2014). Additionally, 11

unlike of the works of Ionita et al. (2008) and Gámiz-Fortis et al. (2010, 2011), instead of defining a significant and stable predictor region as the average of a given number of grid cells within that region, this study uses regions with complete spatial structures. So, all the grid points of each region presenting significant and stable correlations are considered for the subsequent analysis. Finally, to extract the stable correlation maps from the previous analysis the correlation values from the 44 windows of 30-yr were averaged. The stability analysis allowed the selection of those regions of SST, Pt, and Tm with significant correlations throughout the study period, which would improve the predictions obtained for Qs (Ionita et al., 2008; Rimbu et al., 2005). After selecting the stable regions of the predictor fields, a Principal Component Analysis (PCA) is applied on each of them. A more detailed explanation of the PCA can be found in Preisendorfer (1988), Björnsson and Venegas (1997) and von Storch and Navarra (1995). PCA allows the grouping of the most important common variability of different regions of the predictor fields identified as significant and stable, and it is temporarily represented by a few Principal Components (PCs) series associated with each field. The PCs series are uncorrelated and, thus, the problem of multicollinearity of the predictors initially found is avoided. For each predictor field, the first PCs established are evaluated using the steps outlined above in order to check its significance and stability. Finally, the PCs that maintain a significant and stable correlation with Qs are considered as potential predictors, representative of the associated fields, while the significant and stable regions represented for each PC are shown by the corresponding Empirical Orthogonal Function (EOF). The predictor PCs

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are eventually used in a linear regression model for predicting the Qs anomalies of MR, through the process called leave-one-out cross-validation (LOOCV). In the LOOCV process, each model is run for a training base of N-1 years and is validated over the previously extracted year. Assuming that Qt is the streamflow series for a season of a given year, with t = 1, 2, 3, ..., N (years), a particular value Qi (validation) is extracted from the Qt series and the model is applied over the remaining dataset with N-1 years (calibration) to predict the Qi value. This process is repeated N times to establish the Q't series that contains the N predicted values. A potential source of dependence or artificial skill is eliminated by subtracting the mean and trend from the series (predictor/predictand) at each step of the cross validation (von Storch and Zwiers, 1999). The ability of the prediction process is evaluated through the expected error (S) (Wilks, 1995) between the seasonal series of predicted streamflow (Q') and the original data of streamflow (Qs), using the equation (1).

S  1

var(Q ' Qs) var(Qs)

(1)

where var is the variance. The S statistic was proposed by Lorenz (1956) and has been widely used in prediction processes (Wilks, 2005; von Storch and Zwiers, 1999; Jolliffe and Stephenson, 2003). This parameter can take values between  and +1; S > 0 indicates that the prediction has certain skill, while S = 1 means a perfect prediction (Fritts, 1976). This methodology has been applied to each of the lags set between the streamflow anomalies and the predictor fields of SST, Pt, and Tm anomalies. For better clarity, the 13

acronym of the year seasons corresponding to the predictor field is denoted in lowercase letters (jfm, amj, jas, and ond), while the acronym assigned to the seasonal streamflow is in capital letters (JFM, AMJ, JAS and OND). The term (+1) at the end of these acronyms (e.g. JFM+1) indicates that the seasonal streamflow corresponds to the season of the following year regarding the year of the predictor field. Additionally, in order to analyze the predictive ability of the main atmospheric-oceanic teleconnection indices (Table 1) over the Qs of MR, a similar methodology to the previously described has been used. To this end, we calculated running correlations between these indices (Itels) and the Qs anomalies, using 29 moving 30-yr windows, taking into account the common period 19502009 among all these Itels and the Qs data for the four lags considered. 4. Results 4.1. Identification of stable teleconnections The correlation analysis between the Qs and the predictor fields) SST, Pt and Tm, for each established lag, during the period 19362009 (figures not shown), revealed that there are many regions where these fields (SST, Pt or Tm) significantly correlate (positive > 0.2 \ negative < -0.2) with the Qs of MR, in different seasons and lags. Figures 2, 3 and 4 show the correlation maps (by averaging the correlations obtained from the 44 moving windows of 30 years), with significant and stable correlations between the Qs anomalies and the SST, Pt and Tm anomalies, respectively, for the period 1936-2009 and for all the established lags. Only regions with significant correlations above 80% significance level are shown.

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For the case of SST (Figure 2), the delays Lag_1 and Lag_2 present extensive regions with significant and stable correlations (positive and negative) over the Pacific Ocean, the relationship found between autumn SST and the following winter Qs (map ond_JFM+1, Lag_1) being more marked, and the correlations between winter SST and the following summer Qs (map jfm_JAS, Lag_2) less relevant. The map of stable correlations between autumn SST and winter Qs (map ond_JFM+1, Lag_1) shows a nucleus of strong negative correlations extending from the coast of America to cover much of the eastern-central tropical Pacific, bordered by positive correlations on the north and south in the western Pacific, thus setting a boomerang-shaped pattern over the Pacific Ocean. This pattern appears less defined for the correlations during the seasons of AMJ, JAS, and OND at Lag_1, weakens at Lag_2, and finally disappears at Lag_3 and Lag_4. This configuration involves the SST regions of the tropical Pacific, where El Niño phenomenon occurs (Rasmusson and Carpenter, 1982; Ropelewski and Halpert, 1987; Trenberth, 1997; 2002) and highlights the important relationship between SST anomalies over the tropical Pacific and Qs of MR. Particularly, the significant negative correlations between the Qs of MR and tropical Pacific SST on the El Niño region, have been described in the past by several authors (Gutiérrez and Dracup, 2001; Poveda and Mesa, 1997; Poveda, 2004; Velasco and Granados, 2006; Tootle et al, 2008). The seasonal SST from various regions on the Atlantic and Indian Ocean, to lesser extent, exhibits significant and stable correlations with the Qs of MR, standing out the positive (negative) correlations registered for the Indian Ocean, shown on the map jfm_JFM+1 at Lag_4 (ond_JFM+1 at Lag_1). For the case of the significant and stable correlations between the Qs and South America Pt (Figure 3), important areas are identified, highlighting cores with positive 15

correlations (> 0.4) over the north (maps ond_JFM+1, jfm_AMJ, and jas_OND, at Lag_1, and maps jas_JFM+1 and ond_AMJ+1, at Lag_2). . The most notable regions (in extent and magnitude) for Pt, with stable negative correlations (< -0.4) at Lag_1 (Lag_2) are registered for the map ond_JFM+1 (jas_JFM+1; ond_AMJ+1) over the south (center and south) of South America. The stable positive significant correlations identified over northern South America, show the strong relationship between the Qs and the Pt of the immediately previous season, indicating that positive anomalies (negative) of Pt, are associated with positive (negative) Qs anomalies of the MR in the following season. Maps of significant and stable correlations between the Qs and Tm (Figure 4) shows large areas with negative correlations on South America, for all the seasons of the year at Lag_1. At Lag_2, the regions with stable correlations are more reduced and they are fundamentally placed along the western border. Also, at this lag positive stable and significant correlations are found between the autumn Tm in the southern of South America and the following spring Qs (ond_AMF+1 map), while there are no stable significant correlations between winter Tm and the summer Qs. Overall, in most maps the average correlations found with the 44 moving 30-yr windows, for all the predictor fields, recorded stable positive (negative) correlation values higher (lower) than 0.4 (-0.4), significant at 90% level. The results reveal that SST is the predictor field that has wider stable regions significantly correlated with the Qs of MR, located mainly over the Pacific Ocean. Furthermore, it is known that the SST of the Pacific Ocean is related to the Pt and Tm in many regions of the world (Weng et al., 2009; Trenberth and Shea, 2005; Córdoba-Machado et al., 2015a, 2015b; Ropelewski and Halpert, 1987; Barnett and Preisendorfer, 1987; Barnston and Smith, 16

1996; Barros and Silvestri, 2002). So, it is conceivable that largely the teleconnections found between the Qs and Pt and Tm fields, could be driven by the SST, being these teleconnections of Qs with the continental variables a reflection of the SST variability. Such stable relationships found from the seasonal lags established between the predictor fields and the Qs of MR are the basis for the development of forecasting models for the seasonal streamflow of MR. 4.2. Establishing stable predictors The predictor variables of Qs are identified through a PCA applied to the standardized anomalies of the regions that showed significant and stable correlations previously identified between each predictor field and the Qs of MR. The PCA is conducted on each predictor field individually. The regions configured by the first variability mode (EOF1) of each predictor field for all seasons and lags are shown in Figures 2, 3 and 4, by means of contours. Table 2 presents the percentage of explained variance by each EOF1. These modes (EOFs1), for all seasons and lags considered, consistently explain more than 30%, 32% and 40% of the total variance of the stable predictor field for Pt, SST and Tm, respectively, Figure 5 shows the running correlations found with the 30-yr moving windows between the Qs and the first stable PCs (PCs1), found through the PCA of the predictor fields, for all the seasons and lags considered. In all cases, the PC1 is stable, showing that more than 80% of the correlation values exceed a significance level of 90%.

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On the other hand, PCs2 (PCs3) obtained from the PCA for each predictor field do not present stable correlations with the Qs. For this reason, only the PCs1 of the SST, Pt and Tm fields were considered as predictor variables. PC1 resulting from Pt field records the highest values of correlation with the Qs during the entire period, 19362009, at Lag_1 and Lag_2 (green boxes in Figure 5). Exceptions occur for the correlations between the PC1 of spring SST and the Qs of summer (0.65) and autumn (0.60), (maps amj_JAS at Lag_1 and amj_OND at Lag_2, respectively). At Lag_3 and Lag_4, the PC1 of the SST obtains, in all cases, an average correlation value above 0.4 (in absolute value), showing that in most cases the correlations easily exceed the thresholds for significance and stability tests. The correlation between Qs and PC1_Pt series, for the cases that this predictor variable presents the highest values, ranges between 0.55 and 0.78 in absolute value, and in all cases, proved to be significant and stable at the 95% level. The contemporaneous correlations between the PC1 of SST and the PC1 of Pt and Tm fields are presented in Table 3. These values range from 0.35 (0.69) to 0.81 (0.85), in absolute value, when the correlation is between the PC1_SST and the contemporaneous PC1_Pt (PC1_Tm) at Lag_1 and Lag_2 with respect to Qs. These results indicate that, as was mentioned in Section 4.1, in large measure, the relationships found between the Qs of MR and the Pt and Tm fields could be dominated by the SST. 4.3 Potential predictability of Qs from teleconnection indices There are several teleconnection patterns such as the NAO, PDO, and ENSO, for which significant relationships with precipitation and discharge in Colombia have already been documented (Poveda et al., 2002; Poveda, 2004; Velasco and Granados, 2006; Tootle et 18

al., 2008). Taking this into consideration, we analyzed the predictive ability of the main atmospheric-oceanic teleconnection indices (Table 1) over the Qs of MR. Figure 6 shows the running correlations found only for those Itels that fulfill the stability criterion. As shown, the correlations found are weaker compared to correlations between Qs and the PC1 of the predictor fields of Pt and SST, principally. Furthermore, we found that for some seasons, depending on the lag considered (e.g. for the JAS Qs at Lag_2 and Lag_3), there were no significant stable correlations with either Itels. The Itels showing the best results were those associated with the ENSO phenomenon, mainly at Lag_1. In particular, just for the JFM streamflow, El Niño4 and El Niño3.4 Itels at Lag_1 and Lag_2, respectively, show correlation values that can equate to those obtained for these delays with PC1 series. Additionally, at Lag_1 and Lag_2, mainly, significant stable correlations are obtained between the Qs of MR and some Itels such as EA, EP-NP, EA-WR, NPGO, EMI, WP, and PNA. Also, it is remarkable the significant and stable correlations found at Lag_4 for the Indian Ocean indices (DMI and II) for JFM+1 and JAS+1 Qs. 4.4 Streamflow prediction The stable PCs1 previously selected for the predictor fields (SST, Pt and Tm) from regions with significant and stable correlations with the Qs, were used individually in a regression model to predict the Qs of MR. The prediction model was evaluated by the LOOCV process, for the period 19362009, for each of the lags established. Figure 7 shows the original series of Qs (black line) and the predicted series by the PC1 of each predictor field. The expected error values (S) and the correlation (r) between these series are presented in Table 4. 19

For all the lags established, a portion of the original Qs variability can be predicted, resulting a better prediction when the PC1 of Pt is used as predictor variable at Lag _1 and Lag_2, in relation with those found with any of the other predictors (Table 4). Exceptions occur for the cases amj_JAS at Lag_1 and amj_OND at Lag_2, for which the best predictor is the PC1 of the SST field. . Moreover, the value of S for the best predictor of the original Qs is greater than 0.1 in all cases, recording the highest values (> 0.2) primarily at Lag_1 and Lag_2 (Table 4, values in bold). Likewise, the values of r among the best predictor and the original Qs range from 0.3 (ond_JAS+1, Lag_3) and 0.74 (ond_JFM+1, Lag_1). The best prediction of Qs was found for winter when the PC1 of Pt of the previous autumn was used as a predictor (Table 4, ond_JFM+1 at Lag_1). This prediction records an S value of 0.33 and a correlation of 0.74 between the original and predicted series. The results reveal that the Qs of MR can be forecasted with acceptable capacity using the Pt from the previous seasons. This predictive ability decreases as the lag increases. Additionally, the SST has proved to have an acceptable skill for prediction of the RM Qs, even for longer delays (Lag_3 and Lag_4). Finally, we can say that although most of the highest values of S and r (Table 4) are recorded from the Qs series predicted by the PCs1 of Pt and SST fields, the values of S and r resulting from Qs series predicted by the Tm field also recorded considerable values, exhibiting an acceptable prediction capability of this field on the Qs of MR, mainly at Lag_1. Furthermore, from Table 4, it can be concluded that, although the forecasting model is not perfect (S = 1), it consistently shows some prediction ability (S > 0.1). 20

5. Discussion and concluding remarks This study examines the seasonal predictability (JFM, AMJ, JAS and OND) of the Magdalena River (MR) streamflow anomalies (Qs), using the global SST and the South America Pt and Tm anomalies from previous seasons as potential predictors, during the period 19362009. For the SST predictor field a delay set of one to four seasons (Lag_1, Lag_2, Lag_3 and Lag_4) was considered, while only two seasons in advance (Lag_1 and Lag_2) were considered for Pt and Tm predictor fields. The stability of the significant correlations between the predictor fields and the Qs has been analyzed, and a prediction scheme, based on linear regression models, has been developed. For all the lags established, we found regions of SST, Pt and Tm that show significant and stable correlations with the Qs anomalies of MR. Regarding the SST field, wide stable regions with significant correlations on the tropical Pacific Ocean, mainly at Lag_1 and Lag_2 are highlighted. These regions include areas where the ENSO phenomenon unfolds, evidencing the strong relationship that this phenomenon has over the hydrology of the country (Poveda et al., 2001). Consistent with these results, Poveda and Mesa (1997) showed through a Principal Component Analysis that a pattern associated with El Niño phenomenon is strongly linked to the hydro-climatology of Colombia. Similarly, Tootle et al. (2008), applying a SVD analysis between the streamflow series of several main rivers in the country (including the MR) and the SST of the Pacific, Atlantic and Pacific/Atlantic (together), concluded that both the first mode of variability of the Pacific and the Pacific/Atlantic SST reflect ENSO variability and are significantly related to the streamflow of Colombia. It should be noted that the predictive capacity of the Pacific SST on the hydro-climatology of Colombia is not evaluated in those works, as has been analyzed in the present study. 21

The Pt and Tm anomaly fields over South America show multiple regions with stable correlations with the Qs of MR for the two lags established (Lag_1 and Lag_2). Seasonal Magdalena River streamflow anomalies are related not only to climatic anomalies in nearby regions but also with climatic anomalies from several regions located far from Magdalena catchment region in the southern of South America. The negative correlations between T and Qs found (Figure 4) could be explained by the strong increase in net radiation and a lack of rainfall that generally coincides with decreased cloudiness associated with atmospheric stability conditions, as suggested by Teuling et al. (2013). Further and deeper analysis are required to clearly establish the physical processes evolved in these relationships that could explain the results found here. To a large extent, many of the stable relationships found between the Qs and Pt and Tm fields could be controlled by the SST, showing the strong influence of the SST on the Pt and Tm in different regions of the planet (Ropelewski and Halpert, 1987; Pabón and Montealegre, 1992; Li and Chen, 2013; Weng et al., 2009; Trenberth and Shea, 2005; Córdoba-Machado et al., 2015a, 2015b). However, we have shown that the long-term prediction skill improves when these remote and nearby predictors are considered as a whole in the forecast scheme. The study shows that SST, Pt, and Tm, anomalies from several regions provide a significant source of predictability for MR seasonal streamflow. The corresponding time series (PCs1 of each field), which show stable correlations, are used as predictors for the streamflow anomalies. Results show that Qs anomalies of MR are predicted with an acceptable ability using the PC1 of the SST and Pt predictor fields, mainly, providing better results at lags of one and two seasons (Lag_1 and Lag_2). For winter, the best Qs forecast is achieved using the PC1 of Pt during previous autumn as predictor, 22

registering an error between the original and predicted streamflow series S of 0.33 and a correlation of 0.74. However, this PC1_Pt presents a high correlation (0.81) with the PC1 of SST of the same season, whereby it is possible that this best prediction made from the Pt, is really driven by the SST. Also for winter the highest values of stable correlations between the Qs and SST are presented, and are associated with the ENSO pattern. In agreement with these results, Poveda et al. (2001) identified a strong seasonality in the influence of ENSO on the hydro-climatology of Colombia and affirmed that, particularly, river discharges respond most during winter (DJF of the following year) and summer (JJA) as a result of the combined anomalies in precipitation, soil moisture, and evapotranspiration (using NDVI as a surrogate). Different authors have found non-negligible relationships between several of the climate patterns (PDO, NAO, ENSO) and the hydro-climatology of Colombia (Poveda et al., 2002; Velasco and Granados, 2006; Gutiérrez and Dracup, 2001). However, many of the teleconnection indices that represent these patterns, although having significant correlations with the Qs of MR, lack stability depending on the selected lag, therefore showing a limited predictive capacity for the Qs of MR, at least when a linear methodology is used. So, some authors suggest that the study of non-linear relationships and interactions between Itels (Kiem and Frank, 2004; Kiem et al., 2003) could contribute to the acknowledgement of the hydro-climatic variability of a region, and therefore, to a improved predictability. The largest number of teleconnection indices presenting significant and stable correlations with the Qs is found at Lag_1, the indices associated with the ENSO phenomenon being those showing the highest correlation values. It is important to note that at Lag_1 and Lag_2, mainly, several indices that have received less attention in the 23

study of their influence on the country's hydro-climatology show significant and stable correlations with the Qs of MR, depending on the season of the year. This is the case of the EA, EP-NP, EA-WR, and EMI indices with the winter streamflow; WP, EA, PNA, and EMI indices with the spring streamflow; WP, EP-NP and NPGO with the summer streamflow; and EP-NP and NPGO for the autumn streamflow. At Lag_4, the Indian Ocean indices present also a potential predictability ability for the winter (II index) and summer (DMI index) streamflow. The fact that the SST, Pt, and Tm fields, through their respective PC1, present stronger linear correlations with Qs (compared with Itels) reveals the higher predictive skill of these fields compared with that from the Itels. The reason is that the PCs1 of the SST, Pt, and Tm represent many stable regions which have a considerable influence on the Qs of MR, not included in the Itels. In agreement with these results, Tootle et al. (2008) showed that the indices resulting from the expansion coefficients that represent entire regions of the SST of Pacific and Atlantic, constructed through an analysis of Singular Value Decomposition (SVD) between SST and the streamflow of several rivers of Colombia (including the MR), have greater predictive power than do the indices that represent particular regions of ENSO (El Niño3.4), the PDO, or AMO. In addition, these authors conclude that the use of the ocean basins, as a whole, could result in improved streamflow predictability. There are many studies about the ENSO–PDO relationship and its associated climate variability in different regions. For example, the PDO is correlated with SST and precipitation anomalies of North Pacific regions as well as a modulation of ENSO teleconnection (Gershunov and Barnett, 1998). Regards ENSO-AMO coupling, Kayano and Capistrano (2014) have analyzed its influence on the South American rainfall, 24

showing that negative (positive) tropical Atlantic SST anomalies reinforce the El Niño (La Niña) through an anomalous Atlantic Walker circulation, intensifying the ENSOrelated precipitation anomalies over South America. So, the ENSO influence on different regions can be modulated by the PDO or AMO (López-Parages and Rodríguez-Fonseca, 2012; Gallant et al., 2012). These potential coupling between teleconnections could augment or diminish ENSO impacts in the MR region and contribute to an improved forecasting. Finally, we establish that the predictability of seasonal streamflow reached in this study, is higher than the seasonal precipitation predictability over Colombia, found through the first two EOFs of Pacific tropical SST (El Niño and El Niño Modoki, respectively), shown in Córdoba-Machado et al. (2015a, 2015b). This study, in addition to quantify the skill of the MR Qs prediction from three different fields, and to contribute to the development of predictive linear models for streamflow, could be considered by the institutions involved in the planning and management of natural resources of the country, in order to make seasonal forecasts of the streamflow of MR and other basins in Colombia. Future research focusing on the prediction of the streamflow in Colombia could propose the additional incorporation of new predictor variables such as soil moisture or some of the teleconnection indices such as the EA. Moreover, taking into account that the results and conclusions of this work are based on linear correlations and do not consider nonlinear relationships neither interactions between teleconnections, the inclusion of these aspects could improve the forecasting skill over the hydrology of the country.

25

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Figure captions Figure 1. (a) Mainstream of Magdalena River (Colombia) and location of the streamflow-gauging stations used. (b) Correlations between station 2 and other 13 streamflow stations located on different basins in Colombia during the common period 1971-2009. (c) Annual cycle and seasonal mean discharge (upper) for the period 19362009. Figure 2. Stability maps of the significant correlations (mean correlation from 44 moving windows of 30 yr) between the seasonal streamflow and the SST predictor field, for all lags established, during 1936-2009 period. Only significant correlations at the 80% confidence level, for more than 80% of the moving windows, are shown. Contours show the regions configured by the EOF1 associated to the first PC of the stable regions of SST. Columns 1 to 4 correspond to Lag_1 to Lag_4, respectively. Figure 3. As Figure 2, but for Pt. Columns 1 and 2 correspond to Lag_1 and Lag_2, respectively. Figure 4. As Figure 3, but for Tm. Figure 5. Running correlations (30-yr windows) between seasonal streamflow and the stable PCs series of the predictor fields: (a) SST, (b) Pt, and (c) Tm, for all the lags defined. The green box shows the PC that presents the highest correlation with the streamflow and its value during the entire period 19362009. Figure 6. Running correlations (30-yr windows) between seasonal streamflow and teleconnection indices for all the lags defined. The green box shows the index that

39

presents the highest correlation with the streamflow and its value during the entire period 1951-2009. Figure 7. Standardized time series of observed (black line) and predicted by the PC1 of each predictor field, for each season and lag considered. Time series in dashed line corresponds with the Qs prediction obtained from the best predictor selected from the highest values of S and r.

40

List of Tables Table 1. Teleconnection indices used in this study, for the common time period 19502009. In columns, the name, and the data source. Table 2. Explained variance by the EOF1 for each potential predictor field, at all lags established. Table 3. Correlation coefficients between the PC1 time series of SST and the contemporaneous PC1 of the Pt and Tm fields, for the lags defined with respect to Qs. Table 4. Seasonal forecast skill scores (r and S) between the observed and predicted seasonal streamflow for the period 19362009, based on the stable PCs1 of each predictor field. The best predictors are in bold.

41

1 2

Table 1. Teleconnection indices used in this study, for the common time period 19502009. In columns, the name, and the data source. Index Niño 1+2 Niño 3 Niño 4 Niño 3,4 SOI EMI PDO NPGO DMI

Name El Niño region 1+2 El Niño region 3 El Niño region 3,4

3

http://ftp.cpc.ncep.noaa.gov

El Niño region 4 Southern Oscillation Index El Niño Modoki Pacific Decadal Oscillation North Pacific Gyre Oscillation Dipole Mode Index

Indonesian Index Western WeMO Mediterranean Oscillation Artic Oscillation AO North Atlantic NAO Oscillation East Atlantic EA East Atlantic EA/WR Western Russian SCAND Scandinavian Atlantic Multidecadal AMO Oscillation Western Pacific WP East Pacific North EP/NP Pacific Pacific North PNA American II

Source

http://www.esrl.noaa.gov http://www.jamstec.gov.jp http://www.esrl.noaa.gov http://www.o3d.org./ http://www.jamstec.go.jp/frsgc/research/d1/iod/e/index. html Verdon and Franks (2005) http://www.ub.edu/gc/ http://www.esrl.noaa.gov

http://ftp.cpc.ncep.noaa.gov

1 2

Table 2. Explained variance by the EOF1 for each potential predictor field, at all lags established. Var. Expl. EOF1s (%)

JFM

AMJ

JAS

OND

3

Lag_1

Lag_2

Lag_3

Lag_4

Pt

30

31

--

--

Tm

45

53

--

--

SST

44

44

38

36

Pt

42

35

--

--

Tm

56

40

--

--

SST

56

64

68

70

Pt

36

45

--

--

Tm

42

--

--

--

SST

45

52

32

40

Pt

36

57

--

--

Tm

52

56

--

--

SST

46

40

40

38

1 2

Table 3. Correlation coefficients between the PC1 time series of SST and the contemporaneous PC1 of the Pt and Tm fields, for the lags defined with respect to Qs.

3 PC1 (SST vs Pt)

Lag_1

Lag_2

jfm

0,81

0,68

amj

0,64

0,73

jas

0,58

-0,35

ond

0,73

0,51

Lag_1

Lag_2

jfm

0,83

0,83

amj

0,82

0,69

jas

0,76

--

ond

0,85

0,82

PC1 (SST vs Tm)

4

1 2 3

Table 4. Seasonal forecast skill scores (r and S) between the observed and predicted seasonal streamflow for the period 19362009, based on the stable PC1s of each predictor field. The best predictors for each seasonal Qs at each lag are in bold.

4

SKILL SCORE Qs (PC1s) SEASON

JFM

AMJ

JAS

OND

Lag_1

Lag_2

Lag_3

Lag_4

r

S

r

S

r

S

r

S

Pt

0,74

0,33

0,70

0,30

--

--

--

--

Tm

0,54

0,16

0,45

0,10

--

--

--

--

SST

0,69

0,28

0,62

0,20

0,50

0,12

0,52

0,15

Pt

0,60

0,20

0,60

0,20

--

--

--

--

Tm

0,39

0,10

0,50

0,14

--

--

--

--

SST

0,50

0,13

0,42

0,10

0,40

0,10

0,33

0,10

Pt

0,50

0,13

0,41

0,10

--

--

--

--

Tm

0,55

0,17

--

--

--

--

--

--

SST

0,60

0,20

0,39

0,10

0,30

0,10

0,40

0,10

Pt

0,70

0,30

0,45

0,11

--

--

--

--

Tm

0,57

0,18

0,52

0,15

--

--

--

--

SST

0,61

0,21

0,60

0,20

0,43

0,10

0,40

0,10

5

1

Highlights Development of a forecasting scheme for seasonal streamflow in Colombia Better streamflow prediction than using teleconnection indices Usefulness for the planning and management of natural resources in Colombia

42