Sub seasonal streamflow forecast assessment at large-scale basins

Journal Pre-proofs Research papers Sub Seasonal Streamflow Forecast Assessment at Large-Scale Basins Erik Schmitt Quedi, Fernando Mainardi Fan PII: DOI: Reference:

S0022-1694(20)30095-0 https://doi.org/10.1016/j.jhydrol.2020.124635 HYDROL 124635

To appear in:

Journal of Hydrology

Received Date: Revised Date: Accepted Date:

11 July 2019 15 December 2019 26 January 2020

Please cite this article as: Schmitt Quedi, E., Mainardi Fan, F., Sub Seasonal Streamflow Forecast Assessment at Large-Scale Basins, Journal of Hydrology (2020), doi: https://doi.org/10.1016/j.jhydrol.2020.124635

This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

© 2020 Published by Elsevier B.V.

SUB SEASONAL STREAMFLOW FORECAST ASSESSMENT AT LARGESCALE BASINS ERIK SCHMITT QUEDI*1, FERNANDO MAINARDI FAN1 *Corresponding author at Instituto de Pesquisas Hidráulicas – IPH, Universidade Federal do Rio Grande do Sul – UFRGS, Av. Bento Gonçalves, 9500, Porto Alegre 90050-260, RS, Brazil. E-mail address: [email protected] 1Instituto

de Pesquisas Hidráulicas, Universidade Federal do Rio Grande do Sul (IPH-UFRGS), Porto Alegre, RS, Brazil.

1. Introduction The Quantitative Precipitation Forecast (QPF) originated from numerical weather prediction models is frequently being adopted as input information for hydrological models, aiming better streamflow prediction, as shown by recent operational and scientific literature (Anghileri et al., 2016; Baker et al., 2019; Cuo et al., 2011; Fan et al., 2016, 2015a, 2014a; Golding, 2009; Schwanenberg et al., 2015; White et al., 2017). Despite the widespread usage of QPF and its improvements over the last few decades (Pappenberger, 2019), it is recognized that this data’s low skill, or high uncertainty, is an obstacle in further applying it for hydrometeorological modeling. While the QPF skill usually tends to decrease as the forecast lead time increases, benefits such as better inflow to reservoir volume estimations can be obtained through this increase in the predicted horizon (Lettenmaier and Wood, 1993; Bartholmes and Todini, 2005; Cuo et al., 2011). In the last decades, the numerical weather prediction scientific community has developed methods, such as the ensemble approach, that allow the extension of the horizon beyond the short-range lead times while also delineating the uncertainty of the predictions. Such an approach lends it a probabilistic sense, expressing the uncertainties through the assessment of the ensemble members outcomes’ probabilistic distribution, additionally providing valuable information to hydrometeorological prediction systems (Bauer et al., 2015; Demargne et al., 2014; Jaun and Ahrens, 2009; Krzysztofowicz, 2001; Schaake et al., 2006; Verbunt et al., 2007). More recent efforts in ensemble forecasting 1

have been focusing toward better comprehending the forecasts within the sub seasonal timescale (i.e. forecast lead time up to 3 to 7 weeks), which is often considered unfeasible due to the high level of uncertainties and low predictability – as it is placed between the short-range (or weather) and long-range (or seasonal) forecasts (Brunet et al., 2010; Robertson et al., 2018, 2017; Robertson and Vitart, 2018; Shapiro et al., 2010; Vitart, F., 2015; Vitart et al., 2016; Vitart and Robertson, 2018, 2016; White et al., 2017). The sub seasonal hydrometeorological predictions present potential information to meet the needs of users in many socio-economic activities, for both the public and the private sectors. Examples are: supporting decision making in water supply management and the development of early warning systems for droughts and flood control (Bazile et al., 2017; Hao et al., 2018; Hartmann, 2006; Lemos, 2008; O’Donnell and Colby, 2009; Pagano et al., 2002; Sene et al., 2018; Shah et al., 2017); the optimization of hydropower generation by anticipating demands, scheduling reservoir maintenance, water trading and hedging (Fan et al., 2015; Foster et al., 2018; Robertson et al., 2014; Turner et al., 2017); and in shipping and navigation planning, ensuring inland waterway transportation (Meißner et al., 2017). Although it still face many inherent issues which are discussed by White et al., (2017), the sub seasonal predictions are now being endorsed by research initiatives that set their focus on assessing the predictability and usefulness of forecasts within this timescale (Robertson et al., 2018, 2017; Vitart and Robertson, 2018). Regarding streamflow forecasting, the QPF ensemble-based modeling may lead to the development of hydrologic ensemble prediction systems (or H-EPS), which are expected to have greater skill and less inconsistency than deterministic forecasts, also allowing for an evaluation of uncertainties provided by the spread of ensemble members (Bartholmes et al., 2009; Boucher et al., 2011; Buizza, 2008; Cloke et al., 2013; Cloke and Pappenberger, 2009; Cuo et al., 2011; Golding, 2009; Pappenberger et al., 2011;

2

Roulin, 2007; Scherrer et al., 2004; Verkade and Werner, 2011). The H-EPS have been extensively used for short-range forecasting in flood warning systems and natural disaster prediction and, more recently, the development of technologies has led to wider, largescale global flood forecasting (Pappenberger, et al., 2013). In this context, a sub seasonal H-EPS may constitute a powerful tool for decision making in water resource management, providing useful information in regards to drawing adjustments between long-term and short-term planning (Cloke and Pappenberger, 2009; Emerton et al., 2016). As an alternative for medium to long term streamflow forecasts, there is the extended streamflow prediction (ESP) technique, which is nowadays referred to as ensemble streamflow prediction (Day, 1985). It considers historical meteorological data as a possible representation of the future, generating one streamflow scenario (i.e. ensemble member) for each historical year, using the current watershed status as initial conditions for each simulation. The quality of ESP forecasts is strongly tied to the main drivers of predictability within the basin, where it produces high skill in basins where the initial hydrological conditions predominate over other sources. While in basins where the meteorological forcing drives the predictability, it may result in lower ESP forecast skill. Also, the main errors in using the ESP technique arise from the variability of climate, data errors and model calibration. Regardless of the method used to generate the streamflow ensembles, the forecast quality depends on the catchments’ climatic and hydrological conditions, exposing the necessity of correctly assessing the potentials of H-EPS across many regions of the world. Especially in places where this approach it still incipient for scientific and operational applications, such as in most southern hemisphere countries (Pappenberger et. al., 2013). The scarcity of studies concerned with the application of sub seasonal H-EPS is

3

noteworthy. White et al., (2017) reviews potential benefits in applications of sub seasonal-to-seasonal (S2S) predictions and draws attention to the challenges of integrating these forecasts with decision making in socio-economic sectors, as in water resources management, power generation, agriculture, and others. The authors point out key points in improving sub seasonal forecasting such as investigating where and when prediction skill is obtained; quantification of systematic errors and uncertainties; and better communication between forecast producers and users. The study of Shah et al., (2017) is an application of sub seasonal (lead time up to 45 days) precipitation forecasts, tailored to benefit the agricultural sector in India. In this study, total runoff and soil moisture was simulated using daily precipitation forecast, with considered satisfying performance by the authors in terms of performance statistics, in a timescale useful to water resource and agriculture managers. The authors Monhart et al., (2019) compared the traditional ESP approach to a sub seasonal (with a lead time up to 32 days) hydrometeorological ensemble prediction system within three alpine catchments in Switzerland, with distinct hydroclimatic conditions. The study demonstrated the potential of ensemble reforecasts in small to medium mountainous catchments (drainage areas ranging from 185 km² to 1696 km²), where the account of snow-related processes is necessary for proper modeling. The study of Anderson et al (2019), although not focusing on the sub seasonal time scale, points out some aspects regarding ensemble forecast verification across spatial scales. The authors highlight that the catchment area and proprieties must be considered in forecast verification. In addition, for flow forecasts, greater regional variation in forecast reliability must be expected, as it accounts for hydrological variables uncertainties particularly to the basins.

4

As preliminary knowledge of hydrometeorological conditions being of great value for water management operations, it could also be obtained from sub seasonal ensemble forecasting. In this sense, this work seeks to explore the development of a sub seasonal hydrological prediction system and its benefits for tropical climates and large watersheds, expanding the knowledge regarding this forecasting methodology. We believe that such forecasting systems are auspicious in regions of the world where the generation of electricity relies heavily on hydroelectric power dams, as the hydrological variability of the streamflow and uncertainties on estimates directly influences the system’s operation and planning, such as in the areas presented following. 2. Case Study The studied site is the Paraná River Basin (PRB), Brazil, located within the central South America territory, covering regions from South-Central Brazil to the Itaipu hydropower dam, having a drainage area of approximately 900,000 km². The PRB is responsible for more than 50% of the hydroelectric production in the entire country (Adam et al., 2015). Within the basin, there are around 150 large reservoirs along its main river and tributaries – Paraná River, Grande, Tiête, Paranapanema and Iguaçu; ANEEL, 2008). Some of these rivers are also used as inland waterways for navigation, such as the Tietê-Paraná. In Brazil, the oversight of hydroelectric generation and transmission is under the responsibility of the National Electric System Operator (ONS – Operador Nacional do Sistema), and usually uses medium-term average daily flow forecasts to perform the management of power generation (ONS, 2011, 2012a, 2012b, 2014). In this management, various methodologies are used: mostly stochastic methods such as the PREVIVAZ model (Silveira et al., 2017), including, in some cases, conceptual hydrologic modelling.

5

The studied basin presents different hydrological regimes across its large territory, exhibiting a seasonality caused primarily by the activity of air masses in Brazil. The region at the north end of the basin features a tropical climate with dry winters and more rain in the summer; the rainfall is tropical and convective. While the southern region presents steadier rainfall, evenly distributed throughout the seasons (B. Siqueira et al., 2018). In this case study we selected 6 reservoir dams’ locations to proceed with the streamflow forecasts, as shown in Figure 1. We selected locations with distinct hydroclimatic characteristics and large-scale cascading dams with drainage areas ranging from approximately 33.000 km² to 827.000 km². It is expected that the assessment may provide information regarding sub seasonal streamflow forecasting in these different conditions. (Figure 1 here) Figure 1. Location of the Paraná River Basin (until the point of interest), major rivers of the region.

3. Methodology 3.1. MGB-IPH Hydrological Model The MGB-IPH (described by Collischonn et al., 2007; Pontes et al., 2017) is a large-scale distributed model, used in several studies for hydrological simulations in South America (Collischonn et al., 2007b, 2005; Collischonn and Tucci, 2005; Paz et al., 2007; Fan et al., 2014; Meller et al., 2016; Paiva et al., 2013; Siqueira et al., 2018; Tucci et al., 2003). The applied version of this model discretizes the basin into unit catchments whenever there are confluences of streams or at specific points, these units are denominated unit-catchments (Paiva et al., 2013). The soil and vegetation variability are

6

classified by Hydrologic Response Units (HRU), whose parameters are associated with each HRU type (Kouwen et al., 2006); for the evapotranspiration calculation, the model is based on Penman-Monteith (Shuttleworth, 1993); the surface runoff and soil water balance follow the Arno model approach (Todini, 1996); also, the streamflow routing is computed using the Muskingum-Cunge method (in the case of this study) or the full SaintVenant when necessary (Paiva et al., 2013). The basin was discretized into 1424 unit-catchments in this study, while the rainfallrunoff process was simulated using a daily time step. Model calibration was carried out using data from the National Electric System Operator (ONS), spanning the years between 1975 to 1995 for the calibration period and 1995 to 2010 for validation due to data availability and occurrences of extreme events (Collischonn et. al., 2014). Table 1 presents resulting values of the Nash–Sutcliffe efficiency coefficient for streamflow (NS), Nash–Sutcliffe efficiency coefficient for logarithms streamflow (log-NS), and relative volume errors (dV), at each gauging station used in the calibration and verification period. (Table 1 here) Table 1. Performance of MGB model on the study case dams in the calibration and validation periods.

Based on Table 1, we believe that the hydrologic model calibration and verification was satisfactory for further hydrological applications since the NS and log-NS were above 0.75 and the volume error (dV) between ± 10%. 3.2. Meteorological Data The meteorological ensemble used as input for the hydrological model was generated by the Integrated Forecast System (IFS) model, version CY43R3, from the European Centre for Medium-range Weather Forecast (ECMWF) sub seasonal-toseasonal (S2S) dataset (Vitart and Robertson, 2018). This model integrates 51 ensemble

7

members, including one unperturbed initial condition (control member), running twice a week on Monday and Thursday (UTC 00) and forecasts up to lead-day 46. We used the data with a 0.125° grid resolution for daily accumulated time-steps (ECWMF, 2017). The data is available at https://apps.ecmwf.int/datasets/, with a delay of 3 weeks of present time, therefore it may not yet be suited for real-time operations. The study of Fan et al., (2015) in the South American context analyzed medium-range forecasts originated from this research center for inflow verification, demonstrating the best performance of this ensemble among the tested ones. The observed precipitation dataset used to run the hydrological simulations was the Multi Source Weighted Ensemble Precipitation (MSWEP), version 2.1. This is a global dataset, covering the years from 1979 to 2016, with grid resolution of 0.1° and provided as 3-hourly accumulated value, which had to be accumulated from daily values (Beck et al., 2017b, 2017a). Employing a gridded dataset was the selected method in the current study due to its advantages over local in-situ gauges, as it uses complementary information from diverse sources such as satellite, reanalysis and data gauges; also providing information for long temporal availability. The figure 2 shows the evolution of the mean absolute error (MAE) of the S2S data, throughout the forecast horizon, averaged over all forecast issued in this study. Before the MAE computation, a representative data series was calculated using the area-weighted mean for each drainage area (equation 1). n

P=

∑1Ai ∗ Pi n

∑ 1 Ai

(1)

(Figure 2 here) Figure 2. MAE of the precipitation throughout the forecast horizon, for the study locations.

3.3. Ensemble Streamflow Hindcasting Experiments

8

The experiments consisted of assembling a Hydrological Ensemble Prediction System (H-EPS), using the meteorological ensembles as forcing’s to the MGB-IPH model (Table 2). Since the main river basin is discretized into 1424 unit-catchments (elementary areas), the centroid coordinates of each of these was used to interpolate representative precipitation series from the gridded S2S data by taking the nearest QPF grid pixel from the centroid coordinate as its value. The same interpolation was done to the MSWEP dataset. The Extended Streamflow Prediction (ESP) technique was used to generate an ensemble of hydrologic simulations considering the historical rainfall data. Each ESP ensemble member considered the same period (day and month) of the real-time forecast lead-times, and a total of 20 years into the past were used (i.e. number of climatological ensemble members). We also used a reference forecast, a “perfect” rainfall forecast, in which one assumes the predicted precipitation to be equal to the observed. This reference forecast was used to evaluate the model errors themselves, enabling, in the case of this study, the assessment of forecasts that only have to consider the uncertainties associated with the meteorological data. (Table 2 here) Table 2. Summary of the hydrological forecast experiments.

The sub seasonal S2S data-based forecasts have been initialized with MSWEP data from 1990 until the forecast initial date. The same for the ESP simulations, which assumes current basin conditions (the forecast issuing date) for simulations with the sampled rainfall series from previous years.

9

3.4. Results Assessment Approach The hydrological simulations produced results in the streamflow series for all 1424 unit-catchments. However, we selected 6 case studies’ locations (Itaipu, Porto Primavera, Jupiá, Água Vermelha, Furnas and Barra Bonita) for the assessments. In this selection, we favored points with hydropower reservoirs that could possibly benefit from the sub seasonal forecasts, and tried to cover a wide range of watershed spatial scales, as shown in table 3. (Table 3 here) Table 3. Description of the study locations and respective drainage area.

The verification of forecasts for the six selected locations was carried out with the goal to better comprehend the performance of the developed H-EPS across spatial scales, since the main meteorological and hydrological drivers present great variability within the basin. For instance, precipitation systems at the northern part of the basin are characterized by a tropical climate regime with dry winters and rainy summers. Most tropical and convective precipitation systems, in the southern end as well, feature more regular and well distributed precipitation along the year, mostly convective and frontal precipitation in the summer. On the hydrological side, it would be interesting to acknowledge the performance scores of the forecasts across basins with quicker response to the streamflow generating process as well as larger areas with smoother hydrographs response. The ensemble forecasting was evaluated using the Ensemble Verification System (EVS) software described by Brown et al., (2010). We applied selected customary scores in ensemble forecasting assessments, which were the Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), Mean Continuous Ranked Score (MCRPS), Mean

10

Continuous Ranked Probability Skill Score (MCRPSS) and Rank Histogram. These scores are usually employed in ensemble assessments and are highly documented within specific statistical literature (Wilks, 2006; Jolliffe and Stephenson, 2012). The objective of the assessment was to present an overview of the reliability and performance of ensemble forecasting results, in comparison to the deterministic values given by the ensemble mean and ensemble control member – as these values may be representative of a deterministic forecast, and may be used in the absence of ensemble forecasts. Also, in this assessment, the comparison with the ESP provides information on the performance of the ensemble against historical rainfall-based forecasts. The Mean Absolute Error (MAE, equation 2) reduces the ensemble to its mean value for each time step, measuring the difference from the reference benchmark (i.e. “perfect” rainfall simulation). This score assigns the same weight to all errors and primarily measures the magnitude of the errors, the optimal value is equal to zero. Meanwhile, the Root Mean Squared Error (RMSE, equation 3), as a quadratic score rule, penalizes larger errors, providing a measurement on the variability of the errors’ magnitudes, serving as a measure of accuracy. 1

𝑛

𝑀𝐴𝐸𝑡 = 𝑛∑𝑖 = 1|𝑌𝑖,𝑡 ― 𝑥𝑖,𝑡|

(Equation

2). Where: 𝑀𝐴𝐸𝑡 is the mean absolute error in timestep t; n is the number of the forecasts issued; 𝑌𝑖,𝑡 is the ensemble mean in timestep t and 𝑥𝑖,𝑡 is the respective observation in timestep t. 𝑅𝑀𝑆𝐸𝑡 =

[

1

𝑛 ∑ 𝑛 𝑖=1

(𝑌𝑖,𝑡 ―

𝑥𝑖,𝑡)

]

2

1 2

(Equation

3).

11

Where: 𝑅𝑀𝑆𝐸𝑡 is the root mean square error in timestep t; n is the number of the forecasts issued; 𝑌𝑖,𝑡 is the ensemble mean in timestep t and 𝑥𝑖,𝑡 is the respective observation in timestep t. The Continuous Ranked Probability Score (CRPS) summarizes the quality of the ensemble forecast reducing it to a single value, which is obtained by measuring the integrated square difference between the cumulative distribution function of the forecast value and the corresponding function of the observed value. The CRPS, when averaged for all forecast and observation pairs, leads to the Mean CRPS (MCRPS, equation 4), where lower values correspond to the optimal scores. It is important to highlight that the Mean CRPS may be used to compare the ensemble performance to a reference forecast, since it reduces to the MAE for deterministic forecasts. In addition, the Mean Continuous Ranked Probability Skill Score (MCRPSS, equation 5) measures the performance of the forecast system in regards to another in terms of Mean CRPS. The MCRPSS closer to +1 indicates that the main forecast system (for instance the S2S-based) have better skill over the reference system (for instance the ESP-based) opposed to values approaching -1. 1

𝑛

+∞

𝑀𝐶𝑅𝑃𝑆 = 𝑛∑𝑖 = 1∫ ―∞[𝐹𝑦(𝑦) ― 1{𝑦 ≥ 𝑥}]2𝑑𝑄𝑝𝑡,𝑛

(Equation

4). Where: 𝑀𝐶𝑅𝑃𝑆 is the mean continuous ranked probability score; 𝐹𝑦(𝑦) is the CDF of the forecast; 1{y ≥ 𝑥} is a step function that assumes value (probability) 1.0 for forecasted values greater than or equal to the observation, and 0.0 otherwise. 𝑀𝐶𝑅𝑃𝑆𝑆 = 1 ―

𝑀𝐶𝑅𝑃𝑆 𝑀𝐴𝐼𝑁 𝑀𝐶𝑅𝑃𝑆 𝑅𝐸𝐹

(Equation

5). Where: MCRPSS is the mean continuous ranked probability skill score;

𝑀𝐶𝑅𝑃𝑆 𝑀𝐴𝐼𝑁 𝑀𝐶𝑅𝑃𝑆 𝑅𝐸𝐹

is the ratio of MCRPS of the forecast systems issued.

12

In order to allow a comparison between different locations, errors scores (MAE, RMSE and MCPRS) were evaluated after a normalization procedure. The calculated value of the respective scores were divided by the long-term average of the “perfect rainfall” simulated flow series. Thus, the result may disregard the magnitudes and express the errors corresponding to the mean flow. The Rank Histogram (RH) is a measure of reliability (statistical consistency between measurements and simulations) and whether uncertainty is correctly represented in the forecast. It scopes out the fraction of observation that may fall between any two ranked ensemble members in the forecast distribution. This score is optimal (i.e. the forecast system is reliable in terms of Rank Histogram) when the probability of the observation falls between any two ranked members and is approximately uniform. A lack of spreading of the ensemble is indicated by a “U” shaped rank histogram (High probabilities in one or both tails), on the other hand an inverted “U” shape indicates an excessive spreading. 4. Results Figure 3 shows hydrograph examples of the results of ensemble streamflow forecasts. The sub seasonal ECMWF QPFs originated from the S2S database and the ESP series were used as input for generating the streamflow forecasts. The figure depicts a flood event in the Itaipu location, on the upper figures the forecasts were issued two weeks prior a flow peak, whereas the bottom part displays the development of the event. It is noted that the S2S based forecasts followed more in accordance to the “perfect rainfall” than the ESP-based, providing more accurate information on inflows to the Itaipu dam location. (Figure 3 here)

13

Figure 3. Visual analysis of sampled sub seasonal streamflow forecasts at Itaipu HPP. On the left the S2S-based; on the right the ESP-based. The blue line refers to the streamflow benchmark, red line is the control member of the ensemble, gray line is an ensemble member and dashed black line is the ensemble mean.

The results of the MAE and MCRPS analysis throughout the 6 studied locations is shown in figure 4. The MCRPS score is always lower than the MAE of the ensemble mean and the control member, in all locations. Comparing the ensemble MCRPS to a deterministic reference, given by the control member forecast, it is indicated that using the ensemble distribution is more likely to obtain better predictably than the control member forecast (deterministic). The error scores are always greater than zero and readily increase from initial lead-days onwards. In Barra Bonita and Furnas locations the normalized error scores are more prominent, possibly caused by the quicker response of rainfall-runoff generation processes within the catchment drainage area, thereby, suggesting more dependency on streamflow response to the forecasted rainfall. Itaipu (827,000 km²), Porto Primavera (574,000) and Jupiá (479,000 km²), which are located along the main river of the basin (Paraná River), and also the Água Vermelha (139,000 km²), presented magnitudes of MAE and MCRPS scores placed around 0.10 to 0.2 times the long-term flow average. As for the control member, until approximately day 8 the MAE magnitude was akin to the ensemble mean, and after this lead-day its errors were around 0.4 times the long-term flow average. Furnas (52,000 km²), at the northeast region of the basin, presented MAE magnitudes around 0.2 times the long-term flow average, and 0.2 times for the MCRPS. The control member obtained similar magnitudes to the ensemble mean until lead-day 6, and after, values ranged 0.4 times the long-term flow average. As for Barra Bonita (33,000 km²), located at the Mideast region of the basin with the smallest drainage area of all 6 locations, also presented the highest error magnitudes 14

in regard to the long-term flow average, spanning values around 0.6 and 0.4 for MAE and MCRPS, respectively. The control member forecast resulted in close score values until day 8, then 0.8 times the long-term flow average. (Figure 4 here) Figure 4. Evolution on the lead time up to 46 days of the MAE and MCRPS for the forecasts issued.

The RMSE analysis indicates that the errors follow a similar behavior to the MAE and MCRPS, which indicated a tendency to increase as the drainage area decreases. The three larger drainage areas (i.e. Itaipu, Porto Primavera and Jupiá) presented the smallest RMSEs relative to the long-term flow average. As the drainage area decreases (respectively, Água Vermelha, Furnas and Barra Bonita), the RMSE tends to present higher values. At Barra Bonita, a pattern more closely dependent on the forecasts runs on the RMSE results appears along the forecast horizon. This pattern is a result of the rapid response in the hydrograph of the catchment, from intense rainfall events presented in the sub seasonal forecasts, which in turn influence the result in certain lead-days. This does not appear on other locations due to the attenuation of the errors and catchment size. (Figure 5 here) Figure 5. RMSE on all locations, the figure shows that the error tends to increase as the drainage area of the location decreases.

Figures 6, 7, and 8, show the 51-member rank histogram for Itaipu, Furnas and Barra Bonita at sampled lead-days 1, 14, 28 and 42, depicting the behavior of ensemble spread throughout the forecast horizon. The Itaipu rank histograms are similar to that of Porto Primavera, Jupiá and Água Vermelha, which presented a lack of spread and also a small positive on early lead-days bias, or overestimations of streamflow.

15

Furnas rank histograms have a lack of spread on early lead-days and a small tendency towards overestimation of the forecasted streamflow over the entire horizon. The Barra Bonita histograms show that, in early lead-days, the “U” shape is present, indicating a lack of spread. Although, along the forecast evolution, the positive bias (streamflow overestimates) is more pronounced than in the other locations. These results suggest that a bias removal method may have to be applied in order to deal with the tendency towards overestimation in streamflow forecasts across almost all locations. The spread analysis results are similar to what is commonly observed in other ensemble forecasts verification studies, where the lack of spread in early lead-time is presented when considering the precipitation as the only source of uncertainty (Fan et al., 2014). (Figure 6 here) Figure 6. Itaipu Rank Histograms indicating a lack of spread in early lead times. This behavior is akin to the other locations – Porto Primavera, Jupiá and Água Vermelha.

(Figure 7 here) Figure 7. Furnas Rank Histograms indicating right from initial time step a tendency towards overestimation on the forecast streamflow.

(Figure 8 here) Figure 8. Barra Bonita Rank Histograms indicating lack of spread in early lead times, but a tendency towards overestimation (positive bias) along the development of the forecast.

The analysis of the forecast’s skill against a historical reference of forecasts is presented in terms of MCRPSS. Figure 9 shows the results for the 6 locations, delineating the performance of the QPF-based sub seasonal streamflow forecasts in comparison to the ESP-based.

16

For Itaipu, after lead-day 3, the QPF-based forecast outperforms the ESP throughout the entire forecast horizon. At Porto Primavera, Jupiá and Água Vermelha, the behavior is similar to Itaipu, except that approximately after a month (lead-day 30) the ESP presented superior skill than the sub seasonal QPF ensemble. Broadly, these results concur with studies investigating the quality of ESP, which claim that many ensemble predictions systems have difficulties in outperforming ESP after a month of forecasting (Arnal et al., 2018; Lucatero et al., 2018; Monhart et al., 2019). As for the deficient sub seasonal ensemble skill until day 3, this is possibly caused by the favorable ESP skill in forecasting the initial lead-days in large basins, where the inertial memory of hydrological conditions has more influence over the prediction. For Furnas, the sub seasonal QPF based forecasts were slightly better than the ESP until the third week (lead-day 21). As for Barra Bonita, it is the only location that the sub seasonal QPF ensemble outperformed the ESP across all lead-days, possibly because the main predictability drivers on this location were obtained from the meteorological data, in other words, low seasonality is presented, thereby manifesting on the skill of the ESP technique. (Figure 9 here) Figure 9. Mean Continuous ranked probability skill score (CPRSS) for the sub seasonal based forecasts against ESP as reference.

5. Discussion The results presented in this work are one of the first assessments of sub seasonal QPF-based ensemble streamflow forecasts in the South American continent and for tropical climates.

17

Regarding the comparison between the ensemble and the deterministic approach, our results agree with the usual results from other H-EPS assessments against deterministic references. The results from the statistical verification indicate that ensemble hydrological forecasting presents many advantages when compared to the deterministic (control member) in terms of MAE and MCPRS. After approximately a week of lead time, the errors of the ensemble are always lower than the deterministic reference for all six locations. Also, it is suggested that the error scores may be dependent on the catchment scale and hydrologic conditions (e.g. runoff generation process, water storage and flow routing), since smaller ones presented the greater errors (Furnas and Barra Bonita), as it may be attenuated by the streamflow generation processes on larger basins – which is in agreement with other studies regarding ensemble forecast performance assessment across catchments with distinct spatial scales and characteristics (e.g. Anderson et al., 2019). Meteorologically, larger drainage areas performed better possibly due to errors related to the spatial resolution, rainfall location and temporal occurrence of rainfalls of the meteorological input being averaged for greater area values. As well as phase errors on the forecast being compensated by the streamflow generation processes delay time, therefore not greatly contributing for depreciation of forecast quality. Consequently, on larger basins the errors tend to compensate for themselves. On the hydrological model, larger areas result in better performance in the simulations, given that errors on parametrization and discretization are also compensated. One may note that for the larger drainage areas the statistical scores tend to bear better results. Remarkable is the fact that for drainage areas equal to or greater than 479,000 km² (Jupiá, P. Primavera and Itaipu Dam), MAE and RMSE of hydrological forecasting were very similar, suggesting a threshold area for bearing the best results.

18

Regarding Rank Histogram analysis, the score provides an overview of the spread of the ensemble. It is showed that for early lead-times there is a lack of spread in the ensemble, across all locations studied, suggesting that the results are more dependent on the observed initial conditions in the basin rather than on meteorological inputs. Furthermore, the histograms point out systematic bias present in some lead-times, suggesting that some bias removal technique may be applied. The importance of the initial conditions to simulations on large watershed has already been investigated sometimes in literature, frequently relating the area as a predictability related variable (Paiva et. al., 2012; Yossef et. al., 2013). The results regarding skill comparison of S2S based forecast against the ESP approach indicates that the first set have more quality and potential usefulness for inflow forecasting. These results are particularly important for locations such as the studied area, where most of the medium-to-long term (sub seasonal timescale) hydropower operations and management relies on forecasts based on stochastic methods. Also, forecasting within the sub seasonal time scale is very interesting as it provides valuable information on streamflow estimative on a daily or sub-daily basis, issued twice a week, which could be applied for monthly planning of operations. In addition, the forecasts following a distributed hydrological model framework supply information at multiple locations within the interest region, thereby supporting an integrated analysis for sub seasonal water resources management. The figure 10 below shows an overview of normalized MAE for all unit-catchments centroids used in the distributed hydrological framework applied in this study. It is depicted that there are regions of the basin which are more likely to obtain better quality of forecasts, in terms of the statistic presented. This is partially explained by different drivers of predictability (atmospheric and hydrologic processes) acting within the study basin, as described in

19

previous sections. Also, it is noted that along the main river of the basin the errors tends to be in the lower class (< 0.25 until lead time 28, and a small portion with errors ranging between 0.25 to 0.50 on lead time 42), which can be related to the total catchment drainage area, and its hydrological processes such as streamflow generation and propagation. This last statement concurs with studies that instigates the relationship between ensemble statistical evaluation performance in a distributed hydrological forecasting and catchment size, as in Anderson et. al. (2019). Also, in an operational point of view, the forecasts may also be improved with data assimilation and post-processing methods. The results suggest that the ECMWF ensemble may perform differently at distinct catchments among the study basin. It can be noted that the performance results on one location may not be transposed to another. This evidence is also perceived within the studies of Fan et al., (2015b), which tested medium range ensemble forecasts on distinct watersheds within the same hydroclimatic region and Monhart et al., (2019) that investigated the sub seasonal ensemble forecast performance in alpine climate catchments. The climatic characteristic at each location may influence the performance on techniques that rely on a historical series, that is, in cases where little seasonality is presented, using the sub seasonal QPF-based forecasts may achieve better skill, as it considers more accurate meteorological conditions along forecast lead time. Finally, we did not carry out any post-processing on the forecast streamflow, which could be assessed in future studies considering each location’s particularities (Siqueira et al, 2019). (Figure 10 here)

20

Figure 10. Mean Absolute Error (MAE) normalized with long-term average for each individual unit-catchment, on top left is sampled lead time 1, top right is lead time 14, bottom left is lead time 28 and bottom right is lead time 42.

6. Conclusions This research presented one of the first statistical assessments of the sub seasonal to seasonal (S2S) meteorological data as input for hydrological modeling in a tropical and sub-tropical region, where the most important streamflow generation processes mainly comes from the precipitation, considering the location of hydropower plants which could potentially benefit over the streamflow predictions. The results showed that the performance of the issued ensemble forecasts possess some advantages in applications where total inflow is necessary when compared to the deterministic (control member) and to a climatological reference (ESP), which is the approach currently used for hydropower operation in the region. The locations with greater drainage area presented the best performance, when taking into account MAE, MCPRS, and MCPRSS, especially for the Itaipu dam, which presented a higher skill than climatology after day 3 until the end of the forecast horizon. Following the main Paraná River upstream, the direct errors (MAE and MCPRS) presented slight deteriorations, concerning the skill score the results indicated similar behavior to Itaipu, except that after a month of lead time, it has underperformed the historical reference. The other locations, situated in tributaries of the main river, with smaller drainage areas, presented a higher degree of degradation in the results. On Barra Bonita and Furnas, the MAE and MCPRS resulted on the largest values, caused by some degree of bias, on the other hand, the first outperformed the ESP on all timesteps; and the second presented skill above the ESP until week 3 (day 21).

21

Ultimately, we expect that our results will contribute to the usage of sub seasonal horizon forecasts, and its benefits to hydrological forecasting, consolidating ensemble forecasting experiments in large South American basins and tropical to sub-tropical climates as well. In large-scale basins, the sub seasonal streamflow predictions proved to be promising, with better skill than the forecasts generated using the historical rainfall. In addition, the efforts addressed some issues related to the main incitements of the sub seasonal to the seasonal (S2S) project (Vitart et al., 2017), especially on those regarding to the evaluation of the forecasts. In Brazil, it may be particularly important, as it is an alternative to empirical methods commonly used by the National Electric System Operator (such as PREVIVAZ model), also, the sub seasonal QPF based forecast provides integrated information across multiple locations and basin scales. Regarding future works, we believe that more test cases may be useful, considering the meteorological inputs originated from different research centers, as they are freely available from the S2S database – potentially providing a ‘grand’ ensemble with more statistically reliable results. Likewise, succeeding recent efforts in the integrated modeling of complex hydraulic systems in South America (e.g. Siqueira et al., 2018), it is expected that value can be attained from these models towards the use of sub seasonal forecasting (precipitation and other variables) in hydrological forecasts, especially when regarding techniques that only employ historical information. Acknowledgements The authors thank the two anonymous reviewers and Associate Editor MariaHelena Ramos for the comments that helped to improve the paper. Also, we acknowledge the financial support granted for this publication by CAPES - Brazil. References

22

Adam, K., Fan, F., Pontes, P., Bravo, J., Collischonn, W., 2015. Mudanças climáticas e vazões extremas na Bacia do Rio Paraná / Climate Change and Extreme Streamflows in Paraná River Basin. Rev. Bras. Recur. Hídricos 20, 999–1007. https://doi.org/10.21168/rbrh.v20n4.p999-1007. Anderson, S.R., Cole, S.J., Csima, G., Moore, R.J., Mittermaier, M., 2019. Towards operational joint river flow and precipitation ensemble verification : considerations and strategies given limited ensemble records. J. Hydrol. 577, 123966. https://doi.org/10.1016/j.jhydrol.2019.123966 ANEEL, 2008. Energia Hidráulica, Atlas de energia elétrica do Brasil. Anghileri, D., Voisin, N., Castelletti, A., Pianosi, F., Nijssen, B., Lettenmaier, D.P., 2016. Value of long-term streamflow forecasts to reservoir operations for water supply in snow-dominated river catchments. Water Resour. Res. 52, 4209–4225. https://doi.org/10.1002/2015WR017864 Arnal, L., Cloke, H.L., Stephens, E., Wetterhall, F., Prudhomme, C., Neumann, J., Krzeminski, B., Pappenberger, F., 2018. Skilful seasonal forecasts of streamflow over Europe? Hydrol. Earth Syst. Sci. 22, 2057–2072. https://doi.org/10.5194/hess-22-20572018. Baker, S.A., Wood, A.W., Rajagopalan, B., 2019. Developing Subseasonal to Seasonal Climate Forecast Products for Hydrology and Water Management. J. Am. Water Resour. Assoc. 1–14. https://doi.org/10.1111/1752-1688.12746. Bartholmes, J., Todini, E., 2005. Coupling meteorological and hydrological models for flood forecasting. Hydrol. Earth Syst. Sci. Discuss. 9, 333–346. https://doi.org/10.5194/hess-9-333-2005. Bartholmes, J.C., Thielen, J., Ramos, M.H., Gentilini, S., 2009. The european flood alert system EFAS " Part 2: Statistical skill assessment of probabilistic and deterministic operational forecasts. Hydrol. Earth Syst. Sci. 13, 141–153. https://doi.org/10.5194/hess-13-141-2009 Bauer, P., Thorpe, A., Brunet, G., 2015. The quiet revolution of numerical weather prediction. Nature 525, 47–55. https://doi.org/10.1038/nature14956 Bazile, R., Boucher, M.A., Perreault, L., Leconte, R., 2017. Verification of ECMWF System 4 for seasonal hydrological forecasting in a northern climate. Hydrol. Earth Syst. Sci. 21, 5747–5762. https://doi.org/10.5194/hess-21-5747-2017 Beck, H.E., Van Dijk, A.I.J.M., Levizzani, V., Schellekens, J., Miralles, D.G., Martens, B., De Roo, A., 2017a. MSWEP: 3-hourly 0.25° global gridded precipitation (1979-2015) by merging gauge, satellite, and reanalysis data. Hydrol. Earth Syst. Sci. 21, 589–615. https://doi.org/10.5194/hess-21-589-2017 Beck, H.E., Vergopolan, N., Pan, M., Levizzani, V., Van Dijk, A.I.J.M., Weedon, G.P., Brocca, L., Pappenberger, F., Huffman, G.J., Wood, E.F., 2017b. Global-scale evaluation of 22 precipitation datasets using gauge observations and hydrological modeling. Hydrol. Earth Syst. Sci. 21, 6201–6217. https://doi.org/10.5194/hess-21-6201-2017 Boucher, M.A., Anctil, F., Perreault, L., Tremblay, D., 2011. A comparison between ensemble and deterministic hydrological forecasts in an operational context. Adv. Geosci. 29, 85–94. https://doi.org/10.5194/adgeo-29-85-2011 Brown, J.D., Demargne, J., Seo, D.J., Liu, Y., 2010. The Ensemble Verification System (EVS): A software tool for verifying ensemble forecasts of hydrometeorological and hydrologic variables at discrete locations. Environ. Model. Softw. 25, 854– 872. https://doi.org/10.1016/j.envsoft.2010.01.009 Brunet, G., Shapiro, M., Hoskins, B., Moncrieff, M., Dole, R., Kiladis, G.N., Kirtman, B., Lorenc, A., Mills, B., Morss, R., Polavarapu, S., Rogers, D., Schaake, J., Shukla, J., 2010. Collaboration of the Weather and Climate Communities to Advance Subseasonal-to-Seasonal Prediction. Bull. Am. Meteorol. Soc. 91, 1397–1406. https://doi.org/10.1175/2010bams3013.1

23

Buizza, R., 2008. The value of probabilistic prediction. Atmos. Sci. Lett. https://doi.org/10.1002/asl.170 Cloke, H.L., Pappenberger, F., 2009. Ensemble flood forecasting: A review. J. Hydrol. 375, 613–626. https://doi.org/10.1016/j.jhydrol.2009.06.005 Cloke, H.L., Pappenberger, F., van Andel, S.J., Schaake, J., Thielen, J., Ramos, M.H., 2013. Hydrological ensemble prediction systems. Hydrol. Process. 27, 1–4. https://doi.org/10.1002/hyp.9679 Collischonn, W., Allasia, D., da Silva, B.C., Tucci, C.E.M., 2007a. The MGB-IPH model for large-scale rainfall-runoff modelling. Hydrol. Sci. J. https://doi.org/10.1623/hysj.52.5.878 Collischonn, W., Morelli Tucci, C.E., Clarke, R.T., 2005. Previsão Sazonal de Vazão na Bacia do Rio Uruguai 2: Previsão Climática-Hidrológica. Rev. Bras. Recur. Hídricos 10, 61–72. Collischonn, W., Morelli Tucci, C.E., Clarke, R.T., Chou, S.C., Guilhon, L.G., Cataldi, M., Allasia, D., 2007b. Medium-range reservoir inflow predictions based on quantitative precipitation forecasts. J. Hydrol. 344, 112–122. https://doi.org/10.1016/j.jhydrol.2007.06.025 Collischonn, W., Tucci, C.E.M., 2005. Previsão Sazonal de Vazão na Bacia do Rio Uruguai 1 : Ajuste e Verificação do Modelo Hidrológico Distribuído. Rbrh 10, 43–59. Collischonn, W.; Bravo, J. M.; da Silva, B. C.; Rodriguez, D. A. (2014). Chapter 3: “Modelagem Hidrológica”. In: LIMA, J. W. M., COLLISCHON, W., MARENGO, J. A, 2014. Efeitos das mudanças climáticas na geração de energia elétrica. Editora BH. São Paulo, Brasil. Cuo, L., Pagano, T.C., Wang, Q.J., 2011. A Review of Quantitative Precipitation Forecasts and Their Use in Short- to MediumRange Streamflow Forecasting. J. Hydrometeorol. 12, 713–728. https://doi.org/10.1175/2011JHM1347.1 Day, G.N., 1985. Extended Streamflow Forecasting Using NWSRFS. J. Water Resour. Plan. Manag. 111, 157–170. https://doi.org/10.1061/(asce)0733-9496(1985)111:2(157) Demargne, B., Lee, H., Hartman, R., Fresch, M., Schaake, J., 2014. Operational Hydrologic. ECMWF, E. C.-R. (2017). IFS DOCUMENTATION - Cy43r3. PART V: ENSEMBLE PREDICTION SYSTEM. Emerton, R.E., Stephens, E.M., Pappenberger, F., Pagano, T.C., Weerts, A.H., Wood, A.W., Salamon, P., Brown, J.D., Hjerdt, N., Donnelly, C., Baugh, C.A., Cloke, H.L., 2016. Continental and global scale flood forecasting systems. Wiley Interdiscip. Rev. Water 3, 391–418. https://doi.org/10.1002/wat2.1137 Fan, F.M., Collischonn, W., Meller, A., Botelho, L.C.M., 2014. Ensemble streamflow forecasting experiments in a tropical basin: The São Francisco river case study. J. Hydrol. 519, 2906–2919. https://doi.org/10.1016/j.jhydrol.2014.04.038 Fan, F.M., Collischonn, W., Quiroz, K.J., Sorribas, M. V., Buarque, D.C., Siqueira, V.A., 2016. Flood forecasting on the Tocantins River using ensemble rainfall forecasts and real-time satellite rainfall estimates. J. Flood Risk Manag. 9, 278–288. https://doi.org/10.1111/jfr3.12177 Fan, F.M., Schwanenberg, D., Collischonn, W., Weerts, A., 2015. Verification of inflow into hydropower reservoirs using ensemble forecasts of the TIGGE database for large scale basins in Brazil. J. Hydrol. Reg. Stud. 4, 196–227. https://doi.org/10.1016/j.ejrh.2015.05.012 Foster, K., Uvo, C.B., Olsson, J., 2018. The development and evaluation of a hydrological seasonal forecast system prototype for predicting spring flood volumes in Swedish rivers. Hydrol. Earth Syst. Sci. 22, 2953–2970. https://doi.org/10.5194/hess-222953-2018 Golding, B.W., 2009. Long lead time flood warnings: Reality or fantasy? Meteorol. Appl. https://doi.org/10.1002/met.123

24

Hao, Z., Singh, V.P., Xia, Y., 2018. Seasonal Drought Prediction: Advances, Challenges, and Future Prospects. Rev. Geophys. 56, 108–141. https://doi.org/10.1002/2016RG000549 Hartmann, H.C., 2006. Use of Climate Information in Water Resources Management. Encycl. Hydrol. Sci. https://doi.org/10.1002/0470848944.hsa213 Jaun, S., Ahrens, B., 2009. Evaluation of a probabilistic hydrometeorological forecast system. Hydrol. Earth Syst. Sci. 13, 1031– 1043. https://doi.org/10.5194/hess-13-1031-2009 Jolliffe, I.T., Stephenson, D.B. (Eds.), 2012. Forecast Verification: A Practitioner’s Guide. In Atmospheric Science. , second ed. Kouwen, N., Soulis, E.D., Pietroniro, A., Donald, J., Harrington, R.A., 2006. Grouped Response Units for Distributed Hydrologic Modeling. J. Water Resour. Plan. Manag. https://doi.org/10.1061/(asce)0733-9496(1993)119:3(289) Krzysztofowicz, R., 2001. The case for probabilistic forecasting in hydrology. J. Hydrol. 249, 2–9. https://doi.org/10.1016/S00221694(01)00420-6 Lemos, M.C., 2008. What influences innovation adoption by water managers? Climate information use in Brazil and the United States. J. Am. Water Resour. Assoc. 44, 1388–1396. https://doi.org/10.1111/j.1752-1688.2008.00231.x Lettenmaier, D.P., Wood, E.F., 1993. Hydrologic forecasting, in: Maidment, D.R. (Ed.), Handbook of Hydrology. McGraw-Hill, New York Lucatero, D., Madsen, H., Refsgaard, J.C., Kidmose, J., Jensen, K.H., 2018. On the skill of raw and post-processed ensemble seasonal meteorological forecasts in Denmark. Hydrol. Earth Syst. Sci. 22, 6591–6609. https://doi.org/10.5194/hess-22-65912018 Meißner, D., Klein, B., Ionita, M., 2017. Development of a monthly to seasonal forecast framework tailored to inland waterway transport in central Europe. Hydrol. Earth Syst. Sci. 21, 6401–6423. https://doi.org/10.5194/hess-21-6401-2017 Meller, A., Collischonn, W., FAN, F., Buarque, D., Paiva, R., DIAS, P., MOREIRA, D., 2016. Previsão de Cheias por Conjunto em Curto Prazo. Rev. Bras. Recur. Hídricos. https://doi.org/10.21168/rbrh.v19n3.p33-49 Monhart, S., Zappa, M., Spirig, C., Schär, C., Bogner, K., 2019. Subseasonal hydrometeorological ensemble predictions in smalland medium-sized mountainous catchments: Benefits of the NWP approach. Hydrol. Earth Syst. Sci. 23, 493–513. https://doi.org/10.5194/hess-23-493-2019 O’Donnell, M., Colby, B., 2009. Dry-Year Water Supply Reliability Contracts: A Tool for Water Managers 21. ONS – Operador Nacional do Sistema, 2011. Procedimentos de Rede Submódulo 9.5: Previsão de Vazões e Gerac¸ ão de Cenáriosde Afluências, vol. 2., pp. 9. ONS – Operador Nacional do Sistema, 2012a. Diretrizes para as Regras de Operac¸ ão de Controle de Cheias – Bacia do Rio SãoFrancisco (Ciclo 2012–2013). ONS RE 3/166/2012., pp. 158. ONS – Operador Nacional do Sistema, 2012b. Inventário das Restric¸ ões Operativas Hidráulicas dos Aproveitamentos Hidrelétri-cos (Revisão 1 de 2012). ONS RE 3/0105/2012., pp. 154. ONS – Operador Nacional do Sistema, 2014. Diretrizes para as Regras de Operac¸ ão de Controle de Cheias – Bacia do Rio Iguac¸ u(Ciclo 2013–2014). ONS RE 3/0064/2014., pp. 48. Pagano, T.C., Hartmann, H.C., Sorooshian, S., 2002. Factors affecting seasonal forecast use in Arizona water management: A case study of the 1997-98 El Niño. Clim. Res. https://doi.org/10.3354/cr021259 Paiva, R. C. D.; collischonn, W. ; Bonnet, M. P. ; de Gonçalves, L. G. G. . On the sources of hydrological prediction uncertainty in the Amazon. Hydrology and Earth System Sciences , v. 16, p. 3127-3137, 2012.

25

Paiva, R.C.D., Collischonn, W., Bonnet, M.P., De Gonçalves, L.G.G., Calmant, S., Getirana, A., Santos Da Silva, J., 2013. Assimilating in situ and radar altimetry data into a large-scale hydrologic-hydrodynamic model for streamflow forecast in the Amazon. Hydrol. Earth Syst. Sci. https://doi.org/10.5194/hess-17-2929-2013 Pappenberger, F., 2019. ECMWF: progress and plans. Geophysical Research Abstracts, vol. 21, 8348. Pappenberger, F., Stephens, L., Van Andel, S.J., Verkade, J.S., Ramos, M.H., Alfieri, L., Brown, J.D., Zappa, M., Ricciardi, G., Wood, A., Pagano, T., Marty, R., Collischonn, W., Le Lay, M., Brochero, D., Cranston, M., Meissner, D., 2013. Operational HEPS systems around the globe. . Pappenberger, F., Thielen, J., Del Medico, M., 2011. The impact of weather forecast improvements on large scale hydrology: Analysing a decade of forecasts of the European Flood Alert System. Hydrol. Process. 25, 1091–1113. https://doi.org/10.1002/hyp.7772 Pappenberger, F., Wetterhall, F., Dutra, E., Di Giuseppe, F., Bogner, K., Alfieri, L., Cloke, H., 2013. Seamless forecasting of extreme events on a global scale. Clim. L. Surf. Chang. Hydrol. 359, 3–10. https://doi.org/10.1111/jvs.12224 Paz, A.R., Collischonn, W., Tucci, C.E.M., Clarke, R.T., Allasia, D., 2007. Data assimilation in a large-scale distributed hydrological model for medium-range flow forecasts. IAHS-AISH Publ. Pontes, P.R.M., Fan, F.M., Fleischmann, A.S., de Paiva, R.C.D., Buarque, D.C., Siqueira, V.A., Jardim, P.F., Sorribas, M.V., Collischonn, W., 2017. MGB-IPH model for hydrological and hydraulic simulation of large floodplain river systems coupled with open source GIS. Environ. Model. Softw. https://doi.org/10.1016/j.envsoft.2017.03.029 Robertson, A.W., Baethgen, W., Block, P., Lall, U., Sankarasubramanian, A., de Assis de Souza Filho, F., J Verbist, K.M., 2014. Climate risk management for water in semi–arid regions. Earth Perspect. 1, 12. https://doi.org/10.1186/2194-6434-1-12 Robertson, A.W., Camargo, S.J., Sobel, A., Vitart, F., Wang, S., 2017. Summary of workshop on sub-seasonal to seasonal predictability of extreme weather and climate. npj Clim. Atmos. Sci. 1, 8. https://doi.org/10.1038/s41612-017-0009-1 Robertson, A.W., Kumar, A., Peña, M., Vitart, F., 2018. Improving and Promoting Subseasonal to Seasonal Prediction. Bull. Am. Meteorol. Soc. 2016, ES49–ES53. https://doi.org/10.1175/bams-d-14-00139.1.2016.1.test Robertson, A.W., Vitart, F., 2018. Sub-seasonal to seasonal prediction : the gap between weather and climate forecasting 569. Roulin, E., 2007. Skill and relative economic value of medium-range hydrological ensemble predictions. Hydrol. Earth Syst. Sci. 11, 725–737. https://doi.org/10.5194/hess-11-725-2007 Schaake, J., Franz, K., Bradley, A., Buizza, R., 2006. The Hydrologic Ensemble Prediction EXperiment (HEPEX). Hydrol. Earth Syst. Sci. Discuss. 3, 3321–3332. https://doi.org/10.5194/hessd-3-3321-2006 Scherrer, S.C., Appenzeller, C., Eckert, P., Cattani, D., 2004. Analysis of the Spread–Skill Relations Using the ECMWF Ensemble Prediction System over Europe. Weather Forecast. 19, 552–565. https://doi.org/10.1175/15200434(2004)019<0552:aotsru>2.0.co;2 Schwanenberg, D., Fan, F.M., Naumann, S., Kuwajima, J.I., Montero, R.A., Assis dos Reis, A., 2015. Short-Term Reservoir Optimization for Flood Mitigation under Meteorological and Hydrological Forecast Uncertainty: Application to the Três Marias Reservoir in Brazil. Water Resour. Manag. 29, 1635–1651. https://doi.org/10.1007/s11269-014-0899-1 Sene, K., Tych, W., Beven, K., 2018. Exploratory studies into seasonal flow forecasting potential for large lakes. Hydrol. Earth Syst. Sci. 22, 127–141. https://doi.org/10.5194/hess-22-127-2018 Shah, R., Sahai, A.K., Mishra, V., 2017. Short to sub-seasonal hydrologic forecast to manage water and agricultural resources in India. Hydrol. Earth Syst. Sci. 21, 707–720. https://doi.org/10.5194/hess-21-707-2017

26

Shapiro, M., Shukla, J., Brunet, G., Nobre, C., Béland, M., Dole, R., Trenberth, K., Anthes, R., Asrar, G., Barrie, L., Bougeault, P., Brasseur, G., Burridge, D., Busalacchi, A., Caughey, J., Chen, D., Church, J., Enomoto, T., Hoskins, B., Hov, Ø., Laing, A., Le Treut, H., Marotzke, J., McBean, G., Meehl, G., Miller, M., Mills, B., Mitchell, J., Moncrieff, M., Nakazawa, T., Olafsson, H., Palmer, T., Parsons, D., Rogers, D., Simmons, A., Troccoli, A., Toth, Z., Uccellini, L., Velden, C., Wallace, J.M., 2010. An Earth-System Prediction Initiative for the Twenty-First Century. Bull. Am. Meteorol. Soc. 91, 1377–1388. https://doi.org/10.1175/2010bams2944.1 Shuttleworth, W.J., 1993. Evaporation. In: Handbook of hydrology, D.R. Maidment (Ed.), McGraw-Hill, New York, Chap. 4, 4.14.53. Silveira, C. da S., Alexandre, A.M.B., Souza Filho, F. de A. de, Vasconcelos Junior, F. das C., Cabral, S.L., 2017. Monthly streamflow forecast for National Interconnected System (NIS) using Periodic Auto-regressive Endogenous Models (PAR) and Exogenous (PARX) with climate information. Rbrh 22. https://doi.org/10.1590/2318-0331.011715186 Siqueira, B., Nery, J.T., Martins, G., 2018. Variabilidade Sazonal Da Precipitação Na Bacia Do Paraná. Rev. Bras. Climatol. 23. https://doi.org/10.5380/abclima.v23i0.59508 Siqueira, V., Weerts, A., Verkade, J., Klein, B., Fan, F., Paiva, R., Collischonn, W., 2019. Improving reliability and skill of medium-range hydrological ensemble forecasts over South America using EMOS. Geophysical Research Abstracts, vol. 21, 9683. Siqueira, V.A., Paiva, R.C.D., Fleischmann, A.S., Fan, F.M., Ruhoff, A.L., Pontes, P.R.M., Paris, A., Calmant, S., Collischonn, W., 2018. Toward continental hydrologic-hydrodynamic modeling in South America. Hydrol. Earth Syst. Sci. 22, 4815–4842. https://doi.org/10.5194/hess-22-4815-2018 Todini, E., 1996. The ARNO rainfall-runoff model. J. Hydrol. https://doi.org/10.1016/S0022-1694(96)80016-3 Tucci, C.E.M., Clarke, R.T., Collischonn, W., Da Silva Dias, P.L., De Oliveira, G.S., 2003. Long-term flow forecasts based on climate and hydrologic modeling: Uruguay River basin. Water Resour. Res. 39, 1–11. https://doi.org/10.1029/2003WR002074 Turner, S.W.D., Bennett, J.C., Robertson, D.E., Galelli, S., 2017. Complex relationship between seasonal streamflow forecast skill and value in reservoir operations. Hydrol. Earth Syst. Sci. 21, 4841–4859. https://doi.org/10.5194/hess-21-4841-2017 Verbunt, M., Walser, A., Gurtz, J., Montani, A., Schär, C., 2007. Probabilistic Flood Forecasting with a Limited-Area Ensemble Prediction System: Selected Case Studies. J. Hydrometeorol. 8, 897–909. https://doi.org/10.1175/JHM594.1 Verkade, J.S., Werner, M.G.F., 2011. Estimating the benefits of single value and probability forecasting for flood warning. Hydrol. Earth Syst. Sci. 15, 3751–3765. https://doi.org/10.5194/hess-15-3751-2011 Vitart, F., Ardilouze, C., Bonet, A., Brookshaw, A., Chen, M., Codorean, C., Déqué, M., Ferranti, L., Fucile, E., Fuentes, M., Hendon, H., Hodgson, J., Kang, H.-S., Kumar, A., Lin, H., Liu, G., Liu, X., Malguzzi, P., Mallas, I., Manoussakis, M., Mastrangelo, D., MacLachlan, C., McLean, P., Minami, A., Mladek, R., Nakazawa, T., Najm, S., Nie, Y., Rixen, M., Robertson, A.W., Ruti, P., Sun, C., Takaya, Y., Tolstykh, M., Venuti, F., Waliser, D., Woolnough, S., Wu, T., Won, D.-J., Xiao, H., Zaripov, R., Zhang, L., 2016. The Subseasonal to Seasonal (S2S) Prediction Project Database. Bull. Am. Meteorol. Soc. 98, 163–173. https://doi.org/10.1175/bams-d-16-0017.1 Vitart, F., R.A. and the S. steering group, 2015. SEAMLESS PREDICTION OF THE EARTH SYSTEM: FROM MINUTES TO MONTHS World Meteorological Organization, Seamless prediction of the earth system: from minutes to months.

27

Vitart, F., Robertson, A.W., 2016. Subseasonal to Seasonal Prediction Project: Bridging the gap between weather and climate Subseasonal to Seasonal Prediction Project: bridging the gap between weather and. Vitart, F., Robertson, A.W., 2018. The sub-seasonal to seasonal prediction project (S2S) and the prediction of extreme events. npj Clim. Atmos. Sci. 1, 3. https://doi.org/10.1038/s41612-018-0013-0 White, C.J., Carlsen, H., Robertson, A.W., Klein, R.J.T., Lazo, J.K., Kumar, A., Vitart, F., Coughlan de Perez, E., Ray, A.J., Murray, V., Bharwani, S., MacLeod, D., James, R., Fleming, L., Morse, A.P., Eggen, B., Graham, R., Kjellström, E., Becker, E., Pegion, K. V., Holbrook, N.J., McEvoy, D., Depledge, M., Perkins-Kirkpatrick, S., Brown, T.J., Street, R., Jones, L., Remenyi, T.A., Hodgson-Johnston, I., Buontempo, C., Lamb, R., Meinke, H., Arheimer, B., Zebiak, S.E., 2017. Potential applications of subseasonal-to-seasonal (S2S) predictions. Meteorol. Appl. 24, 315–325. https://doi.org/10.1002/met.1654 Wilks, D.S. (Department of E. and A.S.C.U., 2006. Statistical methods in the atmospheric sciences, International Geophysics Series. https://doi.org/10.1002/met.16 Yossef, N.C., Winsemius, H., Weerts, A., Van Beek, R., Bierkens, M.F.P., 2013. Skill of a global seasonal streamflow forecasting system, relative roles of initial conditions and meteorological forcing. Water Resour. Res. 49, 4687–4699. https://doi.org/10.1002/wrcr.20350

Figure 1. Location of the Paraná River Basin (until the point of interest), major rivers of the region.

Figure 2. MAE of the precipitation throughout the forecast horizon, for the study locations.

Figure 3. Visual analysis of sampled sub seasonal streamflow forecasts at Itaipu HPP. On the left the S2S-based; on the right the ESP-based. The blue line refers to the streamflow benchmark, red line is the control member of the ensemble, gray line is an ensemble member and dashed black line is the ensemble mean.

Figure 4. Evolution on the lead time up to 46 days of the MAE and CRPS for the forecasts issued.

28

Figure 5. RMSE on all locations, the figure shows that the error tends to increase as the drainage area of the location decreases.

Figure 6. Rank Histograms indicating a lack of spread in early lead times. This behavior is akin to the other locations along the main river of the basin (Paraná River) – Porto Primavera, Jupiá and Água Vermelha.

Figure 7. Rank Histograms indicating right from initial time step a tendency towards overestimation on the forecast streamflow.

Figure 8. Rank Histograms indicating lack of spread in early lead times, but a tendency towards overestimation (positive bias) along the development of the forecast.

Figure 9. Mean Continuous ranked probability skill score (MCPRSS) for the sub seasonal based forecasts against ESP as reference.

Figure 10. Mean Absolute Error (MAE) normalized with long-term average for each individual unit-catchment, on top left is sampled lead time 1, top right is lead time 14, bottom left is lead time 28 and bottom right is lead time 42.

   

A first statistical assessment of sub seasonal streamflow forecast in a tropical large-scale basin; First assessment of data from S2S database for hydrological forecasting in South American context; The statistical performance of sub seasonal streamflow forecasts outcome is spatio-temporal dependent; Sub seasonal QPF-based streamflow forecasts outperformed the ESP in most locations;

Table 1. Performance of MGB model on the study case dams in the calibration and validation periods.

Location Água Vermelha Barra Bonita Furnas Itaipu Jupiá Porto Primavera

Calibration (1975-1995) NS log-NS dV(%) 0,85 0,83 -10,10 0,76 0,67 5,30 0,81 0,82 -9,90 0,86 0,85 -2,80 0,87 0,85 -3,50 0,86 0,82 -3,60

Verification (1995-2010) NS log-NS dV(%) 0,85 0,88 -6,10 0,76 0,75 -6,50 0,84 0,87 -2,50 0,85 0,85 -3,90 0,87 0,88 -2,70 0,88 0,87 -1,50

29

Table 2. Summary of the hydrological forecast experiments.

Simulation Experiment

Frequency

ECMWF ensemble ECMWF control ESP ensemble "Perfect Rainfall"

Tuesdays and Thursdays Tuesdays and Thursdays Tuesdays and Thursdays Everyday

Input data ECMWF 51-member ensemble ECMWF control member MSWEP 20-member ensemble of past observations MSWEP

Table 3. Description of the study locations and respective drainage area. Study Sites

Drainage Area (km²)

Itaipu

827,000

Porto Primavera

574,000

Jupiá

479,000

Água Vermelha

139,000

Furnas

52,000

Barra Bonita

33,000

Abstract: The sub seasonal forecast horizon, with lead-times up to 7 weeks, has a number of possibilities for operational applications. This sub seasonal time scale is only recently motivated for research on applications, as it is often recognized as being in the gray zone of predictability in both meteorological and hydrological sciences. This work is one of the first assessments of ensemble sub seasonal meteorological inputs to large-scale basin hydrological modelling within a tropical climate – where it could benefit hydropower generation. The quantitative precipitation forecast (QPF) data were provided by the European Centre for Medium-Range Weather Forecasts (ECMWF), within the sub seasonal-to-seasonal (S2S) project’s context. To assess the quality of the forecasts, a statistical evaluation was performed, including a comparison with the traditional extended streamflow prediction (ESP) technique. Results allowed for an estimation of the error

30

magnitudes and the potential to the benefit of the ensemble over the deterministic reference forecast and the ESP approach. We showed that the sub seasonal QPF-based forecasts have advantages over the ESP, although, generally their skill deteriorates in lead times after day 30. The evaluation across multiple locations considering drainage area and hydrometeorological conditions, suggests that the statistical performance outcome is also spatio-temporal dependent. Keywords: Sub seasonal streamflow forecasting; S2S; MGB-IPH model

ERIK SCHMITT QUEDI: Writing original draft, Conceptualization, Formal Analysis and Investigation. FERNANDO MAINARDI FAN: Supervision, Conceptualization and Writing – Review & Editing. Declaration of interests

☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

31

32

33

34

35

36