# Advancing Medium-Range Streamflow Forecasting for Large Hydropower Reservoirs in Brazil by Means of Continental-Scale Hydrological Modeling

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

## 3. Study Area

#### 3.1. Observed Streamflow Data

#### 3.2. Streamflow Forecasts

#### 3.2.1. Forecast Input Data and Hydrological Model

#### 3.2.2. Quantile Mapping Applied to Streamflow Forecasts

_{o}is the inverse of the CDF of the observed discharge, F

_{s}is the CDF of the simulated discharge, and Z

_{i}is the raw forecast ensemble trace.

#### 3.2.3. Autoregressive Model (AR)

_{t}) is defined as a combination of past values of the time series itself plus a random noise (ε

_{t}), where t is the time index. Thus, in the AR

_{(p)}model, where p is the order of the model, one has as input the past values Q

_{t}

_{−1}, Q

_{t}

_{−2}, …, Q

_{t}

_{−p}, multiplied by optimized parameters α to predict the next value Q

_{t}. In Equation (2), an example is given of what an AR-only model would look like:

#### 3.3. Operational Forecasts from the Brazilian National Electric Service Operator (ONS)

#### 3.4. Forecast Assessment

_{75}of non-exceedance flows) and moderate to low discharges (<Q

_{50}), as well as in terms of characteristics such as streamflow seasonality and flashiness (Appendix A).

_{i}and Fcst

_{i}are the observed and predicted discharges, respectively, and i and N are the current and total number of forecasts.

_{i}(x) is the CDF of the forecast ensemble x and forecast day i, 1(x ≥ y

_{i}) is a Heaviside step function that equals one when forecast values are greater than the observed value y

_{i}and zero otherwise, and N is the total number of forecasts.

_{fcst}/CRPS

_{benchmark}) using both daily streamflow climatology and persistence as benchmarks. Streamflow climatology was computed for each calendar day by sampling 50 equally distanced quantiles (1/51, 2/51, 3/51, …, 50/51) from the empirically observed CDF, that is, the same number of ensemble members as the MGB-ECMWF, since the number of ensemble members is known to affect the CRPS value [67]. In turn, for the persistence, it is assumed that all forecast lead times have the same predicted value equal to the last observed discharge (i.e., a deterministic forecast), so the CRPS reduces to the mean absolute error [66]. Maximum skill is achieved when CRPSS = 1, and values below 0 indicate no skill.

_{i}and Fcst

_{i}are the observed and predicted discharges, respectively; i and N are the current and total number of forecasts, and $\underset{\_}{{Obs}_{i}}$ is the mean of observed values.

## 4. Results

#### 4.1. Skill Assessment of Raw and Corrected Continental-Scale Streamflow Forecasts

_{clim}) and persistence (CRPSS

_{pers}) as benchmarks, and the results were conditioned on high (>Q

_{75}of non-exceedance) (Figure 6) and low to moderate (<Q

_{50}) flows (Figure 7). For high flows and a lead time of 1–7 days, both the raw forecasts and the QM exhibit positive skill relative to persistence in 72% of the HPPs, which increases to 94% after applying the QM+AR corrections. For the 8–15-day lead time, raw MGB-ECMWF forecasts already show significant positive CRPSS

_{pers}for the majority of SIN locations (>90%), and the overall skill improvement by using QM or QM+AR correction is relatively small. When compared to climatology (8–15 days ahead), the raw forecasts exhibit positive skill in 70% of the HPPs, and performance increases slightly for the QM (77%) and QM+AR (87%) configurations, while for the lead time of 1–7 days, the patterns of skill are similar to those observed against persistence.

_{pers}> 0 after applying the QM method, despite the substantial performance gain over the no correction configuration. Even when both correction approaches (QM+AR) are used, MGB-ECMWF forecasts exhibit positive skill in only 56% of the HPPs, which indicates difficulty in overcoming a naive forecast. For 8–15 days in advance, the percentage of HPPs where forecasts exhibit positive skill relative to persistence (climatology) improves from 29% (69%) to 64% (91%) and 76% (96%) for the QM and QM+AR configurations, respectively.

_{50}) and high (>Q

_{75}, no exceedance) flows. In general, the results relative to climatology and persistence are similar. For higher flows, skill improvements are larger (ΔCRPSS > 1) for flashiness usually lower than 0.1 (i.e., rapid day-to-day discharge variations) regardless of seasonality, but in some HPPs, larger skill gains can be observed for flashiness values closer to 0.2 and a seasonality index around 5 (moderate seasonality). For flashiness larger than 0.2, smaller performance gains are obtained (ΔCRPSS < 0.3). For low to moderate flows, ΔCRPSS > 1 is observed even in locations where rapid flow variations may occur (flashiness ~0.5), but with some degree of seasonality.

#### 4.2. Comparison between Continental-Scale and ONS Operational Streamflow Forecasts

## 5. Discussion

## 6. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

#### Appendix A.1. Seasonality Index (SI)

#### Appendix A.2. Richard-Baker Flashiness Index (RBI Index)

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**Figure 1.**Flowchart of the methodology used in this study, highlighting the two experiments, which are demarcated by the dashed lines in red and light blue.

**Figure 2.**Locations of the 147 Hydroelectric power plants of the SIN for which forecasts were evaluated.

**Figure 3.**Typical schedule of forecast generation for Monthly Operation Programs (PMO) and their weekly revisions. Forecast issue dates for a given PMO/revision are indicated by the corresponding-colored boxes. Source: adapted from [55].

**Figure 4.**Forecasts of average weekly flow (ensemble mean) for the lead time of 1–7 days at (

**a**) Pedra do Cavalo, (

**b**) Itaipu, (

**c**) Itá, (

**d**) Tucuruí, (

**e**) Euclides da Cunha, and (

**f**) Furnas hydropower plant.

**Figure 5.**Percent bias of MGB-ECMWF streamflow forecasts for raw, bias correction (QM), and bias correction + updating (QM+AR) configurations. The relative frequency refers to the number of SIN hydropower plants falling into each category. The graphs show results for the lead times of (

**a**) 1–7 and (

**b**) 8–15 days.

**Figure 6.**CRPS skill of MGB-ECMWF forecasts for the raw, bias correction (QM), and bias correction + updating (QM+AR) configurations, considering only high flows (>Q

_{75}of non-exceedance flows). The gray dashed horizontal line denotes skill = 0.

**Figure 7.**CRPS skill of MGB-ECMWF forecasts for the raw, bias correction (QM), and bias correction + updating (QM+AR) configurations, considering only low to moderate flows (<Q

_{50}, non-exceedance flows). The gray dashed horizontal line denotes skill = 0.

**Figure 8.**Difference in CRPS skill between raw and corrected forecasts with bias correction + updating (QM+AR) MGB-ECMWF forecasts according to streamflow seasonality and flashiness. Results are shown for low to moderate (<Q

_{50}) and high (>Q

_{75}of non-exceedance) flows and lead times of 1–7 and 8–15 days.

**Figure 9.**Comparison of forecast performance (MGB-ECMWF × ONS) for 1 week in advance, according to season.

**Figure 10.**Multicriteria Distance (MD) differences between ONS and MGB-ECMWF forecasts (May 2015–Dec 2020) for 1 week in advance, according to the installed capacity of the SIN hydropower plants. Positive differences represent better overall performance of the continental-scale forecasts.

**Figure 11.**Spatial patterns of Multicriteria Distance differences (ΔMD between ONS and MGB-ECMWF forecasts (May 2015–December 2020) over SIN locations. Positive differences represent better overall performance of the continental-scale forecasts.

**Figure 12.**Year-to-year performance comparison between MGB-ECMWF and ONS streamflow forecasts for 1 week ahead over the verification period. The graphs show the median and the 25–75% range of performance considering the 147 SIN hydropower plants and are presented for (

**a**) NSE, (

**b**) MAPE, and (

**c**) Multicriteria Distance (MD) metrics.

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## Share and Cite

**MDPI and ACS Style**

Kolling Neto, A.; Siqueira, V.A.; Gama, C.H.d.A.; Paiva, R.C.D.d.; Fan, F.M.; Collischonn, W.; Silveira, R.; Paranhos, C.S.A.; Freitas, C.
Advancing Medium-Range Streamflow Forecasting for Large Hydropower Reservoirs in Brazil by Means of Continental-Scale Hydrological Modeling. *Water* **2023**, *15*, 1693.
https://doi.org/10.3390/w15091693

**AMA Style**

Kolling Neto A, Siqueira VA, Gama CHdA, Paiva RCDd, Fan FM, Collischonn W, Silveira R, Paranhos CSA, Freitas C.
Advancing Medium-Range Streamflow Forecasting for Large Hydropower Reservoirs in Brazil by Means of Continental-Scale Hydrological Modeling. *Water*. 2023; 15(9):1693.
https://doi.org/10.3390/w15091693

**Chicago/Turabian Style**

Kolling Neto, Arthur, Vinícius Alencar Siqueira, Cléber Henrique de Araújo Gama, Rodrigo Cauduro Dias de Paiva, Fernando Mainardi Fan, Walter Collischonn, Reinaldo Silveira, Cássia Silmara Aver Paranhos, and Camila Freitas.
2023. "Advancing Medium-Range Streamflow Forecasting for Large Hydropower Reservoirs in Brazil by Means of Continental-Scale Hydrological Modeling" *Water* 15, no. 9: 1693.
https://doi.org/10.3390/w15091693