Dynamical-statistical downscaling of seasonal hindcasts of temperature and precipitation over South America

Downscaling dinâmico-estatístico de previsões sazonais de temperatura e precipitação para a América do Sul

Abstract

This study aimed to evaluate the performance of the Eta Regional Climate Model in reproducing the seasonal climate over South America for the rainy season from November until April, with emphasis on the Madeira, São Francisco, and Paraná river basins. For this purpose, a 10-year set of 6-month range seasonal hindcasts was produced using the Eta Regional Climate Model at 20-km horizontal resolution driven by the CFSv2 forecasts. In addition to dynamical downscaling, the precipitation and 2-meter temperature were statistically downscaled by applying a Quantile Mapping bias correction. The Eta model forecasts reasonably reproduced the precipitation and temperature patterns in the region, with some errors that were reduced by the statistical downscaling. Precipitation skill scores are higher in the northern and central areas of the continent. Although it has shown mixed performance for extreme events—low in the Paraná basin and limited but useful in the Madeira and São Francisco basins—the dynamical-statistical system developed with the Eta model shows higher skill and added value over the driver model, indicating potential to support water resources management in South America.

Keywords:
Bias correction; Climate extremes; Brazilian river basins; Forecast errors; Eta model

Resumo

Este estudo avaliou o desempenho do Modelo Climático Regional Eta em reproduzir o clima sazonal na América do Sul, com foco nas bacias dos rios Madeira, São Francisco e Paraná. Para isso, foi construído um conjunto de previsões climáticas sazonais retrospectivas de dez anos, com horizonte de previsão de seis meses na resolução horizontal de 20 km, forçadas pelas condições de contorno lateral do modelo CFSv2. Além do downscaling dinâmico, as saídas de precipitação e temperatura a 2 metros passaram por um downscaling estatístico através da aplicação de correção de viés. Os resultados indicaram que o modelo Eta conseguiu reproduzir de forma razoável os padrões de precipitação e temperatura na região, com alguns erros que foram reduzidos pelo downscaling estatístico. As métricas de avaliação mostraram maior desempenho das previsões nas regiões norte e central do continente. Embora tenha mostrado desempenho misto para eventos extremos—baixo na bacia do Paraná e limitado, mas útil, nas bacias do Madeira e São Francisco—o sistema desenvolvido com o modelo Eta demonstra maior habilidade e valor agregado em comparação ao modelo condutor, indicando potencial para apoiar a gestão de recursos hídricos na América do Sul.

Palavras-chave:
Correção de viés; Extremos climáticos; Bacias hidrográficas brasileiras; Erros de previsão; Modelo Eta

INTRODUCTION

Seasonal climate forecasts have become increasingly useful and sought for planning a season ahead for application in various sectors, such as agriculture, water supply, energy generation, and disaster risk management (Mariotti et al., 2018; Endris et al., 2021).

Different weather systems occur over South America, such as cold fronts, the South Atlantic Convergence Zone (SACZ), the Intertropical Convergence Zone (ITCZ), and convective clusters. The Andes Mountains, positioned along the western part of the continent, and the Amazon Forest are both large-scale features that affect those weather systems.

Accurate climate reproduction requires numerical models capable of representing the complexity of topography and atmospheric convective processes. By providing a more detailed description of physical processes and forcings on a regional scale, high-resolution regional climate models (RCMs) reduce the limitations of global models and are more suitable tools for local studies on water balance (World Meteorological Organization, 2012). In this regard, the Eta RCM has produced seasonal forecasts over South America and reproduced the seasonal variability of precipitation and temperature in the region (Bustamante et al., 2006; Chou et al., 2005, 2020). In addition, the model has been widely used in studies of extreme weather events (Ferreira & Chou, 2018) and for climate change studies (Pesquero et al., 2010; Chou et al., 2012, 2014a, 2014b; Dereczynski et al., 2020).

The predictability at the seasonal scale is significantly influenced by sea surface conditions, particularly in tropical regions (Shukla, 1998). The interaction between the atmosphere and the ocean, especially through Walker and Hadley cells, plays a crucial role in modulating seasonal climate variability. However, despite significant advances, climate models still present simplifications and limitations (White et al., 2017) in representing sea surface conditions and, consequently, the model produces errors in climate simulations. Forecast skill varies according to latitude, season, and the type of prevailing climate system. The presence of systematic biases in forecasts requires careful assessment to ensure the reliability of the information generated. Persistent systematic errors can ruin the usefulness of seasonal forecasts in their various applications.

As for water resources, three major river basins play crucial roles in hydropower production, agriculture irrigation, and water supply: the Madeira River, a main tributary of the Amazon River, the Sao Francisco River in Northeast Brazil, and the Parana River in the most populated area in the region. Due to the various water uses in these basins, in years of extreme climate events such as droughts, water use conflicts escalate. Accurate climate forecasts at a seasonal scale can help plan the management of water resources and reduce water conflicts. Therefore, the addition of the step of bias correction (Preston & Dietz,1991; Teutschbein & Seibert, 2012) is crucial for producing more accurate and useful forecasts for the various socio-economic sectors.

Here, we investigate how useful high-resolution seasonal climate forecasts are for water resources management, with emphasis on three major river basins in Brazil: the Madeira, the São Francisco, and the Paraná river Basins. The assessments are based on a dataset of retrospective forecasts, known as hindcasts or reforecasts. Thus, it is important to clarify that, although we may use the term ‘forecasts’ in a general sense throughout this paper, we refer exclusively to hindcasts — forecasts generated from past data to assess the predictability of the regional Eta model. To ensure consistency between the hindcasts and the actual forecasts currently generated by the model, the hindcasts are produced using the same modeling system employed in the real-time forecasts.

The paper is organized as follows: In the Data and Methodology Section 2, the study area and the river basins are described. Then, the Eta Regional Climate Model is briefly described. The construction of the set of past forecasts, the hindcasts, is explained, as is the bias correction methodology. The results are discussed in Section 3, and finally, Conclusions are drawn in Section 4.

DATA AND METHODOLOGY

Study area

The model domain covers the entire South America, within about 55°S and 10°N and 85°W and 25°W (Figure 1). The Andes Mountains are a narrow and high topographic feature running along the western part of the continent, and the Brazilian High Plains are on the eastern part of the continent. The precipitation regime in this region is mostly controlled by the longitudinal displacement of the ITCZ band, the frontal intrusions, subtropical cyclones, the establishment of the South Atlantic Convergence Zone, mesoscale squall lines, and convective systems (Uvo et al., 1998; Quadro, 1999, Carvalho et al., 2004; Salio et al., 2007; Cavalcanti & Kousky, 2009; Reboita et al., 2012; Ambrizzi & Ferraz, 2015; Tomaziello et al., 2016; Ferreira & Reboita, 2022; Laureanti et al., 2024a). At subseasonal and seasonal time scales, the precipitation regime in the tropical part of this region can also be modulated by the Madden-Julian Oscillation (MJO) (Carvalho et al., 2002, 2004; Souza & Ambrizzi, 2006; Fernandes & Grimm, 2023), and the ENSO (El Nino Southern Oscillation; Grimm et al., 1998, 2000; Grimm & Tedeschi, 2009; Cai et al., 2020), and sea surface temperature anomalies in northern and southern Atlantic Ocean (Los et al., 2001; Ronchail et al., 2002; Chen et al., 2011).

Figure 1
Topography of the South America study area, with three major river basins contoured according to the Brazilian National Water Agency (ANA) (Agência Nacional de Águas, 2018). Digital Elevation Map - SRTM 3 Arc-Second (90 m) in shaded (Jarvis et al., 2008).

The extreme precipitation events are identified in three major Brazilian river basins: (1) the Madeira River basin; (2) the Sao Francisco; and (3) the Paraná, as highlighted in Figure 1. The selection of these three basins is based on their strategic significance in energy generation, crop irrigation, transportation, and freshwater supply in Brazil. The Madeira River basin extends across Bolivia, Peru, and Brazil. It is the major tributary of the southern portion of the Amazon Basin, covering 23% of its total area, which represents 1.3 million km². In addition to its socioeconomic relevance, biodiversity conservation stands out, such as the Madeira River Sustainable Development Reserve (MSDR), which is home to endemic species vulnerable to anthropic activities. The Sao Francisco River Basin lies in the eastern part of Brazil. The river runs from the elevated Brazilian High Plains toward the Semiarid region of Northeast Brazil. Its waters are subject to major disputes due to several uses, such as hydroelectric generation, agriculture, irrigation, tourism, and water supply. The disputes are aggravated in this basin in years of severe droughts. The Parana River Basin lies in Southeast and South Brazil, where the largest hydropower in South America, most populated, and intense economic activities are found, therefore water demand is extremely high (Agência Nacional de Águas, 2015; Soares et al., 2008).

The Eta model

The Eta is a regional model originally developed at the University of Belgrade for weather forecasts (Mesinger et al., 1988). The model has been improved and since 2002 has been used for climate predictions over South America by the Brazilian National Institute for Space Research (INPE) (Chou et al., 2005, 2020). The distinctive feature of the model, which gives it its name, is the use of the vertical coordinate eta (ƞ) (Mesinger, 1984). The approximately horizontal surface of this coordinate is a feature suitable for simulations in regions with complex topography, such as the Andes Mountains. Because the topography is represented in the form of discrete steps, errors in the calculation of horizontal derivatives are reduced, especially pressure gradient forces near mountains. To account for sloping flow near mountains, cut-cell features were added to the Eta model topography (Mesinger et al., 2012; Mesinger & Veljovic, 2020).

The model dynamics are based on finite volume discretized on the E-grid (Mesinger et al., 2012). Model physics includes major processes. Deep and shallow convections are parameterized by the Betts-Miller-Janjic scheme (Janjić, 1994). Cloud microphysics follows Ferrier's scheme (Ferrier et al., 2002). Radiative fluxes are treated by the Lacis-Hansen scheme (Lacis & Hansen, 1974), for short waves, and the Fels-Schwarzkopf scheme (Fels & Schwarzkopf, 1975) for long waves. The surface layer is based on the Monin-Obukhov similarity theory and Paulson stability functions (Paulson, 1970). The model resolves turbulent mixing in the atmosphere using the Mellor-Yamada level 2.5 turbulence closure scheme (Mellor & Yamada, 1982). Biosphere-atmosphere interaction processes are represented by the NOAH continental surface scheme (Ek et al., 2003), with 16 vegetation types, 15 soil classes, and 8 soil layers (Pilotto et al., 2012). Recent updates introduced to the model can be found in Gomes et al. (2023).

Seasonal hindcasts

The seasonal hindcasts are produced from the Eta model seasonal runs over South America. The Eta model is driven by the coupled ocean-atmosphere global climate model, the Climate Forecast System, version 2 (CFSv2) model (Saha et al., 2014) for the period between 2013 and 2022. The horizontal resolution is 20 km, and the vertical resolution is 38 levels. The lateral boundary conditions are updated every 6 hours from CFSv2 variables: zonal and meridional wind, air temperature, specific humidity, and surface pressure, at 1° x 1° resolution. Sea surface temperature (SST) is prescribed from CFSv2 forecasts, and it is updated daily as the lower boundary condition. Over the land, soil temperature and moisture are initialized from CFSv2 initial conditions. The integration length is 6.5 months. The initial 0.5 months of output are discarded, and the last 6 months are used as seasonal forecasts. Here, we focus on the hindcasts produced for the November-December-January-February-March-April (NDJFMA) season between 2013 and 2022. This is the rainy season in most of South America.

Additionally, it is important to highlight that, in addition to the updates in the Eta model code, as presented in Gomes et al. (2023), the seasonal hindcasts discussed in this paper differ from the previous version (Chou et al., 2020) mainly in several aspects. The horizontal resolution was improved from 40 km to 20 km, and the integration length increased from 4.5 months to 6.5 months. In addition, there was a change in the driver model used in the runs, which is now CFSv2, instead of CPTEC-T62L28. The period considered for the construction of the dataset was also changed, from 2001-2010 to 2013-2022. Another relevant aspect is the approach in reading the lower boundary conditions, such as SST. In the previous version, the SST used was consistent with the adopted global model (CPTEC-T62L28), which considered persisted SST anomalies throughout the integration. In the current version, as mentioned earlier, daily updated SST values are used.

Bias correction

Bias correction is essential for improving the accuracy of climate forecasts. The systematic errors of the model can lead to significant errors in long-term forecasts. In this study, bias correction was applied to the forecasts using the Empirical Quantile Mapping (EQM) approach (Bárdossy & Pegram, 2011). Among bias correction techniques, the EQM method is particularly suitable for removing errors not only in the mean but also in the variance and frequency of events. A strength of the EQM is its flexibility, as it does not require specific distributional assumptions, making it suitable for a variety of data sets. The method involves constructing cumulative distribution functions (CDFs) from daily observational and model data separately for each grid point and month. The underlying principle is that aligning the CDFs of simulations with those of observations can effectively reduce systematic biases.

The bias correction of the hindcast used the ERA5 reanalysis (Hersbach et al., 2020) to correct the 2-m temperature forecasts, and the Multi-Source Weighted-Ensemble Precipitation (MSWEP; Beck et al., 2017) to correct precipitation forecasts. ERA5, with its horizontal resolution of 0.25° × 0.25° (about 25 km), stands out as one of the atmospheric reanalysis sets with the highest spatial resolution currently available. Although an even higher resolution dataset, ERA5-Land (Muñoz-Sabater et al., 2021), has been developed, comparative evaluations with in situ observations have indicated that ERA5 demonstrates superior performance in capturing seasonal variability, especially over the Amazon and Northeast Brazil. Due to its quality and reliability, ERA5 reanalysis has been widely used to correct and improve seasonal forecasts from other numerical models (Lorenz et al., 2021; Johnson et al., 2019). The MSWEP dataset is built from precipitation information from rain gauge stations, satellite products, and atmospheric reanalysis. It has global coverage at a horizontal resolution of 0.1° × 0.1° (∼ 10 km) and a daily temporal resolution. The excellent performance of MSWEP relative to other satellite products and in situ data makes it the ideal choice for studies requiring high spatial resolution in precipitation data (Sun et al., 2018; Moreira et al., 2019; Brêda et al., 2022). For this reason, it was used to correct the Eta model outputs. The datasets used as observational reference were interpolated to the same horizontal resolution and domain as the hindcast. The bilinear method was used for horizontal interpolation.

Identification of precipitation extremes

The identification of extreme precipitation events may vary according to the choice of the observational precipitation dataset. The uncertainty among the precipitation estimates is large. Different observational precipitation estimates have been shown to exhibit significant variations in spatial distribution, both at regional and global scales (Prein & Gobiet, 2017; Gibson et al., 2019; Kotlarski et al., 2019; Pathak et al., 2023). These differences can be attributed to several sources of uncertainty, such as the quality and coverage of in situ observations, which are lacking in South America; the limitations of the interpolation methods used in generating gridded products; restrictions on precipitation retrieval methods from satellite observations and discrepancies among the climate models that produced the atmospheric reanalysis.

A strategy to minimize these uncertainties is to use more than one observational precipitation dataset or combined products (in situ + satellite data, reanalysis + satellite, etc.). Here, 12 different datasets of precipitation estimates are organized in the same grid, resolution, domain, and time span as the Eta model hindcast. Table 1 describes the datasets used. It was decided to estimate the monthly values using the data median instead of the mean to minimize the influence of extreme values (outliers) and obtain a more robust representation of the precipitation patterns. It is anticipated that this approach will allow for a more reliable identification of years characterized by extreme climatic conditions, whether due to excess or deficit of precipitation.

Table 1
Description of selected precipitation datasets.

Datasets	Spatial resolution	Spatial coverage	Reference
1. BR-DWGD (Brazilian Daily Weather Gridded Data)	0.1°	Brazil	Xavier et al. (2022)
2. CHIRPS (Climate Hazards Group InfraRed Precipitation with Station data)	0.05°	Quasi-global (50° S-50 °N)	Funk et al. (2015)
3. CMAP (CPC Merged Analysis of Precipitation)	2.5°	Global	Xie et al. (2003)
4. CMORPH-CDR (Climate Prediction Center Morphing technique dataset - Climate Data Record)	0.25°	Global	Xie et al. (2017)
5. CPC (NOAA Climate Prediction Center datasets)	0.5°	Global	Xie et al. (2010)
6. CRUv4 (Climatic Research Unit dataset, version 4)	0.5°	Global	Harris et al. (2020)
7. GPCC (Global Precipitation Climatology Centre dataset)	1°	Global	Schneider et al. (2016)
8. GPCP (Global Precipitation Climatology Project)	2.5°	Global	Adler et al. (2012)
9. MERGE	0.1°	South America	Rozante et al. (2010)
10. PERSIANN-CDR (Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks - Climate Data Record)	0.25°	Quasi-global	Ashouri et al. (2015)
11. PREC/L (Precipitation Reconstruction over Land)	1°	Global	Chen et al. (2002)
12. TerraClimate	0.04°	Global	Abatzoglou et al. (2018)

To assess model skill in reproducing extreme precipitation events, the Standardized Precipitation anomalies Index (SPI; McKee et al., 1993) was calculated. This index quantifies the standard deviations that precipitation diverts from the climatological mean. Here, the years in which the anomalies were greater than or equal to 0.5 were classified as rainy years, and the years with anomalies less than or equal to -0.5 were classified as dry years. Therefore, standardization is similar to a SPI06 calculated for the months of November to April. The climatological period used was the same as adopted in previous subsections, that is, from 2013 to 2022.

Evaluation metrics

Forecast pattern errors are obtained by subtracting the seasonal mean of the observations (O) from the seasonal mean of the forecasts (F), $F-O$. The error patterns reveal areas where forecasts overestimate or underestimate the climate variable.

A common metric in seasonal forecasts is the skill score, which is the temporal correlation between the forecasts' anomalies and the observations' anomalies. The anomalies are calculated based on a climatological mean for the period from 2013 to 2023.

In addition to the evaluations for the entire forecast period (six months), analyses were performed considering moving quarters of the one-, two-, three- and four-month forecast lead times. These lead times correspond, respectively, to the months of November to January (NDJ), December to February (DJF), January to March (JFM), and February to April (FMA). Therefore, evaluating the performance of the Eta model and providing early forecasts for these basins, with a margin of six months analyzed here, paves the way for the implementation of measures that can reduce adverse impacts caused by periods of extreme above or below-average rainfall.

Additionally, the mean error (ME), the mean absolute error (MAE), the root mean square error (RMSE), and the Willmott concordance index (d) were calculated for forecast evaluation.

RESULTS AND DISCUSSION

Mean precipitation pattern

Figure 2 shows the average of ten years of precipitation hindcasts for the 6-month season, NDJFMA, and 3-month seasons from hindcasts of different month-lead times: NDJ, DJF, JFM, and FMA. The raw and bias-corrected forecasts, as well as the remaining errors, are shown.

Figure 2
Observed (column a) and forecasted 3-month (rows 1 - 4) and 6-month (row 5) precipitation (mm/day) by the Eta Regional Climate Model (Eta RCM), without (raw) (b) and with bias correction (bc), for the period 2013-2023; and Mean Errors (ME) of the Eta model forecasts without (d) and with bias correction.

Between November and April, South America is marked by a precipitation band that extends from the Amazon region through Southeast Brazil towards the South Atlantic Ocean, known as the South Atlantic Convergence Zone (SACZ) (Figure 2, leftmost column). The average precipitation rate in this band is about 6 to 8 mm/day and over 8 mm/day in the Amazon region. The SACZ is part of the South American Monsoon System (SAMS) and, therefore, responsible for rainfall during the rainy season in most of Central and Southeast Brazil (Kodama, 1992, 1993; Liebmann et al., 1999; Quadro, 1999; Ambrizzi & Ferraz, 2015; Nielsen et al., 2019). The northern part of South America is marked by the precipitation band of the Intertropical Convergence Zone (ITCZ), where average precipitation exceeds 8 mm/day.

The raw (without bias correction) seasonal precipitation hindcasts generally agree well with the observed precipitation pattern. However, a systematic excess of precipitation is shown along the ITCZ over the Pacific and Atlantic oceans, where a double band can be noticed, especially during DJF and JFM seasons. The double ITCZ band contributes to the precipitation overestimate over Northeast Brazil. The coupled ocean-atmosphere models commonly reproduce a double band of precipitation in the ITCZ (Lin, 2007; Zhang et al., 2015; Si et al., 2021; Respati et al., 2024). The hindcasts of the rainy season produced by the Eta model driven by the CPTEC Coupled Ocean-Atmosphere Model also showed this double band of the ITCZ over the Atlantic Ocean (Pilotto et al., 2023). This version of the Eta model shows improvement over the previous version (Chou et al., 2020) when precipitation underestimates, for example, in NDJ occurred in most of the continent.

The model's skill to predict the intensity and positioning of the ITCZ is closely related to the quality of the SST used to integrate the regional model (Misra, 2004; Pilotto et al., 2012; Chou et al., 2020). Pilotto et al. (2012) compared the Eta model hindcasts driven by the CPTEC global atmospheric model against the hindcasts driven by the CPTEC global coupled ocean-atmosphere model. They attributed the double ITCZ band over the Atlantic Ocean to a systematic cold bias in the SST predicted by the global coupled model.

This erroneous double ITCZ band over the Atlantic Ocean has also been identified in studies by Misra (2004) using the Regional Spectral Model (RSM). The persistence of these errors in downscaling runs, as identified in the current study, suggests that the double band in the ITCZ over the Atlantic Ocean is inherited from the boundary conditions, where the precipitation error pattern of the RCM is also found in the driver model (see Figure S1 of the Supplementary Material).

Despite agreeing with the observations on the continent, the Eta hindcasts systematically overestimate rainfall along the coast and parts of southern Brazil and underestimate it in the Amazon, central Brazil, and northern Argentina. The causes of these biases are complex. They can be associated both with the rain production parameterization schemes (convective and microphysics) of the model and with the boundary conditions provided by the driver model. Another source of the overestimated error may be related to the stronger winds from the driver model as was noticed when the RCM run was driven by CPTEC/T062/L28 global model (Chou et al., 2005).

Although the Eta model may inherit the driver model ́s biases, the downscaling from the Eta forecasts significantly reduces precipitation biases, mainly in the northern portion of South America (Figure S1). It is noteworthy that the application of bias correction significantly reduces the systematic errors of the hindcast ensemble to errors between -0.5 and +0.5 mm/day in most parts of the model simulation area, thus contributing to increasing the degree of reliability of the forecasts (Figure 2). Additionally, unlike forecasts without bias correction, where the model performance declines and the errors increase over time, the bias-corrected ensemble maintains the errors in the same order of magnitude, even at longer time ranges. This means that the model can provide reasonably reliable information even at long-term ranges, as demonstrated in the average for the entire half-year of the model run (NDJFMA).

Mean 2-m temperature pattern

Temperature is a key variable as it is used for the calculation of evapotranspiration, a component of the water budget. The 2-m temperature pattern from the SaMET observational data (Figure 3) shows a strong relation with relief and latitudinal gradients. Steep mountain regions such as the Andean Mountain Range and the Mountain Range between the coastline and the continental plateau (Sea Mountain) present reduced intrinsic temperatures during the entire year. Considering the 10-year data, we notice the high mean annual temperatures in northern Argentina and western Paraguay, as well as in northern and Northeast Brazil.

Figure 3
Observed (column a) and forecasted 3-month (rows 1 - 4) and 6-month (row 5) 2-m temperature (°C) by the Eta Regional Climate Model (Eta RCM), without (raw) (b) and with bias correction (bc), for the period 2013-2023; and Mean Errors (ME) of the Eta model forecasts without (d) and with bias correction (e).

The Eta hindcast simulations reproduce the spatial and seasonal variability of the 2-m temperature (Figure 3). Before the bias correction, the temperature forecasts showed significant negative errors, up to -6 °C, on the entire western coast of South America, mainly over the Andean Mountains and Patagonia. Smaller mean errors (up to -2 °C) are shown near the coast in Northeastern Brazil. In the central part of South America, the mean error is predominantly positive and varies between 1 °C, in the Amazon between 2 and 3 °C, and in the Brazilian Center-West, almost 6 °C in the Mato Grosso do Sul State, around the latitude 20 °S and longitude 60 °W. In comparison with the previous version (Chou et al., 2020), where errors were predominantly negative, the current Eta 2-m temperature errors have changed signs to mostly positive. Several model components can be responsible for the forecast errors, especially the parameterization of land-surface interactions, the surface-layer fluxes, and the convective clouds. As an example of an error source, the Pantanal wetland and its seasonal flooding process are not represented in the model.

Various model uncertainties justify using bias correction as a resource to improve the quality of the forecasts delivered to users. After the bias correction, the 2-m temperature ME was significantly reduced, and it may even have overshot the ITCZ area as the error sign has changed.

The mean errors from the raw simulations (Figure 3, fourth column) have a similar pattern from one season to the other. The largest positive errors are around 20 °S and 60 °W, which is around Paraguay and the Brazilian State of Mato Grosso do Sul, throughout the season. The warm bias in this area has been identified in other RCM models (Solman et al., 2013). Negative mean errors are found along the western coast and over the Patagonian region. These errors clearly show as systematic throughout the seasons. After the bias corrections, the ME has significantly been reduced. The ME that previously varied from -2 °C to +2 °C were practically removed. The remaining temperature errors are more noticeable along the western coast with ME around -1 °C and on the eastern part of South America with ME around 1 °C.

The model integration is stable as the ME does not show any growth; actually, there is a slight decrease with the forecast time. The range of the ME in the last quarter (FMA) is similar to the first quarter, indicating a fair skill in the six months of simulation.

Given the significant improvement in the quality of 2-m temperature and precipitation forecasts, as shown in the previous subsection, the following sections exclusively present the results of the bias-removed dataset. This approach aims to highlight the positive impact of the correction technique and facilitate the analysis of more reliable results.

Precipitation skill score

The skill score is an evaluation of the model's capability in forecasting the climate interannual variability, which is calculated as the temporal correlation between the observed and forecasted anomalies from the time series of each model grid box. The forecast time series are constructed from the hindcast, with bias correction. Figure 4 shows the precipitation skill score for the three-month running mean simulated with one, two, three, and four months in advance, as well as for the entire integrated period (NDJFMA).

Figure 4
Seasonal precipitation skill scores. The seasonal forecasts correspond to the 3-month (a) NDJ, (b) DJF, (c) JFM, (d) FMA forecasts, and 6-month (e) NDJFMA forecasts.

The precipitation skill scores are higher during the first and second quarters (NDJ and DJF), reading the 90% confidence level in North Brazil, extending over the Amazon region. Some small areas of skill are present in central and northern Argentina, southern Uruguay, and parts of southern Brazil. In comparison with the previous version (Chou et al., 2020), the current version shows more areas of similar skill or slightly higher in NDJ.

The skill score is reduced during the third trimester (JFM) compared to the other periods. The highest correlation is an isolated occurrence, with no association with a specific region. This is a remarkable rainy trimester in most parts of Brazil, as it occurs during the development of the monsoon season. However, the skill increases in the fourth trimester (FMA), a characteristic transition season from the rainy to the driest season. In general, The Eta model 3-month skill score is generally higher than the skill of the driver CFSv2 model, as can be seen in National Oceanic and Atmospheric Administration (2024).

Considering the entire simulated period (NDJFMA), the model represents the interannual variability with fair skill in most parts of North Brazil, covering the Brazilian States of Mato Grosso, Goiás, Mato Grosso do Sul, and Minas Gerais. The highest skill coefficients (above 90% confidence) appear in central Argentina, some portions of Uruguay, and southern Brazil. In the remaining domain, the skill prevails at around 0.3.

Temperature skill score

The 2-m temperature skill score shows a much higher value than the precipitation skill score (Figure 5), which indicates the interannual variability of temperature anomalies is much better captured than the interannual variability of precipitation anomalies. The northern part of South America shows the largest temperature skill in all quarters. Unlike the precipitation skill, in the last quarter, FMA, the 2-m temperature shows an extended area with higher skill scores. The highest skills during NDJ occur in western and northern South America. In the JFM and FMA seasons, the areas of high skill scores have extended southward with forecast time. Areas of skills above 90% confidence level prevail in most parts of the domain. The 6-month seasonal temperature anomaly forecasts show suitable values over South America.

Figure 5
Seasonal 2-m temperature skill scores. The seasonal forecasts correspond to the 3-month (a) NDJ, (b) DJF, (c) JFM, (d) FMA forecasts, and 6-month (e) NDJFMA forecasts.

Precipitation in 3 major river basins

Mean errors

This section provides a detailed evaluation of the forecasts for three major river basins in South America (Figure 1): Madeira, Paraná, and São Francisco.

For each basin, Table 2 lists the mean climatological values of precipitation and 2-m temperature, along with other evaluation metrics. The mean precipitation and mean 2-m temperature in each basin are well reproduced by the forecasts. The precipitation and 2-m temperature ME, MAE, or RMSE do not exceed 1 mm/day or 1 °C. The precipitation MAE shows the largest magnitude in the São Francisco Basin. The forecasts of precipitation in the Madeira River have the largest RMSE, but it is also where precipitation amounts are the largest. The best precipitation d index is found in Paraná.

Table 2
Mean precipitation (mm/day) and 2-m temperature (°C): observations and Eta forecasts, mean error (ME), Mean Absolute Error (MAE), Root Mean Square Error (RMSE) of the Eta Model forecasts, and the Wilmott index of agreement (d) for the season from November to April (NDJFMA) from 2013 to 2023.

Variable	River Basin	Obs.	Eta	ME	MAE	RMSE	d
Precipitation (mm/day)	Madeira	6.85	7.30	0.45	0.77	0.95	0.37
	São Francisco	3.92	3.63	-0.28	0.82	0.90	0.43
	Paraná	5.28	4.70	-0.58	0.71	0.93	0.45
2-m temperature (°C)	Madeira	24.66	24.46	-0.21	0.28	0.33	0.66
	São Francisco	25.19	25.54	0.35	0.48	0.62	0.46
	Paraná	23.62	23.91	0.29	0.40	0.60	0.33

The 2-m temperature forecast errors, MAE and RMSE, are generally smaller than precipitation. Madeira Basin showed the smallest errors and the best temperature d index.

Precipitation extremes

Unlike the ME evaluation, the evaluation of extreme precipitation events can show whether the forecasts can distinguish extreme events from normal years. Laureanti et al. (2024b) showed the distinct circulation and sea surface conditions between extremely dry and wet years in the Madeira River.

The standardized precipitation anomalies characterized in this study are normal season, when the values fall within +/-0.5; wet season or dry season, when values fall within |+/-0.5| and |+/-1.0; and very wet or very dry season, when values exceed |+/-1.0|. The CFS standardized precipitation anomaly is included for comparison, although the Eta and the CFS use different parameterization schemes to produce precipitation.

Figure 6 shows the yearly mean standardized precipitation anomaly for each basin for the hindcast period, comparing the forecasts from the Eta and CSFv2 models against the observations.

Figure 6
Standardized precipitation anomalies from the median of observations (bars in shades of blue and red) and forecast by the Eta model (black bars) and the CFSv2 model (grey) for the season from November to April (NDJFMA), from 2013 to 2023, averaged over the (a) Madeira, (b) São Francisco, and (c) Paraná river basins.

Table 3 classifies and summarizes the observed anomaly and forecast performance. A forecast hit (1) was considered for the event when the forecast's standardized anomaly exceeded |+/-0.5| with the same sign as the observed anomaly, otherwise, it was a miss (0).

Table 3
Hits (1) and Misses (0) of the NDJFMA seasonal forecasts from the Eta model and the driver CFSv2 model.

Year of the NDJFMA	Madeira anomaly	Eta	CFS	S. Francisco anomaly	Eta	CFS	Paraná anomaly	Eta	CFS
2013 - 2014	very wet	0	0	normal	0	0	dry	0	0
2014 - 2015	normal	1	1	normal	0	0	wet	1	1
2015 - 2016	very dry	1	1	dry	1	1	very wet	0	0
2016 - 2017	normal	0	0	very dry	0	1	normal	0	1
2017 - 2018	very wet	1	1	normal	1	0	wet	1	0
2018 - 2019	wet	0	0	normal	0	0	normal	0	0
2019 - 2020	normal	0	1	very wet	1	0	normal	0	0
2020 - 2021	normal	1	1	dry	1	1	very dry	1	0
2021 - 2022	normal	1	0	very wet	0	1	very dry	0	0
2022 - 2023	very dry	0	0	wet	0	1	wet	0	0
Total		5/10	5/10		4/10	5/10		3/10	2/10

Every year, the basins present a different extreme anomaly, but in some years, the anomalies coincide in pairs. In 2015, the Madeira and São Francisco basins showed a similar dry anomaly in this year, while the Eta forecasts hit the dry anomaly in these two basins, but they missed the very wet anomaly in Paraná Basin. In 2017, the Eta forecasts captured the extreme flooding event in the Madeira River Basin, as well as the normal and wet conditions in the Sao Francisco and Paraná basins, respectively. In 2020, the normal conditions in the Madeira Basin, the dry conditions in Sao Francisco, and in particular, the very dry conditions in the Parana Basin were captured by the Eta forecasts. In the years 2020 and 2022, the São Francisco Basin showed similar anomalies as the Paraná Basin, which suggests that those extremes were driven by the same meteorological conditions.

In the most intense events, when the standard observed anomaly exceeds |+/-1|, the forecasts captured the anomaly sign of 2 out of 4 years of extremes in the Madeira basin, 1 out of 3 in São Francisco, and 1 of 3 in the Paraná basin. During the study period, the Madeira Basin, where more extreme precipitation anomalies were recorded, performed better than the other two basins in forecasting. Overall, the forecast of extremes was less accurate in the Paraná basin.

Of the four very dry precipitation conditions (years 2015, 2016, 2020, 2022), two occurred in the Madeira River, which shows that this basin has been subject to larger climate variability. The 2016 drought in the Sao Francisco basin was not captured by the forecasts.

During the dry condition years, the CFSv2 forecasted an even higher deviation compared to the observations. Not all anomalies forecasted by the Eta model carried the same sign as the driver CFSv2 model. This is due to the differences in model representation of physics and dynamic processes.

CONCLUSIONS

A 10-year seasonal hindcast set was constructed for the NDJFMA season and the period between 2013 and 2023 over South America using the Eta RCM at 20 km resolution to dynamically downscale the CFSv2 forecasts and, on top of that, a bias correction to statistically downscale to the grid point. This work aims to assess the value of these forecasts for the water resources end-users, emphasizing three major river basins in South America: the Madeira, the Sao Francisco, and the Paraná River Basins.

The forecasts reproduced the precipitation and temperature patterns well in the NDJFMA season, although mean errors showed an underestimate in the interior of the continent and an overestimate in the eastern part of Brazil. The bias correction reduced the errors considerably. The 2-m temperature pattern in this season was also well reproduced by the forecasts, but the mean errors showed an overestimate in the interior of the continent and an underestimate along the western coast. In general, the 6-month seasonal model integration showed stability as the errors do not show clear growth with integration time.

The precipitation skill score, which measures models' ability to reproduce the interannual anomaly, was calculated for the NDJFMA season. The skill scores were higher in northern and parts of central Brazil. As the integration progressed, forecasts in areas in northern Argentina acquired more skill. Overall, the skill score of the Eta precipitation anomaly forecasts is higher than the skill score of the CFSv2, the driver forecasts.

Model performance to capture the extreme events in 3 major river basins was assessed. No clear skill in capturing the extreme events in Paraná Basin as the number of hits is smaller than the number of misses. Some skill, but low, can be attributed to the forecasts in Madeira and Sao Francisco Basins. Increasing the number of cases of extreme events could be beneficial for the results.

Given the current computational constraints of the model development group to run more simulations with Eta, the hindcast was limited to a 10-year period. A longer time series would be necessary to capture more cases of extreme events. Such a series may be generated as computational resources become available for more model runs. However, the high-resolution dynamic-statistical seasonal forecasting system developed using the Eta model for the 6-month interval demonstrates significant utility and added value over the driver global model forecasts, as highlighted in this paper.

Supplementary Material

Supplementary material accompanies this paper.

S1

Observed (column a) and forecasted 3-month (rows 1 - 4) and 6-month (row 5) precipitation (mm/day) by the CFS coupled ocean-atmosphere circulation model version 2 (b) and Eta Regional Climate Model (Eta RCM) (c) for the period 2013-2023; and Mean Errors (ME) of the CFSv2 (d) and Eta model forecasts (e).

This material is available as part of the online article from https://doi.org/10.1590/2318-0331.302520240073

ACKNOWLEDGEMENTS

This work is supported jointly by Fundação de Pesquisa do Estado de São Paulo (FAPESP) 2020/08796-2 and Fundação de Pesquisa do Estado do Amazonas (FAPEAM) 01.02.016301.00268/2021. This work is also supported by the Program Institutos Nacionais de Ciência, Tecnologia e Inovação - Mudanças Climáticas (INCT-Mudanças Climáticas) FAPESP 2024/05084-2, and the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) 88881.688972/2022-01 S.C. Chou thanks CNPq for grant 312742/2021-5. This work used resources of the “Centro Nacional de Processamento de Alto Desempenho em São Paulo (CENAPAD-SP)”.

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Edited by

• Editor-in-Chief:
  Adilson Pinheiro

• Associated Editor:
  Carlos Henrique Ribeiro Lima

Publication Dates

• Publication in this collection
  14 Feb 2025
• Date of issue
  2025

History

• Received
  29 July 2024
• Reviewed
  28 Oct 2024
• Accepted
  09 Nov 2024