Improving GSMaP V06 precipitation products over the Upper Tocantins River basin in the Brazilian Cerrado, based on local rain-gauge network

Gridded precipitation products from remote sensing are currently available and could potentially enhance the use of precipitation data in regions with sparse network of ground rain gauges. Thus, this study aimed to evaluate the performance and propose correction models for Global Satellite Mapping of Precipitation (GSMaP) use in the Upper Tocantins River basin, a key area for food and electricity production in central Brazil, but with sparse network of ground rain gauges, challenging water resources and agriculture decision makers. GSMaP data were compared with data from a rain gauge network between 2000 and 2019. Evaluations were made at daily and monthly temporal scales. In general, GSMaP products show an overestimate bias for drizzle (0.1 ~ 1 mm day−1) and underestimate for rainfalls above 10 mm day−1. The use of monthly scale data significantly reduces the bias observed in the daily scale, but with an underestimation trend of -28.3% and -39.7% for the dry and rainy periods, respectively. Categorical indices showed that the GSMaP system had better hit rates for rain detection in the rainy season (October–April) than in the dry season (May–September). For the studied region, the use of GSMaP data on daily and monthly scales should be preceded by a bias analysis as a function of rain gauge network data. The use of bias coefficient corrected observed rainfall data underestimation on daily and monthly scales, improved correlation between GSMaP and observed rainfall data and reduced errors associated with rainfall network data within the basin influence area. The findings of this study indicate how decision makers could adjust and apply GSMaP products to estimate rainfall for water resources, agriculture and drought management challenges in the Upper Tocantins River basin.


Introduction
Rainfall plays a crucial role in the global energy balance and hydrological cycle, interacting with the hydrosphere, atmosphere, lithosphere, and biosphere (Yuan et al. 2017). Reliable regional-and global-scale rainfall data are crucial for hydrological modeling, water resources management, agriculture, and natural disaster prevention (Germann et al. 2006). However, obtaining reliable rainfall information at regional scales is still a challenge due to its high spatiotemporal distribution heterogeneity (Chen et al. 2019). Although accurate rainfall data can be acquired from rain gauges, their sparse location in developing countries hinders reliable rainfall mapping (Hrachowitz and Weiler, 2011). Remote sensing data can provide information at varied spatiotemporal resolutions on a regional scale, which can be used for systematic mapping of rainfall distribution on the surface of the Earth (Sharifi et al. 2019).
Since the launch of the first atmospheric satellites in the 1960s, many sensors have been developed for monitoring rainfall from space (Sun et al. 2018). They all focus on two main spectral categories: visible and infrared (VIS/IR) onboard geostationary and orbital satellites and low-orbit passive microwave (PMW) sensors (Levizzani et al. 2002). The Global Precipitation Measurement mission (GPM) is a result of a collaboration between the American (NASA) and Japanese (JAXA) space agencies to unify and promote advances in rainfall measurements from an operational constellation of microwave sensors, which have systematically provided global rainfall data on an hourly scale and at different correction levels (Hou et al. 2014).
Google Earth Engine (GEE) is a cloud-based computing platform designed to store and process large sets of atmospheric and earth surface data for analysis and decision making (Kumar and Mutanga, 2018). The platform includes data from several satellites; vectorial, social, demographic, and meteorological data; digital elevation models; and climate data layers (Mutanga and Kumar, 2019). This tool hosts satellite images and stores them in a public data archive that includes historical Earth images dating back more than forty years (https:// earth engine. google. com/ faq/). Both GSMaP (Global Satellite Mapping of Precipitation) products on the GEE platform were produced with the V06 algorithm of the GPM mission. The GSMaP-Reanalysis product was produced from the resampling of data from several sensors and provides rainfall data for the period between 2000 and 2014. The GSMaP-Operational product includes data from the GPM Core Observatory satellite obtained from March 2014 onwards.
The assessment and application of satellite precipitation data is still limited in sparse rain gauges network regions, as the Upper Tocantins River basin, despite its strategic importance for the production of food (Silva, 2019) and electricity (FURNAS, 2021) in Brazil. As mentioned by Pedreira Junior et al. (2021), the sparse distribution of rain gauges limits the effective use of precipitation data to support agriculture and water resources management in the brazilian tropical savanna. In this context, this study aimed to evaluate the performance of GSMaP V06 products and propose the adjustment model and its evaluation to improve precipitation mapping in the Upper Tocantins River basin.

Study area
The study was carried out in the area delimited by the Upper Tocantins River basin, located in the state of Goiás, Brazil (between latitudes 13.5° and 16.1° S, and longitudes 47.5° and 50.0° W). The basin has an area of 56,344 km 2 and its main watercourse is the Tocantins River. According to Köppen's climate classification, the region has an Aw-type climate, which stands for tropical. The dry season lasts from May to September, while the rainy season is along the remaining months, which account for more than 90% of the average annual rainfall. The average annual pluviometric rainfall is 1800 mm and the average temperature in the winter ranges between 10 and 27 °C, while in the summer between 18 and 35 °C, sometimes reaching 38 °C (Cardoso et al. 2014). The Cerrado is the characteristic biome of the region and native vegetation is characterized by forest, savanna, and grassland formations (Ribeiro and Walter, 1998) Fig. 1.

Ground data
Daily rainfall data for the period between 2000 and 2019 were obtained from pluviometric stations managed by the National Water Agency (NWA) within the influence area of the basin. The pluviometric stations that had rainfall data in each year of the period evaluated were considered, which

Satellite precipitation products
Products coming from the GSMaP (Global Satellite Mapping of Precipitation) system are made available by the Japan Aerospace Exploration Agency (JAXA-https:// shara ku. eorc. jaxa. jp/ GSMaP/ index. htm) for hourly global rainfall data distribution, at a spatial resolution of 0.1° × 0.1° (≈ 10 km). The system uses data from several sensors under the Global Precipitation Measurement mission (GPM), which currently has a constellation of low-orbit satellites that operate passive microwave data, and geostationary and low-orbit satellites that operate in the infrared range (Hou et al. 2014). In the present study, GSMap daily rainfall data from the GSMap Reanalysis V06 and GSMaP Operational V06 products were used, both obtained on the GEE (Google Earth Engine) platform. Rainfall data were evaluated based on the separation between dry and rainy seasons in the Upper Tocantins River basin. Thus, a compartmentalized analysis was performed for the period between 2000 and 2019, separating the data between May and September (dry season) from those between October and April (rainy season).

Scale handling of rain gauges and pixels for evaluation of rainfall events
To compare GSMaP and rainfall data, the point-by-pixel method was used. The GSMaP rainfall data was gathered from the rain gauge locations within the basin area to obtain rain gauge-satellite merged data on daily and monthly scales. Rainfall intensity was analyzed by dividing daily data into five categories ): drizzle (0.1 ~ 1 mm day −1 ), light (1 ~ 10 mm day −1 ), moderate (10 ~ 25 mm day −1 ), heavy (25 ~ 50 mm day −1 ), and torrential (> 50 mm day −1 ).

Statistical metrics for evaluating satellite precipitation products
Four statistical indices were used to evaluate continuous estimates from the GSMaP products. First, Pearson's correlation coefficient (CC, Eq. 1) reflects the consistency between GSMaP data and gauge observations. Second, root means square error (RMSE, Eq. 2) measures the deviation between GSMaP data and gauge observations. Then, mean absolute error (MAE, Eq. 3) describes the average difference between GSMaP data and gauge observations. The use of MAE and RMSE together is recommended since MAE applies the same weight to all errors, while RMSE penalizes the variance for assigning greater weights to errors with a higher absolute value (Chai and Draxler, 2014 where n is the total number of satellite product and gauge observation data, i is the i th data value of the satellite product and gauge observation, G i is the gauge observations and G is the average of the gauge observations, S i and S are satellite estimates and averages, respectively. A set of categorical metrics was used to assess the ability of GSMaP products to describe rain or no rain events (Hossain and Huffman 2008). Probability of detection (POD, Eq. 5) evaluates the satellite hit rates concerning the total rain events observed, penalizing by detection failure. False alarm ratio (FAR, Eq. 6) evaluates the proportion of falsely detected rain events to the total rain events correctly detected by the satellite. Frequency of hit (FOH, Eq. 7) measures the frequency at which the satellite detects rain when it occurs, penalizing by the false alarm. Finally, the Heidke skill score (HSS, Eq. 8) measures the accuracy of rainfall estimates, considering detections due to the random effect (Dinku et al. 2008;Mashingia et al. 2014).
where a represents the hit (i.e., the event was detected and observed), b represents the false alarm (i.e., the event was detected but not observed), c represents the missing event (i.e., the event was not detected but observed), and d represents the negative hit (i.e., the satellite hit when event was not detected nor observed).

Bias correction procedure for GSMaP rainfall estimate
After comparing the GSMaP and rainfall data, a bias correction method was tested for GSMaP data, using a bias coefficient acquisition (Bias Factor, Eq. 9) and a bias coefficient application (GSMaPcorr, Eq. 10) (Saber and Yilmaz, 2018). The acquisition and application of the bias correction coefficient for GSMaP were applied using observed (rain gauge) and estimated (GSMaP) monthly rainfall during the dry and rainy seasons of the region. To do so, we considered historical series between March/2000 and February/2014 (GSMaP Reanalysis), and between March/2014 and December/2019 (GSMaP Operational).
where GSMaP (T m ) and Rain Gauge (T m ) are the GSMaPbased and rain gauge-based rainfall estimates on a monthly scale with one bias factor calculated for each month within a year, GSMaP(P (x,y), Ti) and GSMaP corr (P (x,y), T i ) are the GSMaP data for day Ti at point P (x,y) before and after bias correction procedure, respectively.

Performance of GSMaP corrected products over the Upper Tocantins River Basin
After applying the bias correction to GSMaP daily historical rainfall data, the method was assessed for performance,

Bias Factor(T m )
using the following statistical indices: Kling-Gupta efficiency -KGE (Eq. 11) (Gupta et al. 2009), which is used to diagnose the relative importance of correlation components, bias, and variability between estimated and reference data; Nash-Sutcliffe efficiency -NSE (Eq. 12) (Nash and Sutcliffe 1970), which determines the relative magnitude of residual variance compared to observed data variance; as well as Correlation Coefficient (CC), RMSE, PBias, and MAE.
where r is the linear correlation coeficient between observed (O i ) and estimated (Pi) data, α is the variability ratio or ratio between estimated and observed value standard deviations (σ p /σ o ), β is the ratio between estimated and observed means (µ p/ µ o or P∕O ), s r, s α, and s β are scaling factors. The weights of scaling factors are conventionally equal, i.e., s r = s α = s β = 1, Bi is the benchmark series at time-step i. In its original form j = 2 and Bi = O. Figure 3a shows the average number of rainy days for values ≥ 0.5 mm day −1 . Figure 3b demonstrates the annual averages of observed (rain gauge network) and estimated (GSMaP-Reanalysis and GSMaP-Operational products) rainfall, for the periods from 2000 to 2014 and from 2014 to 2019, respectively. Considering the number of rainy days, the observed rainfall data were frequently smaller than the GSMaP estimated data throughout the period. However, except for 2007, annual averages between GSMaP-estimated and observed rainfall values showed similar trends. Moreover, the observed rainfall data showed greater variability than did the GSMaP-estimated data, which was expected since rainfall detection from rain gauge are point-based. Conversely, GSMaP estimation integrates the rainfall within a pixel area (~ 100 km 2 ). By comparing annual averages between observed and satellite-estimated rainfall data (Fig. 3B), GSMaP data showed accumulated values lower than the observed ones for the entire period evaluated. Still, observed data had greater variability than that estimated by GSMaP.

Precipitated totals evaluation
The number of rainy days estimated by the GPM can be influenced by its algorithms and measurements. Such tools are developed to obtain greater accuracy in instantaneous rainfall estimates, particularly for light rainfalls (> 0.5 mm h −1 ) (Hou et al. 2014). When evaluating GSMaP over a Cerrado area in Brazil, Salles et al. (2019) pointed out that spatial differences between area (GSMaP grid) and point (rain gauge) scale influence conclusions due to rain gauge locations and distribution. Therefore, rainfall events identified by satellites may not be detected by rain gauges, as it might rain at other locations within the GSMaP grid area. Regarding annual rainfall values, large-scale rainfalls are commonly underestimated by GSMaP. Deng et al. (2018) analyzed the performance of GSMaP over the Hanjiang River basin in China and found that it can overestimate and underestimate small-scale and large-scale rainfalls, respectively. After integrating the data into annual accumulated, annual averages of observed rainfall in a river basin can be underestimated. Figure 4 shows the monthly rainfall averages between 2000 and 2019 estimated by the GSMaP products and observed in the local rain gauge network. These results show GSMaP capacity to reproduce inter-seasonal variations between dry and rainy periods in the region. The months between May and September are marked as the dry season, while from October to April is the rainy season.
Just as the annual cumulative, monthly rainfall is underestimated by GSMaP concerning the observed in the region, mainly between November and April.

Quantitative statistics
A comparison of statistical indices (CC, MAE, RMSE, and PBias) between GSMaP and rain gauge data demonstrated differences in satellite data performance between dry and  (Fig. 5). During the dry season, CC values ( Fig. 5a) had greater variability. Although some CC values can be considered high, it was not verified here since 50% was below 0.4 for the dry seasons from 2000 to 2019. In the rainy season, the variability of correlations between GSMaPestimated and observed data was smaller; yet, 75% of the CC for this period were below 0.5. This difference was already expected since, in dry periods, rains are substantially less frequent and more irregular, in addition to being in lesser quantity or almost zero, compared to rainy periods; consequently, the variability between rainfall observation (rain gauge) and detection (satellite) during this period is greater. During the rainy months in the Cerrado environment, seasonal rainfall is marked by high variability in the dry-rainy and rainy-dry transition months (Nimer, 1989). Furthermore, the point-based observation from the rain gauge network had greater variability compared to GSMaP-estimated data. Such variability increases errors when comparing the ground and satellite data (Darand and Siavashi, 2021). The Upper Tocantins River basin lies in Brazil midwest region, and its rainfall regime is governed by atmospheric mechanisms, fostering a regional and homogeneous climatic pattern. However, the local terrain, with altitudes between 325 and 1606 m (Fig. 5), can create a certain heterogeneity in rainfall distribution over the basin area. In almost the entire Midwest region, more than 70% of the total rainfall accumulated during the year occurs from November to March. Conversely, the months from June to September are excessively dry, with an average of 4 to 5 days of rainfall per month (Nimer, 1989).
Another factor affecting ground-observed and GSMaPestimated rainfall correlations is the low coverage density of rain gauges, despite their unlimited database between 2000 and 2019. In this regard, Darand and Siavashi, (2021) applied GSMaP over Iran to compare regions with different rain gauge densities. These authors found correlations between 0.1 and 0.7 for regions with low rain gauge densities, and between 0.4 and 0.9 (more often above 0.6) for regions with higher densities. Moreover, Hrachowitz and Weiler (2011) found that more sparse rain gauge networks tend to have different deviations, depending on the local rainfall regime. The larger and the more uniform the rainfall events occur within a basin, the smaller the data deviations observed in rain gauges. On the other hand, small summer storms or localized rain events are registered differently by rainfall gauge networks, wherein some events may not be observed, or only detected individually.
Given the variability in the rainfall formation process, studies using different algorithms and sensors have shown that topographic variations and convective rains have a significant influence on satellite rainfall estimation. This can therefore result in unexpected errors between embedded pixel values and gauge point values Wang et al. 2019). Our rainfall analysis between 2000 and 2019 may also have been influenced by local atmospheric irregularities, which can cause rainfall to have distinct totals each year and far-from-normal values (Nimer, 1989). The MAE and RMSE values (Figs. 5b, c) demonstrate a great difference in data performance between dry and rainy seasons. In the dry season, rainfall events and volumes both for observed (rain gauge) and estimated (GSMaP) values were extremely lower than those in the rainy season. This can cause misinterpretation regarding the GSMaP system performance in the dry season. Darand and Siavashi et al. (2021) found RMSE values from 5 to 15 mm day −1 between March and December of 2018 in Iran. These authors highlighted the use of GSMaP-Gauge product calibrated with data from rain gauges rather than GSMaP-NRT (Near Real-Time) and GSMaP-MVK (research product) products to obtain more accurate estimates. PBias (Fig. 5d) had greater variability and amplitude for comparisons in the dry season. In the rainy season, PBias values were mostly negative, which denotes rainfall underestimation by GSMaP. Ma et al. (2016) evaluated the TRMM 3B42V7 and GPM IMERG rainfall data for the Tibet region and observed BIAS rates between -20 and 80% and between -30 and 70%, respectively, during the rainy seasons between 2014 and 2017. In the Upper Tocantins River basin, between 2000 and 2019, average PBias values for GSMaP data ranged between -80% and 103%, and between -68% and 80% for the dry and rainy periods, respectively. Figure 6 shows a set of categorical metrics used in qualitatively evaluating the performance of GSMaP products. In the dry season, POD values (Fig. 6A) varied highly, with 50% being below 0.8, and reaching a minimum of 0.3. In the rainy season, POD values are concentrated above 0.7, showing greater efficiency or probability of success in detecting rains between October and April. Such a higher detection probability in the rainy season reduced false alarm rates (FAR) (Fig. 6B). Otherwise, the lower performance in terms of POD in the dry period (May to September) promoted higher FAR values. Notably, FAR has a negative effect since the lower the value, the lower the false alarm rate. Therefore, during the rainy season, the sensor could properly detect the rainfall events observed in the rain gauge network (Wilks, 2006). Lastly, FOH values (Fig. 6C) showed significant differences in averages between both periods; therefore, the frequency of accurate estimates was higher in the rainy season, corroborating FAR results.

Qualitative analysis
HSS index (Fig. 6D) compares a system quality or ability of prediction to other forecasts occurring randomly, in other words, statistically independent from reference observations (rain gauges). A perfect prediction would have an HSS equal to 1, while a random forecast receives 0 (Tuan-Trinh et al. 2019). As in other indices, HSS variability in the dry period was greater, but its average was slightly higher than that in the rainy season. In short, only one observation in the rainy season was deemed random based on HSS.
The high variability of categorical indices in both seasons can be attributed to the seasonal effect of rainfall in the region under study. Salles et al. (2019) evaluated IMERG-v5 and GSMaP-v7 rainfall estimates for the Distrito Federal in Brazil, which is near the Upper Tocantins (Fig. 5), and observed that both products had the best performances during the rainy season and the worst in the dry one. Moreover, median performances were obtained in intermediate periods between the dry and rainy seasons.

Performance analysis of monthly and daily
GSMaP estimate Figure 7 displays the accuracy of GSMaP Reanalysis and GSMaP Operational products on daily and monthly scales. After comparing with rain gauge data, rainfall tended to be underestimated on both temporal scales and analyzed periods. PBias values on the daily scale were -53.3% and -52% for the rainy and dry seasons, respectively, and on a monthly scale were -39.7% and -28.3%, respectively. Data fit was smaller on a daily scale than on a monthly scale, in which CC for daily data was 0.42 in the rainy and 0.35 in the dry season. On a monthly scale, CC values were similar between both products (0.86 for the rainy season and 0.85 for the dry season). For other regions of the globe, the best fit of satellite data with rain gauge data on a monthly scale has often been found in comparative studies with other sensors and GPM mission data. Wang et al. (2019) assessed GPM IMERG and TRMM 3B42V7 products and observed CC of 0.85 and 0.92 on a monthly scale, and 0.50 and 0.41 on a daily scale, respectively. In terms of bias, GSMaP products have shown in previous studies a negative trend, or underestimation, in Bolivia and Distrito Federal, Brazil, -22.4% and -10%, respectively (Satgé et al. 2017;Salles et al. 2019a). To circumvent this problem, a bias correction procedure has been recommended before using a GSMaP product. Boluwade et al. (2017) showed one example of a bias correction method for satellite rainfall estimates.
Satellite rainfall underestimates or overestimates are troublesome in hydrological applications. For instance, problems in streamflow or surface runoff estimates can affect flood predictions or aquifer recharge estimates (Tian et al.  . GSMaP products, as well as other satellite rainfall data, require prior comparison with data from rain gauges distributed throughout the land to identify site-specific errors in satellite estimates (Salles et al. 2019b). Sungmin et al. (2017) evaluated the GPM products IMERG Early, Late, and Final over Austria and faced the need for reference data to assess bias, not only for rainfall volume but also its temporal scale acquisition. Such an approach is recommended to achieve the required accuracy in satellite-estimated rainfall data. Another issue with GSMaP products is the difference in sampling rates between infrared (IR) and passive microwave (PMW) input sources used by the system. Chen et al. (2019) found that a significantly different pattern in sampling frequency for the GPM-GSMaP input sources. In short, IR data is more used than PMW sensor data. Figure 8 shows the probability distributions (PDFv) in terms of daily rainfall volume of rain gauge and GSMaP data. PDFv is a widely used metric for satellite rainfall products and measures accumulated rainfall rates within a rainfall volume ranking (Kirstetter et al. 2012;Tang et al. 2016;Xu et al. 2017). Both products tested here tended to overestimate rainfall for the categories drizzle (0.1 ~ 1 mm day −1 ) and light (1 ~ 10 mm day −1 ). For Wang et al. (2019), satellite overestimation of low rainfall volumes may be related to evaporation, since small rain droplets do not fall into the atmospheric profile. For rainfall volumes above 10 mm, an inverse behavior was observed, with rainfall events being underestimated by both GSMaP products. Similar behavior was observed by Wang et al. (2019), who used GPM IMERG and TRMM 3B42V7 data and noted an overestimating trend for drizzle data (0 ~ 1 mm day −1 ). Concerning heavy (25 ~ 50 mm day −1 ) and torrential (> 50 mm day −1 ) volumes, both GSMaP products showed a low probability of detecting events compared to the rain gauges in the Upper Tocantins River basin. This fact might be related to the distribution of isolated rains within the total pixel area.

Bias correction for GSMaP rainfall data in the Upper Tocantins River basin.
Previous analysis demonstrated that the GSMaP products underestimate rainfall data in the Upper Tocantins River basin from 2000 and 2019. Therefore, a bias correction procedure was required. We thus applied a multiplicative factor to correct GSMaP data bias and improve comparison statistical indices between GSMaP and rain gauge data (  (2018) applied a multiplicative correction factor on GSMaP data and obtained R 2 from 0.81 to 0.98, RMSE from 6.97 to 1.21, NSE from 0.57 to 0.99, and PBias from -56.44 to 0.20. These authors assessed these statistical indices, first on an hourly scale after a daily scale, for different rainfall volume thresholds (from 1 to 10 mm day −1 ). Condom et al. (2011) also used a multiplicative correction model on TRRM data in Peru and obtained greater RMSE reductions compared to additive bias correction models.
The results of bias correction on a monthly scale (Table 2) improved almost all indices. Therefore, the method was efficient for GSMaP data in the Upper Tocantins River basin, both during dry and rainy seasons from 2000 to 2019. Figure 9 shows the scatterplot of monthly rainfall data obtained by GSMaP products, before and after bias correction, for the dry and rainy periods between 2000 and 2019.
If compared to its direct use (without bias correction), biascorrected GSMaP data had a general improvement in terms of bias with rain gauge data.

Summary and conclusion
The comparative analysis of GSMaP and rain gauge network rainfall data demonstrates that the system could detect seasonal variation in rainfall in the Upper Tocantins River basin. However, it overestimates the number of rainy days and underestimates the volume of rain when compared to rain gauge data.
Overall, the GSMaP system's ability to detect rain events, which was demonstrated by categorical indices (POD, FAR, FOH, and HSS), is superior in the rainy season, between October and April.
Bias correction using Bias coefficient reduced underestimation bias of GSMaP historical data in the Upper Tocantins River basin, improved correlations between rainfall data, and reduced errors associated with rainfall observations from 2000 to 2019. Scatterplot of GSMaP monthly data before and after bias correction procedure for dry (a-before, b-after) and wet (c-before, dafter) seasons during the period from 2000 to 2019