Figure 4 shows the precipitation maps from the remote sensing products IMERG (2000–2013), TMPA (1998–2013), TerraClimate database (1972–2013) and data measured from the rain gauge stations and interpolated with IDW (1972–2013).
The IMERG product (PPTIMERG) (Fig. 4a) has a behavior characterized by smoothed regions in terms of the variation of precipitation, with a decrease from southwest to northeast, predominance of values below 620 mm and a gradual increase in values in the southeast region, where it reaches its maximum value. One of the reasons for this variation is due to the proximity to the coast, which leads to greater values of precipitation, while in the central region of the watershed, which is characterized by the semi-arid climate, the smallest values are distributed (TANAJURA et al. 2010; SOUSA, 2016). In addition, this trend was also verified by the other analyzed products.
For the TMPA product (PPTTMPA) (Fig. 4b) the spatial variation rate is more abrupt than for the PPTIMERG, with a continuous trend of precipitation decay from the southwest to the northeast region. Furthermore, due to the spatial resolution of the TMPA product (pixel size), there are abrupt variations between adjacent cells in the image, visually consisting of the most discrepant behavior when compared to the other maps.
The IMERG and TMPA products demonstrate convergent performance in predicting estimates and show a tendency to behave similarly, since GPM is the successor to the TRMM mission. In corroboration, other studies also state that the performance of both is similar (SOUSA, 2016; LELIS et al. 2018), but also that they suffer interference from the region in which they are used in or from the predominant type of precipitation (SERRÃO et al. 2016; ZHOU et al. 2015). In this regard, it is clear that the TRMM has greater sensitivity to variations in regional conditions, which can be explained by its validation with the precipitation recorded in situ (SERRÃO et al. 2016).
According to Yang and Nesbitt (2014) and Dinku et al. (2011), the manifestation of high values of TRMM can be attributed, particularly, to the performance of product estimates in regions with orographic rainfall, which occur due to the influence of the relief, where the air that encounters, a physical barrier is forced to rise and condenses, which can cause heavy and massive rainfall in the highest altitude area (HOUZE, 2011). Another explanation for the sharp rise of values in the western region of the watershed can be attributed to the TRMM's own prediction characteristics in the face of sudden changes in precipitation in specific locations. This effect was also mentioned in other studies and associated with the tendency to overestimate precipitation (YANG and NESBITT, 2014).
It is noted that the data from TerraClimate (PPTTC) (Fig. 4c) and the data interpolated with IDW (PPTIDW) (Fig. 4d) do not maintain a continuous gradient in precipitation values, presenting a range of greater magnitude in the western part of the watershed and more smoothed variations in the other regions. Tanajura et al. (2010) and Sousa (2016) state that the orographic effect, which covers the Chapada Diamantina region (west of the watershed), provides above-average rainfall in regions with a semiarid climate (rates that exceed 1000 mm year− 1). Only the PPTTC and PPTIDW variables produced estimates with this order of magnitude for the western region (1060 mm year− 1 and 1050 mm year− 1, respectively).
The recording of precipitation variations from the TerraClimate data (PPTTC) has good sensitivity, consolidating the transition of spatial variation more clearly, which tends to accompany the watershed relief. The PPTIDW, on the other hand, is represented by the so-called “bull’s eyes” and has greater definition regarding the magnitude variations in the western part the watershed. They are similar trends obtained by different products, where each one of them has its uniqueness.
Typically, the presence of the so-called “bull’s eyes” is attributed to the lack of measuring instruments, causing the formation of concentric surfaces around the rain gauge stations, as occurs in the western region of the watershed. In addition, the northeastern region of the watershed stands out, due to the absence of rain gauge stations in the interpolation with IDW, extrapolations were generated with greater values for the water balance in the semiarid region (Fig. 4).
Despite the fluctuations inherent to the different sources of precipitation, it is clear that, except for the PPTIMERG, the other precipitation estimates were more sensitive to magnitude variations and spatial distribution that occurred in the watershed. Among these, it is noteworthy that PPTIMERG and PPTTMPA showed similar behaviors. Likewise, the variables PPTTC and PPTIDW were the most similar ones and also similar to the results described in other studies about the behavior of the rainfall regime in the Paraguaçu river watershed (SOUSA, 2016; TANAJURA et al. 2010).
In addition to the proximity of the precipitation estimates magnitude in the western region of the watershed, the variables PPTIDW and PPTTC also show equivalent spatial behavior. It is also added that the information on the TerraClimate database fully covers the base period corresponding to the rainfall considered in the study (1972 to 2013) and, therefore, may have contributed to a greater similarity of the PPTIDW results.
Regarding the precipitation qualitative analysis, it appears that the precipitation amplitude variation in the watershed estimated by the four methods is smaller than the amplitude of the observed data from the rain gauge stations. In addition, the annual amplitude of the IMERG (542 to 1151 mm) and TMPA (566 to 1182 mm) products indicated the smallest ranges of variation among the products studied, with a reduction of 804 and 773 mm, respectively, in the maximum values regarding the data from rain gauge stations. The variation range corresponded to 38.4% and 38.8%, respectively, of the value of the observed data variation range.
In essence, with regard to the magnitude of the rainfall analyzed in Fig. 4, it is observed that the PPTIDW was the one that produced the greatest amplitude (1379 mm year− 1) and, in contrast, the PPTIMERG generated the smallest (611 mm year− 1). Furthermore, when verifying the mean annual precipitation value, it was noted that the lowest value was recorded by PPTTMPA (682 mm year− 1), while the highest was also obtained by PPTIDW (743 mm). Valério and Fragoso Junior (2015) also found a value similar to the one obtained by PPTIDW, for the same watershed, using the data period from 1960 to 1990. Although, PPTIDW generated the highest mean value compared to the other estimates, when compared with the mean precipitation value of the rain gauge stations (802 mm), it is noted that it was 7.4% smaller.
Table 1 shows the results of the statistical indexes (MAE, RMSE and PBIAS) used to compare the results of the precipitation values obtained by the different remote sensing products, regarding the precipitation of each rain gauge station in this study.
Performance indices result for the rainfall estimates between gauge and IMERG, TMPA, and TerraClimate
It is noteworthy that the precipitations from the IMERG and TMPA products present high values for the MAE and RMSE indexes, indicating that the estimates were not very accurate. Regarding the PBIAS value, it can be seen that the values were negative, indicating a tendency of underestimation concerning the rain gauge stations values.
The results from the IMERG product corroborate with Teodoro et al. (2020), who, when assessing the accuracy of the IMERG product in a watershed in southeastern Brazil, observed underestimation tendencies regarding the data measured with rain gauge stations. It should be added that the underestimation of these results may be related to the short range of available data for the IMERG (2000–2013), as it showed the shortest range in this study.
It should be noted that the tendency of underestimating the results of the TMPA product is also reflected by its annual mean value and amplitude. Those values were, respectively, 8.2% and 53.3%, lower than the values from rain gauge stations. It must be noted that this behavior has already been observed by other authors, who highlighted the sudden change of the precipitation values in specific locations in the watersheds. Those locations are subject to tendencies of under or overestimation (CERA and FERRAZ, 2015). Thus, even if there is an indication of underestimation of the PPTTMPA, in the general context, the behavior along the watershed varies.
The PPTIDW presented high values for the MAE and RMSE indexes, which were similar to each other and indicated low accuracy of the estimates regarding the observed data, nevertheless, the errors were smaller than those recorded by PPTIMERG and PPTTMPA. With regard to the PBIAS index, the positive value, with a magnitude higher than the others, indicated a tendency to overestimate in relation to the observed values. The performance of PPTIDW shows that the interference resulting from the interpolation with IDW method does not always lead to satisfactory results.
With regard to the PPTTC, the values obtained for the MAE and RMSE indexes were the lowest among the variables (85.91 e 120.39, respectively), and showed that the PPTTC was the most accurate variable. Regarding the PBIAS index, it is noted that the positive value (2.30) indicates that the estimated data tend to be greater than the measured ones.
In this regard, it is noteworthy that in addition to presenting the best statistical performance with reference to the data from rain gauge stations, PPTTC was the variable that showed the greatest sensitivity to variations in the spatial distribution of precipitation, enabling the discretization of each region, such as the orographic effect in the west, the arid climate in the northeast of the watershed. In addition, the variation in the magnitude of values along the Paraguaçu river basin corresponds to what is described in the literature. Therefore, the PPTTC variable was the one that led to the greatest representation of the precipitation behavior in the Paraguaçu river basin. Therefore, the PPTTC variable was the one that led to the greatest representation of the precipitation behavior in the Paraguaçu river watershed.
3.3 Actual evapotranspiration
Figure 5 shows the actual evapotranspiration (ETR) maps from remote sensing products: MOD16 (2000–2013), GLEAM (1980–2013), MOD16rsp (2000–2013) and TerraClimate (1972–2013).
The identification of the ETR behavior is made easier by the spatial resolution of the remote sensing products. As can be seen in Fig. 5a, the MOD16 product, which has the best resolution among the analyzed images (1 km), presents a better discretization of the ETR behavior along the watershed. This behavior is well defined by the spatial distribution and it is highly sensitive to changes in magnitude, a fact evidenced by the sudden changes in ETR values in regions very close to each other.
To the images from the GLEAM product (Fig. 5b), the variation pattern of ETR values is not well defined, it is a trend that results from the spatial resolution (0.25º), and which hinders a better understanding of the ETR variation along the watershed. In addition to this difficulty, there are sudden fluctuations in the ETR magnitudes, however in neighboring cells. These aspects characterize the importance of spatial resolution for obtaining images with more defined behavior patterns and with a better understanding in the results analysis.
The ETRMOD16rsp map (Fig. 5c), generated from the compatibility of the spatial resolution of the MOD16 product with that of the GLEAM (0.25 °) product, shows a trend of variation of the values corresponding to the pattern of the behavior of the ETRMOD16. In addition, it is important to notice that when the spatial resolution of the image originated from MOD16 changes, it causes discretization capacity loss attributed to the product, and makes ETRMOD16rsp as difficult to characterize as the ETR from the GLEAM product.
The ETR obtained with the TerraClimate product (Fig. 5d) makes it easy to identify the ETR spatial behavior, showing good definition in the characterization of the different magnitudes of the ETR and smoothing in the transition areas of the values along the watershed.
The actual evapotranspiration results from four different products are characterized by differences in the discretization of spatial behaviors and magnitude variations along the watershed (Fig. 5). Nevertheless, all products led to lower values of actual evapotranspiration in the northeast region of the watershed and to a gradual increase in the magnitude of the ETR towards the watershed’s mouth.
The MOD16 product (ETRMOD16) (Fig. 5a) presents a behavior characterized by marked variations of the ETR values in the middle portion of the watershed. The ETR is related to the altitude, conditions and characteristics of soil use, types of vegetation and weather conditions (RIBEIRO, 2020; COMPAORÉ et al. 2008), as well as with the way in which they were calculated. MOD16 performs a global classification of land use and occupation, in which 17 different classes are characterized (FRIEDL et al. 2002).
According to Ribeiro (2020), because it has pixels of 1 km², the images from MOD16 provide great detail, however, they can result in ETR estimate inconsistencies, as can be seen by the range of its amplitude variation ETRMOD16 (467 to 1,667 mm year− 1), highest among all products, and due to the high mean value of ETRMOD16 (792 mm year− 1). These inconsistencies can be attributed to errors related to the imprecise classification of land cover types and to the uncertainties associated with the input data, such as the fraction of photosynthetically active radiation, the leaf area index and the GMAO (Global Modeling and Assimilation Office) reanalysis meteorological data (MU et al. 2011).
On the actual evapotranspiration map from the GLEAM product (ETRGLEAM) (Fig. 5b), magnitude variations are unlikely to happen and are irregularly distributed, mainly due to fluctuations in adjacent cells values. An explanation for this behavior is accredited to the way the ETR is calculated the by the GLEAM product, which differentiates only three sources of evaporation based on the type of terrestrial surface: bare soil, short vegetation and vegetation with high canopy (MIRALLES et al. 2011; MARTENS et al. 2017). It is also observed the predominance of values in the range of 700 mm year− 1, which are distributed in the middle region of the watershed. It is also observed the decrease in the magnitude of values in the northeast region. The variation in the amplitude of the ETRGLEAM is the littlest among the products (402 to 1,039 mm year− 1) and its annual average is 650 mm.
The ETRMOD16 and ETRGLEAM spatial distributions follow the rainfall variation pattern, with high ETR magnitudes in regions where there are higher rainfall indexes and lower magnitudes in the regions where these indexes are lower. This trend was also listed by Moreira et al. (2019b) in the Brazilian Pantanal region, and by Moreira and Ruhoff (2019) in eight Brazilian watersheds, in which they analyzed the performance of the MOD16 and GLEAM product. They noted that for the Atlantic Eastern hydrographic region, where the Paraguaçu river watershed is inserted, both products tend to “follow” the occurrence of rain. It is noteworthy that this trend may be related to factors such as solar radiation, air temperature, wind speed, relative humidity and atmospheric pressure, characteristic of the semiarid climate.
On the ETRMOD16rsp map (Fig. 5c) the highest values are concentrated in the middle part of the watershed and close to its mouth, and the minimum values are distributed over a large area, covering the northeast region, a portion of the intermediate part and the far west region of the watershed. The average ETRMOD16rsp value (792 mm year− 1) is the same as the one obtained with ETRMOD16 (792 mm year− 1) however, the variation range of its values is smaller (572 to 1,242 mm year− 1).
The TerraClimate product (ETRTC) (Fig. 5d) grants a better characterization of the variations in the ETR magnitude and spatial distribution when compared to the ETRGLEAM and the ETRMOD16rsp. Therefore, it makes it possible to record a sharp increase in values in the middle part of the watershed, a region that encompasses Chapada Diamantina, and a decrease of values as it approaches the northeast region of the watershed. It is also worth noting the gradual increase in values towards the watershed’s mouth.
The ETRTC behavior along the watershed is similar to the trend already mentioned before for ETRMOD16 and ETRGLEAM, reaffirming the association with the precipitation. The performance of the products in detecting these variations is also noteworthy. In turn, TerraClimate uses climatologically aided interpolation, combining high spatial resolution climatological standards from the WorldClim data set, with more coarse spatial resolution from the Climate Research Unit (CRU Ts4.0) and the Japanese 55-year reanalysis (JRA55) (ABATZOGLOU et al. 2018). Finally, it seems that the ETRTC amplitude varied from 402 to 1,089 mm year− 1 and its average annual value (639 mm) was the lowest among the products.
In short, the MOD16 and TerraClimate products, which have the highest spatial resolutions, are also the ones with the highest amplitudes. The ETRMOD16rsp, on the other hand, produces a variation range with an interval and magnitude lower than the ETRMOD16 origin variable, associated with the lower degree of detail of its spatial resolution. This behavior as well as the better ability of smaller pixels to represent the different changes in land use, and thus directly throwback the ETR response (KHAN et al. 2018; RUHOFF et al. 2013).
In face of the evaluation of real evapotranspiration images in the Paraguaçu river basin, it is noted that the ETR maps are influenced by precipitation variations. However, among the information obtained by the products, the ETRTC variable leads to the most consistent results in terms of spatial distribution and magnitude of values in each region, characterizing variations such as the orographic effect, influence of proximity to the coast and the semiarid climate. Therefore, considering its performance, the ETRTC was the variable that best represented the actual evapotranspiration behavior in the watershed.
3.3 Water balance
In order to assess the water balance representativeness in the water circulation processes in the Paraguaçu River watershed, tests with the combination of precipitation and actual evapotranspiration images are obtained from different ways. Therefore, it is necessary to determine which combination has the best performance and whether the images with the best performance in the independent evaluation produce the best results, when combined.
Figure 6 shows the water balance maps considering the precipitation from the IMERG product, combined with four different sources of actual evapotranspiration (ETRMOD16, ETRMOD16rsp, ETRGLEAM and ETRTC).
The WBIMERG_MOD16 and WBIMERG_MOD16rsp water balance maps, shown in Figs. 6 (a and b), present irregular behavior in terms of spatial distribution and magnitude of values (-709 to 99 mm year− 1 and − 420 to 63 mm year− 1, respectively), in which the great extent of areas with marked negative values stands out (82.17% and 94.56%, respectively). This behavior can be justified by the tendency of the MOD16 product to have higher evapotranspiration values than precipitation (MIRALLES, 2016) due to the difficulty in consistently estimating evapotranspiration (RUHOFF et al. 2013).
The presence of negative values in water balance represents a limitation that can be attributed to the existence of inconsistencies in the product's input data, to the discretization provided by the spatial resolution and to the lower performance of the product in regions with orographic influence or in regions of semi-arid climate, in which have great precipitation variability and ETR high evaporative power.
The occurrence of a negative water balance is physically unlikely, given that, considering the constant water storage variation, this negative water balance results from the difference between the amount of water that comes from precipitation less the amount of water that leaves through evapotranspiration (SENTELHAS et al. 1999). Therefore, it is expected that the WB has a value greater than or equal to zero. The occurrence of negative values would imply the absence of water courses, characterizing the “disappearance” of the water without a physical justification. In the same way values close to or equal to zero would lead to intermittent rivers, since these values would not be enough to guarantee the maintenance/perpetuity of minimum flows, a scenario that also does not reflect the conditions of the negative areas in the watershed.
A determining factor for the existence of negative values in the water balance is the difficulty of estimating variables, such as evapotranspiration, which has a greater limitation for its establishment on large spatial scales (WANG et al. 2014).
In view the limitations inherent to the predominance of negative values in WB, suggest the analysis of other evapotranspiration databases in the estimation of water balance with remote sensing. In this sense, the use of these images (Figs. 6a and 6b) should be rejected, since they are not representative of the hydrological processes in the watershed and produce discrepancies that contradict the physical signs of the watershed.
In the water balances WBIMERG_GLEAM and WBIMERG_TC (Figs. 6c and 6d) the negative values (40% and 25%, respectively) are concentrated in the region where the orographic effect occurs and extends through the semiarid region (Fig. 2) in a less accentuated way than the previous WB ones. In general, the existence of the orographic effect produced a sharp increase in all ETR estimates values, due to the large altitude variations (HOUZE, 2011) and the climate transitions, from semi-arid to dry sub-humid climate. The ETR estimate influence in this process is emphasized, since the precipitation (PPTIMERG) was not altered on the maps. The range of annual variation in the values of WBIMERG_GLEAM and WBIMERG_TC (-177 to 248 mm and − 138 to 257 mm, respectively) shows an increase in the magnitude of positive values and a reduction in the magnitude of negative values regarding the WB values already presented.
Figure 7 shows the water balance maps considering the precipitation from the TMPA product, combined with four different sources of actual evapotranspiration (ETRMOD16, ETRMOD16rsp, ETRGLEAM and ETRTC).
The water balances WBTMPA_MOD16 and WBTMPA_MOD16rsp (Figs. 7a and 7b), have similar characteristics in terms of the spatial distribution of the values, with amplitudes (-482 to 63 mm year− 1 and − 338 to 60 mm year− 1, respectively), indicating the large percentage of areas with negative values (91% and 93%, respectively). It is observed that the use of the MOD16 ETR continues to produce major inconsistencies in the calculation of the water balance and generating high magnitudes in the negative values (see Figs. 7a and 7b). It is also noted that combinations of variables with unsatisfactory performances lead to poor results.
In Figs. 7c and 7d, WBTMPA_GLEAM and WBTMPA_TC present marked variations in the spatial distribution of values, whose amplitude (-152 to 210 mm year− 1 and − 73 to 208 mm year− 1, respectively) includes negative values that are located in the middle portion and in the northeast region of the watershed, and cover about 30% and 16% of the total area. Thus, the GLEAM product performs better for more humid regions, as it leads to a tendency for negative values to take place in regions with a semi-arid climate. The TerraClimate product, on the other hand, performs better in regions with lower rainfall, with a tendency for negative values to take place in regions with dry sub-humid climate (Fig. 7). It should be noted that both perform better than the MOD16 product along the watershed.
Figure 8 shows the water balance maps considering the precipitation data of rain gauge stations, interpolated with IDW, combined with four different sources of actual evapotranspiration (ETRMOD16, ETRMOD16rsp, ETRGLEAM and ETRTC).
The WBIDW_MOD16 and WBIDW_MOD16rsp (Figs. 8a and 8b) water balances show spatial variations close to each other, mostly composed of negative values (about 58% and 70% of the total area). In this case, these inconsistencies may be associated with the shortage of rain gauge stations to detect the spatial variability of the precipitation and support the level of detail presented on the map (RIBEIRO, 2020). The variation range of WBIDW_MOD16 is the largest among all maps (-772 to 855 mm year− 1) and WBIDW_MOD16rsp has the lowest annual range, ranging from − 394 to 533 mm.
Regarding the WBIDW_GLEAM (Fig. 8c), it is observed that the variation of values trend in the watershed (-242 to 731 mm year− 1) corresponds to the behavior of PPTIDW precipitation, especially when estimating high values in the northeast portion of the watershed and to generate areas with negative values (24.88%) in regions with less rainfall, such as the central part of the watershed.
The failure to balance the inputs and outputs of the WB is evidence that reinforces the existence of inaccuracies in the generated estimates, with the use of remote sensing tools. This procedure has an obstacle, when it comes to comparing data with estimates made with models (MOREIRA, 2018). Therefore, the performance evaluation of a product or remote sensing methodology must be carried out together with the behavior analysis of the hydrological processes in the study area, in order to guarantee the representativeness of the results.
WBIDW_TC (Fig. 8d) leads to a spatial distribution similar to the one presented with WBIDW_GLEAM, but with a smaller percentage of negative areas (10.49%) and lesser variation of values range (-166 to 661 mm year− 1). It is noted that the occurrence of negative values is also associated with the precipitation variability and the evapotranspiration interannual variability, since these are strongly related. In semiarid regions, the potential evapotranspiration balance is more or less considered depending on the amount of rainfall during the year (FELIX and PAZ, 2016).
Figure 9 Water balance obtained with the TerraClimate precipitation and the ETRMOD16 (a), ETRMOD16rsp (b), ETRGLEAM (c) and ETRTC (d) for the Paraguaçu river watershed. WBmax corresponds to the maximum value of WB for each source and WBmin corresponds to the minimum value of WB for each source
In the WBTC_MOD16 and WBTC_MOD16rsp water balances (Figs. 9a and 9b) the spatial distribution is characterized, predominantly, by areas with negative values (70% and 82%, respectively). The amplitude variation range of WBTC_MOD16 (-700 to 673 mm year− 1) corresponds to twice the range of variation of WBTC_MOD16rsp (-374 to 292 mm year− 1). According to the study developed by Ribeiro (2020), the use of the MOD16 product in the Jequitinhonha watershed, in the Brazilian semiarid region, also generated negative values in the water balance, due to inconsistencies attributed to the product for regions with low precipitation. It is noteworthy that for the Paraguaçu river watershed the same behavior is observed, where the MOD16 product produced negative values with greater extension and magnitude in all combinations.
In the WBTC_GLEAM water balance (Fig. 9c), the existence of negative values (22.35% of the area) follows the precipitation trend, and is displayed in the regions where it has the lowest magnitude. Regarding the annual amplitude (-179 to 428 mm), WBTC_GLEAM presents positive values that are more representative than the WB generated with MOD16. Performance that may be associated with the way the ETR was calculated with GLEAM (Priestley-Taylor Equation), with a small number of inputs, mainly considering the use of data sets based on satellite observations, from diverse and well validated sources, minimizing the use of data modelling and parameterizations (MOREIRA et al. 2019a).
Lastly, WBTC_TC (Fig. 9d) presents variations characterized by greater magnitudes in the western region and smoothed behavior in the eastern region of the watershed, corresponding to the pluviometric regime and representing variations in the climate types in the watershed (Fig. 2). The WBTC_TC configuration was the only one that did not produce areas with negative values, producing a range of variation (22 to 431 mm year− 1) with consistent behavior and reaffirming its best performance regarding the other products. An explanation for this performance is due to the fact that both components (PPT and ETR) come from the same database (TerraClimate), have the same data range and have presented the best performances in the individualized analysis.
The use of the water balance to evaluate the estimates of its components adds valuable information about the behavior of the hydrological cycle in the watershed. Among the different combinations of WB, the performance of the WBTC_TC and WBIDW_TC variables were superior. WBIDW_TC presented the lowest percentage of areas with negative values and spatial variations that follow the behavior of PPTIDW. The WBTC_TC on the other hand, did not record negative WB values, it was generated by the combination of images, from the TerraClimate product, which presented better performance in the individualized analysis. In addition, the variations along the watershed corroborate with the pattern found in other publications, regarding the characteristics of climate, relief and amplitude range of the values variation. Therefore, the WBTC_TC variable is the one that best represents the conditions of water circulation in the watershed of the Paraguaçu river.