Evaluating the hydrological utility of satellite-based rainfall products using neural network models over the Ghare Ghieh River basin, Iran

Precipitation is an essential component of the global water cycle and important data for various applications, such as water resources, hydrology, and climate (Sun et al. 2018; Vu et al. 2018; Su et al. 2019). Due to the importance of precipitation data, hydrological modelling is challenging in data-scarce regions and poorly gauged basins (Rahman et al. 2020), especially in the northwest part of Iran.

The use of Rain Gauge Stations (RGSs) is the conventional method for preparing precipitation data (Sun et al. 2018). Nonetheless, this method is inadequate for precipitation monitoring owing to the scattered distribution of rain gauges in some areas and basins, especially in the rugged and mountainous regions. Recently, the Satellite-based Rainfall Products (SRPs) with different temporal and spatial resolutions and wide spatial coverage provide alternative sources in data-scarce regions (Rahman et al. 2020). The satellite precipitation estimates have been developed either for single platforms or by merging infrared and microwave sensors to produce multi-sensor precipitation retrievals (Kirstetter et al. 2018). Infrared (IR) sensors on board Geostationary Earth Orbiting (GEO) satellite platforms have been used in algorithms to retrieve surface precipitation because of their comparatively higher spatio-temporal resolution and lower latency relative to satellite estimates from Passive Microwave (PMW) sensors on board Low Earth Orbiting (LEO) satellites (Karbalaee et al. 2017; Kirstetter et al. 2018). Nevertheless, IR sensors are sensitive to the cloud-top properties indirectly related to surface precipitation rates, but PMW observations sense total cloud water and/or ice content and provide information on integrated water content that enables more precise surface precipitation retrievals (Upadhyaya et al. 2020). A plethora of satellite-based precipitation estimations are available for hydrological studies (for overviews, see Beck et al. 2020), such as Tropical Rainfall Measuring Mission (TRMM) Multi-satellite Precipitation Analysis (TMPA; 0.25°; 50°N–S; Huffman et al. 2007), Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks (PERSIANN; 0.25°; 60°N–S; Hsu et al. 1997), Climate Prediction Center (CPC) MORPHing technique (CMORPH; 0.25°; 60°N–S; Joyce et al. 2004), CPC Merged Analysis of Precipitation (CMAP; 2.5°; global; Xie & Arkin 1996, 1997; Xie et al. 2003), Global Satellite Mapping of Precipitation (GSMaP; 0.1°; 60°N–S; Kubota et al. 2007), Cooperative Institute for Climate Studies (CICS) High-resolution Optimally interpolated Microwave Precipitation from Satellites (CHOMPS; 0.25°; 60°N–S; Joseph et al. 2009), Climate Hazards group InfraRed Precipitation with Stations (CHIRPS; 0.05°; 50°N–S; Funk et al. 2015), Integrated Multi-satellitE Retrievals for Global precipitation measurement (IMERG; 0.1°; 60°N–S; Huffman et al. 2015), and Multi-Source Weighted-Ensemble Precipitation (MSWEP; 2.5°; global; Beck et al. 2017a, 2017b, 2017c, 2019). These datasets vary in terms of data sources employed (gauge, satellite, reanalysis, or combinations thereof), spatial coverage (from <50°N–50°S to global), spatial resolution (from 0.05° to 2.5°), and temporal resolution (from 30 min to monthly).

On the other hand, streamflow modelling plays a vital role in many practical hydrological problems (Sorooshian & Chu 2013), such as management of ecosystem services (Wenger et al. 2010), and water resource planning and management (Liu et al. 2018; Zheng et al. 2019). Since existing rainfall–runoff modelling methods require exogenous input with some assumptions, neural networks can be an efficient solution (Chau 2006). During the past few years, Artificial Intelligence (AI) methods have been recurrently used to predict non-linear problems and attain proper results. Due to the non-linear structure, the Artificial Neural Network (ANN) has a high ability to model non-linear and complex processes, such as rainfall–runoff relationships. Dawson & Wilby (1998), Tokar & Johnson (1999), Tokar & Markus (2000), and Zhang & Govindaraju (2003) confirmed the potential of ANNs for modelling the non-linear processes. Also, neural networks are calibrated faster compared to other models. Tokar & Markus (2000) compared the conceptual models (i.e., Watbal, SAC-SMA, and SCRR) and the ANN models for estimating runoff at three basins with various physiographic characteristics and climatic. In all three cases, the ANN models presented a more systematic approach, higher accuracy, and shortened the time spent in training of the models. They stated that ANN could be a potent tool in modelling the rainfall–runoff process for different climate patterns, topography, and time scales. Nonetheless, one of the problems with the ANN model is that depending on the initial weight parameter set before training the network for the same original inputs, it offers different results. Because the backpropagation (BP) optimization method utilized in network training is unstable, each time the optimization process begins, a set of different weight parameters is obtained (Boucher et al. 2009). This indicates the need to develop methods to find the optimal initial weight of neural networks (Yam & Chow 1995). Various methods have been used, including the Genetic Algorithm (GA), to obtain the optimal initial weight parameters and increase the accuracy of neural network models (Chang et al. 2012; Mulia et al. 2013). Lately, it was found that applying the Particle Swarm Optimization (PSO) algorithm can enhance the conventional neural network models' performance considerably (Chau 2006; Kuok et al. 2010; Asadnia et al. 2014). Chau (2006) proposed an approach to predict water levels in which the PSO algorithm was used to train ANNs, for the Shing Mun River in Hong Kong. The results showed that PSO could be used as an alternative training algorithm for ANNs. Kuok et al. (2010) applied the PSO feedforward neural network (PSONN) to model daily rainfall–runoff relationships in the Sungai Bedup Basin of Malaysia. They showed that with combinations of rainfall and runoff at present and previous times as input data, PSONN simulated the current runoff carefully, and it could be used in other basins. Asadnia et al. (2014) applied the improved PSO method for training ANN to estimate water levels using daily data of water levels and rainfall from 1988 to 2000, for the Heshui watershed in China. They first used different algorithms, including the Levenberg–Marquardt neural network (LMNN) algorithm, to train ANNs, then compared the best results, which were for the LMNN algorithm with the PSO-based ANNs. The results showed that the PSO-based ANNs performed better than LMNN.

In past years, various SRPs have been used to simulate streamflow in several studies. For instance, Bitew & Gebremichael (2011) evaluated the efficiency of four satellite precipitation products as input to the Soil Water Assessment Tool (SWAT) model for simulation of daily streamflow in the Koga and Gilgel Abay watersheds of the Ethiopian part of the East African highlands. The results showed that the efficiency of satellite precipitation products relied on the type of product. The simulations of CMORPH and TMPA-3B42RT revealed consistent skills in their simulations but underestimated the large flood peaks, while the simulations of PERSIANN and TMPA-3B42 had an inconsistent efficiency with poor skills. Li et al. (2012) compared the TRMM product with RGS data at various time scales and also, they assessed the utility of the TRMM-3B42V6 precipitation product to simulate hydrological processes at the Xinjiang catchment, in China. Daily hydrological processes simulation revealed that the Water Flow Model for Lake Catchment (WATLAC) model using rain gauge data produced an overall good fit, but the results of the simulation using the TRMM product were not satisfactory. The assessment results showed that the TRMM precipitation product was unsuccessful to simulate daily streamflow with desired accuracies in this study area. However, good efficiency was achieved by applying the TRMM product for simulations of monthly streamflow. Alazzy et al. (2017) assessed four satellite-based precipitation datasets versus precipitation data from rain gauges and they indicated their relative potential impacts on the simulation of hydrological processes using the Hydrologic Modelling System (HEC-HMS) model on the Ganzi River Basin in the Tibetan Plateau. The results showed that 3B42 and CMORPH-CRT were better than 3B42RT and PERSIANN-CDR at seasonal and annual scales. Generally, 3B42 presented the best performance to simulate streamflow and even outperformed simulation driven by the rain gauge observations in the validation period. Also, PERSIANN-CDR showed the worst performance. They stated that the TMPA-3B42 was more suited to driving hydrological models and could be a substitute source of scattered data on the Tibetan Plateau basins. In the study of Liu et al. (2017), the ability of the PERSIANN-CDR was evaluated to simulate daily streamflow using the Hydro-Informatic Modelling System (HIMS) model in the upper Yangtze River and upper Yellow basins on the Tibetan Plateau. The results showed that the PERSIANN-CDR was proper for streamflow simulation. They stated that for the hydrological and climate change studies on the Tibetan Plateau, it could be a substitute source of the scattered gauge network. Su et al. (2017) evaluated four satellite-based precipitation estimations in daily streamflow simulation using the Variable Infiltration Capacity (VIC) model, which is grid-based, on the upper Yellow River basin in China from 2001 to 2012. The results showed that the performances of TMPA-3B42V7 and CMORPH-BLD were close to the RGS data. Ren et al. (2018) assessed three satellite precipitation products on the Luanhe River basin in China, between 2001 and 2012. They investigated the efficiencies of these products by applying the SWAT model. The results showed that 3B42RT and 3B42 overestimated precipitation with R_bias values of 62.80 and 20.17%, respectively, but PERSIANN underestimated precipitation with an R_bias of −6.38%. In general, 3B42 had the highest CC and the lowest root-mean-square error (RMSE) and MAE values on daily and monthly time scales and performed better than PERSIANN and 3B42RT. Therefore, 3B42 revealed the best hydrological efficacy, while PERSIANN showed poor efficacy. Su et al. (2019) assessed the hydrological simulation utility of the three IMERGV5 products using the VIC model on the Upper Huaihe River Basin. The dense rain gauge network observations showed very good performance for the whole simulation period. Also, IMERG-F indicated acceptable performance in the entire simulation, while IMERG-L and IMERG-E showed poor performance. Kha et al. (2020) proposed a method to examine the use of SRPs in monthly streamflow modelling on the Lam River Basin. For this purpose, they merged satellite-based rainfall GSMaP-MVK and ground-based observations and used the SWAT model. The results showed the usefulness of merging precipitation data for monthly streamflow simulation. The details of these studies, as well as other important studies, are summarized in Table 1.

According to Table 1, in the last decades, a lot of hydrological models have been adopted for rainfall–runoff modelling to solve basins problems. Physical-based models generally require different hydrological variables and more effort to simulate the physical processes of the basin, while AI models have shown the ability to capture the non-linearity relationship between the predictors and predicted without advanced knowledge with less input hydrological parameters. A neural network which is a data-driven method acts as a black box and learns to predict the value of a specific output variable given sufficient input data. Therefore, it needs comprehensive historical data to train a model. Nonetheless, the neural networks have specifications such as no need for any exogenous input, data-error tolerance, and built-in dynamism in predicting (Chau 2006). On the other, Moazami et al. (2013) compared three satellite rainfall products including TRMM-3B42V7, TRMM-3B42RT, and PERSIANN against observations from rain gauge stations over the whole country of Iran from 2003 to 2006. Therefore, the main purpose of this study is daily streamflow modelling using these three satellite-based precipitation products (at 0.25° spatial resolutions) in a basin where ground gauges are sparse or nonexistent, by developing models with high speed, and acceptable accuracy. First, two neural network models are developed. Then, these models are trained and tested with different input patterns from ground-based data. The best-trained models in the test period are selected. Finally, the satellite-based precipitation datasets (before and after calibration) are applied as input variables to these best-trained models for daily streamflow simulations.

Zarinehrud basin with an area of 13,685 is situated in the southern part of the Urmia Lake in the northwest of Iran (45°76′ to 47°38′ east longitude and 35°67′ to 37°71′ north latitude). Urmia Lake is mostly fed by the Zarinehroud river. Due to the decrement of inflow to the lake and the improper management of water use in the basin, Urmia Lake is being dried up. The data were not available at all stations, and only limited numbers of stations have suitable records over the basin. In this research, as shown in Figure 1, the Ghare Ghieh River basin of Zarinehrud, with an area of 2,404 ⁠, was chosen because of having continuous data of its RGS and its stream gauge station which is placed at the outlet of the sub-basin.

Daily precipitation, average air temperature, and stream discharge recorded as ground-based data from water years of 1988 to 2008 are applied to simulate the streamflow in this study (http://wrbs.wrm.ir). For training and testing of the proposed models, 75% of data from 23 September 1988 to 22 September 2003, and 25% remain from 23 September 2003 to 21 September 2008 are used, respectively. The summary of the ground-based data is presented in Table 2.

In this study, for the construction of model structure and model training, based on the Pearson correlation and lag analysis between output and input variables at different time steps, networks are trained with different combinations of variables including precipitation, temperature, and stream discharge at present and previous time steps. These input patterns are shown in Table 3. Thus, the current stream discharge as output data and these patterns as inputs are considered for models training. Next, the best-fit pattern is chosen in the test period of the networks.

The TRMM satellite was launched by the National Aeronautics and Space Administration (NASA) and Japan Aerospace Exploration Agency (JAXA) in 1997 to study and monitor precipitation over the tropics. According to Huffman et al. (2007), the TMPA products are produced with the combination of ground observations and three kinds of observations including infrared (IR), PMW, and precipitation radar (PR) sensors from LEO and multiple GEO satellites at a 0.25° × 0.25° spatial resolution and a 3-hourly temporal resolution. In the TMPA algorithm, the PMW estimates are integrated and calibrated to produce highly accurate PMW estimation. Then, the calibrated PMW is applied to create IR estimates. Eventually, the PMW and IR estimates are combined to prepare the best precipitation estimates of TMPA. In this study, the TMPA product's latest version, version 7 (V7), with a spatial coverage of 50°N–50°S was utilized that consists of two standard products including near-real-time (about 8 h after real-time) version (3B42RT) and post-real-time (about 2 months after the end of each month) version (3B42). The main difference between the near-real-time and research products of the TMPA is gauge correction along with the TRMM Combined Instrument (TCI) (https://disc.gsfc.nasa.gov/).

First, Hsu et al. (1997) established the original PERSIANN that is satellite precipitation algorithms for estimating historical precipitation for spatial coverage of 60°N–60°S from March 2000 to the present. The PERSIANN algorithm has been developed for global precipitation estimation by merging PMW and IR observations from LEO and GEO satellite imagery, respectively. The local cloud textures prepared by the geostationary satellite long-wave infrared images approach are utilized for surface rainfall rates estimation, depending on an ANN model in the PERSIANN algorithm and updates its network parameters according to the TMI-2A12 product from the low-inclination orbiting TRMM satellite. As explained above, the characteristics of these three satellite-derived precipitation products, which are used in this study, are according to Table 4.

Thus, the TRMM-3B42V7, TRMM-3B42RT, and PERSIANN products at the daily temporal scale are used. The spatial resolution of these products is square pixels with a size of 0.25° (∼25 km), and precipitation values of products are obtained at each pixel. Therefore, the daily precipitation data of satellite pixel in which RGS is located are used from 2003 to 2008 (Figure 1). For comparison, according to Table 5 and because of the limited availability of ground-based data, this similar period was selected to evaluate the satellite-based datasets. Since the 3B42RT product provides quick precipitation estimates, it is especially suitable for near-real-time monitoring and modelling processes, and also for flood forecasting studies. In this study, in addition to the 3B42V7 product, 3B42RT also is evaluated. The TRMM-3B42V7 and 3B42RT products can be obtained from https://pmm.nasa.gov/data-access/downloads/trmm, and the PERSIANN product is achieved from the Center for Hydrometeorology and Remote Sensing (http://chrsdata.eng.uci.edu).

For comparison, we evaluated these satellite precipitation datasets before and after calibration in streamflow simulation. Thus, we used the Geographical Difference Analysis (GDA) method to reduce the difference between the SRPs and the rain gauge data. Laurent et al. (2013) used this method to calibrate the TRMM-3B42RT product. The GDA calibration method was developed by Cheema & Bastiaanssen (2012), which is as follows:

• (1)
  Compute the difference between the measured precipitation from RGS and the corresponding satellite pixel. The formula is as follows.

  

  (1)

  where is the precipitation difference between the satellite and rain gauge data at a given point. and are the satellite-based precipitation, and RGS values at a specific location ⁠, respectively.
• (2)
  Spatial interpolation of precipitation differences by Inverse Distance Weighting (IDW) technique and creation of the difference maps. We can write:

  

  (2)

  where is the spatially interpolated difference map.
• (3)
  Calibration of satellite precipitation products with the difference map. At this stage, which is the last step, the values of the difference maps were subtracted from the satellite precipitation values. We can write:

  

  (3)

  where is the calibrated precipitation after correction, and is the spatial precipitation estimate attained from the satellite. The location of the RGS in the study area is 47.1 longitude and 36.4 latitude. The steps of the GDA calibration method are shown in Figure 2.

The ANN includes a simple interconnected processor named a neuron. A neuron is a unit of information-processing which is essential to the performance of a neural network and consists of weights and an activation function. The important parameters acting as the ANN memory are the weights, and the non-linear mapping potential with the network is provided by the activation function.

The architecture of ANNs is determined by the ANNs neurons' structure (Haykin 1999). Generally, three types of network architecture include a single-layer feedforward network without hidden layers, a multilayer feedforward network with more than one hidden layer, and a recurrent neural network with at least one feedback loop. The training algorithm determines the weight parameters on the links between neurons. The most general algorithm is the BP training algorithm that includes a forward and a backward process. The input signals move forward via the network, and the error is computed in the output layer. Then, the error is propagated back to the input layer from the output layer while updating parameters for the direction where the performance function most quickly decreases. There are several alterations in training algorithms of BP on the basic algorithm, which are based on other methods of standard optimization, such as the conjugate gradient-based algorithm, the steepest descent-based algorithm, and Newton's method. Among different methods of BP, the Levenberg–Marquardt (LM) algorithm (Marquardt 1963), a kind of Newton's method, has been well applied to the ANN training for streamflow prediction, presenting considerable speedup and faster convergence compared to the conjugate gradient algorithm, and the steepest descent algorithm (Zamani et al. 2009).

In this study, the LM algorithm is applied for training the network, and since the multilayer feedforward neural network with one hidden layer is able to approximate most of the non-linear functions (Mulia et al. 2013), the three-layer neural network with one hidden layer is utilized. For each pattern of Table 3, the number of neurons in the hidden layer, and the number of repetitions is obtained to get the optimum function with the purpose of minimizing the error factor, by a trial-and-error procedure. The activation function of the hidden layer was Logsig, and Purelin neuron linear function with the number of outlets was the output layer activation function. Also, the data are normalized between 0 and 1, due to the use of stimulant function Logsig. The flowchart of the LMNN model, which is used in this study, is shown in Figure 3.

The ANNs training is a procedure of updating the connection weights and biases, in a way that the network presents desirable behaviour. For training the ANNs, the BP algorithm is the most usable algorithm that minimizes the error between the target and the network output by modifying the weights and biases. Thus, the training algorithm plays a vital role in the ANN models' performance. In recent years, although the BP algorithm has been generally applied to perform the training, some drawbacks are encountered in its application that consist of the easy entrapment in a local minimum and the slow training convergence speed (Chau 2006; Kuok et al. 2010; Asadnia et al. 2014). The BP algorithm can drop into the local optimal solution, and its efficiency is dependent on the initial weights and biases of ANN. If those are far from the optimal values that can provide global optimal solutions, ANN may be trapped at the local minimum. The BP algorithm is combined with metaheuristic optimization algorithms in many types of research to dominate these defects of the BP algorithm and improve the accuracy of models. Among them, the PSO method can be a substitute ANNs training algorithm and be utilized for hydrological applications (Chau 2006).

In this study, the PSO algorithm is used to train the ANN model to make a hybrid algorithm. The hybrid BP-PSO algorithm employs the capability to fast convergence of the BP algorithm. It also applies the global searchability of the PSO algorithm to attain the ANN initial weights and biases, which can steer the network to the global minimum of the error function. The optimal initial weights and biases, which are achieved by the PSO algorithm, are employed in the training of the BP algorithm to enhance the performance of ANN. In this hybrid algorithm, by flying the particles in the search space, the optimal set of weights and biases are determined. The algorithm finds a set of weights and biases at each iteration that their fitness is evaluated. It happens by assigning these weights and biases to the nodes and predicting the target value. Then, the precision of the prediction via assigned weights and biases is appraised as the discrepancy of predicted and actual values, which must be minimized by the optimization process. The best fitness of the particle that has been obtained, as the individual best (pbest) and the best fitness of the swarm, as the global best (gbest) are considered, respectively. Until reaching the optimized weights and biases for the ANN model, this process is repeated for a specific number of iterations. The stages of optimization ANN model by the PSO algorithm are as follows, wherein W is as the weights and biases.

The standard deviation of observed discharge (⁠⁠) is utilized to choose the best-fit input pattern to the neural network models in the test period. If the root-mean-square error (⁠⁠) is considerably smaller than ⁠, the model prediction will be accurate. Mutually, if is greater than or equal to ⁠, the model will not give an accurate prediction (McCuen 1993; Tokar & Markus 2000). Thus, the higher accuracy of streamflow prediction of the model is obtained by the lower ratio of / (Tokar & Johnson 1999). To evaluate the efficiency of satellite precipitation products, the Multiplicative bias (M_bias) is used in this study. The ratio of satellite-based precipitation dataset to the measured precipitation value from RGS is the M_bias. The ideal value of M_bias is 1. The values of less than 1 show underestimation, while the values greater than 1 show overestimation (Moazami et al. 2013). To assess the streamflow simulation results, several statistical metrics are considered including the Pearson correlation coefficient (CC) to describe the linear correlation among the observed and simulated stream discharges, the coefficient of determination (square of the CC; ⁠), the RMSE, and the mean absolute error (MAE). The RMSE and MAE are utilized to show the mean value of the error, but RMSE gives greater weight to larger errors than MAE. The bias is defined as the average difference among the observed and simulated stream discharges and may be positive or negative. The positive bias and the negative bias show overestimation and underestimation of stream discharge, respectively. The systematic bias of the simulated stream discharges is described as the Relative bias (R_bias) and behaves the same as bias. The Nash–Sutcliffe model efficiency coefficient, as hydrological assessment criteria, is also applied. In the Appendix (Table A1 in supplementary material), formulas and perfect values of these statistical evaluation indices are mentioned.

In this study, in order to evaluate the performance of satellite rainfall products in streamflow simulation, we trained neural network models based on ground data and different input patterns. Then we selected the best-trained pattern for each model in the test period. Next, we used these best-trained patterns to simulate streamflow with satellite precipitation datasets in the study area. Therefore, at first, according to the input patterns of Table 3, neural network models constructed by different combinations of ground-based data were trained and tested for streamflow simulation. According to different statistical goodness-of-fit indices, the best-fit pattern for each model was chosen. These indices to select the best-fit patterns were the ratio of the standard error estimate (⁠⁠) to the standard deviation (⁠⁠) of stream discharge. shows the inexplicable variance and is commonly compared to the standard deviation of the observed values of the dependent variable (⁠⁠; Tokar & Johnson 1999). According to Table 2, in the test period, the value of the standard deviation of the observed stream discharge (⁠⁠) was 12.36. The evaluation results of the neural network models in the test period are shown in Table 6. These results for the LMNN model showed that the pattern of No. 4 with and had higher accuracy than other patterns in daily streamflow simulation and selected as the final pattern. Also, these values indicated that the best-fit pattern for the PSONN model was the pattern of No. 5 with and the lowest in the network test period.

The statistical goodness-of-fit indices for the networks tested with six input patterns are shown in Figure 5. The simulation results for most patterns by the PSONN model showed an increase in the coefficient of determination. Thus, the selection of the best-fit patterns for the LMNN and PSONN models was accomplished.

In the case of satellite measurements, the uncertainty of data is dependent on the spatial scale and time accumulation of the estimate (Steiner 1996). Moazami et al. (2013) compared three satellite rainfall products (i.e., TRMM-3B42V7, TRMM-3B42RT, and PERSIANN) versus observations from rain gauge stations over the whole country of Iran from 2003 to 2006. Their results indicated that the 3B42V7 product had higher estimates of daily precipitation than the other products. By comparing the original satellite-based precipitation datasets against the rain gauge data in the study area, it can be seen from Figure 6 that these satellite precipitation products tend to overestimate precipitation. Also, the calculated M_bias index values for the TRMM-3B42V7, 3B42RT, and PERSIANN products were 1.12, 1.24, and 1.73, respectively. Because of all these values were larger than 1; all satellite precipitation products overestimated precipitation over the study area.

Next, these best-trained networks were tested with the original satellite precipitation estimates. Thus, in the following, to assess the performance of satellite precipitation products in daily streamflow simulations, three products of TRMM-3B42V7, 3B42RT, and PERSIANN were applied as inputs to the best-trained networks (i.e., the pattern of No. 4 for the LMNN model, and No. 5 for the PSONN model) instead of the RGS data. The obtained results are shown in Table 7.

According to the results, it can be concluded that the satellite precipitation products used in this study had a good ability for daily streamflow simulations over the study area, similar to the performance of the RGS data. The simulation results of the LMNN model indicated that the TRMM-3B42V7 product with CC = 0.94 and NS = 0.89 had higher accuracy than the other two products. Also, its error rate (RMSE = 3.88 mm/day and MAE = 1.50 mm/day) was lower than the 3B42RT and PERSIANN products. The results of the PSONN model also showed that the TRMM-3B42V7 product with CC = 0.95 and NS = 0.90 had higher accuracy, and its error rate (RMSE = 3.80 mm/day and MAE = 1.49 mm/day) was lower than the other products. Thus, in both models, the TRMM-3B42V7 product offered the best performance in daily streamflow simulation. However, in both models, the accuracy of the 3B42RT and PERSIANN products was within acceptable limits. Altogether, by applying the PSONN model, the CC, and the Nash–Sutcliffe model efficiency coefficient were improved compared to the LMNN model and were closer to 1. The simulation results showed that by using the PSONN model compared to the LMNN model, the RMSE index of the RGS data, TRMM-3B42V7, 3B42RT, and PERSIANN decreased by 2.3, 2.1, 7.1, and 14%, respectively. Therefore, on average, the RMSE index reduced about 6.4%. Also, the reduction of MAE by using the PSONN model compared to the LMNN model for the rain gauge data, TRMM-3B42V7, 3B42RT, and PERSIANN were 7.6, 0.7, 5.5, and 8.9%, respectively, with an average of about 5.7%. Kuok et al. (2010) and Asadnia et al. (2014) also revealed in their research that the PSONN model outperformed the basic ANN model.

As mentioned earlier, the satellite-based precipitation datasets overestimated precipitation over the study area. The R_bias values were obtained in simulation with the LMNN model using the TRMM-3B42 product equal to 3.08% and in the PSONN model for this product equal to 2.24%. This index also improved in the PSONN model compared to the LMNN model. However, the positive values of the R_bias indicated that both models tend to overestimate streamflow. Figure 7 shows the scatter plots of the observed stream discharges against the simulated stream discharges, and also the distribution of these data from the line ⁠, based on the RGS data and each product using the LMNN and PSONN models. According to Figure 8, the satellite-based precipitation products could not estimate most of the observed peak stream discharges, and the neural network models based on the satellite precipitation products as inputs tend to underestimate the peak flow. Vu et al. (2018) stated this issue in their research.

In the previous section, we used and evaluated the original satellite-based precipitation datasets in daily streamflow simulation. In the following, we applied the calibrated data of satellite precipitation, which were calibrated by the GDA method. The M_bias index values were again calculated for the calibrated satellite precipitation data and these data were compared with the RGS data, the results of which are shown in Figure 9. The ideal value for the M_bias index was 1, and the calculated M_bias index values for the calibrated datasets of TRMM-3B42V7, 3B42RT, and PERSIANN were 1.05, 0.99, and 0.85, respectively. These results indicated that after calibration, the M_bias index for the TRMM-3B42RT product has reached the ideal value, and the calibration method has been useful for this product, which can be due to its data source type. The value of M_bias for the TRMM-3B42 product was close to 1, but the PERSIANN product underestimated precipitation.

These calibrated satellite precipitation data were evaluated in the simulation of the basin streamflow with both neural network models. Thus, three calibrated products of TRMM-3B42, 3B42RT, and PERSIANN were applied as inputs to the best-trained models (i.e., the pattern of No. 4 for the LMNN model and No. 5 for the PSONN model). The obtained results are shown in Table 8.

The results of streamflow simulation using both neural network models and based on the calibrated satellite precipitation data showed that the accuracy of simulation has increased, and the error rate has decreased significantly. Also, the performance of these calibrated data was close to the performance of the RGS data. Regarding the simulation with the LMNN model, it can be said that the values of CC and NS index have increased in all three calibrated products. Also, the RMSE and MAE index values have significantly reduced compared to the case where the original data were used in the simulation. However, the negative values of the R_bias index showed that the LMNN model tends to underestimate streamflow based on all three products, such as the RGS data. Another noteworthy point is that in the LMNN model, the performance of the TRMM-3B42RT product has been better than the other two products. The results also showed that the PSONN model has significantly improved simulation accuracy with the calibrated satellite precipitation data compared to the LMNN model. In the PSONN model also, the TRMM-3B42RT product performed better than the other two products. The values of the R_bias index have improved compared to the case of the original products used in simulation with the PSONN model, and the positive values of this index in all three products showed that the PSONN model tends to overestimate streamflow but their performance has been better than the RGS data.

The results showed that in both models, after calibration by the GDA method, the TRMM-3B42RT data performed better than the other two products in daily streamflow simulation over the study area. We compared the RMSE and MAE indices for both models in the streamflow simulation with the original and calibrated satellite precipitation data, as illustrated in Figure 10. According to the simulation results with the PSONN model, based on the use of the TRMM-3B42, TRMM-3B42RT, and PERSIANN datasets, after calibration, the R_bias index decreased by 48, 72, and 73%, respectively. In Figure 11, the R_bias index for the PSONN model compared the original and calibrated satellite-based precipitation data in simulation.

Figure 12 shows the scatter plots of the observed stream discharges against the simulated stream discharges, and also the distribution of these data from the line ⁠, based on each calibrated product and using the LMNN and PSONN models. Also, the observed and simulated hydrographs are illustrated in Figure 13. According to Figure 13, after calibration of satellite-based data by the GDA method, the PSONN model has improved slightly in estimating the peak flow.

Altogether, the results of the streamflow simulation in this study showed that using the hybrid PSONN model compared to the LMNN model improved the accuracy of the results and significantly reduced the simulation error rate. The satellite-based precipitation products also showed a high ability to simulate daily streamflow for the study area, similar to the performance of the RGS data.

Iran is located in the semi-arid regions of the world, and in recent years, several major water bodies of this country have been dried up, for example, the Urmia Lake and Zarinehroud River. Daily stream discharges forecasting as a non-linear and complex process is an important issue in water resource planning, especially in ungauged basins owing to the lack of reputable ground-based rainfall measurements. In this study, we evaluated the usefulness of the satellite-based precipitation products before and after calibration for streamflow modelling over the basin with a lack of ground-based precipitation data, using neural network models. It is worth noting that due to the existence of continuous data in the selected study area, which is important for the training of neural networks, in this study, we had the limitation of the spatial coverage of satellite precipitation products (the size of the study area was about three pixels). The results showed that:

• (1)

  Before calibrating the satellite precipitation products, all products overestimated precipitation over the study area. But, after calibrating them using the GDA method, the M_bias index for the TRMM-3B42RT product reached the ideal value of 1, and for the TRMM-3B42 product it was close to 1.

• (2)

  All three satellite precipitation products were able to simulate daily streamflow effectively over the study area, in such a way that the satellite precipitation products had a very close performance to the rain gauge data and could be a good substitute source to the scattered rain gauge network for streamflow simulation. The study of Su et al. (2017) also provided a similar result, in data-scarce basins using the satellite precipitation data. Therefore, the satellite-based rainfall products can be used in the future hydrological and climate change studies for the study area.

• (3)

  In general, the PSONN model performed better than the LMNN model. This study demonstrated that the PSONN model could accurately model non-linear relationships between input and output variables and presented a systematic method with reduced time spent on the network's training. Kuok et al. (2010) and Asadnia et al. (2014) also revealed in their research that the PSONN model outperformed the basic ANN model.

• (4)

  In both models, before calibration of satellite precipitation products, TRMM-3B42 showed better performance in daily streamflow simulation. This finding is consistent with the results from studies by Su et al. (2017), Ren et al. (2018), and Vu et al. (2018) in their study area. But, after calibration using the GDA method, TRMM-3B42RT performed much better.

• (5)

  After calibration of satellite precipitation products using the GDA method, in simulation with the PSONN model and use of TRMM-3B42, TRMM-3B42RT, and PERSIANN, the R_bias index decreased by 48, 72, and 73%, respectively. Thus, in general, calibration of satellite precipitation products before evaluating their performance in streamflow simulation can increase the accuracy of results.

• (6)

  In acknowledging the results of Cheema & Bastiaanssen (2012), it can be said that the GDA calibration method can be used to calibrate satellite precipitation products in regions with limited RGS data and can provide a sufficiently accurate estimate of the key hydrological process that can be applied in water management applications.

In the end, it is worth noting that the hydrological assessment of different satellite rainfall products is essential, especially for areas with a lack of rainfall data. To further examine the proposed models, we suggest the potential assessment of other satellite rainfall products such as IMERG, and CHIRPS with higher spatial resolutions for streamflow simulation over ungauged basins at different time scales. It is suggested that the hydrological evaluation of the SRPs and rainfall–runoff modelling be conducted using the deep-learning convolutional neural networks (for more information see Van et al. 2020). Also, the impact of other variables, such as topographical and soil characteristics, on streamflow simulation accuracy should be studied in future research. Furthermore, in future studies, it is suggested to investigate the spatial downscaling of these products from the original resolution to 1 km spatial resolution.

The authors would like to thank the Iran Water Resources Management Company for providing the ground-based data used in this study.

All relevant data are included in the paper or its Supplementary Information.