A Generalized Regression Neural Network Model for Accuracy Improvement of Global Precipitation Products: A Climate Zone-Based Local Optimization

: The ability to obtain accurate precipitation data from various geographic locations is crucial for many applications. Various global products have been released in recent decades for estimating precipitation spatially and temporally. Nevertheless, it is extremely important to provide reliable and accurate products for estimating precipitation in a variety of environments. This is due to the complexity of topographic, climatic, and other factors. This study proposes a multi-product information combination for improving precipitation data accuracy based on a generalized regression neural network model using global and local optimization strategies. Firstly, the accuracy of ten global precipitation products from four different categories (satellite-based, gauge-corrected satellites, gauge-based, and reanalysis) was assessed using monthly precipitation data collected from 1896 gauge stations in Iran during 2003–2021. Secondly, to enhance the accuracy of the modeled precipitation products, the importance score of effective and auxiliary variables—such as elevation, the Enhanced Vegetation Index (EVI), the Land Surface Temperature (LST), the Soil Water Index (SWI), and interpolated precipitation maps—was assessed. Finally, a generalized regression neural network (GRNN) model with global and local optimization strategies was used to combine precipitation information from several products and auxiliary characteristics to produce precipitation data with high accuracy. Global precipitation products scored higher than interpolated precipitation products and surface characteristics. Furthermore, the importance score of the interpolated precipitation products was considerably higher than that of the surface characteristics. SWI, elevation, EVI, and LST scored 53%, 20%, 15%, and 12%, respectively, in terms of


Introduction
Various applications require high-precision precipitation data, including weather predictions, extreme climate event monitoring, water resources management, agricultural management, and urban planning [1][2][3][4][5][6].Ground stations collect the most reliable and accurate precipitation data.However, ground station-derived precipitation data face challenges such as a limited topographical distribution and a relatively short time series.In addition, these stations are converting point-based precipitation data into area-based precipitation information.
A series of satellites equipped with various sensors monitor the earth from space at specific time intervals, each capable of obtaining unique data from the components of the earth system (atmosphere, lithosphere, hydrosphere, and biosphere) [7][8][9][10][11].To date, remote sensing satellite sensors have been widely used in a variety of fields [12][13][14][15][16][17][18].There is a wide range of meteorological phenomena recorded by meteorological satellites over a wide range of geographical regions that can provide both quantitative and numerical data.These data provide a more in-depth understanding of dynamic weather conditions and precipitation systems [19][20][21][22][23].
Satellite-based precipitation products have become popular due to their high spatial and temporal resolution as well as their global coverage.Previous studies have revealed the significant potential of these products in a diverse range of climate-related fields [24][25][26][27].While providing high temporal and spatial resolution, satellite data can also be used to estimate precipitation in highlands and other difficult-access locations [19,[28][29][30][31][32][33][34].Nevertheless, a variety of studies have shown that satellite products often provide information about precipitation with uncertainty and significant errors [35][36][37].Underestimation and overestimation can significantly affect the quality of satellite products [25,38].A significant part of the effectiveness of natural hazard and climate change prediction depends on the accuracy of precipitation products both spatially and temporally [4,39].In this regard, it is necessary to investigate the accuracy of the currently available precipitation products before utilizing them for various purposes.Additionally, a strategy should be developed to enhance the accuracy of precipitation data derived from satellites.
Previous studies on precipitation can be reviewed from several different perspectives.Several studies have focused on evaluating the accuracy of precipitation products [26,29,33,[40][41][42][43].In a study conducted by Liu, Aryastana, Liu, and Huang [34], the performance of three global precipitation datasets for Bali Island was evaluated at various elevations, rainfall intensity levels, and temporal scales during 2015-2017.Camici et al. [44] showed that the performance of global precipitation products varies in different parts of the world, making it necessary to evaluate their performance before operational applications.
Several studies have evaluated the accuracy of precipitation satellite products for regional, sub-regional, and climatic zones [25,31].There can be no conclusive claim that any particular precipitation satellite product is always more or significantly less accurate than another in different conditions.In this respect, combining satellite-based products with ground and supplementary data can yield a more accurate precipitation product under a variety of conditions [43,45,46].Global precipitation products can be divided into four categories: satellite-based, gauge-corrected satellites, gauge-based, and reanalysis products [25,43].Due to the combination of several data sources in recent decades, different global precipitation products have been made available, such as Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks (PERSIANN) [35], Tropical Rainfall Measuring Mission (TRMM), US National Climate Service Forecasting Center (CMORPH) [47], Global Precipitation Measurement (GPM), Multi-Satellite Precipitation Analysis (TMPA) [48], Multi-Satellite Integrated Recovery for GPM (IMERG) [49], and the Naval Research Laboratory's (NRL) blended satellite (NRL-Blend) for precipitation estimates from laboratory NRL Naval Research [50].Some studies have focused on developing methods and products based on gauge data, satellite data, or their combination [35,46,51].According to Ceccherini et al. [46], a downscaling method has been developed that utilizes the Digital Elevation Model (DEM) and Enhanced Vegetation Index (EVI) to quantify Mean Annual Precipitation (MAP) using various precipitation products based on gauge data and satellite-based predictions.Additionally, studies such as Chen et al. (2020) and Bui et al. (2019) showed that satellite precipitation products or base models can be adjusted with ground precipitation data.This leads to the generation of a more precise precipitation product using the advantages of each dataset.Oliazadeh et al. [52] developed an algorithm for the optimal integration of different precipitation products to enable more precise estimations.They evaluated and combined the PERSIANN-CDR, TMPA-3B42, GPM-IMERG, and GSMaP MKV (SBPs) products.In previous studies, various models based on machine learning algorithms have been used to produce more accurate products by combining different precipitation products and other effective characteristics.These models had varying efficiency levels in preparing the combined precipitation product under different conditions.
This study proposes a multi-product information combination for improving precipitation data accuracy based on a neural network model using global and local optimization strategies.The accuracy of several available products was assessed for this purpose.A generalized regression neural network (GRNN) model was then employed to combine multiple global products, gauge station data, and surface characteristics to create a more accurate and reliable precipitation product.The rationale behind the model presented in this study is that a group of precipitation products can complement each other to provide additional information and improve results compared with a single product, which is supported by the collaborative decision-making principle [53].Previous research has shown that the efficiency of different precipitation products varies under different climatic conditions.In line with the collaborative decision-making principle, this study focuses on using a group of precipitation products based on the fusion of multi-source information to improve their accuracy and performance compared with individual products.

Study Area
This study was performed in Iran.The characteristics of the study area and the location of the gauge stations are shown in Figure 1.Various criteria were considered for selecting the study area, including (1) the diversity of climatic conditions (five climates), (2) the diversity of topographic conditions (plain and mountainous areas), (3) the diversity of land cover types (built-up, bare land, agriculture, forest, grassland, shrubland, water body, etc.), and (4) the variation of weather conditions in different months.Located in the northwest of Asia (at latitude 25-40 • N and longitude 44-64 • E), Iran is the 18th-largest country in the world.It is connected to the Gulf of Oman and the Persian Gulf from the south and to the Caspian Sea from the north.Its area spans 1,648,195 km 2 .The altitude of different geographical locations in Iran varies from −60 to 5590 m above sea level.The Alborz mountain range stretches from the northwest to the northeast, and the Zagros mountain range lies in the northwest-to-southwest direction.The central regions of Iran have arid climatic conditions and include the two large deserts of Kavir and Lut.Iran has a variety of climatic conditions, including humid, semi-arid, arid, and very arid.

Data
This study used data from both ground and satellite sources, including precipitation data (monthly) collected by 1896 ground stations (https://www.irimo.ir/)(accessed on 18 August 2022), global precipitation products (https://giovanni.gsfc.nasa.gov/giovanni/)(accessed on 1 August 2022), the monthly Soil Water Index (SWI) (https://land.copernicus.eu/) (accessed on 27 August 2022), the monthly Enhanced Vegetation Index (EVI) (https: //modis.gsfc.nasa.gov/data/dataprod/mod13.php) (accessed on 10 August 2022), the monthly Land Surface Temperature (LST) (https://modis.gsfc.nasa.gov/data/dataprod/mod11.php)(accessed on 22 August 2022), DEM (https://www.eorc.jaxa.jp/ALOS/en/dataset/aw3d30/aw3d30_e.htm) (accessed on 25 August 2022), and latitude data for the 2003-2021 period.Ground station information was collected by the Ministry of Energy and the Iranian Meteorological Organization (IRIMO).The initial number of stations was more than 4650.In the pre-processing step, station data were monitored for gaps, coordinates, and elevation.Afterwards, 1896 distinct stations with monthly records of precipitation were selected during the 2003-2021 period.Then, the precipitation stations were grouped into three categories as follows: (1) 1122 stations used for mapping precipitation using interpolation (Figure 1c); (2) 447 stations used for GRNN model calibration (Figure 1d); and (3) 327 stations used for both GRNN model validation and the validation of the precipitation products (Figure 1e).Random sampling was used to assign stations to different categories.To avoid cherry-picking, the user was not involved in selecting stations for each group.
Table 1 provides an overview of the global precipitation products used in this study.Although there are a wide variety of global precipitation products, this study focuses on those currently available.The MODIS MODIS11C3 products with a spatial resolution of 5000 m were used to assess the effect of surface temperature on precipitation modeling (accessible at the LAADS DAAC website).Additionally, Metop ASCAT's SWI product with a spatial resolution of 10,000 m was utilized to calculate soil moisture for precipitation modeling (accessible at the Copernicus global land service website).In the precipitation modeling process, an elevation variable was represented by the DEM of ALOS World 3D, which has a 30 m spatial resolution (accessible at the JAXA website).A cubic convolution interpolation method was used to convert the spatial resolutions of different datasets to 25 km.

Methods
Figure 2 illustrates the methodological process of the proposed strategy for generating improved precipitation products.Initially, the accuracy of the precipitation products was assessed at the study area and climatic region scales were assessed using point-to-pixel and pixel-to-pixel strategies.The next step involved assessing the importance of various factors that affect precipitation modeling accuracy, such as precipitation interpolation maps, EVI, LST, SWI, elevation, and latitude.Thirdly, a generalized regression neural network (GRNN) machine learning algorithm was utilized to combine information from several global precipitation products and supplementary data to produce an improved precipitation product.
Sustainability 2023, 15, x FOR PEER REVIEW 6 of 21 pixel and pixel-to-pixel strategies.The next step involved assessing the importance of various factors that affect precipitation modeling accuracy, such as precipitation interpolation maps, EVI, LST, SWI, elevation, and latitude.Thirdly, a generalized regression neural network (GRNN) machine learning algorithm was utilized to combine information from several global precipitation products and supplementary data to produce an improved precipitation product.

Accuracy Assessment of Precipitation Products
To evaluate the accuracy of precipitation products, a variety of metrics and strategies based on ground data were employed in this study.The metrics included Relative Bias (RBias), Root Mean Squared Error (RMSE), Random Error (RE), Systematic Error (SE), Variability Ratio (VR), Correlation Coefficient (R), and Kling-Gupta Efficiency (KGE).Rbias measures the level of underestimation (negative values) or overestimation (positive values) of predictions.Errors are smaller when the index is close to zero.RMSE is used to calculate the magnitude of the average error.Lower RMSE values indicate higher performance.Pearson's correlation coefficient (R) is used to quantify the linear relationship between estimated and actual precipitation.The accuracy of the precipitation estimation increases as the R value increases.There are two types of errors in variable estimation: systematic and random errors.The term "random errors" refers to the unpredictable fluctuations in estimated precipitation as a result of measurements, while the term "systematic errors" refers to the predictable and repeatable errors in estimated precipitation.A KGE

Accuracy Assessment of Precipitation Products
To evaluate the accuracy of precipitation products, a variety of metrics and strategies based on ground data were employed in this study.The metrics included Relative Bias (RBias), Root Mean Squared Error (RMSE), Random Error (RE), Systematic Error (SE), Variability Ratio (VR), Correlation Coefficient (R), and Kling-Gupta Efficiency (KGE).Rbias measures the level of underestimation (negative values) or overestimation (positive values) of predictions.Errors are smaller when the index is close to zero.RMSE is used to calculate the magnitude of the average error.Lower RMSE values indicate higher performance.Pearson's correlation coefficient (R) is used to quantify the linear relationship between estimated and actual precipitation.The accuracy of the precipitation estimation increases as the R value increases.There are two types of errors in variable estimation: systematic and random errors.The term "random errors" refers to the unpredictable fluctuations in estimated precipitation as a result of measurements, while the term "systematic errors" refers to the predictable and repeatable errors in estimated precipitation.A KGE combines linear correlation, bias, and variability.In this case, the optimal value is 1, which can be calculated as follows: where r is the Pearson correlation coefficient (optimal value = 1), β is the bias (optimal value = 1), and γ represents the variability ratio (optimal value = 1).The details of the calculation of these variables and evaluation metrics are presented in Saemian, Hosseini-Moghari, Fatehi, Shoarinezhad, Modiri, Tourian, Tang, Nowak, Bárdossy, and Sneeuw [25].Two strategies were used to calculate each of these metrics: "point-to-pixel" and "pixel-to-pixel".A point-to-pixel approach was utilized to evaluate the accuracy of global precipitation products through ground data (from the validation map, Figure 1e).By using this strategy, accuracy assessment results were reported and displayed according to the ground station scale.A pixel-to-pixel approach was used to evaluate the accuracy of global precipitation products by comparing them with a precipitation map derived from ground data interpolation (Figure 1e).The Ordinary Kriging (OK) method was employed for interpolation [61].The accuracy assessment results were reported and displayed at the pixel level using this strategy.

Climate Zone-Based Local Optimization Strategy
According to the proposed strategy, Equation ( 2) was used to estimate the amount of precipitation.
Precipitation Proposed model = f(LST, Elevation, EVI, SWI, Global precipitation products, Interpolated precipitation map) The function f represents the relationship between the dependent variable (precipitation) and the independent variables.The GRNN model was utilized to calculate the function f.
The GRNN is based on radial basis functions and nonparametric regression analysis.With the help of the probability density function of the training data, the GRNN establishes a functional relationship between the dependent and independent variables [62,63].GRNN, in addition to its nonlinear mapping ability and learning ability, can achieve convergence in regression analysis with a much larger sample size.The prediction output is generally very accurate when the sample size is small [64].This study employed a K-fold cross-validation method to determine which GRNN parameters should be adjusted between the training and test data to achieve the lowest Mean Square Error (MSE).Five advantages of GRNN include (i) one-pass learning, which eliminates the need for backpropagation; (ii) a high accuracy in estimation since Gaussian functions are employed; (iii) the input noise can be handled; (iv) even with sparse data in a multidimensional measurement space, the model provides a smooth transition between observed values; and (v) it is a memory-based model.The GRNN model can be shown through Equation (3).
where X is the n-dimensional input vector, Y is the predicted value of the GRNN model, E(Y|X) is the expected value of output Y according to the input vector X, and f(Y.X) is the joint probability density function of X and Y.
As part of its architecture, GRNN has four layers: input, pattern, aggregation, and output.After receiving information, the input layer stores the input vector X, which is equal to the number of neurons in the input vector.Afterward, neurons in the input layer feed data to the pattern layer.Input space to pattern space is transformed non-linearly by the pattern layer.Neurons in the pattern layer can memorize the relationship between input neurons and the appropriate response of the pattern layer.Moreover, the number of neurons is equal to the number of input variables.The Gaussian function (p i ) pattern is calculated using Equation (4).
where σ is the smoothing parameter, X is the input variable of the network, and X i is the specific training vector of neuron i in the pattern layer.The aggregation layer has two addition operations: S s and S w .The simple aggregation (S s ) performs the mathematical addition resulting from the pattern layer outputs, and its connection weight is equal to 1.
In a weighted aggregation (S w ), the pattern layer outputs are summed together with their connection weight (w).The S s and S w can be determined from Equations ( 4) and (5).
where w i is the weight of pattern neuron i which is connected to the aggregation layer.The number of neurons in the output layer is equal to the dimension k of the output vector Y.
After aggregating the neurons in the aggregation layer, the Y output of the GRNN model can be calculated using Equation (7).
In this study, a second group of ground data was used to calibrate the parameters of the GRNN model, which estimates precipitation (dependent variable) from independent variables (Figure 1d).Prior to implementing the GRNN model, an importance score was calculated for the variables, including global precipitation products, ground-based interpolated precipitation map, EVI, LST, SWI, and elevation.In order to reduce the processing volume and time, the global precipitation products with an importance degree of less than 5% were not included in the precipitation estimation process as required by the proposed model.In calibrating the proposed model, two scenarios were used: (1) a global scenario, where all ground data were used for determining the optimal structure of the GRNN; and (2) a local scenario, where ground data were used for determining the optimal structure of the GRNN based on the climate zone.In this scenario, the GRNN model was trained separately according to the climate zone (Figure 1a).

Determining the Importance Score of Effective Variables
The evaluation results of the importance scores for the effective variables in improving precipitation estimation accuracy are presented in Figure 3.The importance score for different variables was calculated based on the contribution of each one to reducing the MAE between the estimated and measured precipitation values (calibration data).The importance scores of the global precipitation products were higher than those of the interpolated precipitation product and the surface variables in generating a final precipitation product.Different climatic conditions resulted in varying importance scores for each variable.In semi-arid climates, the surface characteristics play a greater role in estimating precipitation than in other climates.
CCS, and GSMaP-Gauge (for very dry climates) were ignored in the precipitation estimation process.
Compared with semi-arid and humid climates, LST had a higher importance score in very dry and arid climates.As for EVI, the highest importance score was achieved under semi-arid climatic conditions, while the lowest importance score was achieved under very dry conditions.IMERGFinal, TRMM3B43, PERSIANN-CDR, and ERA5 had the highest importance scores concerning the final precipitation product across the study area.The contribution of global precipitation products to the GRNN model output varies by climate zone.In very arid, arid, semi-arid, and humid climates, TRMM3B43, GSMaP-Gauge, PERSIANN-CDR, and PERSIANN-CDR were the most significant, respectively.Global precipitation products with an importance degree of less than 5% were not used in the precipitation estimation process.Hence, PERSIANN, PERSIANN-CCS, and GSMaP-NRT products were not included in the estimation of precipitation based on the global strategy.Moreover, in the local strategy, PERSIANN and PERSIANN-CCS products (for humid climates), PERSIANN-CDR and PERSIANN products (for semi-arid climates), PERSIANN-CCS, GSMaP-NRT, and GSMaP-Gauge products (for dry climates), and PRECL, PERSIANN-CCS, and GSMaP-Gauge (for very dry climates) were ignored in the precipitation estimation process.
Compared with semi-arid and humid climates, LST had a higher importance score in very dry and arid climates.As for EVI, the highest importance score was achieved under semi-arid climatic conditions, while the lowest importance score was achieved under very dry conditions.

Evaluation of Global Precipitation Products by a Point-to-Pixel Approach
Table 2 presents the accuracy evaluation of different precipitation products using the data collected from the validation stations.Here, the dark green and dark red colors indicate the lower and higher values of various accuracy evaluation metrics, respectively.In terms of RMSE, PRECL had the lowest value and ERA5 the highest value.Among the evaluated precipitation products, the average RMSE values for the satellite-based, gauge-corrected satellites, gauge-based, and reanalysis products were 40.2, 34.4,42.5, and 28.9 mm/mo, respectively.Reanalysis products and satellite-based products performed the best and the worst.Based on the proposed GRNN-Global (local) model, the precipitation estimate had an RMSE of 15.6 (13.2) mm/mo.The research results show that the developed product is more effective than existing products in providing precipitation estimates.In the proposed model, the local approach to optimization had a higher efficiency than the global approach.The highest and lowest RMSE values among the PERSIANN set of products were associated with PERSIANN-CDR and PERSIANN-CCR.A point-to-pixel evaluation revealed a lower precipitation estimation accuracy than a pixel-to-pixel evaluation for global precipitation products.There is a smaller variation in precipitation amounts derived from global products than actual precipitation amounts based on variability ratios (VRs) for all products.According to the Rbias statistic, precipitation values at PRECL, GSMaP-Gauge, and PERSIANN were less than actual precipitation amounts.While the precipitation values of CHIRPS, GSMaP-NRT, and PERSIANN-CCS were higher than the actual precipitation amounts recorded at ground stations.The KGE values calculated using a point-to-pixel strategy were lower than those calculated using a pixel-to-pixel strategy.A systematic error (SE) is typically greater than 0.5 in precipitation products; despite this, there were systematic errors (SE) of 0.28, 0.35, 0.33, and 0.40 for TRMM3B43, PERSIANN-CDR, ERA5, and IMERGFinal, respectively.The results of the proposed GRNN-Global and local products showed SE values of 0.18 and 0.15, respectively, indicating the developed product's remarkable reliability in estimating precipitation.Figure 4 illustrates the geographic distribution of KGEs at validation sites over the study period.TRMM3B43, IMERG-Final, and PRECL offer better performance than others, with KGE averages of 0.30, 0.32, and 0.28.The PERSIANN set products exhibited low efficiency in estimating precipitation, with PERSIANN-CCS having negative KGE values at numerous stations, thus having the poorest performance among the set products.The precipitation estimation by the ERA5 product showed reasonable performance, especially in western Iran.However, this product performed poorly in the Alborz Mountains.Precipitation products generally performed better in western Iran, including the Zagros Mountains, than in other regions, especially in the Alborz Mountains and in the central and northwestern regions of the country.According to the proposed GRNN-Global (local) model, all the stations have KGE values greater than 0, with an average KGE of 0.56 (0.65), which indicates the superior performance of the proposed model.

Evaluation of Global Precipitation Products by a Pixel-to-Pixel Approach
In this approach, the accuracy assessment of the precipitation products was conducted using the interpolated precipitation map produced by the OK method.Here, the dark green and dark red colors indicate the lower and higher values of various accuracy evaluation metrics, respectively.In terms of the RMSE values according to Table 3, the IMERGFinal (13.7),TRMM3B43 (15.6), PERSIANN-CDR (18.5),ERA5 (19.9), and GSMaP-Gauge (24.8 mm/mo) products had the lowest values.Across the entire study area, these products provided the most accurate precipitation estimates, with KGE values of 0.89, 0.86, 0.77, 0.78, and 0.60, respectively.As far as precipitation estimation accuracy is concerned, GSMaP-NRT and PERSIANN-CCS had the least accuracy.PRECL, PERSIANN, and GSMaP-Gauge overestimated, whereas GSMaP-NRT and PERSIANN-CCS underestimated, the precipitation amounts.According to the recorded amounts, the correlation coefficient between satellite-based and gauge-based products was low.Gauge-corrected satellite products were more accurate than other product groups.
Five of the evaluated precipitation products showed a similar variability to the recorded data (VRs between 0.90 and 1.10).Nevertheless, the other three products have different trends from the recorded data, such as PERSIANN-CCS, which had a VR of 1.68.Based on the research results, the RMSE for the proposed GRNN-Global (local) precipitation product was 9.6 (8.5 mm/mo), and the KGE value was 0.92 (0.94), indicating a higher level of accuracy for the developed product when compared with the global precipitation products.A total of 95 (96%) errors in the proposed GRNN-Global (local) products can be classified as random errors.
At the pixel level, Figure 6 illustrates the geographic distribution of KGEs over the study period.The evaluated precipitation products were more accurate in areas with very arid and arid climates than in semi-arid and humid climates.Nonetheless, there are some products that are less accurate in very arid climates than in semi-arid or arid climates.The accuracy of the products under evaluation in this study in the northern sub-basins of Iran was less than in other sub-basins.It is imperative to note that global precipitation products vary in accuracy from region to region.Persian-CCS had the highest KGE class area with values below zero.In more than 50% of regions, IMERGFinal, TRMM3B43, PERSIANN-CDR, and ERA5 all had a KGE of 0.8, indicating the high degree of accuracy with which these products can be used to estimate precipitation.The proportion of regions with KGE values greater than 0.8 in the proposed precipitation products was significantly higher compared with the evaluated precipitation products.

Evaluation of Global Precipitation Products by a Pixel-to-Pixel Approach
In this approach, the accuracy assessment of the precipitation products was conducted using the interpolated precipitation map produced by the OK method.Here, the dark green and dark red colors indicate the lower and higher values of various accuracy evaluation metrics, respectively.In terms of the RMSE values according to Table 3, the IMERGFinal (13.7),TRMM3B43 (15.6), PERSIANN-CDR (18.5),ERA5 (19.9), and GSMaP-Gauge (24.8 mm/mo) products had the lowest values.Across the entire study area, these products provided the most accurate precipitation estimates, with KGE values of 0.89, 0.86, 0.77, 0.78, and 0.60, respectively.As far as precipitation estimation accuracy is concerned, GSMaP-NRT and PERSIANN-CCS had the least accuracy.PRECL, PERSIANN, and GSMaP-Gauge overestimated, whereas GSMaP-NRT and PERSIANN-CCS underestimated, the precipitation amounts.According to the recorded amounts, the correlation coefficient between satellite-based and gauge-based products was low.Gauge-corrected satellite products were more accurate than other product groups.Five of the evaluated precipitation products showed a similar variability to the recorded data (VRs between 0.90 and 1.10).Nevertheless, the other three products have different trends from the recorded data, such as PERSIANN-CCS, which had a VR of 1.68.Based on the research results, the RMSE for the proposed GRNN-Global (local) precipitation product was 9.6 (8.5 mm/mo), and the KGE value was 0.92 (0.94), indicating a higher level of accuracy for the developed product when compared with the global precipitation products.A total of 95 (96%) errors in the proposed GRNN-Global (local) products can be classified as random errors.
At the pixel level, Figure 6 illustrates the geographic distribution of KGEs over the study period.The evaluated precipitation products were more accurate in areas with very arid and arid climates than in semi-arid and humid climates.Nonetheless, there are some products that are less accurate in very arid climates than in semi-arid or arid climates.The accuracy of the products under evaluation in this study in the northern sub-basins of Iran was less than in other sub-basins.It is imperative to note that global precipitation products vary in accuracy from region to region.Persian-CCS had the highest KGE class area with values below zero.In more than 50% of regions, IMERGFinal, TRMM3B43, PERSIANN-CDR, and ERA5 all had a KGE of 0.8, indicating the high degree of accuracy with which these products can be used to estimate precipitation.The proportion of regions with KGE values greater than 0.8 in the proposed precipitation products was significantly higher compared with the evaluated precipitation products.
Figure 7 represents the KGE box plot for the evaluated precipitation products at the whole study area scale and under different climatic conditions.Considering the KGE median, product performance varies between climatic classes.Most products perform better in regions with arid climates, with only a few precipitation products, such as PERSIANN-CCS, performing poorly in these regions.The length of the box plot in regions with arid climates is shorter than in other climates, indicating low changes in precipitation products in these regions.In general, humid climates have lower KGE values than arid climates.Since the arid climate covers a large proportion of the study area, the accuracy of any product in these regions (precipitation is below 300 mm per year) is of significant importance.Since the study area contains a large area of arid climates, PERSIANN-CCS has the lowest accuracy in estimating precipitation.For regions with a humid climate, TRMM3B43, PERSIANN-CDR, and CHIRPS were more efficient than other products.At all scales, including the study area and climatic classes, the proposed model had a higher accuracy than the evaluated precipitation products.Furthermore, the developed product performed well in pixels of different climatic classes, indicating that it is stable and capable of accurately estimating precipitation under a variety of conditions.In the proposed model, the local approach had a higher efficiency than the global approach.PERSIANN-CCS and ERA5 products showed high variability in KGE values under different conditions, indicating poor performance.

Discussion
This study examined whether global precipitation products are efficient under a variety of conditions.Both point-to-pixel and pixel-to-pixel approaches were used to evaluate the accuracy of some global precipitation products [36,65].The calculated accuracy values for the pixel-to-pixel approach were significantly higher for different products compared with the point-to-pixel approach.Nevertheless, both strategies ranked the products similarly.Thus, the two strategies can be employed interchangeably to rank products.The pixel-to-pixel approach can be more useful than the point-to-pixel approach

Discussion
This study examined whether global precipitation products are efficient under a variety of conditions.Both point-to-pixel and pixel-to-pixel approaches were used to evaluate the accuracy of some global precipitation products [36,65].The calculated accuracy values for the pixel-to-pixel approach were significantly higher for different products compared with the point-to-pixel approach.Nevertheless, both strategies ranked the products similarly.Thus, the two strategies can be employed interchangeably to rank products.The pixelto-pixel approach can be more useful than the point-to-pixel approach for evaluating precipitation product accuracy because, based on this approach, precipitation products can also be evaluated in areas without ground stations.
Based on the accuracy assessment results, global precipitation products perform differently for each region.Here, IMERGFinal, TRMM3B43, and PERSIANN-CDR performed better than the others.This study showed that systematic error contributes to the total error in PRECL and PERSIANN.This conclusion is confirmed by Prakash [19].On average, 95% of the error in the developed precipitation product was random error, which is one of the strengths of the proposed product compared with the existing precipitation products.The evaluation results indicate that the PERSIANN set products estimate precipitation at different accuracy levels.As shown in PERSIANN-CCS and PERSIANN, the precipitation amounts were overestimated and underestimated, respectively, compared with the ground measurements.A study conducted by Nguyen, Ombadi, Sorooshian, Hsu, AghaKouchak, Braithwaite, Ashouri, and Thorstensen [30] concluded that PERSIANN-CCS overestimates precipitation amounts.Given the high accuracy of PERSIANN-CDR, it is evident that a gauge-based adjustment is crucial for improving satellite estimation [24,26].
This study also indicates that gauge-corrected satellite products are more efficient than gauge-based, satellite-based, and reanalysis products.Gauge-corrected satellite products utilize data collected from gauge stations in the generation of their estimations, which can enhance their accuracy [27,66].As a result of some previous studies [1,26,40], reanalysis products have been proven to be more accurate than other products in providing estimates of precipitation in warm and dry regions.Additionally, Xu, Chen, Moradkhani, Zhang, and Hu [21] indicated that reanalysis products are more accurate than satellite-based precipitation products in Australia, Europe, and North America.However, Chen, Chen, and Azorin-Molina [41] demonstrated that satellite-based products are more accurate than reanalysis products.Overall, previous studies have shown that the efficiency of different groups of precipitation products varies in different regions, so it is not possible to choose a suitable product for all conditions [67,68].Despite their strengths and weaknesses, these products can be used together to achieve higher accuracy.
It is generally accepted that precipitation products vary in performance based on precipitation type, climate, and topography [2].This study found that results are also affected by climatic conditions.Global precipitation products will differ in efficiency ranking depending on the conditions under which they are evaluated.Based on the research conducted by Hosseini-Moghari and Tang [29], global precipitation products vary in accuracy depending on precipitation type and climatic conditions.As a result, a machine learning method was employed in this study to combine information from several precipitation products, recorded precipitation data, and surface characteristics to develop a more accurate precipitation product.It was found that combining multi-product information improved precipitation estimates.Each dependent variable had a different importance score in terms of accuracy improvement.The combination of precipitation products and different surface characteristics based on the GRNN model resulted in a precipitation product with higher accuracy.Unlike the existing precipitation products, the precipitation product obtained by the proposed model had appropriate accuracy in all four climatic conditions: very arid, arid, semi-arid, and humid.The precipitation product of the proposed model showed similar levels of accuracy in all these climates, which shows its stability.
There were still some limitations to this study.First, the global precipitation products and correction variables, such as LST, EVI, SWI, and elevation, had different spatial resolutions.Second, there was some temporal inconsistency between the ground station data and the global precipitation products.Another, or perhaps the most significant, limitation of the proposed model is the time and volume of calculations required to produce a more accurate precipitation product.This is because the 10 existing precipitation products, along with biophysical and topographical characteristics, are combined based on the GRNN model.Of course, the number of these inputs can be reduced, which will affect the output accuracy.Depending on the application and the expected sensitivity to precipitation estimation accuracy, the volume and time of calculations can be reduced by reducing model inputs.On the other hand, other effective parameters can be considered as inputs.This increases the accuracy of the proposed model while also increasing computational costs.

Conclusions
It is important to assess the efficiency of global precipitation products under varying conditions.Various products have different levels of efficiency given the geographical, climatic, and topographic conditions, as demonstrated in this study.In order to create a product that is accurate in a variety of conditions, it has been proposed to combine existing global precipitation products with complementary data.TRMM3B43, IMERGFinal, PERSIANN-CDR, and PERSIANN products have the highest impact on very dry, arid, semi-arid, and humid conditions, respectively.In terms of importance, the interpolated precipitation map has higher significance than topography and surface biophysical variables.Among the surface biophysical variables, SWI has a higher importance score than LST and EVI.These results show that a precipitation product alone cannot be suitable for various geographical locations in a country such as Iran with a diverse climate.Even at a particular geographical location, the efficiency of different precipitation products differs at different times.As a result, combining the capabilities of different precipitation products can improve precipitation estimation accuracy in areas with diverse conditions.As a result of the accuracy evaluation, the developed product provides a more stable and accurate estimate of precipitation amounts than global precipitation products.In the proposed model, the local approach to optimization had a higher efficiency than the global approach.As opposed to existing precipitation products, the accuracy of precipitation estimation using the proposed model was close to each other under varied climate conditions, which indicates the stability of this model under different conditions.A basic concept of this study is to develop a model that uses the collaborative decision-making principle and integrates findings at the decision-making level to produce a more accurate precipitation product using existing precipitation products and their varying capabilities.As the proposed model uses multiple variables in the production process, it is limited in terms of time and the volume of calculations.Future studies should concentrate on determining effective and optimal variables (inputs) that can reduce the time and volume of the calculations required.

Figure 1 .
Figure 1.Maps of (a) climatic conditions, (b) DEM, and location of gauge stations in Iran that are used for (c) mapping precipitation using the interpolation method, (d) GRNN model calibration, and (e) GRNN model validation and validation of the global precipitation products.

Figure 1 .
Figure 1.Maps of (a) climatic conditions, (b) DEM, and location of gauge stations in Iran that are used for (c) mapping precipitation using the interpolation method, (d) GRNN model calibration, and (e) GRNN model validation and validation of the global precipitation products.

Figure 2 .
Figure 2. The methodology flowchart of the study.

Figure 2 .
Figure 2. The methodology flowchart of the study.

Figure 3 .Figure 3 .
Figure 3.The effective variables and their relative importance in enhancing precipitation estimation accuracy (GPPs: global precipitation products; IPP: interpolated precipitation product; SPTC: surface biophysical and topographical characteristics; EVI: enhanced vegetation index; LST: land surface temperature; SWI: soil water index).

Sustainability 2023 , 21 Figure 4 .
Figure 4. Geographic distribution of KGEs at validation sites based on point-to-pixel approach.Figure 4. Geographic distribution of KGEs at validation sites based on point-to-pixel approach.

Figure 4 .
Figure 4. Geographic distribution of KGEs at validation sites based on point-to-pixel approach.Figure 4. Geographic distribution of KGEs at validation sites based on point-to-pixel approach.

Figure 5 21 Figure 5 .
Figure 5 illustrates the KGE box plot of the evaluated precipitation products at the ground stations.IMERGFinal, TRMM3B43, PRECL, GSMaP-Gauge, and CHIRPS had higher KGE values than other products.GSMaP-NRT and PERSIANN-CCS had the lowest KGE values.In comparison with other global precipitation products, PRECL, TRMM3B43, and IMERGFinal had median values of 0.52, 0.30, and 0.41, respectively, which indicates

Figure 5 .
Figure 5. Graph of KGE values over Iran during the 2003-2021 period derived from a point-to-pixel evaluation approach.

Figure 6 .
Figure 6.Geographic distribution of KGEs based on a pixel-to-pixel approach.

Figure 6 .
Figure 6.Geographic distribution of KGEs based on a pixel-to-pixel approach.

Figure 7 .
Figure 7. Graph of KGE values throughout Iran and climate zones during the 2003-2021 period derived from a pixel-to-pixel evaluation strategy.

Figure 7 .
Figure 7. Graph of KGE values throughout Iran and climate zones during the 2003-2021 period derived from a pixel-to-pixel evaluation strategy.

Table 2 .
Accuracy assessment results for the point-to-pixel approach (Different colors (from dark green to dark red) indicate different values (from lower to higher) of various accuracy evaluation metrics respectively).

Table 3 .
Accuracy assessment results for the pixel-to-pixel approach (Different colors (from dark green to dark red) indicate different values (from lower to higher) of various accuracy evaluation metrics respectively).