Precipitation has a strong and constant impact on different economic sectors, environment, and social activities all over the world. An increasing interest for monitoring and estimating the precipitation characteristics can be claimed in the last decades. However, in some areas the ground-based network is still sparse and the spatial data coverage insufficiently addresses the needs. In the last decades, different interpolation methods provide an efficient response for describing the spatial distribution of precipitation. In this study, we compare the performance of seven interpolation methods used for retrieving the mean annual precipitation over the mainland Portugal, as follows: local polynomial interpolation (LPI), global polynomial interpolation (GPI), radial basis function (RBF), inverse distance weighted (IDW), ordinary cokriging (OCK), universal cokriging (UCK) and empirical Bayesian kriging regression (EBKR). We generate the mean annual precipitation distribution using data from 128 rain gauge stations covering the period 1991 to 2000. The interpolation results were evaluated using cross-validation techniques and the performance of each method was evaluated using mean error (ME), mean absolute error (MAE), root mean square error (RMSE), Pearson's correlation coefficient (R) and Taylor diagram. The results indicate that EBKR performs the best spatial distribution. In order to determine the accuracy of spatial distribution generated by the spatial interpolation methods, we calculate the prediction standard error (PSE). The PSE result of EBKR prediction over mainland Portugal increases form south to north.

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Over the last decades, climatic changes have triggered considerable impacts across the globe with detrimental effects on all ecosystems. Given the complexity of topography and climate, Romania is one of the most exposed countries in the South‐Eastern Europe to extreme hydrological events. As a consequence, the spatial distribution of precipitation is of greater importance for future analysis. This study examines the performance of Empirical Bayesian Kriging Regression Prediction (EBKRP) and Geographically Weighted Regression (GWR) to predict the spatial distribution of annual and seasonal precipitation over Romania. Twelve co‐variables derived from topography, and remote sensing products data were used to improve the prediction. The co‐variable selection process was performed prior to the regression model to reduce the complexity and processing time, using the Boruta Algorithm (BA), which is an innovative approach. The performance of BA was compared with Gini Coefficient. Our findings confirmed that 10 co‐variables were relevant to predict annual precipitation and nine for seasonal. The overall prediction of precipitation is more influenced by topography (altitude, slope, surface roughness) and the distance to marine bodies (Black Sea and Adriatic Sea). Cross‐validation and five statistical metrics were applied to assess the performance of the regression models. The results show similar spatial distribution pattern of precipitation, whereas the highest annual precipitation is found in the Carpathian Mountains (EBKRP: 1,399.2 mm, GWR: 1,249.7 mm) and the lowest in the lowlands (EBKRP: 355.9 mm, GWR: 346.8 mm). For seasons, both methods predicted the highest precipitation in summer and lowest in autumn. In all seasons, the precipitation is underestimated by both methods, however, for annual, only GWR does so. Our study revealed GWR as the best method to predict annual and seasonal precipitation over Romania, as it yielded the highest correlation coefficient Spearman (S), Pearson (P), determination coefficient (R2) and lowest mean absolute error (MAE) and root mean square error (RMSE).

Precipitation has a strong and constant impact on different economic sectors, environment, and social activities all over the world. An increasing interest for monitoring and estimating the precipitation characteristics can be claimed in the last decades. However, in some areas the ground-based network is still sparse and the spatial data coverage insufficiently addresses the needs. In the last decades, different interpolation methods provide an efficient response for describing the spatial distribution of precipitation. In this study, we compare the performance of seven interpolation methods used for retrieving the mean annual precipitation over the mainland Portugal, as follows: local polynomial interpolation (LPI), global polynomial interpolation (GPI), radial basis function (RBF), inverse distance weighted (IDW), ordinary cokriging (OCK), universal cokriging (UCK) and empirical Bayesian kriging regression (EBKR). We generate the mean annual precipitation distribution using data from 128 rain gauge stations covering the period 1991 to 2000. The interpolation results were evaluated using cross-validation techniques and the performance of each method was evaluated using mean error (ME), mean absolute error (MAE), root mean square error (RMSE), Pearson’s correlation coefficient (R) and Taylor diagram. The results indicate that EBKR performs the best spatial distribution. In order to determine the accuracy of spatial distribution generated by the spatial interpolation methods, we calculate the prediction standard error (PSE). The PSE result of EBKR prediction over mainland Portugal increases form south to north.