Comparison of spatial interpolation methods for estimating the precipitation distribution in Portugal

Abstract

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.

A Comparison of the Performance of Different Interpolation Methods in Replicating Rainfall Magnitudes under Different Climatic Conditions in Chongqing Province (China)

“…Recently, spatial interpolation has become one commonly used method in climatic research and spatial analyses of climate elements, including precipitation [22]. Different interpolation methods provide an efficient response for describing the spatial distribution of precipitation [23], using the data of sparse stations to obtain precipitation surfaces [24]. Generally, interpolation methods for spatial pattern analysis includes steps for (1) identification of the characteristics of georeferenced data, especially as they are portrayed on maps, (2) tests on hypotheses about mapped patterns, and (3) construction of models that give meaning to relationships among georeferenced variables [25].…”

“…Several spatial interpolation methods exist which are normally classified into two major categories: deterministic and geostatistical methods. Deterministic interpolation methods, for instance, Inverse Distance Weighting (IDW), Radial Basis Function (RBF), Diffusion Interpolation with Barrier (DIB), Kernel Interpolation with Barrier (KIB) and so forth, generate continuous distribution of precipitation, starting from measured points using mathematical formulas to determine the similarity or degree of smoothing [23]. Geostatistical interpolation methods, including Ordinary Kriging (OK), Empirical Bayesian Kriging (EBK) and other derived kriging methods, quantify the spatial autocorrelations among sampling points and create unbiased predictions with minimum variance [26,27].…”

“…To this end, the deterministic methods including IDW, RBF, DIB, KIB and geostatistical methods including OK, EBK have been applied in the current research; these techniques are part of the tool kit of the Geostatistical Analyst based on a GIS environment, in which the interpolated estimates in IDW are based on values at a nearby location without any spatial relationship among them. This method was used primarily due to its simplicity and the advantage of capturing extreme precipitation [23,27]. RBF is a method for rapidly predicting precipitation, and generates better prediction when used for a larger dataset, while it is not suitable if precipitation presents high variance in short distance [23].…”

“…This method was used primarily due to its simplicity and the advantage of capturing extreme precipitation [23,27]. RBF is a method for rapidly predicting precipitation, and generates better prediction when used for a larger dataset, while it is not suitable if precipitation presents high variance in short distance [23]. The method is also one of primary tools for interpolating multidimensional scattered data [27].…”

“…The semivariogram model depicts the spatial variability in a regionalized variable, and its parameters require manual adjustments in GIS to receive accurate results for classical kriging methods [26]. EBK acts as a recent development to build valid spatial models by automatically searching model parameters through a process of subsetting and simulations based on the Bayesian standpoint, which has been applied to the spatial interpolation of annual and monthly precipitation with favorable results [23,26,29]. Previous studies indicated that a more precise prediction might be the technique of geostatistical methods than deterministic interpolation [26,[29][30][31][32], whereas some studies have reached different conclusions [33].…”