Existing Work on the Interpolation of Precipitation Data

A review of existing research in which elevational data has been incorporated in the interpolation of precipitation data was conducted and is presented here. However, all the literature found examine large study areas; research regarding the interpolation on the much larger scale of a metropolitan area or regional district such as the GVRD was not found.

Martinez-Cob (1996) supported that topographic influence is an important factor for precipitation and should therefore be considered in the spatial estimation of rainfall. He described that there has been a considerable amount of research on the performance of interpolation methods applied to mountainous terrain (e.g. Detrended Kriging, Modified Residual Kriging, and Cokriging; see Martinez-Cob for additional references), but that no method had ever been clearly established as the superior approach. This is a result of the differences in attribute variables, spatial configurations or data and the assumptions used in different studies. Any given model is only “best” for a specific case (Martinez-Cob, 1996). However, he did purport that Cokriging has a strong theoretical foundation because “no assumptions are made about the nature of the correlation between the two variables” (Martinez-Cob, 1996). The cross-semivariogram is used to account for the spatial structure and degree of correlation.

Pardo-Iguzquiza (1998) compared three different geostatistical procedures with the classical Theissen polygon method for estimating areal average climatological rainfall mean in a river basin in southern Spain. He further supported that, “if there is a correlation between climatological rainfall mean and altitude, it seems logical that the inclusion of topographic information should improve the estimates” (Pardo-Iguzquiza, 1998). It was determined that in this study scenario, Kriging with external drift performed best. Cokriging had greater requirements, with the calculation of two direct variograms and one cross-variogram. The sample density of 51 stations over an area of 6240 km2 was considered statistically adequate but fairly high density from a hydrological or climatological perspective.

Nalder and Wein (1998) conducted a spatial interpolation of climatic normals in the Canadian boreal forest. The study area was an area of relatively low relief, containing 32 stations within a coverage of hundreds of square kilometers. They found that the method they had developed, “gradient plus inverse distance squared” (GIDS), provided the most robust and simple interpolation. Price et al. (2000) followed this up with a comparison between GIDS and ANUSPLIN, an interpolation technique that calculates and optimizes thin plate smoothing splines fitted to data sets distributed across a limited number of climate station locations. They found that ANUSPLIN performed better. GIDS is an exact interpolator. The greater variability results in a rougher surface, producing large root-mean-square errors (RMSE) at locations between stations, whereas ANUSPLIN’s smoothing routines result in smaller average errors in the interpolated surface. GIDS is sensitive to local gradients but ANUSPLIN minimizes changes in gradients therefore producing smoother transitions in surface values across the data set. These transitions are generally more interpretable and intuitive than those produced by GIDS.
Prudhomme and Reed (1999) used geostatistical techniques to map extreme rainfall in a mountainous region in Scotland. They found that modified residual Kriging was the most suitable for mapping the median of annual maximum daily rainfall (RMED). Incorporating the topographical information indirectly produced a map of RMED which more closely corresponded with the effects of topography than simple spatial interpolation methods.

Ninyerola et al. (2000) used multiple regression analysis to model precipitation in Catalonia, to the northeast of the Iberian Peninsula.

Goovaerts (2000) evaluated the performance of three multivariate geostatistical techniques for incorporating elevation data into the spatial interpolation of rainfall in southern Portugal, as well as comparing these results with those of three commonly used univariate methods. Multivariate geostatistical algorithms performed better than linear regression except when considering low rainfall amounts. He found that simple Kriging with local means and Kriging with external drift performed slightly better than Colocated Cokriging but that overall the additional complexity of these models did not pay off in terms of performance. It was found that procedures that incorporated elevation using multivariate techniques generally showed an improvement in error over Ordinary Kriging as long as the coefficient of correlation between elevation and precipitation was greater than 0.75. Furthermore he concluded that the introduction of secondary information to improve estimates is only worthwhile when the coefficient of correlation is greater than 0.4, otherwise the benefits of multivariate techniques become marginal. This may occur with smaller time steps.

Boer et al. (2001) interpolated a variety of climate variables for 136 stations in the Mexican state of Jalisco. Only months with a correlation greater than 0.5 for precipitation and elevation were examined. Interpolation methods that did not include elevation as an input variable were found to be less accurate than those that did. When the correlation between elevation and precipitation was high, the accuracy of the interpolation method was correspondingly high. Trivariate thin plate splines and Trivariate Regression-Kriging seemed to perform the best. The assumption of a linear relationship between elevation and climate variables used in Cokriging resulted in poor accuracy.

Marquinez et al. (2003) applied multivariate analysis to develop estimation models for precipitation in a mountainous region in northern Spain.

Table 2 provides a summary of the methods investigated in these studies and Table 3 provides a summary of study site specifications, where available. It can be seen that although our study region has a smaller area than the other studies examining monthly or annual means, the station density and cells-to-stations ratio are both comparable to existing work.