Civil Engineering Association

Estimation of mean annual precipitation as affected by elevation using multivariate geostatistics

This paper presents the results of the interpolation of annual precipitation over a regular grid performed in Aragón (Spain). The main objective was the quantification of the improvement in estimation uncertainty by including elevation in the interpolation and by using base 10 logarithms of both annual precipitation and elevation versus the original values.

Long-term annual precipitation (APRE) was available at 182 weather stations. Elevation above sea level (ELEV) was available at those stations and at 1913 additional points over a regular 5 km grid. The spatial variability of APRE, ELEV and their base 10 logarithms (LAPRE and LELEV, respectively), and the spatial correlation between APRE and ELEV, APRE and LELEV, LAPRE and ELEV, and LAPRE and LELEV were described by gaussian direct- and cross-semivariogram models with nugget effects.

Geostatistical interpolation methods, ordinary kriging and cokriging, were used to estimate APRE and LAPRE at the 1913 additional elevation points. Estimates of LAPRE were transformed back to APRE values. Cokriging estimates were in general higher than kriging ones, mainly at points of high elevation. The average percent difference among cokriging and kriging estimates was 9–12%. Cokriging estimates obtained with the different sample data sets were in general terms similar. However, at points of high elevation, cokriging with ELEV as the auxiliary variable seemed to overestimate annual precipitation.

Estimation error standard deviations (EESD) also were computed in each interpolation point. For all points, the EESD obtained using LAPRE values were lower than those obtained using APRE values, being the average percent differences of −38 to −42%. Likewise, for all interpolation points, cokriging EESD were lower than kriging ones. Using LAPRE and LELEV values, the average percent difference among cokriging and kriging EESD was −11.0%, with minimum and maximum percent differences of −6.7 and −35.8%, respectively.