Antonio Martínez-Cob

MULTIVARIATE GEOSTATISTICAL ANALYSIS OF EVAPOTRANSPIRATION AND PRECIPITATION IN MOUNTAINOUS TERRAIN

Abstract This paper reports the evaluation of three geostatistical interpolation methods (ordinary kriging, cokriging and modified residual kriging) to interpolate long-term mean total annual reference evapotranspiration (AETO) and long-term mean total annual precipitation (APRE) in a mountainous region, where the stationarity hypothesis probably do not hold for the whole region, but do hold locally. AETO and APRE estimates and estimation errors were evaluated at validation stations. Estimates and computed estimation error variances (used as indicators of estimation uncertainty) were also obtained at 1913 5 km grid points. In general, estimates at validation stations were in good agreement with observed values for all interpolation methods, although modified residual kriging estimates of APRE were slightly worse than those obtained by the other two methods. Based on mean absolute error (MAE) and mean squared error (MSE) at validation stations, no method ranked clearly above other for interpolation of AETO. At grid points, AETO estimation uncertainty was improved by cokriging by about 11.5% and 8.4% compared with ordinary kriging and modified residual kriging, respectively. Likewise, cokriging was superior for interpolation of APRE in terms of MAE and MSE obtained at validation stations. At grid points, cokriging reduced estimation uncertainty by 18.7% and 24.3% compared with ordinary kriging and modified residual kriging, respectively, whereas modified residual kriging in general did not improve ordinary kriging results. Computed estimation error variance values indicated that modified residual kriging would reduce estimation uncertainty in areas where very few weather stations are available for interpolation.

Influence of elevation on regional evapotranspiration using multivariate geostatistics for various climatic regimes in Oregon

Abstract An investigation of the application of multivariate geostatistics for analysis of regional evapotranspiration is reported. The focus of the research was analysis and modeling of the spatial correlation between evapotranspiration and elevation above sea level. The main goal was to investigate whether the use of cokriging could improve the accuracy of evapotranspiration estimates over a regular grid by including elevation in the estimation procedure. A total of 11 study cases for each of four different climatic regions (Willamette Valley, North Central, South Central and East) within the state of Oregon were analyzed. Long-term monthly (February to November) averages of daily reference evapotranspiration (ET r ) and values of annual ET r were available at 199 locations within the regions. Values of elevation were available at the 199 locations and at 8570 additional locations spaced at approximately 5 km intervals on a grid. Experimental direct- and cross-semivariograms were computed to describe the spatial variability of ET r and elevation, and their correlation. Experimental direct-semivariograms for ET r showed best fit with isotropic spherical models with small nugget effects. Experimental direct-semivariograms for elevation showed best fit with isotropic models with nugget effects and two nested structures (spherical and gaussian) for the Willamette Valley region, one structure (spherical) for the North Central region, and two nested structures (spherical and linear) for the South Central and East regions. The experimental cross-semivariograms showed best fit with isotropic spherical models. Monthly and annual ET r values were estimated at 8570 locations situated at an approximately 5 km grid spacing using kriging and cokriging in conjunction with the previously fitted direct- and cross-semivariograms. Kriging and cokriging estimation error standard deviations were computed for each study case at all locations. ET r estimates and estimation error standard deviations were plotted as contour maps. Maximum, minimum and average kriging and cokriging estimates of ET r were in general agreement, although minimum and average values tended to be lower for cokriging. However, contour lines of cokriged ET r more closely reflected the elevation features of the climatic regions. Maximum and average estimation errror standard deviations were lower for cokriging, although minimum values were very similar for both kriging and cokriging. Average cokriging standard deviations decreased by about 20–30% in the Willamette Valley and North Central regions and by 5–13% in the South Central and East regions. These differences between regions were due to the lower correlation coefficients between ET, and elevation observed in the latter two regions. Contour maps of standard deviations showed cokriging had a more uniform distribution of estimation errors than kriging, for which errord tended to decrease in the vicinity of the sample ET, points at the weather stations. Errors increased along regional borders for both kriging and cokriging, although maximum estimation error values were lower for cokriging.

Evapotranspiration and crop coefficients of rice (Oryza sativa L.) under sprinkler irrigation in a semiarid climate determined by the surface renewal method

The evapotranspiration (ETc) of sprinkler-irrigated rice was determined for the semiarid conditions of NE Spain during 2001, 2002 and 2003. The surface renewal method, after calibration against the eddy covariance method, was used to obtain values of sensible heat flux (H) from high-frequency temperature readings. Latent heat flux values were obtained by solving the energy balance equation. Finally, lysimeter measurements were used to validate the evapotranspiration values obtained with the surface renewal method. Seasonal rice evapotranspiration was about 750–800 mm. Average daily ETc for mid-season (from 90 to 130 days after sowing) was 5.1, 4.5 and 6.1 mm day−1 for 2001, 2002 and 2003, respectively. The experimental weekly crop coefficients fluctuated in the range of 0.83–1.20 for 2001, 0.81–1.03 for 2002 and 0.84–1.15 for 2003. The total growing season was about 150–160 days. In average, the crop coefficients for the initial (Kcini), mid-season (Kcmid) and late-season stages (Kcend) were 0.92, 1.06 and 1.03, respectively, the length of these stages being about 55, 45 and 25 days, respectively.

Using Thermal Units for Crop Coefficient Estimation and Irrigation Scheduling Improves Yield and Water Productivity of Corn (Zea mays L.)

AbstractEstimates of the daily crop coefficient (Kc) for corn and irrigation scheduling were performed during 2009 and 2010 by means of two approaches: Treatment I, computation of Kc using the Food and Agriculture Organization of the United Nations (FAO) method; and Treatment II, computation of Kc from relative fraction of thermal units. Corn crop water requirements and irrigation gross depth for Treatment I were approximately 25 to 33% lower than those for Treatment II in 2009 and 2010, respectively. However, the performance of Treatment II was better in terms of grain yield, which was 9.2  Mg ha−1 (in 2009) and 9.4  Mg ha−1 (in 2010), approximately 37 and 29% higher, respectively, than that for Treatment I. Water productivity was approximately 10% higher for Treatment II during 2009 and practically the same percentage higher than that for Treatment I during 2010. Because of year-to-year variability, water productivity was approximately 25% (Treatment II) and 11% (Treatment I) higher for 2010 than for 20...

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.