title: Spatial Variability and Error Limits of Reference Evapotranspiration Estimates
Creators: name: Ley, Thomas W.
Publisher: name: Utah State University
Year: 1995

description: The overall objective of this research was to develop a methodology for assessing the spatial variability and error limits of reference evapotranspiration (ETr) estimates from a weather station network. Likely errors introduced into ETr estimates due to sensor measurement variability and nonstandard site conditions were investigated. Temporal and spatial correlation structures of the weather variables used to compute ETr and of ETr data collected over a three-year period by an operational agricultural weather station network were studied.
Results indicated that ETr errors are minimal compared to inherent model error when sensors (of the type studied) are maintained and calibrated to operate with measurement errors that are within the limits of manufacturer's specifications of accuracy. Sensor evaluation studies showed new and recalibrated/reconditioned sensors often were operating within the limits of accuracy specifications.
A methodology for adjusting maximum, minimum, and dewpoint temperature data collected at arid weather measurement sites to reflect the conditions of an irrigated measurement site was developed. Positive bias in air temperatures and negative bias in dewpoint temperatures measured at arid sites resulted in positive bias in ETr. as much as 17% greater (approximately 1.4 mm d-1) in July and August, at some arid sites as compared to an irrigated reference site. Weather data adjustment algorithms based on daily energy and soil water balances at the dry sites were developed. These provided effective removal of bias in the dry station data and ETr estimates.
Univariate autoregressive models of daily weather parameters--maximum and minimum temperature, solar radiation, dewpoint temperature and wind speed, and daily ETr--were developed using standard time series analysis approaches. These models can be used to forecast/estimate weather variables or ETr at the weather station sites studied. Space-time models were developed for each variable as multivariate AA(1) processes, having lag one temporal correlation and lag zero and lag one spatial correlation. The lag zero cross correlation matrixes of standardized zero-mean, and spatially and seasonally detrended residuals of each variable were analyzed with interstation distances and with contoured isoline plots imposed on the network area. This revealed that geographically nearest neighbor stations were not always the most correlated. Interpolation of observations between and among network sites should include consideration of spatial correlation structure as well as physical proximity.
The multivariate AR(1) models were used in state-space representation with the Kalman filter to determine statistically optimal estimates of the true state of a network variable at a given time. The effects of maximum and minimum weather data measurement errors found during the course of this research were evaluated in the Kalman filter. Kalman filter ETr estimation error was equivalent to the reported error of the Penman-Wright ETr model. The Kalman filter was shown to be an effective spatial interpolation technique for ETr. Using stations that were best correlated to a suppressed fictitious point interpolation site was more efficient than using stations that were geographically closest, i.e., only three best correlated stations provided the same ETr estimation error as was obtained using six nearest neighbors.