Stochastic Models to Generate Geospatial-, Temporal-, and Cross-Correlated Daily Maximum and Minimum Temperatures

Guillermo A Baigorria

doi:10.1155/2014/365362

Abstract

Weather generators are tools used to downscale monthly to seasonal climate forecasts, from numerical climate models to daily values for use as inputs for crop and other environmental models. One main limitation of most of weather generators is that they do not incorporate neither the spatial/temporal correlations between/within sites nor the cross-correlations between variables, characteristics specially important when aggregating, for example, simulated crop yields, freeze events, or heat waves in a watershed or region. Three models were developed to generate realization of daily maximum and minimum temperatures for multiple sites. The first model incorporates only spatial correlation, whereas temporal correlation using a 1-day lag and cross-correlation between variables were added to model one, respectively, by the other two models. Vectors of correlated random numbers were rescaled to temperature values by multiplying each element with the standard deviation and adding the mean of the corresponding weather station. An extension of Crout's algorithm was developed to enable the factorization of nonpositive definite matrices. Monthly spatial correlations of generated daily maximum and minimum temperatures between all pairs of weather stations closely matched their observed counterparts. Performance was analyzed by comparing the root mean squared error, temporal semivariograms, correlation/cross-correlation matrices, multiannual monthly means, and standard deviations.

Highlights

Because of the geospatially homogeneous nature of daily temperatures, few publications have investigated the generation of daily temperatures while reproducing the observed spatial variability [1, 2]
The present approach is based on the assumption of spatialtemporal covariance stationarity, which implies that the autocovariance functions of the data series, the spatial correlations between the data series, and the cross-correlation between variables of the data series do not change during the time period considered
The use of semivariograms based on the spatial correlation could help if one wants to apply the model on a region where the length of the dataset is too short to permit a proper calculation of the correlation matrices

Summary

Introduction

Because of the geospatially homogeneous nature of daily temperatures, few publications have investigated the generation of daily temperatures while reproducing the observed spatial variability [1, 2]. Most of these methods [3, 4], including those presented in the current paper, are based on Wilks’ parametric model [5]. The applicability of Wilks’ methods is potentially limited if the correlation matrix cannot be factorized, such as the case when a matrix is nonpositive definite. The probability of facing nonpositive definite matrix increases exponentially for large number of locations or the use of more complex matrices, which includes lag time and cross-correlations.

Objectives

Methods

Results

Conclusion