A New Method for Generating Stochastic Simulations of Daily Air Temperature for Use in Weather Generators

Abstract

stochastic harmonic autoregressive parametric (SHArP) weather generator is presented that simulates trended, nonstationary temperature values directly, circumventing the conventional approach of adding simulated standardized anomalies of temperature to a prescribed cyclostationary mean. The model mean makes autocorrelated transitions between wet- and dry-state values, and its parameters are determined by optimizing harmonic and trend terms. The precipitation-responsive autocorrelated transitions yield more realistic temperature behavior during frontal passage in comparison with prior models that switch abruptly between wet- and dry-state means. If the stochastic (noise) term is assumed to have constant amplitude, analytical results are available via maximum likelihood estimation (MLE) and are equivalent to least squares estimation (LSE). Where observations motivate a seasonally varying noise coefficient, MLE becomes nonlinear, and an analytical solution is formulated via LSE. For illustration, SHArP is shown to produce realistic representations of daily maximum air temperature at a single site, which for the study is the Salt Lake City International Airport (KSLC). SHArP reduces the temperature bias following frontal passages by over 2°C in three seasons. A method for generalizing the model to multiple variables at multiple sites is discussed.