Preserving spatial linear correlations between neighboring stations in simulating daily precipitation using extended Markov models

Most stochastic weather generators have their focus on precipitation because it is the most important variable affecting environmental processes. One of the methods to reproduce the precipitation occurrence time series is to use a Markov process. But, in addition to the simulation of short-term autocorrelations in one station, it is sometimes important to preserve the spatial linear correlations (SLC) between neighboring stations as well. In this research, an extension of one-site Markov models was proposed to preserve the SLC between neighboring stations. Qazvin station was utilized as the reference station and Takestan (TK), Magsal, Nirougah, and Taleghan stations were used as the target stations. The performances of different models were assessed in relation to the simulation of dry and wet spells and short-term dependencies in precipitation time series. The results revealed that in TK station, a Markov model with a first-order spatial model could be selected as the best model, while in the other stations, a model with the order of two or three could be selected. The selected (i.e., best) models were assessed in relation to preserving the SLC between neighboring stations. The results depicted that these models were very capable in preserving the SLC between the reference station and any of the target stations. But, their performances were weaker when the SLC between the other stations were compared. In order to resolve this issue, spatially correlated random numbers were utilized instead of independent random numbers while generating synthetic time series using the Markov models. Although this method slightly reduced the model performances in relation to dry and wet spells and short-term dependencies, the improvements related to the simulation of the SLC between the other stations were substantial.