Approximate Bayesian computation methods for daily spatiotemporal precipitation occurrence simulation

Abstract

Stochastic precipitation generators (SPGs) produce synthetic precipitation data and are frequently used to generate inputs for physical models throughout many scientific disciplines. Especially for large data sets, statistical parameter estimation is difficult due to the high dimensionality of the likelihood function. We propose techniques to estimate SPG parameters for spatiotemporal precipitation occurrence based on an emerging set of methods called Approximate Bayesian computation (ABC), which bypass the evaluation of a likelihood function. Our statistical model employs a thresholded Gaussian process that reduces to a probit regression at single sites. We identify appropriate ABC penalization metrics for our model parameters to produce simulations whose statistical characteristics closely resemble those of the observations. Spell length metrics are appropriate for single sites, while a variogram‐based metric is proposed for spatial simulations. We present numerical case studies at sites in Colorado and Iowa where the estimated statistical model adequately reproduces local and domain statistics.

Testing tests before testing data: an untold tale of compound events and binary dependence

“…This setting mimics the analysis of daily records on an annual basis in terms of sample size. The values of q 1 and H cover a wide range of serial dependence scenarios, from independence to fairly strong persistence, while the values of p X i 1 and p X j 1 are consistent with the possible combinations of average probabilities of occurrence of daily rainfall in various climates (e.g., Harrold et al 2003;Robertson et al 2004;Serinaldi 2009;Olson and Kleiber 2017). For each combination of parameters, simulation and JOP test are repeated 10000 times in order to compute the empirical rejection rate.…”

“…3.1) implicitly assume that the theoretical values of p X i 1 and p X j 1 (and p X i 0 and p X j 0 ) are constant over the period of analysis. However, the seasonal patterns of rainfall occurrence (e.g., Harrold et al 2003;Robertson et al 2004;Serinaldi 2009;Mehrotra et al 2012;Olson and Kleiber 2017) make this assumption quite unrealistic for daily data over annual time windows, which is the time interval suggested by De Michele et al ( 2020) for JOP analysis. Therefore, it is important to understand the effect of seasonally varying p X i 1 and p…”

Multisite Weather Generators Using Bayesian Networks: An Illustrative Case Study for Precipitation Occurrence

“…(2012). A similar measure has been analyzed in Olson and Kleiber (2017), in which they consider wet spell counts.…”

“…Here we also analyze spells occurring simultaneously in more than 90% of the stations, as done for the model introduced in Kleiber et al (2012). A similar measure has been analyzed in Olson and Kleiber (2017), in which they consider wet spell counts. Wilks (1998) shows that the Wilks model precisely adjusts probabilities for the events (1,1) and (0,0) between pairs of stations.…”

“…Existing approaches for multisite weather generation build on many different techniques to generate synthetic spatially consistent series, such as empirical orthogonal function analysis (Zhou et al., 2019), weather typing (Ailliot et al., 2015), nearest neighbours (Yates et al., 2003), and Gaussian processes (Kleiber et al., 2012) —which permit the interpolation to locations where there are no direct observations—or more sophisticated approximate Bayesian computation (ABC) methods for thresholded Gaussian processes (Olson & Kleiber, 2017). In general, there is no overall best method, and the Wilks seminal contribution is still a good first choice in terms of complexity and performance, as shown in different intercomparison studies (Keller et al., 2015; Mehrotra et al., 2006).…”