Simulation of temperature series and small networks from data

Abstract

It is often desirable to simulate a single temperature series or a collection (network) of temperature series. Accurate simulations can enhance our understanding of temperature trends and variabilities. Simulation can also be used to generate data with known specifications, which are useful in assessing climate data processing routines such as quality control and homogenization algorithms. Possessing multiple realistic temperature series is often beneficial as only one natural record of our climate is available. The current popularity of general circulation models (GCMs) demonstrates how important simulation techniques are. However, even with sophisticated downscaling, it is difficult to replicate station temperature data that have realistic seasonal cycles as well as realistic temporal and spatial correlations. This paper reviews and studies statistical time series methods that can replicate a single series or a network of series from data. The methods are purely statistical—no atmospheric dynamics are involved—and attempt to produce replicates of the records under study. The work here develops (a) methods that simulate temperatures from a fixed season (say a particular day or month of the year) that match the distributional characteristics of the observed data; (b) methods for simulating an entire series that matches the series' temporal autocorrelations and seasonal cycle; and (c) methods for simulating a network of series that reproduce the data's observed seasonal cycles and spatial and temporal autocorrelations. Applications are given throughout, including one where a GCM series and local station data are used in tandem to describe long‐term trends and inject realistic station‐level short‐term fluctuations. This paper can be used as a tutorial for the simulation of a single climate observation, an entire climate series, or a network of multiple climate series simultaneously. Extensions of the ideas that involve GCMs are also examined.

Comparing climate time series – Part 2: A multivariate test

“…Box et al (2008) define four different approximate estimates: least-squares estimates, approximate maximum likelihood estimates, conditional least-squares estimates, and Yule-Walker estimates (see their Appendix A7.4). For a climate example based on Yule-Walker estimates, see Washington et al (2019). However, for moderate and large samples, the differences between the estimates are small.…”

An adapted vector autoregressive expectation maximization imputation algorithm for climate data networks

“…Thus we have 70 years × 12 months × 15 stations, for a total of 12,600 observations. Sometimes, it is desirable to seasonally standardize all observations across season and station as in Lund, Hurd, Bloomfield, and Smith (1995) and Washington, Seymour, Lund, and Willett (2019). This is likely to remove (or at least reduce) any nonstationary components in a network.…”