The first stage fits the mean, variance, skewness and kurtosis of temperature as smooth functions of day of year. It combines Generalized Additive Models for Location, Scale and Shape with a Sinh-Arcsinh, or SHASH, distribution, whose tail-weight parameter provides a way to represent the observed platykurtosis. The resulting quantile residuals were close to the ideal standard-normal benchmarks of mean 0, standard deviation 1, skewness 0 and kurtosis 3. GSAT’s Akaike information criterion was 78.4 units better than that of Gaussian GAMLSS, a difference the authors describe as decisive by information-criterion standards: the corresponding relative likelihood for the Gaussian specification was approximately 10^−17. This stage also produced the largest gains in the Monte Carlo comparison, reducing standard-deviation root-mean-square error by 80.5% and skewness RMSE by 26.7%, while kurtosis RMSE was 11.6% higher.

The second stage accounts for dependence among days through an autoregressive moving-average model of order (3,1), while the third uses an exponential generalized autoregressive conditional heteroscedasticity model of order (1,1) to represent changing residual volatility. The authors reported a possible warm-anomaly leverage asymmetry, but presented it with bootstrap uncertainty and did not treat it as a main source of performance. Across 1,000 Monte Carlo replications, GSAT beat the Fourier–ARMA–Normal benchmark on six of eight measures. Component ablation experiments attributed the improvement primarily to the stages that modeled seasonal variance and distributional shape, and leave-one-year-out testing supported out-of-sample generalization.

Evidence from six UAE stations—Abu Dhabi, Dubai, Sharjah, Al Ain, Ras Al Khaimah and Fujairah—broadened the assessment beyond the five-year Abu Dhabi record. The station records covered 13 to 39 complete years, five of the country’s seven emirates and both coastlines. Every station showed a highly significant seasonal variance cycle, with Bartlett p-values below 10^−55 and below 10^−200 at the four longest-record stations. The four-moment GAMLSS-SHASH specification improved on Gaussian GAMLSS by 73 to 462 AIC units at the stations. Tail weight also varied by season and location, indicating that UAE temperatures are not uniformly platykurtic. A peaks-over-threshold analysis was consistent with a bounded, or light, upper tail, although both GSAT and the benchmark overestimated the maximum length of warm spells.

Further validation used temporally blocked cross-validation across 31 test blocks, each containing as many as five complete years, with eight to 35 training years per fold. Four folds required strict forward testing. Held-out monthly-climatology Nash–Sutcliffe efficiencies ranged from 0.947 to 0.995, while ensemble-mean daily-scale values ranged from 0.85 to 0.93; monthly-mean mean absolute percentage error was 1.2–3.5%. GSAT had lower held-out standard-deviation RMSE than the identically fitted benchmark in 30 of 31 folds. Its synthesis stage also mapped the simulated latent process through the fitted residuals’ empirical cumulative distribution function, with probability-integral-transform calibration verified directly. Synthetic series reproduced the observed autocorrelation of anomalies and squared anomalies. The study presents GSAT as a way to generate synthetic temperature series while preserving not only seasonal averages but also evolving variability, skewness, kurtosis and short-range temporal structure; its validation is regional and observational rather than evidence of operational forecasting skill.

Subject of Research: Evaluation of GSAT for generating synthetic daily temperature series in the United Arab Emirates

Article Title: Gsat: a higher-order stochastic framework for synthetic daily temperature generation in the United Arab Emirates

Article References: Elseidi, M. (2026). Gsat: a higher-order stochastic framework for synthetic daily temperature generation in the United Arab Emirates. Theoretical and Applied Climatology, 157(11), Article 738. https://doi.org/10.1007/s00704-026-06666-1

Image Credits: AI Generated

DOI: 10.1007/s00704-026-06666-1

Keywords: synthetic weather generation, daily temperature, United Arab Emirates, GAMLSS-SHASH, stochastic modeling, seasonal variance, ARMA models, eGARCH, cross-validation, climate extremes, Gsat, higher-order