Uncertainty and hotspots in 21st century projections of agricultural drought from CMIP5 models.

Future climate changes could alter hydrometeorological patterns and change the nature of droughts at global to regional scales. However, there are considerable uncertainties in future drought projections. Here, we focus on agricultural drought by analyzing surface soil moisture outputs from CMIP5 multi-model ensembles (MMEs) under RCP2.6, RCP4.5, RCP6.0, and RCP8.5 scenarios. First, the annual mean soil moisture by the end of the 21st century shows statistically significant large-scale drying and limited areas of wetting for all scenarios, with stronger drying as the strength of radiative forcing increases. Second, the MME mean spatial extent of severe drought is projected to increase for all regions and all future RCP scenarios, and most notably in Central America (CAM), Europe and Mediterranean (EUM), Tropical South America (TSA), and South Africa (SAF). Third, the model uncertainty presents the largest source of uncertainty (over 80%) across the entire 21st century among the three sources of uncertainty: internal variability, model uncertainty, and scenario uncertainty. Finally, we find that the spatial pattern and magnitude of annual and seasonal signal to noise (S/N) in soil moisture anomalies do not change significantly by lead time, indicating that the spreads of uncertainties become larger as the signals become stronger.

Maximum likelihood estimation with binary-data regression models: small-sample and large-sample features.

Many inferential procedures for generalized linear models rely on the asymptotic normality of the maximum likelihood estimator (MLE). Fahrmeir & Kaufmann (1985, Ann. Stat., 13, 1) present mild conditions under which the MLEs in GLiMs are asymptotically normal. Unfortunately, limited study has appeared for the special case of binomial response models beyond the familiar logit and probit links, and for more general links such as the complementary log-log link, and the less well-known complementary log link. We verify the asymptotic normality conditions of the MLEs for these models under the assumption of a fixed number of experimental groups and present a simple set of conditions for any twice differentiable monotone link function. We also study the quality of the approximation for constructing asymptotic Wald confidence regions. Our results show that for small sample sizes with certain link functions the approximation can be problematic, especially for cases where the parameters are close to the boundary of the parameter space.