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This paper develops a method for determining whether two vector time series originate from a common stochastic process. The stochastic process considered incorporates both serial correlations and multivariate annual cycles. Specifically, the process is modeled as a vector autoregressive model with periodic forcing, referred to as a VARX model (where X stands for exogenous variables). The hypothesis that two VARX models share the same parameters is tested using the likelihood ratio method. The resulting test can be further decomposed into a series of tests to assess whether disparities in the VARX models stem from differences in noise parameters, autoregressive parameters, or annual cycle parameters. A comprehensive procedure for compressing discrepancies between VARX models into a minimal number of components is developed based on discriminant analysis. Using this method, the realism of climate model simulations of monthly mean North Atlantic sea surface temperatures is assessed. As expected, different simulations from the same climate model cannot be distinguished stochastically. Similarly, observations from different periods cannot be distinguished. However, every climate model differs stochastically from observations. Furthermore, each climate model differs stochastically from every other model, except when they originate from the same center. In essence, each climate model possesses a distinct fingerprint that sets it apart stochastically from both observations and models developed by other research centers. The primary factor contributing to these differences is the difference in annual cycles. The difference in annual cycles is often dominated by a single component, which can be extracted and illustrated using discriminant analysis. [ABSTRACT FROM AUTHOR]

The 2014-2018 drought over South Africa's winter rainfall zone (WRZ) created a critical water crisis which highlighted the region's drought and climate change vulnerability. Consequently, it is imperative to better understand the climatic characteristics of the drought in order to inform regional adaptation to projected climate change. In this paper we investigate the spatio-temporal patterns of drought intensity and the recent rainfall trends, focusing on assessing the consistency of the prevailing conceptual model of drought drivers with observed patterns. For this we use the new spatial subdivision for the region encompassing the WRZ introduced in our companion paper (Conradie et al., 2022). Compared to previous droughts since 1979, the 2014-2018 drought in the WRZ core was characterised by a markedly lower frequency of very wet days (exceeding the climatological 99.5th percentile daily rainfall -- including dry days) and of wet months (SPI1 > 0:5), a sub-seasonal attribute not previously reported. There was considerable variability in the spatial footprint of the drought. Short-term drought began in the south-western core WRZ in spring 2014. The peak intensity gradually spread north-eastward, although a spatially near-uniform peak is seen during mid-2017. The overall drought intensity for the 2015--2017 period transitions radially from most severe in the WRZ core to least severe in the surroundings. During 2014 and 2015, the drought was most severe at those stations receiving the largest proportion of their rainfall from westerly and north-westerly winds; by 2018, those stations receiving the most rain from the south and south-east were most severely impacted. This indicates an evolving set of dynamic drivers associated with distinct rain-bearing synoptic flows. No evidence is found to support the suggestion that the drought was more severe in the mountain catchments of Cape Town's major supply reservoirs than elsewhere in the core nor that rain day frequency trends since 1979 are more negative in this subdomain. Rainfall and rain day trend rates also exhibit some connections to the spatial seasonality structure of the WRZ, although this is weaker than for drought intensity. Caution should be applied in assessing South African rain day trends given their high sensitivity to observed data shortcomings. Our findings suggest an important role for zonally asymmetric dynamics in the region's drought evolution. This analysis demonstrates the utility of the spatial subdivisions proposed in the companion paper by highlighting spatial structure in drought intensity evolution linked to rainfall dynamics. [ABSTRACT FROM AUTHOR]