A Hidden Climate Indices Modeling Framework for Multivariable Space‐Time Data.

Risk assessment for climate‐sensitive systems often relies on the analysis of several variables measured at many sites. In probabilistic terms, the task is to model the joint distribution of several spatially distributed variables, and how it varies in time. This paper describes a Bayesian hierarchical framework for this purpose. Each variable follows a distribution with parameters varying in both space and time. Temporal variability is modeled by means of hidden climate indices (HCIs) that are extracted from observed variables. This is to be contrasted with the usual approach using predefined standard climate indices (SCIs) for this purpose. In the second level of the model, the HCIs and their effects are assumed to follow temporal and spatial Gaussian processes, respectively. Both intervariable and intersite dependencies are induced by the strong effect of common HCIs. The flexibility of the framework is illustrated with a case study in Southeast Australia aimed at modeling "hot‐and‐dry" summer conditions. It involves three physical variables (streamflow, precipitation, and temperature) measured on three distinct station networks, with varying data availability and representing hundreds of sites in total. The HCI model delivers reliable and sharp time‐varying distributions for individual variables and sites. In addition, it adequately reproduces intervariable and intersite dependencies, whereas a corresponding SCI model (where hidden climate indices are replaced with standard ones) strongly underestimates them. It is finally suggested that HCI models may be used as downscaling tools to estimate the joint distribution of several variables at many stations from climate models or reanalyzes. Plain Language Summary: The management of hydroclimatic hazards such as droughts and heatwaves relies on the estimation of probabilities of occurrence for extreme events. Standard approaches are available for this task when one given hazard is studied at one particular location. However, this is often not sufficient. For instance, the impact of droughts or heatwaves strongly depends on their spatial extent, which requires analyzing them over many sites. It is also useful to analyze droughts and heatwaves together rather than separately, because their joint occurrence creates favorable conditions for other hazards such as bushfires to occur. In this paper, we propose a methodological framework to analyze in a probabilistic way data sets describing several hazards at many sites over many years. The principle of this approach is to identify unobserved processes called "hidden climate indices" that are pulling the strings that make data vary. This is illustrated with a case study analyzing "hot‐and‐dry" summers in Southeast Australia (https://vimeo.com/600898709). Key Points: We propose a general probabilistic model for describing the space‐time variability of multivariable dataThe model is based on hidden climate indices extracted from the target data, as opposed to predefined standard climate indicesThe model is general and flexible, and can handle a wide range of hydrometeorological data sets [ABSTRACT FROM AUTHOR]