Statistical properties of multi-year droughts in climate models and observations with corresponding theoretical estimates

Abstract Multi-year droughts (MYDs) can have major impacts on ecosystems, agriculture, water resources, economies, people and societies. Here, we examine statistical properties of MYDs consisting of uninterrupted sequences of years in which annual precipitation falls below a given threshold. We examine statistics including the proportion of years that are part of droughts of duration $$\ge n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>≥</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> </mml:math> years, the proportion of droughts that have duration $$\ge n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>≥</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> </mml:math> years, and both the duration and the number of droughts with duration $$\ge n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>≥</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> </mml:math> years, in thirty-eight 200-year-long simulations of CMIP6 coupled global climate models under pre-industrial control conditions. We also derive formulae that approximate the average value of these and other statistics using simple stochastic models. The theoretical values obtained agree reasonably well with their Multi-Model Mean (MMM) climate model counterparts over the globe. Regional contrasts in the value of the statistics for MYDs consisting of uninterrupted sequences of years with below-average precipitation can be largely explained by spatial variations in the percentile of the mean. Corresponding formulae that account for non-zero temporal autocorrelation tend to agree somewhat more closely with the MMM values. MYD statistics are estimated using observational data and compared with theoretical and climate model estimates. The formulae incorporating non-zero autocorrelation provide a better estimate of the observational values than do MMM values or formulae derived assuming zero autocorrelation.