Future Occurrence of Threshold-Crossing Seasonal Rainfall Totals: Methodology and Application to Sites in Africa

Asher B. Siebert Department of Geography, Rutgers, The State University of New Jersey, Piscataway, New Jersey

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M. Neil Ward International Research Institute for Climate and Society, Columbia University, Palisades, New York

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Abstract

A statistical simulation framework is developed to explore the future frequencies of threshold-crossing events, focusing here on low seasonal rainfall totals. Global change (GC) is represented by a trend on the seasonal mean rainfall total. Natural decadal to multidecadal variability (MDV) is represented by an autoregressive process. Interannual variability (IV) of seasonal totals is represented by white noise with either a normal or skew normal distribution consistent with parameters observed in the historical record at the location being modeled. Monte Carlo simulations are undertaken for various combinations of the above components, and the authors evaluate the extent to which future event frequencies can be estimated from the statistics of previous years. The sample of four study locations used to illustrate the approach is drawn from the Millennium Villages Project in Africa, where the potential of index insurance as a development and adaptation tool has been considered, thereby bringing a targeted problem setting to the analyses. The simulations highlight a number of general principles. For example, it is shown that a 10% change in the mean rainfall can lead to a change of order times 2 in the number of threshold-crossing low seasonal rainfall totals, even without invoking any change in the characteristics of the IV. The magnitudes of change are also shown to be sensitive to the threshold studied, as well as to site-specific climate features (here, coefficient of variation and skewness). The framework developed permits quantification of how, especially in the near term (of order 30 years), MDV can strongly add to uncertainty about future event frequencies. Therefore, statistical treatment of estimated MDV magnitudes will often be a key input to optimal risk management, with further enhancements expected through explicit MDV forecasts. The results highlight the importance of finding optimal ways to update climate statistics such as event thresholds, in the presence of GC and MDV.

Corresponding author address: Asher Siebert, Room #B214, Lucy Stone Hall, Livingston Campus, Rutgers University, Piscataway, NJ 08854. Email: asherb.siebert@gmail.com

Abstract

A statistical simulation framework is developed to explore the future frequencies of threshold-crossing events, focusing here on low seasonal rainfall totals. Global change (GC) is represented by a trend on the seasonal mean rainfall total. Natural decadal to multidecadal variability (MDV) is represented by an autoregressive process. Interannual variability (IV) of seasonal totals is represented by white noise with either a normal or skew normal distribution consistent with parameters observed in the historical record at the location being modeled. Monte Carlo simulations are undertaken for various combinations of the above components, and the authors evaluate the extent to which future event frequencies can be estimated from the statistics of previous years. The sample of four study locations used to illustrate the approach is drawn from the Millennium Villages Project in Africa, where the potential of index insurance as a development and adaptation tool has been considered, thereby bringing a targeted problem setting to the analyses. The simulations highlight a number of general principles. For example, it is shown that a 10% change in the mean rainfall can lead to a change of order times 2 in the number of threshold-crossing low seasonal rainfall totals, even without invoking any change in the characteristics of the IV. The magnitudes of change are also shown to be sensitive to the threshold studied, as well as to site-specific climate features (here, coefficient of variation and skewness). The framework developed permits quantification of how, especially in the near term (of order 30 years), MDV can strongly add to uncertainty about future event frequencies. Therefore, statistical treatment of estimated MDV magnitudes will often be a key input to optimal risk management, with further enhancements expected through explicit MDV forecasts. The results highlight the importance of finding optimal ways to update climate statistics such as event thresholds, in the presence of GC and MDV.

Corresponding author address: Asher Siebert, Room #B214, Lucy Stone Hall, Livingston Campus, Rutgers University, Piscataway, NJ 08854. Email: asherb.siebert@gmail.com

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