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Assessing Goodness of Fit to a Gamma Distribution and Estimating Future Projection on Daily Precipitation Frequency Using Regional Climate Model Simulations over Japan with and without the Influence of Tropical Cyclones

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  • 1 Meteorological Research Institute, Tsukuba, Ibaraki, Japan
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Abstract

Goodness of fit in daily precipitation frequency to a gamma distribution was examined, focusing on adverse effects originating from the shortage of sampled tropical cyclones, using precipitation data with and without the influence of tropical cyclones. The data used in this study were obtained through rain gauge observations and regional climate model simulations under the RCP8.5 scenario and the present climate. An empirical cumulative distribution function (CDF), calculated from a sample of precipitation data for each location, was compared with a theoretical CDF derived from two parameters of a gamma distribution. Using these two CDFs, the root-mean-square error (RMSE) was calculated as an indicator of the goodness of fit. The RMSE exhibited a decreasing tendency when the influence of tropical cyclones was removed. This means that the empirical CDF derived from sampled precipitation more closely resembled the theoretical CDF when compared with the relationship between empirical and theoretical CDFs, including precipitation data associated with tropical cyclones. Future changes in the two parameters of the gamma distribution, without the influence of tropical cyclones, depend on regions in Japan, indicating a regional dependence on changes in the shape and scale of the CDF. The magnitude of increases in no-rain days was also dependent on regions of Japan, although the number of no-rain days increased overall. This simplified approach is useful for analyzing climate change from a broad perspective.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Akihiko Murata, amurata@mri-jma.go.jp

Abstract

Goodness of fit in daily precipitation frequency to a gamma distribution was examined, focusing on adverse effects originating from the shortage of sampled tropical cyclones, using precipitation data with and without the influence of tropical cyclones. The data used in this study were obtained through rain gauge observations and regional climate model simulations under the RCP8.5 scenario and the present climate. An empirical cumulative distribution function (CDF), calculated from a sample of precipitation data for each location, was compared with a theoretical CDF derived from two parameters of a gamma distribution. Using these two CDFs, the root-mean-square error (RMSE) was calculated as an indicator of the goodness of fit. The RMSE exhibited a decreasing tendency when the influence of tropical cyclones was removed. This means that the empirical CDF derived from sampled precipitation more closely resembled the theoretical CDF when compared with the relationship between empirical and theoretical CDFs, including precipitation data associated with tropical cyclones. Future changes in the two parameters of the gamma distribution, without the influence of tropical cyclones, depend on regions in Japan, indicating a regional dependence on changes in the shape and scale of the CDF. The magnitude of increases in no-rain days was also dependent on regions of Japan, although the number of no-rain days increased overall. This simplified approach is useful for analyzing climate change from a broad perspective.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Akihiko Murata, amurata@mri-jma.go.jp
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