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New Techniques for the Detection and Adjustment of Shifts in Daily Precipitation Data Series

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  • 1 Climate Research Division, Atmospheric Science and Technology Directorate, Science and Technology Branch, Environment Canada, and Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada
  • | 2 Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio
  • | 3 Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada
  • | 4 Climate Research Division, Atmospheric Science and Technology Directorate, Science and Technology Branch, Environment Canada, Toronto, Ontario, Canada
  • | 5 Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada
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Abstract

This study integrates a Box–Cox power transformation procedure into a common trend two-phase regression-model-based test (the extended version of the penalized maximal F test, or “PMFred,” algorithm) for detecting changepoints to make the test applicable to non-Gaussian data series, such as nonzero daily precipitation amounts or wind speeds. The detection-power aspects of the transformed method (transPMFred) are assessed by a simulation study that shows that this new algorithm is much better than the corresponding untransformed method for non-Gaussian data; the transformation procedure can increase the hit rate by up to ∼70%. Examples of application of this new transPMFred algorithm to detect shifts in real daily precipitation series are provided using nonzero daily precipitation series recorded at a few stations across Canada that represent very different precipitation regimes. The detected changepoints are in good agreement with documented times of changes for all of the example series. This study clarifies that it is essential for homogenization of daily precipitation data series to test the nonzero precipitation amount series and the frequency series of precipitation occurrence (or nonoccurrence), separately. The new transPMFred can be used to test the series of nonzero daily precipitation (which are non Gaussian and positive), and the existing PMFred algorithm can be used to test the frequency series. A software package for using the transPMFred algorithm to detect shifts in nonzero daily precipitation amounts has been developed and made freely available online, along with a quantile-matching (QM) algorithm for adjusting shifts in nonzero daily precipitation series, which is applicable to all positive data. In addition, a similar QM algorithm has also been developed for adjusting Gaussian data such as temperatures. It is noticed that frequency discontinuities are often inevitable because of changes in the measuring precision of precipitation, and that they could complicate the detection of shifts in nonzero daily precipitation data series and void any attempt to homogenize the series. In this case, one must account for all frequency discontinuities before attempting to adjust the measured amounts. This study also proposes approaches to account for detected frequency discontinuities, for example, to fill in the missed measurements of small precipitation or the missed reports of trace precipitation. It stresses the importance of testing the homogeneity of the frequency series of reported zero precipitation and of various small precipitation events, along with testing the series of daily precipitation amounts that are larger than a small threshold value, varying the threshold over a set of small values that reflect changes in measuring precision over time.

Corresponding author address: Dr. Xiaolan L. Wang, Climate Research Division, ASTD, STB, Environment Canada, 4905 Dufferin St., Toronto, ON M3H 5T4, Canada. Email: xiaolan.wang@ec.gc.ca

Abstract

This study integrates a Box–Cox power transformation procedure into a common trend two-phase regression-model-based test (the extended version of the penalized maximal F test, or “PMFred,” algorithm) for detecting changepoints to make the test applicable to non-Gaussian data series, such as nonzero daily precipitation amounts or wind speeds. The detection-power aspects of the transformed method (transPMFred) are assessed by a simulation study that shows that this new algorithm is much better than the corresponding untransformed method for non-Gaussian data; the transformation procedure can increase the hit rate by up to ∼70%. Examples of application of this new transPMFred algorithm to detect shifts in real daily precipitation series are provided using nonzero daily precipitation series recorded at a few stations across Canada that represent very different precipitation regimes. The detected changepoints are in good agreement with documented times of changes for all of the example series. This study clarifies that it is essential for homogenization of daily precipitation data series to test the nonzero precipitation amount series and the frequency series of precipitation occurrence (or nonoccurrence), separately. The new transPMFred can be used to test the series of nonzero daily precipitation (which are non Gaussian and positive), and the existing PMFred algorithm can be used to test the frequency series. A software package for using the transPMFred algorithm to detect shifts in nonzero daily precipitation amounts has been developed and made freely available online, along with a quantile-matching (QM) algorithm for adjusting shifts in nonzero daily precipitation series, which is applicable to all positive data. In addition, a similar QM algorithm has also been developed for adjusting Gaussian data such as temperatures. It is noticed that frequency discontinuities are often inevitable because of changes in the measuring precision of precipitation, and that they could complicate the detection of shifts in nonzero daily precipitation data series and void any attempt to homogenize the series. In this case, one must account for all frequency discontinuities before attempting to adjust the measured amounts. This study also proposes approaches to account for detected frequency discontinuities, for example, to fill in the missed measurements of small precipitation or the missed reports of trace precipitation. It stresses the importance of testing the homogeneity of the frequency series of reported zero precipitation and of various small precipitation events, along with testing the series of daily precipitation amounts that are larger than a small threshold value, varying the threshold over a set of small values that reflect changes in measuring precision over time.

Corresponding author address: Dr. Xiaolan L. Wang, Climate Research Division, ASTD, STB, Environment Canada, 4905 Dufferin St., Toronto, ON M3H 5T4, Canada. Email: xiaolan.wang@ec.gc.ca

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