G-2024-34
Statistical testing of scaling models for precipitation Intensity-Duration-Frequency curves
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Producing accurate precipitation Intensity-Duration-Frequency (IDF) curves necessitates robust statistical methodologies. Employing a scaling model to combine information across the various precipitation accumulation durations is desirable for reducing uncertainty and facilitating interpolation to durations not observed. A variety of such scaling models exist, yet there is currently no formal goodness-of-fit testing procedure for selecting an appropriate one. In this paper, we develop a goodness-of-fit procedure to determine if a scaling model is suitable for precipitation IDF data. The proposed test extends the Anderson-Darling test and involves dividing the database into training and validation sets. The training set is used to estimate the parameters of the target model, while the validation set is utilized to compute the test statistic. The asymptotic distribution of the test statistic is established within a general framework, enabling analytical calculation of the critical region for the test. In our application to precipitation IDF curves, data corresponding to the shortest accumulation duration are chosen for the validation set. We validate the performances of the test through a simulation study, demonstrating that under the null hypothesis, the test maintains the nominal rejection rate even for small samples ranging from 5 to 20 years. Under an alternative hypothesis, the rejection rate increases with the discrepancy between the models as well as with the sample size. When applied to historical data, the test suggests the use of different scaling models for Montréal (QC) and Vancouver (BC).
Published May 2024 , 27 pages
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