Evaluation of probability density functions in precipitation models for the Pacific Northwest

Recent work has found that a one-parameter Weibull model of wet day precipitation amount based on the Weibull distribution provides a better fit to historical daily precipitation data for eastern U.S. sites than other one-parameter models. The general two-parameter Weibull distribution was compared in this study to other widely used distributions for describing the distribution of daily precipitation event sizes at 99 sites from the U.S. Pacific Northwest. Surprisingly little performance was sacrificed by reducing the two-parameter Weibull to a single-parameter distribution. Advantages of the single-parameter model included requiring only the mean wet day precipitation amount for calibration, invertibility for simulation purposes, and ease of analytical manipulation. The fit of the single-parameter Weibull to the 99 stations included in this study was significantly better than other single-parameter models tested, and performed as well as the widely endorsed, more cumbersome, two-parameter gamma model. Both the one-and two-parameter Weibull distributions are shown to have L-moments that are consistent with historical precipitation data, while the ratio of L-skew and L-variance in the gamma model is inconsistent with the historical record by this measure. In addition, it was found that the two-parameter gamma distribution was better fit using the method of moments estimators than maximum likelihood estimates. These findings suggested that the distribution in precipitation among sites in the Pacific Northwest with dramatically different settings are nearly identical if expressed in proportion to the mean site event size.