Biological and Environmental Research - Earth and Environmental System Sciences
Earth and Environmental System Modeling
20 July 2020

A Unified Approach to Evaluating Precipitation Frequency Estimates with Uncertainty Quantification: Application to Florida and California Watersheds


Intensity, duration, and frequency (IDF) curves, also known as precipitation-frequency (PF) estimates, are the estimates of the probable intensity of precipitation associated with different durations (e.g., 6-hr, 24-hr) and recurrence intervals (2-year, 5-year, etc.).  This study presents a unified framework for computing PF estimates in a dataset using regional frequency analysis, uncertainty quantification, and kriging (an interpolation method).


A simple methodology, applicable in a variety of regions, produces IDF estimates that are statistically indistinguishable from NOAA Atlas 14 reports and are less uncertain than those from NOAA Atlas 14. A novel aspect is the results are calibrated using probability integral transform (PIT) histogram, a popular approach in probabilistic forecasting used to estimate the accuracy of forecasts.


The methodology employed is as follows.  (i) First, Regional frequency analysis (RFA) with the L-moments method. RFA combines data from nearby stations with similar characteristics (e.g., geographical proximity, elevation, and mean precipitation, etc.). L-moments are defined as certain linear combinations of order statistics of a random sample. In order statistics, random samples are ordered from the smallest to the largest. L-moments-based methods are less sensitive to outliers (unusually high) values in the data. (ii) Second, Kriging is applied to interpolate station data to the grid.  Kriging is an interpolation method considered better than conventional interpolation methods (e.g., distance weighting) because kriging accounts for proximity in data, spatial correlation, and also estimates interpolation uncertainty. (iii) Third, we quantify uncertainty in PF estimates. The methodology is shown to be applicable to two widely different regions, the Kissimmee-Southern Florida watershed (flat topography) and the Sacramento-San Joaquin watershed (complex topography). The PF estimates obtained from our methodology are shown to be statistically indistinguishable from the NOAA-Atlas 14 estimates. Moreover, our estimates are shown to be reasonably calibrated using probability integral transform (PIT)- a method popular in probabilistic forecasting used to estimate the accuracy of forecasts. 

Abhishekh Srivastava
University of California - Davis