Estimating Precipitation Extremes using Log-Histospline

TL;DR

The paper introduces the Log-Histospline method as a new approach for modeling precipitation extremes, providing a unified analysis of the entire data range without threshold selection.

Contribution

It proposes the LHSpline method that models the full data density, including tails, using smoothing splines on log-transformed data, addressing limitations of the peaks-over-threshold approach.

Findings

LHSpline effectively models precipitation data tails.

The method captures polynomial tail behavior.

Application to Houston rainfall data demonstrates its utility.

Abstract

One of the commonly used approaches to modeling extremes is the peaks-over-threshold (POT) method. The POT method models exceedances over a threshold that is sufficiently high or low so that the exceedance has approximately a generalized Pareto distribution (GPD). This method requires the selection of a threshold that might affect the estimates. Here we propose an alternative method, the Log-Histospline (LHSpline), to explore modeling the tail behavior and the remainder of the density in one step using the full range of the data. LHSpline applies a smoothing spline model to a finely binned histogram of the log transformed data to estimate its log density. By construction, a LHSpline estimation is constrained to have polynomial tail behavior, a feature commonly observed in daily rainfall observations. We illustrate the LHSpline method by analyzing precipitation data collected in Houston, Texas.