Non-Stationary Flood Frequency Analysis

This program fits a non-stationary LPIII distribution to peak discharge data via Bayesian Inference

bayes_LPIII.m estimates the parameters of stationary (ST) and nonstationary (NS) LPIII models using Bayesian inference.
Post-processing calculates and plots selected return periods vs return levels,
input time series vs the mean of distribution, and the denisty of return level estimates for a selected return period.
Required input data is an annual maximum discharge record. For methodological details
please see:
Luke, A., Vrugt, J. A., AghaKouchak, A., Matthew, R., & Sanders, B. F. (2017).
Predicting nonstationary flood frequencies: Evidence supports an updated
stationarity thesis in the United States. Water Resources Research.

In the NS model, the mean of the LPIII distribution changes as a function of time. Return periods are not calculated in a true non-stationary sense, but rather for a fixed value of the mean. In other words, return periods are calculated assuming the distribution remains fixed in time. The updated ST return periods are calculated and displayed by default when applying bayes_LPIII.m for estimated of the NS LPIII model parameters. The updated ST return periods are obtained by calculating the return periods associated with the NS mean at the end of the fitting period,
or t = t(end), assuming the distribution remains fixed in time following the end of the record.

Required function files (must be in same directory)
bayes_LPIII.m -> main program
dream_zs.m -> MCMC algorithm
lp3inv.m -> inverse of lp3 CDF based on Wilson - Hilferty transformation
lp3pdf.m -> PIII probability denisty function calcualted in log-space (returns actual density)
prior_pdf.m -> computes prior density of parameter combination
prior_rnd.m -> random draw from prior (for initialization)
post_pdf.m -> computes unnormalized posterior density for at proposal theta and data X. Likelihood function in this file
record.txt -> example record

Please see comments in program and Luke et al. 2017 for more details.