aluke1 / bayesian-flood-frequency-analysis

This program fits a log-pearson Type III distribution to peak stream flow records using Bayesian methods

Bayesian-Flood-Frequency-Analysis in MATLAB

This program fits a log-pearson Type III distribution to peak stream flow records using Bayesian methods

bayes_LPIII.m fits the stationary (ST) and non-stationary (NS) LPIII distributions to peak streamflow data using Bayesian inference.
Post-processing following parameter estimation calculates and plots selected return periods vs return levels, input time series vs. the mean of distribution, and the density of return level estimates for a selected return period.

Required input data is an annual maximum discharge record. Note: This program is not intended to inform design or insurance products. Please refer to federal and state guidelines for such procedures. For methodological details please see sections 4.1.1 - 4.1.3 of "Predicting nonstationary flood frequencies: Evidence supports an updated stationarity thesis in the United States". Luke et al 2017, Water Resources Research

In the NS model, the mean of the LPIII distribution changes as a function of time. Return periods are not calculated assuming changing probabilities. 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). We refer to this approach as updating ST return periods. The updated ST return periods are calculated and displayed by default when applying bayes_LPIII.m for estimation of the NS LPIII model parameters.

Required function files (must be in same directory)

bayes_LPIII.m -> main program

dream_zs.m -> MCMC algorithm

lp3inv.m -> inverse of LPII CDF based on Wilson - Hilferty transformation

lp3pdf.m -> PIII probability density function calculated 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 (United States Geological Survey site number 08074500, available at: URL:http://nwis.waterdata.usgs.gov/nwis/peak?)

Please see comments in program files and "Predicting nonstationary flood frequencies: Evidence supports an updated stationarity thesis in the United States" for further details. Luke et al 2017, Water Resources Research