Nonstationary Extreme Value Analysis (NEVA) Software Package. User Guide
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1 Nonstationary Extreme Value Analysis (NEVA) Software Package User Guide Update: 10/23/2014
2 Nonstationary Extreme Value Analysis (NEVA) Software Package User Guide Center for Hydrology & Remote Sensing University of California, Irvine
3 Authors: Linyin Cheng and Amir AghaKouchak
4 Disclaimer: The Nonstationary Extreme Value Analysis (NEVA) software package is provided 'as is' without any endorsement made and without warranty of any kind, either express or implied. While we strive to ensure that NEVA is accurate, no guarantees for the accuracy of the codes, output information and figures are made. NEVA codes and outputs can only be used at your own discretion and risk and with agreement that you will be solely responsible for any damage and that the authors and their affiliate institutions accept no responsibility for errors or omissions in NEVA codes, outputs, figures, and documentation. In no event shall the authors, developers or their affiliate institutions be liable to you or any third parties for any special, direct, indirect or consequential damages and financial risks of any kind, or any damages whatsoever, resulting from, arising out of or in connection with the use of NEVA. The user of NEVA agrees that the codes and algorithms are subject to change without notice.
5 Nonstationary Extreme Value Analysis (NEVA) Software Package: User Guide Linyin Cheng, and Amir AghaKouchak University of California, Irvine Abstract The Nonstationary Extreme Value Analysis (NEVA) software package has been developed to facilitate extreme value analysis under both stationary and nonstationary assumptions. In a Bayesian approach, NEVA estimates the extreme value parameters with a Differential Evolution Markov Chain (DE MC) approach for global optimization over the parameter space. NEVA includes posterior probability intervals (uncertainty bounds) of estimated return levels through Bayesian inference, with its inherent advantages in uncertainty quantification. The software presents the results of non stationary extreme value analysis using various exceedance probability methods. We evaluate both stationary and nonstationary components of the package for a case study consisting of annual temperature maxima for a gridded global temperature dataset. The results show that NEVA can reliably describe extremes and their return levels. The source code can be downloaded from here: Main reference publication: Cheng L., AghaKouchak A., Gilleland E., Katz R.W., 2014, Non stationary Extreme Value Analysis in a Changing Climate, Climatic Change, doi: /s
6 Table of Contents 1 Overview of NEVA Components Run NEVA GEV Open NEVA.m in MATLAB Specify the path to the package in NEVA.m Navigate to ReadData folder in NEVA_GEV Configure NEVA GEV Edit GEV_sta_nonsta.txt to set the model parameters (ReadData folder): Edit input data file si1.txt (ReadData folder): Edit names.txt (ReadData folder) Edit prior.txt (ReadData folder) Read the ReadMe File (zreadme.txt in NEVA_GEV) Run NEVA GEV Run NEVA GPD Open NEVA.m in MATLAB Specify the path to the package in NEVA.m Navigate to ReadData folder in NEVA_GPD Configure NEVA GPD Edit GPD_sta_nonsta.txt to set the model parameters (ReadData folder): Edit input data file si1.txt (ReadData folder): Edit names.txt (ReadData folder) Edit prior.txt (ReadData folder) See ReadMe File (zreadme.txt in NEVA_GPD) Run NEVA_GPD Save Outputs Errors and Warnings... 9 References and Relevant Literature... 10
7 Page 1 1 Overview of NEVA Components NEVA includes two components: (1) The Generalized Extreme Value (GEV) distribution for analysis of annual maxima (block maxima). (2) The Generalized Pareto Distribution (GPD) for analysis of extremes above a certain threshold (i.e., peak over threshold (POT) approach). Both NEVA GEV and NEVA GPD can be used for stationary (time independent) and nonstationary (transient) extreme value analysis.
8 Page 2 The package includes the following files and folders: 1 Folder NEVA_GEV: Includes source codes for stationary and nonstationary Generalized Extreme Value (GEV) distribution for analysis of annual maxima (block maxima). 2 Folder NEVA_GPD: Includes source codes for stationary and nonstationary Generalized Pareto Distribution (GPD) for analysis of extremes above a certain threshold (i.e., peakover threshold (POT) approach). 3 File Disclaimer.txt: By using NEVA users agree with this disclaimer. Please read the disclaimer before using NEVA. 4 NEVA_ReferencePublication.pdf: Reference publication of NEVA. 5 NEVA_User_Guide.pdf: This document 2 Run NEVA GEV Follow the below steps to run NEVA: 2.1 Open NEVA.m in MATLAB Note that both NEVA_GEV, and NEVA_GPD include NEVA.m. For annual maxima analysis, select the one in NEVA_GEV folder. For POT analysis, open the one in NEVA_GPD folder (see Section 3).
9 Page Specify the path to the package in NEVA.m For example: dirr= 'C:\Users\Amir\Google Drive\AMIR\MySoftware\NEVA_GEV'; 2.3 Navigate to ReadData folder in NEVA_GEV 2.4 Configure NEVA GEV You can configure NEVA GEV by editing the files in ReadData folder. There four files that can be edited: GEV_sta_nonsta.txt, names.txt, si1.txt, prior.txt GEV_sta_nonsta.txt: includes model parameters names.txt: includes figure titles and axes labels (they appear in the output figures) prior.txt: include prior parameters (ranges of model parameters used for sampling) si1.txt: includes input data In GEV_sta_nonsta.txt make sure the stationary and nonstationary assumptions are correctly configured: Nonsta=0 indicates stationary Nosta=1 represents nonstationary with time varying location parameter Nosta=2 represents nonstationary with time varying location and scale
10 Page Edit GEV_sta_nonsta.txt to set the model parameters (ReadData folder): da: evl: bur: cha: sts: siteno: Nonsta: end year of the observations number of random samples for parameter estimation number of burned samples chain number (5 is reasonable) after burn in, if want to further reduce sample size edit sts number of sites/gauges 0: stationary simulation; 1: nonstationarity in location parameter; 2: nonstationarity in location and scale parameters tt: done: plottrend: GEVQQ: wait: lir: BF: Quic: Simulation time or return period Notify by when simulation is complete: 0: No; else: Yes plot trend lines; 0: No; else: Yes generate QQ plots to evaluate if data fits GEV; 0: No; else: Yes Simulation based on the waiting time theory likelihood ratio test; 0: No; else: Yes Bayes factor calculation; 0: No; else: Yes likelihood profile estimation; 0:No; else:yes (the default Quic=0 offers parameter estimation and uncertainty bounds based on the method outlined in Cheng et al., For faster simulation, the user can choose the maximum likelihood method Quic=1. The latter requires the optimization toolbox Edit input data file si1.txt (ReadData folder): Last column: year Other columns: Block maxima (annual maxima) from stations/gauges/model simulations
11 Page Edit names.txt (ReadData folder) This file only changes titles and labels in the output figures: First line: title that appears in the output figure. Use the first line for stationary plots Second line: title that appears in the output figure. Use the first line for nonstationary plots Third line: xlabel (label of x axis) Fourth line: ylabel (label of y axis) Edit prior.txt (ReadData folder) The default values should be reasonable for most applications: SIGMA: the range of the scale parameter in GEV distribution K: the range of the shape parameter in GEV distribution Apha: Beta: Asig: Bsig: the range of the slope for the location parameter under nonstationary the range of the intercept for the location parameter under nonstationary the range of the slope for the scale parameter under nonstationary the range of the intercept for the scale parameter under nonstationary 2.5 Read the ReadMe File (zreadme.txt in NEVA_GEV) See the readme file to learn more about the input variables and parameters in GEV_sta_nonsta.txt, names.txt, si1.txt, prior.txt 2.6 Run NEVA GEV Run NEVA.m in Matlab (NEVA_GEV folder).
12 Page 6 3 Run NEVA GPD Follow the below steps to run NEVA: 3.1 Open NEVA.m in MATLAB Note that both NEVA_GEV, and NEVA_GPD include NEVA.m. For annual maxima analysis, select the one in NEVA_GEV folder (Section 2). For POT analysis, open the one in NEVA_GPD folder. 3.2 Specify the path to the package in NEVA.m For example: dirr= 'C:\Users\Amir\Google Drive\AMIR\MySoftware\NEVA_GPD'; 3.3 Navigate to ReadData folder in NEVA_GPD 3.4 Configure NEVA GPD You can configure NEVA GPD by editing the files in ReadData folder. There four files that can be edited: GPD_sta_nonsta.txt, names.txt, si1.txt, prior.txt GPD_sta_nonsta.txt: includes model parameters names.txt: prior.txt: includes figure titles and axes labels (appear in the output figures) include prior parameters (ranges of model parameters
13 Page 7 si1.txt: includes input data In GPD_sta_nonsta.txt make sure the stationary and nonstationary assumptions are correctly configured: Nonsta=0 Nonsta=1 indicates stationary simulation represents nonstationary simulation Edit GPD_sta_nonsta.txt to set the model parameters (ReadData folder): da: evl: bur: cha: sts: siteno: Nonsta: tt: done: plottrend: GPQQ: thp: lir: BF: Quic: end year of the observations number of random samples for parameter estimation number of burned samples chain number (5 is reasonable) after burn in, if want to further reduce sample size edit sts number of sites/gauges 0: stationary simulation; 1: nonstationarity simulation; Simulation time or return period Notify by when simulation is complete: 0: No; else: Yes plot trend lines; 0: No; else: Yes generate QQ plots to evaluate if data fits GPD; 0: No; else: Yes GPD threshold likelihood ratio test; 0: No; else: Yes Bayes factor calculation; 0: No; else: Yes likelihood profile estimation; 0:No; else:yes (the default Quic=0 offers parameter estimation and uncertainty bounds based on the method outlined in Cheng et al., For faster simulation, the user can choose the maximum likelihood method Quic=1. The latter requires the optimization toolbox.
14 Page Edit input data file si1.txt (ReadData folder): Last column: year Other columns: Block maxima (annual maxima) from stations/gauges/model simulations Edit names.txt (ReadData folder) This file only changes titles and labels in the output figures: First line: title that appears in the output figure. Use the first line for stationary plots Second line: title that appears in the output figure. Use the first line for nonstationary plots Third line: xlabel (label of x axis) Fourth line: ylabel (label of y axis) Edit prior.txt (ReadData folder) The default values should be reasonable for most applications: SIGMA: the range of the scale parameter in GPD K: the range of the shape parameter in GPD Apha: Beta: the range of the slope for the scale parameter under nonstationary the range of the intercept for the scale parameter under nonstationary See ReadMe File (zreadme.txt in NEVA_GPD) Read the readme file to learn more about the input variables and parameters in GPD_sta_nonsta.txt, names.txt, si1.txt, prior.txt. 3.5 Run NEVA_GPD Run NEVA.m in Matlab.
15 Page 9 4 Save Outputs In both NEVA_GEV and NEVA_GPD, all the sampled parameters are automatically saved into savedata folder at the end of the simulation. For example, smp1.mat: nonsmp1.mat: non5smp1.mat acceptancer.mat nonacceptancer includes sampled parameters for station 1 under stationary assumption; includes sampled parameters for station 1 under nonstationary assumption with time varying location parameter; includes sampled parameters for station 1 under nonstationary assumption with time varying location and scale parameters; summarize the R_hat values to check the model convergence under stationary assumption (see Cheng et al., 2014). summarize the R_hat values to check the model convergence under nonstationary assumption (see Cheng et al., 2014). 5 Errors and Warnings In both NEVA_GEV and NEVA_GPD, errors and warnings are automatically saved in report.txt (stationary) and reportnon.txt (nonstationary).
16 Page 10 References and Relevant Literature AghaKouchak, A., D. Easterling, K. Hsu, S. Schubert, and S. Sorooshian (2013) Extremes in a Changing Climate, Springer, Springer Netherlands. Cheng L., AghaKouchak A., Gilleland E., Katz R.W., (2014), Non stationary Extreme Value Analysis in a Changing Climate, Climatic Change, doi: /s Cooley, D. (2009) Extreme value analysis and the study of climate change. Climatic Change, 97, Gilleland, E., Katz, R.W. (2011) New software to analyze how extremes change over time Eos, 92(2), Katz, R. (2010), Statistics of extremes in climate change, Climatic Change, 100(1), Katz, R., et al., (2002) Statistics of extremes in hydrology, Advances in Water Resources, 25, Renard, B., et al. (2006) An application of Bayesian analysis and Markov chain Monte Carlo methods to the estimation of a regional trend in annual maxima. Water resources research, 42. Renard, B., et al. (2013) Bayesian methods for non stationary extreme value analysis, Extremes in a Changing Climate, Springer Netherlands.
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