MvCAT is developed in Matlab as a user-friendly toolbox (software) to help scientists and researchers perform rigorous and comprehensive multivariate dependence analysis. It uses 26 copula families with 1 to 3 parameters to describe the dependence structure of two random variables. MvCAT uses local optimization and also Markov chain Monte Carlo simulation within a Bayesian framework to infer the parameter values of the copula families by contrasting them against available data. If Bayesian analysis with MCMC simulation is performed, an estimate of uncertainty for each copula family can be obtained from the posterior distribution of copula parameters. MCMC within Bayesian framework not only provide a robust estimate of the global optima, but also approximate the posterior distribution of the copula families which can be used to construct a prediction uncertainty range for the copulas. Local optimization methods are prone to getting trapped in local optima (see Sadegh et al., 2017 for more information). The user ca select any subset of the available 26 copulas and MvCAT will perform the analysis and rank the selected copula families based on their performance. Performance metrics used in this toolbox are Likelihood, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Nash-Sutcliffe Efficiency (NSE), and Root Mean Squared Error (RMSE). While Likelihood, NSE and RMSE only focus on minimizing the residuals between observations and model simulations, the other metrics take into consideration additional criteria. For example, AIC takes into account the model complexity and BIC account for model complexity and number of observations.
Sadegh M., Ragno E. and AghaKouchak A., 2017, Multivariate Copula Analysis Toolbox (MvCAT): Describing dependence and underlying uncertainty using a Bayesian framework , Water Resources Research, 53, doi:10.1002/2016WR020242. (pdf)
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 non-stationary 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.
Cheng L., AghaKouchak A., Gilleland E., Katz R.W., 2014, Non-stationary Extreme Value Analysis in a Changing Climate , Climatic Change, doi: 10.1007/s10584-014-1254-5. (pdf)
SDAT can be used to generate nonparametric standardized drought indicators such as Standardized Precipitation Index (SPI), Standardized Soil Moisture Index (SSI), Standardized Runoff Index (SRI) Standardized Streamflow Index (SSFI), Standardized Relative Humidity Index (SRHI), Standardised Groundwater level Index (SGI), Standardized Surface Water Supply Index (SSWSI), Standardized Water Storage Index (SWSI).
Hao Z., AghaKouchak A., Nakhjiri N., Farahmand A., 2014, Global Integrated Drought Monitoring and Prediction System, Scientific Data, 1:140001, 1-10, doi: 10.1038/sdata.2014.1. (pdf)
Farahmand A., AghaKouchak A., 2015, A Generalized Framework for Deriving Nonparametric Standardized Drought Indicators, Advances in Water Resources, 76, 140-145, doi: 10.1016/j.advwatres.2014.11.012. (pdf)
Multivariate Standardized Drought Index (MSDI) offers a multi-index drought monitoring framework for combining drought information from multiple variables (e.g., precipitation, soil moisture). The following code compares the parameteric and nonparametric MSDI described in the below two papers:
Hao Z., AghaKouchak A., 2013, Multivariate Standardized Drought Index: A Parametric Multi-Index Model, Advances in Water Resources, 57, 12-18, doi: 10.1016/j.advwatres.2013.03.009. (pdf)
Hao Z., AghaKouchak A., 2014, A Nonparametric Multivariate Multi-Index Drought Monitoring Framework, Journal of Hydrometeorology, 15, 89-101, doi:10.1175/JHM-D-12-0160.1. (pdf)
Performance Metrics for Evaluation of Remote Sensing Observations and Climate Model Simulations: A simple and easy to use Validation Toolbox (MATLAB source code) that can be used for validation of gridded data including satellite observations, reanalysis data, and weather and climate model simulations. In addition to the commonly used categorical indices, the toolbox includes the Volumetric Hit Index (VHI), Volumetric False Alarm Ration (VFAR), Volumetric Missed Index (VMI), and Volumetric Critical Success Index (VCSI).
Authors: Mehran A., and AghaKouchak A.
AghaKouchak A., Mehran A., 2013, Extended Contingency Table: Performance Metrics for Satellite Observations and Climate Model Simulations, Water Resources Research, 49, 7144-7149, doi:10.1002/wrcr.20498.
AghaKouchak A., Behrangi A., Sorooshian S., Hsu K., Amitai E., 2011, Evaluation of satellite-retrieved extreme precipitation rates across the Central United States, Journal of Geophysical Research, 116, D02115, doi:10.1029/2010JD014741.
MATLAB source code of the modified version of the HBV hydrologic model model including automatic parameter uncertainty estimation based on the Generalized likelihood uncertainty estimation (GLUE).
Authors: Nakhjiri N., Habib E., and AghaKouchak A.
AghaKouchak A., Habib E., 2010, Application of a Conceptual Hydrologic Model in Teaching Hydrologic Processes, International Journal of Engineering Education, 26(4), 963-973.
MATLAB source code of the HBV_Ensemble (ensemble streamflow simulation using HBV).
Authors: Nakhjiri N., Habib E., and AghaKouchak A.
AghaKouchak A., Nakhjiri N., and Habib E., 2013, An educational model for ensemble streamflow simulation and uncertainty analysis, Hydrology and Earth System Sciences, 17, 445-452, doi:10.5194/hess-17-445-2013.