Browsing by Author "Majumder, Reetam"
Now showing 1 - 8 of 8
Results Per Page
Sort Options
Item Assessing Water Budget Sensitivity to Precipitation Forcing Errors in Potomac River Basin Using the VIC Hydrologic Model CyberTraining: Big Data + High-Performance Computing + Atmospheric Sciences(2019) Majumder, Reetam; Walid, Redwan; Zheng, Jianyu; Zhang, Zhibo; Wang, Jianwu; Gobbert, Matthias K.; Gangopadhyay, Aryya; Barajas, Carlos; Guo, Pei; Rajapakshe, Chamara; Markert, Kel; Mehta, Amita; Neerchal, Nagaraj K.The Potomac River Basin is a watershed located on the East Coast of the USA across West Virginia, Virginia, Pennsylvania, Maryland, and the District of Columbia. Inter-annual variations in precipitation makes it challenging to plan for water allocation within the basin. Therefore, understanding seasonal to inter-annual variations in water availability within the basin is important for planning water resources management. We set up on a distributed-memory cluster and used the hydrologic model Variable Infiltration Capacity (VIC) to estimate the water budget components for the Potomac river basin from April to September 2017. We also assessed the effect of precipitation forcing errors and its variability on the water balance for the same time period. We were able to identify April and May as the months where the water balance was most sensitive to variability. Sub-basins with the highest sensitivity over the course of the six months of interest were also identified, and variability in water balance increased as we increased the variability in precipitation.Item Copula-based Correlation Structure for Multivariate Emission Distributions in Hidden Markov Models(2020) Majumder, Reetam; Mehta, Amita; Neerchal, Nagaraj K.Hidden Markov models (HMM) for multi-site daily precipitation usually assume that precipitation at each location is independently distributed conditional on the daily state; correlation in precipitation at different locations is induced by the state process. In practice, however, spatial correlations are underestimated especially when working with remote sensing data. This results in simulated data which cannot recreate the spatiotemporal patterns of the historical data. We construct a daily precipitation generator based on a hidden Markov model with Gaussian copulas (HMM-GC) using GPM-IMERG (Integrated Multi-satellitE Retrievals for Global Precipitation Measurement) remote sensing data for the Chesapeake Bay watershed on the East Coast of the USA. Daily precipitation from 2000–2019 for the wet season months of July to September is modeled using a 6-state HMM. Positive precipitation at each location is given by a two-part distribution with a delta function at zero and a mixture of two Gamma distributions; Gaussian copulas are used to accommodate the correlation in precipitation at different locations. Based on 20 years of synthetic data simulated from an HMM and an HMM-GC, we conclude that the HMM-GC captures key statistical properties of IMERG precipitation better than the HMM.Item Daily Precipitation Generation using a Hidden Markov Model with Correlated Emissions for the Potomac River Basin(UMBC, 2020-06-30) Kroiz, Gerson C.; Majumder, Reetam; Gobbert, Matthias K.; Neerchal, Nagaraj K.; Markert, Kel; Mehta, AmitaA daily precipitation generator based on a hidden Markov model with Gaussian copulas (HMM-GC) is constructed using remote sensing data from GPM-IMERG for the Potomac river basin on the East Coast of the USA. Daily precipitation over the basin from 2001–2018 for the wet season months of July to September is modeled using a 4-state HMM, and correlated precipitation amounts are generated from a mixture of Gamma distributions using Gaussian copulas for each state. Synthetic data from a model using a mixture of two Gamma distributions for the non-zero precipitation is shown to replicate the historical data better than a model using a single Gamma distribution.Item Hidden Markov Models for High Dimensional Data with Geostatistical Applications(2021-01-01) Majumder, Reetam; Neerchal, Nagaraj K; Mathematics and Statistics; StatisticsStochastic precipitation generators (SPGs) are a class of statistical models which generate synthetic data that can simulate dry and wet rainfall stretches for long durations. Generated precipitation time series data are used in climate projections, impact assessment of extreme weather events, and water resource and agricultural management. In this thesis, we construct SPGs for daily precipitation data that is specified as a semi-continuous distribution with a point mass at zero for no precipitation and a mixture of Exponential or Gamma distributions for positive precipitation. Our generators are obtained as hidden Markov models (HMMs) where the underlying climate conditions form the states.Maximum likelihood estimation of an HMM's parameters has historically relied on the Baum-Welch algorithm, which is a modification of the Expectation Maximization algorithm. We implement variational Bayes (VB) as an alternative estimation procedure for HMMs with semi-continuous emissions. Stochastic optimization in the form of stochastic variational Bayes (SVB) has been employed for computational speedup in practical cases. A univariate state process is often unable to adequately capture the underlying weather conditions over large watersheds, since different areas can have local weather regimes. We extend the HMM to a linked HMM (LHMM) where locations are divided into clusters. Each cluster's emissions are assumed to arise from a cluster-specific state process; the state processes are correlated and together form a multivariate Markov chain (MMC). The MMC provides more flexibility to accommodate heterogeneity that might be present in larger geographical areas. A Gaussian copula is constructed to capture the correlation structure of the MMC. Finally, we also construct a Gaussian copula for the emissions of the HMM to explicitly parameterize the pairwise correlations of observed positive precipitation. Daily precipitation data over the Chesapeake Bay watershed in the Eastern coast of the USA is used as a demonstrative case study. Remote sensing precipitation data is sourced from the GPM-IMERG dataset for the wet season between July to September from 2000-2019. Synthetic data generated from the clustered LHMM can reproduce the monthly precipitation statistics as well as the spatial correlations present in the historical GPM-IMERG data.Item A Modified Minibatch Sampling Method for Parameter Estimation in Hidden Markov Models using Stochastic Variational Bayes(Wiley, 2021-12-14) Majumder, Reetam; Gobbert, Matthias; Neerchal, Nagaraj K.Parameter estimation using stochastic variatonal Bayes (SVB) under a mean field assumption can be carried out by sampling a single data point at each iteration of the optimization algorithm. However, when latent variables are dependent like in hidden Markov models (HMM), a larger sample is required at each iteration to capture that dependence. We describe a minibatch sampling procedure for HMMs where the emission process can be segmented into independent and identically distributed blocks. Instead of sampling a block and using all elements within it, we divide the block into subgroups and sample subgroups from different blocks using simple random sampling with replacement. Simulation results are provided for an HMM for precipitation data, where each block of 90 days represents 3 months of wet season data. SVB based on the proposed sampling method is shown to provide parameter estimates comparable with existing methods.Item Stochastic Precipitation Generation for the Chesapeake Bay Watershed using Hidden Markov Models with Variational Bayes Parameter Estimation(2022-10-09) Majumder, Reetam; Neerchal, Nagaraj K.; Mehta, AmitaStochastic precipitation generators (SPGs) are a class of statistical models which generate synthetic data that can simulate dry and wet rainfall stretches for long durations. Generated precipitation time series data are used in climate projections, impact assessment of extreme weather events, and water resource and agricultural management. We construct an SPG for daily precipitation data that is specified as a semi-continuous distribution at every location, with a point mass at zero for no precipitation and a mixture of two exponential distributions for positive precipitation. Our generators are obtained as hidden Markov models (HMMs) where the underlying climate conditions form the states. We fit a 3-state HMM to daily precipitation data for the Chesapeake Bay watershed in the Eastern coast of the USA for the wet season months of July to September from 2000–2019. Data is obtained from the GPMIMERG remote sensing dataset, and existing work on variational HMMs is extended to incorporate semi-continuous emission distributions. In light of the high spatial dimension of the data, a stochastic optimization implementation allows for computational speedup. The most likely sequence of underlying states is estimated using the Viterbi algorithm, and we are able to identify differences in the weather regimes associated with the states of the proposed model. Synthetic data generated from the HMM can reproduce monthly precipitation statistics as well as spatial dependency present in the historical GPM-IMERG data.Item Stochastic Precipitation Generation for the Potomac River Basin Using Hidden Markov Models(UMBC) Kroiz, Gerson C.; Basalyga, Jonathan N.; Uchendu, Uchendu; Majumder, Reetam; Barajas, Carlos A.; Gobbert, Matthias K.; Markert, Kel; Mehta, Amita; Neerchal, Nagaraj K.A daily precipitation generator based on hidden Markov models (HMM) using satellite precipitation estimates is studied for the Potomac river basin in Eastern USA over the wet season months of July to September. GPM-IMERG data between 2001–2018 is used for the study, which at a 0.1◦ × 0.1◦ spatial resolution results in 387 grid points across the basin. A 4-state model has been considered for the state process, and the semi-continuous emission distribution for precipitation at each location is modeled using a mixture comprising a delta function at 0 and two Gamma distributions. The underestimation of the observed spatial correlations between the grid points based on this model is noted, and the HMM is extended using Gaussian copulas to generate spatially correlated precipitation amounts. Performance of this model is examined in terms of dry and wet day stretches, spatial correlations between grid points, and extreme precipitation events. The HMM with Gaussian copulas (HMM-GC) is shown to outperform the classical HMM formulation for precipitation generation when using remote sensing data in the Potomac river basin.Item Variational Bayes Estimation of Hidden Markov Models for Daily Precipitation with Semi-Continuous Emissions(UMBC HPCF, 2021) Majumder, Reetam; Gobbert, Matthias K.; Mehta, Amita; Neerchal, Nagaraj K.Stochastic precipitation generators can simulate dry and wet rainfall stretches for long durations. Generated precipitation time series data are used in climate projections, impact assessment of extreme weather events, and water resource and agricultural management. Daily precipitation is specified as a semi-continuous distribution with a point mass at zero and a mixture of Exponential or Gamma distributions for positive precipitation. Our generators are obtained as hidden Markov models (HMM) where the underlying climate conditions form the states. Maximum likelihood estimation for HMMs has historically relied on the Baum-Welch algorithm. We implement variational Bayes as an alternative for parameter estimation in HMMs. In our simulation study for a 3-state HMM with positive rainfall specified as a mixture of 2 Exponential distributions, we get good posterior estimates when the model is initialized with the correct number of states and mixture components. We also fit a similar model to a single grid point within the Chesapeake Bay watershed based on GPM-IMERG remote sensing data for the wet season between July to September from 2000–2019. Synthetic data generated from the fitted model is able to replicate the monthly proportion of dry days at the location, as well as the total monthly precipitation.