Daily Precipitation Generation using a Hidden Markov Model with Correlated Emissions for the Potomac River Basin

Abstract

A 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.

Stochastic Precipitation Generation for the Xilingol League Using Hidden Markov Models with Variational Bayes Parameter Estimation

“…Conducting an in-depth study of precipitation patterns in the Xilingol League is essential for implementing a flexible grazing strategy in the region and ensuring the sustainable use of its grasslands. Existing studies have mainly focused on stochastic simulation of daily precipitation data during the rainy season [21,22], which has confirmed to a certain extent the rationality of SPGs for daily precipitation simulation. However, the stochastic simulation of annual daily precipitation data has not received due attention, and the study of the emission distribution used to generate positive precipitation in HMM is also lacking.…”

“…However, while there is a large amount of literature on VB estimation implemented for state space models and HMM models [16][17][18][19][20], these studies usually focus only on precipitation-positive distributions as a Gaussian distribution or a mixture of Gaussian distributions. Kroiz et al [21] determined the optimal parameter configuration of the model by comparing the BIC scores when HMMs follow exponential and gamma distributions for positive precipitation under different numbers of states and mixture components, respectively, and by combining the background of the actual problem. Then, Majumder et al [22] outlined VB estimation for HMMs with semi-continuous emission and constructed an SPG for daily precipitation using a combination of two exponential distributions.…”

The Advanced Meteorology Explorer: a novel stochastic, gridded daily rainfall generator

“…Parametric Hidden Markov Models (HMMs) have also been developed for multi-site daily stochastic rainfall simulation (Holsclaw et al, 2016;Kroiz et al, 2020). HMMs characterise rainfall as being associated with one of a finite number of 'hidden' states (e.g.…”

“…a grid) within the modelled domain. Similar to this, in multi-site (non-gridded) examples, Gaussian copulas or multivariate Normal distributions are often used to capture the dependence between locations (Serinaldi and Kilsby, 2012;Kroiz et al, 2020;Chandler, 2019). A possible limitation of such methods is their underlying assumption of Gaussianity in the dependence structure.…”

“…Most often in spatially coherent rainfall models, such as Wilks (2008), Verdin et al (2015), Kleiber et al (2012) and Kroiz et al (2020), the dependence between locations is modelled using a Multivariate Normal distribution (equivalent to a Gaussian copula), or a GP spatial dependence model. The Gaussian copula assumes asymptotic independence between random variables, meaning that the largest values of the variables are represented as rarely occurring together (Coles et al, 1999).…”