Bivariate modelling of precipitation and temperature using a non-homogeneous hidden Markov model

Aiming to generate realistic synthetic times series of the bivariate process of daily mean temperature and precipitations, we introduce a non-homogeneous hidden Markov model. The non-homogeneity lies in periodic transition probabilities between the hidden states, and time-dependent emission distributions. This enables the model to account for the non-stationary behaviour of weather variables. By carefully choosing the emission distributions, it is also possible to model the dependance structure between the two variables. The model is applied to several weather stations in Europe with various climates, and we show that it is able to simulate realistic bivariate time series

Improving Time Structure Patterns of Orthogonal Markov Chains and its Consequences in Hydraulic Simulations

Rainfall1 occurrences understood as rain events are relevant for agricultural practices because temporal distribution of rainfall highly affects yield production. A few stochastic models satisfactorily generate daily rainfall events while preserving temporal and spatial dependence among multiple sites. I evaluated an extension on the traditional Orthogonal Markov chain (TOMC) model in reproducing the temporal structure of rainfall events at multiple sites in Florida (FL), Nebraska (NE) and California (CA). In addition, a simulation of watershed runoff from rainfall events, reproduced by a single- and multi-site weather generator, was conducted. Results shows that (i) a temporal structure extended Orthogonal Markov chain (EOMC) maintained the spatial correlation between observed and generated rainfall events; (ii) EOMC used a smaller number of yearlong simulations for generating the observed frequencies of wet spells than TOMC requires for similar accuracy; (iii) using EOMC generated rainfall data in SWMM produced similar median runoff values to those generated using observed data; and (iv) EOMC reduces 50% of computing time for generating rainfall data. EOMC can benefit modeling of future climate scenarios by economical reduction of hardware need. 1Liquid precipitation Adviser: Guillermo A. Baigorri

Stochastic Precipitation Generation for the Chesapeake Bay Watershed using Hidden Markov Models with Variational Bayes Parameter Estimation

Stochastic 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 GPM-IMERG 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

Stochastic generation of annual, monthly and daily climate data: A review

International audienceThe generation of rainfall and other climate data needs a range of models depending on the time and spatial scales involved. Most of the models used previously do not take into account year to year variations in the model parameters. Long periods of wet and dry years were observed in the past but were not taken into account. Recently, Thyer and Kuczera (1999) developed a hidden state Markov model to account for the wet and dry spells explicitly in annual rainfall. This review looks firstly at traditional time series models and then at the more complex models which take account of the pseudo-cycles in the data. Monthly rainfall data have been generated successfully by using the method of fragments. The main criticism of this approach is the repetitions of the same yearly pattern when only a limited number of years of historical data are available. This deficiency has been overcome by using synthetic fragments but this brings an additional problem of generating the right number of months with zero rainfall. Disaggregation schemes are effective in obtaining monthly data but the main problem is the large number of parameters to be estimated when dealing with many sites. Several simplifications have been proposed to overcome this problem. Models for generating daily rainfall are well developed. The transition probability matrix method preserves most of the characteristics of daily, monthly and annual characteristics and is shown to be the best performing model. The two-part model has been shown by many researchers to perform well across a range of climates at the daily level but has not been tested adequately at monthly or annual levels. A shortcoming of the existing models is the consistent underestimation of the variances of the simulated monthly and annual totals. As an alternative, conditioning model parameters on monthly amounts or perturbing the model parameters with the Southern Oscillation Index (SOI) result in better agreement between the variance of the simulated and observed annual rainfall and these approaches should be investigated further. As climate data are less variable than rainfall, but are correlated among themselves and with rainfall, multisite-type models have been used successfully to generate annual data. The monthly climate data can be obtained by disaggregating these annual data. On a daily time step at a site, climate data have been generated using a multisite type model conditional on the state of the present and previous days. The generation of daily climate data at a number of sites remains a challenging problem. If daily rainfall can be modelled successfully by a censored power of normal distribution then the model can be extended easily to generate daily climate data at several sites simultaneously. Most of the early work on the impacts of climate change used historical data adjusted for the climate change. In recent studies, stochastic daily weather generation models are used to compute climate data by adjusting the parameters appropriately for the future climates assumed

Bayesian Detection of Changepoints in Finite-State Markov Chains for Multiple Sequences

We consider the analysis of sets of categorical sequences consisting of piecewise homogeneous Markov segments. The sequences are assumed to be governed by a common underlying process with segments occurring in the same order for each sequence. Segments are defined by a set of unobserved changepoints where the positions and number of changepoints can vary from sequence to sequence. We propose a Bayesian framework for analyzing such data, placing priors on the locations of the changepoints and on the transition matrices and using Markov chain Monte Carlo (MCMC) techniques to obtain posterior samples given the data. Experimental results using simulated data illustrates how the methodology can be used for inference of posterior distributions for parameters and changepoints, as well as the ability to handle considerable variability in the locations of the changepoints across different sequences. We also investigate the application of the approach to sequential data from two applications involving monsoonal rainfall patterns and branching patterns in trees

A spatiotemporal precipitation generator based on a censored latent Gaussian field

A daily stochastic spatiotemporal precipitation generator that yields precipitation realizations that are quantitatively consistent is described. The methodology relies on a latent Gaussian field that drives both the occurrence and intensity of the precipitation process. For the precipitation intensity, the marginal distributions, which are space and time dependent, are described by a composite model of a gamma distribution for observations below some threshold with a generalized Pareto distribution modeling the excesses above the threshold. Model parameters are estimated from data and extrapolated to locations and times with no direct observations using linear regression of position covariates. One advantage of such a model is that stochastic generator parameters are readily available at any location and time of the year inside the stationarity regions. The methodology is illustrated for a network of 12 locations in Sweden. Performance of the model is judged through its ability to accurately reproduce a series of spatial dependence measures and weather indices. © 2015. American Geophysical Union. All Rights Reserved

A framework for the simulation of regional decadal variability for agricultural and other applications

The SimGen software, including ancillary files and scripts, can be found at http://iri.columbia.edu/~amg/CCAFS/simgen/Climate prediction on decadal time scales is currently an active area of research. Although there are indications that predictions from dynamical models may have skill in some regions, assessment of this skill is still underway, and reliable model-based predictions of regional ‘near-term’ climate change, particularly for terrestrial regions, have not yet been demonstrated. Given the absence of such forecasts, synthetic data sequences that capture the statistical properties of observed near-term climate variability have potential value. Incorporation of a climate change component in such sequences can aid in estimating likelihoods for a range of climatic stresses, perhaps lying outside the range of past experience. Such simulations can be used to drive agricultural, hydrological or other application models, enabling resilience testing of adaptation or decision systems. The use of statistically-based methods enables the efficient generation of a large ensemble of synthetic sequences as well as the creation of well-defined probabilistic risk estimates. In this report we discuss procedures for the generation of synthetic climate sequences that incorporate both the statistics of observed variability and expectations regarding future regional climate change. Model fitting and simulation are conditioned by requirements particular to the decadal climate problem. A method for downscaling annualized simulations to the daily time step while preserving both spatial and temporal subannual statistical properties is presented and other possible methods discussed. A ‘case-study’ realization of the proposed framework is described

Long-term-robust adaptation strategies for reservoir operation considering magnitude and timing of climate change: application to Diyala River Basin in Iraq

2020 Spring.Includes bibliographical references.Vulnerability assessment due to climate change impacts is of paramount importance for reservoir operation to achieve the goals of water resources management. This requires accurate forcing and basin data to build a valid hydrology model and assessment of the sensitivity of model results to the forcing data and uncertainty of model parameters. The first objective of this study is to construct the model and identify its sensitivity to the model parameters and uncertainty of the forcing data. The second objective is to develop a Parametric Regional Weather Generator (RP-WG) for use in areas with limited data availability that mimics observed characteristics. The third objective is to propose and assess a decision-making framework to evaluate pre-specified reservoir operation plans, determine the theoretical optimal plan, and identify the anticipated best timeframe for implementation by considering all possible climate scenarios. To construct the model, the Variable Infiltration Capacity (VIC) platform was selected to simulate the characteristics of the Diyala River Basin (DRB) in Iraq. Several methods were used to obtain the forcing data and they were validated using the Kling–Gupta efficiency (KGE) metric. Variables considered include precipitation, temperature, and wind speed. Model sensitivity and uncertainty were examined by the Generalized Likelihood Uncertainty Estimation (GLUE) and the Differential Evolution Adaptive Metropolis (DREAM) techniques. The proposed RP-WG was based on (1) a First-order, Two-state Markov Chain to simulate precipitation occurrences; (2) use of Wilks' technique to produce correlated weather variables at multiple sites with conservation of spatial, temporal, and cross correlations; and (3) the capability to produce a wide range of synthetic climate scenarios. A probabilistic decision-making framework under nonstationary hydroclimatic conditions was proposed with four stages: (1) climate exposure generation (2) supply scenario calculations, (3) demand scenario calculations, and (4) multi-objective performance assessment. The framework incorporated a new metric called Maximum Allowable Time to examine the timeframe for robust adaptations. Three synthetic pre-suggested plans were examined to avoid undesirable long-term climate change impacts, while the theoretical-optimal plan was identified by the Non-dominated Sorting Genetic Algorithm II. The multiplicative random cascade and Schaake Shuffle techniques were used to determine daily precipitation data, while a set of correction equations was developed to adjust the daily temperature and wind speed. The depth of the second soil layer caused most sensitivity in the VIC model, and the uncertainty intervals demonstrated the validity of the VIC model to generate reasonable forecasts. The daily VIC outputs were calibrated with a KGE average of 0.743, and they were free from non-normality, heteroscedasticity, and auto-correlation. Results of the PR-WG evaluation show that it exhibited high values of the KGE, preserved the statistical properties of the observed variables, and conserved the spatial, temporal, and cross correlations among the weather variables at all sites. Finally, risk assessment results show that current operational rules are robust for flood protection but vulnerable in drought periods. This implies that the project managers should pay special attention to the drought and spur new technologies to counteract. Precipitation changes were dominant in flood and drought management, and temperature and wind speed changes effects were significant during drought. The results demonstrated the framework's effectiveness to quantify detrimental climate change effects in magnitude and timing with the ability to provide a long-term guide (and timeframe) to avert the negative impacts