Probabilistic Assessment of Drought Characteristics using a Hidden Markov Model

Droughts are evaluated using drought indices that measure the departure of meteorological and hydrological variables such as precipitation and stream flow from their long-term averages. While there are many drought indices proposed in the literature, most of them use pre-defined thresholds for identifying drought classes ignoring the inherent uncertainties in characterizing droughts. In this study, a hidden Markov model (HMM) [1] is developed for probabilistic classification of drought states. The HMM captures space and time dependence in the data. The proposed model is applied to assess drought characteristics in Indiana using monthly precipitation and stream flow data. The comparison of HMM based drought index with standard precipitation index (SPI) [2] suggests that the HMM index provides more intuitive results

Hidden Markov model-based probabilistic assessment of droughts

Droughts are one of the most expensive and least understood natural disasters. Existing methods of drought assessment use drought indices that rely on subjective thresholds, and hence cannot be universally applied across different climatic regions. Many of the popular methods of drought characterization ignore temporal dependence in the data. In addition, current drought indices are not amenable to probabilistic treatment which is essential for quantifying model uncertainties in drought classification. This study explores the use of graphical models, specifically hidden Markov models (HMMs), to develop a new drought index that overcomes some of the limitations of current drought indices. This HMM-based drought index (HMM-DI) does not require specification of subjective thresholds. The parameters of the HMM model are determined from historical data. The HMM-DI reveals new insights into the frequency and severity of droughts and their spatio-temporal variations. The HMM-DI is applied to monthly precipitation and stream flow data over Indiana, and to gridded precipitation data over India. The results suggest that HMM-DI can be a promising alternative to conventional drought indices. However, available data records do not support a full HMM model with all the classifications adopted by the community as reflected in the U.S. Drought Monitor. This study suggests that simpler models may be more appropriate if memory is to be preserved

Drought Characterization Using Probabilistic Models

Droughts are complex natural disasters caused due to deficit in water availability over a region. Water availability is strongly linked to precipitation in many parts of the world that rely on monsoonal rains. Recent studies indicate that the choice of precipitation datasets and drought indices could influence drought analysis. Therefore, drought characteristics for the Indian monsoon region were reassessed for the period 1901-2004 using two different datasets and standard precipitation index (SPI), standardized precipitation-evapotranspiration index (SPEI), Gaussian mixture model-based drought index (GMM-DI), and hidden Markov model-based drought index (HMM-DI). Drought trends and variability were analyzed for three epochs: 1901- 1935, 1936-1970 and 1971-2004. Irrespective of the dataset and methodology used, the results indicate an increasing trend in drought severity and frequency during the recent decades (1971-2004). Droughts are becoming more regional and are showing a general shift to the agriculturally important coastal south-India, central Maharashtra, and IndoGangetic plains indicating food security challenges and socioeconomic vulnerability in the region. Drought severities are commonly reported using drought classes obtained by assigning pre-defined thresholds on drought indices. Current drought classification methods ignore modeling uncertainties and provide discrete drought classification. However, the users of drought classification are often interested in knowing inherent uncertainties in classification so that they can make informed decisions. A probabilistic Gamma mixture model (Gamma-MM)-based drought index is proposed as an alternative to deterministic classification by SPI. The Bayesian framework of the proposed model avoids over-specification and overfitting by choosing the optimum number of mixture components required to model the data − a problem that is often encountered in other probabilistic drought indices (e.g., HMM-DI). When sufficient number of components are used in Gamma-MM, it can provide a good approximation to any continuous distribution in the range (0,∞), thus addressing the problem of choosing an appropriate distribution for SPI analysis. The Gamma-MM propagates model uncertainties to drought classification. The method is tested on rainfall data over India. A comparison of the results with standard SPI shows significant differences, particularly when SPI assumptions on data distribution are violated. Finding regions with similar drought characteristics is useful for policy-makers and water resources planners in the optimal allocation of resources, developing drought management plans, and taking timely actions to mitigate the negative impacts during droughts. Drought characteristics such as intensity, frequency, and duration, along with land-use and geographic information, were used as input features for clustering algorithms. Three methods, namely, (i) a Bayesian graph cuts algorithm that combines the Gaussian mixture model (GMM) and Markov random fields (MRF), (ii) k-means, and (iii) hierarchical agglomerative clustering algorithm were used to find homogeneous drought regions that are spatially contiguous and possess similar drought characteristics. The number of homogeneous clusters and their shape was found to be sensitive to the choice of the drought index, the time window of drought, period of analysis, dimensionality of input datasets, clustering method, and model parameters of clustering algorithms. Regionalization for different epochs provided useful insight into the space-time evolution of homogeneous drought regions over the study area. Strategies to combine the results from multiple clustering methods were presented. These results can help policy-makers and water resources planners in the optimal allocation of resources, developing drought management plans, and taking timely actions to mitigate the negative impacts during droughts

A Machine Learning Approach to Predict Watershed Health Indices for Sediments and Nutrients at Ungauged Basins

Effective water quality management and reliable environmental modeling depend on the availability, size, and quality of water quality (WQ) data. Observed stream water quality data are usually sparse in both time and space. Reconstruction of water quality time series using surrogate variables such as streamflow have been used to evaluate risk metrics such as reliability, resilience, vulnerability, and watershed health (WH) but only at gauged locations. Estimating these indices for ungauged watersheds has not been attempted because of the high-dimensional nature of the potential predictor space. In this study, machine learning (ML) models, namely random forest regression, AdaBoost, gradient boosting machines, and Bayesian ridge regression (along with an ensemble model), were evaluated to predict watershed health and other risk metrics at ungauged hydrologic unit code 10 (HUC-10) basins using watershed attributes, long-term climate data, soil data, land use and land cover data, fertilizer sales data, and geographic information as predictor variables. These ML models were tested over the Upper Mississippi River Basin, the Ohio River Basin, and the Maumee River Basin for water quality constituents such as suspended sediment concentration, nitrogen, and phosphorus. Random forest, AdaBoost, and gradient boosting regressors typically showed a coefficient of determination R2>0.8 for suspended sediment concentration and nitrogen during the testing stage, while the ensemble model exhibited R2>0.95. Watershed health values with respect to suspended sediments and nitrogen predicted by all ML models including the ensemble model were lower for areas with larger agricultural land use, moderate for areas with predominant urban land use, and higher for forested areas; the trained ML models adequately predicted WH in ungauged basins. However, low WH values (with respect to phosphorus) were predicted at some basins in the Upper Mississippi River Basin that had dominant forest land use. Results suggest that the proposed ML models provide robust estimates at ungauged locations when sufficient training data are available for a WQ constituent. ML models may be used as quick screening tools by decision makers and water quality monitoring agencies for identifying critical source areas or hotspots with respect to different water quality constituents, even for ungauged watersheds

Effects of Drought on Water Quality in Streams

The objective of this research is to understand the relationship between low stream flows during droughts and their impact on water quality. The area chosen for this study is the Cedarville sub-watershed that drains into Massie Creek, a tributary to the Little Miami River, Ohio. By using stream flow and water quality data collected from the Massie Creek in Ohio, we will be able to study the impact of droughts on water quality