Shivam Tripathi

Probabilistic Assessment of Drought Characteristics Using Hidden Markov Model

AbstractDroughts are characterized by drought indexes that measure the departures of meteorological and hydrological variables, such as precipitation and streamflow, from their long-term averages. Although many drought indexes have been proposed in the literature, most use predefined thresholds for identifying drought classes, ignoring the inherent uncertainties in characterizing droughts. This study employs a hidden Markov model (HMM) for the probabilistic classification of drought states. Apart from explicitly accounting for the time dependence in the drought states, the HMM-based drought index (HMM-DI) provides model uncertainty in drought classification. The proposed HMM-DI is used to assess drought characteristics in Indiana by using monthly precipitation and streamflow data. The HMM-DI results were compared to those from standard indexes and the differences in classification results from the two models were examined. In addition to providing the probabilistic classification of drought states, the HM...

Watershed reliability, resilience and vulnerability analysis under uncertainty using water quality data

A method for assessment of watershed health is developed by employing measures of reliability, resilience and vulnerability (R-R-V) using stream water quality data. Observed water quality data are usually sparse, so that a water quality time-series is often reconstructed using surrogate variables (streamflow). A Bayesian algorithm based on relevance vector machine (RVM) was employed to quantify the error in the reconstructed series, and a probabilistic assessment of watershed status was conducted based on established thresholds for various constituents. As an application example, observed water quality data for several constituents at different monitoring points within the Cedar Creek watershed in north-east Indiana (USA) were utilized. Considering uncertainty in the data for the period 2002-2007, the R-R-V analysis revealed that the Cedar Creek watershed tends to be in compliance with respect to selected pesticides, ammonia and total phosphorus. However, the watershed was found to be prone to violations of sediment standards. Ignoring uncertainty in the water quality time-series led to misleading results especially in the case of sediments. Results indicate that the methods presented in this study may be used for assessing the effects of different stressors over a watershed. The method shows promise as a management tool for assessing watershed health.

Change detection in rainfall and temperature patterns over India

The changes in rainfall and temperature patterns over India were detected using Mann-Kendall trend test, Bayesian change point analysis, and a hidden Markov model. A regionalization method was developed to identify homogeneous regions that experience similar weather states. The regionalization helped in finding contiguous regions with strong change signals. The data were investigated at different temporal and spatial resolution to explore the nature of changes. The study found that all India summer monsoon is stable, but the winter or the north-east monsoon is gradually intensifying. It also detected an abrupt drop in the winter and spring temperature over north-central India and a gradual increase in the summer temperature over the peninsular India. Robustness of the detected changes were evaluated using recent reanalysis datasets.

Engaging uncertainty in hydrologic data sets using principal component analysis: BaNPCA algorithm

[1] Principal component analysis (PCA) is the most widely used method for dimensionality reduction, data reconstruction, feature extraction, and data visualization in geosciences. However, in its standard form, PCA makes no distinction between data points for which the associated measurement errors vary in both space and time. Using the backdrop of sea surface temperature (SST) data, a Bayesian variant of noisy principal component analysis (BaNPCA) was developed to incorporate observation uncertainty when performing PCA. The algorithm was first assessed using synthetic data sets. Comparison of BaNPCA results with current PCA techniques showed that BaNPCA has lower data reconstruction error; that is, for a given number of principal components, it explains more variance in SST data. Using the automatic relevance determination method, BaNPCA could correctly identify the appropriate number of principal components in the data. BaNPCA was shown to exhibit distinct advantages in filling missing values in the data when compared to existing methods. In addition, the extracted principal vectors from BaNPCA were found to be smoother and more representative of large-scale signals like El Nino-Southern Oscillation and Pacific Decadal Oscillation. To classify extreme states of all India summer monsoon rainfall, we used robust optimization that utilizes the PCs along with computed uncertainty from BaNPCA algorithm as inputs, thus engaging uncertainty in data. Results from this study demonstrate the value of utilizing uncertainty information available with hydrologic data sets.

Aggregate Measures of Watershed Health from Reconstructed Water Quality Data with Uncertainty.

Risk-based measures such as reliability, resilience, and vulnerability (R-R-V) have the potential to serve as watershed health assessment tools. Recent research has demonstrated the applicability of such indices for water quality (WQ) constituents such as total suspended solids and nutrients on an individual basis. However, the calculations can become tedious when time-series data for several WQ constituents have to be evaluated individually. Also, comparisons between locations with different sets of constituent data can prove difficult. In this study, data reconstruction using a relevance vector machine algorithm was combined with dimensionality reduction via variational Bayesian noisy principal component analysis to reconstruct and condense sparse multidimensional WQ data sets into a single time series. The methodology allows incorporation of uncertainty in both the reconstruction and dimensionality-reduction steps. The R-R-V values were calculated using the aggregate time series at multiple locations within two Indiana watersheds. Results showed that uncertainty present in the reconstructed WQ data set propagates to the aggregate time series and subsequently to the aggregate R-R-V values as well. This data-driven approach to calculating aggregate R-R-V values was found to be useful for providing a composite picture of watershed health. Aggregate R-R-V values also enabled comparison between locations with different types of WQ data.

On the identification of intra-seasonal changes in the Indian summer monsoon

Intra-seasonal changes in the Indian summer monsoon are generally characterized by its active and break (A&B) states. Existing methods for identifying the A&B states using rainfall data rely on subjective thresholds, ignore temporal dependence in the data, and disregard inherent uncertainty in their identification. This paper develops a method to identify intra-seasonal changes in the monsoon using a hidden Markov model (HMM) that allows objective classification of the monsoon states. The method facilitates probabilistic interpretation which is especially useful during the transition period between the two monsoon states. The developed method can also be used to - (i) identify monsoon states in real time, (ii) forecast rainfall values, and (iii) generate synthetic data. Comparisons of the results from the proposed model with those from existing methods suggest that the new method is a promising for detecting intra-seasonal changes in the Indian summer monsoon.

Appraisal of Statistical Predictability under Uncertain Inputs: SST to Rainfall

Climatic variables that are used as inputs in hydrologic models often have large measurement uncertainties that are mostly ignored in hydrologic applications because of lack of appropriate tools. This study develops a set of algorithms to engage uncertainty information in three of the most common statistical procedures applied on climatic data, namely correlation (BaNCorr), principal component analysis (VBaNPCA), and regression (VNRVM). These new algorithms are developed within a common framework of Bayesian learning, and together they provide a comprehensive tool to account for uncertainty in various stages of model development. The developed algorithms are first tested and compared with traditional methods and state-of-the-art algorithms on synthetic data. Practical application of the proposed algorithms is demonstrated by developing a seasonal prediction model for all India summer monsoon rainfall by using sea surface temperature (SST) data and associated measurement errors as inputs. The results sugge...

Support Vector Machine Approach to Downscale Precipitation in Climate Change Scenarios

Concern over changes in global climate has increased in recent years with improvement in understanding of atmospheric dynamics and growth in evidence of climate link to long‐term variability in hydrologic records. Climate impact studies rely on climate change information at fine spatial resolution. Towards this, the past decade has witnessed significant progress in development of downscaling models to cascade the climate information provided by General Circulation Models (GCMs) at coarse spatial resolution to the scale relevant for hydrologic studies. While a plethora of downscaling models have been applied successfully to mid‐latitude regions, a few studies are available on tropical regions where the atmosphere is known to have more complex behavior. In this paper, a support vector machine (SVM) approach is proposed for statistical downscaling to interpret climate change signals provided by GCMs over tropical regions of India. Climate variables affecting spatio‐temporal variation of precipitation at each meteorological sub‐division of India are identified. Following this, cluster analysis is applied on climate data to identify the wet and dry seasons in each year. The data pertaining to climate variables and precipitation of each meteorological sub‐division is then used to develop SVM based downscaling model for each season. Subsequently, the SVM based downscaling model is applied to future climate predictions from the second generation Coupled Global Climate Model (CGCM2) to assess the impact of climate change on hydrological inputs to the meteorological sub‐divisions. The results obtained from the SVM downscaling model are then analyzed to assess the impact of climate change on precipitation over India.

Statistical Forecasting of Indian Summer Monsoon Rainfall: An Enduring Challenge

Forecasting All India Summer Monsoon Rainfall (AISMR), one or more seasons in advance, has been an elusive goal for hydrologists, meteorologists, and astrologers alike. In spite of advances in data collection facilities, improvements in computational capabilities, and progress in our understanding of the physics of the monsoon system, our ability to forecast AISMR has remained more or less unchanged in past several decades. On one hand, physically based numerical prediction models that are considered a panacea for daily weather forecasting have not evolved to a stage where they can realistically predict or even simulate annual variations in Indian monsoon. On the other hand, statistical models that have traditionally been used for making operational forecasts have failed in forecasting extreme monsoon rainfall years. It has been suggested that, in future, physically based models may improve to an extent where they can produce useful forecasts. However, until then, it would be prudent to develop statistical forecast models using state-of-the-art soft-computing techniques.

Application of Relevance Vector Machine for Sediment Transport Estimation

Estimation of sediment concentrations in streams and rivers is important for water resources management and projects. Sediment concentration is generally determined from direct measurements, or estimated from sediment transport equations that require detailed information about the flow and sediment characteristics. However, there is often a large discrepancy between these models and observations. The complexity of sediment transport processes presents an opportunity for the application of alternate methods. As a fairly recent computing tool, relevance vector machines (RVMs) are gaining popularity in the fields of machine learning and pattern recognition. The objective of this study is to develop an RVM approach for estimation of sediment concentrations. The resulting RVM model is then trained and tested on a large data set and the performance of the RVM approach is compared with more conventional transport formulae.