Rajeshwar Mehrotra

A Multivariate Quantile-Matching Bias Correction Approach with Auto- and Cross-Dependence across Multiple Time Scales: Implications for Downscaling

AbstractA novel multivariate quantile-matching nesting bias correction approach is developed to remove systematic biases in general circulation model (GCM) outputs over multiple time scales. This is a significant advancement over typical quantile-matching alternatives available for bias correction, as they implicitly assume that correction of individual variable attributes will lead to correction of dependence biases between multiple variables. Furthermore, existing approaches perform bias correction at a given time scale (e.g., daily), whereas applications often require biases to be addressed at more than one time scale (such as annual in the case of most water resources planning projects). The proposed approach addresses all these issues, and additionally attempts to correct for lag-1 dependence (and cross-dependence) attributes across multiple time scales. The approach is called multivariate recursive quantile nesting bias correction (MRQNBC). The fidelity of the approach is demonstrated by applying it...

A programming tool to generate multi-site daily rainfall using a two-stage semi parametric model

Many problems in hydrology and agricultural science require extensive records of rainfall from multiple locations. Temporal and/or spatial coverage of rainfall data is often limited, so that stochastic models may be required to generate long synthetic rainfall records. This study describes a multi-site rainfall simulator (MRS) to stochastically generate daily rainfall at multiple locations. The MRS is available as an open-source software package in the R statistical computing environment. The software includes statistical analysis and graphics functions, and can display statistics and graphs at multiple time scales, including from individual sites and areal averages. The MRS thus provides a detailed set of modelling functions to simulate and analyse daily rainfall. The capabilities of the package are demonstrated using 30 gauges located in Sydney, Australia, and the results show that the model preserves observed year-to-year variability, interannual persistence and various daily distributional and space-time dependence attributes. A multi-site rainfall simulator to stochastically generate daily rainfall at multiple locations.Available as an open-source software package.Includes statistical analysis and graphics functions at multiple time scales.Preserves observed year-to-year variability and interannual persistence.Preserves various daily distributional and space-time dependence attributes.

Spatiotemporal variation of long-term drought propensity through reliability-resilience-vulnerability based Drought Management Index

This paper characterizes the long-term, spatiotemporal variation of drought propensity through a newly proposed, namely Drought Management Index (DMI), and explores its predictability in order to assess the future drought propensity and adapt drought management policies for a location. The DMI was developed using the reliability-resilience-vulnerability (RRV) rationale commonly used in water resources systems analysis, under the assumption that depletion of soil moisture across a vertical soil column is equivalent to the operation of a water supply reservoir, and that drought should be managed not simply using a measure of system reliability, but should also take into account the readiness of the system to bounce back from drought to a normal state. Considering India as a test bed, 5 year long monthly gridded (0.5° Lat × 0.5° Lon) soil moisture data are used to compute the RRV at each grid location falling within the study domain. The Permanent Wilting Point (PWP) is used as the threshold, indicative of transition into water stress. The association between resilience and vulnerability is then characterized through their joint probability distribution ascertained using Plackett copula models for four broad soil types across India. The joint cumulative distribution functions (CDF) of resilience and vulnerability form the basis for estimating the DMI as a five-yearly time series at each grid location assessed. The status of DMI over the past 50 years indicate that drought propensity is consistently low toward northern and north eastern parts of India but higher in the western part of peninsular India. Based on the observed past behavior of DMI series on a climatological time scale, a DMI prediction model comprising deterministic and stochastic components is developed. The predictability of DMI for a lead time of 5 years is found to vary across India, with a Pearson correlation coefficient between observed and predicted DMI above 0.6 over most of the study area, indicating a reasonably good potential for drought management in the medium term water resources planning horizon.

Does improved SSTA prediction ensure better seasonal rainfall forecasts

Seasonal rainfall forecasts in Australia are issued based on concurrent sea surface temperature anomalies (SSTAs) using a Bayesian model averaging (BMA) approach. The SSTA fields are derived from the Predictive Ocean-Atmosphere Model for Australia (POAMA) initialized in the preceding season. This study investigates the merits of the rainfall forecasted using POAMA SSTAs in contrast to that forecasted using a multimodel combination of SSTAs derived using five existing models. In addition, seasonal rainfall forecasts derived from multimodel and POAMA SSTA fields are subsequently combined to obtain a single weighted forecast over Australia. These three forecasts are compared against “idealized” forecasts where observed SSTAs are used instead of those predicted. The results indicate that while seasonal rainfall forecasts derived using multimodel-based SSTA indices offer improvements in selected seasons over a majority of grid cells in comparison to the case where a single SSTA model is used in two seasons, these improvements are not as significant as the improvements in the SSTA field that drive the rainfall forecasting model. The forecasts derived from the combination of multimodel and POAMA SSTA indices forecasts are found to offer greater improvements over the multimodel or the POAMA forecasts for a majority of grid cells in all seasons. It is also observed that these combined forecasts are touching the upper limits of forecastability, which are reached when observed SSTAs are used to forecast the rainfall. This suggests that further improvements in rainfall forecasting are only possible through the use of an improved forecasting algorithm, and not the driver (SSTA) information used in the current study.

Representing low‐frequency variability in continuous rainfall simulations: A hierarchical random Bartlett Lewis continuous rainfall generation model

Low-frequency variability, in the form of the El Nino-Southern Oscillation, plays a key role in shaping local weather systems. However, current continuous stochastic rainfall models do not account for this variability in their simulations. Here a modified Random Pulse Bartlett Lewis stochastic generation model is presented for continuous rainfall simulation exhibiting low-frequency variability. Termed the Hierarchical Random Bartlett Lewis Model (HRBLM), the model features a hierarchical structure to represent a range of rainfall characteristics associated with the El Nino-Southern Oscillation with parameters conditioned to vary as functions of relevant climatic states. Long observational records of near-continuous rainfall at various locations in Australia are used to formulate and evaluate the model. The results indicate clear benefits of using the hierarchical climate-dependent structure proposed. In addition to accurately representing the wet spells characteristics and observed low-frequency variability, the model replicates the interannual variability of the antecedent rainfall preceding the extremes, which is known to be of considerable importance in design flood estimation applications.

A programming tool for nonparametric system prediction using Partial Informational Correlation and Partial Weights

Identification of system predictors forms the first step towards formulating a predictive model. Approaches for identifying such predictors are often limited by the need to assume a relationship between the predictor and response. To address this limitation, (Sharma and Mehrotra, 2014) presented a nonparametric predictive model using Partial Informational Correlation (PIC) and Partial Weights (PW). This study describes the open source Nonparametric Prediction (NPRED) R-package. NPRED identifies system predictors using the PIC logic, and predicts the response using a k-nearest-neighbor regression formulation based on a PW based weighted Euclidean distance. The capabilities of the package are demonstrated using synthetic examples and a real application of predicting seasonal rainfall in the Warragamba dam near Sydney, Australia. The results show clear improvements in predictability as compared to the use of linear predictive alternatives, as well as nonparametric alternatives that use an un-weighted Euclidean distance. Open source R package NPRED for system identification and prediction.Estimate Partial Informational Correlation (PIC) and Partial Weight (PW).Improves predictability compared to existing alternatives.

Can the variability in precipitation simulations across GCMs be reduced through sensible bias correction

This work investigates the performance of four bias correction alternatives for representing persistence characteristics of precipitation across 37 General Circulation Models (GCMs) from the CMIP5 data archive. The first three correction approaches are the Simple Monthly Bias Correction (SMBC), Equidistance Quantile Mapping (EQM), and Nested Bias Correction (NBC), all of which operate in the time domain, with a focus on representing distributional and moment attributes in the observed precipitation record. The fourth approach corrects for the biases in high- and low-frequency variability or persistence of the GCM time series in the frequency domain and is named as Frequency-based Bias Correction (FBC). The Climatic Research Unit (CRU) gridded precipitation data covering the global land surface is used as a reference dataset. The assessment focusses on current and future means, variability, and drought-related characteristics at different temporal and spatial scales. For the current climate, all bias correction approaches perform reasonably well at the global scale by reproducing the observed precipitation statistics. For the future climate, focus is drawn on the agreement of the attributes across the GCMs considered. The inter-model difference/spread of each attribute across the GCMs is used as a measure of this agreement. Our results indicate that out of the four bias correction approaches used, FBC provides the lowest inter-model spreads, specifically for persistence attributes, over most regions/ parts over the global land surface. This has significant implications for most hydrological studies where the effect of low-frequency variability is of considerable importance.

Impacts of the tropical trans-basin variability on Australian rainfall

A large-scale mode of sea level pressure variability between the Pacific and Atlantic basins—referred to as the tropical trans-basin variability (TBV)—has shown multi-year predictability beyond that normally associated with El Niño Southern Oscillation (ENSO). Here we examine the relationship between the TBV and regional rainfall, which, if significant, would imply that the TBV predictability could be used to improve rainfall forecasts. We find TBV to be significantly related to rainfall, a relationship that is strongest over Australia during spring. We find Australia to experience drier conditions during the positive phase of TBV and wetter conditions during the negative phase, a pattern similar to that of ENSO. Furthermore, TBV is associated with rainfall responses that are of similar magnitude to ENSO, but there is some degree of independence between TBV and the Pacific modes defined by sea surface temperature indices. The global teleconnections related to the different TBV phases suggest that though many TBV and ENSO events overlap, pure ENSO events are primarily driven by the Pacific whereas pure TBV events are driven by the Atlantic Ocean. An El Niño coupled with a positive TBV event leads to significant drying over the east coast of Australia while the combined negative phase leads to widespread wetting over most of the country, which can be attributed to an enhancement of the anomalous Walker Circulation and the resulting moisture convergence and wind patterns.

Global seasonal precipitation forecasts using improved sea surface temperature predictions

Climate models driven by observed or modeled sea surface temperature (SST) or SST anomalies (SSTA) are used as a standard tool in seasonal climate predictions. This study investigates the merit of seasonal rainfall predictions obtained by using multimodel SSTA to drive a climate model over a single model case. The multimodel SSTA predictions are obtained by combining the predictions of five climate models, whereas the stand-alone model predictions come from the Predictive Ocean Atmosphere Model for Australia. The climate model used is the Australian Community Climate and Earth System Simulator (ACCESS). The use of multimodel SSTA over a single model shows marginal improvements in seasonal rainfall predictions across the entire globe. Further improvements in rainfall forecasts are possible either through improved parameterizations in the ACCESS model or by using another climate model. As a final step, the rainfall forecasts from the multimodel and the single model SSTA (two-member hierarchical rainfall forecasts, denoted as HIER) are combined and to gain further improvements over the individual multimodel or single model rainfall predictions for most of the grid cells in all seasons.

Correcting systematic biases across multiple atmospheric variables in the frequency domain

A procedure for correcting systematic biases across multiple variables is presented. This procedure operates in the frequency domain, using the cross-spectrum across variables to correct bias across each frequency band. The proposed approach is termed multivariate frequency bias correction or MFBC. The approach is illustrated using global climate model (GCM) simulations of multiple atmospheric variables, with variables selected based on recommended usage in downscaling applications. Results indicate clear benefits of using MFBC in representing both intra- and inter-variable dependence in corrected simulations. This has important implications in applications which require multiple atmospheric variables, and a need to correctly simulate both inter- and intra-variable dependence attributes. MFBC offers a mean to correct raw GCM atmospheric variables prior to downscaling or correct dynamically or statistically downscaled simulations prior to derived simulations of other variables of interest. Use of MFBC can have significant implications on derived hydrologic simulations, such as in sizing of storage reservoirs, or devising water sharing plans for the future.