Nonlinear ensemble prediction of chaotic daily rainfall

The significance of treating rainfall as a chaotic system instead of a stochastic system for a better understanding of the underlying dynamics has been taken up by various studies recently. However, an important limitation of all these approaches is the dependence on a single method for identifying the chaotic nature and the parameters involved. Many of these approaches aim at only analyzing the chaotic nature and not its prediction. In the present study, an attempt is made to identify chaos using various techniques and prediction is also done by generating ensembles in order to quantify the uncertainty involved. Daily rainfall data of three regions with contrasting characteristics (mainly in the spatial area covered), Malaprabha, Mahanadi and All-India for the period 1955-2000 are used for the study. Auto-correlation and mutual information methods are used to determine the delay time for the phase space reconstruction. Optimum embedding dimension is determined using correlation dimension, false nearest neighbour algorithm and also nonlinear prediction methods. The low embedding dimensions obtained from these methods indicate the existence of low dimensional chaos in the three rainfall series. Correlation dimension method is done on th phase randomized and first derivative of the data series to check whether the saturation of the dimension is due to the inherent linear correlation structure or due to low dimensional dynamics. Positive Lyapunov exponents obtained prove the exponential divergence of the trajectories and hence the unpredictability. Surrogate data test is also done to further confirm the nonlinear structure of the rainfall series. A range of plausible parameters is used for generating an ensemble of predictions of rainfall for each year separately for the period 1996-2000 using the data till the preceding year. For analyzing the sensitiveness to initial conditions, predictions are done from two different months in a year viz., from the beginning of January and June. The reasonably good predictions obtained indicate the efficiency of the nonlinear prediction method for predicting the rainfall series. Also, the rank probability skill score and the rank histograms show that the ensembles generated are reliable with a good spread and skill. A comparison of results of the three regions indicates that although they are chaotic in nature, the spatial averaging over a large area can increase the dimension and improve the predictability, thus destroying the chaotic nature. (C) 2010 Elsevier Ltd. All rights reserved.

Multivariate nonlinear ensemble prediction of daily chaotic rainfall with climate inputs

The basic characteristic of a chaotic system is its sensitivity to the infinitesimal changes in its initial conditions. A limit to predictability in chaotic system arises mainly due to this sensitivity and also due to the ineffectiveness of the model to reveal the underlying dynamics of the system. In the present study, an attempt is made to quantify these uncertainties involved and thereby improve the predictability by adopting a multivariate nonlinear ensemble prediction. Daily rainfall data of Malaprabha basin, India for the period 1955-2000 is used for the study. It is found to exhibit a low dimensional chaotic nature with the dimension varying from 5 to 7. A multivariate phase space is generated, considering a climate data set of 16 variables. The chaotic nature of each of these variables is confirmed using false nearest neighbor method. The redundancy, if any, of this atmospheric data set is further removed by employing principal component analysis (PCA) method and thereby reducing it to eight principal components (PCs). This multivariate series (rainfall along with eight PCs) is found to exhibit a low dimensional chaotic nature with dimension 10. Nonlinear prediction employing local approximation method is done using univariate series (rainfall alone) and multivariate series for different combinations of embedding dimensions and delay times. The uncertainty in initial conditions is thus addressed by reconstructing the phase space using different combinations of parameters. The ensembles generated from multivariate predictions are found to be better than those from univariate predictions. The uncertainty in predictions is decreased or in other words predictability is increased by adopting multivariate nonlinear ensemble prediction. The restriction on predictability of a chaotic series can thus be altered by quantifying the uncertainty in the initial conditions and also by including other possible variables, which may influence the system. (C) 2011 Elsevier B.V. All rights reserved.

A comparison of three methods for downscaling daily precipitation in the Punjab region

Many downscaling techniques have been developed in the past few years for projection of station-scale hydrological variables from large-scale atmospheric variables simulated by general circulation models (GCMs) to assess the hydrological impacts of climate change. This article compares the performances of three downscaling methods, viz. conditional random field (CRF), K-nearest neighbour (KNN) and support vector machine (SVM) methods in downscaling precipitation in the Punjab region of India, belonging to the monsoon regime. The CRF model is a recently developed method for downscaling hydrological variables in a probabilistic framework, while the SVM model is a popular machine learning tool useful in terms of its ability to generalize and capture nonlinear relationships between predictors and predictand. The KNN model is an analogue-type method that queries days similar to a given feature vector from the training data and classifies future days by random sampling from a weighted set of K closest training examples. The models are applied for downscaling monsoon (June to September) daily precipitation at six locations in Punjab. Model performances with respect to reproduction of various statistics such as dry and wet spell length distributions, daily rainfall distribution, and intersite correlations are examined. It is found that the CRF and KNN models perform slightly better than the SVM model in reproducing most daily rainfall statistics. These models are then used to project future precipitation at the six locations. Output from the Canadian global climate model (CGCM3) GCM for three scenarios, viz. A1B, A2, and B1 is used for projection of future precipitation. The projections show a change in probability density functions of daily rainfall amount and changes in the wet and dry spell distributions of daily precipitation. Copyright (C) 2011 John Wiley & Sons, Ltd.

Assessing future rainfall projections using multiple GCMs and a multi-site stochastic downscaling model

Impact of global warming on daily rainfall is examined using atmospheric variables from five General Circulation Models (GCMs) and a stochastic downscaling model. Daily rainfall at eleven raingauges over Malaprabha catchment of India and National Center for Environmental Prediction (NCEP) reanalysis data at grid points over the catchment for a continuous time period 1971-2000 (current climate) are used to calibrate the downscaling model. The downscaled rainfall simulations obtained using GCM atmospheric variables corresponding to the IPCC-SRES (Intergovernmental Panel for Climate Change - Special Report on Emission Scenarios) A2 emission scenario for the same period are used to validate the results. Following this, future downscaled rainfall projections are constructed and examined for two 20 year time slices viz. 2055 (i.e. 2046-2065) and 2090 (i.e. 2081-2100). The model results show reasonable skill in simulating the rainfall over the study region for the current climate. The downscaled rainfall projections indicate no significant changes in the rainfall regime in this catchment in the future. More specifically, 2% decrease by 2055 and 5% decrease by 2090 in monsoon (HAS) rainfall compared to the current climate (1971-2000) under global warming conditions are noticed. Also, pre-monsoon (JFMAM) and post-monsoon (OND) rainfall is projected to increase respectively, by 2% in 2055 and 6% in 2090 and, 2% in 2055 and 12% in 2090, over the region. On annual basis slight decreases of 1% and 2% are noted for 2055 and 2090, respectively.

Large scale features and assessment of spatial scale correspondence between TMPA and IMD rainfall datasets over Indian landmass

Daily rainfall datasets of 10 years (1998-2007) of Tropical Rainfall Measuring Mission (TRMM) Multi-satellite Precipitation Analysis (TMPA) version 6 and India Meteorological Department (IMD) gridded rain gauge have been compared over the Indian landmass, both in large and small spatial scales. On the larger spatial scale, the pattern correlation between the two datasets on daily scales during individual years of the study period is ranging from 0.4 to 0.7. The correlation improved significantly (similar to 0.9) when the study was confined to specific wet and dry spells each of about 5-8 days. Wavelet analysis of intraseasonal oscillations (ISO) of the southwest monsoon rainfall show the percentage contribution of the major two modes (30-50 days and 10-20 days), to be ranging respectively between similar to 30-40% and 5-10% for the various years. Analysis of inter-annual variability shows the satellite data to be underestimating seasonal rainfall by similar to 110 mm during southwest monsoon and overestimating by similar to 150 mm during northeast monsoon season. At high spatio-temporal scales, viz., 1 degrees x1 degrees grid, TMPA data do not correspond to ground truth. We have proposed here a new analysis procedure to assess the minimum spatial scale at which the two datasets are compatible with each other. This has been done by studying the contribution to total seasonal rainfall from different rainfall rate windows (at 1 mm intervals) on different spatial scales (at daily time scale). The compatibility spatial scale is seen to be beyond 5 degrees x5 degrees average spatial scale over the Indian landmass. This will help to decide the usability of TMPA products, if averaged at appropriate spatial scales, for specific process studies, e.g., cloud scale, meso scale or synoptic scale.

Wet and dry spell characteristics of global tropical rainfall

In this study, we analyze satellite-based daily rainfall observations to compare and contrast the wet and dry spell characteristics of tropical rainfall. Defining a wet (dry) spell as the number of consecutive rainy (nonrainy) days, we find that the distributions of wet spells appear to exhibit universality in the following sense. While both ocean and land regions with high seasonal rainfall accumulation (humid regions; e. g., India, Amazon, Pacific Ocean) show a predominance of 2-4 day wet spells, those regions with low seasonal rainfall accumulation (arid regions; e. g., South Atlantic, South Australia) exhibit a wet spell duration distribution that is essentially exponential in nature, with a peak at 1 day. The behavior that we observed for wet spells is reversed for the dry spell characteristics. In other words, the main contribution to the dry part of the season, in terms of the number of nonrainy days, appears to come from 3-4 day dry spells in the arid regions, as opposed to 1 day dry spells in the humid regions. The total rainfall accumulated in each wet spell has also been analyzed, and we find that the major contribution to seasonal rainfall for arid regions comes from 1-5 day wet spells; however, for humid regions, this contribution comes from wet spells of duration as long as 30 days. We also explore the role of chance as well as the influence of organized convection in determining some of the observed features.

Fuzzy State Real-Time Reservoir Operation Model for Irrigation with Gridded Rainfall Forecasts

A short-term real-time operation model with fuzzy state variables is developed for irrigation of multiple crops based on earlier work on long-term steady-state policy. The features of the model that distinguish it from the earlier work are (1) apart from inclusion of fuzziness in reservoir storage and in soil moisture of crops, spatial variations in rainfall and soil moisture of crops are included in the real-time operation model by considering gridded command area with a grid size of 0.5 degrees latitude by 0.5 degrees longitude; (2) the water allocation model and soil moisture balance equations are integrated with the real-time operation model with consideration of ponding water depth for Paddy crop; the model solution specifies reservoir releases for irrigation in a 10-day time period and allocations among the crops on a daily basis at each grid by maintaining soil moisture balance at the end of the day; and (3) the release policy is developed using forecasted daily rainfall data of each grid and is implemented for the current time period using actual 10-day inflow and actual daily rainfall of each grid. The real-time operation model is applied to Bhadra Reservoir in Karnataka, India. The results obtained using the real-time operation model are compared with those of the standard operating policy model. Inclusion of fuzziness in reservoir storage and soil moisture of crops captures hydrologic uncertainties in real time. Considerations of irrigation decisions on a daily basis and the gridded command area result in variations in allocating water to the crops, variations in actual crop evapotranspiration, and variations in soil moisture of the crops on a daily basis for each grid of the command area. (C) 2015 American Society of Civil Engineers.

Variability of Indian summer monsoon rainfall in daily data from gauge and satellite

It has long been thought that tropical rainfall retrievals from satellites have large errors. Here we show, using a new daily 1 degree gridded rainfall data set based on about 1800 gauges from the India Meteorology Department (IMD), that modern satellite estimates are reasonably close to observed rainfall over the Indian monsoon region. Daily satellite rainfalls from the Global Precipitation Climatology Project (GPCP 1DD) and the Tropical Rainfall Measuring Mission (TRMM) Multisatellite Precipitation Analysis (TMPA) are available since 1998. The high summer monsoon (June-September) rain over the Western Ghats and Himalayan foothills is captured in TMPA data. Away from hilly regions, the seasonal mean and intraseasonal variability of rainfall (averaged over regions of a few hundred kilometers linear dimension) from both satellite products are about 15% of observations. Satellite data generally underestimate both the mean and variability of rain, but the phase of intraseasonal variations is accurate. On synoptic timescales, TMPA gives reasonable depiction of the pattern and intensity of torrential rain from individual monsoon low-pressure systems and depressions. A pronounced biennial oscillation of seasonal total central India rain is seen in all three data sets, with GPCP 1DD being closest to IMD observations. The new satellite data are a promising resource for the study of tropical rainfall variability.

Simulating the daily discharge of the Mandovi River, west coast of India

A hydrological modelling framework was assembled to simulate the daily discharge of the Mandovi River on the Indian west coast. Approximately 90% of the west-coast rainfall, and therefore discharge, occurs during the summer monsoon (June-September), with a peak during July-August. The modelling framework consisted of a digital elevation model (DEM) called GLOBE, a hydrological routing algorithm, the Terrestrial Hydrological Model with Biogeochemistry (THMB), an algorithm to map the rainfall recorded by sparse rain-gauges to the model grid, and a modified Soil Conservation Service Curve Number (SCS-CN) method. A series of discharge simulations (with and without the SCS method) was carried out. The best simulation was obtained after incorporating spatio-temporal variability in the SCS parameters, which was achieved by an objective division of the season into five regimes: the lean season, monsoon onset, peak monsoon, end-monsoon, and post-monsoon. A novel attempt was made to incorporate objectively the different regimes encountered before, during and after the Indian monsoon, into a hydrological modelling framework. The strength of our method lies in the low demand it makes on hydrological data. Apart from information on the average soil type in a region, the entire parameterization is built on the basis of the rainfall that is used to force the model. That the model does not need to be calibrated separately for each river is important, because most of the Indian west-coast basins are ungauged. Hence, even though the model has been validated only for the Mandovi basin, its potential region of application is considerable. In the context of the Prediction in Ungauged Basins (PUB) framework, the potential of the proposed approach is significant, because the discharge of these (ungauged) rivers into the eastern Arabian Sea is not small, making them an important element of the local climate system.

Modeling non-stationarity in intensity, duration and frequency of extreme rainfall over India

Significant changes are reported in extreme rainfall characteristics over India in recent studies though there are disagreements on the spatial uniformity and causes of trends. Based on recent theoretical advancements in the Extreme Value Theory (EVT), we analyze changes in extreme rainfall characteristics over India using a high-resolution daily gridded (1 degrees latitude x 1 degrees longitude) dataset. Intensity, duration and frequency of excess rain over a high threshold in the summer monsoon season are modeled by non-stationary distributions whose parameters vary with physical covariates like the El-Nino Southern Oscillation index (ENSO-index) which is an indicator of large-scale natural variability, global average temperature which is an indicator of human-induced global warming and local mean temperatures which possibly indicate more localized changes. Each non-stationary model considers one physical covariate and the best chosen statistical model at each rainfall grid gives the most significant physical driver for each extreme rainfall characteristic at that grid. Intensity, duration and frequency of extreme rainfall exhibit non-stationarity due to different drivers and no spatially uniform pattern is observed in the changes in them across the country. At most of the locations, duration of extreme rainfall spells is found to be stationary, while non-stationary associations between intensity and frequency and local changes in temperature are detected at a large number of locations. This study presents the first application of nonstationary statistical modeling of intensity, duration and frequency of extreme rainfall over India. The developed models are further used for rainfall frequency analysis to show changes in the 100-year extreme rainfall event. Our findings indicate the varying nature of each extreme rainfall characteristic and their drivers and emphasize the necessity of a comprehensive framework to assess resulting risks of precipitation induced flooding. (C) 2014 Elsevier B.V. All rights reserved.

Cluster analysis of rainfall stations of the Indian peninsula

Principal component analysis is applied to derive patterns of temporal variation of the rainfall at fifty-three stations in peninsular India. The location of the stations in the coordinate space determined by the amplitudes of the two leading eigenvectors is used to delineate them into eight clusters. The clusters obtained seem to be stable with respect to variations in the grid of stations used. Stations within any cluster occur in geographically contiguous areas.

Stochastic modelling of monthly rainfall

A transformation is suggested which can transform a non-Gaussian monthly hydrological time series into a Gaussian one. The suggested approach is verified with data of ten Indian rainfall time series. Incidentally, it is observed that once the deterministic trends are removed, the transformation leads to an uncorrelated process for monthly rainfall. The procedure for normalization is general enough in that it should be also applicable to river discharges. This is verified to a limited extent by considering data of two Indian river discharges.

A conditional random field-based downscaling method for assessment of climate change impact on multisite daily precipitation in the Mahanadi basin

Downscaling to station-scale hydrologic variables from large-scale atmospheric variables simulated by general circulation models (GCMs) is usually necessary to assess the hydrologic impact of climate change. This work presents CRF-downscaling, a new probabilistic downscaling method that represents the daily precipitation sequence as a conditional random field (CRF). The conditional distribution of the precipitation sequence at a site, given the daily atmospheric (large-scale) variable sequence, is modeled as a linear chain CRF. CRFs do not make assumptions on independence of observations, which gives them flexibility in using high-dimensional feature vectors. Maximum likelihood parameter estimation for the model is performed using limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) optimization. Maximum a posteriori estimation is used to determine the most likely precipitation sequence for a given set of atmospheric input variables using the Viterbi algorithm. Direct classification of dry/wet days as well as precipitation amount is achieved within a single modeling framework. The model is used to project the future cumulative distribution function of precipitation. Uncertainty in precipitation prediction is addressed through a modified Viterbi algorithm that predicts the n most likely sequences. The model is applied for downscaling monsoon (June-September) daily precipitation at eight sites in the Mahanadi basin in Orissa, India, using the MIROC3.2 medium-resolution GCM. The predicted distributions at all sites show an increase in the number of wet days, and also an increase in wet day precipitation amounts. A comparison of current and future predicted probability density functions for daily precipitation shows a change in shape of the density function with decreasing probability of lower precipitation and increasing probability of higher precipitation.

Rainfall changes over tropical montane cloud forests of southern Western Ghats, India

The southern Western Ghats tropical montane cloud forest sites (Gavi, Periyar, High wavys and Venniyar), which are characterized by frequent or seasonal cloud cover at the vegetation level, are considered one of the most threatened ecosystems in India and the world. Three out of four montane cloud forest sites studied in the southern Western Ghats had experienced diminishing trends of seasonal average and total rainfall, especially during summer monsoon season. The highest level of reduction for summer monsoon season was observed at Gavi rainforest station (>20 mm/14 years) in Kerala followed by Venniyar (>20 mm/20 years) site in Tamil Nadu. Average annual and total precipitation increased during the study period irrespective of the seasons over Periyar area, and the greatest values were recorded for season 2 (>25 mm/28 years). Positive trends for winter monsoon rainfall has been observed for three stations (Periyar, High wavys and Venniyar) except Gavi, and the trend was positive and significant (90%) for Periyar and High wavys. Increase in summer monsoon rainfall was observed for Periyar site and the trend was found to be significant (95%).