Regionalization Of Hydrometeorological Variables In India Using Cluster Analysis

Abstract

Regionalization of hydrometeorological variables such as rainfall and temperature is necessary for various applications related to water resources planning and management. Sampling variability and randomness associated with the variables, as well as non-availability and paucity of data pose a challenge in modelling the variables. This challenge can be addressed by using stochastic models that utilize information from hydrometeorologically similar locations for modelling the variables. A set of locations that are hydrometeorologically similar are referred to as homogeneous region or pooling group and the process of identifying a homogeneous region is referred to as regionalization. The thesis concerns development of new approaches to regionalization of (i) extreme rainfall,(ii) maximum and minimum temperatures, and (iii) rainfall together with maximum and minimum temperatures. Regionalization of extreme rainfall and frequency analysis based on resulting regions yields quantile estimates that find use in design of water control (e.g., barrages, dams, levees) and conveyance structures (e.g., culverts, storm sewers, spillways) to mitigate damages that are likely due to floods triggered by extreme rainfall, and land-use planning and management. Regionalization based on both rainfall and temperature yield regions that could be used to address a wide spectrum of problems such as meteorological drought analysis, agricultural planning to cope with water shortages during droughts, downscaling of precipitation and temperature. Conventional approaches to regionalization of extreme rainfall are based extensively on statistics derived from extreme rainfall. Therefore delineated regions are susceptible to sampling variability and randomness associated with extreme rainfall records, which is undesirable. To address this, the idea of forming regions by considering attributes for regionalization as seasonality measure and site location indicators (which could be determined even for ungauged locations) is explored. For regionalization, Global Fuzzy c-means (GFCM) cluster analysis based methodology is developed in L-moment framework. The methodology is used to arrive at a set of 25 homogeneous extreme rainfall regions over India considering gridded rainfall records at daily scale, as there is dearth of regionalization studies on extreme rainfall in India Results are compared with those based on commonly used region of influence (ROI) approach that forms site-specific regions for quantile estimation, but lacks ability to delineate a geographical area into a reasonable number of homogeneous regions. Gridded data constitute spatially averaged rainfall that might originate from a different process (more synoptic) than point rainfall (more convective). Therefore to investigate utility of the developed GFCM methodology in arriving at meaningful regions when applied to point rainfall data, the methodology is applied to daily rainfall records available for 1032 gauges in Karnataka state of India. The application yielded 22 homogeneous extreme rainfall regions. Experiments carried out to examine utility of GFCM and ROI based regions in arriving at quantile estimates for ungauged sites in the study area reveal that performance of GFCM methodology is fairly close to that of ROI approach. Errors were marginally lower in the case of GFCM approach in analysis with observed point rainfall data over Karnataka, while its converse was noted in the case of analysis with gridded rainfall data over India. Neither of the approaches (CA, ROI) was found to be consistent in yielding least error in quantile estimates over all the sites. The existing approaches to regionalization of temperature are based on temperature time series or their related statistics, rather than attributes effecting temperature in the study area. Therefore independent validation of the delineated regions for homogeneity in temperature is not possible. Another drawback of the existing approaches is that they require adequate number of sites with contemporaneous temperature records for regionalization, because the delineated regions are susceptible to sampling variability and randomness associated with the temperature records that are often (i) short in length, (ii) limited over contemporaneous time period and (iii) spatially sparse. To address these issues, a two-stage clustering approach is developed to arrive at regions that are homogeneous in terms of both monthly maximum and minimum temperatures ( and ). First-stage of the approach involves (i) identifying a common set of possible predictors (LSAVs) influencing and over the entire study area, and (ii) using correlations of those predictors with and along with location indicators (latitude, longitude and altitude) as the basis to delineate sites in the study area into hard clusters through global k-means clustering algorithm. The second stage involves (i) identifying appropriate LSAVs corresponding to each of the first-stage clusters, which could be considered as potential predictors, and (ii) using the potential predictors along with location indicators (latitude, longitude and altitude) as the basis to partition each of the first-stage clusters into homogeneous temperature regions through global fuzzy c-means clustering algorithm. A set of 28 homogeneous temperature regions was delineated over India using the proposed approach. Those regions are shown to be effective when compared to an existing set of 6 temperature regions over India for which inter-site cross-correlations were found to be weak and negative for several months, which is undesirable. Effectiveness of the newly formed regions is demonstrated. Utility of the proposed maxTminT homogeneous temperature regions in arriving at PET estimates for ungauged locations within the study area was demonstrated. The estimates were found to be better when compared to those based on the existing regions. The existing approaches to regionalization of hydrometeorological variables are based on principal components (PCs)/ statistics/indices determined from time-series of those variables at monthly and seasonal scale. An issue with use of PCs for regionalization is that they have to be extracted from contemporaneous records of hydrometeorological variables. Therefore delineated regions may not be effective when the available records are limited over contemporaneous time period. A drawback associated with the use of statistics/indices is that they (i) may not be meaningful when data exhibit nonstationarity and (ii) do not encompass complete information in the original time series. Consequently the resulting regions may not be effective for the desired purpose. To address these issues, a new approach is proposed. It considers information extracted from wavelet transformations of the observed multivariate hydrometeorological time series as the basis for regionalization by global fuzzy c-means clustering procedure. The approach can account for dynamic variability in the time series and its nonstationarity (if any). Effectiveness of the proposed approach in forming homogeneous hydrometeorological regions is demonstrated by application to India, as there are no prior attempts to form such regions over the country. The investigations resulted in identification of 29 regions over India, which are found to be effective and meaningful. Drought Severity-Area-Frequency (SAF) curves are developed for each of the newly formed regions considering the drought index to be Standardized Precipitation Evapotranspiration Index (SPEI).