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Rain gauges are considered the most accurate method to estimate rainfall and are used as the "ground truth" for a wide variety of applications. The spatial density of rain gauges varies substantially and hence influences the accuracy of gridded gauge-based rainfall products. The temporal changes in rain gauge density over a region introduce considerable biases in the historical trends in mean rainfall and its extremes. An estimate of uncertainty in gauge-based rainfall estimates associated with the nonuniform layout and placement pattern of the rain gauge network is vital for national decisions and policy planning in India, which considers a rather tight threshold of rainfall anomaly. This study examines uncertainty in the estimation of monthly mean monsoon rainfall due to variations in gauge density across India. Since not all rain gauges provide measurements perpetually, we consider the ensemble uncertainty in spatial average estimation owing to randomly leaving out rain gauges from the estimate. A recently developed theoretical model shows that the uncertainty in the spatially averaged rainfall is directly proportional to the spatial standard deviation and inversely proportional to the square root of the total number of available gauges. On this basis, a new parameter called the "averaging error factor" has been proposed that identifies the regions with large ensemble uncertainties. Comparison of the theoretical model with Monte Carlo simulations at a monthly time scale using rain gauge observations shows good agreement with each other at all-India and subregional scales. The uncertainty in monthly mean rainfall estimates due to omission of rain gauges is largest for northeast India (~4% uncertainty for omission of 10% gauges) and smallest for central India. Estimates of spatial average rainfall should always be accompanied by a measure of uncertainty, and this paper provides such a measure for gauge-based monthly rainfall estimates. This study can be further extended to determine the minimum number of rain gauges necessary for any given region to estimate rainfall at a certain level of uncertainty. [ABSTRACT FROM AUTHOR]

Recent decades have witnessed rapid urbanization and urban population growth resulting in urban sprawl of cities. This paper analyzes the spatiotemporal dynamics of the urbanization process (using remote sensing and spatial metrics) that has occurred in Delhi, the capital city of India, which is divided into nine districts. The urban patterns and processes within the nine administrative districts of the city based on raw satellite data have been taken into consideration. Area, population, patch, edge, and shape metrics along with Pearson's chi statistics and Shannon's entropy have been calculated. Three types of urban patterns exist in the city: 1) highly sprawled districts, namely, West, North, North East, and East; 2) medium sprawled districts, namely, North West, South, and South West; and 3) least sprawled districts-Central and New Delhi. Relative entropy, which scales Shannon's entropy values from 0 to 1, is calculated for the districts and time spans. Its values are 0.80, 0.92, and 0.50 from 1977 to 1993, 1993 to 2006, and 2006 to 2014, respectively, indicating a high degree of urban sprawl. Parametric and nonparametric correlation tests suggest the existence of associations between built-up density and population density, area-weighted mean patch fractal dimension (AWMPFD) and area-weighted mean shape index (AWMSI), compactness index and edge density, normalized compactness index and number of patches, and AWMPFD and built-up density. [ABSTRACT FROM AUTHOR]