The Himalayan glaciers contribute significantly to regional water resources. However, limited field observations restrict our understanding of glacier dynamics and behaviour. Here, we investigated the long-term in situ mass balance, meteorology, ice velocity and discharge of the Chhota Shigri Glacier. The mean annual glacier-wide mass balance was negative, −0.46 ± 0.40 m w.e. a−1 for the period 2002–2019 corresponding to a cumulative wastage of −7.87 m w.e. Winter mass balance was 1.15 m w.e. a−1 and summer mass balance was −1.35 m w.e. a−1 over 2009–2019. Surface ice velocity has decreased on average by 25–42% in the lower and middle ablation zone (below 4700 m a.s.l.) since 2003; however, no substantial change was observed at higher altitudes. The decrease in velocity suggests that the glacier is adjusting its flow in response to negative mass balance. The summer discharge begins to rise from May and peaks in July, with a contribution of 43%, followed by 38% and 19% in August and September, respectively. The discharge pattern closely follows the air temperature. The long-term observation on the ‘Chhota Shigri – a benchmark glacier’, shows a mass wastage which corresponds to the slowdown of the glacier in the past two decades.
Analytical solutions are obtained for one-dimensional advection-diffusion equation with variable coefficients in a longitudinal finite initially solute free domain, for two dispersion problems. In the first one, temporally dependent solute dispersion along uniform flow in homogeneous domain is studied. In the second problem the velocity is considered spatially dependent due to the inhomogeneity of the domain and the dispersion is considered proportional to the square of the velocity. The velocity is linearly interpolated to represent small increase in it along the finite domain. This analytical solution is compared with the numerical solution in case the dispersion is proportional to the same linearly interpolated velocity. The input condition is considered continuous of uniform and of increasing nature both. The analytical solutions are obtained by using Laplace transformation technique. In that process new independent space and time variables have been introduced. The effects of the dependency of dispersion with time and the inhomogeneity of the domain on the solute transport are studied separately with the help of graphs.
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