Himalayan lakes represent critical water resources, culturally important waterbodies, and potential hazards. Some of these lakes experience dramatic waterlevel changes, responding to seasonal monsoon rains and postmonsoonal draining. To address the paucity of direct observations of hydrology in retreating mountain glacial systems, we describe a field program in a series of high altitude lakes in Sagarmatha National Park, adjacent to Ngozumba, the largest glacier in Nepal. In situ observations find extreme (>12 m) seasonal waterlevel changes in a 60m deep lateralmorainedammed lake (lacking surface outflow), during a 16month period, equivalent to a 5
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Abstract m$$\times 10^6$$ $\times {10}^{6}$ volume change annually. The water column thermal structure was also monitored over the same period. A hydraulic model is constructed, validated against observed water levels, and used to estimate hydraulic conductivities of the moraine soils damming the lake and improves our understanding of this complex hydrological system. Our findings indicate that lake level compared to the damming glacier surface height is the key criterion for large lake fluctuations, while lakes lying below the glacier surface, regulated by surface outflow, possess only minor seasonal waterlevel fluctuations. Thus, lakes adjacent to glaciers may exhibit very different filling/draining dynamics based on presence/absence of surface outflows and elevation relative to retreating glaciers, and consequently may have very different fates in the next few decades as the climate warms.$$^3$$ ${}^{3}$Free, publiclyaccessible full text available December 1, 2024 
Abstract A Hamiltonian reduction approach is defined, studied, and finally used to derive asymptotic models of internal wave propagation in density stratified fluids in twodimensional domains. Beginning with the general Hamiltonian formalism of Benjamin (1986
J. Fluid Mech. 165 445–74) for an ideal, stably stratified Euler fluid, the corresponding structure is systematically reduced to the setup of two homogeneous fluids under gravity, separated by an interface and confined between two infinite horizontal plates. A longwave, smallamplitude asymptotics is then used to obtain a simplified model that encapsulates most of the known properties of the dynamics of such systems, such as bidirectional wave propagation and maximal amplitude travelling waves in the form of fronts. Further reductions, and in particular devising an asymptotic extension of Dirac’s theory of Hamiltonian constraints, lead to the completely integrable evolution equations previously considered in the literature for limiting forms of the dynamics of stratified fluids. To assess the performance of the asymptotic models, special solutions are studied and compared with those of the parent equations 
Abstract Wave front propagation with nontrivial bottom topography is studied within the formalism of hyperbolic long wave models. Evolution of nonsmooth initial data is examined, and, in particular, the splitting of singular points and their short time behavior is described. In the opposite limit of longer times, the local analysis of wave fronts is used to estimate the gradient catastrophe formation and how this is influenced by the topography. The limiting cases when the free surface intersects the bottom boundary, belonging to the so‐called “physical” and “nonphysical” vacuum classes, are examined. Solutions expressed by power series in the spatial variable lead to a hierarchy of ordinary differential equations for the time‐dependent series coefficients, which are shown to reveal basic differences between the two vacuum cases: for nonphysical vacuums, the equations of the hierarchy are recursive and linear past the first two pairs, whereas for physical vacuums, the hierarchy is nonrecursive, fully coupled, and nonlinear. The former case may admit solutions that are free of singularities for nonzero time intervals, whereas the latter is shown to develop nonstandard velocity shocks instantaneously. Polynomial bottom topographies simplify the hierarchy, as they contribute only a finite number of inhomogeneous forcing terms to the equations in the recursion relations. However, we show that truncation to finite‐dimensional systems and polynomial solutions is in general only possible for the case of a quadratic bottom profile. In this case, the system's evolution can reduce to, and is completely described by, a low‐dimensional dynamical system for the time‐dependent coefficients. This system encapsulates all the nonlinear properties of the solution for general power series initial data, and, in particular, governs the loss of regularity in finite times at the dry point. For the special case of parabolic bottom topographies, an exact, self‐similar solution class is introduced and studied to illustrate via closed‐form expressions the general results.