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Glacial lakes are a potential threat to the livelihoods and precious infrastructures in the Himalayan region. The expansion of these lakes under the influence of global warming further poses a grievous risk of natural disasters in the form of glacial lake outburst flood (GLOF) that necessitates regular monitoring to reduce and mitigate its implications. This research focuses on the regional scale distribution and evolution of glacial lakes in the Himalayan mountain range with their causes. We used Landsat thematic mapper (TM) and operational land imager (OLI) images, Google Earth imageries, Shuttle radar topographic mission (SRTM) Digital Elevation Model, and Aphrodite climatic data to study lake evolution and its controlling parameters. A total of the 5,409 glacial lakes was taken for the size expansion analysis, which excludes supraglacial lakes. An expansion rate of 2.98%/yr and 1.01%/yr in glacial lakes number and size was found from 1990 to 2020, respectively. The glacial lakes are distributed mainly in Langtang, Bhutan, Sikkim and Everest region; while, new lakes are forming at higher elevations continuously. The highest lake size expansion was noted in 2015–2020 (36.51%) followed by 2000–2010 (21.72%) and 2010–2015 (10.65%), while 1990–2000 (3.36%) showed a lowest expansion rate. The highest expansion rate was noticed near an elevation band of 5000–5500 m. Moreover, lakes in the central and eastern Himalaya are highly decrease by climatic change, i.e., increase in temperature a decrease precipitation. The feature selection algorithm was used to identify the importance of various controlling parameters, which showed temperature change rate, glacier fed lake, glacier snout steepness, proximal distance, glacier calving frontal width, precipitation change rate and lake type gave higher weightage towards lake size change.

The wetting deformation of the upstream dam shell material during the impoundment of the core wall rockfill dam seriously affects the safety of the dam. Based on the proposed Ew−νw wetting model, this paper proposes its corresponding two methods to simulate the collapse settlement of the rockfill dam: the initial strain method and the initial stress method. By simulating the collapse settlement of the Guanyinyan core wall rockfill dam, it is found that the simulated result using the initial stress method is in good agreement with the field monitoring data, while the displacement simulated using the initial strain method is larger. The distribution of displacement contours simulated using the initial strain method is obviously inconsistent in the area where the wetting deformation occurs, and the simulation results of the initial stress method are more reasonable. With the rise in the water level, the wetting deformation of the upstream dam shell material causes the tensile stress zone at the top of the dam. Therefore, the wetting deformation is the direct cause of the crack at the top of the dam, and the initial stress method should be preferred in the simulation of the wetting deformation of rockfill materials.

The present study deals with the estimation of dependences, spatio-temporal trends, change points, and stationarity in rainfall and rainy day series (1901–2013) for five (out of six) different climatic regions of India. Only one-fourth of the station rainfall and rainy day datasets exhibits long-term dependence on an annual and seasonal basis. The presence of lag-one serial correlation is prominent for almost all the climatic regions of India. The significant decreasing trend is found mainly for the stations of semi-arid and humid sub-tropical regions. The magnitude of rainfall is decreasing for most parts of the study area by 10% for annual and monsoon seasons. The change point is presented in a smaller number of stations. Non-stationary behaviour is observed for the rainy day series of semi-arid and humid sub-tropical regions, which may increase the temporal variability of rainfall over the same regions. The findings of this study could be very useful for the planning and management of water resources of different climatic regions of India. HIGHLIGHTS We analyse short-term and long-term dependences, spatio-temporal trends, change point, and stationarity in rainfall and rainy day datasets over five different climatic regions of India.; Change point detection for different climatic regions over parts of India.; The trend stationarity and non-stationarity is comparatively lower in rainfall datasets than the rainy day datasets for annual and monsoon seasons.;

In this paper, the limit equilibrium method with the pseudo-static approach is developed in the evaluation of the influence of slope on the bearing capacity of a shallow foundation. Particle swarm optimisation (PSO) technique is applied to optimise the solution. Minimum bearing capacity coefficients of shallow foundation near slopes are presented in the form of a design table for practical use in geotechnical engineering. It has been shown that the seismic bearing capacity coefficients reduce considerably with an increase in seismic coefficient. Be sides, the magnitude of bearing capacity coefficients decreases further with an increase in slope inclination.

Let $B^H$ be a fractional Brownian motion with Hurst index $\frac12\leq H<1$. In this paper, we consider the self-repelling diffusion $X^H_t=B^H_t+\displaystyle \int_0^t\displaystyle \int_0^sg(u){\rm{d}}X^H_u{\rm{d}}s+\nu t$,where $\nu\in {\mathbb R}$, and $g$ is a nonnegative Borel function. The process is an analogue of linear self-interacting diffusion (M. Cranston and Y. Le Jan Math. Ann. 303 (1995), 87-93.). Based on the asymptotic behavior of the weight function $g$ at infinity, we establish the large time behavior of the recursive convergence of the solution $X^H$. For example, when $g\in C^\infty({\mathbb R}_{+})$ and $0

Flash droughts, characterised by their rapid onset and significant impacts on local communities and agriculture, pose challenges for monitoring and mitigation efforts due to their unpredictable nature. Therefore, this study aims to investigate the occurrence, characteristics and influencing factors of flash droughts in the Ganga River Basin (GRB) for the period 1981–2020. Flash droughts are identified using the pentad averaged root zone soil moisture (PRZSM). The Mann‐Kendall trend test is used to determine the spatial and temporal pattern of flash drought characteristics. Furthermore, a multivariate flash drought index (MFDI) is developed to account for the combined effects of flash drought characteristics. Finally, wavelet coherence analysis evaluates the relationship between climatic oscillations and MFDI at the sub‐basin scale. Utilising a revised flash drought identification approach incorporating non‐stationary cumulative distribution functions (CDFs), the study identifies flash droughts in the GRB, particularly emphasising higher occurrences in the Chambal and Upper Yamuna Sub‐basins. Analysis of flash drought characteristics under stationary and non‐stationary conditions reveals increased frequency, severity and decline rates, highlighting the impact of evaporation and latent heat flux. Furthermore, the Upper Ganga Sub‐basin demonstrates coherence with the DMI at shorter time scales (1 to 4‐year time scales), while the Lower Ganga Sub‐basin displays a pronounced association with the NINO3.4 index (5.65‐year time scale), indicating the impact of climate oscillations on flash drought dynamics in these regions. These findings provide valuable insights for drought monitoring, prediction and management strategies in a changing climate, emphasising the need for integrated approaches to address the complex interplay between climate variability and flash drought occurrences in the GRB. [ABSTRACT FROM AUTHOR]

Abstract Let u ( t , x ) $u(t,x)$ be the solution to a stochastic heat equation ∂ ∂ t u = 1 2 ∂ 2 ∂ x 2 u + ∂ 2 ∂ t ∂ x X ( t , x ) , t ≥ 0 , x ∈ R $$ \frac{\partial }{\partial t}u=\frac{1}{2} \frac{\partial ^{2}}{\partial x^{2}}u+ \frac{\partial ^{2}}{\partial t\,\partial x}X(t,x),\quad t\geq 0, x\in { \mathbb{R}} $$ with initial condition u ( 0 , x ) ≡ 0 $u(0,x)\equiv 0$ , where Ẋ is a space-time white noise. This paper is an attempt to study stochastic analysis questions of the solution u ( t , x ) $u(t,x)$ . In fact, it is well known that the solution is a Gaussian process such that the process t ↦ u ( t , x ) $t\mapsto u(t,x)$ is a bi-fractional Brownian motion with Hurst indices H = K = 1 2 $H=K=\frac{1}{2}$ for every real number x. However, the many properties of the process x ↦ u ( ⋅ , x ) $x\mapsto u(\cdot ,x)$ are unknown. In this paper we consider the generalized quadratic covariations of the two processes x ↦ u ( ⋅ , x ) , t ↦ u ( t , ⋅ ) $x\mapsto u(\cdot ,x),t\mapsto u(t,\cdot )$ . We show that x ↦ u ( ⋅ , x ) $x\mapsto u(\cdot ,x)$ admits a nontrivial finite quadratic variation and the forward integral of some adapted processes with respect to it coincides with “Itô’s integral”, but it is not a semimartingale. Moreover, some generalized Itô formulas and Bouleau–Yor identities are introduced.