A semi-implicit multiple-nested grid model for simulation of flow in a tropical storm

ABSTRACT .A three-layer three-dimensional, triply-nested primitive equation model. suitable to simulate tropical storm, has been designed. A grid telescopic technique has been used with a fine grid mesh of 18 km grid length in the centre which is surrounded by a medium mesh of 54 km grid length; this is again surrounded by a course grid mesh of 162 km grid length. Each mesh consists of 32 X 32 array of momentum points enclosing 31 X 31 array of mass points. The variables are staggered in space which reduces the amount of averaging to a minimum and hence improves accuracy. To suppress non-linear instability an improved finite difference scheme has been applied. A two-way interaction method has been adopt to match the solutions between grids of different lengths. To increase the time step for integration, a semi-implicit scheme has been used. The speed of the solution of the system of Helmholtz equations arising out of semi-implicit scheme has been appreciably increased by devising an iterative method. To examine the role of surface friction as postulated by Yamasaki (1977) and forced subsidence as hypothesized by Arnold (1977), Gray (1977) and Yanai (1961) at the initial stage of development of a tropical storm. numerical experiments have been accomplished with this model varying coefficient of surface drag. and specifying heat around the centre of the to disturbance which is considered as the effect of forced subsidence through an analytical function similar to one used by Harrison (1973). The integration was started from a weak barotropic vortex in &r8dient balance en and continued for 48 hours in two cases and 60 hours in one case. It is observed that surface friction may not be an essential factor at the initial stage of development of tropical storm when the vortex is weak. On the other hand, initial development could be initiated by forced subsidence. But in the subsequent stage, surface friction plays an important role to induce mass convergence in the boundary layer and to reduce horizontal of the disturbance. This preliminary experiment has yielded smooth and encouraging results.

Stability properties of a projector-splitting scheme for dynamical low rank approximation of random parabolic equations

We consider the Dynamical Low Rank (DLR) approximation of random parabolic equations and propose a class of fully discrete numerical schemes. Similarly to the continuous DLR approximation, our schemes are shown to satisfy a discrete variational formulation. By exploiting this property, we establish stability of our schemes: we show that our explicit and semi-implicit versions are conditionally stable under a “parabolic” type CFL condition which does not depend on the smallest singular value of the DLR solution; whereas our implicit scheme is unconditionally stable. Moreover, we show that, in certain cases, the semi-implicit scheme can be unconditionally stable if the randomness in the system is sufficiently small. Furthermore, we show that these schemes can be interpreted as projector-splitting integrators and are strongly related to the scheme proposed in [29, 30], to which our stability analysis applies as well. The analysis is supported by numerical results showing the sharpness of the obtained stability conditions.

Modeling Snow Depth and Snow Water Equivalent Distribution and Variation Characteristics in the Irtysh River Basin, China

Accurate simulation of snow cover process is of great significance to the study of climate change and the water cycle. In our study, the China Meteorological Forcing Dataset (CMFD) and ERA-Interim were used as driving data to simulate the dynamic changes in snow depth and snow water equivalent (SWE) in the Irtysh River Basin from 2000 to 2018 using the Noah-MP land surface model, and the simulation results were compared with the gridded dataset of snow depth at Chinese meteorological stations (GDSD), the long-term series of daily snow depth dataset in China (LSD), and China’s daily snow depth and snow water equivalent products (CSS). Before the simulation, we compared the combinations of four parameterizations schemes of Noah-MP model at the Kuwei site. The results show that the rainfall and snowfall (SNF) scheme mainly affects the snow accumulation process, while the surface layer drag coefficient (SFC), snow/soil temperature time (STC), and snow surface albedo (ALB) schemes mainly affect the melting process. The effect of STC on the simulation results was much higher than the other three schemes; when STC uses a fully implicit scheme, the error of simulated snow depth and snow water equivalent is much greater than that of a semi-implicit scheme. At the basin scale, the accuracy of snow depth modeled by using CMFD and ERA-Interim is higher than LSD and CSS snow depth based on microwave remote sensing. In years with high snow cover, LSD and CSS snow depth data are seriously underestimated. According to the results of model simulation, it is concluded that the snow depth and snow water equivalent in the north of the basin are higher than those in the south. The average snow depth, snow water equivalent, snow days, and the start time of snow accumulation (STSA) in the basin did not change significantly during the study period, but the end time of snow melting was significantly advanced.

An Implicit Algorithm for Finding a Fixed Point of a Q -Nonexpansive Mapping in Locally Convex Spaces

In this paper, the notion of the q -duality mappings in locally convex spaces is introduced. An implicit method for finding a fixed point of a Q -nonexpansive mapping is provided. Finally, the convergence of the proposed implicit scheme is investigated. Some examples in order to illustrate of the main results are presented.

A Comparison Study of Explicit and Implicit 3-D Transient Electromagnetic Forward Modeling Schemes on Multi-Resolution Grid

This study compares the efficiency of 3-D transient electromagnetic forward modeling schemes on the multi-resolution grid for various modeling scenarios. We developed time-domain finite-difference modeling based on the explicit scheme earlier. In this work, we additionally implement 3-D transient electromagnetic forward modeling using the backward Euler implicit scheme. The iterative solver is used for solving the system of equations and requires a proper initial guess that has significant effect on the convergence. The standard approach usually employs the solution of a previous time step as an initial guess, which might be too conservative. Instead, we test various initial guesses based on the linear extrapolation or linear combination of the solutions from several previous steps. We build up the implicit scheme forward modeling on the multi-resolution grid, which allows for the adjustment of the horizontal resolution with depth, hence improving the performance of the forward operator. Synthetic examples show the implicit scheme forward modeling using the linearly combined initial guess estimate on the multi-resolution grid additionally reduces the run time compared to the standard initial guess approach. The result of comparison between the implicit scheme developed here with the previously developed explicit scheme shows that the explicit scheme modeling is more efficient for more conductive background models often found in environmental studies. However, the implicit scheme modeling is more suitable for the simulation with highly resistive background models, usually occurring in mineral exploration scenarios. Thus, the inverse problem can be solved using more efficient forward solution depending on the modeling setup and background resistivity.