Xie Zhenghui

A reduced MFE formulation based on POD for the non-stationary conduction-convection problems

Abstract In this article, a reduced mixed finite element (MFE) formulation based on proper orthogonal decomposition (POD) for the non-stationary conduction-convection problems is presented. Also the error estimates between the reduced MFE solutions based on POD and usual MFE solutions are derived. It is shown by numerical examples that the results of numerical computation are consistent with theoretical conclusions. Moreover, it is shown that the reduced MFE formulation based on POD is feasible and efficient in finding numerical solutions for the non-stationary conduction-convection problems.

DIFFERENCE SCHEME AND NUMERICAL SIMULATION BASED ON MIXED FINITE ELEMENT METHOD FOR NATURAL CONVECTION PROBLEM

The non-stationary natural convection problem is studied. A lowest order finite difference scheme based on mixed finite element method for non-stationary natural convection problem, by the spatial variations discreted with finite element method and time with finite difference scheme was derived, where the numerical solution of velocity, pressure, and temperature can be found together, and a numerical example to simulate the close square cavity is given, which is of practical importance.

A Simulation Study on Climatic Effects of Land Cover Change in China

Abstract The regional climate model RegCM4 was used to investigate the regional climate effects of land cover change over China. Two 24-year simulations (1978–2001), one with the land cover derived from the MODIS data and the other with the CLCV (Chinese land cover derived from vegetation map) data, were conducted for a region encompassing China. The differences between the MODIS and CLCV data reflect characteristics of desertification and degradation of vegetation in China. Results indicate that the land cover change has important impacts on local climate through mechanisms related to changes in surface energy, water budgets and macro-scale circulation. In summer, the land cover change leads to a decrease in surface air temperature over southern China, a reduction in precipitation and an increase in surface air temperature in the transitional climate zone and the northern Tibetan Plateau, and an increase in inter-annual variability of surface air temperature in the marginal monsoon zone and northwestern China. Strengthened southwesterly winds increase precipitation to some extent in central and eastern Inner Mongolia by enhancing water vapor transport. In winter, enhanced northerly winds, bringing more dry and cold air, lead to a reduction in precipitation and temperature over areas south of the Yellow River. Citation Yu, Y., and Z.-H. Xie, 2013: A simulation study on climatic effects of land cover change in China. Adv. Clim. Change Res.,4(2), doi: 10.3724/SP.J.1248.2013.117.

A reduced second-order time accurate finite element formulation based on POD for parabolic equations

A proper orthogonal decomposition (POD) method is applied to a usual second-order time accurate Crank-Nicolson finite element (CNFE) formulation for parabolic equations such that it is reduced into a second- order time accurate CNFE formulation with fewer degrees of freedom and high enough accuracy. The errors between the reduced second-order time accurate CNFE solutions and the usual second-order time accurate CNFE solutions are analyzed. It is shown by numerical examples that the reduced second-order time accurate CNFE formulation can greatly save degrees of freedom in a way that guarantees a sufficiently small errors between the reduced second-order time accurate CNFE solutions and the usual second-order time accurate CNFE solutions. The time step of the reduced second-order time accurate CNFE formulation is ten times that of the first-order time accurate reduced finite element formulation such that it could obtain very quickly the numerical solution at the moment wanted, alleviate the computer truncation error, and improve rate and accuracy in the computational process. Moreover, it is also shown that the reduced second-order time accurate CNFE formulation is feasible and efficient solving parabolic equations.

A subsurface runoff parameterization with water storage and recharge based on the Boussinesq-Storage Equation for a Land Surface Model

Subsurface runoff in a land surface model is usually parameterized as a single-valued function of total storage in a basin aquifer reservoir. This kind of parameterization is often single-valued function of storage-discharge under a steady or “quasi-steady” state, which cannot represent the influence of aquifer recharge on subsurface runoff generation. In this paper, a new subsurface runoff parameterization with water storage and recharge based on the Boussinesq-storage equation is developed. This model is validated by a subsurface flow separation algorithm for an example river basin, which shows that the new model can simulate the subsurface flow reasonably.

A reduced FE formulation based on POD method for hyperbolic equations

A proper orthogonal decomposition (POD) method was successfully used in the reduced-order modeling of complex systems. In this paper, we extend the applications of POD method, namely, apply POD method to a classical finite element (FE) formulation for second-order hyperbolic equations with real practical applied background, establish a reduced FE formulation with lower dimensions and high enough accuracy, and provide the error estimates between the reduced FE solutions and the classical FE solutions and the implementation of algorithm for solving reduced FE formulation so as to provide scientific theoretic basis for service applications. Some numerical examples illustrate the fact that the results of numerical computation are consistent with theoretical conclusions. Moreover, it is shown that the reduced FE formulation based on POD method is feasible and efficient for solving FE formulation for second-order hyperbolic equations.

A New Way to Predict Forecast Skill

Forecast skill (Anomaly Correlated Coefficient, ACC) is a quantity to show the forecast quality of the products of numerical weather forecasting models. Predicting forecast skill, which is the foundation of ensemble forecasting, means submitting products to predict their forecast quality before they are used. Checking the reason is to understand the predictability for the real cases. This kind of forecasting service has been put into operational use by statistical methods previously at the National Meteorological Center (NMC), USA (now called the National Center for Environmental Prediction (NCEP)) and European Center for Medium-range Weather Forecast (ECMWF). However, this kind of service is far from satisfactory because only a single variable is used with the statistical method. In this paper, a new way based on the Grey Control Theory with multiple predictors to predict forecast skill of forecast products of the T42L9 of the NMC, China Meteorological Administration (CMA) is introduced. The results show: (1) The correlation coefficients between “forecasted” and real forecast skill range from 0.56 to 0.7 at different seasons during the two-year period. (2) The grey forecasting model GM(1,8) forecasts successfully the high peaks, the increasing or decreasing tendency, and the turning points of the change of forecast skill of cases from 5 January 1990 to 29 February 1992.

The Long-Term Field Experiment Observatory and Preliminary Analysis of Land-Atmosphere Interaction over Hilly Zone in the Subtropical Monsoon Region of Southern China

Abstract To improve current understanding of the water cycle, energy partitioning and CO2 exchange over hilly zone vegetative land surfaces in the subtropical monsoon environment of southern China, a long-term field experiment observatory was set up at Ningxiang, eastern Hunan Province. This paper presents a preliminary analysis of the field observations at the observatory collected from August to November 2012. Results show that significant diurnal variations in soil temperature occur only in shallow soil layers (0.05, 0.10, and 0.20 m), and that heavy rainfall affects soil moisture in the deep layers (≥ 0.40 m). During the experimental period, significant diurnal variations in albedo, radiation components, energy components, and CO2 flux were observed, but little seasonal variation. Strong photosynthesis in the vegetation canopy enhanced the CO2 absorption and the latent heat released in daylight hours; Latent heat of evaporation was the main consumer of available energy in late summer. Because the field experiment data are demonstrably reliable, the observatory will provide reliable long-term measurements for future investigations of the land-atmosphere interaction over hilly land surfaces in the subtropical monsoon region of southern China.

Evaluation of the Community Microwave Emission Model Coupled with the Community Land Model over East Asia

Abstract The Community Microwave Emission Model (CMEM) developed by the European Centre for Medium-Range Weather Forecasts (ECMWF) can provide a link between surface states and satellite observations and simulate the passive microwave brightness temperature of the surface at low frequencies (from 1 GHz to 20 GHz). This study evaluated the performance of the CMEM coupled with the Community Land Model (CLM) (CMEM-CLM) using C-band (6.9 GHz) microwave brightness temperatures from the Advanced Microwave Scanning Radiometer on Earth Observing System (AMSR-E) over East Asia. Preliminary results support the argument that the simulated brightness temperatures of CMEM-CLM from July 2005 to June 2010 are comparable to AMSR-E observational data. CMEM-CLM performed better for vertical polarization, for which the root mean square error was approximately 15 K, compared to over 30 K for horizontal polarization. An evaluation performed over seven sub-regions in China indicated that CMEM-CLM was able to capture the temporal evolution of C-band brightness temperatures well, and the best correlation with AMSR-E appeared over western Northwest China (over 0.9 for vertical polarization). However, larger biases were found over southern North China and the middle and lower reaches of the Yangtze River.

Mixed finite element methods for the shallow water equations including current and silt sedimentation (I)—The continuous-time case

An initial-boundary value problem for shallow equation system consisting of water dynamics equations, silt transport equation, the equation of bottom topography change, and of some boundary and initial conditions is studied, the existence of its generalized solution and semidiscrete mixed finite element (MFE) solution was discussed, and the error estimates of the semidiscrete MFE solution was derived. The error estimates are optimal.