In this paper, we present a decomposition method of multivariate functions. This method shows that any multivariate function f on [0, 1]d is a finite sum of the form ∑jφjψj , where each φj can be extended to a smooth periodic function, each ψj is an algebraic polynomial, and each φjψj is a product of separated variable type and its smoothness is same as f . Since any smooth periodic function can be approximated well by trigonometric polynomials, using our decomposition method, we find that any smooth multivariate function on [0, 1]d can be approximated well by a combination of algebraic polynomials and trigonometric polynomials. Meanwhile, we give a precise estimate of the approximation error.
The East Asian summer monsoon(EASM) is a distinctive component of the Asian climate system and critically influences the economy and society of the region. To understand the ability of AGCMs in capturing the major features of EASM, 10 models that participated in Coupled Model Intercomparison Project/Atmospheric Model Intercomparison Project(CMIP5/AMIP), which used observational SST and sea ice to drive AGCMs during the period 1979–2008, were evaluated by comparing with observations and AMIP II simulations. The results indicated that the multi-model ensemble(MME) of CMIP5/AMIP captures the main characteristics of precipitation and monsoon circulation, and shows the best skill in EASM simulation, better than the AMIP II MME. As for the Meiyu/Changma/Baiyu rainbelt, the intensity of rainfall is underestimated in all the models. The biases are caused by a weak western Pacific subtropical high(WPSH) and accompanying eastward southwesterly winds in group I models, and by a too strong and west-extended WPSH as well as westerly winds in group II models. Considerable systematic errors exist in the simulated seasonal migration of rainfall, and the notable northward jumps and rainfall persistence remain a challenge for all the models. However, the CMIP5/AMIP MME is skillful in simulating the western North Pacific monsoon index(WNPMI).
The default fractional vegetation cover and terrain height were replaced by the estimated fractional vegetation cover, which was calculated by the Normalized Difference Vegetation Index(NDVI) of Earth Observing System Moderate-Resolution Imaging Spectroradiometer(EOS-MODIS) and the Digital Elevation Model of the Shuttle Radar Topography Mission(SRTM) system. The near-surface meteorological elements over northeastern China were assimilated into the three-dimensional variational data assimilation system(3DVar) module in the Weather Research and Forecasting(WRF) model. The structure and daily variations of air temperature, humidity, wind and energy fields over northeastern China were simulated using the WRF model. Four groups of numerical experiments were performed, and the simulation results were analyzed of latent heat flux, sensible heat flux, and their relationships with changes in the surface energy flux due to soil moisture and precipitation over different surfaces. The simulations were compared with observations of the stations Tongyu, Naiman, Jinzhou, and Miyun from June to August, 2009. The results showed that the WRF model achieves high-quality simulations of the diurnal characteristics of the surface layer temperature, wind direction, net radiation, sensible heat flux, and latent heat flux over semiarid northeastern China in the summer. The simulated near-surface temperature, relative humidity, and wind speed were improved in the data assimilation case(Case 2) compared with control case(Case 1). The simulated sensible heat fluxes and surface heat fluxes were improved by the land surface parameterization case(Case 3) and the combined case(Case 4). The simulated temporal variations in soil moisture over the northeastern arid areas agree well with observations in Case 4, but the simulated precipitation should be improved in the WRF model. This study could improve the land surface parameters by utilizing remote sensing data and could further improve atmospheric elements with a data assimilation system. This w
A method is introduced in this paper to study the effect of future climatic change on the economy.The researchers determine the economic output of climate change from historical data,and provide a method to quantitatively predict economic output of climate change by an economic-climatic model.A historical reciprocating examination is used to analyze output data for various crops in eight agricultural areas in China and meteorological data from 160 observatories in China from 1980 to 2000.The results show that the methods used are reasonable to a certain extent and good in application.
