On the applicability of Kirchoff’s law and the principle of heat balance in thermal infrared remote sensing: A non-isothermal system

This paper proposes a basic equation of thermal radiation interaction between surface objects on the basis of the principle of heat balance in the interface. The solution of this equation takes account of the contribution of sensible heat flux and latent heat flux more completely, compared with traditional solution for surface cooling and heating processes. By the aid of the experimental data conducted in the Xiaotangshan experimental site, Beijing, both the non-applicability of Kirchoff’s law and the measurability of surface emissivity in a non-isothermal system have been highlighted. Two methods called ventilation and time-delay compensations have been proposed to reduce the error induced by change of surface temperatures of non-isothermal objects during the measurement of emissivity. Based on the solution of the basic equation, this paper has analyzed and pointed out the misunderstanding in comprehension and application of Kirchoff’s law published in literature.     

Vegetation pattern of Istanbul from the Landsat data and the relationship with meteorological parameters

This paper discusses the preliminary results of a study on the vegetation pattern and its relationship with meteorological parameters in and around Istanbul. The study covers an area of over 6800 km² consisting of urban and suburban centers, and uses the visible and near-infrared bands of Landsat. The spatial variation of the Normalized Difference Vegetation Index (NDVI) and meteorological parameters such as sensible heat flux, momentum flux, relative humidity, moist static energy, rainfall rate and temperature have been investigated based on observations in ten stations in the European (Thracian) and Anatolian parts of Istanbul. NDVI values have been evaluated from the Landsat data for a single day, viz. 24 October 1986, using ERDAS in ten different classes. The simultaneous spatial variations of sensible heat and momentum fluxes have been computed from the wind and temperature profiles using the Monin-Obukhov similarity theory. The static energy variations are based on the surface meteorological observations. There is very good correlation between NDVI and rainfall rate. Good correlation also exists between: NDVI and relative humidity; NDVI, sensible heat flux and relative humidity; NDVI, momentum flux and emissivity; and NDVI, sensible heat flux and emissivity. The study suggests that the momentum flux has only marginal impact on NDVI. Due to rapid urbanization, the coastal belt is characterized by reduced NDVI compared to the interior areas, suggesting that thermodynamic discontinuities considerably influence the vegetation pattern. This study is useful for the investigation of small-scale circulation models, especially in urban and suburban areas where differential heating leads to the formation of heat islands. In the long run, such studies on a global scale are vital to gain accurate, timely information on the distribution of vegetation on the earth’s surface. This may lead to an understanding of how changes in land cover affect phenomena as diverse as the atmospheric CO² concentrations, the hydrological cycle and the energy balance at the surface-atmosphere interface.     

On the development of the crater population on the moon with time under meteoroid and solar wind bombardment

In this paper a theory is evaluated to describe the development of the lunar crater population with time under the bombardment by meteoroids and solar wind. Starting from a general mass distribution law a differential equation has been established and solved separately for meteoroid impact and solar wind bombardment. The theory permits the calculation of absolute formation ages of the lunar surface as well as the particle flux, supposing the crater distributions on the moon have been measured. As an important result it includes a D⁻² equilibrium crater distribution law (D =crater diameter), actually measured in Mare Tranquillitatis and Oceanus Procellarum. Additionally, the exponential decrease of particle flux with time is confirmed.     

Field temperature measurements at Erta'Ale Lava Lake, Ethiopia

The shield volcano Erta'Ale, situated in the Danakil Depression, Ethiopia, is known for its active lava lake. In February 2001, our team visited this lake, located inside an 80-m-deep pit, to perform field temperature measurements. The distribution and variation of temperature inside the lake were obtained on the basis of infrared radiation measurements performed from the rim of the pit and from the lake shores. The crust temperature was also determined from the lake shores with a thermocouple to calibrate the pyrometer. We estimated an emissivity of the basalt of 0.74 from this experiment. Through the application of the Stefan-Boltzmann law, we then obtained an estimate of the total radiative heat flux, constrained by pyrometer measurements of the pit, and visual observations of the lake activity. Taking into account the atmospheric convective heat flux, the convected magma mass flux needed to balance the energy budget was subsequently derived and found to represent between 510 and 580 kg s^-1. The surface circulation of this mass flux was also analyzed through motion processing techniques applied to video images of the lake. Electronic supplementary material to this paper can be obtained by using the Springer LINK server located at http://dx.doi.org/10.1007/s00445-002-0224-3.     

人为热源对城市边界层结构影响的数值模拟研究

用南京大学多尺度模式系统在不同区域进行了多种人为热源引入方案的研究，结果表明：考虑时空变化的人为热源按比例分别引入到地表能量平衡方程和大气热量守恒方程是将人为热源引入模式的最优方案.人为热通量密度变化的敏感性试验结果发现：人为热源的存在对城市热岛的生成有重要作用.计算结果表明，南京现有的人为热源排放量对该地区的城市热岛贡献率约为296％，若人为热通量密度在现有量值的基础上增大1倍，则其热岛贡献率可达429％；此外，人为热的排放对清晨城市边界层逆温结构有一定程度的破坏作用，能明显升高夜间近地层气温达05～10℃，并能使白天湍流活动的影响范围增大，混合层高度抬高，使夜间城市热岛环流的影响范围扩大.     

基于双温度差分双源模型的遥感方法反演四川汶川地区的潜热通量

研究表明,在很多地震前都出现了潜热通量异常。文中基于Modis遥感数据,结合研究区(四川省汶川地区)的高光谱数据及地面观测的气象数据,利用一种简化的双层模型(双温度差分双源模型)反演显热通量,并通过地表能量平衡方程计算研究区的潜热通量。还探讨了该模型的特点,并对龙门山断裂带通过地区进行了潜热通量的遥感反演,发现在2008年5月12日汶川MS8.0地震前48h内,研究区内的震中地区、龙门山断裂周边地区潜热通量值出现了明显的高值,5月12日中午12时7分沿龙门山断裂带潜热通量值达到300～400W/m2,可能是汶川8.0级地震前的异常反应     

Matrix expression of thermal radiative characteristics for an open complex

The directionality of thermal radiance of a homogeneous isothermal non-black plane surface is totally decided by its directional emissivity, which depends on the complex dielectric constant and roughness of surface. It can be expressed by This paper proves that it is necessary to express emissivity by a matrix when a target becomes an inhomogeneous non-isothermal open complex with complicated inner geometric structure. The matrix describes the inner radiative interaction among components accurately and also expresses its thermal radiative directionality and structural characteristics completely. Advantages of matrix expression are as follows: first, the physical mechanics of effective emissivity of an open complex is described in a simple and perfect way; second, it becomes easy to understand the principle and method to retrieve components temperature from multi-angle thermal remotely sensed data; and third, the differences of directionalities between an open complex and a homogeneous isothermal non-black plane body are expressed by just using an effective emissivity matrix instead of an emissivity vector. Formula in classic physics is only the special case of matrix expression; therefore, the matrix is a universal unconditional expression to describe the directionality of thermal radiance.     

Determination of regional land surface heat fluxes over a heterogeneous landscape of the Jiddah area of Saudi Arabia by using Landsat‐7 ETM data

In this study, a parameterization method based on Landsat‐7 Enhanced Thematic Mapper (ETM) data and field observations is presented and tested for deriving the regional land surface variables, vegetation variables and land surface heat fluxes over a heterogeneous landscape. As a case study, the method and two Landsat‐7 ETM images are applied to the Jiddah area of Saudi Arabia. The regional distribution maps of surface reflectance, normalized difference vegetation index, modified soil adjusted vegetation index (MSAVI), vegetation coverage, leaf area index, surface temperature, net radiation flux, soil heat flux, sensible heat flux and latent heat flux have been determined over the Jiddah area. The derived results have been validated by using the ‘ground truth’. The results show that the more reasonable regional distributions of land surface variables (surface reflectance, surface temperature), vegetation variables (MSAVI and vegetation coverage), net radiation, soil heat flux and sensible heat flux can be obtained by using the method proposed in this study. Further improvement of the method is also discussed. Copyright © 2006 John Wiley & Sons, Ltd.     

Propagator matrix formulation of heat transfer in spherically stratified media

Summary In the paper we have transformed the steady and unsteady conductive heat transfer differential equation in spherical coordinates into a system of first order differential equations and processed them by method of propagator matrices to extrapolate the known surface heat flux and temperature to any desired depth. The elements of propagator matrices have been summarised for various piecewise continuous conductivity and rate of heat generation functions to approximate inhomogeneities in the earth. In the analysis the rate of heat generation is either assumed to depend linearly upon temperature or correspond to first order irreversible chemical reactions.     

Non-isothermal soil water transport and evaporation

A detailed model was formulated to describe the non-isothermal transport of water in the unsaturated soil zone. The model consists of the coupled equations of mass conservation for the liquid phase, gas phase and water vapor and the energy conservation equation. The water transport mechanisms considered are convection in the liquid phase, and convection, diffusion and dispersion of vapor in the gas phase. The boundary conditions at the soil–atmosphere interface include dynamical mass flux and energy flux that accounts for radiation transport. Comparison of numerical simulations results with published experimental data demonstrated that the present model is able to describe water and energy transport dynamics, including situations of low and moderate soil moisture contents. Analysis of field studies on soil drying suggests that that dispersion flux of the water vapor near the soil surface, which is seldom considered in soil drying models, can make a significant contribution to the total water flux.     

Spatial characterization of land surface energy fluxes and uncertainty estimation at the Salar de Atacama,Northern Chile

We use Advanced Spaceborne Thermal Emission and Reflection radiometer (ASTER) data to estimate spatial energy flux and evaporation distributions at the Salar de Atacama, a playa in Northern Chile. Our approach incorporates ASTER surface kinetic temperature, emissivity, and reflectance data, ground-based meteorological measurements, and empirical parameters. Energy flux distributions are estimated using either spatially constant or spatially distributed values of model parameters, with spatially distributed parameters assigned separately to each land cover category in an image classification. We test the sensitivity of energy budget calculations to state variable and parameter values by conducting Monte Carlo simulations for regions with ground energy budget measurements. Results show that assigning spatially distributed model parameters via land cover classifications yields significant improvements to ground and sensible heat flux predictions. Latent heat fluxes cannot, however, be predicted with sufficient accuracy to allow estimation of area-integrated evaporative moisture loss at this low-evaporation playa.     

沙漠陆面过程参数化与模拟

沙漠地区植被稀疏、干旱少雨,其陆面物理过程具有与全球其它地区显著不同的特点.本文利用巴丹吉林沙漠观测资料,分析和计算了地表反照率、比辐射率、粗糙度和土壤热容量、热传导系数等关键陆面过程参数,建立了适合于沙漠地区的陆面过程模式DLSM (Desert Land Surface Model),并与NOAH陆面过程模式的模拟结果和观测资料进行了比较.结果表明:巴丹吉林沙漠地表反照率为0.273,比辐射率为0.950,地表粗糙度为1.55×10^-3 m,土壤热容量和热扩散系数分别为1.08×10⁶ J·m^-3·K^-1和3.34×10^-7 m²·s.辐射传输、感热输送和土壤热传导过程是影响沙漠地区地表能量平衡的主要物理过程.通过对这三种过程的准确模拟检验,DLSM能够较准确地模拟巴丹吉林沙漠地气能量交换特征;短波辐射、长波辐射和感热通量的模拟结果与观测值间的标准差分别为7.98,6.14,33.9 W·m^-2,与NOAH陆面过程模式的7.98,7.72,46.6 W·m^-2的结果接近.地表反照率是沙漠地区最重要的陆面过程参数,地表反照率增大5%,向上短波辐射通量随之增加5%,感热通量则减小2.8%.本文研究结果对丰富陆面过程参数化方案,改进全球陆面过程模式、气候模式具有参考意义.     

陆面微波比辐射率的卫星观测研究进展

复杂多变的陆地表微波比辐射率,造成陆面上星载微波观测反演大气参数较为困难,也使得许多卫星微波资料不易同化应用到数值模式,因此迫切需要提供准确可靠的陆面微波地表比辐射率信息.随着卫星观测技术的迅速发展,利用丰富的星载被动微波观测直接反演陆面微波比辐射率成为一种主要手段.国外针对星载微波成像仪和微波垂直探测器开展较为系统的陆面微波比辐射率研究,建立不同类型的地表比辐射率反演方法,开发地表比辐射率参数化方法并应用于辐射资料同化.对于卫星观测反演陆面微波比辐射率存在的问题,开展了评估分析和方法订正.国内利用卫星观测也开展了一些陆面微波比辐射率研究工作,尚需要系统、综合的提炼.对于地表特征复杂的中国地区,还需要评估认识不同陆面微波比辐射率反演方法在我国适用情况,需要增强陆面微波比辐射率数据质量的认识以及业务应用.     

Spatial distribution of surface energy fluxes over the Loess Plateau in China and its relationship with climate and the environment

China's Loess Plateau is located at the edge of the Asian summer monsoon in a transition zone of climate and ecology. In the Loess Plateau, climate and environments change along with space, which has an obvious impact on the spatial distribution of surface energy fluxes. Because of scarce land-surface observation sites and short observation time in this area, previous studies have failed to fully understand the land-surface energy balance characteristics over the entire the Loess Plateau and their effect mechanisms. In this paper, we first test the simulation ability of the Community Land Model(CLM) model by comparing its simulated data with observed data. Based on the simulation data for the Loess Plateau over the past thirty years, we then analyze the spatial distribution of surface energy fluxes and compare the pattern differences between the area averages for the driest year and wettest year. Furthermore, we analyze the relationship between the spatial distribution of the components of the surface energy balance with longitude, latitude, altitude, precipitation and temperature. The main results are as follows: the spatial distribution of surface energy fluxes are significantly different, with the surface net radiation and sensible heat flux increasing from south to north and latent heat flux and soil heat flux decreasing from southeast to northwest. The sensible heat flux at the driest point is nearly twice as high as that at the wettest point, whereas the latent heat flux and soil heat flux at the driest point are half as much as that at the wettest point. The impact of variations of annual precipitation on the components of the surface energy balance is also obvious, and the maximum magnitude of the changes to the sensible heat flux and latent heat flux is nearly 30%. To a certain extent, geographical factors(including longitude, latitude, and altitude) and climate factors(including temperature and precipitation) affect the surface energy fluxes. However, the surface net radiation is more closely related to latitude and altitude, sensible heat flux is more closely related to the monsoon rainfall and latitude, and latent heat flux and soil heat flux are more closely related to the monsoon rainfall.     

On the heat budget of the moon and the surface temperature variation during a lunar eclipse

Summary The analysis of surface temperature variations of the moon is based on the equations of heat conduction and heat continuity in the interior of the moon andStefan's law. During a well-defined process, as exemplified by a lunar eclipse, the local heat budget equation establishes a boundary condition at the moon surface which must be satisfied by solutions of the thermal diffusion equation in the interior. Three simplified models of the general case are discussed. They are characterized by special assumptions regarding the depth and time dependency of the thermic qualities of the material underlying the moon's surface. In short, the thermal diffusivity is assumed to be constant in the first model, a linear depth function in the second and a time function in the third. A unique solution can be obtained for model No. I such that the absolute surface temperature is approximately inversely proportional to the 6th root of time during the phase of total eclipse.Epstein's conclusion that the average surface of the moon might consist of highly porous rocks or fine dust is confirmed by the order of magnitude of the heat conductivity which produces the best fit between the theoretical curves and a plot ofPettit's observational data during the lunar eclipse of 1939. Existing differences between the observed and theoretical curves during the totality phase of the eclipse can be reduced by the employment of the second model. A crude estimate shows that the average dust cover resting on more solid ground of lunar rocks might possibly have a thickness of approximately 0.5 meters.     

Numerical and approximate solutions for lithospheric thickening and thinning

Lithospheric thickness, surface heat flow and subsidence are calculated numerically as functions of time since the formation of oceanic lithosphere at a ridge crest. These numerical results confirm the validity of a previously derived approximate solution to the same problem. A numerical solution is also calculated for lithospheric thinning due to a sudden increase of heat flux into the base of the lithosphere. With this solution as a standard, an approximate solution is derived which can accurately predict thickness, heat flow, and uplift as functions of time. Lithospheric thinning and surface uplift begin immediately with the increase of heat flux at depth, but the increase in surface heat flow begins 20–40 m.y. later.     

An Asymptotic Analysis of a Simple Model for the Structure and Dynamics of the Ramdas Layer

This paper presents a complete asymptotic analysis of a simple model for the evolution of the nocturnal temperature distribution on bare soil in calm clear conditions. The model is based on a simplified flux emissivity scheme that provides a nondiffusive local approximation for estimating longwave radiative cooling near ground. An examination of the various parameters involved shows that the ratio of the characteristic radiative to the diffusive timescale in the problem is of order 10⁻³, and can therefore be treated as a small parameter (μ). Certain other plausible approximations and linearization lead to a new equation whose asymptotic solution as μ → 0 can be written in closed form. Four regimes, consisting of a transient at nominal sunset, a radiative-diffusive boundary (‘Ramdas’) layer on ground, a boundary layer transient and a radiative outer solution, are identified. The asymptotic solution reproduces all the qualitative features of more exact numerical simulations, including the occurrence of a lifted temperature minimum and its evolution during night, ranging from continuing growth to relatively sudden collapse of the Ramdas layer.     

地-空界面上天然中子辐射场的数理模型

本文论述了地－空界面上天然宇宙中子流的来源;将天然中子按能量分为快中子组（En＞01MeV）与慢热中子组,建立了地－空界面上天然快中子流与慢热中子流粒子注量率随空间分布的数理方程.理论与实测结果相互验证表明：（1）地－空界面上天然中子流粒子注量率随距近地表高度的增加而呈指数规律减小;（2）地－空界面上天然中子流粒子注量率随海拨高程增加而呈指数规律增加;（3）地－空界面上上升中子流粒子注量率随地表介质含水率的增加而减少.     

The age of the inner core

The energy conservation law, when applied to the Earth’s core and integrated between the onset of the crystallization of the inner core and the present time, gives an equation for the age of the inner core. In this equation, all the terms can be expressed theoretically and, given values and uncertainties of all relevant physical parameters, the age of the inner core can be obtained as a function of the heat flux at the core–mantle boundary and the concentrations in radioactive elements. It is found that in absence of radioactive elements in the core, the age of the inner core cannot exceed 2.5 Ga and is most likely around 1 Ga. In addition, to have an inner core as old as the Earth, concentrations in radioactive elements needed in the core are too high to be acceptable on geochemical grounds.     

南京城市化进程对大气边界层的影响研究

为了研究城市化进程对城市边界层结构的影响，通过高分辨率的卫星遥感资料获得土地利用类型,以及地表反照率、植被指数等地表参数，以南京为例，运用数值模拟手段进行了研究，结果显示这是一种可行的手段.数值模拟结果表明，随着城市的发展，城市反照率减小、植被减少、地表湿度减小，蒸发耗热减少，感热通量增加140 W/m2，城市波恩比增加.地表和大气之间热量交换加强，湍流热量通量增大了一倍，湍流交换发展加剧，14：00混合层高度抬高了500 m.地表湍流水汽通量和空气中水汽含量都减小，这也使更多的热量用于加热地表和大气，使地温、气温的日变化幅度增加.