RETRIEVING OVER-OCEAN PRECIPITABLE WATER FROM THE SSM/I MEASUREMENTS WITH SEVERAL REGRESSION ALGORITHMS*

A collocated SSM/I and radiosonde measurement data set provided by the NASDA(Japan) was used to retrieve the total precipitable water(PW) over oceans.The retrieval results obtained with several regression algorithms were compared against the radiosonde measurements.It is shown that:(a) the routinely operational algorithm of Alishouse et al.(1990) yields significant underestimation in high PW regime and overestimation in low PW regime;(b) a cubic correction by Colton and Poe(1994) is not sufficient and globally improves slightly the retrieval results;and(c) the regression algorithm with the form of brightness temperature(T_b) function In(280-T_b) gives a little largely scattered retrievals in whole PW range but without considerable over-and underestimates in low and high PW regimes.To improve the estimation of the oceanic precipitable water from the SSM/I measurements,a composite algorithm with different forms of T_b function in low.medium and high PW regimes is proposed and tested.     

CRA40在中国地区GNSS水汽反演中的适用性评估与分析

基于中国气象局发布的CRA40气象再分析资料,计算地基GNSS水汽反演中涉及气压、气温、大气水汽加权平均温度（T_m）、天顶对流层总延迟（ZTD）等关键参数,并分别以地面气象站（气压、气温）、无线电探空测站（T_m）以及地基GNSS测站（ZTD）为参考,对这些参数在中国地区的精度和可靠性开展了系统的评估.计算结果与欧洲中期天气预报中心（ECWMF）最新一代ERA5产品的计算结果进行比较,结果表明：基于CRA40计算的测站处气压和ZTD的平均RMS（均方根）分别为0.91 hPa和13.5 mm,略差于ERA5;计算的测站处气温和T_m平均RMS分别为2.67 K和1.47 K,略优于ERA5.三类参数（气压、气温、ZTD）的日变化总体趋势与实际观测符合较好.     

Tropical cyclones and polar lows: Velocity,size, and energy scales,and relation to the 26°C cyclone origin criteria

The goal of this paper is to quantitatively formulate some necessary conditions for the development of intense atmospheric vortices. Specifically, these criteria are discussed for tropical cyclones (TC) and polar lows (PL) by using bulk formulas for fluxes of momentum, sensible heating, and latent heating between the ocean and the atmosphere. The velocity scale is used in two forms: (1) as expressed through the buoyancy flux b and the Coriolis parameter l_c for rotating fluids convection, and (2) as expressed with the cube of velocity times the drag coefficient through the formula for total kinetic energy dissipation in the atmospheric boundary layer. In the quasistationary case the dissipation equals the generation of the energy. In both cases the velocity scale can be expressed through temperature and humidity differences between the ocean and the atmosphere in terms of the reduced gravity, and both forms produce quite comparable velocity scales. Using parameters b and l_c, we can form scales of the area and, by adding the mass of a unit air column, a scale of the total kinetic energy as well. These scales nicely explain the much smaller size of a PL, as compared to a TC, and the total kinetic energy of a TC is of the order 10¹⁸-10¹⁹ J. It will be shown that wind of 33 m s^-1 is produced when the total enthalpy fluxes between the ocean and the atmosphere are about 700 W m^-2 for a TC and 1700 W m^-2 for a PL, in association with the much larger role of the latent heat in the first case and the stricter geostrophic constraints and larger static stability in the second case. This replaces the mystical role of 26^oC as a criterion for TC origin. The buoyancy flux, a product of the reduced gravity and the wind speed, together with the atmospheric static stability, determines the rate of the penetrating convection. It is known from the observations that the formation time for a PL reaching an altitude of 5--6 km can be only a few hours, and a day, or even half a day, for a TC reaching 15--18 km. These two facts allow us to construct curves on the plane of T^s and ΔT=T_s-T_a to determine possibilities for forming an intense vortex. Here, T_a is the atmospheric temperature at the height z=10 m. A PL should have ΔT>20^oC in accordance with the observations and numerical simulations. The conditions for a TC are not so straightforward but our diagram shows that the temperature difference of a few degrees, or possibly even a fraction of a degree, might be sufficient for TC development for a range of static stabilities and development times.     

我国东西部地区地气温差的年代际变化特征

利用1960~2006年我国地温、气温逐日4个时次[02:00(北京时间,下同)、08:00、14:00和20:00]的台站观测资料,计算并分析了我国东南、西北地区各季地气温差的年代际变化特征。分析结果表明:我国东南部地区各季地气温差在20世纪70年代末以前,大部分年份偏高,高于平均值,而在20世纪70年代末以后,我国东南部地区各季地气温差偏低,在夏季和冬季表现尤为明显。我国西北地区春季和夏季地气温差在20世纪70年代末以前大部分年份偏低,低于平均值;而在20世纪70年代末以后,地气温差则大部分年份明显偏高。我国西北地区秋季地气温差的年代际变化特征不明显,而冬季地气温差的年代际变化趋势与春夏季相反,在20世纪70年代末以前大部分年份偏高,高于平均值,而在20世纪70年代末以后偏低。另外,发现地温和气温对我国东南、西北地区各季地气温差的年代际变化在各季所起的贡献作用不同。     

热带太平洋表面水中CO2对El Niño事件响应的数值模拟

文中用一个带生物泵的三维全球海洋碳循环模式模拟了热带太平洋表面水中CO2总量(TCO2)在ElNi     

Analysis of the Weighted Mean Temperature of China Based on Sounding and ECMWF Reanalysis Data

Weighted mean temperature (Tm) is one of the most important conversion parameters for calculating precipitable water vapor by the signal path wet delay in ground-based GPS meteorology. This paper first discusses the Tmregression models for Hong Kong (HK) and the associated error statistics relative to the true values of Tmfrom the numerical method. The results show that there is little difference in precision between annual and seasonal Tmregression models for HK. The Bevis Tm-Ts(surface temperature) regression model is more suitable for northeastern China and the Qinghai-Tibetan Plateau than the local models. For areas lack of historical sounding data, the Kriging interpolation method and the ECMWF reanalysis product ERA-interim were employed to set up local Tm-Ts models. The results indicate that the Tmderived by the ERA-interim data coincides well with that by the sounding data, and the Kriging interpolation method can successfully obtain the coefficients of local Tm-Tsmodels, suggesting that these two approaches may serve as effective ways in the acquisition and localization of Tm.     

The diurnal cycle of surface air temperature in simulated present and doubled CO2 climates

 The diurnal range of surface air temperature (rT _a ) simulated for present and doubled CO₂ climates by the CSIRO9 GCM is analysed. Based on mean diurnal cycles of temperature and surface heat fluxes, a theory for understanding the results is developed. The cycles are described as the response to a diurnal forcing which is represented well by the diurnal mean flux of net shortwave radiation at the surface (SW) minus the evaporative (E) and sensible (H) fluxes. The response is modified by heat absorbed by the ground, and by the cycle in downward longwave (LW) radiation, but these effects are nearly proportional to the range in surface temperature. Thus in seasonal means, rT _a is approximately given by SW–E–H divided by 6 W m^-2/^°C. A multiple regression model for (rT _a ) is developed, based on quantities known to influence SW, E and H, and applied to both spatial variation in seasonal means, and day-to-day variation at a range of locations. In both cases, rT _a is shown to be influenced by cloud cover, snow extent and wind speed. It is influenced by soil moisture, although this effect is closely tied to that of cloud. In seasonal means rT _a is also well correlated with precipitable water, apparently because of the latter’s influence on E+H. The regression model describes well the spatial variation in the doubled CO₂ change in rT _a . The annual mean change in rT _a over land on doubling CO₂ was −0.36 ^°C, partly because of a decrease in the mean diurnal forcing (as defined in the theory), but also apparently because of the effect of nonlinearity in T _s of the upward longwave emission. A diagnostic radiation calculation indicates that the CO₂ and water vapour provide a small increase in rT _a through the downward LW response, which partially counters a decrease due to a reduction of SW by the gases. Received: 8 November 1995 / Accepted: 3 January 1997     

A new method for estimation of near surface specific humidity over global oceans

Summary A new methodology for deriving daily averages of near surface specific humidity (Q _a ) is developed. Remotely sensed parameters, total water vapor (W), boundary-layer water vapor (W _b ), and sea-surface temperature (SST) are used to derive Q _a . Genetic algorithm (GA) is used to find the empirical function relating the input (W, W _b , and SST) and output (Q _a ) parameters. The input data consist of 2 years (1999–2000) of daily W, W _b , from SSM/I (Special Sensor Microwave Imager), and SST data from AVHRR (Advanced Very High Resolution Radiometer). COADS (Comprehensive Ocean Atmospheric Data Set) observations of Q _a are used to develop and evaluate the new methodology. The performance of the algorithm is measured with COADS observations, which are not used in the development phase. The global mean rms error for daily averages Q _a is 1.5 ± 0.40 g/kg. Slightly higher discrepancies between Q _a derived from the new method and COADS observations are found over the Northwestern Pacific, North Atlantic oceans and Arabian Sea. This method improves upon the humidity retrieval of Liu (1986), Schulz et al (1993), and Chou et al (1997).     

A global annually-averaged climate model with cloud,water vapor and CO2 feedbacks

In consideration of the radiation transfer, latent and sensible heat exchange between oceans and at-mosphere, a three-dimensional autonomous nonlinear ordinary differential equation is established by statis-tical parameterization method. The variables of the model are the mean ocean surface temperature Ts, mean atmospheric temperature Ta and atmospheric relative humidity f, and the feedbacks of clouds, water vapor and CO2 are involved. The steady state corresponding to the present-day climate can be obtained from this model. The analysis of parameter sensibility in the steady state indicates that clouds have consid-erable negative feedback effects and water vapor may affect the sign of CO2 feedback. The stability analysis of the steady state to small disturbance indicates that with increase of the positive feedback effect of clouds, the steady state goes through such a structural variance series as a stable node→a stable focal point→an unstable focal point→an unstable node, and when the steady state becomes unstable it undergoes a subcritical Hopf bifurcation. When the steady state is at a focal point, the periodic oscillation solutions of damping or amplifying can be obtained with the period being about two years.     

TROPOSPHERIC WATER VAPOR OBSERVATIONS USING A RAMAN LIDAR OVER HEFEI*

This paper presents a Raman lidar for measuring tropospheric water vapor profiles over Hefei(31.9°N,117.17°E),China.Intercomparisons of water vapor mixing ratio obtained by this Raman lidar and GZZ-59 type radiosonde observations show the good agreements when relative humidity is higher than 20%.Typical vertical profiles and seasonal variations of water vapor mixing ratio distribution are reported.Many observation eases indicate that the high moisture layer corresponds to large aerosol scattering ratios in the lower troposphere.     

Evaluation of Haney-Type Surface ThermalBoundary Conditions Using a CoupledAtmosphere and Ocean Model

A coupled atmosphere-ocean model developed at the Institute for Space Studies at NASA Goddard Space Flight Center (Russell et al., 1995) was used to verify the validity of Haney-type surface thermal boundary condition, which linearly connects net downward surface heat flux Q to air / sea temperature difference △T by a relaxation coefficient k. The model was initiated from the National Centers for Environmental Prediction (NCEP) atmospheric observations for 1 December 1977, and from the National Ocean Data Center (NODC) global climatological mean December temperature and salinity fields at 1° ×1° resolution. The time step is 7.5 minutes. We integrated the model for 450 days and obtained a complete model-generated global data set of daily mean downward net surface flux Q, surface air temperature TA,and sea surface temperature To. Then, we calculated the cross-correlation coefficients (CCC) between Q and △T. The ensemble mean CCC fields show (a) no correlation between Q and △T in the equatorial regions, and (b) evident correlation (CCC≥ 0.7) between Q and △T in the middle and high latitudes.Additionally, we did the variance analysis and found that when k= 120 W m-2K-1, the two standard deviations, σQ and σk△T, are quite close in the middle and high latitudes. These results agree quite well with a previous research (Chu et al., 1998) on analyzing the NCEP re-analyzed surface data, except that a smaller value of k (80 W m-2K-1) was found in the previous study.     

Estimation of precipitable water at different locations using surface dew-point

Summary The Reitan (1963) regression equation of the form lnw =a +bT _d has been examined and tested to estimate precipitable water vapor content from the surface dew point temperature at different locations. The results of this study indicate that the slopeb of the above equation has a constant value of 0.0681, while the intercepta changes rapidly with latitude. The use of the variable intercept technique can improve the estimated result by about 2%.With 6 Figures     

A Study of Linke Turbidity Factor over Qena / Egypt

Data on instantaneous atmospheric Linke turbidity factor TL (m) are reported for clear days at Qena/Egypt in the period from June 1992 to May 1993.TL(m) is determined using the values of irradiance of direct solar radiation (I),which are calculated from global (G) and diffuse (D) - solar radiation measurements.Monthly and seasonally variations of both diurnal and daily average values of TL (m) increases steadily in the direction of sunset in the months from June to December 1992 as well as Summer and Autumn seasons,while it falls generally in this direction for the months from January to March and Winter season.In April and May,TL (m) fluctuates obviously through the day hours,it is also shown that the average values of TL(m) are particularly large during Summer months compared to other months of the year.This behavior of TL(m) is discussed in view of the variations of some weather elements,which affect the content of water vapor and dust particle in the atmosphere of the study region.It seems t be of s     

Atmospheric turbidity of urban and desert areas of the Nile Basin in the aftermath of Mt. Pinatubo’s eruption

Summary  The Linke T _L , ?ngstr?m β and Unsworth-Monteith δ _a turbidity parameters are investigated for two sites in Egypt: Cairo, a densely populated urban area, and Aswan, an arid unpolluted area. These three turbidity parameters are calculated from broadband pyrheliometric measurements recorded hourly over the period 1992–96. Monthly averages of T _L , β and δ _a show relatively flat and identical seasonal variations with a marked main maxima during spring at both sites, due to Khamsin depressions coming from the Great Sahara. A secondary maximum is observed at Aswan in summer, due to dust haze which prevails during that season, and at Cairo in autumn, due to the northern extension of the Sudan monsoon trough, which is accompanied by small scale depressions with dust particles. Annual mean values of T _L , β and δ _a (5.59, 0.250 and 0.372, respectively) at Cairo are larger than at Aswan (3.89, 0.139 and 0.213, respectively). In the same way, the seasonal mean values of T _L , β and δ _a at Cairo are larger than at Aswan. More generally, the monthly and yearly average turbidity values are significantly larger in Cairo than in Aswan for the whole period 1992–96, which is attributable in part to the urbanization/industrialization effect of Cairo. An estimate of the corresponding overburden is obtained by comparison between the present data and older T _L data from 1922–27. It is also shown that turbidity over both sites is largest during 1992, just after the eruption of Mount Pinatubo in 1991. The dependence of β on some meteorological parameters such as wind speed and direction, precipitable water, relative humidity, temperature and visibility, is also analyzed. This reveals in particular that visibility is not a good predictor of turbidity at either site. Conversely, the wind direction and speed have a definite effect on turbidity, and consequently, largest turbidities occur when the wind carries aerosols from the main industrial particle source areas around Cairo. For any season of the year, the average turbidity at the latter site is larger than that at other big cities such as Athens, Rome, and Toronto, but is lower than at Dhahran, Saudi Arabia. Received February 3, 2000 Revised August 25, 2000     

An assessment of the potential impact of a downward shift of tropospheric water vapor on climate sensitivity

This work uses an energy balance climate model (EBCM) with explicit infrared radiative transfer, parametrized tropospheric temperature and humidity profiles, and separate stratosphere, troposphere, and surface energy balances, to investigate claims that a downward redistribution of tropospheric water vapor in response to surface warming could serve as a strong negative feedback on climatic change. A series of sensitivity tests is carried out using: (1) a variety of relationships between total precipitable water in the troposphere and temperature; (2) feedbacks between surface temperature and the vertical distribution of tropospheric water vapor at low latitudes; and (3) feedback between surface temperature or meridional temperature gradient and lapse rate. Fixed relative humidity (RH) enhances the global mean surface temperature response to a CO₂ doubling by only 50% compared to fixed absolute humidity, giving a response of 1.8 K. When water vapor is assumed to be redistributed downward between 30°S–30°N such that a 1 K surface warming reduces total precipitable water above 600 hPa by 10%, the global mean surface air temperature response is reduced to 1.2 K. Assuming a stronger downward redistribution in relation to surface temperature change has a rapidly diminishing marginal effect on global mean and tropical surface temperature response, while slightly increasing the warming at high latitudes due to the parametrized dependence of middle-to-high latitude lapse rate on the meridional temperature gradient. A modest downward water vapor redistribution, such that absolute humidity in the upper troposphere at subtropical latitudes is constant as total precipitable water increases, can reduce the tropical temperature sensitivity to less than 1 K, while increasing the equator-to-pole amplification of the surface air temperature response from a factor of about three to a factor of four. However, it is concluded that whatever changes in future GCM response might occur as a result of new parametrizations of subgrid-scale processes, they are exceedingly unlikely to produce a climate sensitivity to a CO₂ doubling of less than 1 K even if there is a strong downward shift in the water vapor distribution as climate warms. Received: 23 February 1998 / Accepted: 1 November 1999     

中国区域性大气加权平均温度线性模型精度评估

以欧洲中期天气预报中心的再分析资料ERA5为参考数据,评估由探空数据建立的中国区域88个单站大气加权平均温度（T_m）与地表气温（T_s）线性关系模型的精度.各站T_m-T_s线性模型计算的T_m（计算值）与ERA5 气压层数据积分所得的T_m（参考值）间偏差均方根值（RMSE）为1.8~5.5 K.不同站模型计算值与参考值间存在-1.22~4.54 K 的系统性偏差,且绝大多数测站（82个站）系统性偏差为正值,即模型计算值总体上大于参考值.补偿各站系统性偏差后,模型计算值与参考值间RMSE降为1.5~3.5 K.与使用中国区域统一模型相比,使用单站模型平均能提高0.6 K的T_m计算精度,尤其在中国西部、西北和内蒙区域,精度提高可达1~3.9 K.对所有测站模型计算值和参考值间偏差时序进行分析,发现超过半数测站的偏差存在明显季节性变化.     

卫星遥感结合气象资料计算的青藏高原地面感热特征分析

本文选取1981年7月至2012年12月美国国家航空和航天局（NASA）制作的归一化的动态植被指数（NDVI）资料、根据NDVI值计算地表热力输送系数（C_H）的参数化关系式（C_H-I_NDV）和青藏高原70个常规气象观测资料,计算了青藏高原全区的逐月地表热力输送系数（C_H）,讨论了其时空分布特征,并在此基础上计算了高原70个常规台站的感热通量（SSHF）序列,并与已有感热资料进行了对比。随后,探讨了地面感热通量的气候特征及其年际变化与气候因子的关系。结果表明:高原地区的C_H值具有明显的空间差异和季节差异,表现为东高西低、夏季大、冬季小的特点。感热的年际变化在冬季主要响应于地气温差的变化,夏季则受地面风速影响较大;由于风速减小趋缓,地气温差增大,变化趋势在2003年前后由减弱趋势转变为增强趋势,这种趋势的转变最早发生在2001年秋季,且在高原全区具有较好的一致性。     

A Study of the Internal Boundary Layer due to a Roughness Change in Neutral Conditions Observed During the LINEX Field Campaigns

Summary As an aspect of the LINEX field studies (1996–1997; Lindenberg near Beeskow, Germany), the characteristics of the internal boundary layer (IBL) that is associated with a step change of the surface roughnesses in neutral constant stress layers was investigated and is reported in this paper. Both smooth to rough (in 1996) and rough to smooth (in 1997) types of flow, have been studied based upon the profiles of mean wind and temperature realised from a 10-m mast and eddy correlation measurements taken at two levels (2 m and 5 m). Depending upon wind direction, the fetch at the site varied between 140 m and 315 m within the wind sector (200° to 340°) used for the field investigations. The height of the IBL, δ, had been determined from the intersect of the logarithmic wind-profiles below (< 2 m) and above (> 6 ) the interface. Values of δ obtained at the experimental site compared fairly well to the existing theoretical/empirical fetch-height relationships of the form: δ=aċx ^b , where a, b, are empirical constants. The ratio for the friction velocities below and above the IBL as measured directly by the eddy correlation techniques showed that for fetches less than 250 m there was an increase (decrease) of about 20% of the momentum flux arising from the smooth to rough (rough to smooth) transitions. Influences of distant obstructions (e.g., bushes, pockets of trees) on the surface flow were markedly important on the examined wind profiles and such can be indicative as multiple IBLs. Received September 1, 1997 Revised August 5, 1998     

A study of the seasonal migration of ITCZ and the quasi-periodic oscillations in a simple monsoon system using an energy balance model

Summary A zonally averaged global energy balance model with feedback mechanisms was constructed to simulate (i) the poleward limits of ITCZ over the continent and over the ocean and (ii) a simple monsoon system as a result of differential heating between the continent and the ocean. Three numerical experiments were performed with lower boundary as (1) global continent, (2) global ocean and (3) continent-ocean, with freezing latitudes near the poles. Over the continent, midlatitude deserts were found and the ITCZ migrates 25° north and south with seasons. Over a global swamp ocean results do not show migration of ITCZ with time but once the ocean currents are introduced the ITCZ migrates 5° north and south with seasons. It was found that the seasonal migration of ITCZ strongly depends on the meridional distribution of the surface temperature. It was also found that continent influences the location of the oceanic ITCZ. In the tropics northward progression of quasi-periodic oscillations called events are found during the pre- and post-monsoon periods with a period of 8 to 15 days. This result is consistent with the observed quasi-periodic oscillations in the tropical region. Northward propagation of the surface temperature perturbation appears to cause changes in the sensible heat flux which in turn causes perturbations in vertical velocity and latent heat flux fields.List of Symbols vertical average - ₀ zonal average - vertical mean of the zonal average - _0s zonal average at the surface - _0a zonal average at 500 mb level - latitude We now define the various symbols used in the model rate of atmospheric heating due to convective cloud formation (K/sec) - dp/dt (N/m²/sec) - density - potential temperature (K) - rate of rotation of the earth (rad/sec) - empirical constant - humidity mixing ratio - ^* saturated humidity mixing ratio - opacity of the atmosphere - ₁,₂ factors for downward and upward effective black body long wave radiation from the atmosphere - Stefan-Boltzmann constant - emissivity of the surface - _D subsurface temperature (K) - a specific volume - _0xs ,_0ys eastward and northward components of surface frictional stress - ^* vertical velocity at the top of the boundary layer (N/m²/sec) - P Thickness of the boundary layer (mb) - nondimensional function of pressure - P pressure - P _a pressure of the model atmosphere (N/m²) - P _s pressure at the surface (N/m²) - t time (sec) - U eastward wind speed (m/sec) - V northward wind speed (m/sec) - surface water availability - T absolute temperature (K) - heat addition due to water phase changes - g acceleration due to gravity (m²/sec) - a radius of the earth (m) - R gas constant for dry air (J/Kg/K) - C _p specific heat of air at constant pressure (J/Kg/K) - k R/C _p - L latent heat of condensation (J/Kg) - f coriolis parameter (rad/sec) - H _s H _0s ⁽¹⁾ +H _0s ⁽²⁾ +H _0s ⁽³⁾ +H _0s ⁽⁴⁾ +H _0s ⁽⁵⁾ (J/m²/Sec)=sum of the rates of vertical heat fluxes per unit surface area, directed toward the surface - H _a H _0a ⁽¹⁾ +H _0a ⁽²⁾ +H _0a ⁽³⁾ +H _0a ⁽⁴⁾ (J/m²/Sec)=sum of the rates of heat additions to the atmospheric column per unit horizontal area by all processes - H _0s ⁽¹⁾ ,H _0a ⁽¹⁾ heat flux due to short wave radiation - H _0s ⁽²⁾ ,H _0a ⁽²⁾ heat flux due to long wave radiation - H _0s ⁽³⁾ ,H _0a ⁽³⁾ heat flux due to small scale convection - H _0s ⁽⁴⁾ heat flux due to evaporation - H _0a ⁽⁴⁾ heat flux due to condensation - H _0s ⁽⁵⁾ heat flux due to subsurface conduction and convection - e ^* saturation vapor pressure - R solar constant (W/m²) - r _a albedo of the atmosphere - r _s albedo of the surface - b ₂ empirical constant (J/m²/sec) - c ₂ empirical constant (J/m²/sec) - e ₂ nondimensional empirical constant - f ₂ empirical constant (J/m₂/sec) - factor proportional to the conductive capacity of the surface medium - a _s constant used in Sellers model - b _s positive constant of proportionality used in the Sellers model (kg m²/J/sec²) - K _HT coefficient for eddy diffusivity of heat (m²/sec) - K _HE exchange coefficient for water vapor (m²/sec) - h depth of the water column (m) - z height (m) - V _0ws meridional component of surface current (m/sec) - n cloud amount - G _0,n long wave radiation form the atmosphere for cloud amount n (W/m²) - B ₀ long wave radiation from the surface (W/m²) - S _0,n short wave radiation from the atmosphere for cloud amount n (W/m²) - A _n albedo factor for a cloud amount n - R _f1 large scale rainfall (mm/day) - R _f2 small scale rainfall (mm/day) With 22 Figures