Atmospheric longwave radiation under cloudy skies for HAM simulation programs

Transcription

1 Atmospheric longwave radiation under cloudy skies for HAM simulation programs Claudia Finkenstein, Prof. Peter Häupl Institute of Building Climatology, Dept. of Architecture, TU Dresden, D- 162 Dresden Abstract Atmospheric longwave radiation is one of the needed climatic boundary conditions in Heat-Air-Moisture (HAM) simulation programs. The paper presents principal procedures for the computation of atmospheric longwave radiation under clear and cloudy skies by means of simple near-ground weather data. Several approaches have been calculated and validated against measured data from Schleswig (D). New parameterisations for clear and cloudy skies are proposed. Special attention has been paid to the determination of atmospheric radiation under cloudy skies. Therefore three cases of initial data situation have been distinguished. The proposed approaches, based on shortwave radiation data and therefore usable for daytime data only, correspond very well with the measurements. 1 Introduction 1.1 Growing demands on accuracy of longwave radiation data Growing demands on the energy efficiency of a building and on thermal comfort demand the prediction of the hygrothermal behaviour of building parts with a very high accuracy in order to avoid damages. The thermal balance of a building part is also influenced by longwave radiation processes, although their importance has often been neglected. One can recognise the effect of longwave radiation e.g. by the growing number of moisture-related damages (algae growth and others) on northbound thermal insulation composite systems. 1.2 Meteorological background Considering Stefan-Boltzmann s law, natural surfaces (and buildings) emit longwave radiation, which is normally defined by means of wave lengths over 3 μm. As mean surface temperature is about 15 C, the application of Wien s law about the wavelength of maximum irradiance intensity indicates wavelengths around 1 μm. The atmosphere absorbs most of the terrestrial radiation and emits most of it back to the earth s ground. In the concerning wave length region, there is the atmospheric window between 8 and 13 μm wave length, with peaks of water vapour and carbon dioxide density. Therefore, the content of the atmosphere on water vapour on the one hand and carbon dioxide on the other hand are the most influencing parameters on the amount of atm. radiation. 1.3 Longwave radiation balance at a building part Considering the two- stream approximation of the Radiative Transfer Equation, explained e.g. by Paltridge, Platt [14], the longwave radiation balance at a building part consists of 3 parts: 1) the terrestrial radiation, in case of building part the emission of the building part at its (surface) temperature, 2) the atmospheric radiation coming from the clear or cloudy sky and 3) the reflected atmospheric radiation. The building part radiation flux density E lw,b and the reflected atmospheric radiation flux density R lw,atm-refl can be determined relatively easy:

2 Building part emission E lw,b The building part emits longwave radiation as a grey body. One minor problem thereby is the choice of the emission coefficient. As proposed in the Guidelines of the German Engineers association [6], an emission coefficient of ε body =, 93 has been used within this study. Reflected atmospheric radiation R lw,atm-refl Similarly, the part of the atmospheric radiation, that is being reflected at the body s surface, can be determined relatively easy. As for most building parts the effective longwave transmission coefficient is supposed to be, the reflectance is given as ( 1 ε body ). The total (upward) thermal radiation from the body or building part therefore sums up to: E upward 4 ( 1 εbody ) R lw, atm = Elw,b + R lw,atm refl = εbody σ T + (1) T surface temperature ε body =,93 body s emission coefficient [1] σ Stefan-Boltzmann constant σ = W m Atmospheric longwave radiation R lw,atm The determination of the (downward) atmospheric longwave radiation flux density R lw,atm remains a difficult issue within the longwave radiation balance. In contrast to shortwave radiation, data of longwave radiation is being measured very rarely. Its importance is underestimated, and - which seems to be a more important reason - it is much more complex. Of course, standard weather data, such as the German Test Reference Years provide longwave radiation data, that can be used in HAM simulations. However, HAM simulations are often done in special climatic situations, where simple weather data such as air temperature, relative humidity and shortwave radiation are available. In this case, one needs to determine also the longwave radiation balance in consideration of the available weather data. Pure physical models have been presented by several authors, e.g. by Monteith and Unsworth [12]. However, as the needed atmospheric conditions, such as vertical profiles of temperature and humidity or distribution of aerosols are not available, these physical equations do not help to solve the problem. Therefore, empirical models are the only solution for the provision of proper longwave radiation data. Many authors have tried to give physical reasons for the type of their equations, which seems prudential. Most of the publications refer to clear sky and provide satisfying formulae for it. However, the approaches for the determination of cloudy sky longwave radiation are rare and often very unsatisfying. The aim of this paper is to close this gap. It focuses especially on the situation of no available cloud cover data, which are rarely recorded. In this case, atmospheric longwave radiation can be computed by means of shortwave radiation data, which implies the sky properties determining also atmospheric longwave radiation. Three cases of initial data situation have been distinguished: 1) There is cloud cover data available, which allows a very good computation of atmospheric longwave radiation data. 2) There is no cloud cover data available. However, the available shortwave global and diffuse radiation data allow a good determination of atmospheric longwave radiation values during daytime. 3) There is no cloud cover and no shortwave diffuse radiation data available. Correlations to calculate atmospheric longwave radiation must be found by means of shortwave global radiation data only. This is possible for daytime data with satisfying results. 2 K 4

3 2 Atmospheric longwave radiation determination - approaches 2.1 Clear sky models Following Stefan-Boltzmann s law, the cloudless atmosphere behaves as a grey radiator: 4 R lw,atm, = ε σ T (2) R lw,atm, atm. longwave radiation flux density under clear skies [W/m²] T ε atmosphere s (absolute) temperature [K] (longwave) emission coefficient of the cloudless atmosphere As mentioned before, the vertical profile of temperature is rarely available, thus most researchers have tried to find correlations between atmospheric longwave radiation and ground based climatic parameters such as temperature or humidity. This seems reasonable, as - following several authors - more than half of the atmospheric longwave radiation received at the ground is emitted within the lowest 1m [9] or more than 2/3 of it are emitted within the lowest 15m [6]. Therefore the thermal radiative characteristics can be expressed in terms of the effective emittance or atmosphere s emissivity, defined as: R ε = (3) lw,atm, 4 σ T ε R lw,atm, T atmosphere s (longwave) emissivity of clear sky [1] atmospheric longwave radiation flux density of clear sky [W/m²] absolute air temperature near the ground [K] Those radiative characteristics, expressed in mentioned terms of emissivity, depend on temperature and humidity near the ground. First important publishers in this field were Brunt and Ångström in the early 4ies of the last century. Other publications have seized their suggestions. Five of the most interesting of them will be shortly mentioned in the following. Swinbank [17]. Swinbank presented in 1963 a very simple approach for the determination of atm. longwave radiation under clear skies. It depends only on air temperature. Swinbank underlined the principal dependence of the atmospheric emissivity on air temperature, as the atmosphere is neither an infinite isothermal atmosphere nor of constant greyness. He proposed: ε 6 = T 2 Brutsaert [1]. Brutsaert proposed in 1975 the following formula for clear sky emissivity: ε = 1.24 p 1/ 7 ( p / T ) water vapour pressure at sea-level [mbar] or [hpa] This approach has been developed without any measured data in order to validate the formula, but derived from the fundamental physical laws. So he combined a simplified version of the Radiative Transfer Equation with conditions of the ICAO standard atmosphere, inserting the standard vertical profiles of air temperature, air pressure and vapour density. The result is a quite simple formula depending on near-ground water vapour pressure and air temperature. (4) (5)

4 Idso [7]. Idso published in 1981 a new formula. It is based on the theory of water vapour emittance variations depending on the variable concentration of water dimers (pairs of water molecules linked together by weak hydrogen bonds). The approach is empirical, but conducted by physical considerations: ε = p exp(15 / T ) (6) Comment: In the original publication, the second parameter is given as would lead to very bad results and is therefore supposed to be a typing error. 5,95 1 5, but this Prata [15]. Prata presented in 1996 a new approach which also seems promising: 2 ε = { 1 ( ( p / T )) exp ( p / T ) } 1/ (7) [ ] It is loosely based on radiative transfer theory and includes the precipitable water content. The approach has also been fitted against measured data. Iziomon et al [8]. Iziomon et al. presented in 23 a new parameterisation for clear sky and cloudy conditions. Based on measurements, they found a non-negligible difference between a lowland and a mountain site. As the used data within this study has been registered at a lowland site, this case will be applied here: ε =.35 exp( 1 p / T ) (8) All sky models In the previous chapter, several approaches for the calculation of atmospheric longwave radiation under cloudless skies have been shown. However, in reality clouds do appear, increase the atmospheric longwave radiation and therefore must necessarily be considered. According to the temperature vertical profile, the lower the undersurface of a cloud, the higher is the longwave emission. Clouds also appear as black radiators, hence the temperature at the lower surface of the cloud is the needed parameter. However, and similarly to clear skies, these data are generally not available. Cloudy sky models are all based on the theoretical value of clear sky radiation by means of the given near-ground weather data. For the determination of the influence of clouds, also several empirical approaches have been developed. There are three cases to be distinguished (chapter ): Cloud cover data available Cloud cover data is sometimes registered, which means a very favourable situation concerning atmospheric longwave radiation determination. Several approaches for the determination of atmospheric longwave radiation under cloudy skies by means of clear sky radiation and cloud cover data have been published: Maykut and Church [11] Maykut and Church proposed in 1973 a widely used empirical formula, which is based on radiation data from Alaska: R lw,atm,all lw,atm, 2.75 ( n ) = R (9) R lw,atm, atm. longwave radiation flux density under clear skies [W/m²] n cloud cover [1]

5 Konzelmann et al. [1] Another approach is that of Konzelmann from 1994, which has been validated against measured data from the Greenland ice sheet: R lw,atm,all [ ε ( 1 n ) n ] σ T = (1) Iziomon et al. [8] Iziomon et al. presented in 23 new formulae based on measurements taken at a lowland and at a mountain site in Southern Germany. The lowland site parameterisation which will be used here, is: R lw,atm,all lw,atm, 2 ( N ) = R (11) N cloud cover [okta] No cloud cover, but shortwave global and diffuse radiation data available Cloud cover data is also very seldom measured, that s why the application of the case-1-models is limited. If shortwave global and diffuse radiation are available, important properties of the sky are given. It should be possible to find a correlation between the diffuse fraction k d and a value named cloud cover index n', which describes the cloud cover properties of the sky by means of the diffuse fraction. Of course, only daytime data sets are applicable to this correlation. R k d sw,diff,hor k d = (12) R sw,glob R sw,diff,hor R sw,glob horizontal shortwave diffuse radiation flux density [W/m²] shortwave global radiation flux density [W/m²] The author of this paper proposes the following correlation between the diffuse fraction k d and the first cloud cover index n '. The values of A n' and B n ' have to be parameterised in application of the measured data (see chapter 3.2.2). n',5 k d A n' = B (13) n' No cloud cover, but shortwave global radiation data available Even if only shortwave global radiation is given, approaches to describe the radiative properties of the sky can be found. This is possible by using the clearness index k t, which is defined as the relation of measured global radiation and the potential extraterrestrial solar radiation. Correlations between clearness index and diffuse fraction k d have been developed by many authors, e.g. by Reindl, Beckman and Duffie [16]. In this paper, a direct dependence between a second cloud cover index n' ' and k will be found. R t sw,glob k t = (14) R sw,extrterr n' ' R sw,extrterr potential extraterrestrial solar radiation flux density [W/m²],5 A n'' k t = B (15) n''

6 3 Validation of the presented models and new parameterisations The presented approaches for clear sky and all sky longwave radiation have been validated against measured data, which were provided by Germany s National Meteorological Service (Deutscher Wetterdienst DWD). The hourly measurements were taken in Schleswig, a lowland site in Northern Germany from January 24 to December 25. Measured and considered values are: air temperature, relative humidity, shortwave global radiation, shortwave diffuse radiation, atmospheric longwave radiation and cloud cover. 3.1 Clear sky models For the clear sky model investigation, the clear sky cases were obtained from the data. Altogether, from hourly values (2 years with some data losses) over 12 hourly values without cloud cover were chosen. Calculations were made for the 5 presented clear sky models. Four statistical values were computed for their evaluation. These are the results: Table 1: Statistical values of the clear sky model validation Mean Bias Error [W/m²] Mean Absolute Error [W/m²] Root Mean Square Error [W/m²] Correlation Coefficient [ ] Swinbank -2,92 12,1 16,52,934 Brutsaert -,59 8,3 12,24,966 Idso -12,35 16,52 22,11,943 Prata 6,24 1,46 13,6,961 Iziomon -1,96 8,13 12,13, Swinbank Brutsaert Idso Prata Iziomon 4 3 Bias Error [W/m²] time [d] (= :) Figure 1: Bias Error for 5 approaches determining the clear sky longwave radiation

7 Regarding the mean bias error, nearly all models underestimate the atmospheric longwave radiation. All in all, the approach of Brutsaert represents the measured data best, closely followed by the approach of Iziomon. Figure 1 shows the bias error for the 5 approaches. Bias Errors vary approximately from 3 to -2 W/m². Possible sources of errors could be, among others, season- or time-of-day-depending variations. Regarding figure 1, one could remark some slight seasonal variations for some of the approaches. However, the chosen approach of Brutsaert is supposed to be non-dependent of season. Figure 2 shows the Bias Error of the different times of day (mean values of all data). One will recognise a strong dependence on time of day. Bias Error [W/m²] time of day [d] (=:,.25=6: a.m. etc. ) Figure 2: Bias Error for different times of day ( for determination of atmospheric longwave radiation of clear sky by Brutsaert s approach Therefore, a new parameterisation for the determination of atmospheric longwave radiation has been developed by the author. It is based on Brutsaert s approach, but includes the dependence on time of day by a sine term. The results of the new parameterisation are very good concerning their correspondence to the measured data, as shown in figure 3. Longwave radiation flux density [W/m²] Flw,sk / 7 p T 4 = 1,24 σ T + [( 8 sin(2,3 π ( td +,1834) ) 3, 5] (16) td time of day [d] Brutsaert/new p. Measurement MBE=-,3W/m² MAE=7,3W/m² RMSE=11,1W/m² CC=, time [d] (= :) Figure 3: Clear sky data- Measurement vs. New parameterisation of Brutsaert-approach

8 3.2 All sky modelling Case 1: Cloud cover data available According to the results for the case of clear sky, the new parameterisation of Brutsaert s approach has been chosen as basis for the all sky computations. Atmospheric longwave radiation has been determined by the use of the 3 presented models, which depend on measured cloud cover data. The resulting statistical deviation values show the fairly good quality of the 3 models: Table 2: Statistical values of the first all sky model validation (case 1) Mean Bias Error [W/m²] Mean Absolute Error [W/m²] Root Mean Square Error [W/m²] Correlation Coefficient [ ] MaykutChurch -12,6 18,7 26,683,883 Konzelmann -11,5 15,8 2,634,928 Iziomon -9,1 17,8 25,663,88 All 3 approaches underestimate the all sky atmospheric longwave radiation. This may caused by geographical differences- e.g. the approach of Maykut and Church has been developed by the use of measured data from Alaska. Figure 4 shows the Bias Errors for the first 1 days. The approach of Konzelmann performs best, closely followed by the Iziomon approach. While the Iziomon approach is a pure statistical product, Konzelmann et al. have tried to find a correlation based on physical understanding. Their approach has therefore been chosen for further computations. As the approach of Konzelmann et al. has been validated against Greenland ice sheet data, a new parameterisation in order to apply the approach to the geographical situation of the measured data has been performed. Bias Error [W/m²] 7 6 MaykutChurch Konzelmann Iziomon time [d] (= :) Figure 4: All sky data Bias Error of the three cited approaches during the first 1 days (1-3/24)

9 The Konzelmann- approach changes therewith into: F lw,allsky p p 4 [ ε ( 1 n ) + ε n σ T = ] (16) ε p = 5 ε oc =,97 oc clear sky emissivity, e.g. by Brutsaert- approach (5) or (16) exponent in function for cloud influence emissivity of overcast sky The new parameterisation of Konzelmann s approach shows a very good correspondence between measured and calculated results: Longwave radiation flux density [W/m²] Measurement Konzelmann/new p. MBE=-,1 W/m² MAE=12,7 W/m² RMSE=17,8 W/m² CC=, time [d] (= :) Figure 5: Atmospheric longwave radiation and statistical error values by new parameterisation of Konzelmannapproach Case 2: No cloud cover, but shortwave global and diffuse radiation data available If there is no cloud cover data available, conclusions about sky properties, thus the atmospheric longwave radiation, can be made by means of the diffuse fraction (relation between diffuse and global radiation). Of course, this is possible only for daytime data sets. Therefore, the night time data sets were separated. The author proposes the creation of a cloud cover index n, which is leaned against the original cloud cover. The cloud cover index depends on the diffuse fraction k d (see eq. 12). The form of the interrelation between k d and n has been developed by the author and by means of the interrelation of original cloud cover n and k d. The parameterisation has been performed by the use of the measured data, which leads to: n',5 k d = (17) The correspondence between measured and calculated data is good. Of course, statistical error values are worse than for case 1 computation, but they are still good (see figure 6).

10 Longwave radiation flux density [W/m²] Measurement New p. with n' MBE=1,98 W/m² MAE=13,57 W/m² RMSE=18,9 W/m² CC=, time [d] (= :) Figure 6: Atmospheric longwave radiation and statistical error values for new parameterisation with first cloud cover index n (case 2) Case 3: No cloud cover, but shortwave global radiation data available This case represents the worst initial data situation, because conclusions about sky properties, hence atmospheric longwave radiation must be made only by means of measured shortwave global radiation. Few authors have worked on this subject, a short overview is given e.g. by Kjaersgaard et al. [9]. An interesting approach has been proposed e.g. by Crawford and Duchon [3]. They propose a so-called cloud cover function depending on the relation of measured global incoming radiation and potential clear-sky (near-ground) radiation. Another procedure could be to find reliable correlations between the so-called clearness index k t (eq. 14) and the diffuse fraction k d (eq. 12). For creating k t one must first calculate the potential extraterrestrial solar radiation on the horizontal surface. This is easily done by the use of solar constant, transient distance Earth-sun, true local time and sun height. A popular model for k d by means of k t is proposed e.g. by Reindl, Beckman and Duffie [16]. One could then continue with the approach proposed in chapter (case 2 of initial data situation). However, the author of this paper proposes a direct correlation between the clearness index k t and a second cloud cover index n, which is usable as cloud cover in further computations. Again, the form of the interrelation between k t and n has been developed by the author and by means of the interrelation between original cloud cover n and clearness index. n' ' k t,5,85 k t = (18).73 The statistical error deviations are worse than for the other 2 cases of initial data situation which is not surprising -, but the correspondence between measured and correlated data is still satisfying (see figure 7).

11 Longwave radiation flux density [W/m²] Measurement New p. with n'' MBE=-,65 W/m² MAE=15,29 W/m² RMSE=21, W/m² CC=, time [d] (= :) Figure 7: Atmospheric longwave radiation and statistical error values for new parameterisation with second cloud cover index n (case 3) 4 Conclusion and Perspectives Within the paper, important contributions to the proper determination of atmospheric longwave radiation for HAM simulation programs, especially for the cloudy sky case, have been made. As measurements and needed values for analytical formulas are mostly not available, empirical approaches based on near-ground weather data (temperature, relative humidity, cloud cover) have been presented by many authors. The most important approaches have been presented and validated against measured data from Schleswig (Northern Germany), provided by Germany s National Meteorological Service. Within the calculation of atmospheric longwave radiation, two main cases must be distinguished: clear sky and all sky calculations (the latter involving clear and cloudy sky). Approaches for the calculation of atmospheric longwave radiation under clear skies have been presented by many authors with partially excellent results. In the validation with the aforementioned measured data, the approach of Brutsaert has performed best. It is recommendable also for another reason: While most approaches are pure statistical formulas, the Brutsaert-approach is based on physical considerations and presents the combination of a simplified radiation transfer equation with standard atmospheric conditions. However, the author of this paper has still recognised time-of-day depending deviations. The Brutsaertapproach has therefore been advanced by a time-of-day-depending term. The correspondence of the new parameterisation of Brutsaert s approach with the measured data is excellent. The number of publications regarding the determination of atmospheric longwave radiation for cloudy or all skies are much more rare than those for clear skies. In either case the all sky approaches depend directly on the clear sky approaches- one will always first determine (a theoretical value of) clear sky radiation and then add the cloud influence on the radiation.

12 For the determination of atmospheric longwave radiation under cloudy skies, the author has distinguished three initial data situations: 1. There is cloud cover data available, which represents the most advantageous situation. The three presented approaches have been computed and compared to the measured data. The approach of Konzelmann has been chosen due to its very good performance and again - due to the fact, that its form is based on physical considerations and not only on statistical analysis. However, as the proposed parameterisation affiliates to measured data from Greenland, a new parameterisation seemed convenient and has been undertaken by the author of this paper. The correspondence between the new parameterisation and the measured is very good. 2. If there is no cloud cover data available, it is possible to describe the (longwave-) radiative properties of the sky by means of shortwave radiation data. If shortwave global and shortwave diffuse radiation data is available, one is able to make quite reliable suggestions about the cloudiness of the atmosphere. The author has therefore introduced a new value called first cloud cover index n, which is based on the relation between shortwave diffuse and global radiation and which is usable in e.g. the Konzelmann-approach for cloudy skies. The computations with the new Konzelmann- approach and the newly introduced first cloud cover index n show good results concerning their correspondence to the measured data. 3. If there no cloud cover data and only shortwave global radiation data available, the author proposes the definition of a so-called second cloud cover index n. This second cloud cover index n depends on the clearness index, which is defined as relationship between measured global radiation and potential extraterrestrial radiation. As information about sky properties is still fewer than in case 2, the correspondence and reliability decreases in comparison with the case 1 or 2. However, the correspondence is still satisfying and presents a good possibility to determine the atmospheric longwave radiation under cloudy skies under the aforementioned difficult conditions. Table 3: Overview for the determination of atmospheric longwave radiation. Statistical error values for the different cases of clear/ cloudy sky and initial data situations: Mean Bias Error MBE, Mean Absolute Error MAE, Root Mean Square Error RMSE [W/m²], Correlation Coefficient CC [1] Case MBE MAE RMSE CC Clear sky: Brutsaert-approach -,59 8,3 12,24,966 Clear sky - Brutsaert-approach with new parameterisation -,3 7,3 11,1,971 All sky - Case 1: Cloud cover available, Konzelmann-approach -11,5 15,8 2,63,928 All sky - Case 1: Cloud cover available, Konzelmann-approach -,1 12,7 17,8,93 with new parameterisation All sky - case 2: No cloud cover, but shortwave global and diffuse +1,98 13,6 18,86,99 radiation available All sky - case 3: No cloud cover, but shortwave global radiation available -,65 15,3 2,95,885 One disadvantage of the new approaches for the cloudy sky (case 2 and 3 of initial data situation) is of course- its usage for daytime data sets only. The author therefore is working on the transition to night time data by simple averaging between the last and the first given daytime value. Of course, the correspondence and the reliability of the approaches will therewith decrease. However, there is no other way for the determination of atmospheric longwave radiation if there is no cloud cover data available. Altogether, the new approaches present a very good solution to close the gap of missing atmospheric longwave radiation data for HAM simulation programs.

13 References [1] Brutsaert W. 1975: On a derivable formula for long-wave radiation from clear skies. Water Resources Research Vol.11, pp [2] Coombes C.A. and Harrison A.W. 1986: Angular distribution of downward longwave radiance and their met. applications. Journal of Climate and Applied Meteorology Vol. 25, pp [3] Crawford T.M. and Duchon C.E. 1999: An improved parameterization for estimating effective atmospheric emissivity for use in calculating daytime downwelling long-wave radiation. Journal of Applied Meteorology Vol. 38, pp [4] Finkenstein C. and Häupl P. 27: Atmospheric longwave radiation being a climatic boundary condition in hygrothermal building part simulation. Proc. of 12 th Symposium for Building Physics Dresden. Institute of Building Climatology. TU Dresden. pp [5] Germany s National Meteorological Service (Deutscher Wetterdienst) 24: Test Reference Years for Germany. [6] Guidelines of German Engineers association (VDI- Richtlinie) 1994: Nr Environmental meteorology - Part 2: Interactions between atmosphere and surfaces. Calculation of short-wave and long-wave radiation. Beuth. 52 pp. [7] Idso S. B. 1981: A set of equations for full spectrum and 8 to 14 μm and 1.5 to 12.5 μm thermal radiation from cloudless skies. Water Resources Res. Vol. 17, pp [8] Iziomon M.G., Mayer H. and Matzarakis A. 23: Downward atmospheric longwave irradiance under clear and cloudy skies: Measurement and parameterization. Journal of Atmospheric and Solar-terrestrial Physics Vol. 65, pp [9] Kjaersgaard J.H. et al. 26 : Comparison of models for calculating daytime longwave irradiance using long term data set. Agriculture and Forest Met.. In press. [1] Konzelmann T. et al. 1994: Parameterisation of global and longwave incoming radiation for the Greenland ice sheet. Global Planetary Change Vol. 9, pp [11] Maykut G.A. and Church P.E. 1973: Radiation climate of Barrow, Alaska. Journal of Applied Meteorology Vol. 12, pp [12] Monteith J.L. and Unsworth M. 199: Principles of environmental physics. Second edition. Butterworth Heinemann. 291 pp. [13] Niemelä S., Räisänen P. and Savijärvi H. 21: Comparison of surface flux parameterizations Part 1: Longwave radiation. Atmospheric Res. Vol. 58, pp [14] Paltridge G.W. and Platt C.M.R : Radiative processes in meteorology and climatology. Elsevier. 318 pp. [15] Prata A. J. 1996: A new longwave formula estimating downward clear sky radiation at the surface. Quart. J. R. Met. Soc. Vol. 122, pp [16] Reindl D., Beckman W. and Duffie J. 199: Diffuse fraction correlations. Solar Energy Vol. 45, pp.1-7. [17] Swinbank W.C. 1963: Long-wave radiation from clear skies. Quarterly Journal of the Royal Meteorological Society Vol. 89, pp Acknowledgements This paper, being part of a PhD- thesis, has been generously supported by fellowships of the Free State of Saxony, the Federal Republic of Germany and the Technical University of Dresden. Thanks are also due to Germany s National Meteorological Service (Deutscher Wetterdienst) for the provision of the measured data.