Effect of remote clouds on surface UV irradiance

Clouds affect local surface UV irradiance, even if the horizontal distance from the radiation observation site amounts to several kilometers. In order to investigate this effect, which we call remote clouds effect, a 3-dimensional radiative transfer model is applied. Assuming the atmosphere is subdivided into a quadratic based sector and its surrounding, we quantify the influence of changing cloud coverage within this surrounding from 0% to 100% on surface UV irradiance at the sector center. To work out this remote clouds influence as a function of sector base size, we made some calculations for different sizes between 10 km × 10 km and 100 km × 100 km. It appears that in the case of small sectors (base size ≤20 km × 20 km) the remote clouds effect is highly variable: Depending on cloud structure, solar zenith angle and wavelength, the surface UV irradiance may be enhanced up to 15% as well as reduced by more than 50%. In contrast, for larger sectors it is always the case that enhancements become smaller by 5% if sector base size exceeds 60 km × 60 km. However, these values are upper estimates of the remote cloud effects and they are found only for special cloud structures. Since these structures might occur but cannot be regarded as typical, different satellite observed cloud formations (horizontal resolution about 1 km × 1 km) have also been investigated. For these more common cloud distributions we find remote cloud effects to be distinctly smaller than the corresponding upper estimates, e.g., for a sector with base size of 25 km × 25 km the surface UV irradiance error due to ignoring the actual remote clouds and replacing their influence with periodic horizontal boundary conditions is less than 3%, whereas the upper estimate of remote clouds effect would suggest an error close to 10%.

Abstract. Clouds aect local surface UV irradiance, even if the horizontal distance from the radiation observation site amounts to several kilometers. In order to investigate this eect, which we call remote clouds eect, a 3-dimensional radiative transfer model is applied. Assuming the atmosphere is subdivided into a quadratic based sector and its surrounding, we quantify the in¯uence of changing cloud coverage within this surrounding from 0% to 100% on surface UV irradiance at the sector center. To work out this remote clouds in¯uence as a function of sector base size, we made some calculations for dierent sizes between 10 km Â 10 km and 100 km Â 100 km. It appears that in the case of small sectors (base size 20 km Â 20 km) the remote clouds eect is highly variable: Depending on cloud structure, solar zenith angle and wavelength, the surface UV irradiance may be enhanced up to 15% as well as reduced by more than 50%. In contrast, for larger sectors it is always the case that enhancements become smaller by 5% if sector base size exceeds 60 km Â 60 km. However, these values are upper estimates of the remote cloud eects and they are found only for special cloud structures. Since these structures might occur but cannot be regarded as typical, dierent satellite observed cloud formations (horizontal resolution about 1 km Â 1 km) have also been investigated. For these more common cloud distributions we ®nd remote cloud eects to be distinctly smaller than the corresponding upper estimates, e.g., for a sector with base size of 25 km Â 25 km the surface UV irradiance error due to ignoring the actual remote clouds and replacing their in¯uence with periodic horizontal boundary conditions is less than 3%, whereas the upper estimate of remote clouds eect would suggest an error close to 10%.
Key words: Atmospheric composition and structure (transmission and scattering of radiation) ± Meteorology and atmospheric dynamics (radiative process)

Introduction
Clouds have considerable impact on the ultraviolet (UV) radiation reaching the ground. As is known from measurements, interactions between UV radiation and clouds may result in surface UV irradiances ranging from less than 5% and to more than 125% of the clear sky value (Estupinan et al., 1996;Mims and Frederick, 1994). Clouds are clearly 3-dimensional (3d) formations. Therefore, correct analysis of their in¯uence on surface UV irradiance requires 3d radiative transfer modeling in combination with a suitable cloud description, which may be derived e.g., from satellite data or large eddy simulations. In practice it is not possible to model the in¯uence of arbitrary large broken cloud ®elds, but it is possible to consider a certain fraction of the cloudy sky. Thus, the uncertainty caused by this inevitable limitation has to be quanti®ed for meaningful analyses of surface UV irradiance. Such a quanti®cation is useful not only for modeling purposes, but also for interpretation of ground-based UV measurements.
Although many papers have investigated the eects of 3d cloud structures on atmospheric radiative transfer (e.g., O'Hirok and Gautier, 1998a, b;Hignett and Taylor, 1996), the question still remains as to which part of a cloud ®eld is of signi®cance for surface UV irradiance. In most studies the in¯uence of speci®c cloud distributions on the radiation ®eld is investigated for a spatially limited atmospheric sector. The radiative interaction between this sector and the surrounding atmosphere is described by horizontal boundary conditions. Because it is impossible to specify the true horizontal boundary conditions (this would require an a priori knowledge of the radiative transfer within the whole atmosphere), they are frequently de®ned as specular or periodic. However, this de®nition implies an atmosphere of some regular structure, which generally is an unrealistic assumption for cloudy conditions (Zhu et al., 1992;Lee et al., 1994). Consequently, since the in¯uence of the real cloud ®eld outside the atmospheric sector, termed remote clouds, cannot be taken into account, but has to be replaced by horizontal boundary conditions, assumptions are introduced which could be perfectly wrong.
In order to investigate the impact of this potential source of error on surface UV irradiance, in the current study the eect of remote clouds is systematically analyzed and quanti®ed by means of a 3d radiative transfer model (Spherical Harmonics Discrete Ordinate Method or SHDOM, Evans, 1998). After describing the modeling procedure in Sect. 2, we present in Sect. 3 the remote clouds eect (RCE) on surface UV irradiance for dierent cloud constellations. Since the RCE is the superposition of dierent mechanisms that enhance as well as reduce surface UV irradiance, in a ®rst step investigations focus on remote cloud distributions which maximize the eects of these mechanisms. Because calculations are made for atmospheric sectors of dierent size, the RCE dependence on the horizontal distance between observer and remote clouds is obtained. In a second step cloud ®elds as observed with the AVHRR instrument onboard the NOAA satellites (horizontal resolution about 1 km Â 1 km) are studied. For each scene the error in surface UV irradiance due to neglecting the in¯uence of the actual remote clouds is determined. Finally, in Sect. 4, we discuss the possible extrapolation of the results presented to conditions not explicitly considered in our model calculations.
2 Modeling surface UV irradiance

Radiative transfer model
In the radiative transfer model SHDOM the optical properties of the atmosphere and the surface re¯ection are speci®ed at the points of a spatial grid and of a grid covering the ground, respectively. Radiances are calculated at the points of an additional spatial grid, which is not necessarily identical with the property grid, by integrating the equation of radiative transfer along discrete ordinates. This is done by assuming linear variation of the extinction coecient and the product of extinction coecient and source function inside each grid cell. The UV radiation ®eld is determined, taking into account absorption by ozone and aerosol particles, as well as scattering by air molecules, cloud and aerosol particles.
In order to check the accuracy of SHDOM, in a ®rst step comparisons with a matrix operator model (horizontally homogeneous atmosphere) (MeerkoÈ tter et al., 1997) and a 3d Monte Carlo model (broken clouds) (B. Mayer, 1999, private communication) were performed. The dierences found for the calculated surface irradiances were around 3% for wavelength 300 nm and around 1% for wavelength 330 nm. In a second step the results of SHDOM were compared with measurements taken under clear sky conditions without snow coverage. The model results deviate by less than 6% (10%) from the measurements for wavelengths greater (smaller) than 330 nm (DeguÈ nther et al., 1998) and the spectral dependence of the observed deviation is very similar to that found for 1d models (e.g., Mayer et al., 1997). Although the comparison between measured and calculated surface UV irradiances so far is encouraging, the general evaluation of SHDOM is still an outstanding issue.

Model input
The optical properties of the cloud-free atmosphere are derived from vertical pro®les of ozone density and meteorological data as prescribed by a midlatitude standard atmosphere (McClatchey et al., 1972). The ozone pro®le is scaled to give a total of 300 DU. The aerosol optical depth is 0.2, 0.33 and 0.35 at 550 nm, 330 nm and 300 nm wavelength, respectively, and the underlying aerosol pro®le corresponds to the continental model (CON-I) after WMO (1986). Cloud microphysics is described by lognormal droplet size distributions related to either stratocumulus or cumulus congestus type (Table 1), and it is assumed to be constant within the cloud. Depending on the respective problem, the atmospheric optical properties are speci®ed in 21 to 24 dierent vertical levels with a horizontal resolution of 200 m to 250 m. Finally, surface optical properties are described by a Lambertian re¯ector with albedo 0.03. In the UV spectral range this value is a reasonable mean for snow-free surfaces excluding deserts and salt¯ats (Eck et al., 1987;Blumthaler and Ambach, 1988).

Results
The RCE on surface UV irradiance is essentially a superposition of the three mechanisms illustrated in Fig. 1, all of them depending in a dierent manner on cloud structure, wavelength and solar zenith angle (SZA). The ®rst mechanism, the albedo eect, leads to an enhancement of surface UV irradiance if the surface is not snow covered. Photons which would have hit the surface under clear sky conditions are re¯ected by clouds and afterwards backscattered by the atmosphere above the clouds. Thus, instead of being absorbed at the surface, these photons contribute to a diuse skylight enhancement. The second mechanism, termed scattering eect, enhances the observed diuse skylight as well, since scattering by clouds partly changes photon propagation directions towards the observer. However, cloud scattering may also result in de¯ection of photons, which would have reached the radiation observation site at the ground in the cloud-free case. This third mechanism attenuates surface UV irradiance and it is called the extinction eect. In the following section two special con®gurations of remote clouds are investigated, allowing us to assess the impact of maximum attenuation and intensi®cation eects on surface UV irradiance. Using two wavelengths and two SZA we show the relative signi®cance of these eects varies with the distance between observer and remote clouds. In the second section we present the RCE as calculated for three dierent satellite observed, i.e., real, cloud scenes typical for scattered and broken clouds as well as for complete cloud coverage.

Maximum surface UV irradiance attenuation and intensi®cation by remote clouds
To obtain maximum eects of the three described surface UV irradiance aecting mechanisms in dependence on remote clouds distance from the observer, ®rstly the atmosphere is assumed to be subdivided into a sector with base size S km Â S km and its surrounding (Fig. 2). Secondly, sectors with dierent base sizes containing either the given cloud structures or being cloud-free are de®ned. Thirdly, for each constellation two 3d radiative transfer simulations are carried out. In the ®rst one there are no clouds outside the sector and as a result the eect of each single mechanism illustrated in Fig. 1 is zero. In the second simulation the atmospheric sector is assumed to be surrounded by a complete cloud cover. This ensures maximum attenuation and intensi-®cation of surface UV irradiance by the extinction eect and by the albedo plus scattering eect, respectively. Finally, ratios relating surface UV irradiances calculated for these two extreme conditions are determined. The ratio obtained for sector center X (Fig. 2) is taken as a measure of the RCE which results from superposing maximum eects of the attenuation and intensi®cation mechanisms.
In Fig. 3a±f this ratio is displayed as function of S and sector base size for the two SZA 30 and 60 and the two wavelengths 300 nm and 330 nm. The product 0X56 Á S can be interpreted as the mean distance between an observer located at sector center X and the nearest remote clouds beyond the horizontal sector boundaries (Fig. 2). The two selected wavelengths represent radiation strongly absorbed by ozone as well as radiation not much aected by ozone absorption. Calculations are performed for cloud-free and homogeneously cloud-®lled sectors. Clouds in the sector as well as the remote clouds are located within the same layer CL (Fig. 2). Figure. 3a±f shows results for CL = 1±2 km, CL = 4±5 km and CL = 1±5 km, respectively. The microphysics of clouds with 1km vertical extension is of stratocumulus type, whereas thick clouds between 1 km and 5 km height are assumed to be of cumulus congestus type (Table 1). All clouds have a uniform volume extinction coecient of 20 km À1 (at 550 nm). Fig. 1a±c. In¯uence of remote clouds on surface UV irradiance. The albedo and scattering eect enhance surface UV irradiance, whereas the extinction eect leads to a decrease. In cases a and b scattering of photons by remote clouds increase the diuse skylight at the observation site, while in case c remote clouds redirect photons that otherwise would have reached the observer. The white r in the dark circle symbolizes cloud scattering, while the black r indicates atmospheric backscattering Fig. 2. Illustration of the atmospheric subdivision in a sector and its surrounding. The quadratic sector has a base size of S km Â S km and is embedded in a horizontally in®nite atmosphere. Base and top of clouds in the sector as well as in the surrounding atmosphere are identical. The vertical cloud extension is denoted by CL. X marks sector center. TOA is the abbreviation for top-of-atmosphere CL = 1±2 km (Fig. 3a, b). Remote clouds enhance surface UV irradiance for all sector sizes in the range from S 10 to S 100 km. Thus, the scattering and in particular the albedo eect outweigh the extinction eect. The RCE depends more strongly on wavelength than on SZA. This is for two reasons: ®rstly, the atmospheric absorption above the clouds is stronger for the wavelength 300 nm. Therefore, considerably less radiation re¯ected by the clouds is backscattered. Secondly, the spectral atmospheric transmittance is smaller for 300 nm not only in the stratospheric ozone layer, but also in the troposphere. Consequently, less of the radiation scattered by remote clouds reaches the sector center later and, in addition, the radiation extinction by remote clouds is of minor importance. Although the RCE dependence on S is very similar for SZA=30 and SZA=60 , dierences are found for small sector sizes (S 16 km). The reason is that with a low Sun angle more radiation incidents with larger zenith angles and occur e.g., for S 10 km the surrounding remote clouds shade radiation with zenith angles larger than about 70 . Therefore, extinction eectively counteracts the scattering and albedo eect. Furthermore, radiation laterally penetrating into the sector below layer CL is more eciently`trapped' under clouds, and hence has a stronger impact on surface UV irradiance. Thus, extinction of this radiation by remote clouds is especially eective if the Sun is low and the sector small and, moreover; Calculations are performed for homogeneously cloud-®lled as well as for cloud-free sectors taking into account two SZA (30 , 60 ) and two wavelengths (300 nm, 330 nm). Clouds in and outside the sector are embedded within layer CL (Fig. 2). Results are presented for a, b CL = 1±2 km, c, d CL = 4±5 km and e, f CL=1±5 km. The mean distance between the observer at sector center and the nearest remote clouds is 0X56 Á S. The inset in Fig. 3d shows the ratio H RÀCloud aH RÀClear for S ! 40 km on a zoomed scale CL = 4±5 km (Fig. 3c, d). In the case of small sectors and low Sun remote clouds decrease surface UV irradiance. For S 10 km (S 16 km) about 65% (50%) of the sky as observed from the sector center is covered with remote clouds. Thus, under low Sun conditions not only the direct, but also a signi®cant part of the diuse radiation is shaded leading to a clearly dominating extinction eect. Furthermore, due to thè trapping eect' described, extinction is dominant for small clouded sectors even in combination with a high Sun angle (SZA=30 ). The predominance of the extinction eect is further supported by a comparatively small albedo eect. Because the atmospheric layer above the clouds has a smaller optical depth than e.g., in the case CL = 1±2 km, less cloud re¯ected radiation is backscattered. This albedo eect reduction becomes particularly obvious where the extinction eect is negligible, i.e., for large sectors. In that case surface UV irradiance enhancements are distinctly smaller than for clouds embedded between 1 km and 2 km. Since the extinction eect is especially marked in the range of small S, the RCE depends more strongly on SZA than on wavelength. However, for larger S where the albedo eect becomes dominant, the RCE varies with wavelength but is nearly independent of SZA. Finally, the extinction as well as the albedo eect is more pronounced for wavelength 330 nm when compared to 300 nm. Therefore, in the case of low Sun with prevailing extinction for small S and dominating albedo eect for larger S, the two dashed curves representing the RCE dependence on S for SZA=60 and wavelengths 300 nm and 330 nm must have a cross-over point close to H RÀCloud aH RÀClear =1. CL = 1±5 km (Fig. 3e, f). With a vertical extension of 4 km the clouds have four times the geometrical depth of the clouds in the cases CL = 1±2 km and CL = 4± 5 km. Hence, especially for small sectors, illumination of the clouds vertical interfaces plays an important role. Regarding cloud-free sectors, RCE depends in a very similar manner on S as found for CL = 4±5 km for both wavelengths and SZA. Because of the greater geometrical depth of remote clouds backscattering at their vertical interfaces is enhanced and in particular for small sectors the ratio H RÀCloud aH RÀClear is to some degree higher. Furthermore, a greater cloud optical depth increases their re¯ectivity resulting in a stronger albedo eect. For small clouded sectors (S=10 km) the horizontal distance between sector center X and its edge is comparable to cloud geometrical depth. Therefore, the contribution of radiation entering the sector cloud through its vertical interfaces is important and the extinction of this radiation by remote clouds leads to a distinct decrease of surface UV irradiance. For wavelength 300 nm as well as for 330 nm in combination with low Sun this radiation attenuation is the dominating eect. By contrast, when SZA=30 and wavelength 330 nm the ratio H RÀCloud aH RÀClear is greater than 1, which means that the sum of scattering and albedo eect still outweighs extinction. Increasing S to more than about 20±25 km results in a predominance of the albedo eect causing a ratio H RÀCloud aH RÀClear greater than 1 for all SZA-wavelength combinations and a stronger dependence of RCE. Table 2 gives an idea which section of a cloudy sky has to be taken into account in order to avoid RCE exceeding a given limit. It illustrates, that for higher clouds (CL = 4±5 km) the RCE decreases quickly with increasing S. A sector size of 30 km Â 30 km suces to keep maximum in¯uence by remote clouds on surface UV irradiance clearly below 5%. With lower stratus (CL = 1±2 km) RCE is considerably lower for small sectors, but it decreases only slowly with sector enlargement. Consequently, in order to keep the maximum RCE smaller than 5%, the cloud distribution in a sector of 2500 km 2 has to be taken into account. Finally, for CL = 1±5 km the maximum eects for small sectors are similar to those found for CL = 4±5 km, whereas for larger S they become comparable to the eects found for stratus clouds between 1 km and 2 km above ground. This is explained by the fact, that for small sectors the extinction of diuse and eventually direct radiation is very pronounced with high cloud tops and therefore dominates RCE. For larger sectors the magnitude of the albedo eect is decisive. On the one hand, when compared to CL = 1±2 km, the larger cloud optical depth for CL = 1±5 km enhances cloud re¯ectivity, on the other hand the smaller optical depth of the atmosphere above the clouds leads to less backscattering of cloud re¯ected radiation. Thus, for CL = 1±2 km and for CL = 1±5 km the albedo eect is similar resulting in similar RCE for large sectors.

Remote clouds eect in satellite observed cloud scenes
As already mentioned it is impossible to investigate the in¯uence of arbitrary large 3d structured cloud ®elds on atmospheric radiation. Only that part within a spatially limited atmospheric sector can be taken into account and RCE has to be replaced by highly uncertain horizontal boundary conditions. In order to assess how this uncertainty aects surface UV irradiance for typical cloud structures, we have looked at sectors of 25 km Â 25 km. This base size is large enough to ensure RCE below 10% (Table 2) and simultaneously it is small enough to keep the required CPU-time for 3d radiative transfer calculations with reasonable spatial resolution in the order of hours. The distribution of cloud optical depth within the sector is derived from NOAA/AVHRR satellite data using the APOLLO algorithm (Kriebel et al., 1989). The cloud base is assumed to be 1 km above the ground, whereas cloud top height depends on cloud optical depth as illustrated in Fig. 4. The investigated cloud scenes were observed on July 01, 1996, at about 13 UTC over southern Germany. The corresponding SZA and solar azimuth angle is 31.3 and 211.0 (southwest), respectively. As in the foregoing section two 3d radiative transfer model simulations are performed for each sector. In the ®rst simulation the horizontal boundary conditions are periodic, i.e., a photon leaving the sector through one of its vertical bounding planes is assumed to re-enter through the opposite plane. Thus, the actual RCE is neglected and the radiative transfer is calculated as if the whole atmosphere consisted of equal sized sectors each containing identical the same cloud distribution as its neighbours. By contrast, in the second simulation the real (satellite observed) cloud ®eld that surrounds the investigated atmospheric sector is considered. From both simulations we obtain an average of surface UV irradiance over an area of 4 km Â 4 km located around the sector center. To quantify RCE the ratio calculated from these two averages is considered. Figure 5a±c shows three distributions of cloud optical depth. The sectors represent situations with scattered clouds (Fig. 5a), broken clouds (Fig. 5b) and complete cloud coverage (Fig. 5c). For Fig. 5a±c the RCE is 1.2%, 2.5% and 2.2%, respectively. These values are calculated for the wavelength 330 nm, but the numbers are very similar for the wavelength 300 nm. The smaller eect for Fig. 5a can be explained by the fact that direct radiation, which of course is not aected by remote clouds, signi®cantly contributes to surface UV irradiance. Looking only at the diuse component, Fig. 4. Correlation between optical and geometrical cloud depth. In the case of satellite observations the cloud base is assumed to be uniformly 1 km above ground, whereas the top heights (given by the italic numbers) depends on the optical depth class to which the cloud belongs. The vertical cloud extensions are chosen to ensure a cloud extinction coecient of 20 km À1 (at 550 nm) for the mean of each optical depth class a c b Fig. 5a±c. Cloud optical depth distributions obtained from NOAA/ AVHRR data using the APOLLO algorithm (Kriebel et al., 1989). Due to remapping the pixel size is 500 m Â 500 m. All three scenes a, b and c are observed on July 01, 1997, over southern Germany at about 13 UTC. The Sun is located in the southwest, i.e., the lower left image corner. The square within each scene marks the atmospheric sector having a horizontal extension of 25 km Â 25 km, whereas the clouds outside are the remote clouds remote clouds induced eects are comparable to those in Fig. 5b and c. From these comparisons it can be inferred, that replacing the actual remote clouds by periodic horizontal boundary conditions results in surface UV irradiance errors no larger than about 2.5%. This is valid for scattered and broken clouds as well as for complete cloud coverage. Thus, for the selected satellite observed scenes the RCE is considerably smaller than the corresponding value which is obtained assuming the eects of attenuation and intensi®cation mechanisms to be maximum. Nevertheless, although for sectors with base size of 25 km Â 25 km cloud distributions as discussed in the preceding section are seldom seen, they might occur. Consequently, the occurrence of RCE distinctly larger than 2.5% cannot be excluded.

Summary and concluding remarks
The in¯uence of remote clouds on surface UV irradiance has been investigated using a 3d radiative transfer model. Firstly, special remote cloud con®gurations are taken into account, ensuring maximum eects of the surface UV irradiance attenuation and intensi®cation mechanisms. The RCE is obtained as a function of atmospheric sector base size for the two dierent SZA 30 and 60 , for the two dierent wavelengths 300 nm and 330 nm and for dierent cloud structures within the sector. Secondly the RCE is determined for real cloud scenes as observed with the AVHRR instrument onboard the NOAA satellites.
For small sectors (S 15±20 km) the RCE on surface UV irradiance is very important and may be highly variable. Depending on wavelength, SZA and vertical cloud extension, surface UV irradiance may be enhanced up to 15% as well as reduced by more than 50%. Therefore, for small sectors the maximum errors induced by neglecting RCE and the errors due to uncertainties of parameters describing the atmospheric optical properties (Schwander et al., 1997) are comparable. In larger sectors remote clouds have less in¯uence but, in all cases, they do enhance surface UV irradiance. The in¯uence is smallest for remote clouds with low or moderate optical depths and tops at high altitudes. In all cases the RCE is below 5% for sectors with base of 60 km Â 60 km or larger.
Since cloud formations leading to maximum eects of the three described surface UV irradiance aecting mechanisms are not common, we also investigated satellite observed cloud scenes. These scenes represent broken and scattered clouds as well as complete cloud coverage within a sector of 25 km Â 25 km. The 3d model simulations show that replacing the actual remote clouds by periodic horizontal boundary conditions causes surface UV irradiance errors not greater than about 2±3%. Thus, for atmospheric sectors with base size 25 km Â 25 km the RCE is in general distinctly less than the corresponding potential maximum, and consequently this sector size normally should suce to reliably analyze ground results with satisfactory accuracy. Nevertheless, although an atmospheric sector of 25 km Â 25 km does not guarantee negligible RCE, in each case the structure of the respective cloud ®eld has to be carefully analyzed.
The results presented are valid for a plane surface with low albedo, (i.e., no snow coverage), for an ozone column of 300 DU and for one speci®c aerosol optical depth. Provided the UV radiation observation side is not shaded due to orography and no great altitude dierences exist, the assumption of a plane surface is a good approximation. Since ground re¯ected photons do not contribute signi®cantly to the observed UV irradiance in case of low surface albedo, eventually surface slopes and peaks are of minor importance. In contrast, a snowcovered surface (albedo ! 0.6±0.8) leads to very dierent results, since the albedo eect is completely dierent and multiple re¯ection between surface and atmosphere/ clouds may become important. Finally, enhancing the tropospheric ozone and aerosol content reduces the RCE. This is because the tropospheric extinction is increased and less of the radiation scattered by remote clouds reaches the observer afterwards.
Despite the unavoidable restriction to a limited number of SZA, wavelengths and atmospheric/surface conditions investigated, the results presented can be regarded as representative for a broad variety of snowfree conditions. They may be helpful to other experimentators in making meaningful data analysis and interpretation. Furthermore, the errors of 3d radiative transfer calculations induced by inadequate description of RCE can be estimated.