Retrieving cloud top structure from infrared satellite data

Transcription

1 Retrieving cloud top structure from infrared satellite data Richard M van Hees, and Jos Lelieveld Institute for Marine and Atmospheric Research Utrecht, Utrecht, Netherlands Abstract A new retrieval method to detect steep temperature gradients between the convective overshoots of cumulonimbus clouds and the surrounding cirrus has been applied to determine gradients and their orientation in the image plane of infrared data of the advanced very high resolution radiometer (AVHRR) These orientations are used to derive cloud elevations which are brightened by the Sun or are in shadow, which strongly affects the visible signal The impact of temperature gradients on the visible radiances is illustrated by two examples that indicate deep convective overshoots Both examples show that the illuminated side of the overshoots can exceed the cloud top reflectivity by %, while the shadows account for % of the cloud top reflectance The shadows usually extend several pixels beyond the base of the overshoots Here we show that statistical analyses of cloud optical depth are affected by the cloud top structure, based on month of high-resolution AVHRR satellite data The contribution of shadow side pixels with steep temperature gradients ( 6 K) can exceed 3% for small optical depths ( 3) The contribution of illuminated sides of cloud top structures and cloud sides with steep temperature gradients can exceed 7% for large optical depths ( 32) Introduction In a previous paper [van Hees et al, 999], we have introduced a new method to identify active convective cloud regions in infrared satellite data from the advanced very high resolution radiometer (AVHRR) This edge method identifies active convective regions by the presence of steep temperature gradients between the deep convective overshoots of cumulonimbus clouds and the surrounding optically thick cirrus The edge method assumes a correlation between cloud top structure and steep temperature gradients for optically thick clouds Monte Carlo simulations have shown that cloud sides can enhance the amount of incident solar radiation intercepted by the cloud, which can also occur by structured cloud tops [Loeb et al, 997] For example, a convective overshoot can obscure the incoming sunlight at low solar elevation angle, resulting in a shadow on the surrounding anvil As a result, cloud top structure may bias the retrieved optical depth from visible radiances In this paper, we show that gradients in AVHRR infrared data, depending on size and orientation, are a good predictor for observations with spurious visible radiances These observations may be excluded or handled with special care to improve the performance of plane-parallel radiative transfer models and models based in the horizontal spatial coherence of a cloudy region, such as the spatial coherence method [Coakley, 987] In section 2, we present two images of regions with deep Now at Space Research Organization Netherlands, Utrecht, Netherlands convective overshoots illustrating the effect of cloud top elevation on visible radiances AVHRR data collected during the Central Equatorial Pacific Experiment (CEPEX) [Ramanathan et al, 993] is used to show the bias in cloud optical depth from reflection and shadowing (section 3) In section 4, we show that the size and orientation of the Sobel operator, applied to AVHRR infrared data, shows a good correlation with spurious visible radiances A discussion of the implications of this work is presented in section 2 Examples of Cloud Top Elevation We have selected two events to illustrate the enhanced reflection from the sunlit side of a deep convective overshoot surrounded by an optically thick cirrus anvil The first was observed by NOAA 2 on March, 993, and the second was observed by NOAA on March, 993, both over the central Pacific Ocean The average satellite zenith angles in both examples are small, only 6, and the resolution in both images is nearly km Figure a shows a 3 3 pixel brightness temperature image derived from NOAA 2 AVHRR channel 4 data Figure a shows an almost elliptical cold area where the brightness temperature, derived from the infrared channel 4 (BT4), is below 8 K, while BT4 of the surrounding anvil is below 2 K The temperature difference of 2 K implies a cloud top difference between the overshoot and the anvil of nearly 3 km, assuming a lapse rate of 7 K km Note that the convective overshoot is not likely to be in thermodynamic equi-

2 2 HEES AND LELIEVELD a) BT4 b) c) Sobel d) Angle Figure Convective cloud scene of a region represented by 3 3 pixels derived from NOAA 2 AVHRR km radiometric data Figure a shows the brightness temperature (channel 4) Six levels of grey scale are used to indicate 8, 9, 9, 2, 2, and 2 K (from dark to almost white) Figure b shows the reflectances (channel ) Seven levels of grey scale are used to indicate 2, 4,, 6, 7, 9, and (from dark to almost white) Figure c shows the derived Sobel values Six levels of grey scale are used to indicate,, 3, 4, 6, and 7 K (from dark to almost white) Figure d shows the derived gradient direction Four levels of grey scale are used to indicate shadow side, left side, right side, and sunlit side (from dark to almost white, respectively) librium and appears to be colder due to non adiabatic expansion The convective overshoots reported in the literature are usually smaller; Shenk [974] studied 23 convective overshoots all with maximum heights 2 km Figure b shows the visible data as reflectances, ie, reflectivity divided by the cosine of the solar zenith angle The solar zenith angle in this scene is 69 with the Sun positioned to the right and slightly to the bottom of the picture The average relative azimuth angle is about 9, where the relative azimuth angle ψ is defined as in case of forward reflection and 8 in case of backward reflection Figure 2 shows that the maximum reflectance occurs at the illuminated side of the overshoot (sunlit side) The minimum reflectance occurs behind the overshoot (shadow side) The shadow extends about pixels beyond the base of the overshoot, where the reflectance is nearly equal to the reflectance on the right side of the overshoot The size of the shadow and the illumination of the sunlit side can be illustrated by a very simple model, where we assume Lambertian reflectance, absence of scattering, and an elevated cloud top: h c x h 2 cos π x w where h is the maximum height of the overshoot, w is the width, and x is the distance to the center of the overshoot Figure 3 shows the theoretical reflectance for an overshoot with h 3 km and w km The reflectance increases at the base of the overshoot and decreases to zero behind the overshoot because we neglect scattering and transmission In this case, the shadow extends only 2 pixels beyond the base of the overshoot, but it is clear from Figure 2 that the real overshoot is much more irregular Figure 4 shows two deep convective overshoots with different strengths or in a different stage of their evolution The largest cloud top elevation can be identified just at the right

3 CLOUD TOP STRUCTURE 3 a) BT4 b) c) Sobel d) Angle Figure 4 Convective cloud scene of a region represented by 3 3 pixels derived from NOAA AVHRR km radiometric data Figure 4a shows the brightness temperature (channel 4) Six levels of grey scale are used to indicate 9, 2, 2, 2, 22, and 23 K (from dark to almost white) Figure 4b shows the reflectances (channel ) Six levels of grey scale are used to indicate 4,, 6, 7, 9, and (from dark to almost white) Figure 4c shows the derived Sobel values Six levels of grey scale are used to indicate,, 3, 4, 6, and 7 K (from dark to almost white) Figure 4d shows the derived gradient direction Four levels of grey scale are used to indicate shadow side, left side, right side, and sunlit side (from dark to almost white, respectively) of the center of Figure 4a, and a small elevation can be found about 7 pixels to the left Figure 4b shows the reflectances The average solar zenith angle in this example is 2 The sunlit sides of the overshoots are located toward the right and top of the images because the average relative azimuth angle is 3 Note that the illuminated sides of both overshoots are brighter than the average found in the area surrounding them The shadows of both overshoots are also clearly visible The visible and infrared data presented in both examples yield a coherent picture of a deep convective overshoot penetrating an optically thick cirrus cloud We assume that the gradients in the AVHRR BT4 data are caused by differences in cloud top height This is supported by the observed enhancement of the visible radiances on the sunlit side of the cloud top structure and the shadow on the opposite side and cirrus anvil One might wonder if the convective overshoots can affect cloud statistics because the area coverage by optically thick cirrus anvils is several magnitudes larger than the area coverage by convective overshoots However, the visible radiances are also affected by cloud sides 3 Cloud Optical Depth Derived From Visible Radiances Loeb et al [997] concluded from Monte Carlo simulations involving three-dimensional cloud fields that cloud sides enhance the amount of incident solar radiation intercepted by the cloud, allowing more radiation to be scattered upward in the nadir direction Structured cloud tops change the slope of illuminated cloud top surfaces, such that the nadir reflectance at low solar elevations increases with the slope of the illuminated surface The examples presented in section 2 have shown that the enhancement can easily

4 ! $ " # " 4 HEES AND LELIEVELD Position (pixels) Figure 2 Horizontal cross section through the center of the convective overshoot shown in Figure after the image is rotated by the average relative azimuth angle The solid line shows the reflectance, and the dashed line shows BT Position (pixels) Figure 3 Theoretical reflectance as a function of cloud top elevation, satellite zenith angle (66 ), and solar zenith angle (689 ) The reflectance (solid line) is calculated for an overshoot (dotted line) of 3 km and a diameter of km (see text) be detected from high-resolution AVHRR data They also show that structured cloud tops may shade other parts of the cloud, which appear to be darker Consequently, cloud optical depth retrieved using radiative transfer theory without prior knowledge of a structured cloud top will systematically be overestimated for sunlit sides and underestimated for cloud sides in the shade Larger solar zenith angles will increase the errors made by enlarging the shadow and increasing the relative amount of intercepted solar radiation However, the resolution of the AVHRR data decreases as the satellite zenith angle increases At large satellite zenith angles the shadows and the sunlit sides may become comparable to the pixel resolution, which on average, will de " τ Figure Frequency distribution of cloud optical depth as a function of satellite zenith angle The distribution is normalized with the frequency distribution of cloud optical depth shown in Figure 6 Six levels of grey scale are used to indicate various percentiles of the distribution: %,, 2,, 7, and 9 (from dark grey to almost white, respectively) crease the discrepancy with plane-parallel calculations Furthermore, the sunlit sides of clouds and structured cloud tops may be obscured in the forward scattering direction The possible impact of structured cloud tops on the cloud optical depth derived from visible radiances is illustrated by a comparison with cloud optical depths derived from infrared radiances, which are less sensitive to cloud top structures The statistics presented in this section are derived from the NOAA data set collected during CEPEX, comprising nearly month of km nadir AVHRR data from March 7, 993 to April 6, 993 Included are 47 daytime over passes, covering an area between 4 E, 2 S and 4 W, N We have omitted pixels with Sun zenith angles % 87 and BT4 % 287 K to exclude cloud-free pixels and to reduce computing time The visible radiances are converted to cloud optical depth using the cirrostratus model proposed by Minnis et al [993] Cirrostratus clouds are modeled as homogeneous ice clouds with randomly oriented hexagonal ice crystals having equivalent length-to-width ratios (LD) of 8 µm4 µm The parameterization accounts for ozone absorption, Rayleigh scattering, and open-sea surface albedo (including sea glint) Figure shows the normalized frequency distribution of cloud optical depth as a function of the satellite zenith angle θ The satellite zenith angle is defined to be negative for backscattered radiation (& ψ&'% 9 ) and positive for forward scattered radiation (& ψ&( 9 ) The frequency distribution is normalized with the number of occurrences of cloud optical depth as shown in Figure 6 The frequency distribution is not homogeneous; almost all pixels with τ % 2 are detected

5 * CLOUD TOP STRUCTURE Frequency τ) Figure 6 Frequency distribution of cloud optical depth derived from Central Equatorial Pacific Experiment (CEPEX) NOAA AVHRR channel data, using a radiative transfer parameterization proposed by Minnis et al [993] Note that the frequency at τ 64 is equal to the number of pixels with τ 64 with θ 2 The pixels with τ % and τ 3 have a clear tendency to small satellite zenith angles, and the pixels with τ have a tendency to toward large positive satellite zenith angles However, before we can draw any conclusions from these observations, one should realize that the derived optical depth is very sensitive to the cloud particle size and shape Therefore we will compare the cloud optical depth derived from visible radiances with AVHRR infrared data It is impossible to derive cloud optical depth from infrared radiances because the results are sensitive to cloud top height, which is unknown However, the performance of the used radiative transfer parameterization can be verified, at least qualitatively, by a comparison of the theoretical BT4 as a function of θ and BT4 for an interval of cloud optical depth The theoretical relation between BT4 and satellite zenith angle is calculated with the radiative transfer model called Streamer [Key and Schweiger, 998] Also, for this model we have assumed single-layered homogeneous ice clouds with cloud top heights between 2 and 7 km However, the effective particle radius r e and ice water content (IWC) are a function of optical depth, as proposed by McFarquhar and Heymsfield [997] (Table ) The atmospheric profiles used by the Discrete Ordinates Radiative Transfer (DISORT) model are derived from a number of (pressure, temperature, humidity, and ozone) soundings launched from the RV Vickers during CEPEX, combined with a maritime aerosol optical model with background aerosol concentrations ( km visibility) Figure 7 shows the normalized frequency distribution of BT4 as a function of satellite zenith angle for six intervals of cloud optical depths The frequency distribution is normalized with the number of pixels found within a satellite zenith Table Streamer Cloud Parameters τ IWC, gm 3 r e µm Figure a(2, ) a(, 7) and b(2, ) b(, 7) and c(2, 4) c(4, 6) and d(2, 4) 68 d() 6 8 d(6) and e(2, 4) 32 e(7) and f(2, 4, 7) Cloud parameters used by Streamer to calculate BT4 for a given optical depth Listed are ice water content (IWC), effective particle radius r e, and the plot in Figure 7 in which these cloud parameters are used The numbers after the plot number are (in parentheses) the cloud top heights in kilometers angle interval of Most pixels are concentrated in a band with a maximum BT4 around nadir and decreasing BT4 values for larger satellite zenith angles This band moves to lower BT4 values for higher cloud optical depths, except for pixels with τ % 32 The shape of this band is in reasonable agreement with the theoretical relation between BT4 and satellite zenith angle However, pixels with cloud optical depth between 4 and 32 and large positive satellite zenith angles have a narrower distribution and are, on average, colder than pixels with the same negative satellite zenith angle The broadening of the BT4 distribution is due to relatively warm illuminated cloud sides, where the enhanced reflectance results in the overestimation of visible optical depth τ VIS, as will be shown in section 4 4 Derivation of Cloud Top Geometry The statistics presented in section 3 indicate that cloud optical depth is affected by cloud top structure and cloud sides However, we can not differentiate between the impact of cloud top structures and cloud microphysics on the derived cloud optical depth In this section, we introduce the Sobel edge enhancement operator [Davis, 97], hereafter Sobel operator, to detect cloud top structure in AVHRR infrared imagery data The reflectances of the detected elevations will be assigned to four classes, depending on the orientation of the elevation with respect to the Sun: sunlit side, right side, left side, and shadow side First, we illustrate the use of the Sobel operator using the examples shown in section 2 Subsequently, statistics on the reflectance of the four different classes of elevations as a function of the Sobel operator are used to answer most of the questions raised in section 3

6 6 HEES AND LELIEVELD 6 2 < τ + < < + τ < , , < τ + < < + τ < , , < τ + < < τ < , , Figure 7 The normalized frequency distribution of BT4 as a function of satellite zenith angle for six intervals of cloud optical depth One month of AVHRR data from the NOAA satellite collected during CEPEX is used as input Six levels of grey scale are used to indicate various percentiles of the distribution: %,, 2,, 7, and 9 (from dark grey to almost white, respectively)

7 I H " CLOUD TOP STRUCTURE 7 The Sobel operator is applied on a 3 3 region: A A A 2 A 7 P i j A 3 A 6 A A 4 2 G > 3 D K The Sobel operator is defined as G i j23& G x &4& G y & G x A 2 2A 3 A 4 6 A 2A 7 A 6 G y A 2A A 2 6 A 6 2A A 4 7 where G x and G y represent estimates of the derivatives in the x and y direction, respectively The direction of the gradient is defined by 8 9 : G arctan ; y if G y φ G i j2 arctan ; G x < G y G x < otherwise Hereafter φ G is adjusted with the relative azimuth angle ψ to represent the direction of the gradient relative to the direction of the incoming sunlight Figure c shows the Sobel values calculated for for the first AVHRR image presented in section 2 Figure c shows that pixels with Sobel values % 3 K can be used to outline the convective overshoot The direction of the BT4 gradients are shown in four intervals: shadow side (φ G = 3 or φ G % 3 ), left side (φ G > 3 and φ G? 4 ), right side (φ G 4 and φ G 3 ), and sunlit side (φ G %@ 4 and φ G 4 ) A comparison of Figures b and d shows that the shadow side pixels are, on average, darker and the sunlit pixels are, on average, brighter than the other pixels However, Figure shows an ideal case of a completely overcast scene with very optically thick clouds Gradients in the infrared signal can only be due to changes in cloud height, shown by the good correlation between reflectances and size and orientation of the Sobel operator Inhomogeneities in cloudy regions, including partly overcasted pixels or pixels with τ A 6 (ε 99), can change the emissivity and result in gradients in BT4 not exclusively due to changes in cloud top height To discriminate these regions in our further analyses, we have excluded pixels with BT4 % 2 K This threshold removes most of the nadir pixels with τ IR 6 with a cloud top above km Figure 8 shows the reflectance as a function of the Sobel operator value for nadir pixels with BT4 2 K for the CEPEX NOAA data set Four φ G intervals are defined: 8 CB (shadow side), 9 CB (right side), B (sunlit side), and 9 B (left side) The median of the reflectances of shadow side pixels decreases nearly linearly as a function of the Sobel value from 6 (G K) to 4 (G 4 K) and remains nearly constant for larger Sobel values The signal is noisy for G % 3 K because of the small number statistics The median reflectances of the sunlit side pixels increase as a function of the Sobel value from 6 (G K) to nearly 8 (G 3 K) The median reflectances E -4 F -2 G " 2 " 4 " 6 Figure 9 As in Figure 8, except the reflectance is shown as a function of satellite zenith angle for shadow side pixels with G % 3 K from the right side and left side pixels are nearly independent of the Sobel values and equal to the shadow side and sunlit side reflectances for G J K It is not understood why the reflectance of nearly 2% of the sunlit pixels remains nearly constant as a function of G Conversely, for shadow side pixels the variation remains nearly constant as a function of G The reflectances of shadow side pixels with & θ&' decrease as a function of G The reflectance for pixels with larger satellite zenith angles remains almost constant as a function of G (see Figure 9), probably for two reasons: the resolution of the AVHRR data is comparable to the size of the shadows at large satellite zenith angles, and the shadows may be obscured for large negative satellite zenith angles (ie, backward scattering direction) by the cloud top elevation within the line of sight Figure shows that the reflectance of all sunlit side pixels increases as a function of the Sobel value, especially in the backward scattering direction, for which there is a clear view at the sunlit sides of clouds and cloud top structures Table 2 shows the relative contribution of shadow side, rightleft side, and sunlit side pixels with small and large gradients in the six plots of Figure 7 More than 7% of the pixels with τ 32 are sunlit side pixels with large gradients; only a very small fraction of 2% represents shadow side pixels The intermediate optical depths (between 4 and 32) are dominated by small BT4 gradients with relatively more sunlit side pixels at large optical depths On the otherhand, small optical depth observations (τ 4) are dominated by pixels with large gradients, especially shadow side pixels With this knowledge we can explain the deviations between the frequency distribution of BT4 per cloud optical depth interval as a function of satellite zenith angle as shown

8 L L L L 8 HEES AND LELIEVELD 2 Shadow side K (nadir) 2 Right side M (nadir) Sunlit side M (nadir) 2 Left side (nadir) Figure 8 as a function of Sobel value for nadir pixels with BT4 2 K Shown are φ G (relative to the incoming sunlight) within the intervals 8 B (shadow side), 9 B (right side), B (sunlit side), and 9 B (left side), respectively The frequency of occurrence in the CEPEX NOAA data set is shown by drawing, from bottom to top, the,, 2,, 7, 9, and 9 percentile levels Table 2 τ Shadow Side RightLeft Side Sunlit Side A B A B A B Relative contributions of shadow side, rightleft side, and sunlit side pixels in Figure 7 Each orientation class is further divided in to pixels with small temperature gradients (A is G 6 K) and large gradients (B is G 6 K) in Figure 7 The two top plots are dominated by shadow side pixels where the deviation from the theoretical curves occurs at & θ&n (see Figure 9) The shadow side pixels appear to be darker and are thus interpreted as relatively optically thin However, the infrared signal is not affected, and the distribution shown in the two top plots appear too cold Note that the deviation disappears for large satellite zenith angles Sunlit side pixels in the backward scattering direction with steep BT4 gradients (G 6 K) are responsible for the tail of pixels with large negative satellite zenith angles and high BT4 values In this case, the cloud optical depth derived from visible radiances is overestimated Discussion and Conclusions We have presented a new method to detect cloud top structure, in particular convective overshoots and cloud sides, from high-resolution AVHRR satellite data The method is based on the extent (G) and orientation (φ G ) of gradients in the AVHRR infrared data, quantified using the Sobel non-

9 I H " CLOUD TOP STRUCTURE G > 3 D K -6 E -4 F -2 G " 2 " 4 " 6 Figure As in Figure 8, except the reflectance is shown as a function of satellite zenith angle for sunlit side pixels with G % 3 K linear edge enhancement operator The orientation of the gradients in the AVHRR image plane is transformed to represent the direction of the gradient relative to the direction of the incoming sunlight using the relative azimuth angle The gradients are divided into four intervals: shadow side (φ G O 7 or φ G % 7 ), left side (φ G P and φ G 8 ), right side (φ G 8 and φ G ), and sunlit side (φ G %Q and φ G ) The size of these intervals is arbitrary; for example, a larger interval will slightly smooth the differences The reflectance of shadow side pixels decreases linearly as a function of G, and the reflectance of sunlit side pixels increases as a function of G, whereas the reflectance of right-side and left side pixels remain constant A statistical comparison of month of AVHRR data from the NOAA satellite collected during CEPEX has shown that cloud optical depth derived from visible radiances is in good agreement with cloud optical depth derived from infrared radiances, considering the limitations of both radiative transfer models We recall that the radiative transfer parameterization for visible light is based on the cirrostratus model proposed by Minnis et al [993] using randomly oriented hexagonal ice crystals, while the radiative transfer model for the infrared spectrum is based on Mie calculations using spherical particles Both methods assume the satellite field of view to be completely overcasted with a plane parallel single layer homogeneous cloud Model deviations occur for optically thin clouds as well as for optically thick clouds Pixels with τ VIS 3 are on average too cold because % 3% of these pixels are relatively dark cold shadow side pixels with large gradients Pixels with τ VIS % 32, especially those detected in the backward scattering direction, are, on average, too warm because % 7% of these pixels are relatively warm sunlit side pixels with large BT4 gradients Possible applications of this work include the detection of cloud top structures and cloud sides Especially shadow side pixels are likely to be rejected by threshold methods based on visible radiances Note that these are not likely compensated by sunlit side pixels in AVHRR data because the size of a shadow is, in general, larger than the illuminated side of cloud top structures for Sun zenith angles % 4 A possible improvement to the visible threshold methods and methods based on the spatial coherence of visible data could be to flag pixels with G % 6 K and assign these in a second iteration to adjacent cloudy areas The most straightforward application of our method is the improved interpretation of high-resolution images of visible and infrared satellite data, for example, the convective cloud scenes presented in Figures and 4 Acknowledgments This work was supported by the NSF Science and Technology Center for Clouds, Chemistry and Climate (C 4 ) and the Space Research Organization Netherlands (SRON) We thank P Minnis for providing the parameterization of reflectance of cirrostratus ice-crystal and water-droplet size distributions The paper was improved considerably by reviews from two anonymous referees This paper is report R 223 from C 4 References Coakley, J A, Jr, A dynamic threshold method for obtaining cloud cover from satellite imagery data, J Geophys Res, 92, , 987 Davis, L S, A survey of edge detection techniques, Comp Graph Image Proc, 4, , 97 Key, J, and A J Schweiger, Tools for atmospheric radiative transfer: Streamer and FluxNet, Comput Geosci, 24, 443 4, 998 Loeb, N G, T Várnai, and R Davies, Effect of cloud inhomogeneities on the solar zenith angle dependence of nadir reflectance, J Geophys Res, 2, , 997 McFarquhar, G M, and A J Heymsfield, Parameterization of tropical cirrus ice crystal size distributions and implications for radiative transfer: Results from CEPEX, J Atmos Sci, 4, , 997 Minnis, P, K-N Liou, and Y Takano, Inference of cirrus cloud properties using satellite-observed visible and infrared radiances, I, parameterization of radiance fields, J Atmos Sci,, , 993 Ramanathan, V, R Dirks, R Grossman, A Heymsfield, J Kuettner, and F Valero, Central Equatorial Pacific Experiment Design, Center for Clouds, Chemistry, and Climate (C 4 ), Univ of Calif, San Diego, 993 Shenk, W E, Cloud top height variability of strong convective cells, J Appl Meteorol, 3, , 974 van Hees, R M, J Lelieveld, and W D Collins, Detecting tropical convection using AVHRR satellite data, J Geophys Res, 4, , 999 J Lelieveld, Institute for Marine and Atmospheric Research Utrecht, University of Utrecht, Princetonplein, 384 CC Utrecht, Netherlands R M van Hees, Space Research Organization Netherlands, Sorbonnelaan 2, 384 CA Utrecht, Netherlands (RMvanHees@sronnl) Received June, 999; revised February, 2; accepted February 7, 2

10 HEES AND LELIEVELD This preprint was prepared with AGU s LATEX macros v, with the extension package AGUSTS by P W Daly, version 6b from 99989