The influence of radiation on cloud-surface feedback mechanisms using Large Eddy Simulation

Transcription

1 The influence of radiation on cloud-surface feedback mechanisms using Large Eddy Simulation Natalie Theeuwes Supervisor: Thijs Heus Max Planck Institute for Meteorology, Hamburg, Germany August 2010 Abstract A broken cloud layer, such as shallow cumulus, cast shadows on the surface and change the radiation budget at the surface. A large eddy simulation is used to investigate these cloud-shadow effects. Including the shadows of shallow cumulus clouds in a simulation leads to a decrease in the net radiation, the surface heat fluxes and results in a lower buoyancy flux in the boundary layer. This causes clouds to die out. When looking at the difference between a homogeneously and heterogeneously spread radiation budget significant differences were observed. Two simulations were done; one where the net radiation depended on the presence of a cloud above (heterogeneous) and one where the net radiation in columns with and without clouds were averaged and spread out over the entire domain (homogeneous). In this case the heterogeneity of the radiation budget caused a decrease in the surface heat fluxes below the clouds and an increase of the surface heat fluxes in the non-cloudy parts. In addition, a decrease in the liquid water content was observed. The cloud cover did not change significantly, but the clouds themselves had a lower liquid water mixing ratio and were thinner. Heterogeneity also had a negative effect on the cloud activity, lifetime and size. These findings may be important in cloud parameterizations in global circulation models. 1. Introduction There are many ways the surface influences cloud formation (e.g. Garrett, 1982, Schär et al., 1999 and Hohenegger et al, 2009). These influencing factors include effects of surface heterogeneity, soil moisture by precipitation history and alteration of the heat budget due to radiation. This study will focus on the later factor. Cumulus clouds at the top of the convective boundary layer, cast a shadow on the surface. This shadow has consequences for the turbulent structure of the partly cloud-topped boundary layer. Clouds block the shortwave radiation from reaching the surface, but increase the emission of longwave radiation in the lower atmosphere. However, the effect of low clouds on the change in downward shortwave radiation is larger than the effect of longwave radiation at the surface during the day-time (Sch är et al., 1999). Therefore, the net radiation decreases underneath the cloud. This leads to a cooling of the surface and thus a decrease in the sensible heat flux, which is driving day-time turbulence in the boundary layer over land. The convection in this layer is likely to decrease and clouds will die out. The topic of cloud-shadow effects has not been studied in great detail. Schumann et al. (2002) performed a first, exploratory study on the influence of small cumulus cloud shadows on the turbulent structure of the boundary layer. They studied a simplified case using Large Eddy Simulation (LES) and confirmed this reduced scale of convection when the shadow of the clouds was included. Another study by Markowski and Harrington (2005) analyzed the effects of shadow induced cooling behind an anvil cloud of a supercell. In this case they found a detrimental effect on the convective storm. However, they argued that this cooling could have a positive effect on convection in other storms. In these studies, they did not discuss the horizontal heterogeneity of the energy balance due to a broken cloud layer and its effect on the formation, structure and lifetime of clouds. The cloud-shadow effects of a broken cloud layer will lead to a heterogeneous distribution of the surface fluxes. The effect of spatial variability of surface fluxes on boundary layer properties has been the subject of a few studies. Zhong and Doran (1995 and again in 1997) found that spatially varying land-use categories with a scale of about 100 km, did not significantly impact the boundary layer structure. However, the spatially 1

2 varying wind speed (for example due to topography) was a more important factor. In a slightly later study Avissar and Schmidt (1998) varied the surface heat fluxes (sensible and latent) sinusoidally over a domain on several length scales and found on scales smaller then 5-10 km, surface flux patchiness is important. Circulations in the convective boundary layer become stronger and more organized. When a broken cumulus cloud layer is present the shadow effects are horizontally variable. In this study an attempt will be made to determine the effects of an horizontally heterogeneously distributed radiation budget. We will mainly focus on boundary layer and the development, structure and lifetime of the clouds. In order to examine these cloud-surface feedback mechanisms a Large Eddy Simulation (LES) will be used, in this case the Dutch Atmospheric Large Eddy Simulation (DALES) (Heus et al., 2010). An idealized case will be simulated, based on a case of shallow cumulus convection in the Netherlands (Cabauw) on June 17 th, Using this case several simulations will be done including and excluding the effects of short and longwave radiation due to a broken cloud layer, as well as simulations with homogeneous and heterogeneous radiation budgets. In chapter 2 a description of the LES will be given and the set-up of the experiments will be explained. Chapter 3 shows the results of the simulations for two different experiment and an attempt is made to explain these results. This is followed by a discussion in chapter 4 and finally the conclusions are given in chapter Model & Method In this chapter the LES used in this study will be described. We will give an outline of the radiation parameterization and briefly explain the land surface model. Next, the different experimental setups will be described. 2.1 DALES In this study the Dutch Atmospheric Large Eddy Simulation (DALES) was used, of which the code is described by Heus et al. (2010). The main purpose of DALES, like other LES models, is to resolve turbulence up to a certain grid size and parametrize the rest. The model uses one-and-a-half order closure to model scalar fluxes and subfilter-scale stress tensor (Deardorff, 1973). Radiation In this study we use a parametrized longwave and shortwave radiation. This is done for faster computation time and easier adjustability. The longwave radiation in a column with liquid water is parametrized as follows: 4 F rad L x,y,z =0. 8 σ T x,y,z e b LWP x,y,z,ztop (1) Without liquid water in the column: F rad L x,y,z =0. 8 σ T x,y,z 4 (2) Where σ is the Stefan-Boltzmann constant (=5.67 x 10-8), T is the absolute temperature and b represents an extinction coefficient. In clouds the liquid water path (LWP) is the vertically integrated liquid water mixing ratio multiplied by the density of the air. In this approximation for the shortwave radiation the cloud optical depth was defined as (Heus et al.,2010): 3 LWP x,y,z,zt τ x,y,z = 2 r e ρw (3) Where τ is the optical depth, re the cloud droplet effective radius and ρw the density of water. The single scattering albedo (ω0), the ratio between the scattering coefficient and the extinction coefficient, is approximated by Fouquart (1985) as: 2

3 ω0 = μ 0 1 e τ t (4) Where μ0 is the cosine of the solar zenith angle (α), and τ t is the total optical depth of the subcloud layer. The downward shortwave radiation is then estimated by: F rad s [ 4 x,y,z =F 0 p C 1 e k τ x,y,z C 2 e k τ' x,y,z βe 3 τ' x,y,z μ 0 ] +μ0 F 0 e τ' x,y,z μ 0 (5) Where F0 is the total solar radiation at the top of the domain. Estimated by the solar constant (=1376 W/m 2) multiplied by a simple tuned parametrization for the transmissivity (Burridge and Gadd, 1974) (suggested by Stull, 1988) above the domain: sin(α). C1 and C2 are constants dependent on the albedo, solar zenith angle, optical depth and a factor (g = 0.85) that takes into account the asymmetric scattering angle of the cloud droplet. The variables k, p and β are calculated as follows: k= 3 1 ω0 ' 1 ω0 'g' p= 3 1 ω 0 ' 1 ω0 'g' β= 3ω0 'μ g' 1 ω0 ' μ k 2 μ20 (6) (7) (8) The asymmetry factor g, single-scattering albedo ω0 and the optical depth τ are transformed using the deltaeddington equations (Joseph et al., 1976): g'= g 1 +g ω0 = 1 g 2 ω0 1 ω 0 g 2 τ'= 1 ω 0 g 2 τ (9) (10) (11) This radiation parameterization has a lot of assumptions and there are more accurate schemes available. However, for the purpose of this exploratory study it is an advantage to have an easily adjustable scheme with a preferably short computing time. Most importantly it should produce differences in short- and longwave radiation between columns with and without clouds. Land Surface Model DALES (Heus et al., 2010) also contains a land surface model, used in this research. This model has a skin layer and four soil layers. At the skin layer the surface energy balance is calculated as follows: C sk dt s dt =Q net ρc p w'θ' ρlv w'q' G (12) Here Csk is the skin layer heat capacity, T s is the surface temperature, Q net is the net radiation, C p is the heat capacity of dry air (1004 J kg -1k-1), w'θ' is the surface heat flux, w'q' the moisture flux, ρ the air density, L v the latent heat release for vaporization (2.5 x 10 6 J/kg) and G the ground heat flux. The ground heat flux is calculated using: G=Λ T s T soil1 (13) Where Λ is a bulk conductance for the stagnant air in the skin layer and Tsoil1 is the temperature of the first 3

4 soil layer. Using a simple diffusion equation the heat is transported through the soil layers. The transport of moisture through the soil layers was not included because the effect is presumed to be small. The soil is not extremely dry and there is no precipitation. 2.2 Experimental setup The 17th of June, 2008 started as a fair day in the central part of the Netherlands. As the day progressed shallow cumulus developed with a maximum cloud cover of about 0.25 around 15 UTC. The clouds had a bases at around 2 km and typical depth of about 300 meter. During this day the mean windspeed was between 2 and 4 m/s. However, in this study it is important to have non-moving clouds, because moving clouds have less effect on the surface. Therefore, the boundary conditions of the horizontal windspeed in the x and y directions were set to zero at all heights. In addition, the domain surface was created to be homogeneous and have a size of by meters with a vertical resolution of 20 m, with a domain top of 6050 m. Several experiments were done by varying the net radiation at the surface. First of all, three small simulations (horizontal resolution of 100 m) were performed with a uniform net radiation over the entire domain. In the first case the net radiation beneath the clouds was taken, then averaged and spread out over the whole domain. This simulation will be referred to as SHD. The next run, further referred to as CLR, spread out the averaged net radiation in the columns without clouds over the entire domain. In the last simulation, AVG, the net radiation of the columns with and without clouds was averaged and spread them out over the entire domain. In this simulation the mean net radiation in the domain is the same as the mean net radiation in a regular, heterogeneous simulation. All the averaging in the simulations was done after the longwave and shortwave (up- and downward) radiation in each column was calculated. Depending on the simulation type (CLR or SHD), the longwave and shortwave, upward and downward radiation in the surface layer were averaged for the gridpoints that satisfied a certain threshold (column-sum liquid water of 0 g/kg or larger then 0 g/kg, respectively). When all four radiation components for both thresholds were calculated, they were added to give a net radiation for both thresholds (CLR and SHD). For AVG each component was averaged using both thresholds with a weight depending on the number of gridpoints that satisfy each threshold. In these simulations the effect of the shortwave and longwave radiation on the atmosphere is not horizontally averaged at this time. The difference is considered to be consistent and should not be noticeable when looking at the difference between the simulations. Table 1: An overview of the simulations Experiments Resolution Net Radiation SHD 100 m Average of cloudy columns CLR 100 m Average of non-cloudy columns AVG 100 m Average of all columns HOM 50 m Average of all columns HET 50 m Heterogeneous Last, two larger simulations (resolution of 50 m) were done to look at the physical processes in more detail. The first is similar to AVG described above. The only difference is the resolution. This experiment will be referred to as HOM. The second is a heterogeneous simulation. The net radiation is not averaged over the entire domain, but is calculated separately for each column. 3. Results This chapter will highlight the main results from the LES simulations. First the three small experiments will be analyzed to test the hypothesis of a decrease in boundary layer convection due to the change in the radiation budget. Second, the effect of a heterogeneous radiation balance over the domain on the clouds themselves will be explained using the large simulations which were described in section

5 3.1 Testing basic theory In this section the theory presented in the introduction will be examined using the three small simulations. The first step in this theory is a decrease in shortwave radiation causing a decrease of the net radiation at the surface. Figure 1 shows the net radiation and the surface heat fluxes for the three small simulations described in section 2.2. As a reference the cloud cover of SHD is also displayed in the net radiation figure. Figure 1: (a)the domain-averaged net radiation [W/m 2], an indication of the cloud cover [-] is given by the gray full line. This is the cloud cover for the "shadow" simulation. (b)the sensible (red) and latent (blue) heat fluxes [W/m2] of the SHD (dashed), CLR (dotted) and the AVG (full lines) simulations. The first thing to notice in figure 1a is that the CLR simulation does not have a clean sinusoidal shape. Sensitivity tests showed the fluctuations are amplified due to the lack of mixing by horizontal wind, but as of yet it is unknown what causes this variability. The net radiation of SHD is smaller compared to the AVG and CLR simulations when clouds are present, with a maximum of about 100 W/m 2. This maximum is not fixed but strongly depends on the liquid water content threshold value at which clouds are defined. In the SHD simulations clouds are defined to be present if a column of air has a sum of more than 0 g/kg liquid water. Changing this threshold to 0.1 g/kg liquid water can already lead to a maximum difference of 200 W/m 2 (not shown here). The difference between the AVG and the CLR simulation is not as large because the cloud cover is only 0.25 at best. The decrease in net radiation leads to a decrease in the surface heat fluxes figure 1b (sensible and latent). In absolute terms the difference in latent heat is larger between the three simulations and the difference in sensible heat is small. The ratio between the two fluxes (not shown here) changes very little. Due to the reduced sensible heat flux, thermally induced convection in the boundary layer decreases. Figure 2 shows the total buoyancy flux of the model at 18:00 local time. This is the buoyancy flux resolved in LES added to the subfilter-scale contribution. At this time of the day cloud cover is high and the clouds are most developed, thus the difference between the three simulations is expected to be large. This figure verifies the reduced heat flux when clouds influence the surface radiation budget. The SHD simulation has a clearly reduced buoyancy flux in the boundary layer. Near the top of the subcloud layer, from about 2000 meters, the influence of the surface heat budget is less distinct. In the cloud, above 2600 meter, the buoyancy flux is less intense when clouds are included in the surface radiation budget as in the boundary layer. These findings fit to the conclusions of Schumann et al. (2002). The turbulence decreases when the shadows of clouds are taken into account. In order to observe the change in cloud formation and structure the domain averaged liquid water content is plotted as a function of height and time in figure 3. 5

6 Figure 2: The total buoyancy flux [K m/s] at 16:00 UTC, 18:00 local time. The AVG simulation is indicated in solid lines, SHD in dashed and CLR in dotted lines. Figure 3: (a) The liquid water mixing ratio (g/kg) in the SHD simulation (contours) and the CLR simulation (colors) averaged over the entire domain. (b) The difference between the two simulations (CLR - SHD). Lines are solid if the liquid water content in the CLR simulation is larger than in the SHD simulation. In this figure the liquid water mixing ratio of the CLR and the SHD simulation are displayed in the same graph, it shows the two extreme simulations. The AVG simulation had results between the CLR and SHD simulation. The first thing to notice that the experiment with a net radiation uninfluenced by clouds has a higher cloud top. This higher cloud top is confirmed in the difference plot (figure 3b) as well. Around 2800 meter the liquid water in the atmosphere is much higher in the CLR simulation. In general the liquid water is 6

7 much lower in the SHD experiment. This can have two reasons, first there is less condensed water in the clouds or the overall area of the clouds is less. The later is most likely the case. When determining the cloud cover (not shown here) a difference of about 0.05 was found between the CLR and SHD experiments. At times this difference was larger. For example, at 17:30 local time the cloud cover in the CLR simulation was about 0.26, but in the SHD simulation the fraction of clouds covering the area of the domain was only This difference is small at the start of the simulation but increases as the simulations progress. At first the start of the simulation the clouds are small and the net radiation is similar in the three experiments (figure 1), this is likely to have little effect on the turbulence of the boundary layer. It is hypothesized that as the clouds increase in size and number, the difference in surface heat fluxes between the simulations becomes larger and buoyancy is affected. This decrease or increase in buoyancy will presumably lead to a dying out of clouds or the formation of deeper clouds respectively. These results all coincide well with the hypothesis described in the introduction. 3.2 Heterogeneous and homogeneous net radiation In this section the influence of horizontally heterogeneous radiation budget is discussed. In one simulation the net radiation is kept constant over the entire domain, HOM. In the other simulation the net radiation is heterogeneous over the domain. In figure 4 the net radiation in the domain is displayed. Figure 4: The net radiation at the surface [W/m2] (colors) and the column integrated liquid water content [kg/kg * m2/kg] (contours) for the (a) HET and (b) HOM simulations at 15:00 UTC and 17:00 local time. From this figure we can say that the net radiation below a cloud (minimum of 100 W/m 2) in the HET simulation is obviously lower then the surrounding columns without clouds (around 365 W/m 2). In figure 4b a uniform net radiation is displayed. At this time the net radiation is about 54 W/m 2 lower than the clear air net radiation in the heterogeneous simulation. Therefore, in the HOM simulation the clouds account for about 54 W/m2 loss in net radiation. The change in radiation due to clouds will have an effect on the surface heat fluxes and their ratio. In figure 5 the latent and sensible heat flux are shown with the Bowen ratio (sensible heat flux / latent heat flux) for the two simulations. In the HET simulation we see an expected result. The net radiation decreases below the cloud and therefore the sensible and latent heat fluxes decrease. The radiation that does reach the surface is mainly used for evaporation and the Bowen ratio is lower below the clouds. In the columns without clouds the Bowen ratio higher thus the influence of sensible heat increases. Thus the thermally driven turbulence plays a bigger role. In the HOM experiment something different happens. We expect the surface heat fluxes to be the same below the cloud as below a clear column of air. However, the Bowen ratio below the clouds becomes larger, the sensible heat flux increases and the latent heat flux mostly decreases. This study can not provide an explanation for this effect. 7

8 Figure 5: The latent heat flux [W/m2] (a,d), sensible heat flux [W/m 2] (b,e) and Bowen ratio [-] (c,f) for the HET (a-c) and HOM (d-f) simulations at 15:00 UTC and 17:00 local time. The contours show the integrated liquid water [kg/kg] over the entire column. Next, we will sketch the influence these changes in surface heat fluxes have on the boundary layer and cloud formation. Figure 6 gives vertical profiles of the liquid water potential temperature the amount of total and liquid water in the atmosphere and the total cloud cover of the domain. The profiles were averaged over the entire domain within a time period of two hours (16:00-18:00 UTC) with well developed clouds. 8

9 Figure 6: Profiles of (a) The mean liquid water potential temperature [K] (b) the mean total water mixing ratio [g/kg] and (d) the mean liquid water mixing ratio [g/kg] averaged over 2 hours (16:00-18:00 UTC). (c) Time series of the total cloud cover of the domain [-]. The solid lines show the HET simulation and dashed lines the HOM. At first glance there does not seem to be much of a difference in the profiles of the total specific humidity and potential temperature. However, above the cloud layer the liquid water potential temperature and the total water specific humidity are slightly higher in the HOM simulation. This means that the boundary layer is slightly higher in that experiment. The water vapor in the boundary layer or cloud top itself is somewhat less. This is likely to be caused by the slight increase in Bowen ratio below the clouds in the HOM simulation. The sensible heat flux increases and causes the boundary layer to grow more and the decreased latent heat presumably causes a slight drying of the boundary layer. This does not seem to have much influence on the actual cloud cover (figure 6c). There is some difference between the two simulations, but the cloud cover in one of the simulations is not significantly larger or smaller. However, the total liquid water mixing ratio (figure 6d) is larger in the HOM experiment. Keeping in mind that the difference in the cloud cover between the two experiments was insignificant, the liquid water in the clouds themselves must have increased, not the area of clouds. In figure 6d it is also shown that the average cloud top in the HET simulation is lower than the cloud top in the HOM experiment. This was also displayed in the potential temperature and specific humidity profiles, where on average the boundary layer was higher in the HOM simulation. This is most likely to be due to increased turbulence in the boundary layer. 9

10 Finally, in figure 7 the fraction of clouds and cloud cores are given. Clouds are defined by liquid water content above zero and cloud cores are defined by a liquid water content above zero as well as a positive buoyancy. Figure 7: The fraction of clouds (black) and cloud cores (gray) in the HET (solid) and HOM (dashed) simulations averaged over 2 hours (16:0018:00 UTC). The figure shows that there are more buoyant cloud cores in the simulation with a homogeneous net radiation compared to the heterogeneous experiment. Figure 7 shows the fraction of clouds in HOM is smaller in the lower cloud layer. Meaning that the area of clouds in the HET simulation is actually larger. At the top of the cloud layer this difference is reversed, partly because the cloud top is higher in the HOM simulation. Comparing this with figure 6d there must be an increase in liquid water in the clouds of HOM themselves. This change in liquid water content can be better explained using a joint probability distribution of the liquid water mixing ratio as a function of height (figure 8a-b). The last plot (figure 8c) gives the difference between the HET and HOM simulations. 10

11 Figure 8: The joint probability distribution of the liquid water content as a function of height for the heterogeneous (a) and the homogeneous (b) simulation and the difference between the two experiments (HOM - HET) (c). The joint probability distributions in figures 8 a-c again show a higher cloud top in the homogeneous experiment. The maximum cloud top is about 3150 m in HET and 3250 m in HOM. In general the liquid water mixing ratio increases with height due to the increase of condensation higher in the atmosphere. However, the probability of a high liquid water content is higher in HOM. In HET, higher up in the cloud, the probability of a lower liquid water content is higher. In HOM it is more likely to have a higher liquid water mixing ratio higher in the cloud. The difference plot shows a higher probability for HOM near the cloud base. Meaning that the cloudbase in the homogeneous experiment is slightly lower than in the heterogeneous experiment. This may be due to the entrainment of dry air in non-cloudy parts around the clouds being higher in the HET experiment, because the clouds are smaller and more scattered. Leading to a dryer subcloud layer in that simulation and the cloud base is higher. It is only a hypothesis and needs further investigation. Not only does the liquid water of the clouds change but the cloud-lifetime and distribution over the domain change as well. Figure 9 displays four Hovmöller diagrams, one is taken at the edge of the domain and one in the center. The liquid water and total water content were summed over each vertical column. 11

12 Figure 9: Hovmöller diagram of the column integrated total water content [kg/kg] (colors) and the column integrated liquid water mixing ratio [kg/kg] (contours) derived from two different cross-sections, at the edge of the domain (a,b) and one in the center of the domain (c,d). This is done for the HET (a,c) and HOM (b,d) simulations. One of the most important difference between the two simulations that can be seen in this figure is the clustering of the clouds. In the HOM simulation most of the cloud fraction is in one specific area and the cloud stays there over a longer period of time. In the HET experiment the clouds are spread more evenly in the x-direction and dissipate quicker. In this study it is suggested the life-cycle and spatial scattering of the clouds have to do with the same process. In the experiment with a heterogeneous radiation budget, as a cloud forms the surface heat fluxes below it become very small and the cloud is not fed by the necessary energy to stay in that place and dissipates. However in other non-cloudy parts of the domain there is enough energy (sensible and latent heat) available for a new cloud to be formed. This causes horizontally scattered clouds with a short lifetime. In the HOM simulation the amount of energy is almost the same over the whole domain. Once a cloud forms, the net radiation stays the same below this cloud and the cloud stays in the same place for a longer period of time. It is able to grow. As for the total liquid water content, there does not seem to be a clear difference in the size and duration of moist or dry conditions in the domain. This makes sense because the amount of water vapor in this radiation parameterization does not influence the radiation. The theory that applied to the liquid water in the atmosphere does not apply to the total water content. 12

13 In order to get a sense of the difference in cloud size and lifetime, probability distributions (figure 10) were computed. The method used to compute these plots was as follows; first the liquid water content was integrated over each column in the domain. Using this cloud-projection each individual cloud was determined in three dimensions (time, length and width). A cloud will be connected in 6 directions, so forwards and backwards in time and in four directions spatially. In addition the cloud needed to have an integrated liquid water mixing ratio of at least 0.05 kg/kg * m 2/kg, otherwise most clouds would somehow be connected. Each cloud was labeled with the length, width and duration and the cloud-samples were counted. Finally, the probability a cloud-sample would be part of a cloud with a certain length, width and duration was calculated. Figure 10: The probability distributions of the cloud width (a), length (b) and duration (c). The plots in figure 10 clearly show a difference between the heterogeneous and homogeneous simulation. Concerning the size of a cloud, the probability in HOM is higher for one sample to be in a large cloud with a size of about 24 km2. The probability of a sample being in a smaller cloud is smaller. The cloud size in HET is typically about 10 km2. In addition, clouds in that simulation have a larger chance of being smaller. When it comes to the lifetime of a cloud, most cloud samples in the HET simulation reside inside a cloud with a shorter lifetime than in the homogeneous case. In that case nearly 60 percent of the samples are in a cloud of a lifetime of about 6310 seconds (about an hour and 45 minutes). This all means that besides being larger and longer-living, the clouds in HOM are more active as well. In contrast to this the cloud fraction near the cloud base seems to be higher in the heterogeneous simulation. Possibly, this is due to the different lifetimes of the clouds. In HET the clouds decay faster, meaning there are relatively more decaying and thus non-active clouds in the boundary layer. Whereas in HOM the clouds have a longer lifetime and are active for a longer period of time. So, there may be a larger fraction of buoyant cloud cores (figure 7) in the boundary layer, but it does not mean the total cloud fraction is high also. 13

14 4. Discussion The main part of this study was exploratory and further investigation needs to be done. The results comparing a heterogeneous and homogeneous radiation budget are based on two simulations of one specific case of shallow cumulus convection over land. For more statistics larger simulations can be done using a larger domain, but also different cases can be analyzed. In the HOM simulation there was only one large and long-lived cloud where most of the statistics were based on. Even though it is reasonable to have much fewer clouds in HOM then in HET, more data are needed in order to quantify the effects. As mentioned in section 2.1 the radiation parameterization is not accurate as many other available schemes. It does not take into account three dimensional effects important in a cloudy atmosphere (O'Hirok and Gautier, 1998). For example: Three-dimensional shortwave radiation scattering was not included in the model. More solar radiation reaches the surface in the cloudless columns than in a completely cloudless simulation, because of scattering from the sides of the clouds. The longwave radiation was assumed to be emitted per cloudy or non-cloudy column only, while in reality longwave radiation is emitted in all directions. The shadow of a cloud (assuming only a change in shortwave radiation) is only directly underneath that cloud and does not depend on the solar zenith angle. Schumann et al. (2002) already looked at this effect and saw that in the LES simulations the difference was minor. However, what they did not take into account was the influence of the solar zenith angle(α) already starts at the cloud top and not the cloud base. Therefore the shadow will not only be shifted by [cloudbase * tan(α)], but the shadow will be horizontally increased by approximately [(cloudtop-cloudbase) * tan(α)]. Wapler and Mayer (2008) developed an accurate and fast three-dimensional radiative transfer method to be used in LES, that includes solutions for the above-mentioned inaccuracies. This method can be used in the next step of exploring the effect of a heterogeneous radiation budget. Besides taking into account the inaccuracies of the radiation parameterization, it is still unknown what the exact role of longwave radiation is for this kind of shallow cumulus. The other studies analyzing cloudshadow effects did not include the influence longwave radiation. It would be useful to explore the role of shortwave and longwave radiation by doing simulations with only shortwave or only the longwave radiative parameterization activated. However, in order to have a more realistic grasp of the different processes involved a more accurate radiative transfer method is necessary. Based on some sensitivity tests it is clear that cloud-shadow effects are strongly dependent on surface conditions. These sensitivity tests were set-up like the first experiments in section 3.1 and included sensitivity to soil moisture, surface albedo and heat capacity. For example a higher soil moisture leads to more evaporation and a change in Bowen ratio (decrease) and more moisture in the boundary layer. This increases the cloud cover, depth and liquid water in the cloud and thus the difference between the SHD and CLR simulations increased. Thicker clouds have a higher optical depth and a larger influence on the shortwave radiation at the surface. The heat capacity of the soil is also a very important variable when looking at the surface radiation budget. If the soil is able to store more heat, the surface will not be very sensitive to changes in the radiation budget. Therefore, the difference between SHD and CLR is smaller. Finally, when lowering the surface albedo the net radiation at the surface is higher. This increases the surface fluxes and thicker, more active clouds are able to form. This means that the difference between SHD and CLR is larger. The sensitivity to surface properties is likely to reappear when analyzing the heterogeneity of the radiation budget. The wind in this case was assumed to be zero to have the maximum effect of the clouds on the surface and the surface back to the clouds. However, realistically the windspeed is never zero. It is likely increasing the wind will lead to less visible effects between the surface and the clouds. More tests need to be done how sensitive the results in chapter 3 are to a change in windspeed. 5. Conclusions Schumann et al. (2002) looked at the way in which turbulence in the boundary layer changed when cloud shadows were taken into account. They found turbulence decreased. This study confirmed the hypothesis that this decrease boundary layer turbulence has a negative effect on cloud development. That makes it important to include the radiation effects of shallow cumulus as all other clouds in a model, so that the 14

15 boundary layer turbulence and cloud development are not overestimated. Besides this, the study tried to analyze the importance of a heterogeneous radiation budget. Overall a horizontally heterogeneous radiation budget means a lower net radiation and lower surface fluxes below the clouds. While the surface fluxes in non-cloudy parts are higher. The Bowen ratio changes and relatively more of the available energy goes into evaporation below the clouds. Most importantly, the clouds themselves change as well. They are less developed, have a shorter lifetime and are smaller than the clouds that are produced with a horizontally homogeneous radiation budget. This change in cloud properties is due tot the heterogeneity of the surface fluxes. When a cloud is formed the radiation decreases, there is no energy to feed the cloud and it dies out. In the non-cloudy parts there is enough energy at the surface for a new cloud to form. This causes clouds to be short-lived and scattered. A heterogeneous radiation budget has significant consequences for the surface cloud feedbacks, including the cloud lifetime, size and activity. This information can be used in global weather and climate models where shallow cumulus clouds are parameterized. This can hopefully improve the representation of clouds in those models to get a better understanding of the global radiative forcing and possibly the future climate. References Avissar, R. and Schmidt, T., 1998: An Evaluation of the Scale at which Ground-Surface Heat Flux Patchiness Affects the Convective Boundary Layer Using Large-Eddy Simulations, J. Atmos. Sci Burridge, D. M. and Gadd, A. J., 1974: The Meteorological Office operational 10 level numerical weather prediction model (December 1974). U.K. Met. Office Tech. Notes 12 and 48, 57 pp. Deardorff, J. W., 1973: The use of subgrid transport equations in a three-dimensional model of atmospheric turbulence. J. Fluids Eng Fouquart, Y., 1985: Radiation in boundary layer clouds, in: Report, JSC/CAS Workshop on Modelling of Cloud-Topped Boundary Layer, Fort Collins, CO, WMO/TD 75, Appendix D, 40 pp. Garrett, A.J., 1982: A parameter study of interactions between convective clouds, the convective boundary layer, and forested surface. Mon. Wea. Rev., Heus, T., van Heerwaarden, C. C., Jonker, H. J. J., Siebesma, A. P., Axelsen, S., van den Dries, K., Geoffroy, O., Moene, A. F., Pino, D., de Roode, S. R., and Vila-Guerau de Arellano, J., 2010: Formulation of and numerical studies with the dutch atmospheric large-eddy simulation (DALES). Geosci. Model Dev. Discuss Hohenegger, C., Brockhaus, P., Bretherton, C.S. and Schär, C., 2009: The soil moisture-precipitation feedback in simulations with explicit and parameterized convection J. Clim Joseph, J.H., Wiscombe, W.J., Weinman, J.A., 1976: The delta-eddington approximation for radiative flux transfer. J. Atmos. Sci Markowski, P., and J. Harrington, 2005: A simulation of a supercell thunderstorm with emulated radiative cooling beneath the anvil. J. Atmos. Sci O Hirok W., and C. Gautier, 1998: A three-dimensional radiative transfer model to investigate the solar radiation within a cloudy atmosphere. Part I: Spatial effects. J. Atmos. Sci Schär, C., Lüthi, D., Beyerle, U., and Heise, E., 1999: The soil precipitation feedback: A process study with a regional climate model. J. Climate Schumann, U., A. Dörnbrack, and B. Mayer, 2002: Cloud-shadow effects on the structure of the convective boundary layer. Meteor. Z Stull, R. B., 1988: An Introduction to Boundary Layer Meteorology. Kluwer Academic, 666 pp. Wapler, K. and Mayer, B., 2008: A fast three-dimensional approximation for the calculation of surface 15

16 irradiance in large-eddy simulation models. J. Appl. Meteor Zhong, S., and Doran, J. C., 1995: A modeling study of the effects of inhomogeneous surface fluxes on boundary-layer properties. J. Atmos. Sci Zhong, S., and Doran, J. C., 1997: A study of the effects of spatially varying fluxes on cloud formation and boundary layer properties using data from the Southern Great Plains Cloud and Radiation Testbed. J. Climate