1. Introduction
The atmospheric boundary layer (ABL) dynamics are strongly influenced by the surface–atmosphere exchange of heat and moisture, which, over vegetated land, is conditioned by CO2 concentration. Variations in atmospheric conditions due to turbulent motions locally modify surface fluxes at scales within a few hundreds of meters in the horizontal (Huang and Margulis 2010), and modify the spatial average latent and sensible heat fluxes at regional scales (between 10 and 50 km). These interactions are representative of the so-called land–atmosphere feedbacks. As an illustrative example of the role of dynamics on such a large-scale coupling, De Bruin et al. (1989) already found that warm and dry entrained air was critical for sustaining high evaporation rates at the surface. Van Heerwaarden et al. (2009) presented an overview of the factors within the ABL affecting evapotranspiration. The heterogeneities of the surface characteristics, or static heterogeneities, add to the complexity of land–atmosphere interactions by varying air temperature (Baldocchi and Ma 2013) and the surface fluxes at a scale of several kilometers (Avissar and Schmidt 1998; Esau and Lyons 2002). At a regional scale, such surface heterogeneities have the potential to trigger secondary circulations (Garcia-Carreras et al. 2010).
A key factor that affects plant activity is the partitioning of radiation into direct and diffuse components, which depends on the transfer of radiation through the atmosphere, influenced by clouds and aerosols and through the canopy itself. Canopies convert radiation from direct to diffuse by the scattering of light with leaves (Goudriaan 1977; Norman 1979). Aerosols and clouds are known to decrease total radiation and increase the diffuse fraction through light scattering. Barbaro et al. (2014) showed the relevant impact of aerosol–radiation interactions on the boundary layer, but did not consider the effect that diffuse radiation would exert on the vegetated canopy. Diffuse radiation is known to increase the carbon (from here on representing only carbon from CO2) assimilation of vegetated canopies (Kanniah et al. 2012) due to a more homogeneous spread of radiation in the canopy, thus reducing the saturation of leaves at the top of the canopy and increasing the available radiation at the bottom and shaded parts of the canopy. Min and Wang (2008) found increased CO2 uptake by plants for conditions with an atmospheric transmittance index below 1, which favor the scattering of radiation and promote diffuse radiation. An increase in carbon uptake over forests and under shallow cumulus clouds has been reported by several studies (Betts et al. 1999; Freedman et al. 2001; Oliphant et al. 2011) in spite of a reduction of global radiation. Since the vegetation–atmosphere system couples water and carbon cycles through photosynthesis, evapotranspiration and sensible heat flux exchanges are also affected by diffuse radiation (Wang et al. 2008; Oliveira et al. 2011).
Similar to aerosols, clouds also influence the partitioning between direct and diffuse radiation. However, the optical thickness of clouds can be larger than that for aerosols. Thick clouds absorb most direct radiation (Min 2005), and little diffuse radiation reaches the surface. Below optically thin clouds the reduction in direct radiation can be significant but limited, and diffuse radiation is greatly enhanced (Cheng et al. 2016). We here follow the convention by Min (2005), where thin clouds are defined as the ones with cloud optical depth τ < 8 and thick clouds for larger τ. The motivation was that clouds with τ > 8 did not allow any direct radiation go through. Similarly, Cheng et al. (2016) set the threshold at τ = 7. As we found in our study, however, such thresholds vary during the day, thus making the definition of thin and thick clouds quite arbitrary.
Convective clouds impose some additional effects on surface–atmosphere interactions compared to aerosols. Their onset, development, and characteristics depend on surface conditions (Golaz et al. 2001; Garcia-Carreras et al. 2011; Chlond et al. 2014). They are known to vent air from the boundary layer to higher layers, reducing the momentum, moisture, and subcloud-layer growth (Betts 1973; Neggers et al. 2006), thereby altering the surface fluxes. More important to our study are the dynamic heterogeneities created at the surface by (inhomogeneous) cloud shading. As a result, clouds disrupt the surface energy balance by modifying surface temperature and specific humidity, creating inhomogeneities that vary the turbulent mixing near the surface. Lohou and Patton (2014) found a higher evaporative fraction (EF) on shaded surface because the latent heat flux (LE) decreased less compared to the sensible heat flux (SH). The shade-induced energy reduction at the surface promotes the narrowing of space between updrafts and, subsequently, the reduction of intercloud distance (Horn et al. 2015). Moreover, Gronemeier et al. (2017) found that cloud shading is able to generate secondary circulations, although its strength and significance depend on the solar zenith angles.
Most of these studies were idealized numerical experiments designed to disentangle the complexity of the cloud–surface interactions and assumed free convective conditions with an instantaneous surface response. None of them, however, considered explicitly the impact of direct and diffuse radiation on active vegetation at the surface. This possibility poses interesting questions, such as whether the local impact of radiation partitioning by clouds on vegetation has a domain-averaged effect, given the distinct responses for thin and thick clouds, or, in addition, whether the direct–diffuse partitioning of radiation near the surface ultimately influences the characteristics of boundary layer clouds themselves.
To our knowledge, no systematic study on the impact of shortwave direct and diffuse radiation (
Aiming to shed light on the issues posed above, the research questions of this study are the following:
Does direct and diffuse radiation modulation by shallow cumulus affect evapotranspiration and CO2 assimilation locally? And over the whole domain? How does this impact the partitioning of sensible and latent heat flux?
Under these nonstationary surface conditions, do the direct and diffuse radiation alterations from clouds feed back into boundary layer dynamics? Do cloud characteristics depend on it too?
The remaining part of this study is structured as follows: section 2 describes the methodology and tools used for this study, including the implementation of a canopy radiative transfer scheme accounting for direct and diffuse radiation, as well as the research strategy. Section 3 contains the main findings and points of discussion of our analysis. Finally, the concluding summary of the research and recommendations are provided in section 4.
2. Methods and numerical experiments
a. Explicit simulation of the coupling: DALES
The Dutch Atmospheric Large-Eddy Simulation (DALES) has been under continuous development since the 1980s (Nieuwstadt and Brost 1986; Heus et al. 2010; Böing et al. 2012; Ouwersloot et al. 2017). It incorporates an interactive land surface scheme responding to atmospheric processes described in Jacobs and de Bruin (1997), van Heerwaarden et al. (2010), and Vilà-Guerau de Arellano et al. (2015). Within the land surface scheme, we use the plant physiological model A-gs (Jacobs and de Bruin 1997) to simulate the behavior of vegetation and assuming an instantaneous response of vegetation to atmospheric and radiation forcings. This study uses DALES, version 4.1, with additional upgrades concerning the radiation transfer within the canopy [section 2c(2)] and conditional sampling at the surface (section 2d). We present here the most relevant parts of the land surface model, that is, the contribution of vegetation to latent heat flux, the sensible heat flux, and the carbon assimilation rate by vegetation.
For a detailed description on the treatment of direct and diffuse radiation in the canopy resistance calculations, the reader is referred to the supplemental material.
b. Conceptual analysis: CLASS
To support the analysis of the results in DALES, in section 3a(2) we make use of the Chemistry Land-Surface Atmosphere Soil Slab (CLASS) model (Vilà-Guerau de Arellano et al. 2015). This box model is based on the mixed-layer equations to obtain the temporal evolution of the boundary layer and surface processes. The land surface model in CLASS (van Heerwaarden et al. 2010) is similar to that of DALES, and the schemes described in sections 2c(1) and 2c(2) are also present and used in CLASS. With this box model we analyze the response of vegetation to temporal changes in cloud optical depth and radiation in a more controlled environment than in DALES, where explicit turbulence makes interpretation difficult. By using CLASS, it is easier to fix the surface conditions and untangle the effects of different factors affecting carbon assimilation. We prescribe the onset, duration, and disappearance of a cloud in CLASS by prescribing the cloud optical depth for each time step.
c. Direct and diffuse radiation partitioning
1) Radiative transfer in clouds: Delta-Eddington approximation
The Eddington method for shortwave radiative transfer was originally proposed by Shettle and Weinman (1970) and later approximated and further developed including a delta function by Joseph et al. (1976). This method has been already expanded for aerosols and successfully tested in DALES by Barbaro et al. (2014).
Ratio of (a) total, (b) direct, and (c) diffuse radiation at the surface to the total radiation at the top of the domain 
Citation: Journal of Hydrometeorology 18, 6; 10.1175/JHM-D-16-0279.1
Ratio of (a) total, (b) direct, and (c) diffuse radiation at the surface to the total radiation at the top of the domain
Citation: Journal of Hydrometeorology 18, 6; 10.1175/JHM-D-16-0279.1
Ratio of (a) total, (b) direct, and (c) diffuse radiation at the surface to the total radiation at the top of the domain
Citation: Journal of Hydrometeorology 18, 6; 10.1175/JHM-D-16-0279.1
For a complete explanation and derivation of the delta-Eddington method, the reader is referred to Shettle and Weinman (1970) for the original Eddington method, to Joseph et al. (1976) for the delta-Eddington approximation, and to Heus et al. (2010) and Barbaro et al. (2014) for its application.
2) Radiative transfer in canopy: Gaussian method
The limitation of single big leaf models, like applied by Vilà-Guerau de Arellano et al. (2014), to account for canopy radiative transfer is tackled by explicitly calculating radiation profiles for direct and diffuse radiation. This is especially relevant for the current work, where both diffuse and direct radiation components are accurately calculated at the top of the canopy. To this end, we employ the scheme used by Jacobs and de Bruin (1997) and inspired from the radiative transfer approximations used in Goudriaan (1977) and adapted by Spitters (1986). A detailed description of the canopy radiative transfer and canopy upscaling is given in the supplemental material. In short, the main characteristics of the scheme are the following:
Diffuse radiation has a (constant) extinction coefficient inside the canopy that is smaller (for most of the day) than that of the (solar angle dependent) direct radiation.
The direct radiation that is not transmitted nor absorbed is scattered by leaves or the ground and converted into diffuse radiation inside the canopy.
Leaves are distributed spherically in the canopy and affect the radiation penetration accordingly.
Total stomatal conductance is obtained at three levels inside the canopy after calculating the radiation profiles and the amount of shaded and sunlit leaves per level. For the calculations of stomatal conductance at leaf level, we use the A-gs model described by Jacobs et al. (1996) and Jacobs and de Bruin (1997). Bulk stomatal conductance of CO2 for the canopy is obtained through the Gaussian integration method described in Goudriaan (1986) and implemented in the IFS model by the European Centre for Medium-Range Weather Forecasts (ECMWF; Boussetta et al. 2013). As in other studies (Jacobs and de Bruin 1997; Boussetta et al. 2013), we assume that radiation transfer is the most relevant factor throughout the canopy. Thus, we use bulk values for other dynamic variables such as leaf temperature, vapor pressure deficit, or CO2 mixing ratio, and keep them invariable throughout the canopy. Multilayer canopy models that have to resolve the surface energy balance and all dynamic variables at each canopy level are computationally more expensive. As a result, our approach is faster, while still considering radiation variations within the canopy.
d. Conditional averaging
The alteration in radiation by clouds affects the surface locally (Horn et al. 2015). It is therefore convenient to apply a two-dimensional conditional averaging of surface properties dependent on cloud properties above. We classify the surface response according to cloud optical depth in bins of gradually increasing width: bins of 0.5 width between values of cloud optical depth τ = 0 and τ = 5, and in bins of 1.0 width between values of τ = 5 and τ = 10 to obtain more information on the properties at the surface for cloud optical depths typical of shallow cumulus clouds (McFarlane and Grabowski 2007; Slawinska et al. 2008). Three more bins are defined for thicker clouds: two bins with a width of 5.0 between 10 <τ ≤ 15 and 15 < τ ≤ 20 and a bin for τ > 20.
Since we are also interested in the properties of the clouds during the experiment, we make further use of a three-dimensional conditional average over the grid, similar to that used in other studies (Siebesma et al. 2003; Ouwersloot et al. 2013; Sikma and Ouwersloot 2015). In this case, we mainly focus on the conditional averages for clouds 
e. Research strategy
We reproduce a representative warm and initially clear early autumn day of September in the Netherlands developing a convective boundary layer. Surface and upper observations are initially obtained from observations at the Cabauw Experimental Site for Atmospheric Research (CESAR). The case has been adapted to allow the onset of active shallow cumulus (Vilà-Guerau de Arellano et al. 2014). First, shallow cumulus develops between 1000 and 1100 UTC, after which a maximum cloud cover of ~20% is reached between 1300 and 1500 UTC. The numerical experiments simulate 10 h, from 0700 to 1700 UTC (0900 to 1900 local time), with an initially well-mixed boundary layer of around 120 m and with no prescribed horizontal wind. We define the boundary layer height as the height at which the gradient in potential temperature θ equals 50% of the maximum vertical gradient (Ouwersloot et al. 2011). We make use of an all-or-nothing microphysics scheme, assuming condensation of all specific humidity above local saturation point and none if saturation is not reached. The surface consists of a homogeneous grassland of leaf area index (LAI) equal to 2 with radiative and dynamic properties typical of short grass, and a vegetation cover of 90%. The domain is 24 × 24 × 5.4 km3 with a gridbox size of 50 × 50 × 12 m3. Such a vertical resolution ensures the explicit resolution of clouds and its dynamics.
We design three experiments: reference or control (REF), direct (DIR), and diffuse (DIF). The REF experiment calculates the amount of direct and diffuse radiation below the clouds using the delta-Eddington approximation [section 2c(1)] and sets the response of the surface to radiation through the canopy scheme as described in section 2c(2) and with more detail in the supplemental material. The DIR experiment uses the same radiation below the cloud, but treats all radiation reaching the canopy as direct radiation. In turn, the DIF experiment considers all radiation reaching the canopy to be diffuse as long as there is a cloud above. With these three experiments, we explore the sensitivity of the surface and boundary layer to the direct radiation and diffuse radiation ratio below clouds. Two additional experiments are carried out to put the aforementioned numerical experiments in perspective. The first one (AER) mimics the effect of downward diffuse radiation due to Rayleigh scattering above the domain by converting 7% of the direct radiation 
3. Results and discussion
a. Impact of shallow cumulus at surface
1) Impact on surface fluxes
Figure 1b shows the exponential decay in shortwave direct radiation, as stated in Eq. (8). There is a solar-angle-dependent maximum in diffuse radiation for τ between τ = 1 and τ = 8 (Fig. 1c). Increasing cloud thickness converts more direct to diffuse radiation, while at the same time reduces the overall radiation going through the cloud (Fig. 1a). This increase in diffuse fraction is of critical importance for the feedbacks and interactions in our numerical experiments, since the cloud optical depth of the shallow cumulus created during the day ranges around those values. In fact, McFarlane and Grabowski (2007) observed that in the tropics the optical depth of the most common shallow cumulus ranges between τ = 5 and τ = 10, a finding also supported through numerical experiments by Slawinska et al. (2008). To our knowledge, such a study on typical optical thickness of shallow cumulus has not been carried out for midlatitudes, where our study focuses. The results shown in Fig. 1 are consistent with the satellite measurements by Cheng et al. (2016), supporting the use of a broadband radiation scheme like the delta-Eddington for our purposes.
The perturbation of radiation by clouds has an immediate effect at the surface turbulent fluxes. The presence of any cloud locally reduces the total radiation at surface, from around 15% for very thin clouds (τ < 3) to almost 85% for very deep clouds (τ ~ 40; Fig. 1a). In our study we focus on the effect of shallow cumulus. Thus, we pay special attention to clouds with τ < 8. Figure 2 depicts the evolution of a single cloud in the REF experiment and shows how the surface responds according to the cloud thickness. Figures 2a and 2b illustrate the relation between the cloud optical depth and shortwave radiation, both direct and diffuse. For very thin clouds with τ < 3 (see the area at x = 400 m, y = 750 m in Fig. 2, left) the decrease in 
(a) Values of cloud optical depth τ (black), shortwave direct SWdir (red), shortwave diffuse SWdif (green), and total radiation SWtot (blue) along the cross section (horizontal yellow dashed line) displayed in (b). (b) Instantaneous horizontal cross sections of τ (shaded) with 
Citation: Journal of Hydrometeorology 18, 6; 10.1175/JHM-D-16-0279.1
(a) Values of cloud optical depth τ (black), shortwave direct SWdir (red), shortwave diffuse SWdif (green), and total radiation SWtot (blue) along the cross section (horizontal yellow dashed line) displayed in (b). (b) Instantaneous horizontal cross sections of τ (shaded) with
Citation: Journal of Hydrometeorology 18, 6; 10.1175/JHM-D-16-0279.1
(a) Values of cloud optical depth τ (black), shortwave direct SWdir (red), shortwave diffuse SWdif (green), and total radiation SWtot (blue) along the cross section (horizontal yellow dashed line) displayed in (b). (b) Instantaneous horizontal cross sections of τ (shaded) with
Citation: Journal of Hydrometeorology 18, 6; 10.1175/JHM-D-16-0279.1
Although the total radiation at the surface is locally reduced compared to cloudless conditions, the higher efficiency of diffuse radiation in the canopy explains the growth in 
In the conditions in Fig. 2, 
To quantify the changes at the surface along the day, we show the temporal variation in vegetation carbon uptake and surface fluxes under clear skies and for a few cloud optical depth bins in Fig. 3. For thick clouds (τ > 20), both latent and sensible heat fluxes are reduced on average compared to clear sky conditions (Figs. 3b,c), as also found by Lohou and Patton (2014) and Horn et al. (2015). A similar effect is found in net carbon assimilation 
Time series of (a) 
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Time series of (a)
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Time series of (a)
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To further quantify the dependencies of surface fluxes and net carbon uptake on cloud thickness, Fig. 4 shows 1-h-averaged carbon uptake and latent and sensible heat fluxes as a function of cloud optical depth between 1100 and 1200 UTC for the REF and DIR experiments and normalized by clear sky values. We first define a few relevant concepts. We call enhanced regime to the range of cloud optical depths at which we observe enhanced surface exchange. Threshold τ is defined for each flux as that cloud optical depth for which the flux (LE or 
(a) Mean 
Citation: Journal of Hydrometeorology 18, 6; 10.1175/JHM-D-16-0279.1
(a) Mean
Citation: Journal of Hydrometeorology 18, 6; 10.1175/JHM-D-16-0279.1
(a) Mean
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The enhanced regimes show that the character of diffuse radiation is able to compensate in 
In Fig. 4a an interesting effect is observed: at this time of the day, thin and thick clouds enhance and decrease plant activity, respectively, thus acting in opposing directions regarding surface responses. This means that the presence of thin and thick clouds may lead to similar domain-averaged carbon uptake or surface fluxes in situations where the spatial variability within the domain clearly differs. Note that the thresholds and maximum τ values vary during the day since the solar angle and surface conditions are not constant during the daytime, thus affecting this compensation effect.
For a quantification on the relative changes in Fig. 4, we show the evaporative fraction 
As in Fig. 4, but for EF and WUE for the (a) REF and (b) DIR experiments.
Citation: Journal of Hydrometeorology 18, 6; 10.1175/JHM-D-16-0279.1
As in Fig. 4, but for EF and WUE for the (a) REF and (b) DIR experiments.
Citation: Journal of Hydrometeorology 18, 6; 10.1175/JHM-D-16-0279.1
As in Fig. 4, but for EF and WUE for the (a) REF and (b) DIR experiments.
Citation: Journal of Hydrometeorology 18, 6; 10.1175/JHM-D-16-0279.1
2) Impact on carbon assimilation budget
To disentangle how components in the plant physiological model contribute to the overall increase of carbon assimilation by plants, we perform an offline study using the mixed-layer model CLASS. The conditions for the experiment are set as similar as possible to those of our LES study. In addition, we prescribe the onset, thickening, and disappearance of a very thin cloud (τ = 1).
The plant physiological model in CLASS is identical to the one used in DALES and described in the supplemental material, and calculates the net carbon uptake at canopy level according to Eq. (3). A budget analysis enables us to understand the contribution of each component of 
We name the terms following the derivative in time: plant–atmosphere carbon gradient, aerodynamic, and stomata or canopy resistance terms. The first term on the right-hand side of Eq. (9) represents the change in carbon assimilation due to a variation in the CO2 gradient between the atmosphere and inside the leaf. An increase (decrease) over time in such a gradient implies an increase (decrease) in carbon assimilation. The second term on the right-hand side accounts for the effect of atmospheric dynamics on the carbon assimilation. Being so, an increase (decrease) in aerodynamic resistance over time, possibly related to a decrease in wind speed or higher atmospheric stability, would decrease (increase) the carbon uptake. The third term on the right-hand side shows the relation between the vegetation resistance to CO2 transport and 
Figure 6a shows an enhancement in 
(a) Net carbon assimilation calculated with CLASS (full line) and prescribed cloud optical depth (dashed line). (b) Time derivative of 
Citation: Journal of Hydrometeorology 18, 6; 10.1175/JHM-D-16-0279.1
(a) Net carbon assimilation calculated with CLASS (full line) and prescribed cloud optical depth (dashed line). (b) Time derivative of
Citation: Journal of Hydrometeorology 18, 6; 10.1175/JHM-D-16-0279.1
(a) Net carbon assimilation calculated with CLASS (full line) and prescribed cloud optical depth (dashed line). (b) Time derivative of
Citation: Journal of Hydrometeorology 18, 6; 10.1175/JHM-D-16-0279.1
In the additional DALES experiments, an increase in LAI (from 2 to 5) increases the absorbed radiation by the canopy. The increase is mostly due to the larger number of leaves keeping most of the light inside the canopy. The amount of direct light converted to diffuse light inside the canopy increases with increasing LAI (from 25% to 40% of available direct radiation for LAI = 5), but the direct light converted to diffuse light is not the driving factor for the increased absorbed radiation. In particular, the diffuse radiation causes the latent heat and 
When accounting for the fraction of diffuse radiation (7% of the total radiation) at the top of the boundary layer due to Rayleigh scattering above (AER experiment), we still find an enhanced regime with higher LE and 
b. Impact of surface on boundary layer and shallow cumulus
In section 3a(1) it was already shown that the partition between direct and diffuse radiation plays a critical role in the surface response. Therefore, it is interesting to investigate whether these changes at the surface feedback to the boundary layer dynamics and subsequently to cloud characteristics, such as their formation and vertical development. Focusing on the whole domain, Horn et al. (2015) found significant changes in domain-averaged sensible and latent heat flux when the cloud shading was considered. Yet, they did not quantify the separate contributions of direct and diffuse radiation. Although small spatial variations in surface fluxes are observed starting at the time first clouds develop (1100 UTC), we find that the domain-averaged SH and LE do not change significantly between experiments, as we account for the cloud shading in all our experiments. Domain-averaged vegetation carbon uptake shows larger differences, although still below 5% compared to the REF experiment (not shown).
The reason for smaller differences in evapotranspiration than in 
The main reason for the little difference in domain-averaged surface fluxes lies on the limited enhancement of atmosphere–vegetation exchange (less than 10% and 20% at their maxima for LE and 
Cloud optical depth at which values for LE (blue) and 
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Cloud optical depth at which values for LE (blue) and
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Cloud optical depth at which values for LE (blue) and
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Total cloud cover (black) and clouded area depending on whether 
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Total cloud cover (black) and clouded area depending on whether
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Total cloud cover (black) and clouded area depending on whether
Citation: Journal of Hydrometeorology 18, 6; 10.1175/JHM-D-16-0279.1
Given the very similar response of the surface as a whole to cloud-driven changes in radiation, the boundary layer height evolves almost identically for the three experiments. The boundary layer top starts rising from an initial height of 120 m at sunrise, around 0815 UTC. The appearance of clouds, at around 1000 UTC in our experiments, decelerates the mixed-layer growth by venting air containing high moisture and momentum within the mixed layer to higher levels (Neggers et al. 2006; van Stratum et al. 2014). The maximum boundary layer height, similar for three experiments, reaches around 1950 m at 1630 UTC (not shown). In addition, vertical profiles of potential temperature and specific humidity at the subcloud layer are almost identical between the three experiments. Domain-averaged heat and humidity fluxes along the boundary layer show small differences between experiments and are similar to previous studies (Brown et al. 2002; Siebesma et al. 2003). These findings support the results by Patton et al. (2005), who found little impact of short-scale (i.e., 2 km) surface heterogeneities on vertical flux profiles. In all experiments, first very thin convective clouds appear at around 1000 UTC. As the day evolves, cloud cover increases with shallow clouds growing larger both on horizontal and vertical scales (not shown). In the afternoon, the number of clouds decreases, although the large extension of the remaining ones keeps the cloud cover fairly similar. The cloud cover oscillates around a maximum value of almost 20% in the afternoon for the three experiments (Fig. 8 for REF), and we find a similar maximum cloud area fraction (the maximum cloud cover in a single vertical level) and maximum cloud core area fraction for the different experiments, thus suggesting that the strength of updrafts and mass flux within the clouds is not affected by changes at the surface.
The three-dimensional conditional averaging method for clouds presented in section 2d allows us to carry out a much more detailed and precise analysis on the characteristics of clouds. In Fig. 9a we show the water content of cloud and cloud cores between 1400 and 1420 UTC in the REF, DIR, and DIF experiments when the cloud cover is maximum. All experiments show a larger content on cloud cores than in clouds, as already documented in literature (Siebesma et al. 2003; Zhao and Austin 2005). The direct or diffuse character of light does not affect the properties of clouds, as shown in Fig. 9a. The differences between experiments in 
Conditional average on clouds (full) and cloud cores (dashed) of (left) liquid water mixing ratio and (right) mass flux for the REF (blue), DIR (red), and DIF (green) experiments. The profiles have been averaged between 1400 and 1420 UTC. Std dev for the temporal average is shaded.
Citation: Journal of Hydrometeorology 18, 6; 10.1175/JHM-D-16-0279.1
Conditional average on clouds (full) and cloud cores (dashed) of (left) liquid water mixing ratio and (right) mass flux for the REF (blue), DIR (red), and DIF (green) experiments. The profiles have been averaged between 1400 and 1420 UTC. Std dev for the temporal average is shaded.
Citation: Journal of Hydrometeorology 18, 6; 10.1175/JHM-D-16-0279.1
Conditional average on clouds (full) and cloud cores (dashed) of (left) liquid water mixing ratio and (right) mass flux for the REF (blue), DIR (red), and DIF (green) experiments. The profiles have been averaged between 1400 and 1420 UTC. Std dev for the temporal average is shaded.
Citation: Journal of Hydrometeorology 18, 6; 10.1175/JHM-D-16-0279.1
The differences in treatment of radiation between the experiments allow us to give an indication for future parameterizations: while the partitioning of diffuse and direct components has some impact at the surface, locally affecting the surface fluxes and vegetation performance, it does not noticeably impact the dynamics of the boundary layer and the formation of low convective clouds.
The additional LAI5 experiment yields a lower boundary layer, cloud height, and slightly larger water content on clouds (not shown) than for lower LAI (REF experiment). These differences are driven by the larger transpiration due to a denser canopy. Although domain-averaged surface fluxes are very similar between AER and REF, all clouds after 1300 UTC reduce the latent heat flux compared to clear sky in AER. This is due to the very narrow enhanced regime for LE in AER. We find a slightly lower ABL height and very similar cloud cover and cloud characteristics for this additional experiment.
4. Summarized conclusions and recommendations
By coupling radiation, surface and turbulence processes in the Dutch Atmospheric Large-Eddy Simulation (DALES), we study the effects of direct and diffuse radiation in a diurnal boundary layer over vegetation. We pay special attention to how the direct and diffuse partitioning perturbed by clouds is further disturbed in the canopy, modifying photosynthesis, plant evapotranspiration, and sensible heat flux. We design three idealized experiments to clarify the role of diffuse and direct radiation at the vegetated canopy, boundary layer, and clouds under free convective conditions (no mean horizontal wind). To disentangle the effects of cloud thickness on direct and diffuse radiation, we apply a conditional averaging at the surface dependent on the cloud optical depth above.
By calculating the radiative transfer in clouds with the delta-Eddington radiative scheme, we find a decrease in total radiation at the surface under all cloud thicknesses. The fraction of diffuse radiation, however, increases for thin clouds and peaks at values of cloud optical depth between 1 and 8, typical values for shallow cumulus clouds. The sensitivity of radiation to cloud optical depth leads to different partitions of direct and diffuse radiation at the canopy top, which has an impact on the transfer of radiation inside the canopy, as diffuse radiation has larger penetrative capacity. In consequence, vegetation resistance is reduced under very thin clouds (as much as 11% at 1200 UTC), thus allowing for a larger exchange of water vapor (latent heat flux) and CO2 (vegetation carbon assimilation). We find a compensating effect between thin and thick clouds over the domain: thin clouds enhance the latent heat flux and photosynthesis, whereas thick clouds decrease them. Diffuse radiation from clouds is also responsible for the photosynthesis-driven increase in water use efficiency and evaporative fraction compared to the case when all radiation is direct.
To support the DALES results, we perform an offline analysis using an atmospheric mixed-layer model to isolate and break up the complexity on the response of vegetation to prescribed cloud shading. We find changes in stomatal opening to lead the increased carbon uptake under very thin clouds. The CO2 gradient between the leaf and its environment and the aerodynamic resistance are of secondary relevance. Yet, they effectively reduce the enhancement of carbon uptake under very thin clouds.
As for the impact of dynamic surface heterogeneities on the boundary layer structures, diffuse radiation does not play a relevant role in our experiments: similar domain-averaged latent and sensible heat fluxes, boundary layer heights, and cloud characteristics are found regardless of the character of radiation under clouds. Slightly larger differences are found for domain-averaged carbon uptake, although below 5%. The reduced difference in domain-averaged responses to diffuse radiation has several reasons. At its maximum, the latent heat flux and carbon assimilation enhancement is 10% and 20% for thin clouds. In addition, the regime for cloud thickness under which we observe an enhanced exchange is restricted and short lived. As a consequence, we observe a smaller area over which the enhanced evapotranspiration and carbon uptake are present (a maximum of 8% and 13% of the whole surface, respectively). In addition, the area under which latent heat flux and carbon uptake are reduced is comparable or larger than the enhanced area, especially in the afternoon, thus compensating the effect of thin clouds by thick clouds. All factors combined limit the sensitivity of domain-averaged boundary layer and cloud dynamics to direct and diffuse radiation.
We extend our study by performing sensitivity analysis to various canopy conditions (LAI) and atmospheric conditions (background diffuse radiation). It is found that an increase in LAI, in our study from 2 to 5, raises evapotranspiration, thus lowering boundary layer and cloud-base height and slightly increasing the water content on clouds. However, the increase in LAI does not change the sensitivity of the canopy to cloud optical properties. In the experiment accounting for background diffuse radiation, the enhanced activity under thin clouds is dampened, but the main features of the reference experiment remain.
Our findings invite investigations under a wider range of meteorological and plant conditions. The response of vegetation is very likely to change under water-stress conditions or different temperature or water content in the atmosphere. A more realistic behavior of plants would include a gradual response of stomata to changing light conditions, which may affect the surface fluxes. Further research should include the variations in longwave radiation due to clouds, as they may lay on the order of the enhanced and decreased surface fluxes due to shading. In addition, a study of the shaded surface, paying attention to local vertical motions, could provide a more complete understanding of the local effects of diffuse radiation in the boundary layer. Numerical experiments with background wind or a more realistic (noninstantaneous) light response of vegetation would contribute to the understanding on the role of diffuse radiation. An assessment of the sensitivity of our results to the leaf angle distribution in the plant physiological model would be of interest for a better understanding of the role of the canopy in the system. Furthermore, the low cloud cover characteristic of shallow cumulus situations (maximum of 20% and restricted to less than 3 h in this study) limits the impact of cloud-dependent surface fluxes on the boundary layer. Thus, different results are possible on more sensitive cases, such as a boundary layer topped by stratocumulus. The optical depths of stratocumulus are usually constrained to τ < 20 and do not reach locally as high values as those for certain shallow cumulus, while the cloud cover can be much larger than in our study. Although in stratocumulus clouds the updrafts are not the trigger for clouds, they do play a role in the evolution of the cloud layer and its breakup. Thus, diffuse and direct radiation partition may be relevant in the evolution of a stratocumulus-topped boundary layer. Finally, our results, located in midlatitudes, may differ from those closer to the equator with smaller zenith angles, and thus larger amounts of diffuse radiation for thin clouds, as well as a wider range of cloud optical depths with significant diffuse radiation.
Acknowledgments
The authors acknowledge the valuable comments and suggestions by three anonymous reviewers. The numerical simulations were performed with the supercomputer facilities at SURFsara and financially sponsored by the Netherlands Organisation for Scientific Research (NWO) Physical Science Division (project number SH-312-15). This study was supported by the grant from the NWO ALW Open Programme (824.15.013). The main conclusions of this study were presented at an international conference thanks to the partial funding by the “Fonds Landbouw Export-Bureau 1916/1918” foundation.
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