Shallow cumulus convection = Ondiepe cumulus convectie

<font size="2">Clouds play an important role in the earth's climate. Firstly, they are important in the radiative energy budget of the global atmosphere. Clouds absorb and reflect ultraviolet solar radiation, and emit infrared radiation depending on their temperature. Secondly, an important part of the vertical transport of heat, moisture and momentum in the atmosphere is associated with the relatively strong vertical motions inside certain types of clouds, also called convective clouds. These clouds often produce intense precipitation, and play an important role in the global water cycle. In the tropics near the equator, these clouds act as the engine for whole large-scale atmospheric circulations.This thesis is concerned with clouds in the lowest few kilometers of the atmosphere surrounding the earth. This sphere is also known as the atmospheric or planetary <em>boundary layer</em> (PBL), defined as the part of the atmosphere directly influenced by the proximity of the surface of the earth. In this layer the exchange takes place of heat and moisture between the earth and the atmosphere. Basically the boundary layer is formed and maintained by vertical motions of air, known as <em>turbulence</em> . The turbulence is driven by heating of air close to the surface, and by the drag on the horizontal winds by the roughness of the earth's surface. The resulting turbulent eddies mix heat, moisture and momentum throughout the boundary layer. As rising air cools adiabatically, some eddies can get cooled so much in certain situations that water droplets form inside them, forming cumuliform clouds. This type of clouds is the main subject of this thesis. More specifically, the research is focused on <em>shallow cumulus</em> clouds, also known as <em>fair-weather</em> cumulus.Because of their important role in the earth's radiative budget and in the vertical transport of air, it is essential for weather and climate prediction modelling to know where, when and to what extent cumuliform clouds occur. Since a few decades ago numerical models for the general circulation are used to make weather and climate predictions. Despite the rapid developments in supercomputing, the typical spatial and temporal resolutions used in state of the art models are still as large as 30 to 50km. These grid-spacings are still much too large to realistically resolve shallow cumulus clouds, as their dimensions are in the order of a few kilometers at maximum. Nevertheless, their strength lies in their numbers, as these clouds typically occur in whole populations covering large areas of the globe. In order to represent the impact of these clouds on the general atmospheric circulation which is to be resolved by the models, it is necessary to implement simplified formulas which mimic the presence of shallow cumulus clouds. This technique is known as <em>parameterization.</em> These formulations typically are dependent on a few relevant meteorological parameters. Due to the complexity of this problem much effort has already been put in the scientific research on cumulus convection.In parameterizations for cumulus it is custom to separate the modeling of turbulent transport in the cloud layer and in the dry air below the clouds. This often leads to unwanted interactions of the modeling of these mechanisms in the lower atmosphere. The purpose of the research project behind this thesis was twofold: firstly to comprehend and model the exchange of air between the subcloud layer and the cumulus clouds, and secondly to quantify and model the mixing of this ventilated air over the cloud layer. Associated with this approach is a study of the typical turbulent and geometrical variability of cumulus cloud populations. The research is performed using observations of natural cumulus clouds by aircraft, surface-based meteorological instrumentation, remote sensing devices on satellites and cloud radar. To supplement these datasets which are often scarce and incomplete on important points, use is also made of high-resolution numerical models for atmospheric flow, also known as <em>large-eddy simulation</em> . These models simulate a domain of ten by ten by five kilometers, including whole populations of cumulus clouds. These simulated fields are used as a virtual laboratory to study cumulus convection.Large-eddy simulation results on shallow cumulus convection are directly evaluated against detailed cloud observations in Chapter 3, using aircraft-measurements of the Small Cumulus Microphysics Study (SCMS) as well as high-resolution Landsat images. The results show that given the correct initial and boundary conditions the LES concept is capable of realistically predicting the bulk thermodynamic properties of temperature, moisture and liquid water content of the cumulus cloud ensemble as observed in SCMS. Furthermore the vertical component of the in-cloud turbulent kinetic energy and the cloud size distribution in LES were in agreement with the observations. Several hypotheses which make use of conditionally sampled fields were tested on the SCMS data. The magnitudes and the decrease with height of the bulk entrainmen t rate following from the SCMS data confirm the typical values first suggested by Siebesma and Cuijpers (1995) using LES results on the Barbados Oceanic and Meteorological Experiment (BOMEX). An alternative formulation of the lateral entrainment rate as a function of the liquid water content and the mean lapse rate agrees well with the original form based on the conserved variables. Applying the simplified equation for the cloud vertica l velocity by Simpson and Wiggert (1969) to the aircraft-measurements results in a reasonably closed budget. These results support the credibility of cloud statistics as produced by LES in general, and encourage its use as a tool for testing hypotheses and developing parameterizations of shallow cumulus cloud processes.The geometrical variability of shallow cumulus cloud populations is assessed in Chapter 4 by means of calculating cloud size densities. We find a power-law scaling at the small cloud sizes and the presence of a scale break. The corresponding functional parameters have values which are typical for observed populations. The scale-break size appears to be the relevant length-scale to non-dimensionalize the cloud size, as this causes a data-collapse of the cloud size densities over several different cumulus cases. These findings suggest that a universal functional form exists for the cloud size density of shallow cumulus. A better understanding of the scale-break size is essential for for a complete definition this function. The scale-break co-determines the cloud size density, and defines the intermediate dominating size in the mass flux and cloud fraction decompositions. Its intermediate position between the largest clouds and the grid-spacing in LES implies that the clouds which do matter are resolved well by LES.In Chapter 5 the (thermo)dynamic variability of shallow cumulus is visualized by means of conserved variable diagrams, showing the joint pdfs of the conserved thermodynamic variables and (vertical) momentum. This approach inspired the formulation of a multi parcel model, meant to at least partially reproduce the joint pdfs. A new conceptual model for the lateral mixing of such an updraft-parcel is presented, based on an adjustment time-scale for the dilution of the excess of the conserved properties of this updraft parcel over its environment. A statistical analysis of many LES clouds showed that this adjustment time-scale is constant in all clouds, which implies a lateral mixing rate which is inversely proportional to the vertical velocity. This dynamical feedback between thermodynamics and vertical momentum is shown to be capable of reproducing the cloud population-average characteristics as well as the increase of the in-cloud variances with height.Chapter 6 deals with the cloud-subcloud coupling, which manifests itself in many aspects of shallow cumulus topped boundary layers, not in the last place in the turbulent variability. The parameterization of the transport properties of the simplified top-hat pdf is expressed in the mass flux model, of which the closure at cloud base represents this cloud-subcloud interaction. Three closure methods for shallow cumulus are critically examined for the difficult case of a diurnal cycle of shallow cumulus over land. First the various closures are diagnostically evaluated in a large-eddy simulation of a diurnal cycle. Subsequently they are implemented in an offline 1D model to study their impact on the development of the modelled cloudy boundary layer. Significant moistening occurs in the subcloud mixed layer in the first hours after cloud onset in LES, which makes the boundary-layer equilibrium closure Tiedtke (1989) substantially overestimate the mass flux at cloud base. As a result the boundary layer deepens unrealistically rapid at that stage in the single column model. The adjustment closure on the convective available potential energy (CAPE) of Fritsch and Chappell (1980) fails at the early and final stages of the diurnal cycle, when the cloud base transport is controlled by subcloud layer properties. The subcloud convective velocity scale closure of Grant (2001) is promising, as it reproduces the timing of both the maximum and the final decrease of the cloud base mass flux in LES. Apparently this closure catches the coupling between the two layers at cloud base. As a consequence the development of the thermodynamic structure of the boundary layer in the 1D model strongly resembles that in LES.The validation of global weather and climate models with observations in general shows that in many situations the characteristics of clouds are not represented well. Especially concerning low convective clouds it has become clear that existing parameterizations for important meteorological parameters such as cloud cover and occurrence of different type of clouds do not always give realistic results. Misrepresentations of these parameters can lead to serious deviations in the modelled circulation and climatology. It is clear that further research and development is required in this field of meteorology. The results as presented in this thesis have contributed to this in several ways. The thermodynamic variability and population statistics of cumulus cloud fields has been further charted and quantified. The interaction between shallow cumulus cloud layers and subcloud layers has been analyzed and the performance of several well-known conceptual models for this interaction has been compared. The dynamics of mixing between cumulus clouds and their environment has been studied and captured in a coneptual model. Finally, it has been shown that the cloud populations as produced by LES models have realistic cloud size statistics and thermodynamic properties.