scholarly journals Theoretical Understanding of the Linear Relationship between Convective Updrafts and Cloud-Base Height for Shallow Cumulus Clouds. Part I: Maritime Conditions

2019 ◽  
Vol 76 (8) ◽  
pp. 2539-2558 ◽  
Author(s):  
Youtong Zheng
Keyword(s):  
Cooling Rate ◽  
Large Scale ◽  
Buoyancy Flux ◽  
Cloud Base ◽  
Radiative Cooling ◽  
Cumulus Clouds ◽  
Shallow Cumulus ◽  
Surface Buoyancy ◽  
Cloud Base Height ◽  
Surface Buoyancy Flux

Abstract Zheng and Rosenfeld found linear relationships between the convective updrafts and cloud-base height zb using ground-based observations over both land and ocean. The empirical relationships allow for a novel satellite remote sensing technique of inferring the cloud-base updrafts and cloud condensation nuclei concentration, both of which are important for understanding aerosol–cloud–climate interactions but have been notoriously difficult to retrieve from space. In Part I of a two-part study, a theoretical framework is established for understanding this empirical relationship over the ocean. Part II deals with continental cumulus clouds. Using the bulk concept of mixed-layer (ML) model for shallow cumulus, I found that this relationship arises from the conservation law of energetics that requires the radiative flux divergence of an ML to balance surface buoyancy flux. Given a certain ML radiative cooling rate per unit mass Q, a deeper ML (higher zb) undergoes more radiative cooling and requires stronger surface buoyancy flux to balance it, leading to stronger updrafts. The rate with which the updrafts vary with zb is modulated by Q. The cooling rate Q manifests strong resilience to external large-scale forcing that spans a wide range of climatology, allowing the slope of the updrafts–zb relationship to remain nearly invariant. This causes the relationship to manifest linearity. The physical mechanism underlying the resilience of Q to large-scale forcing, such as free-tropospheric moisture and sea surface temperature, is investigated through the lens of the radiative transfer theory (two-stream Schwarzschild equations) and an ML model for shallow cumulus.

The Influence of Wind Speed on Shallow Marine Cumulus Convection

2012 ◽  
Vol 69 (1) ◽  
pp. 168-184 ◽  
Author(s):  
Louise Nuijens ◽  
Bjorn Stevens
Keyword(s):  
Wind Speed ◽  
Heat Fluxes ◽  
Buoyancy Flux ◽  
Cloud Base ◽  
Cumulus Convection ◽  
Shallow Marine ◽  
Surface Moisture ◽  
Surface Buoyancy ◽  
Cloud Base Height ◽  
Surface Buoyancy Flux

Abstract The role of wind speed on shallow marine cumulus convection is explored using large-eddy simulations and concepts from bulk theory. Focusing on cases characteristic of the trades, the equilibrium trade wind layer is found to be deeper at stronger winds, with larger surface moisture fluxes and smaller surface heat fluxes. The opposing behavior of the surface fluxes is caused by more warm and dry air being mixed to the surface as the cloud layer deepens. This leads to little difference in equilibrium surface buoyancy fluxes and cloud-base mass fluxes. Shallow cumuli are deeper, but not more numerous or more energetic. The deepening response is necessary to resolve an inconsistency in the subcloud layer. This argument follows from bulk concepts and assumes that the lapse rate and flux divergence of moist-conserved variables do not change, based on simulation results. With that assumption, stronger winds and a fixed inversion height imply larger surface moisture and buoyancy fluxes (heat fluxes are small initially). The consequent moistening tends to decrease cloud-base height, which is inconsistent with a larger surface buoyancy flux that tends to increase cloud-base height, in order to maintain the buoyancy flux at cloud base at a fixed fraction of its surface value (entrainment closure). Deepening the cloud layer by increasing the inversion height resolves this inconsistency by allowing the surface buoyancy flux to remain constant without further moistening the subcloud layer. Because this explanation follows from simple bulk concepts, it is suggested that the internal dynamics (mixing) of clouds is only secondary to the deepening response.

scholarly journals Theoretical Understanding of the Linear Relationship between Convective Updrafts and Cloud-Base Height for Shallow Cumulus Clouds. Part II: Continental Conditions

2020 ◽  
Vol 77 (4) ◽  
pp. 1313-1328 ◽  
Author(s):  
Youtong Zheng ◽  
Mirjana Sakradzija ◽  
Seoung-Soo Lee ◽  
Zhanqing Li
Keyword(s):  
Empirical Relationship ◽  
Bowen Ratio ◽  
Surface Fluxes ◽  
Cloud Base ◽  
Free Atmosphere ◽  
Cumulus Clouds ◽  
Theoretical Understanding ◽  
Shallow Cumulus ◽  
Early Afternoon ◽  
Cloud Base Height

Abstracts This is the Part II of a two-part study that seeks a theoretical understanding of an empirical relationship for shallow cumulus clouds: subcloud updraft velocity covaries linearly with the cloud-base height. This work focuses on continental cumulus clouds that are more strongly forced by surface fluxes and more deviated from equilibrium than those over oceans (Part I). We use a simple analytical model for shallow cumulus that is well tested against a high-resolution (25 m in the horizontal) large-eddy simulation model. Consistent with a conventional idea, we find that surface Bowen ratio is the key variable that regulates the covariability of both parameters: under the same solar insolation, a drier surface allows for stronger buoyancy flux, triggering stronger convection that deepens the subcloud layer. We find that the slope of the Bowen-ratio-regulated relationship between the two parameters (defined as λ) is dependent on both the local time and the stability of the lower free atmosphere. The value of λ decreases with time exponentially from sunrise to early afternoon and linearly from early afternoon to sunset. The value of λ is larger in a more stable atmosphere. In addition, continental λ in the early afternoon more than doubles the oceanic λ. Validation of the theoretical results against ground observations over the Southern Great Plains shows a reasonable agreement. Physical mechanisms underlying the findings are explained from the perspective of different time scales at which updrafts and cloud-base height respond to a surface flux forcing.

scholarly journals Dynamics of Subsiding Shells in Actively Growing Clouds with Vertical Updrafts

2020 ◽  
Vol 77 (4) ◽  
pp. 1353-1369 ◽  
Author(s):  
Vishnu Nair ◽  
Thijs Heus ◽  
Maarten van Reeuwijk
Keyword(s):  
Shell Thickness ◽  
Large Scale ◽  
Cloud Environment ◽  
Initial State ◽  
Cumulus Clouds ◽  
Mean Velocity ◽  
Flow Parameters ◽  
Shallow Cumulus ◽  
Order Of Magnitude ◽  
Self Similar

Abstract The dynamics of a subsiding shell at the edges of actively growing shallow cumulus clouds with updrafts is analyzed using direct numerical simulation. The actively growing clouds have a fixed in-cloud buoyancy and velocity. Turbulent mixing and evaporative cooling at the cloud edges generate a subsiding shell that grows with time. A self-similar regime is observed for first- and second-order moments when normalized with respective maximum values. Internal scales derived from integral properties of the flow problem are identified. A self-similarity analysis using these scales reveals that contrary to classical self-similar flows, the turbulent kinetic energy budget terms and velocity moments scale according to the buoyancy and not with the mean velocity. The shell thickness is observed to increase linearly with time. The buoyancy scale remains time invariant and is set by the initial cloud–environment thermodynamics. The shell accelerates ballistically with a magnitude set by the saturation value of the buoyancy of the cloud–environment mixture. In this regime, the shell is buoyancy driven and independent of the in-cloud velocity. Relations are obtained for predicting the shell thickness and minimum velocities by linking the internal scales with external flow parameters. The values thus calculated are consistent with the thickness and velocities observed in typical shallow cumulus clouds. The entrainment coefficient is a function of the initial state of the cloud and the environment, and is shown to be on the same order of magnitude as fractional entrainment rates calculated for large-scale models.

scholarly journals Investigating the Diurnal Evolution of the Cloud Size Distribution of Continental Cumulus Convection Using Multiday LES

2019 ◽  
Vol 76 (3) ◽  
pp. 729-747 ◽  
Author(s):  
Thirza W. van Laar ◽  
Vera Schemann ◽  
Roel A. J. Neggers
Keyword(s):  
Power Law ◽  
Cloud Cover ◽  
Large Scale ◽  
Correlation Coefficients ◽  
Scale Model ◽  
Cloud Base ◽  
Size Distributions ◽  
Total Cloud Cover ◽  
Surface Precipitation ◽  
Shallow Cumulus

Abstract The diurnal dependence of cumulus cloud size distributions over land is investigated by means of an ensemble of large-eddy simulations (LESs). A total of 146 days of transient continental shallow cumulus are selected and simulated, reflecting a low midday maximum of total cloud cover, weak synoptic forcing, and the absence of strong surface precipitation. The LESs are semi-idealized, forced by large-scale model output but using an interactive surface. This multitude of cases covers a large parameter space of environmental conditions, which is necessary for identifying any diurnal dependencies in cloud size distributions. A power-law exponential function is found to describe the shape of the cloud size distributions for these days well, with the exponential component capturing the departure from power-law scaling at the larger cloud sizes. To assess what controls the largest cloud size in the distribution, the correlation coefficients between the maximum cloud size and various candidate variables reflecting the boundary layer state are computed. The strongest correlation is found between total cloud cover and maximum cloud size. Studying the size density of the cloud area revealed that larger clouds contribute most to a larger total cloud cover, and not the smaller ones. Besides cloud cover, cloud-base and cloud-top height are also found to weakly correlate with the maximum cloud size, suggesting that the classic idea of deeper boundary layers accommodating larger convective thermals still holds for shallow cumulus. Sensitivity tests reveal that the results are only minimally affected by the representation of microphysics and the output resolution.

scholarly journals Scaling Laws for the Heterogeneously Heated Free Convective Boundary Layer

2014 ◽  
Vol 71 (11) ◽  
pp. 3975-4000 ◽  
Author(s):  
Chiel C. van Heerwaarden ◽  
Juan Pedro Mellado ◽  
Alberto De Lozar
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Convective Boundary Layer ◽  
Scaling Laws ◽  
Fixed Ratio ◽  
Buoyancy Flux ◽  
Convective Boundary ◽  
Optimal State ◽  
Surface Buoyancy ◽  
Surface Buoyancy Flux

Abstract The heterogeneously heated free convective boundary layer (CBL) is investigated by means of dimensional analysis and results from large-eddy simulations (LES) and direct numerical simulations (DNS). The investigated physical model is a CBL that forms in a linearly stratified atmosphere heated from the surface by square patches with a high surface buoyancy flux. Each simulation has been run long enough to show the formation of a peak in kinetic energy, corresponding to the “optimal” heterogeneity size with strong secondary circulations, and the subsequent transition into a horizontally homogeneous CBL. Scaling laws for the time of the optimal state and transition and for the vertically integrated kinetic energy (KE) have been developed. The laws show that the optimal state and transition do not occur at a fixed ratio of the heterogeneity size to the CBL height. Instead, these occur at a higher ratio for simulations with increasing heterogeneity sizes because of the development of structures in the downward-moving air that grow faster than the CBL thickness. The moment of occurrence of the optimal state and transition are strongly related to the heterogeneity amplitude: stronger amplitudes result in an earlier optimal state and a later transition. Furthermore, a decrease in patch size combined with a compensating increase in patch surface buoyancy flux to maintain the energy input results in decreasing KE and a later transition. The simulations suggest that a CBL with a heterogeneity size smaller than the initial CBL height has less entrainment than a horizontally homogeneous CBL, whereas one with a larger heterogeneity size has more.

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