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Chiel C. van Heerwaarden and Juan Pedro Mellado

Abstract

The growth and decay of a convective boundary layer (CBL) over a surface with a constant surface temperature that develops into a linear stratification is studied, and a mathematical model for this system is derived. The study is based on direct numerical simulations with four different Reynolds numbers; the two simulations with the largest Reynolds numbers display Reynolds number similarity, suggesting that the results can be extrapolated to the atmosphere. Because of the interplay of the growing CBL and the gradually decreasing surface buoyancy flux, the system has a complex time evolution in which integrated kinetic energy, buoyancy flux, and dissipation peak and subsequently decay. The derived model provides characteristic scales for bulk properties of the CBL. Even though the system is unsteady, self-similar vertical profiles of buoyancy, buoyancy flux, and velocity variances are recovered. There are two important implications for atmospheric modeling. First, the magnitude of the surface buoyancy flux sets the time scale of the system; thus, over a rough surface the roughness length is a key variable. Therefore, the performance of the surface model is crucial in large-eddy simulations of convection over water surfaces. Second, during the phase in which kinetic energy decays, the integrated kinetic energy never follows a power law, because the buoyancy flux and dissipation balance until the kinetic energy has almost vanished. Therefore, the applicability of power-law decay models to the afternoon transition in the atmospheric boundary layer is questionable; the presented model provides a physically sound alternative.

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Chiel C. van Heerwaarden, Juan Pedro Mellado, and Alberto De Lozar

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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Pierre Gentine, Gilles Bellon, and Chiel C. van Heerwaarden

Abstract

The inversion layer (IL) of a clear-sky, buoyancy-driven convective boundary layer is investigated using large-eddy simulations covering a wide range of convective Richardson numbers. A new model of the IL is suggested and tested. The model performs better than previous first-order models of the entrainment and provides physical insights into the main controls of the mixed-layer and IL growths. A consistent prognostic equation of the IL growth is derived, with explicit dependence on the position of the minimum buoyancy flux, convective Richardson number, and relative stratification across the inversion G. The IL model expresses the interrelationship between the position and magnitude of the minimum buoyancy flux and inversion-layer depth. These relationships emphasize why zero-order jump models of the convective boundary layer perform well under a strong inversion and show that these models miss the additional parameter G to fully characterize the entrainment process under a weak inversion. Additionally, the position of the minimum buoyancy flux within the new IL model is shown to be a key component of convective boundary layer entrainment. The new IL model is sufficiently simple to be used in numerical weather prediction or general circulation models as a way to resolve the IL in a low-vertical-resolution model.

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Chiel C. van Heerwaarden and Jordi Vilà Guerau de Arellano

Abstract

The influence of land surface heterogeneity on potential cloud formation is investigated using relative humidity as an indicator. This is done by performing numerical experiments using a large-eddy simulation model (LES). The land surface in the model was divided into two patches that had the same sum of latent and sensible heat flux but different Bowen ratios to simulate heterogeneous land surfaces. For heterogeneity in the meso-γ scale (2–20 km), sensitivity analyses were carried out on the heterogeneity amplitude (Bowen ratio difference between contrasting areas) and the inversion strength of potential temperature and specific humidity. The competition between absolute temperature decrease by ABL growth and dry air entrainment in heterogeneous conditions is analyzed using the LES results. First, it is shown that entrainment is located and enhanced over patches with higher Bowen ratios (warm patches) than their surroundings (cold patches). The heterogeneity-induced strong thermals can further penetrate the inversion at the ABL top, thereby reaching lower absolute temperatures than in homogeneous conditions. Second, because of the heterogeneity-induced circulations the moisture is located over the warm patch, and higher time-averaged RH values at the ABL top (RHzi) than over the cold patches are found here, even for dry atmospheres. These RHzi exceed values found over homogeneous land surfaces and are an indication that surface heterogeneity may facilitate cloud formation. In vertical profiles of RH, few differences are found between the homogeneous and heterogeneous cases, but the essential heterogeneity-induced modifications are within the domain variability.

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Malte Rieck, Cathy Hohenegger, and Chiel C. van Heerwaarden

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This study analyzes the effects of land surface heterogeneities at various horizontal scales on the transition from shallow to deep convection and on the cloud size distribution. An idealized case of midlatitude summertime convection is simulated by means of large-eddy simulations coupled to an interactive land surface. The transition is accelerated over heterogeneous surfaces. The simulation with an intermediate patch size of 12.8 km exhibits the fastest transition with a transition time two-thirds that over a homogeneous surface. A similar timing is observed for the precipitation onset whereas the total accumulated rainfall tends to increase with patch size. The cloud size distribution can be approximated by a power law with a scale break. The exponent of the power law is independent of the heterogeneity scale, implying a similar cloud cover between the simulations. In contrast, the scale break varies with patch size. The size of the largest clouds does not scale with the boundary layer height, although their maximum size scales with the patch size. Finally, the idea that larger clouds grow faster, known from homogeneous surface conditions, is not fully valid over heterogeneous surfaces. These various aspects can be understood from the complex interplay between the characteristics of the triggered mesoscale circulations and a cloud development acting in response to the diurnal cycle in surface heating. The results also call for adequate representation of such effects in convective parameterizations.

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Imme Benedict, Chiel C. van Heerwaarden, Ruud J. van der Ent, Albrecht H. Weerts, and Wilco Hazeleger

Abstract

Assessment of the impact of climate change on water resources over land requires knowledge on the origin of the precipitation and changes therein toward the future. We determine the origin of precipitation over the Mississippi River basin (MRB) using high-resolution (~25 km) climate model simulations for present and future climate (RCP4.5). Moisture resulting in precipitation over the MRB is tracked back in time using Eulerian offline moisture tracking, in order to find out from where this water originally evaporated (i.e., the moisture sources). We find that the most important continental moisture sources are the MRB itself and the area southwest of the basin. The two most relevant oceanic sources are the Gulf of Mexico/Caribbean and the Pacific. The distribution of sources varies per season, with more recycling of moisture within the basin during summer and more transport of moisture from the ocean toward the basin in winter. In future winters, we find an increase in moisture source from the oceans (related to higher sea surface temperatures), resulting in more precipitation over the MRB. In future summers, we find an approximately 5% decrease in moisture source from the basin itself, while the decrease in precipitation is smaller (i.e., lower recycling ratios). The results here are based on one climate model, and we do not study low-frequency climate variability. We conclude that Mississippi’s moisture sources will become less local in a future climate, with more water originating from the oceans.

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Monica Górska, Jordi Vilà-Guerau de Arellano, Margaret A. LeMone, and Chiel C. van Heerwaarden

Abstract

The effects of the horizontal variability of surface properties on the turbulent fluxes of virtual potential temperature, moisture, and carbon dioxide are investigated by combining aircraft observations with large-eddy simulations (LESs). Daytime fair-weather aircraft measurements from the 2002 International H2O Project’s 45-km Eastern Track over mixed grassland and winter wheat in southeast Kansas reveal that the western part of the atmospheric boundary layer was warmer and drier than the eastern part, with higher values of carbon dioxide to the east. The temperature and specific humidity patterns are consistent with the pattern of surface fluxes produced by the High-Resolution Land Data Assimilation System. However, the observed turbulent fluxes of virtual potential temperature, moisture, and carbon dioxide, computed as a function of longitude along the flight track, do not show a clear east–west trend. Rather, the fluxes at 70 m above ground level related better to the surface variability quantified in terms of the normalized differential vegetation index (NDVI), with strong correlation between carbon dioxide fluxes and NDVI.

A first attempt is made to estimate the ratios of the flux at the entrainment zone to the surface flux (entrainment ratios) as a function of longitude. The entrainment ratios averaged from these observations (β θυ ≈ 0.10, βq ≈ −2.4, and β CO2 ≈ −0.58) are similar to the values found from the homogeneous LES experiment with initial and boundary conditions similar to observations.

To understand how surface flux heterogeneity influences turbulent fluxes higher up, a heterogeneous LES experiment is performed in a domain with higher sensible and lower latent heat fluxes in the western half compared to the eastern half. In contrast to the aircraft measurements, the LES turbulent fluxes show a difference in magnitude between the eastern and western halves at 70 and 700 m above ground level. Possible reasons for these differences between results from LES and aircraft measurements are discussed.

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Chiel C. van Heerwaarden, Jordi Vilà-Guerau de Arellano, Amanda Gounou, Françoise Guichard, and Fleur Couvreux

Abstract

A method to analyze the daily cycle of evapotranspiration over land is presented. It quantifies the influence of external forcings, such as radiation and advection, and of internal feedbacks induced by boundary layer, surface layer, and land surface processes on evapotranspiration. It consists of a budget equation for evapotranspiration that is derived by combining a time derivative of the Penman–Monteith equation with a mixed-layer model for the convective boundary layer. Measurements and model results for days at two contrasting locations are analyzed using the method: midlatitudes (Cabauw, Netherlands) and semiarid (Niamey, Niger). The analysis shows that the time evolution of evapotranspiration is a complex interplay of forcings and feedbacks. Although evapotranspiration is initiated by radiation, it is significantly regulated by the atmospheric boundary layer and the land surface throughout the day. In both cases boundary layer feedbacks enhance the evapotranspiration up to 20 W m−2 h−1. However, in the case of Niamey this is offset by the land surface feedbacks since the soil drying reaches −30 W m−2 h−1. Remarkably, surface layer feedbacks are of negligible importance in a fully coupled system. Analysis of the boundary layer feedbacks hints at the existence of two regimes in this feedback depending on atmospheric temperature, with a gradual transition region in between the two. In the low-temperature regime specific humidity variations induced by evapotranspiration and dry-air entrainment have a strong impact on the evapotranspiration. In the high-temperature regime the impact of humidity variations is less pronounced and the effects of boundary layer feedbacks are mostly determined by temperature variations.

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Bart J. H. van Stratum, Jordi Vilà-Guerau de Arellano, Chiel C. van Heerwaarden, and Huug G. Ouwersloot
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Lennert B. Stap, Bart J. J. M. van den Hurk, Chiel C. van Heerwaarden, and Roel A. J. Neggers

Abstract

Observations have shown that differences in surface energy fluxes over grasslands and forests are amplified during heat waves. The role of land–atmosphere feedbacks in this process is still uncertain. In this study, a single-column model (SCM) is used to investigate the difference between forest and grassland in their energy response to heat waves. Three simulations for the period 2005–11 were carried out: a control run using vegetation characteristics for Cabauw (the Netherlands), a run where the vegetation is changed to 100% forest, and a run with 100% short grass as vegetation. A surface evaporation tendency equation is used to analyze the impact of the land–atmosphere feedbacks on evapotranspiration and sensible heat release under normal summer and heat wave conditions with excessive shortwave radiation.

Land–atmosphere feedbacks modify the contrast in surface energy fluxes between forest and grass, particularly during heat wave conditions. The surface resistance feedback has the largest positive impact, while boundary layer feedbacks generally tend to reduce the contrast. Overall, forests give higher air temperatures and drier atmospheres during heat waves. In offline land surface model simulations, the difference between forest and grassland during heat waves cannot be diagnosed adequately owing to the absence of boundary layer feedbacks.

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