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    Functions used to control the strength of the relaxation in (a) the atmosphere [see Eq. (2)] and (b) the soil.

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    (a) Temperature profile (°C) for the CTL simulation (solid black line), STABLE (dashed black line), and UNSTABLE (dashed–dotted black line) and profiles for zonal wind (m s−1, gray solid line) and meridional wind (m s−1, gray dashed line). (b) Profiles of relative humidity (%) for DRY (dotted line), CTL (solid line), and WET (dashed line). RH1 and RH2 [cf. Eq. (3)] are shown by the gray lines. (c) Profiles of soil saturation (%, solid line) and soil temperature (K, dashed line).

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    Time series of domain mean values of (a) the vertical mean temperature (°C), (b) pressure (hPa) in the lowest atmospheric layer, (c) surface precipitation rate (mm h−1), (d) soil saturation (%) of the uppermost 0.5-cm-deep soil layer (solid line) and lowest hydrologically active layer (dashed line), and (e) soil temperature (K) of the uppermost soil layer (solid line) and the lowest hydrologically active layer (dashed line). The lowest hydrologically active layer is situated at 1.47-m depth.

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    Profiles of (a) specific humidity (g kg−1), (b) temperature (°C), (c) zonal wind (solid) and meridional wind (dashed line) (m s−1), and (d) soil moisture saturation S (%) as a function of soil depth. Black lines show the prescribed profiles; gray shading simulates hourly values for the CTL simulation averaged over the computational domain.

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    Clouds (gray shading), surface precipitation (colored shading, mm h−1), upward velocity at 860 hPa (red contour lines), and horizontal wind field at 977 hPa (black arrows) at (a) 1530, (b)1830, and (c) 2130 UTC at day 23 of the simulation. A cloud is identified by QC > 10−6 kg kg−1 somewhere in the vertical column above. Upward velocity was determined by w > 0.2 m s−1.

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    Mean diurnal cycle of (a) specific cloud water content (kg kg−1, shaded area), specific cloud ice content (kg kg−1, contour lines), and surface precipitation (mm h−1, solid black line; the variability of the domain mean value over the 15 days is indicated by the black shading showing minimum and maximum values); (b) convective mass flux (shaded area, kg m−2 s−1); (c) surface net shortwave radiation (SW, solid line), longwave net radiation (LW, dashed line), sensible heat flux (H, dotted line) and latent heat flux (LE, dashed–dotted line) in W m−2; (d) CAPE (J kg−1); and (e) CIN (J kg−1), with domain mean values in black and mean of cloudy profiles in gray. Mean values are shown with solid lines; the 10th and 90th percentiles are dashed. The 10th and 90th percentiles were calculated by considering all grid points at all 15 days at each time of the day. (f) Height of the domain mean value (solid line) and 10th and 90th percentiles (dashed lines) of the LCL (black line) and the LFC (gray line). All panels are for the CTL simulation. Averages are taken here and in the following figures over days 16–30 and over the computational domain except where differences are noted.

  • View in gallery

    Mean diurnal cycle of normalized saturation deficit [cf. Eq. (5)] with the 0.01 g kg−1 contour line of cloud condensate (black line) for CTL.

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    Vertical profiles of domain mean values of relative humidity (%) at (a) 0000 and (b) 1000 UTC for DRY, CTL, WET, DRY_CST, CTL_CST, and WET_CST.

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    (top) Mean diurnal cycle of specific cloud water content (kg kg−1, shaded area), cloud ice content (kg kg−1, contour lines), and domain mean surface precipitation (mm h−1, black solid line; minimum and maximum values over the 15 days of simulation are indicated by dark gray shading). The number in the lower left corner gives the mean daily precipitation amount (mm h−1). (bottom) Mean diurnal cycle of convective mass flux (kg m−2 s−1, shaded area).

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    Domain mean specific cloud water content (kg kg−1, shaded area), specific cloud ice content (kg kg−1, contour lines), and surface precipitation (mm h−1, solid black line) for (a) CTL and (b) WET during the first three days.

  • View in gallery

    As in Fig. 9, but for simulations using height-independent relaxation: (a),(d) DRY_CST, (b),(e) CTL_CST, and (c),(f) WET_CST.

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    As in Fig. 9, but for (a),(d) STABLE, (b),(e) CTL, and (c),(f) UNSTABLE.

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    (a) Mean diurnal cycle of surface precipitation (mm h−1, solid lines) and the variability of the domain mean value over the 15 days (shading indicating the range between minimum and maximum values). (b) Vertical profiles of domain mean potential temperature (K) for days 16–30 of the simulation for the STABLE (black), CTL (blue), and UNSTABLE (red) simulations.

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    Vertical profiles of domain mean values of relative humidity (%) at (a) 0000 and (b) 1200 UTC for STABLE, CTL, and UNSTABLE.

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    Skew T–logp diagram of the domain mean values at 0600 UTC averaged over the 15 days of the simulation of STABLE (black) and UNSTABLE (red). The dashed lines indicate a parcel ascent computed from the values at the lowest atmospheric level.

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An Idealized Cloud-Resolving Framework for the Study of Midlatitude Diurnal Convection over Land

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  • 1 Institute for Atmospheric and Climate Science, ETH Zurich, Zurich, Switzerland
  • | 2 Department of Atmospheric Sciences, University of Washington, Seattle, Washington
  • | 3 Institute for Atmospheric and Climate Science, ETH Zurich, Zurich, Switzerland
  • | 4 Department of Atmospheric Sciences, University of Washington, Seattle, Washington
  • | 5 Institute for Atmospheric and Climate Science, ETH Zurich, Zurich, Switzerland
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Abstract

This paper introduces an idealized cloud-resolving modeling (CRM) framework for the study of midlatitude diurnal convection over land. The framework is used to study the feedbacks among soil, boundary layer, and diurnal convection. It includes a setup with explicit convection and a full set of parameterizations. Predicted variables are constantly relaxed toward prescribed atmospheric profiles and soil conditions. The relaxation is weak in the lower troposphere and upper soil to allow the development of a realistic diurnal planetary boundary layer. The model is run to its own equilibrium (30 days).

The framework is able to produce a realistic timing of the diurnal cycle of convection. It also confirms the development of deeper convection in a more unstably stratified atmosphere.

With this relaxation method, the simulated “diurnal equilibrium convection” determines the humidity profile of the lower atmosphere, and the simulation becomes insensitive to the reference humidity profile. However, if a faster relaxation time is used in the lower troposphere, the convection and rainfall become much more sensitive to the reference humidity, consistent with previous studies.

Corresponding author address: Linda Schlemmer, Institute for Atmospheric and Climate Science, ETH Zurich, 8092 Zurich, Switzerland. E-mail: linda.schlemmer@env.ethz.ch

Abstract

This paper introduces an idealized cloud-resolving modeling (CRM) framework for the study of midlatitude diurnal convection over land. The framework is used to study the feedbacks among soil, boundary layer, and diurnal convection. It includes a setup with explicit convection and a full set of parameterizations. Predicted variables are constantly relaxed toward prescribed atmospheric profiles and soil conditions. The relaxation is weak in the lower troposphere and upper soil to allow the development of a realistic diurnal planetary boundary layer. The model is run to its own equilibrium (30 days).

The framework is able to produce a realistic timing of the diurnal cycle of convection. It also confirms the development of deeper convection in a more unstably stratified atmosphere.

With this relaxation method, the simulated “diurnal equilibrium convection” determines the humidity profile of the lower atmosphere, and the simulation becomes insensitive to the reference humidity profile. However, if a faster relaxation time is used in the lower troposphere, the convection and rainfall become much more sensitive to the reference humidity, consistent with previous studies.

Corresponding author address: Linda Schlemmer, Institute for Atmospheric and Climate Science, ETH Zurich, 8092 Zurich, Switzerland. E-mail: linda.schlemmer@env.ethz.ch

1. Introduction

Convection plays a key role in weather and climate through its impact on the water and energy balance of the earth. Numerical models have well-known problems with the simulation of convection (e.g., Yang and Slingo 2001; Arakawa 2004). On weather time scales, convection is considered the prime reason for the large difficulties with warm-season, short-term quantitative precipitation forecasting (Fritsch and Carbone 2004). On climate time scales, the inability of current climate models to represent organized tropical convection is viewed as a major stumbling block in providing confident projections of future climates (Yang and Slingo 2001; Randall et al. 2003; Arakawa 2004; Slingo et al. 2009). Even for key aggregate parameters such as climate sensitivity, associated cloud feedbacks are the largest source of intermodel differences (Bony et al. 2006).

While much of the current research on moist convection focuses on tropical convective systems over sea, recent studies demonstrate that the understanding and simulation of extratropical convection over land needs urgently to be improved. For instance, simulations of present-day and future climates performed with a range of regional climate models (RCMs) over Europe have revealed large differences between simulated precipitation patterns (Christensen et al. 2007). The discrepancies are especially large in summer, when synoptic-scale forcing is weak and thus the influence of the chosen physical model parameterization formulation is large (Vidale et al. 2003; Déqué et al. 2007; Beniston et al. 2007). Summer precipitation is to a large degree determined by moist convection, traditionally represented in RCMs by convective parameterization schemes. An intercomparison of different parameterizations shows that large difficulties exist in the technical formulation of such schemes (e.g., Molinari and Dudek 1992). Many convective schemes also exhibit a too early onset and peak of deep, precipitating convection (Dai et al. 1999; Bechtold et al. 2004; Guichard et al. 2004). Brockhaus et al. (2008) noted that, even in multisummer averages of precipitation over Europe, a strong model shift appears in the convective precipitation peak (3–7 h too early), as well as an incorrect humidity profile.

The increasing computer power allows the use of models with finer grid spacing. The increased resolution enables a more realistic representation of topography and surface fields. Most importantly, the finer grid and the nonhydrostatic model formulation render possible an explicit treatment of convective processes. In numerical weather prediction (NWP), such cloud-resolving models (CRMs) are more and more used on a routine basis (see, e.g., Hohenegger and Schär 2007). In NWP the quality of forecasts can generally be improved using higher resolution (Mass et al. 2002; Done et al. 2004). In a recent study, Hohenegger et al. (2008) have applied a CRM on a monthly time scale. These simulations showed very encouraging results. The overall precipitation distribution and evolution were well captured and improved as compared to simulations using parameterized convection. They also showed in a further study that, for this case, CRMs and models using parameterized convection do not agree in their representation of the soil moisture–precipitation feedback (Hohenegger et al. 2009).

CRMs can also be used to better understand the physical mechanisms underlying moist convection and thus ultimately to help improve convective parameterizations (Randall et al. 2003). Idealized studies of convective processes using CRMs in midlatitude continental regions have mostly been forced with observations (e.g., Xu et al. 2002; Chaboureau et al. 2004; Guichard et al. 2004; Grabowski et al. 2006). The CRMs are relaxed toward observed profiles while at the surface fluxes of latent and sensible heat are prescribed. The response of convection over sea to different idealized atmospheric humidity contents has been investigated by Derbyshire et al. (2004). They found a strong impact of midtropospheric humidity on the depth of convection. Dry midtropospheric profiles are able to suppress deep convection entirely by strong entrainment of dry air into convective plumes. Wu et al. (2009) performed two-dimensional idealized studies of moist convection over land to investigate the impact of both humidity and stability on the transition from shallow to deep convection and found deeper clouds both for moister and more unstable soundings. The transition from shallow to deep convection also occurred earlier in these cases.

The aim of the current study is to investigate the sensitivity of moist convection over land to atmospheric stability and humidity. We extend previous work by using a full set of parameterizations including radiation, boundary layer processes, and a soil model to calculate surface heat and moisture fluxes. This setup allows the study of the coupled land surface–atmosphere system. Unlike Wu et al. (2009), we employ a 3D geometry, and unlike most previous studies we investigate convection in the model’s equilibrium. Here the model is no longer in the spinup phase and the upper soil layers are in equilibrium with the atmosphere. The only enforced constraints are the conditions in the upper troposphere and in the lower soil. After extended integration time, a quasi-equilibrium state is reached. Here the term “equilibrium state” does not mean that convection is in equilibrium with the large-scale forcing as defined by Arakawa and Schubert (1974); rather the evolving convection shows a strong diurnal cycle that is distinct from a radiative–convective equilibrium (Manabe and Strickler 1964) and also from equilibrium convection over land as defined by Done et al. (2006). Instead the model is allowed to attain a state where the diurnal cycle repeats itself from day to day. We use the term “diurnal equilibrium” for this state in the following. The boundary layer is enabled to develop into a state where, integrated over the diurnal cycle, the surface latent heat flux balances precipitation and the drying from subsidence, while the surface sensible heat fluxes and subsidence warming are balanced by net radiative cooling as well as evaporative cooling from falling precipitation and warming from condensation (Betts 2000). We will compare this diurnal equilibrium convection with the convection during the first days, when the model has not yet reached its equilibrium. Noteworthy for land surfaces is the strong diurnal cycle of surface fluxes and the fact that it needs a certain time until soil and atmosphere are in equilibrium. In studies of convection over prescribed sea surface temperatures [e.g., as done in Derbyshire et al. (2004)], we expect the equilibrium to be reached more quickly than over land surfaces. Convection will also be more continuous over sea surfaces as the diurnal cycle of heat fluxes is considerably weaker.

The paper is organized as follows. In section 2 we describe the setup of the experiment and the model used. The control simulation and the sensitivity experiments that test the role of tropospheric humidity and stability are presented in section 3. Finally the results are presented in section 4.

2. Experimental setup

a. Model description

The simulations are performed with version 4.0 of the Consortium for Small-Scale Modeling (COSMO) Model in Climate Mode (CCLM). The CCLM is a nonhydrostatic limited-area model that numerically solves the fully compressible equations for a moist atmosphere using the split-explicit approach (see especially Wicker and Skamarock 1998; Steppeler et al. 2003; Doms and Förstner 2004). The model has been validated both at grid spacings of 0.22° and 0.44° (Jaeger et al. 2008) and cloud-resolving scales (Δx = 2.2 km) (Hohenegger et al. 2008).

In our simulations the horizontal grid spacing is Δx = 2.2 km and the large time step 20 s. We refer to the grid spacing of 2.2 km as a cloud-resolving model in the sense that it is able to adequately represent vertical fluxes of heat, moisture, and momentum associated with organized deep convection (see, e.g., Weisman et al. 1997). However, we do not claim to resolve single convective clouds. The computational domain comprises 100 × 100 grid points and 50 vertical levels. In the vertical, a Gal-Chen coordinate (Gal-Chen and Somerville 1975) is used with a grid spacing of 20 m in the lowest levels and ∼400 m in the middle troposphere. Double-periodic lateral boundary conditions are employed. At the upper boundary a Rayleigh damping sponge layer starting at a height of 12 km is used to absorb gravity waves.

A third-order Runge–Kutta scheme is utilized for the time integration (see Förstner and Doms 2004) with a fifth-order advection scheme for horizontal and vertical winds, temperature, and pressure and a second-order Bott scheme (Bott 1989) for horizontal advection of moist quantities. Coriolis forces are set to zero and the spherical geometry is neglected. Disregarding the Coriolis forces, we might miss some enhancement of convection through organization of individual cells into mesoscale convective systems (e.g., Skamarock et al. 1994), but we simplify the setup to ensure consistent lateral boundary conditions.

The model is run with a full parameterization package including a radiation scheme after Ritter and Geleyn (1992), a prognostic turbulent energy-based scheme for turbulent diffusion of order 1.5 (see Raschendorfer 2001) based on Mellor and Yamada (1974), a turbulent kinetic energy-based surface layer scheme (Mironov and Raschendorfer 2001), and a five-category microphysics bulk scheme described in Reinhardt and Seifert (2006) considering prognostic cloud water, cloud ice, rain, graupel, and snow. Furthermore, a subgrid-scale cloud scheme affecting radiation and turbulence is utilized. The model includes a subgrid-scale shallow convection scheme, but this is switched off for the current simulations. To simulate the interactions between the atmosphere and the underlying soil, the multilayer soil model TERRA_ML after Heise et al. (2003) with 10 layers is used with a depth of the uppermost layer of 1 cm. The upper seven soil layers down to a depth of 1.47 m are hydrologically active and the lowest three layers are climatic layers. The soil type is set to loam. Vegetation is parameterized by prescribing plant cover (0.84), leaf-area index (2.96), and root depth (0.56 m) characteristic for European conditions. The surface roughness length is set to 0.0387 m. Evapotranspiration includes bare soil evaporation, evaporation from the interception reservoir, and transpiration from vegetation. The formulation of the terms closely follows the Biosphere–Atmosphere Transfer Scheme (BATS; Dickinson 1984).

The elevation of the surface is set to 489.0 m corresponding to the altitude of Munich. Incoming solar radiation is determined according to 48.25°N, 0°E on 12 July throughout the whole simulation. The model is initialized with a single vertical sounding prescribing temperature, specific humidity, and the horizontal wind components (see section 2c for further details). White noise is applied to the initial temperature at the lowest layer with a maximum amplitude of ±0.02 K to break the symmetry of the initial conditions. The model is run for 30 days.

b. Relaxation method

Our aim is to represent diurnal convection over land in a doubly periodic computational domain. Conceptually we can think of the moist convection interacting with large-scale synoptic forcing as well as boundary layer, radiative, and land surface processes. In our modeling framework the large-scale forcing is represented by relaxing the simulated atmosphere toward an externally prescribed profile, while the other processes are explicitly simulated.

We relax the mean model state toward the prescribed atmospheric profiles using a height-dependent strength of the relaxation with weak and strong relaxation in the lower and upper troposphere, respectively. The reason behind this choice is as follows. First, in the absence of large-scale perturbations, near-surface conditions are primarily controlled by boundary layer and convective parameters, while the upper tropospheric conditions are more nonlocally controlled by horizontal advection by strong winds and deep gravity wave adjustment. Indeed, the general increase of the horizontal wind with height implies stronger advective tendencies at high altitudes. Second, as we include the full sequence of model parameterizations in our framework, we do not merely address the role of convection in some atmospheric environment, but rather the full interaction between the soil and the atmosphere. The relaxation of the lower-tropospheric conditions toward a prescribed profile would thus be difficult to justify, in particular as we allow for a strong diurnal cycle over continental land surfaces. This strong diurnal cycle is in contrast to the diurnal cycle over tropical oceans, where it is much weaker and heat fluxes from the surface are dominated by latent heating.

As our modeling framework includes a soil model, a similar relaxation strategy is also applied here. We relax the soil toward prescribed profiles of soil water content with smaller relaxation coefficients in the upper soil layers. Overall, the system studied corresponds to forcing the system by relaxing in the upper atmosphere and lower soil, while the relevant physical processes are allowed to determine the properties and diurnal cycle near the soil–atmosphere interface.

The height-dependent relaxation is implemented by an additional term that is added to the right-hand side of the prognostic equations:
e1
e2
where Xref are the values of the reference profile (see section 2c), is the domain-mean values of the predicted variables, p is the pressure, T is the temperature, Qv is the specific humidity, U is the zonal wind, V is the meridional wind, and erf is the error function defined as . We set p0 to 500 hPa and b to 300 hPa, yielding the relaxation profile illustrated in Fig. 1a. A relaxation time constant τ of 1 day is chosen. The same profiles are used as input and reference profiles toward which the simulations are relaxed.
Fig. 1.
Fig. 1.

Functions used to control the strength of the relaxation in (a) the atmosphere [see Eq. (2)] and (b) the soil.

Citation: Journal of the Atmospheric Sciences 68, 5; 10.1175/2010JAS3640.1

Soil moisture is relaxed in a similar way to balance gravitational and surface runoff and to restore water that was evaporated into the atmosphere. The chosen relaxation profile is shown in Fig. 1b, where τsoil is set to 2 days. Deep soil temperature remains approximately constant without relaxation and is thus not relaxed.

c. Input and reference profile

We use idealized profiles to drive our simulations. The profiles are motivated by radio soundings from Munich over 12–15 July 2006 and zonal mean climatologies valid at 48°N for summer conditions from Peixoto and Oort (1992). For temperature (Fig. 2a, black lines), a linear decrease with height and constant values above 12 200 m are assumed. Relative humidity in the troposphere (Fig. 2b) is modeled based on the climatology of Peixoto and Oort (1996). The best fit to these profiles is obtained by combining two tanh functions as follows:
e3
where z is the height; RH1 and RH2, the relative humidity in the lower and upper troposphere respectively, are the parameters to be varied in a sensitivity experiment (see below). In the stratosphere we assume a relative humidity of RH3 = 10%. Zonal wind (Fig. 2a, gray solid line) is based on Oort and Peixoto (1983) and is constructed using two quadratic functions. In the troposphere westerly winds increase with height from 2 m s−1 at the surface to their maximum value of 17.5 m s−1 at 200 hPa, as shown in Fig. 2a. In the stratosphere we assume a transition to easterly winds consistent with summer conditions. Meridional winds are set to 0.
Fig. 2.
Fig. 2.

(a) Temperature profile (°C) for the CTL simulation (solid black line), STABLE (dashed black line), and UNSTABLE (dashed–dotted black line) and profiles for zonal wind (m s−1, gray solid line) and meridional wind (m s−1, gray dashed line). (b) Profiles of relative humidity (%) for DRY (dotted line), CTL (solid line), and WET (dashed line). RH1 and RH2 [cf. Eq. (3)] are shown by the gray lines. (c) Profiles of soil saturation (%, solid line) and soil temperature (K, dashed line).

Citation: Journal of the Atmospheric Sciences 68, 5; 10.1175/2010JAS3640.1

The reference soil moisture saturation S amounts to 60% at the surface, increasing to 100% at a depth of 2.50 m following a quadratic function (see Fig. 2c, solid line). The soil temperature is constructed assuming a surface temperature of 18°C, a yearly mean temperature of 8°C at a depth of 12 m, and a linear decrease between these two values (Fig. 2c, dashed line).

To test how convection reacts to a changed humidity content of the lower and middle troposphere the simulations DRY, CTL, and WET are performed, where RH1 and RH2 are changed (values are given in Table 1). To investigate the role of the lower troposphere a fundamentally different set of simulations (DRY_CST, CTL_CST, and WET_CST) is carried out where the relaxation strength is height independent, meaning f(p) = 1 for all values of p. Otherwise, they use the same settings as DRY, CTL, and WET, respectively. To investigate the effect of atmospheric stability on the diurnal cycle of convection the three simulations STABLE, CTL, and UNSTABLE with changed temperature lapse rate are performed (see Table 1).

Table 1.

RH1, RH2, dT/dz, CAPE, CIN, and precipitable water values for the input/reference profiles of the different simulations. The simulations DRY_CST, CTL_CST, and WET_CST use the same settings as DRY, CTL, and WET but are performed with a height-independent, constant relaxation coefficient.

Table 1.
Table 2.

Mean values of precipitation, vertically integrated mass flux, and surface sensible and latent heat flux averaged over days 16–30 for all experiments.

Table 2.

Values for convective available potential energy (CAPE), convective inhibition (CIN) (see, e.g., Emanuel et al. 1994), and precipitable water content for the different input/reference profiles are given in Table 1. As expected, the WET simulations exhibit larger CAPE, smaller CIN values, and more precipitable water than the DRY simulations. Note that CAPE increases with decreasing stability and increasing humidity. Values for precipitable water are largest for the stable soundings as the middle and upper troposphere is warmest in these profiles. With a given value for relative humidity, this results in the largest water amounts.

3. Results

a. The control simulation

In this section we describe the characteristics of the control simulation with a lapse rate of −0.7 K (100 m)−1, and relative humidities of 70% in the lower troposphere and 40% in the upper troposphere (see section 2c). Figure 3 shows simulated time series of the vertical mean temperature, pressure, surface precipitation rate, soil temperature, and soil saturation averaged over the computational domain. As can be clearly seen, diurnal equilibrium is reached after 16 days. This conclusion also holds for other variables. Hence, days 16–30 of the simulation are used to evaluate the mean diurnal cycle of convection. The 15 days can be thought of as an ensemble where each day is a realization of the same experiment with slightly varied initial conditions.

Fig. 3.
Fig. 3.

Time series of domain mean values of (a) the vertical mean temperature (°C), (b) pressure (hPa) in the lowest atmospheric layer, (c) surface precipitation rate (mm h−1), (d) soil saturation (%) of the uppermost 0.5-cm-deep soil layer (solid line) and lowest hydrologically active layer (dashed line), and (e) soil temperature (K) of the uppermost soil layer (solid line) and the lowest hydrologically active layer (dashed line). The lowest hydrologically active layer is situated at 1.47-m depth.

Citation: Journal of the Atmospheric Sciences 68, 5; 10.1175/2010JAS3640.1

The ability of the relaxation to constrain the profiles in the upper troposphere and the deeper soil is demonstrated in Fig. 4 for specific humidity, temperature, wind, and soil water content. The simulated values are close to the reference profile in the upper troposphere and stratosphere but show a strong diurnal cycle in the lower troposphere. Convection furthermore transports low zonal momentum into the upper troposphere. Zonal winds are therefore reduced between 200 and 400 hPa and increased below (Fig. 4c). Soil moisture saturation (Fig. 4d) shows a strong diurnal cycle in the uppermost layer and nearly constant values in the lowest hydrologically active layer.

Fig. 4.
Fig. 4.

Profiles of (a) specific humidity (g kg−1), (b) temperature (°C), (c) zonal wind (solid) and meridional wind (dashed line) (m s−1), and (d) soil moisture saturation S (%) as a function of soil depth. Black lines show the prescribed profiles; gray shading simulates hourly values for the CTL simulation averaged over the computational domain.

Citation: Journal of the Atmospheric Sciences 68, 5; 10.1175/2010JAS3640.1

Figure 5 shows clouds (gray shading), surface precipitation (colored shading), upward velocity (red contour lines), and horizontal winds (black arrows) at different times of the day to illustrate the structure of the ongoing convection. Narrow updraft regions with the vertical velocity w > 0.2 m s−1 and convergence of horizontal winds are visible. Clouds are mostly collocated with those updraft regions. The location of surface precipitation is shifted with respect to the clouds. Regions with divergent wind field caused by the downdrafts due to evaporative cooling of falling precipitation are furthermore visible. Downdraft regions occupy a considerably larger space than updraft regions. At 1530 UTC deep convection is in an early stage with a large number of updraft regions and small precipitation amounts reaching the surface. At 1830 UTC convection is very active with organized updraft and downdraft regions, whereas at 2130 UTC the number of updrafts is decreased but precipitation continues to fall from remaining passive clouds.

Fig. 5.
Fig. 5.

Clouds (gray shading), surface precipitation (colored shading, mm h−1), upward velocity at 860 hPa (red contour lines), and horizontal wind field at 977 hPa (black arrows) at (a) 1530, (b)1830, and (c) 2130 UTC at day 23 of the simulation. A cloud is identified by QC > 10−6 kg kg−1 somewhere in the vertical column above. Upward velocity was determined by w > 0.2 m s−1.

Citation: Journal of the Atmospheric Sciences 68, 5; 10.1175/2010JAS3640.1

Specific cloud water (QC) and cloud ice content (QI) (Fig. 6a) show a distinct diurnal cycle. In the early morning there is a thin midlevel cloud cover and some thin ice clouds (domain mean value of QC and QI < 10−6 kg kg−1) remaining from convection of the previous day, presumably amplified by radiative cooling. In the early afternoon (1430 UTC) deep convection and precipitation is simulated. Deep convection continues for 5–6 h until clouds decay in the evening. Convective mass flux (Fig. 6b) shows a comparable picture. Convective mass flux Mc was calculated (see, e.g., Robe and Emanuel 1996):
e4
where A is the domain and ρ the density of moist air. As a result of the convection a pronounced diurnal cycle of precipitation is simulated (Fig. 6a, black shaded area). The onset of precipitation coincides with the point in time when clouds reach their maximum depth and ice formation sets in. The precipitation peaks at 1730 UTC and daily area-mean precipitation sums are 3.4 mm. The day-to-day variability is small. Precipitation peak time varies by 2 h and precipitation amounts by a factor of 1.6. The domain mean hourly peak rate of 0.9 mm h−1 is at the upper end of the range of simulated values of Guichard et al. (2004), who performed idealized simulations of the diurnal cycle of deep precipitating convection over land with a range of CRMs and single-column models (SCMs).
Fig. 6.
Fig. 6.

Mean diurnal cycle of (a) specific cloud water content (kg kg−1, shaded area), specific cloud ice content (kg kg−1, contour lines), and surface precipitation (mm h−1, solid black line; the variability of the domain mean value over the 15 days is indicated by the black shading showing minimum and maximum values); (b) convective mass flux (shaded area, kg m−2 s−1); (c) surface net shortwave radiation (SW, solid line), longwave net radiation (LW, dashed line), sensible heat flux (H, dotted line) and latent heat flux (LE, dashed–dotted line) in W m−2; (d) CAPE (J kg−1); and (e) CIN (J kg−1), with domain mean values in black and mean of cloudy profiles in gray. Mean values are shown with solid lines; the 10th and 90th percentiles are dashed. The 10th and 90th percentiles were calculated by considering all grid points at all 15 days at each time of the day. (f) Height of the domain mean value (solid line) and 10th and 90th percentiles (dashed lines) of the LCL (black line) and the LFC (gray line). All panels are for the CTL simulation. Averages are taken here and in the following figures over days 16–30 and over the computational domain except where differences are noted.

Citation: Journal of the Atmospheric Sciences 68, 5; 10.1175/2010JAS3640.1

Incoming net shortwave radiation (Fig. 6c, solid line) is the primary driver of the diurnal cycle. The heating of the surface leads to sensible and latent heat fluxes (Fig. 6, dotted and dashed–dotted lines), which activate the growth and moistening of the planetary boundary layer (PBL). Latent heat fluxes are larger than sensible heat fluxes, leading to an average Bowen ratio around 0.4. The simulated values agree well with observed values from the Global Energy and Water Cycle Experiment (GEWEX) Cloud System Study (GCSS) WG4 case 3 (continental convection over the southern Great Plains) intercomparison project (Xu et al. 2002). This is valid both for the surface net radiation (shortwave plus longwave) and the sensible and latent heat fluxes.

Figures 6d and 6e show the diurnal cycle of CAPE and CIN values, and Fig. 6f shows the height of the level of free convection (LFC), the lifting condensation level (LCL), and the PBL. CAPE and CIN values are calculated assuming a mixed layer extending over the lowest 150 hPa. The height of the PBL was determined using the bulk Richardson method. Values of 0.33 under stable conditions (Wetzel 1982) and of 0.22 under convective conditions (Vogelzang and Holtslag 1996) were used as thresholds. To estimate the spatial variability we additionally include the 10th and 90th percentile of the values with a separation between cloudy profiles (QC >10−6 kg kg−1) and the mean value over all points. Not surprisingly, the mean value of CAPE at cloudy points is much smaller than the mean over the whole domain as active convection reduces CAPE at these spots. CAPE reaches a maximum around 1430 UTC, 3 h before the precipitation peak. The maximum amounts to 1500 J kg−1, which is much larger than the CAPE values of the input profile (see Table 1). Thereafter CAPE starts to decrease and becomes comparable to the CAPE of the reference profile.

CIN (see Fig. 6e) starts to decrease already from 0600 UTC onward and falls below 10 J kg−1 around 1200 UTC. The onset of convection roughly coincides with the time when the descending LFC reaches the LCL (see Fig. 6f). As to be expected, there is large spatial variability; already at 1130 UTC the 90th percentile of the LCL and the 10th percentile of the LFC coincide (Fig. 6f). Remarkably, it takes another 3 h for deep convection to develop (see Fig. 6a). One must consider that CIN calculations do not take into account the dilution of ascending parcels, which delays convection. This dilution of plumes could explain why air remains subsaturated and clouds are absent despite small CIN amounts. The increase in CIN from 1500 UTC onward both in the environment and under cloudy points does not limit precipitation activity as for most cloudy points CIN remains zero. PBL height is shown by the dark gray line in Fig. 6f. Its 90th percentile approaches the LFC already at 1300 UTC, while the domain mean value of the ascending PBL height and the descending LFC never reach each other.

The simulated diurnal cycle compares well with observations and earlier studies (e.g., Chaboureau et al. 2004); the only difference is the apparent absence of shallow convection. To clarify ongoing processes we calculate the normalized saturation deficit (NSD) (see Fig. 7) as introduced by Chaboureau et al. (2004):
e5
where r is the mixing ratio, rsat the saturation mixing ratio, and the standard deviation of the saturation deficit rsatr. The saturation deficit is determined by calculating for each hour of the day the mean of the saturation deficit over all points in the domain and all 15 evaluation days. The standard deviation is determined as a function of height using all values in the domain over all 15 evaluation days for each time of the day. Reduced values of the NSD indicate both a moistening of the air by diluting ascending parcels (numerator) and an increased mixing between moist boundary layer air and dry environmental air from above (denominator).
Fig. 7.
Fig. 7.

Mean diurnal cycle of normalized saturation deficit [cf. Eq. (5)] with the 0.01 g kg−1 contour line of cloud condensate (black line) for CTL.

Citation: Journal of the Atmospheric Sciences 68, 5; 10.1175/2010JAS3640.1

In CTL a tongue of reduced values of NSD is present ahead of the presence of cloud condensate from about 1100 UTC (Fig. 7). The tongue of reduced values of NSD indicates that the top of the PBL is approaching saturation as the PBL deepens, a process inherent to shallow convection. Shallow clouds, however, are not simulated, in contrast to the simulations of Chaboureau et al. (2004, see their Fig. 5).

The simulated diurnal cycle corresponds to the expected convective development over the midlatitude continental area in case of weak synoptic-scale forcing. Overall we conclude that the model is able to simulate a reasonable diurnal cycle of convection.

b. Sensitivity experiments

In the following we present the sensitivity experiments introduced in section 2c in order to investigate how the diurnal convection reacts to changes in relative humidity and static stability as well as the role of the relaxation. The simulations are summarized in Table 2.

1) Sensitivity to humidity and role of relaxation

We perform three simulations to investigate the sensitivity of convection to the relative humidity: DRY, CTL, and WET (see Fig. 2b). The three sensitivity experiments use relative humidity values between 60% and 80% in the lower troposphere and between 30% and 50% in the upper troposphere. Figure 8 shows simulated profiles of relative humidity at 0000 and 1000 UTC. Most prominently, the predicted equilibrium values of relative humidity differ only by a few percent among the CTL, WET, and DRY simulations (black lines), despite large differences in the prescribed humidity profiles. Also, the diurnal cycles of cloud water content, ice content, and precipitation in Fig. 9 show strikingly similar diurnal cycles. Likewise, 2-m temperature, 2-m dewpoint depression, and surface heat fluxes are remarkably insensitive to changes in prescribed humidity (not shown).

Fig. 8.
Fig. 8.

Vertical profiles of domain mean values of relative humidity (%) at (a) 0000 and (b) 1000 UTC for DRY, CTL, WET, DRY_CST, CTL_CST, and WET_CST.

Citation: Journal of the Atmospheric Sciences 68, 5; 10.1175/2010JAS3640.1

Fig. 9.
Fig. 9.

(top) Mean diurnal cycle of specific cloud water content (kg kg−1, shaded area), cloud ice content (kg kg−1, contour lines), and domain mean surface precipitation (mm h−1, black solid line; minimum and maximum values over the 15 days of simulation are indicated by dark gray shading). The number in the lower left corner gives the mean daily precipitation amount (mm h−1). (bottom) Mean diurnal cycle of convective mass flux (kg m−2 s−1, shaded area).

Citation: Journal of the Atmospheric Sciences 68, 5; 10.1175/2010JAS3640.1

Results thus show that the evolving diurnal equilibrium state in the lower troposphere is mostly independent of the prescribed moisture profile. This is in contrast to previous studies (e.g., Wu et al. 2009). Using short-term integrations, these studies documented a pronounced sensitivity of convection to environmental humidity. To understand the reasons behind our results we investigate the first phase of the simulations, when the model is not yet in a diurnal equilibrium state. Figure 10 shows the evolutions of cloud water, cloud ice, and surface precipitation during the first three days for CTL and WET. The development of clouds and mass fluxes is considerably delayed in CTL compared to WET during the first day of the simulation. This is in accordance with earlier studies (e.g., Derbyshire et al. 2004; Wu et al. 2009). The entrainment of dry air into ascending plumes delays the deepening of convection. In addition, cloud bases are lower in WET. Already at day three, differences become small as convection has redistributed the moisture in the atmosphere. Latent and sensible heat fluxes explain how the different simulations approach each other. CTL has larger latent heat fluxes than WET, which help to moisten the lower atmosphere (not shown). It is further interesting to note that during the first day of the simulation, shallow convection is simulated in both settings, while on subsequent days the atmosphere is already sufficiently moistened by the convection of the previous day and an immediate transition to deep convection is possible.

Fig. 10.
Fig. 10.

Domain mean specific cloud water content (kg kg−1, shaded area), specific cloud ice content (kg kg−1, contour lines), and surface precipitation (mm h−1, solid black line) for (a) CTL and (b) WET during the first three days.

Citation: Journal of the Atmospheric Sciences 68, 5; 10.1175/2010JAS3640.1

The results show that the simulations are able to “build” their own PBL structure and cloud fields, irrespective of the prescribed humidity profiles. We test this by limiting the freedom of the model in a set of simulations with height-independent relaxation [f (p) = 1 everywhere; see section 2c]. This height-independent relaxation corresponds to a strong external forcing throughout the whole troposphere.

With uniform relaxation the humidity is forced to stay close to the given profile, even in the lower layers. Figure 11 shows the resulting clouds, precipitation, and convective mass fluxes. The resulting diurnal equilibrium state now differs in WET_CST, CTL_CST, and DRY_CST. With the dry profile, the onset of cloud formation is delayed by half an hour, the cloud base is shifted upward (from ∼850 hPa in CTL to ∼820 hPa in DRY_CST), the cloud top is lowered, convective mass fluxes (Figs. 11d–f) start later (1330 UTC in DRY_CST, 1300 UTC in CTL_CST, and 1230 UTC in WET_CST) and are less intense, the onset of precipitation (Figs. 11a–c, black shaded area) is delayed, and the precipitation amounts are reduced.

Fig. 11.
Fig. 11.

As in Fig. 9, but for simulations using height-independent relaxation: (a),(d) DRY_CST, (b),(e) CTL_CST, and (c),(f) WET_CST.

Citation: Journal of the Atmospheric Sciences 68, 5; 10.1175/2010JAS3640.1

The domain mean vertical profiles of relative humidity at 0000 and 1000 UTC are shown in Fig. 8 by the gray lines. In agreement with Fig. 11 and in opposition to WET, CTL, and DRY, they differ among WET_CST, CTL_CST, and DRY_CST and are largest for WET_CST. The unforced profiles (WET, CST, and DRY) show a peak in relative humidity higher up than the forced simulations. The low-level humid layer that has evolved in both the forced and unforced simulations at 1000 UTC is at a similar height in all simulations. It corresponds to the top of the PBL. This humid layer will eventually become moister and reach saturation (not shown). Saturation will first be reached in the WET_CST simulation.

In summary, the simulations demonstrate that the influence of humidity depends on the relaxation strategy when considering the feedback between the land and the atmosphere. With weak relaxation in the lower troposphere, it is soil moisture and the PBL that ultimately control low-level humidity and thus convective activity.

We also performed additional simulations with height-dependent relaxation and profiles where the relative humidity is changed only in the upper troposphere. The change of humidity in the upper troposphere has negligible influence on the convection (not shown). Humidity is transported upward from the soil into the lower and then upper troposphere. This transport dominates the moistening/drying by relaxation.

2) Sensitivity to the vertical stability

As detailed in section 2c we perform three simulations to investigate the sensitivity of convection to the static stability: STABLE, CTL, and UNSTABLE (see also Fig. 2a). All simulations use the same relative-humidity profile with RH1 = 70% and RH2 = 40% but different temperature profiles.

Figure 12 shows the diurnal cycle of cloud water and cloud ice content, precipitation, and convective mass fluxes for the three simulations. The stability of the atmosphere has a decisive influence on the ability of convection to develop. Cloud tops are considerably higher in UNSTABLE (reaching up to ∼130 hPa) and shallower (reaching up to ∼210 hPa) in STABLE. In STABLE, deep clouds start to develop already at 1230 UTC, convective mass fluxes set in at 1230 UTC (Fig. 12f), cloud bases are shifted downward, and the onset and peak of precipitation are slightly advanced. Surface precipitation for the three simulations is shown in Fig. 13a. The day-to-day variability of the peak time varies between 1.5 h in STABLE and 2 h in CTL and UNSTABLE. In UNSTABLE the onset of convective mass fluxes is delayed to 1430 UTC (1400 UTC in CTL), mass fluxes reach up higher, and the base is shifted upward.

Fig. 12.
Fig. 12.

As in Fig. 9, but for (a),(d) STABLE, (b),(e) CTL, and (c),(f) UNSTABLE.

Citation: Journal of the Atmospheric Sciences 68, 5; 10.1175/2010JAS3640.1

Fig. 13.
Fig. 13.

(a) Mean diurnal cycle of surface precipitation (mm h−1, solid lines) and the variability of the domain mean value over the 15 days (shading indicating the range between minimum and maximum values). (b) Vertical profiles of domain mean potential temperature (K) for days 16–30 of the simulation for the STABLE (black), CTL (blue), and UNSTABLE (red) simulations.

Citation: Journal of the Atmospheric Sciences 68, 5; 10.1175/2010JAS3640.1

Vertical profiles of domain mean relative humidity at 0000 and 1200 UTC are shown in Fig. 14 and a skew T–logp diagram at 0600 UTC is shown in Fig. 15. In STABLE, boundary layer moisture is larger, leading to a lower LCL and LFC. The higher PBL moisture content in STABLE reduces outgoing longwave radiation and leads to warmer early-morning near-surface temperatures. As a consequence the LCL coincides with the LFC earlier, which explains the earlier onset of convection (see Fig. 6f for CTL). The level of neutral buoyancy (LNB) is also lower in STABLE and the freezing level is shifted upward due to the smaller lapse rate. Therefore only relatively small amounts of ice clouds are simulated. Because of the thicker midlevel cloud cover in STABLE in the morning, the maximum sensible heat flux is reduced by ∼35 W m−2 and maximum latent heat fluxes is reduced by 20 W m−2 in comparison to CTL (not shown). This reduction in evapotranspiration can explain reduced precipitation amounts in STABLE (cf. Table 2).

Fig. 14.
Fig. 14.

Vertical profiles of domain mean values of relative humidity (%) at (a) 0000 and (b) 1200 UTC for STABLE, CTL, and UNSTABLE.

Citation: Journal of the Atmospheric Sciences 68, 5; 10.1175/2010JAS3640.1

Fig. 15.
Fig. 15.

Skew T–logp diagram of the domain mean values at 0600 UTC averaged over the 15 days of the simulation of STABLE (black) and UNSTABLE (red). The dashed lines indicate a parcel ascent computed from the values at the lowest atmospheric level.

Citation: Journal of the Atmospheric Sciences 68, 5; 10.1175/2010JAS3640.1

As can be seen in Fig. 12, UNSTABLE exhibits the deepest clouds with most ice formation. This is in agreement with the findings of Wu et al. (2009) and Derbyshire et al. (2004). The buildup of clouds is delayed compared to the CTL simulation as the LCL and LFC are considerably higher in the morning. This upward shift of the LCL and LFC is caused by drier low-level conditions. The deepening of the PBL is, however, faster in the UNSTABLE simulation as a smaller temperature gradient needs to be overcome and sensible heat fluxes are larger than in CTL (not shown). Convection starts when the growing PBL coincides with the LFC and it is more intense in UNSTABLE when it finally starts. Despite pronounced differences in convective activity, the overall amount of precipitation is comparable between CTL and UNSTABLE. The reduction in STABLE can be explained by the reduction in evapotranspiration.

Our simulations are able to replicate a significant time delay between maximum net radiation at the surface (at local noon) and the development of convective precipitation (in the afternoon or evening) (e.g., Bechtold et al. 2004). While a detailed analysis would require additional studies, the current simulations are suggestive of the following hypothesis: The simulations confirm that convection is initiated within the diurnal cycle once the descending level of free convection meets the ascending lifting condensation level (Fig. 6f). Both the LFC and LCL changes depend in complex manners upon the accumulation of sensible and latent surface heat fluxes in the PBL. As the accumulation of heat and moisture plays the decisive role (rather than merely the instantaneous fluxes), it is not surprising that a time delay between peak surface radiation and convection occurs. The complexity of the underlying interactions (which in particular involves the growth of a well-mixed boundary layer) allows for a considerable case-to-case sensitivity. Indeed, the different simulations exhibit very different delays. For instance, UNSTABLE has peak precipitation at 2100 UTC, much later than STABLE where it occurs at 1600 UTC (see Fig. 13a).

In opposition to the role of humidity, the evolving state of diurnal equilibrium is dependent on the stability of the atmosphere. The relaxation, however, acts on both humidity and temperature to maintain the desired profile. Why do the simulations preserve the different temperature profiles but not the different moisture profiles?

Figure 13b shows simulated vertical profiles of potential temperature for STABLE, CTL, and UNSTABLE. The simulations have the same surface temperatures at the initial time, but the different temperature gradients imply different temperatures at the tropopause level. During the simulation temperatures are fixed at the tropopause level through the relaxation. Diurnal mean temperatures in the lower troposphere warm by 7.6 K in STABLE relative to the reference profile, but only by 2.4 K in UNSTABLE. The difference in stability between simulations throughout the whole troposphere thereby becomes smaller during the spinup phase but still remains.

Despite the modified stability, the colder upper-tropospheric temperatures in UNSTABLE certainly also have an influence on the precipitation intensity through the larger amount of ice clouds and the latent heat of freezing that is released (e.g., Houze 1993, chapter 8).

From a moisture budget perspective the moisture sink due to the relaxation is small in the simulations with different reference relative humidity profiles but the same temperature profiles (∼17% of the evapotranspiration in CTL). The upper troposphere where the adjustment is active is dry, while the temperature adjustment is working similarly in all three cases. Furthermore, all simulations except the _CST cases have similar mean rainfall rates, corresponding in energy units to about 100 W m−2. This is also understandable from a budget perspective because the latent heat flux is about 130 W m−2, and the adjustment sink of moisture is small, so the rainfall has to nearly balance the surface evaporation. The surface evaporation rate in turn is controlled by the net radiative flux into the surface and the soil moisture. The former is roughly the same in all cases despite some differences in clouds (most pronounced in STABLE). The latter will respond to the mean precipitation, which is similar in all cases. Thus, we do not expect much difference in the mean precipitation between the cases, even those in which static stability is changed. The exception is the _CST cases for which the moisture adjustment sink can be much stronger because it includes a large lower-tropospheric contribution.

4. Summary

We have presented a novel method to study the interaction of the land surface with the atmosphere in convective weather regimes lasting over several days. These regimes are characterized by weak pressure gradients and weak advection in the lower and middle troposphere, whereas stronger advection prevails in the upper troposphere. We simulated such convective regimes using a cloud-resolving model (CRM) in an idealized setting. The effect of the large-scale forcing was prescribed by relaxing temperature, specific humidity, and horizontal wind fields toward a steady-state background profile. The specified relaxation is weak in the lower troposphere, allowing the model to simulate its own boundary layer, land atmosphere exchange, and convection, and strong in the upper troposphere and stratosphere, representing the strong forcing due to upper-level advection. Unlike previous studies we simulated the long-term behavior of the system by coupling a soil model to the atmospheric model and including all relevant parameterizations. The soil water content was relaxed more strongly in the deeper layers to balance gravitational runoff. We let the model run into its equilibrium and evaluated the diurnal convection in this state of diurnal equilibrium.

Our idealized CRM produces a realistic timing of the diurnal cycle of precipitation, convective mass fluxes, clouds, and heat fluxes. Sensitivity tests on the response of convection to variations in static stability show deeper convection in a more unstable environment. This is in agreement with buoyancy principles and earlier studies. The onset and peak of precipitation are also shifted to later times in a more unstable environment, but precipitation amounts remain nearly unchanged.

A change of the prescribed humidity profile, however, has only negligible impacts on convection. In the model equilibrium the convection (determined by the static stability) and evaporation determine the moisture content of the lower atmosphere. This moisture content then regulates the timing and intensity of the diurnal convection. As a result, the external specification of the humidity profile is not necessary. If, however, the lower troposphere is constrained to the large-scale profile by using a height-independent relaxation, a strong sensitivity of convection to humidity is observed, with a later onset of convection, a shift of cloud bases to higher levels, and less precipitation in a drier atmosphere. Dry air entrainment delays the transition of shallow into deep convection considerably. This sensitivity has been described in earlier studies, but we consider it as an internal element of the interactively coupled system.

The idealized cloud-resolving framework developed here applies to multiday episodes of diurnal convection over large-scale landmasses under weak synoptic forcing. We conclude from our simulations that the stability of the atmosphere is a decisive factor regulating the strength of convection and the timing and peak amount of precipitation, while the moisture content of the atmosphere should be considered as an interactive variable rather than a control parameter.

Acknowledgments

This project has been partially funded by the Swiss National Science Foundation through NCCR Climate. The necessary computer resources for the simulations were provided by the Swiss National Supercomputing Center (CSCS) in Manno, partially in the framework of the Swiss-Alps grant. We furthermore wish to thank Daniel Lüthi and Oliver Fuhrer for giving advice using the CCLM.

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