Many analytic, but approximate, expressions have been proposed for the height of the lifting condensation level (LCL), including the popular expressions by Espy, Bolton, and Lawrence. Here, the ...exact, explicit, analytic expression is derived for an air parcel’s LCL as a function of its temperature and relative humidity. Unlike previous analytic expressions, some of which can have errors as high as hundreds or thousands of meters, this exact expression is accurate to within the uncertainty of empirical vapor pressure measurements: this translates into an uncertainty of around 5 m for all temperatures and relative humidities. An exact, explicit, analytic expression for the lifting deposition level (LDL) is also derived, and its behavior is compared to the LCL. At sufficiently cold temperatures, aerosols freeze homogeneously below the LCL; an approximate, implicit, analytic expression is given for this lifting freezing level (LFL). By comparing the LCL, LDL, and LFL, it is found that a well-mixed boundary layer can have an ice-supersaturated layer that is no thicker than 400 m.
Full text
Available for:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
An analytical model is derived for tropical relative humidity using only the Clausius–Clapeyron relation, hydrostatic balance, and a bulk-plume water budget. This theory is constructed for ...radiative–convective equilibriumand compared against a cloud-resolving model. With some reinterpretation of variables, it can be applied more generally to the entire tropics.
Given four variables—pressure, temperature, and the fractional entrainment and detrainment rates—the equations predict the relative humidity (RH) and the temperature lapse rate analytically. The RH is a simple ratio involving the fractional detrainment rate and the water-vapor lapse rate. When integrated upward in height, the equations give profiles of RH and temperature for a convecting atmosphere.
The theory explains the magnitude of RH and the “C” shape of the tropospheric RH profile. It also predicts that RH is an invariant function of temperature as the atmosphere warms, and this behavior matches what has been seen in global climate models and what is demonstrated here with cloud-resolving simulations. Extending the theory to include the evaporation of hydrometeors, a lower bound is derived for the precipitation efficiency (PE) at each height: PE > 1 – RH. In a cloud-resolving simulation, this constraint is obeyed with the PE profile taking the shape of an inverted C shape.
Full text
Available for:
BFBNIB, DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
Two proxies for lightning predict very different responses to global warming: the CAPE times precipitation proxy predicts a large increase in lightning over both the continental United States and the ...tropical oceans, while the ice flux proxy predicts a small increase over the United States and a decrease over the tropical oceans. To date, however, these proxies have been studied only in global climate models with parameterized convection. Here, cloud‐resolving simulations are used to assess their predictions of future lightning rates. Over the United States, all proxies predict a large increase in the lightning rate in the range of 8–16%/K. On the other hand, in the tropics as modeled by radiative convective equilibrium, half of the proxies predict an increase (of 5–12%/K), while the other half predict a decrease (of 1–4%/K). The reasons for the different responses of these proxies is explored, but it remains unclear which proxy is best suited to predicting future lightning rates.
Key Points
Lightning proxies are studied in cloud‐resolving simulations of global warming over the United States and the tropical ocean
All the proxies predict that lightning increases over the United States in the range of 8–16% per kelvin
The proxies disagree over the tropical ocean, predicting either a substantial increase of 5–12%/K or a moderate decrease of 1–4%/K
Full text
Available for:
FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SAZU, SBCE, SBMB, UL, UM, UPUK
Lightning plays an important role in atmospheric chemistry and in the initiation of wildfires, but the impact of global warming on lightning rates is poorly constrained. Here we propose that the ...lightning flash rate is proportional to the convective available potential energy (CAPE) times the precipitation rate. Using observations, the product of CAPE and precipitation explains 77% of the variance in the time series of total cloud-to-ground lightning flashes over the contiguous United States (CONUS). Storms convert CAPE times precipitated water mass to discharged lightning energy with an efficiency of 1%. When this proxy is applied to 11 climate models, CONUS lightning strikes are predicted to increase 12 ± 5% per degree Celsius of global warming and about 50% over this century.
Full text
Available for:
BFBNIB, NMLJ, NUK, PNG, SAZU, UL, UM, UPUK
Abstract
By deriving analytical solutions to radiative–convective equilibrium (RCE), it is shown mathematically that convective available potential energy (CAPE) exhibits Clausius–Clapeyron (CC) ...scaling over a wide range of surface temperatures up to 310 K. Above 310 K, CAPE deviates from CC scaling and even decreases with warming at very high surface temperatures. At the surface temperature of the current tropics, the analytical solutions predict that CAPE increases at a rate of about 6%–7% per kelvin of surface warming. The analytical solutions also provide insight on how the tropopause height and stratospheric humidity change with warming. Changes in the tropopause height exhibit CC scaling, with the tropopause rising by about 400 m per kelvin of surface warming at current tropical temperatures and by about 1–2 km K−1 at surface temperatures in the range of 320–340 K. The specific humidity of the stratosphere exhibits super-CC scaling at temperatures moderately warmer than the current tropics. With a surface temperature of the current tropics, the stratospheric specific humidity increases by about 6% per kelvin of surface warming, but the rate of increase is as high as 30% K−1 at warmer surface temperatures.
Full text
Available for:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
Using high-resolution cloud-resolving simulations with different CO sub(2) concentrations, local precipitation fluxes are found to obey Clausius-Clapeyron (CC) scaling. Previous studies of the effect ...of CO sub(2) concentration on precipitation extremes have used general circulation models, which are poor platforms for studying tropical convection because convection is parameterized. In idealized cloud-resolving simulations, it is possible to identify not only the changes in local precipitation fluxes, but also the factors responsible for those changes. There are many properties of convection that can change as the atmosphere warms, each of which could produce deviations from CC scaling. These properties include the effective water-vapor gradient, cloud pressure depth, and cloud velocity. A simple theory is developed that predicts the changes in these properties consistent with CC scaling. Convection in the cloud-resolving simulations is found to change as predicted by this theory, leading to an 20% increase in local precipitation fluxes when the CO sub(2) concentration is doubled. Overall, an increase in CO sub(2) leads to more vigorous convection, composed of clouds that are wider, taller, and faster.
Full text
Available for:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
Even in a small domain, it can be prohibitively expensive to run cloud-resolving greenhouse gas warming experiments due to the long equilibration time. Here, a technique is introduced that reduces ...the computational cost of these experiments by an order of magnitude: instead of fixing the carbon dioxide concentration and equilibrating the sea surface temperature (SST), this technique fixes the SST and equilibrates the carbon dioxide concentration. Using this approach in a cloud-resolving model of radiative–convective equilibrium (RCE), the equilibrated SST is obtained as a continuous function of carbon dioxide concentrations spanning 1 ppmv to nearly 10 000 ppmv, revealing a dramatic increase in equilibriumclimate sensitivity (ECS) at higher temperatures. This increase in ECS is due to both an increase in forcing and a decrease in the feedback parameter. In addition, the technique is used to obtain the direct effects of carbon dioxide (i.e., the rapid adjustments) over a wide range of SSTs. Overall, the direct effect of carbon dioxide offsets a quarter of the increase in precipitation from warming, reduces the shallow cloud fraction by a small amount, and has no impact on convective available potential energy (CAPE).
Full text
Available for:
BFBNIB, DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
9.
A Direct Measure of Entrainment ROMPS, David M
Journal of the atmospheric sciences,
06/2010, Volume:
67, Issue:
6
Journal Article
Peer reviewed
Open access
A method is introduced for directly measuring convective entrainment and detrainment in a cloud-resolving simulation. This technique is used to quantify the errors in the entrainment and detrainment ...estimates obtained using the standard bulk-plume method. The bulk-plume method diagnoses these rates from the convective flux of some conserved tracer, such as total water in nonprecipitating convection. By not accounting for the variability of this tracer in clouds and in the environment, it is argued that the bulk-plume equations systematically underestimate entrainment. Using tracers with different vertical profiles, it is also shown that the bulk-plume estimates are tracer dependent and, in some cases, unphysical. The new direct-measurement technique diagnoses entrainment and detrainment at the gridcell level without any recourse to conserved tracers. Using this method in large-eddy simulations of shallow and deep convection, it is found that the bulk-plume method underestimates entrainment by roughly a factor of 2. The directly measured entrainment rates are then compared to cloud height and cloud buoyancy. Contrary to existing theories, fractional entrainment is not found to scale like the inverse of height, the cloud buoyancy, or the gradient of cloud buoyancy. On the other hand, fractional detrainment is found to scale linearly with cloud buoyancy. Finally, direct measurement is used to diagnose the spatial distribution of entrainment and detrainment during the evolution of an individual deep cumulonimbus.
Full text
Available for:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
Global climate models robustly predict that global mean precipitation should increase at roughly 2–3% K−1, but the origin of these values is not well understood. Here we develop a simple theory to ...help explain these values. This theory combines the well-known radiative constraint on precipitation, which says that condensation heating from precipitation is balanced by the net radiative cooling of the free troposphere, with an invariance of radiative cooling profiles when expressed in temperature coordinates. These two constraints yield a picture in which mean precipitation is controlled primarily by the depth of the troposphere, when measured in temperature coordinates. We develop this theory in idealized simulations of radiative–convective equilibrium and also demonstrate its applicability to global climate models.
Full text
Available for:
BFBNIB, NMLJ, NUK, PNG, SAZU, UL, UM, UPUK
PDF
