Moist Adiabat Research Articles

An Explicit One-Dimensional Time-Dependent Tilting Cloud Model

Abstract An explicit one-dimensional time-dependent tilting cloud model has been developed for use in cumulus parameterizations. The tilting axis is not necessarily orthogonal to the (r, θ) plane, making the horizontal axisymmetric assumption more reasonable. This explicit time-dependent tilting model (ETTM) consists of an updraft and a downdraft, which are governed by the same dynamic and thermodynamic equations. The updraft is initiated by a moist thermal bubble, while the downdraft is consequently induced by evaporative cooling and the drag force of precipitation separating from the tilting updraft instead of being arbitrarily initialized. The updraft is capable of reproducing the major features of a deep cloud such as overshooting cooling above the cloud top, evaporative cooling near the surface, and drying in the lower atmosphere at dissipating stages. The entrainment–detrainment rate in this model is well defined, and its time variation is quite significant. Moreover, the vertical profile of the air inside the updraft does not follow the moist adiabat after deep convection. For the downdraft, the total precipitation and mass flux at low levels contributed from the downdraft cannot be neglected in this case study. In addition, the downdraft can bring dry air from middle levels to lower levels. Three sensitivity tests—the environmental sounding, the tilting angle, and the radius of the updraft–downdraft— have also been conducted. The cooling–warming of a downdraft near the surface is sensitive to the environmental sounding, consistent with results from Srivastava. The cloud life span, maximum vertical velocity, precipitation amount, and vertical mass flux are strongly influenced by the tilting angle and the radius of the cloud. The results from the ETTM simulation are quite reasonable and promising. However, some deficiencies of this model still exist, and more research will be conducted to improve its performance. The final goal is to implement this 1D model in a mesoscale model's cumulus parameterization scheme.

Origin of Lapse Rate Changes in the Upper Tropical Troposphere

Vertical motions in clouds arise from a variety of thermodynamic processes, including latent heat release, evaporative cooling, melting, and cloud radiative heating. In the Tropics, the net upward vertical mass flux from convective systems should approximately balance subsidence in clear sky regions associated with radiative cooling, provided the exchange of mass with midlatitudes can be assumed small. Tropical climatologies of temperature, water vapor, and ozone are used to calculate the clear sky radiative mass flux, and the derivative of this mass flux with respect to potential temperature, dMr(θ)/dθ, is used as a proxy for net convective outflow. Convective outflow increases rapidly at 345 K (∼11.3 km). This corresponds to the pseudoequivalent potential temperature θe at which air parcels near the surface first attain positive convective available potential energy (CAPE). The rate at which dMr(θ)/dθ decreases above 345 K is similar to the rate at which the near surface θe probability distribution function (PDF) decreases. This behavior is referred to as “scaling.” It suggests that the timescale for removal of an air parcel from the convective boundary layer is independent of θe (once it has positive CAPE), and that the residual vertical mass flux from convective clouds can be described as if air parcels detrain near their level of neutral buoyancy (LNB). It is also suggested that the mean tropical temperature profile above 345 K is controlled, not by mixing, but by the need for the vertical variation in net convective outflow to be consistent with the near-surface θe PDF, and that this accounts for the fact that the mean temperature profile above 345 K increasingly deviates from a moist adiabat. It is also argued that there are sufficient high θe air parcels near the surface to sustain the Brewer–Dobson circulation by detrainment at the LNB followed by radiative ascent into the stratosphere.

Water's two height scales: The moist adiabat and the radiative troposphere

Water's two height scales: The moist adiabat and the radiative troposphere

Water's two height scales: The moist adiabat and the radiative troposphere

AbstractThe temperature structure of the tropical troposphere resembles a moist adiabat, with a lapse‐rate transition toward dry adiabatic where water becomes scarce at an altitude Hma ∼ 8 km (350 hPa). Infrared emission by water vapour cools a deeper layer, extending up to Hrad ∼ 14 km (160 hPa). Five consequences of these unequal heights are reviewed.1. Upper‐tropospheric relative humidity is often low, highly variable, and bimodal, due to the rapidity of drying by radiative subsidence.2. Large‐scale divergent circulations (e.g. equatorial v wind) exhibit a two‐celled vertical structure, with an elevated convergence layer near 8‐10 km in the rising branch.3. The dominant deep convective heating process changes from latent heating at low levels to eddy heat‐flux convergence in the upper troposphere. This requires a substantial updraught‐environment temperature difference, which leads to large entrainment near Hma, yielding stratiform anvil clouds which also contribute radiative heating.4. The rising branches of deep (∼Hrad) vertical circulations export more heat than they import as moisture, so that large‐scale tropical dynamics can be characterized by a ‘gross moist stability’.5. Divergent motions with a vertical wavelength ∼8 km, corresponding to Kelvin or gravity wave speeds of ∼15 m s−1, are excited by simple (e.g. uniform) heating profiles extending through the lapse‐rate change near Hma.

Tropical Cyclone Eye Thermodynamics

In intense tropical cyclones, sea level pressures at the center are 50‐100 hPa lower than outside the vortex, but only 10‐30 hPa of the total pressure fall occurs inside the eye between the eyewall and the center. Warming by dry subsidence accounts for this fraction of the total hydrostatic pressure fall. Convection in the eyewall causes the warming by doing work on the eye to force the thermally indirect subsidence. Soundings inside hurricane eyes show warm and dry air aloft, separated by an inversion from cloudy air below. Dewpoint depressions at the inversion level, typically 850‐500 hPa, are 10‐30 K rather than the ;100 K that would occur if the air descended from tropopause level without dilution by the surrounding cloud. The observed temperature and dewpoint distribution above the inversion can, however, be derived by ;100 hPa of undilute dry subsidence from an initial sounding that is somewhat more stable than a moist adiabat. It is hypothesized that the air above the inversion has remained in the eye since it was enclosed when the eyewall formed and that it has subsided at most a few kilometers. The cause of the subsidence is the enclosed air’s being drawn downward toward the inversion level as the air below it flows outward into the eyewall. Shrinkage of the eye’s volume is more than adequate to supply the volume lost as dry air is incorporated into the eyewall or converted to moist air by turbulent mixing across the eye boundary. The moist air below the inversion is in thermodynamic contact with the sea surface. Its moisture derives from evaporation of seawater inside the eye, frictional inflow of moist air under the eyewall, and from moist downdrafts induced as condensate mixes into the eye. The moist air’s residence time in the eye is much shorter than that of the dry air above the inversion. The height of the inversion is determined by the balance between evaporation, inflow, and inward mixing on one hand and loss to the eyewall updrafts on the other.

CAPE Variations in the Current Climate and in a Climate Change

Abstract Observed variations of convective available potential energy (CAPE) in the current climate provide one useful test of the performance of cumulus parameterizations used in general circulation models (GCMs). It is found that frequency distributions of tropical Pacific CAPE, as well as the dependence of CAPE on surface wet-bulb potential temperature (Θw) simulated by the Goddard Institute for Space Studies’s GCM, agree well with that observed during the Australian Monsoon Experiment period. CAPE variability in the current climate greatly overestimates climatic changes in basinwide CAPE in the tropical Pacific in response to a 2°C increase in sea surface temperature (SST) in the GCM because of the different physics involved. In the current climate, CAPE variations in space and time are dominated by regional changes in boundary layer temperature and moisture, which in turn are controlled by SST patterns and large-scale motions. Geographical thermodynamic structure variations in the middle and upper troposphere are smaller because of the canceling effects of adiabatic cooling and subsidence warming in the rising and sinking branches of the Walker and Hadley circulations. In a forced equilibrium global climate change, temperature change is fairly well constrained by the change in the moist adiabatic lapse rate and thus the upper troposphere warms to a greater extent than the surface. For this reason, climate change in CAPE is better predicted by assuming that relative humidity remains constant and that the temperature changes according to the moist adiabatic lapse rate change of a parcel with 80% relative humidity lifted from the surface. The moist adiabatic assumption is not symmetrically applicable to a warmer and colder climate: In a warmer regime moist convection determines the tropical temperature structure, but when the climate becomes colder the effect of moist convection diminishes and the large-scale dynamics and radiative processes become relatively important. Although a prediction based on the change in moist adiabat matches the GCM simulation of climate change averaged over the tropical Pacific basin, it does not match the simulation regionally because small changes in the general circulation change the local boundary layer relative humidity by 1%–2%. Thus, the prediction of regional climate change in CAPE is also dependent on subtle changes in the dynamics.

Tropical Thermostats and Low Cloud Cover

The ability of subtropical stratus low cloud cover to moderate or amplify the tropical response to climate forcing such as increased CO2 is considered. Cloud radiative forcing over the subtropics is parameterized using an empirical relation between stratus cloud cover and the difference in potential temperature between 700 mb (a level that is above the trade inversion) and the surface. This relation includes the empirical negative correlation between SST and low cloud cover and is potentially a positive feedback to climate forcing. Since potential temperature above the trade inversion varies in unison across the Tropics as a result of the large-scale circulation and because moist convection relates tropospheric temperature within the convecting region to variations in surface temperature and moisture, the subtropical potential temperature at 700 mb depends upon surface conditions within the convecting region. As a result, subtropical stratus cloud cover and the associated feedback depend upon the entire tropical climate and not just the underlying SST. A simple tropical model is constructed, consisting of separate budgets of dry static energy and moisture for the convecting region (referred to as the “warm” pool) and the subtropical descending region (the “cold” pool). The cold pool is the location of stratus low clouds in the model. Dynamics is implicitly included through the assumption that temperature above the boundary layer is horizontally uniform as a result of the large-scale circulation. The tropopause and warm pool surface are shown to be connected by a moist adiabat in the limit of vanishingly narrow convective updrafts. Stratus low cloud cover is found to be a negative feedback, increasing in response to doubled CO2 and reducing the tropically averaged warming in comparison to the warming with low cloud cover held fixed. Increased low cloud cover is shown to result from the increased difference in surface temperature between the warm and cold pools, and the increased low-level static stability over the warm pool, equal to the increase in potential temperature along the moist adiabat originating in the warm pool mixed layer.

A Test of the Strict Quasi-Equilibrium Theory on Long Time and Space Scales

Abstract Quasi-equilibrium convective parameterizations share the common assumption that in regions of sustained deep convection rates of change in convective available potential energy (CAPE) are small compared to the magnitude of the large-scale and boundary layer forcings that act to modify CAPE. The more restrictive strict quasi-equilibrium hypothesis (SQE) is that changes in CAPE are dynamically negligible. Under this assumption, tropospheric temperature and thickness variations largely follow a moist adiabat associated with variations in the boundary layer θe. SQE is an attractive simplification for theories of large-scale circulation in the Tropics but has been inadequately tested to date. In this paper, we test the SQE hypothesis over convecting regions of the tropical oceans using microwave sounding unit tropospheric temperature and precipitation fields, along with COADS surface data, on timescales of a month and longer and on space scales ranging upward from O(300 km). One prediction of SQE, tha...

Relation between Mean Boundary-Layer Structure and Cloudiness at theR/VValdiviaduring ASTEX

Abstract The relationship between boundary-layer thermodynamic structure and cloud fields and their diurnal variation are explored using seven days of data from dw R/V Valdivia during the Atlantic Stratocumulus Transition Experiment. Cloudiness is at a maximum before dawn, when the boundary layer (BL) has the thermodynamic structure of a partially mixed, conditionally unstable stratocumulus layer, which is close to mean saturation below the inversion. Cloudiness falls during the daytime, and in the late afternoon the BL has two distinct layers: a warmer, drier cloud layer (characteristic of trade cumulus) above a more well-mixed subcloud layer. The observed mean profiles are consistent with an earlier suggestion that there is a cloud-cover transition once the BL mixing-line slope exceeds half that of the moist adiabat. In contrast, the BL structure in the ECMWF model for the same week has a much drier, warmer, more stable “cloud” layer than the observations.

Convective Available Potential Energy in the Environment of Oceanic and Continental Clouds: Correction and Comments

In 1980, Zipser and LeMone estimated the convective available potential energy (CAPE) for the Thunderstorm Project cumulonimbus environment to be about 3000 J per kg. By assuming the most adiabat reported by Byers and Braham (1949) to be that of an undilute parcel rather than a reference moist adiabat, a significant error was introduced. On the basis of recent calculations made under similar conditions in Oklahoma and Florida, CAPE is now estimated to be considerably lower. These lower CAPE estimates shed doubt on the suggestion that differences in CAPE account for differences in the vertical velocities in convective updrafts over land and over the ocean.

Self-sustaining intense vortices

We seek to identify an accessible observable for anticipating tornadogenesis in mesocyclones, because such tornadoes are characterized by exceptionally extended lifespan, exceptionally long and wide path, and exceptionally high wind speed. We associate tornadogenesis with the transition from a one-cell vortex to a two-cell vortex. After such a transition, the core (“eye”) of the vortex consists of virtually nonrotating, slowly recirculating, relatively dry air. Rapidly swirling air swiftly ascends in an annulus (“eyewall”), situated at a small but finite distance from the axis of rotation. The swiftly ascending air is described by a locus of thermodynamic states well approximated by a moist adiabat. Such a transition from a one-cell vortex to a two-cell vortex, on vastly large lateral scale, is known to characterize the intensification of a tropical storm to a typhoon. We adopt a simplified, tractable model for our initial analytic efforts. We examine a quasisteady axisymmetric vortex with a four-part structure, consisting of a bulk potential vortex, a near-ground inflow layer, an “eyewall”, and an “eye”. We inquire under what conditions such a four-part intense vortex, formed in convectively unstable stratified air, is self-sustaining. In particular, we inquire whether the vertical profile of the angular momentum outside of the eyewall is a discriminant for identifying the conditions for which an intense (two-cell) vortex could be self-sustaining. Guidance from laboratory experiments would be helpful concerning the turnaround (the portion of the flow field in which the near-ground swirling inflow separates to form the swirling updraft of the eyewall annulus).

A note on the effects of virtual temperature: Research note

Abstract The effects of virtual temperature on parcel buoyancy are investigated and the following results obtained. For descent or unsaturated ascent, the buoyancy acceleration is enhanced if the mixing ratio increases with pressure. However, for saturated ascent, the buoyancy acceleration is inhibited unless the lapse rate of mixing ratio exceeds a value slightly greater than that along a moist adiabat. This criterion is evaluated for several mean soundings. For the case of Oklahoma supercells, the mixing ratio lapse rate is clearly large enough. However, for other cases it often is not. Horizontal gradients in water vapour and condensed water can have a significant influence on the thermal wind.

Atmospheric gravity waves from the impact of comet Shoemaker‐Levy 9 with Jupiter

We study the effect of the Jovian water cloud on internal gravity waves generated by the impact of comet SL9. Vertical structure follows Voyager data to the 1‐bar level, a moist adiabat from 1 to 5 bars, and a dry adiabat below the 5‐bar level. The waves are trapped in the moist layer and propagate horizontally. Their speed is related to the vertical integral of the Brunt‐Väisälä frequency, and varies as the square root of the water abundance (130 m/s for solar composition). The amplitudes are large, e.g., ±1 K at a distance of 8000 km for an energy of 1027 ergs. The circular ripples should be detectable one or two days after the impact in thermal infrared and visible images.

A Study on the “Runaway Greenhouse Effect” with a One-Dimensional Radiative–Convective Equilibrium Model

Abstract A simple one-dimensional radiative–convective equilibrium model is used to investigate the relationship between the surface temperature and the outgoing infrared radiation at the top of the atmosphere. The model atmosphere has a gray infrared absorption coefficient and is composed of a radiative equilibrium stratosphere and a moist adiabat troposphere. An upper limit of the outgoing infrared radiation is found to exist. The existence of the upper limit is characterized by the radiation limits that appear when the optical depth of the entire atmosphere becomes sufficiently deep and the temperature structure around the levels where the optical depth is about unity approaches a fixed profile. This appearance of an upper limit differs from that found by Komabayashi and Ingersoll, which is obtained from the constraint of the stratospheric radiation balance. As one of those radiation limits, the outgoing infrared radiation has an asymptotic limit as the surface temperature increases. This is caused by ...

Convective Stabilization in Midlatitudes

Abstract The upper-air sounding data from PRE-STORM are used to investigate the convective stabilization effect on the large-scale atmosphere. To facilitate comparison between different stages of cumulus convection, the data are divided into four categories: environment, presystem, insystem, and postsystem. It is found that the convective available potential energy of the atmosphere is reduced substantially after cumulus convection, most of which is consumed during the transition from presystem to insystem. Examination of the temperature and moisture changes during cumulus convection suggests that cooling and drying in the subcloud layer are the most important factors in stabilizing the atmosphere. In general, virtual potential temperature profiles in all categories are close to reversible moist adiabats below the 600-mb level and nearly parallel to moist pseudoadiabats above it. The effect of entrainment on parcel buoyancy is also studied. It is found that a small amount of entrainment of ambient air can...

Tropical Cyclone Simulations with the Betts Convective Adjustment Scheme. Part II: Sensitivity Experiments

Abstract Extensive sensitivity experiments with an axisymmetric tropical cyclone model that includes the Bets convective parameterization scheme are carded out. The sensitivity of the model storm evolution to the convective adjustment parameters is studied. These results show that the model storm leads to earlier development as the adjustment time scale becomes small and the stability weight on the moist adiabat in the lower atmosphere is increased. The model storm evolution is very sensitive to variations in the saturation pressure departure at the lowermost model integer level and the storm at mature stage has a lower central pressure as the magnitude of the saturation pressure departure is increased. The adjustment parameters affect the grid-scale precipitation as well as the convective precipitation and the precipitation is especially sensitive to changes in the saturation pressure departure. Sensitivity of the model to variations in the sea surface temperature, latitude, initial vortex amplitude, ini...

The Vertical Distribution of Heating in AMEX and GATE Cloud Clusters

Abstract Tropical cloud clusters that occurred during the Australian Monsoon Experiment (AMEX) are composited and compared to a composite of the GARP Atlantic Tropical Experiment (GATE) systems. The analysis focuses on the evolution of the life cycles and upon the vertical heating profiles. The AMEX and GATE systems were of comparable duration and magnitude, although the former produced more rainfall. However, AMEX convective systems produced maximum heating in the middle troposphere and showed only small variations in the heating with height. In contrast GATE systems began with heating concentrated in the lower troposphere and exhibited a marked upward shift in heating with time. GATE systems always had greater fractions of their total heating at lower levels than did AMEX systems, presumably due to differences in the large flow. The vertical stratification of the atmosphere in both regions resembles that of a reversible moist adiabat at lower levels and of a pseudoadiabat above the freezing level. This ...

A Numerical Study of Lapse-Rate Adjustments in the Tropical Atmosphere

Abstract Observations in the tropics have shown that the lapse rate of virtual Potential temperature θv normally resembles that of a reversible moist adiabat. In the present study, a mesoscale numerical model with parameterized convection is used to examine the adjustment to equilibrium of the tropical atmosphere in the presence of large-scale forcing. The physical processes that enable the model to produce an equilibrium lapse rate similar to what is observed are examined. The results indicate that a spectrum of cloud sizes, which is produced by a variable entrainment rate, is essential to enable the atmosphere to approach an equilibrium state of small conditional instability in the presence of large-scale destabilization. Lateral detrainment is not essential for modeling the large-scale stability of the atmosphere, despite its significance for modeling individual mesoscale convective systems. When downdrafts are removed from the parameterized convection, the model only temporarily produces a realistic l...

Thermodynamic constraint on the cloud liquid water feedback in climate models

The cloud liquid water feedback in climate models consists of the increase (decrease) in optical depth of clouds resulting from higher (lower) liquid water contents that might accompany tropospheric warming (cooling). The change in cloud liquid water with temperature is shown to depend on the rate of change of the slope of the moist adiabat with respect to temperature, and it is a strong function of temperature. The value of this rate of change in the tropics is about half that in mid and high latitudes and is much less than the value obtained by assuming that liquid water scales with the saturation mixing ratio.

Semiprognostic Tests of Kuo–Type Cumulus Parameterization Schemes in an Extratropical Convective System

Abstract Heat and moisture budgets associated with a midlatitude convective system (10–11 April 1979) are used to evaluate several versions of Kuo-type cumulus parameterization schemes on a semiprognostic basis. It is shown that the observed rainfall rate is closely related to the large-scale vertical advection of moisture and to a lesser extent to the large-scale moisture convergence. Both the Kuo and the Anthes schemes show considerable skill in reproducing the convective heating profile (Q1) when a moist adiabat is used to represent the cloud thermodynamic properties and the effect of eddy sensible heat flux is estimated by a steady-state cloud model. However, when a model cloud with a small radius is used to estimate the cloud's thermodynamic properties, both the Kuo and Authes schemes predict convective heating profiles with considerably lower levels of maximum heating than observed. This indicates that entrainment is not very important for the deep convection present in this case. Anthes' scheme is ...