Entropy Potential Temperature Research Articles

The Two‐Energies Turbulence Scheme Coupled to the Assumed PDF Method

AbstractAn update of the two‐energy turbulence scheme is presented, the 2TE + APDF scheme. The original version of the two‐energy scheme is able to successfully model shallow convection without the need of an additional parameterization for non‐local fluxes. However, the performance of the two‐energy scheme is worse in stratocumulus cases, where it tends to overestimate the erosion of the stable layers. We have identified the causes: the non‐local stability parameter does not consider local stratification, the scheme lacks an internal parameter that could distinguish between a shallow convection regime and a stratocumulus regime, and it uses an inflexible turbulence length scale formulation. To alleviate this problem, we propose several modifications: an update of the stability parameter, a modified computation of the turbulence length scale, and the introduction of the entropy potential temperature to distinguish between a shallow convection and a stratocumulus regime. In addition, the two‐energy scheme is coupled to a simplified assumed probability density function method in order to achieve a more universal representation of the cloudy regimes. The updated turbulence scheme is evaluated for several idealized cases and one selected real case in the ICOsahedral Nonhydrostatic (ICON) modeling framework. The results show that the updated scheme corrects the overmixing problem in the stratocumulus cases. The performance of the updated scheme is comparable to the operational setup, and can be thus used instead of the operational turbulence and shallow convection scheme in ICON. Additionally, the updated scheme improves the coupling with dynamics, which is beneficial for the modeling of coherent flow structures in the atmospheric boundary layer.

Towards the use of conservative thermodynamic variables in data assimilation: a case study using ground-based microwave radiometer measurements

Abstract. This study aims at introducing two conservative thermodynamic variables (moist-air entropy potential temperature and total water content) into a one-dimensional variational data assimilation system (1D-Var) to demonstrate their benefits for use in future operational assimilation schemes. This system is assessed using microwave brightness temperatures (TBs) from a ground-based radiometer installed during the SOFOG3D field campaign, dedicated to fog forecast improvement. An underlying objective is to ease the specification of background error covariance matrices that are highly dependent on weather conditions when using classical variables, making difficult the optimal retrievals of cloud and thermodynamic properties during fog conditions. Background error covariance matrices for these new conservative variables have thus been computed by an ensemble approach based on the French convective scale model AROME, for both all-weather and fog conditions. A first result shows that the use of these matrices for the new variables reduces some dependencies on the meteorological conditions (diurnal cycle, presence or not of clouds) compared to typical variables (temperature, specific humidity). Then, two 1D-Var experiments (classical vs. conservative variables) are evaluated over a full diurnal cycle characterized by a stratus-evolving radiative fog situation, using hourly TB. Results show, as expected, that TBs analysed by the 1D-Var are much closer to the observed ones than the background values for both variable choices. This is especially the case for channels sensitive to water vapour and liquid water. On the other hand, analysis increments in model space (water vapour, liquid water) show significant differences between the two sets of variables.

On Moist Potential Temperatures and Their Ability to Characterize Differences in the Properties of Air Parcels

AbstractA framework is introduced to compare moist “potential” temperatures. The equivalent potential temperatureθe, the liquid water potential temperatureθℓ, and the entropy potential temperatureθsare all shown to be potential temperatures, in the sense that they measure the temperatures of certain reference-state systems whose entropy is the same as that of the air parcel. They only differ in the choice of reference-state composition—θℓdescribes the temperature a condensate-free state,θea vapor-free state, andθsa water-free state—required to have the same entropy as the given state. Although in this senseθe,θℓ, andθsare all different flavors of the same thing, onlyθℓsatisfies the stricter definition of a “potential temperature,” as corresponding to a reference temperature accessible by an isentropic and closed transformation of a system in equilibrium; bothθeandθℓmeasure the “relative” enthalpy of an air parcel at their respective reference states, but onlyθsmeasures air-parcel entropy. None mix linearly, but all do so approximately, and all reduce to the dry potential temperatureθin the limit as the water mass fraction goes to zero. As is well known,θdoes mix linearly and inherits all the favorable (entropic, enthalpic, and potential temperature) properties of its various—but descriptively less rich—moist counterparts. All involve quite complex expressions, but admit relatively simple and useful approximations. Of the three moist “potential” temperatures,θsis the least familiar, but the most well mixed in the broader tropics, a property that merits further study as a possible basis for constraining mixing processes.

Comments on “A Third-Law Isentropic Analysis of a Simulated Hurricane”

The atmospheric overturning can be estimated by computing an isentropic streamfunction, defined as the net upward mass transport of all air parcels with the potential temperature less than a given threshold. Here, the streamfunctions for the equivalent potential temperature and the entropy potential temperature are compared in a numerical simulation of a hurricane. It is shown that, when condensate is not taken into account, the two streamfunctions are equivalent and can be related to one another by a coordinate transformation. When condensate content is included, the streamfunctions differ substantially in the upper troposphere because of the large amount of ice water found in some updrafts. It is also shown that using an equivalent potential temperature over ice avoids this problem and offers a more robust way to compute the atmospheric overturning when precipitation is included. While it has been recently recommended to limit the isentropic analysis to the entropy potential temperature, it is argued here that more insights can be gained by comparing a circulation averaged in multiple coordinates over limiting oneself to one specific choice.

Moist Potential Vorticity Vector for Diagnosis of Heavy Rainfall Events in Tanzania

In this paper, we modify the convective vorticity vector (CVV) defined as a cross product of absolute vorticity and gradient of equivalent potential temperature to moist potential vorticity vector (MPVV) defined as a cross product of absolute vorticity () and the gradient of the moist-air entropy potential temperature (). The patterns of (MPVV) are compared with the patterns of heavy rainfall events that occurred over different regions in Tanzania on 20th to 22nd December, 2011 and on 5th to 8th May, 2015. Moreover, the article aimed at assessing the relative contributions of the magnitude, horizontal and vertical components of (MPVV) detecting on the observed patterns of rainfall events. Dynamic and thermodynamic variables: wind speed, temperature, atmospheric pressure and relative humidity from numerical output generated by the Weather Research and Forecasting (WRF) model running at Tanzania Meteorological Agency (TMA) were used to compute MPVV. It is found that MPVV provide accurate tracking of locations received heavy rainfall, suggesting its potential use as a dynamic tracer for heavy rainfall events in Tanzania. Finally it is found that the first and second components of MPVV contribute almost equally in tracing locations received heavy rainfall events. The magnitude of MPVV described the locations received heavy rainfall events better than the components.

On the definition of a moist‐air potential vorticity

AbstractA new potential vorticity is derived by using a specific entropy formulation expressed in terms of a moist‐air entropy potential temperature. The new formulation is compared with Ertel's version and with others based on virtual and equivalent potential temperatures. The new potential vorticity is subject to conservative properties ensured by the Second Law applied to the moist‐air material derivatives. It is shown that the upper tropospheric and stratospheric (dry) structures are nearly the same as those obtained with Ertel's component. Moreover, new structures are observed in the low troposphere, with negative values associated with moist frontal regions. The negative values are observed in the frontal regions where slantwise convection instabilities may take place, but they are smaller than those observed with the equivalent potential vorticity. The main purpose of the article is to diagnose the behaviour of the new potential vorticity from numerical output generated by the ARPEGE NWP model, with the help of isobaric charts and vertical cross‐sections. Two inversion methods are suggested. The first method could be based on the invertibility principle verified by the virtual potential vorticity, with a possibility to control and modify separately potential vorticity components in the (dry) upper and (moist) lower atmospheric levels. The other method may consist of an inversion process directly applied to the new moist‐air entropy potential vorticity, because the negative values and the solenoidal term are smaller than those observed with equivalent potential vorticity, as shown by numerical evaluations.

On a general definition of the squared Brunt–Väisälä frequency associated with the specific moist entropy potential temperature

AbstractThe squared Brunt–Väisälä frequency (BVF) is computed in terms of the moist entropy potential temperature recently defined by Marquet (2011. Q. J. R. Meteorol. Soc. 137: 768–791). Both homogeneously saturated and non‐saturated versions of N2 (the squared BVF) are derived. The method employed for computing these special homogeneous cases relies on the expression of density written as a function of pressure, total water content and specific moist entropy only. The associated conservative variable diagrams are discussed and compared with existing ones. Despite being obtained without any simplification, the formulations for N2 remain nicely compact and are clearly linked with the squared BVF expressed in terms of the adiabatic non‐saturated and saturated lapse rates. As in previous similar expressions, the extreme homogeneous solutions for N2 are of course different, but they are not analytically discontinuous. This allows us to define a simple bridging expression for a single general shape of N2, depending only on the basic mean atmospheric quantities and on a transition parameter, to be defined (or parametrized) in connection with the type of application sought. This integrated result remains a linear combination (with complex but purely local weights) of two terms only, namely the environmental gradient of the moist entropy potential temperature and the environmental gradient of the total water content. Simplified versions of the various equations are also proposed for the case in which the moist entropy potential temperature is approximated by a function of both so‐called moist conservative variables of Betts. Copyright © 2012 Royal Meteorological Society

Definition of a moist entropy potential temperature: application to FIRE‐I data flights

AbstractA moist entropy potential temperature–denoted byθs–is defined analytically in terms of the specific entropy for moist air. The expression forθsis valid for a general mixing of dry air, water vapour and possible condensed water species. It displays the same conservative properties as the moist entropy, even for varying dry air or total water content. The moist formulation forθsis equal to the dry formulationθif dry air is considered, and it displays new properties valid for the moist air cases, both saturated or unsaturated ones. Exact and approximate versions ofθsare evaluated for several stratocumulus cases, in particular by using the aircraft observation datasets from the FIRE‐I experiment. It appears that there is no (or only a small) jump inθsat the top of the planetary boundary layer (PBL). The mixing in moist entropy is almost complete in the PBL, with the same values observed in the clear air and the cloudy regions, including the very top of the entrainment region. The Randall–Deardorff Cloud‐Top Entrainment Instability analysis may be interpreted as a mixing in moist entropy criterion. The iso‐θslines are plotted on skewT–logpand conserved variable diagrams. All these properties could suggest some hints on the use of moist entropy (orθs) in cloud modelling or in mixing processes, with the marine stratocumulus considered as a paradigm of moist turbulence. Copyright © 2011 Royal Meteorological Society