A mass-flux cumulus parameterization scheme for large-scale models: description and test with observations

Abstract

A simple mass-flux cumulus parameterization scheme suitable for large-scale atmospheric models is presented. The scheme is based on a bulk-cloud approach and has the following properties: (1) Deep convection is launched at the level of maximum moist static energy above the top of the boundary layer. It is triggered if there is positive convective available potential energy (CAPE) and relative humidity of the air at the lifting level of convection cloud is greater than 75%; (2) Convective updrafts for mass, dry static energy, moisture, cloud liquid water and momentum are parameterized by a one-dimensional entrainment/detrainment bulk-cloud model. The lateral entrainment of the environmental air into the unstable ascending parcel before it rises to the lifting condensation level is considered. The entrainment/detrainment amount for the updraft cloud parcel is separately determined according to the increase/decrease of updraft parcel mass with altitude, and the mass change for the adiabatic ascent cloud parcel with altitude is derived from a total energy conservation equation of the whole adiabatic system in which involves the updraft cloud parcel and the environment; (3) The convective downdraft is assumed saturated and originated from the level of minimum environmental saturated equivalent potential temperature within the updraft cloud; (4) The mass flux at the base of convective cloud is determined by a closure scheme suggested by Zhang (J Geophys Res 107(D14), doi:10.1029/2001JD001005, 2002) in which the increase/decrease of CAPE due to changes of the thermodynamic states in the free troposphere resulting from convection approximately balances the decrease/increase resulting from large-scale processes. Evaluation of the proposed convection scheme is performed by using a single column model (SCM) forced by the Atmospheric Radiation Measurement Program’s (ARM) summer 1995 and 1997 Intensive Observing Period (IOP) observations, and field observations from the Global Atmospheric Research Program’s Atlantic Tropical Experiment (GATE) and the Tropical Ocean and Global Atmosphere Coupled Ocean–Atmosphere Response Experiment (TOGA COARE). The SCM can generally capture the convective events and produce a realistic timing of most events of intense precipitation although there are some biases in the strength of simulated precipitation.

Appendix

Upon lifting, an air parcel first undergoes dry adiabatic ascent up to its LCL. Below the LCL, the parcel temperature is

$$ T_{c} = T_{LB} \left( {{\frac{p}{{p_{LB} }}}} \right)^{\kappa } , $$

(51)

where k ≡ R _d /c _p . ( ) _LB denotes the variable at the parcel initial level, ( ) _c denotes variable of the ascent parcel. T is temperature in Kevin, p is pressure. The parcel humidity mixing ratio does not change during its ascent and there is q _c  = q _LB .

Above the LCL, the undiluted ascent parcel temperature T _c and moisture q _c can be determined following a moist adiabatic process. The equivalent potential temperature $\theta_{e} (T_{c} ,q_{c} ,p) = \theta \exp (L_{v} q_{c} /c_{p} T_{c} )$ is conserved under moist adiabatic processes including phase changes, in which θ is the potential temperature, L _v the latent heat of vaporization, and c _p  = 1,004.71 J kg⁻¹ the specific heat of dry air. The ascent parcel within cloud is assumed always being saturated, i.e., q _c  = q ^*(T _c ). So, there is $(\theta_{e} )_{LCL} = \theta_{e}^{*} (T_{c} )$ where (θ _e ) _LCL is the saturated equivalent potential temperature at the LCL, and

$$ \theta_{e}^{*} (T_{c} ) \equiv T_{c} \left( {{\frac{{p_{00} }}{p}}} \right)^{\kappa } \cdot \exp \left[ {{\frac{{L_{v} }}{{c_{p} }}}\frac{{q^{*} (T_{c} )}}{{T_{c} }}} \right] $$

(52)

is the saturated equivalent potential temperature. q ^*(T) denotes the saturated humidity mixing ratio with the temperature T. If (θ _e ) _LCL is known, the temperature T _c can be calculated from

$$ \theta_{e}^{*} (T_{c} ) - (\theta_{e} )_{LCL} = 0 $$

(53)

by Newton–Raphson iteration.