3.3
Some notes on the convective parameterizations
The focus of the present study is on simulated precipitation. The generation of precip- itation is strongly governed directly and predominantly by the convection parameter- ization. Accordingly, in chapter 4 a ’mini ensemble’ of sensitivity experiments relying on three different widely used cumulus convection schemes is presented. Thus, a short overview of the main characteristics of the respective schemes will be given in this section.
According to Kain and Fritsch their parameterization can be partitioned into three parts: the trigger function, the mass flux formulation, and the closure assumption. The scheme is triggered by adding a temperature perturbation (or effectively a perturbation of vertical velocity) to a vertical layer beginning at the surface level. If this perturbed ’parcel’ is not able to reach its lifting condensation level (LCL) the base of the potential source layer for a convective cloud is moved upwards one model level and the test gets repeated. If the LCL is reached in one of the iteration steps the unperturbed parcel is allowed to rise, while entraining and detraining, as long as its vertical velocity is positive. The depth of this convective ’test cloud’ at least has to be 4 km for the actual parameterization to be activated. Otherwise the whole sequential iteration falls back to the next test level to be perturbed. If the test parcel originates from more than 300 mbar above the surface the scheme decides on ’no convection’ and moves on to the next grid box. The trigger mechanism is closely related to the mass flux formula- tion, or rather the (single-)cloud model of the scheme, as vertical motion and thus the cloud depth is strongly controlled by entrainment and detrainment. The entraining and detraining plume exchanges equivalent potential temperature and water vapour with its environment. Furthermore various additional moisture variables can be detrained from the cloud. Entrainment rates are higher for higher parcel buoyancy and a moist environment, whereas parcels with low buoyancy are prone to get diluted rapidly into a comparatively dry ambient atmosphere by high detrainment rates. Convective down- drafts driven by evaporation of condensed water within the cloud are designed more or less analogously to the updraft. Environmental subsidence or uplifting, respectively, compensates for the convective mass fluxes, thus inducing a feedback to the large scale variables. The closure assumption bases on the removal of 90% of the convective avail- able potential energy (CAPE) that initially is calculated with respect to the undiluted parcel ascent, i.e. with constant parcel characteristics valid for the starting level of the updraft. The relaxation towards a neutral atmospheric profile is accomplished by inner-cloud and environmental mass fluxes with a time scale that ranges in between 30 and 60 minutes.
The Grell scheme is an Arakawa-Schubert (Arakawa and Schubert 1974) type scheme that resorts to an extremely simplified single cloud model not allowing for any lateral mixing with its environment. Thus the mass flux within the cloud, once determined,
remains constant in the convective process. This is also true for the convective down- draft. Detrainment into the surrounding atmosphere only occurs at the cloud top, where the updraft reaches its level of neutral buoyancy, and correspondingly for the downdraft at the surface. Feedback to the explicitly resolved variables is accomplished by compensating vertical motions of the environmental air, thus redistributing moisture and temperature according to the respective large scale vertical profiles. The closure bases on a quasi-equilibrium assumption, i.e. the effect of convection only compen- sates the rate of destabilization due to the large-scale forcing and thus the inner-cloud mass fluxes are dimensioned to match this requirement without accounting for the total amount of CAPE.
The Betts-Miller scheme also bases on the idea of a quasi-equilibrium between large- scale forcing and convection. Betts and Miller, however, deduce a significantly different approach from this assumption to tackle the effects of convective activity. Convection essentially poses a strong constraint for realistic local vertical profiles as it acts, often quite vigourously, to stabilize the atmosphere. In nature the interplay with large-scale forcing leads to certain vertical structures of moisture and temperature, characteristic for a convective environment. Hence, the Betts-Miller scheme is not focussing on the convective process itself but rather on its outcome, i.e. a target atmospheric strat- ification estimated from appropriate observations to serve as a reference state. The parameterization hence directly performs an adjustment with a fixed time constant of 50 minutes towards the predefined quasi-equilibrium vertical profiles of temperature and moisture. The adjustment thus essentially represents an implicit calculation of the effects of convective mass fluxes. Consequently, the scheme has not implemented any cloud model, such as entraining and detraining plumes. It deliberately ’ignores’ the complex processes of convection itself. This is based on the argument, that these processes are hard to observe in nature as well as hard to implement in sufficient de- tail in numerical models. Generally, the scheme depends strongly on the observational basis and on decisions on which of these observed profiles are valid and to be taken in consideration for the specific case to be simulated. Hence, this approach implies the somewhat awkward need (or convenient room—depending on the respective point of view) for calibration. This, however, should be avoided in principle as far as possible in physically based numerical models. Furthermore, corresponding to its very construc- tion, the scheme lacks the implementation of convective downdrafts that, primarily in cases of severe convection, can strongly affect the resolved atmospheric environment. Last but not least, it has originally been developed for larger scales with rather homoge- nous environments and thus might not be perfectly well suited for areas characterized by complex, fine-scale orographic features.
36 3.4. MM5: SOME MODIFICATIONS