Journal of the Meteorological Society of Japan, Vol. 83, No. 5, pp. 745--770, 2005 745 The Vertical Profile of Entrainment Rate Simulated by a Cloud-Resolving Model and Application to a Cumulus Parameterization Akihiko MURATA and Mitsuru UENO Typhoon Research Department, Meteorological Research Institute, Tsukuba, Japan (Manuscript received 8 June 2004, in final form 2 June 2005) Abstract To investigate the vertical profiles of fractional entrainment rate as to cumulus convection, numerical simulations of a tropical cyclone rainband are conducted, using a high-resolution three-dimensional cloud-resolving model (CRM), with the 200-m horizontal resolution. On the basis of the results of CRM simulations, vertically variable entrainment rate is applied to the Arakawa-Schubert (AS) cumulus pa- rameterization. Fractional entrainment rate, derived from the calculation based on the vertical gradient of cloud mass flux, clearly shows larger near cloud base and top. Between the heights of cloud base and top, en- trainment rate is smaller, and even negative in many cases, suggesting laterally detrained air from a cumulus into the environment. From the analyses where entrainment rate is divided into three terms, it is found that the contributions of updraft is relatively large near the cloud base and top, compared to that in between. The cloud amount contribution depends on whether cloudy areas expand or shrink ac- companying cloud growth or decay, respectively. On the basis of the result of the CRM simulations, vertically variable entrainment rate is applied to the AS scheme. For investigating the effect of the modifications of the scheme, simulations of typhoon Saomai (2000) are conducted. The simulations show significant improvements: underestimates of mois- ture in the mid- to upper troposphere are reduced. The result is predominantly attributed to cloud mass flux, greatly influenced by lateral detrainment. The peak height of the mass flux corresponds to that in the moisture tendency. 1. Introduction tropical cyclone, with some degree of realism, was rather insensitive to such a treatment. It Precipitation in a tropical cyclone appears to was pointed out on the other hand that numer- be sensitive to the formulation for cumulus pa- ical simulations for tropical cyclones provided a rameterization, because latent heat release is useful test for the depth of knowledge about a key factor for tropical cyclone intensification. cumulus parameterization (Ueno 2000). Smith (2000) pointed out that the details of The sensitivity of cumulus parameterization tropical cyclone evolution seemed to be sensi- to tropical cyclone simulations therefore has tive to the treatment of convection in numerical been reported by several studies. For example, models, although the simulation of a mature Baik et al. (1991) indicated a sensitivity of the time of rapid storm deepening to the choice of different convection schemes used in their nu- Corresponding author: Akihiko Murata, Meteoro- merical model. We also have investigated ef- logical Research Institute, Nagamine 1-1, Tsu- fects of a couple of cumulus parameterizations kuba, Ibaraki 305-0052, Japan. E-mail: [email protected] on tropical cyclone simulations. Murata and ( 2005, Meteorological Society of Japan Ueno (2000) investigated the effect of two major 746 Journal of the Meteorological Society of Japan Vol. 83, No. 5 cumulus parameterizations on the intensity of It has been recognized that direct observa- typhoon Flo (1990). The central pressure of the tions of the vertical profile of cloud mass flux is storm in the simulation, with a version of the useful as the truth data for cumulus parame- Arakawa-Schubert (AS) scheme (Arakawa and terization (Ooyama 1971). Yuter and Houze Schubert 1974; Kuma et al. 1993), was more (1995) determined vertical mass fluxes in Flor- realistic than that in the simulation with a ida cumulonimbus by analysis of ground-based moist convective adjustment scheme (Gadd and dual-Doppler radar data. They indicated that Keers 1970). Precipitation averaged within the entrainment of environmental air occurred core region of the storm in the former was sig- along trajectories of parcels in a cumulus and nificantly larger than that in the latter. The thereby most of the updraft parcels did not result was explained by difference in the degree reach the top of the storm, suggesting lateral that the schemes eliminated vertical static in- detrainment from the cumulus into the envi- stability. The degree of the elimination was ronment. Grinnel et al. (1996) examined the also a key factor for representation of a promi- vertical mass flux profile of Hawaiian trade cu- nent rainband in the tropical cyclone (Murata muli, using two ground-based Doppler radars et al. 2003). The vertical instability was exces- and an instrumented aircraft. The profile, sively eliminated when the moist convective which underwent the characteristic evolution adjustment was used, which suppressed the that was relatively independent of cloud size band formation. As a consequence it was found and organization, were compared to those pro- that the AS scheme assured relatively good duced by cloud models included in a couple of performance in tropical cyclone simulations. cumulus parameterizations. They mentioned Fractional entrainment rate is a key param- that typical conceptual models for convective eter in the AS cumulus parameterization. It is clouds, such as the Raymond and Blyth (1992) not only true for the AS scheme, but also for buoyancy sorting model, or entraining plume any other cumulus parameterizations that use models, predicted cloud mass flux profiles simi- the cloud model, in which the concept of mass lar to the early phase of their observations. Al- flux is included (e.g., Tiedtke 1989; Grell 1993). though the vertical mass flux has recently been In these schemes, except for those in which the determined quantitatively by means of Doppler concept of buoyancy sorting is included (e.g., radars, it is difficult to accurately obtain the Kain and Fritsch 1990; Emanuel 1991), en- property from the observations. trainment rate, governing the vertical profile A cloud-resolving model (CRM), a numerical of cloud mass flux, is vertically constant. The model that resolves cloud-scale circulations, same applies to the AS scheme, although en- can be used for the development of cumulus trainment rate depends on the cloud spectrum parameterization. Moncrieff et al. (1997) (i.e., cloud-top height). However, there is no ev- pointed out that, for a larger-scale model, a idence suggesting that entrainment rate is ver- CRM was able to determine the collective tically constant. effects of subgrid-scale processes on the large- Entrainment profiles in real clouds have scale field. They mentioned that bulk proper- been investigated. Reuter (1986) reviewed the ties, such as cloud mass flux, were readily cal- history of ideas related to the dynamical as- culated from the results produced by a CRM. pects of cumulus entrainment. According to his CRMs have recently been used to evaluate review, it had been thought that entrainment and develop physically-based cumulus parame- took place laterally, in a manner similar to terizations. Liu et al. (2001a) examined squall- plumes modeled in laboratory tank experi- type cloud systems in the Global Atmospheric ments. Moreover, he provided evidence that dry Research Program (GARP) Atlantic Tropical air entered through cloud top in addition to the Experiment (GATE), using a two-dimensional side of the cloud. Blyth (1993) also reviewed CRM, and compared the result to that produced pieces of information gathered over more than by the simulation with the Kain-Fritsch con- 40 years, and mentioned that entrainment oc- vective parameterization. In the same way, Liu curred at all levels of a cumulus cloud. He in- et al. (2001b) investigated convective cloud sys- dicated that entrainment occurred at ascending tems in the Tropical Ocean Global Atmosphere cloud top, at least in a growing cloud. Coupled Ocean-Atmosphere Response Experi- October 2005 A. MURATA and M. UENO 747 ment (TOGA /COARE) and pointed out defi- files in numerical simulations for a tropical cy- ciencies of the Kain-Fritsch scheme used on clone. Following it, we discuss the performance the 15-km horizontal grid. The deficiencies in- in greater detail in section 6. Finally, in section cluded, excessive detrainment of water vapor 7, we summarize and conclude the results. and condensate in the upper troposphere, and were attributed to the single-plume model that 2. Numerical model and experimental represented the whole convective updrafts in a design horizontal grid. 2.1 Numerical model It has been pointed out that the vertical pro- The Meteorological Research Institute/ files of entrainment rate in cumulus parame- Numerical Prediction Division Nonhydrostatic terizations did not agree with results simulated Model (MRI/NPD-NHM) (Saito et al. 2001) is by CRMs. Lin and Arakawa (1997), and Lin used as the CRM with which the vertical profile (1999), examined entrainment profiles using of cumulus entrainment rate is investigated. simulated data from a two-dimensional CRM. The model has fully compressible equations They found that entrainment for each cloud with a map factor, and employs a semi-implicit type, which was categorized in terms of cloud- time integration scheme. The vertical coordi- top height, tended to become larger near cloud nate is terrain-following and contains 76 levels, base and top. Cohen (2000) developed a method with variable grid intervals of Dz ¼ 40 m to in which numerical tracers were utilized to 1480 m. The lowest level is located at 20 m diagnose entrainment rates. He applied the from ground surface, while the highest level is method to two-dimensional nonhydrostatic at 28 km. We use the model of 200-m horizon- simulations, and found that the entrainment tal resolution (200 m-NHM). The time-step in- rates in updrafts were large near, and above tervals are Dt ¼ 1s. cloud base. Gregory (2001) discussed entrain- The numerical model includes bulk cloud mi- ment rate linked to the rate of vertical kinetic crophysics, introduced by Ikawa et al.