Why is the simulated climatology of tropical cyclones so sensitive to the choice of cumulus parameterization scheme in the WRF model?

Abstract

The sensitivity of simulated tropical cyclones (TCs) to the choice of cumulus parameterization (CP) scheme in the advanced Weather Research and Forecasting Model (WRF-ARW) version 3.5 is analyzed based on ten seasonal simulations with 20-km horizontal grid spacing over the western North Pacific. Results show that the simulated frequency and intensity of TCs are very sensitive to the choice of the CP scheme. The sensitivity can be explained well by the difference in the low-level circulation in a height and sorted moisture space. By transporting moist static energy from dry to moist region, the low-level circulation is important to convective self-aggregation which is believed to be related to genesis of TC-like vortices (TCLVs) and TCs in idealized settings. The radiative and evaporative cooling associated with low-level clouds and shallow convection in dry regions is found to play a crucial role in driving the moisture-sorted low-level circulation. With shallow convection turned off in a CP scheme, relatively strong precipitation occurs frequently in dry regions. In this case, the diabatic cooling can still drive the low-level circulation but its strength is reduced and thus TCLV/TC genesis is suppressed. The inclusion of the cumulus momentum transport (CMT) in a CP scheme can considerably suppress genesis of TCLVs/TCs, while changes in the moisture-sorted low-level circulation and horizontal distribution of precipitation are trivial, indicating that the CMT modulates the TCLVs/TCs activities in the model by mechanisms other than the horizontal transport of moist static energy.

Appendix A

In all experiments with CMT, the CMT is calculated in each grid cell with convection, and the resulting tendency is added to the zonal and meridional momentum equations. The tendency of the CMT can be expressed as (Gregory et al. 1997),

$$\left( {\frac{{\partial U}}{{\partial t}}} \right)_{{cu}} = g\frac{\partial }{{\partial p}}\left[ {M_{u} U_{u} + M_{d} U_{d} - (M_{u} U_{d} )\overline{U} } \right],$$

(4)

where the subscripts u and d depicts updraft and downdraft averaged quantities, respectively. The overbar represents an environmental average. M is the mass flux assuming the updraft and downdraft areas constitute a very small fraction of the grid box. U is the horizontal component of zonal or meridional wind, g is the gravitational acceleration rate, and p is the air pressure.

The CMT parameterizations are different across CP schemes mainly due to the implementation of entrainment and detrainment in the cloud model. The cloud model is described as:

$$- g\frac{{\partial M_{u} U_{u} }}{{\partial p}} = E_{u} \overline{U} - D_{u} \overline{U} + PGF_{u},$$

(5)

$$- g\frac{{\partial M_{d} U_{d} }}{{\partial p}} = E_{d} \overline{U} - D_{d} \overline{U} + PGF_{d} ,$$

(6)

where E is the entrained mass flux and D is the detrained mass flux. PGF is the pressure gradient term. Note that PGF_u and PGF_d are equal to zero in TDK1 but the pressure gradient effects were represented by an enhanced entrainment rate in the updraught equations for E_u and D_u, namely,

$$E_{u} = E_{u} + \lambda D_{u} ,$$

(7)

$$D_{u} = D_{u} + \lambda D_{u} ,$$

(8)

where $\lambda = 2$ for deep and mid-level convection in TDK1.

Gregory et al. (1997) parameterized the PGF based on the following empirical relationships,

$$PGF_{u} = - C_{u} M_{u} \frac{{\partial U}}{{\partial p}},$$

(9)

$$PGF_{d} = - C_{d} M_{d} \frac{{\partial U}}{{\partial p}},$$

(10)

where C_u and C_d are tunable parameters. In TDK2, PGF_u is parameterized as (9) but PGF_d is zero. If we used the enhanced entrainment/detrainment rate to parameterize pressure gradient effects as in TDK1, the domain averaged tendency profile resembles that calculated using formula (9) with C_u = 0.4. We found that C_u = 0.7 or even higher is an optimal value for TDK2.

For the KF scheme, the tendency due to the CMT is simply expressed as:

$$\left( {\frac{{\partial U}}{{\partial t}}} \right)_{{cu}} = g\frac{\partial }{{\partial p}}\left[ {M_{u} U_{u} + M_{d} U_{d} - (M_{u} U_{d} )\overline{U} } \right] - \overline{\omega } \frac{{\partial U}}{{\partial z}},$$

(11)

where, $\overline{\omega }$ is a value related to vertical advection (Kain and Fritsch 1990, 1993).