High-Resolution Simulation of Hurricane Bonnie (1998). Part II: Water Budget SCOTT A. BRAUN J. Atmos. Sci., 63, 43-64

Introduction The total heat content of normal tropical air, if raised by undilute ascent within cumulus towers, is insufficient to generate a warm core capable of reducing the surface pressure below 1000 mb (Riehl 1954; Palmen and Riehl 1957; Malkus and Riehl 1960; Kurihara 1975). Horizontal advection tended to transport drier air into the core in the boundary layer and moist air from the eye to the eyewall within the low-level outflow above the boundary layer (Zhang et al. 2002). Few studies of the condensed water budget have been conducted for hurricanes (Marks 1985; Marks and Houze 1987; Gamache et al. 1993). In this study, we compute budgets of both water vapor and total condensed water from a high-resolution simulation of Hurricane Bonnie (1998).

Simulation and analysis description a. Simulation description Coarse-resolution: Started at 1200 UTC 22/08/1998 (36 hrs) 36 km: 91× km: 160×160 High-resolution: Started at 1800 UTC 22/08/1998 (30 hrs) 6 km: 225×225 2 km: 226×226 Vertical: 27 levels 8/23 8/24 OBS MM5

TRMM dBZ at 2 km MSL at 1800 UTC 22/08 Simulated dBZ at 2 km MSL valid 1200 UTC 23/08. TRMM dBZ at 1800 UTC 22/08MM5 dBZ at 1200 UTC 23/08 >10 dBZ contoured frequency by altitude diagrams (CFADs; Yuter and Houze 1995) of reflectivity

40 m 2.7km 6.8km 12km

dBZ + w (qcl+qci) + w dBZ + Vr

tangential velocityradial velocity vertical velocity qv qcl + qciqra, qsn, qgr 56ms -1

Budget formulation q v is mixing ratio of water vapor; q c is the mixing ratio of cloud liquid water and ice; q p is the mixing ratio of rain, snow and graupel; V ’ is the storm-relative horizontal air motion; w is the vertical air motion; V T is the hydrometeor motion; + is source; - is sink; C is the condensation and deposition; E is the evaporation and sublimation; B is the contribution from the planetary boundary layer; D is the turbulent diffusion term; Z is the artificial source term associated with setting negative mixing ratios to zero. the azimuthally averaged horizontal advective flux is simply that associated with radial transport U and V are the Cartesian grid storm-relative horizontal velocities in the x and y directions; u and v are the storm-relative radial and tangential winds,

the temporal and azimuthal mean: the time-averaged and vertically integrated amount: the time-averaged, volumetrically integrated amount: h -1 · (kg/m 3 ) · [(kg/kg) · h -1 ] · h =kg·m -3 ·h -1 h -1 · (kg/m 3 ) · [(kg/kg) · h -1 ] ·m· h =kg·m -2 ·h -1 (kg · m -3 · h -1 )·m 3 =kg·h -1 Z x is artificial source terms associated with setting negative mixing ratios (caused by errors associated with the finite differencing of the advective terms) to zero, that is, mass is added to eliminate negative mixing ratios.

Budget results a. Water vapor budget condensation horizontal flux divergence, evaporation vertical flux divergence, (a) + (c) (b) + (d) divergence term boundary layer source term (a), (e), (f) interval: 2 g m -3 h -1 (b) and (d) interval: 20 g m -3 h -1 (c), (g), (h) interval: 0.5 g m -3 h -1 thin solid lines show the zero contour

updraft condensation occurring in updraft much of the eyewall condensation is associated with hot towers. The smaller contribution of stronger updrafts is indicative of the larger role of stratiform precipitation processes outside of the eyewall. eyewall region (30-70 km) outer region ( km)

b. Condensed water budget cloud sinkhorizontal flux divergence net sourcevertical flux divergence boundary layer source added water mass to offset negative mixing ratios condensation (total source of cloud) (a) interval: 2 g m -3 h -1 (b) to (e) interval: 0.5 g m -3 h -1 (f) interval: g m -3 h -1 thin solid lines show the zero contour cloud budget

source for rain source for graupel source for snow sink for rain sink for graupel sink for snow net microphysical source horizontal flux divergence precipitation fallout and vertical flux divergence added water mass to offset negative mixing ratios precipitation budget cloud budget (a) to (f) interval: 2 g m -3 h -1 thin solid lines show the zero contour (a) to (c) interval: 2 g m -3 h -1 (d) interval: 0.5 g m -3 h -1 thin solid lines show the zero contour cloud sink

condensation evaporation precipitation fallout total rain source warm rain source cold rain source graupel source qv 6.8km (a) and (c) interval: 20 kg m -2 h -1 (b) interval: 5 kg m -2 h -1

c. Volume-integrated budgets P/C ~ 65 % Zero/C ~ 13 %Zero/C ~ 12 %

d. The artificial water source cloud liquid water cloud ice rain snow graupel hydrometeors: (a) shaded interval: 0.1 g m -3 (b) to (e) shaded interval: 0.5 g m -3 source terms: (a) to (e) line interval: 0.5 g m -3 h -1

raincloud water graupel

Conclusion A detailed water budget is performed using a high-resolution simulation of Hurricane Bonnie (1998). The simulation generally reproduces the track, intensity, and structure of the storm, but overpredicts the precipitation as inferred from comparison of model and TRMM radar reflectivities. The water vapor budget confirms that the ocean source of vapor in the eyewall region is very small relative to the condensation and inward transport of vapor, with the ocean vapor source in the eyewall (0.7) being approximately 4% of the inward vapor transport into the eyewall (16.8) region. In the eyewall, most of the condensation occurs within convective towers while in the outer regions condensation results from a mix of convective and stratiform precipitation processes, with the stratiform component tending to dominate. Precipitation processes acting outside of the eyewall region are not very dependent on the condensate mass produced within and transported outward from the eyewall. Instead, the precipitation derives from convection in outer rainbands and the subsequent transition to stratiform precipitation processes.

Conclusion Although the artificial water mass source is very small at any given grid point, its cumulative impact over large areas and over time is more substantial, contributing an amount of water that is equivalent to 15%–20% of the total surface precipitation. This problem likely occurs in any MM5 simulation of convective systems, but is probably much less a concern for purely stratiform precipitation systems.