1. Dual-Aircraft Investigation of the inner Core of Hurricane Norbert. Part Ⅲ : Water Budget Gamache, J. F., R. A. Houze, Jr., and F. D. Marks, Jr., 1993: J. Atmos. Sci.,50, 3221- 3243.

2. Introduction Better understanding of microphysical process involved in production hurricane precipitation. They found that cooling associated with the melting of frozen precipitation in the stratiform regions outside the eye wall produced mesoscale downdrafts. The relationship of compute water budget to storm inner core structure and dynamics is evaluated.

3. Description of water budget The continuity equation of condensed water and ice: θ r z

4.  The bulk water budget is the volume integral: condensation evaporation Divergence (horizontal)

5. Divergence (vertical) Mass of precipitation

6. Diffusion (vertical) Diffusion (horizontal)

8. Strom description Hurricane Norbert formed in the eastern Pacific Ocean on 16 September 1984. It made landfall on 26 September along the northern Baja Peninsula. The hurricane Norbert was weaken at 0018-0215 UTC 25. The data used in this paper were obtained in the middle of the last filght.

9. Data The Doppler radar was located on the aircraft the flew at an altitude about 3 Km. Radial precipitation velocities were obtained in the scan perpendicular to this axis. Data for the two horizontal wind components were obtained by flying in two roughly perpendicular direction. Vertical wind was obtained by integrating horizontal divergence and then iteratively to correct the horizontal wind.

10. Retrieval methods Method 1: Precipitation content is determined form a reflectivity mass relationships. Rain→a=14630, b=1.4482 (Jorgense and Willis 1982) ice → a=670, b=1.79 (Black 1990) Z is the radar reflectivity (10 -18 m 3 ) M is the precipitation content (g/m -3 ) R is rainfall (kgm -2 h -1 ) (Jorgense and Willis 1982) Precipitation content is the function of terminal velocity and precipitation production P is form M, the Doppler winds and V T. The first term is three dimensional advective flux divergence of precipitation The second term is the flux divergence owing to the terminal fallspeed relative to the air motion.

11. The distribution of precipitation particles (Marshall-Palmer 1948) N 0 is the zero intercept D is the particle diameter N is the number concentration for a given size interval. The resulting precipitation content is: When P>0, precipitation production is given by M c is cloud content. M c0 is the autoconversion threshold. α is the switch function. Note: E c is the collection efficiency. In this study E c was set 1 for rain and 0.1 for frozen precipitation. Autoconversion of cloud to precipitation was set 0.001 s -1 and 0.0001 s -1 for water and ice (threshold=0.0005kgkg -1 )

12. Method 2: The steady-state equation in three domain are: The perturbation total water mixing ratio is : The acceleration of wind in a steady-state storm in a moving coordinate system is: Those accelerations are used in the thermodynamic retrieval Roux et al. (1984) and Roux (1985, 1988) q s0 is the level mean saturation specific humidity Note: it is assumed the only one kind of precipitation can exist at a given location, either rain (T>0) or precipitation ice (T<0).

13. Axisymmetric budget The mean of all the winds at a given height and a given radius form storm center. These values were then interpolated to a Cartesian grid of the same size as used for methods 1 and 2. The temperature and pressure were then retrieved for this axisymmetric wind field.

14. Result Definitions Precipitation and radar reflection Cloud content Condensation and evaporation Azimuthally average mean structure and advection Azimuthally average advection by quadrant Constant radius analyses of radial advection Bulk water budgets Water vapor convergence Comparison with earlier budget studies

15. Definition 6 ms -1 Vertical wind in meter per second at (a) 3 km and (b) 6km. (a)(b)

16. Precipitation and radar reflection Radial wind in meters per second at constant radii form storm center of (a) 25 km (b) 37.5 km

17. MAX Observed Horizontal cross sections of the three-dimensional composite of radar reflectivity at (a) 0.5 km (b) 3km (c) 6 km Method 2 (a)(b) (c) (b) (a) (c) Radius-height mean radar reflectivity. (a) the observed reflectivity (b) the retrieved reflectivity of method 2

18. Cloud content Method 1Method 2 Constant height analyses of 3-km and 6-km 3 km 6 km More cloud content

19. Condensation and evaporation Method 1 Method 2 3 km 6 km Constant height condensation and evaporation of 3-km and 6-km Bright band error

20. Azimuthally averaged mean structure and advection Radius-height mean advection of water (left) and Radius- height mean evaporation and precipitation (right) in the radial direction Method 1 Method 2 Method 1 Method 2 Symmetric wind field (Method 2)

21. Azimuthally averaged advection by quadrant RR LF RF LR RR LF RF Method 1 Method 2 Radius-height mean advection of water in the radial direction RF RR LF LR RF=327 ° - 57 ° RR=57 ° - 147 ° LR=147 ° - 237 ° LF=237 ° - 327 °

22. Constant radius analyses of radial advection Constant radius plot of radial advection of water for radius form storm center equal to 25 km and 37.5 km Method 1 Method 2

23. Bulk water budget Bulk water budget by quadrant (a) method 1 (b) method 2 Arrows indicate bulk advection through the indicated boundary. RF RR LF LR RF RR LF LR Different: 1. the assumption of steady state storm structure 2. the strong attenuation of the X band radar 3. Radar calibration (2- 4 dbz error) Method 1Method 2

24. Water vapor convergence Vertical profiles of the mean condensation and evaporation rate for the budget region bound by a distance 37.5 km for storm center. Method 2 Completely saturate Method 2 condensation Method 2 evaporation Global saturation condensation Global saturation evaporation

25. Comparison with earlier budget studies Method 2 vapor budget for the annulus form 10-20 nautical miles (18-37 km) for direct comparison with Hawkins and Rubsam (1968). Although budget is similar to that found in Hurricane Hilda (1964), the Hurricane Hilda was intensifying when Hurricane Norbert was dissipation

26. Conclusions Moisture primarily form the front of the storm, most of the condensation occurred on the left side of the storm, and most precipitation occurred in the left rear quadrant of the storm. Most of the vapor entering the budget volume entered through the bottom boundary (500 m), and it greatly exceeded the low level horizontal vapor convergence. Either the inflow form the surface to 500 m, which could not be determined well from Doppler. The similarity in bulk budget between Hurricane Norbert, a dissipating storm, and Hurricane Hilda, an intensifying storm, indicates the need to understand the role of hurricane asymmetries in a number of different cases. The documentation of the asymmetric structure of Hurricane Norbert has allowed the hydrometer budget to be related to the cloud microphysical structure of the storm analyzed in Part Ⅱ