Jhih-Ying(David) Chen Initialization and Simulation of a Landfalling Hurricane Using a Variational Bogus Data Assimilation Scheme Jhih-Ying(David) Chen Reference: Xiao, Q. X. Zou and B. Wang, 2000: Initialization and simulation of a landfalling hurricane using a variational bogus data assimilation scheme. Mon. Wea. Rev., 128, 2252-2269. Zou, X., and Q. Xiao, 2000: Studies on the initialization and simulation of a mature hurricane using a variational bogus data assimilation scheme. J. Atmos. Sci., 57, 836–860.

Introduction Hurricane intensity change is closely related to the evolving 3D structure of the hurricane. The difficulties in the prediction of hurricane intensity and inner-core structure are associated with insufficient observations over the oceans and with the limitations of forecast models.

Hurricane initialization (i) substitute a specified vortex circulation defined by an analytical expression for the analyzed vortex into the initial conditions (Mathur 1991; Ueno 1989; Serrano and Unden 1994; Leslie and Holland 1995), (ii) implant a ‘‘spinup’’ vortex generated by the same forecast model into the initial conditions (Kurihara and Ross 1993; Kurihara et al. 1995; Peng et al. 1993; Liu et al. 1997) (iii) improve the initial conditions by making use of satellite–rain gauge based measurements of rainfall through a physical initialization procedure (Krishnamurti and Ross 1993, 1995, 1997, 1998).

Cumulus parameterization Experimental design Model domain Resolution (km) Dimension ( I × J × K ) Explicit moist scheme Cumulus parameterization A (fixed) 54 76 × 85 Dudiha’s simple ice Grell B1, B2, B3 (move) 18 112 × 130 Reisner mixed phase Kain-Fritsch C1, C2, C3 (move) 6 109 × 127 Reisner graupel No 27 half-σ levels B1 _00hr, B2 _28hr, B3 _66hr C1 _66hr, C2 _70hr, C3 _74hr

Vortex specification The SLP of the hurricane vortex is specified according to Fujita’s formula (1952, Geophys. Mag., 23) r is radial distance from the cyclone center, Pc is the hurricane’s central pressure (according to the NHC), ΔP is a parameter related to the hurricane gradient information, R is the estimated radius of maximum SLP gradient, Vo(r) is gradient wind.

Hurricane Fran(1996) NOAA/HRD(Hurricane Research Division) 1996/09/03 0000 UTC Pc = 977 hPa, Vmax = 75 kt (38.8 ms-1) RMW = 80 km Vertical weighting profile of 1.0, 1.0, 0.95, 0.85, 0.65, and 0.35 at 1000, 850, 700, 500, 400, and 300 hPa.

Minimization procedure A cost function is defined as X = (u, v, w, p’, T, q)T model variables at the initial time, Jb , Jp and Jv is the background, pressure and wind term of the cost function,

X = (u, v, w, p’, T, q)T model variables at the initial time, Xb is the background analysis obtained from standard MM5 analysis fields with a crudely estimated diagonal error covariance matrix B, P(r) is the SLP of the model atmosphere, ti is carried out over half-hour windows at every 5 min. V(r,k) model wind velocity (sea level, 1000, 850, 700, 500, 400, 300 hPa), Ω is the 2D domain in the vicinity of the hurricane center (the area of Ω is related to R, and the average radius of Ω is about 2.5-3.5 times of R), Wp and Wv is 1.6 hPa-2 and 0.185 s2m-2

Numerical experiments Hurricane Fran (1996) using the two-way interactive, triply nested,and movable mesh MM5. CTL : NCEP 2.5o resolution global analysis.

Results from the BDA scheme

CTL_T CTL_q B80_T B80_q

Experimental results from the simulation of Hurricane Fran (1996)

95 kt (49.1 m/s) 90 kt (46.5 m/s) 56.3 m/s 49.6 m/s

T q V w

Characteristic of Hurricane Fran’s (1996) flow and thermodynamic structure 1) The tangential or swirling wind of the hurricane is strongly asymmetric. The maximum wind speed occurred around 900 hPa. 2) The ascending vertical motion around the eye increases the moisture in that region, while the descent inside the eye makes the area of the hurricane center drier in the lower to middle troposphere. Near the surface at the hurricane center, the specific humidity reaches its maximum value. 3) The compensating descent inside the hurricane eye is the main reason for the formation of the warm core.

Domain C (6 km) WSR-88D radar

Sensitivities of the BDA results to the model resolution, RMW, and bogus variable specification

A220V A220P CTL The assimilation of the bogused wind alone could not produce a hurricane SLP field with realistic intensity.

Although the low-level maximum wind of A220V at the beginning was very close to the observation, the forecast became poorer as the time of integration increased. The pressure bogus is more efficient than the wind bogus in reproducing a realistic hurricane intensity forecast.

A220V_T A220V_q A220P_T A220P_q

Summary The BDA scheme is very efficient in recovering the initial structure of the hurricane using very little observational information.(a strong constraint, get a good hurricane track and make a moist warm-core hurricane structure.) The simulation of the hurricane track was sensitive to the model resolution on which the BDA scheme was performed.(A80 and B80) The RMW used in the BDA scheme is a sensitive parameter for the hurricane track and intensity forecast. A220P is more effective than A220V. The hurricane simulation from the initial conditions produced by the use of bogused SLP low data is closer to observation than the use of bogused wind data only.

Thanks For Your Attention

Pc is the central pressure of the hurricane, 963 hPa Fujita’s formula (1952, Geophys. Mag., 23) is used as a basic reference for us to formulate axisymmetric SLP pattern of the bogused surface low. Pc is the central pressure of the hurricane, 963 hPa is the estimation of the SLP at an infinite distance, 1035 hPa is obtained by ship report. r is the radial distance from cyclone center. R0 = 150 km is estimated by NCEP .

ti is carried out at 5-min intervals, R is a circular 2D domain of a 300-km circle centered at the hurricane center at the lowest σ level (σ =0.995), rl is the physical location in the 3D space representing satellite winds available. Hl is a linear interpolation scheme. WP, Wu, and Wv are diagonal weighting matrices and their values are determined empirically. P,u,v, represent SLP, zonal, and meridional wind components. Jb is a simple background term between the model state and the MM5 analysis based on the large-scale NCEP analysis.

f can be any of the model variables (u, v, T, q, p’,and w) k (=1, 2, …, 10) is number of iterations during the minimization procedure. The first major adjustment in the initial condition during the minimization of JBG comes mainly from the dynamical constraint, and the second major adjustment is associated with the latent heat release due to the heavy precipitation that occurred near the center of the initial vortex.

BG BGSAT: change of divergence field at 200 hPa. BGSAT

Initial half-hour rainfall. BGM Initial half-hour rainfall. BGM Initial half-hour rainfall.

BG (36g/kg) BGM (32g/kg)

BGSAT CTL 08/16 1850 UTC 08/16 1800 UTC

BDA_SCHEME_CHARACTERISTIC The dynamic and thermodynamic structures of the initial vortex obtained by the BDA procedures are examined, and the improvements to the prediction of the hurricane track, the intensity change, and the structural features are demonstrated. BDA scheme can generate the asymmetric structure of the initial vortex . BGSAT is able to generate large amounts of precipitation right from the beginning of model integration,alleviating the spinup problem associated with the traditional hurricane bogusing scheme.