Equilibrium translation model – a key to prediction of tropical hurricane intensity

Abstract

Principal challenges with forecasting of tropical hurricane (TH) intensity highlight pressing problem of proper combination of numerical methods with adequate qualitative physical models. In certain degree this gap is bridged by developed previously equilibrium translation model (ETM) introducing physically transparent relationship between main dynamical and thermal parameters of the system TH-ocean at the stage of TH intensification.

 

According to ETM development of TH substantially depends from a degree of conformity of thermal and dynamical environmental fields. Rather strong feedback characteristic for self-induced thermal driving mechanism of TH tends to establish accordance between translation and heat removal. ETM assumes that when main driver of TH - large-scale environmental wind favors establishment of corresponding equilibrium translation, maximum intensification of TH is triggered (alignment effect). It is assumed also that alignment effect occurs at certain constant value of heat involvement factor equal to the share of hurricane heat potential (HHP) removed by TH from an ocean. ETM reveals crucial role of so-called alignment number (representing non-dimensional combination of main dynamical and thermal parameters of the system TH-ocean).

 

 

Fig.1. Scheme of non-circular tropical hurricane translation.

 

Presented in the paper refined version of realization of ETM considers general case of TH of non-circular geometry covering partly land surface (Fig. 1). In addition, new three-zone model is incorporated of heat transfer from ocean upper layer to TH. The last is fitted to tangent wind distribution reflected in regular forecast advisory. Integral heat flow (sensitive and latent) removed by TH from left behind sea strip is written in the following form:

 

                                                                                                   (1)

Here A₃₄ is an area inside tangent velocity 34 kt (17.5 ms^-1); q is averaged inside A₃₄ integral heat flux from sea surface to TH; Q is averaged inside A₃₄ HHP (ocean upper layer heat content down to 26 ⁰C isotherm); C_i is heat involvement factor; W₃₄ is transverse size of A₃₄; U_bb is translation speed of TH back boundary center; U_dr is component of sea surface drift speed parallel to translation. Production W₃₄(U_bb-U_dr), to a certain approximation, determines increment of cooled sea surface. TH geometrics are determined through coordinates of TH centre and 4 values of TH radii at tangent velocity 34 knots in Northeast, Southeast, Southwest, and Northwest quadrants specified in regular advisories.

 

Further, with regard to insignificance of sea surface drift, the following condition of establishment of equilibrium translation is written:

 

                                                                                            (2)

Here N_al is alignment number; R_ef is effective radius of TH (R_ef=2A₃₄/ pW₃₄). Characteristic constant value C_i»1/16 is determined through analysis of the field data on rapid intensification of TH Opal (1995).

 

In addition, equation (2) is supplemented by a relation determining average integral heat flux and correction factors taking account of influence of partial covering of land surface on active sea surface and TH active back boundary.  

 

 

Fig. 2. Correlation of the field data on TH Charley (North West Atlantic, 2004) in the framework of equation (2):  triangles - Q (kJcm^-2); rhomboids - U_max (knot); crosses - regular forecast issued 15:00 (UT) 13.08.2004; squares - N_al; horizontal lines - the range N_al=25±30%; the point 0 corresponds to 9:00 (UT) 11.08. 2004.

Further, consideration is carried out in the framework of refined version of ETM of more than 50 TH observed during last 3 years. Following from the results of comparative analysis of different HHP maps, the maps developed by G. J. Goni and J. Trinanes (http://www.aoml.noaa.gov/phod/cyclone/data/np.html) are selected as the basis for consideration. Some important cases are presented in Figures 2 - 5.

 

 

Fig. 3. Correlation of the field data on TH Katrina (North West Atlantic, 2005):  triangles - Q (kJcm^-2); rhomboids - U_max (knot); crosses - regular forecast (issued 3:00 (UT) and 9:00 (UT) 28.08. 2005); squares - N_al; horizontal lines - the range N_al=25±30%; the point 0 corresponds to 21:00 (UT) 25.08. 2005.

 

 

As it follows from consideration, in general, TH intensity mainly depends from HHP and alignment number. Besides, rapid intensification of TH always takes place inside the range N_al=25±30%. It should be stressed also that in many cases influence of alignment number is much stronger than influence of HHP. Systematic overlooking also is revealed of the stages of rapid intensification by regular predictions.

 

 

Fig. 4. Correlation of the field data on TH Rita (North West Atlantic,  2005):  triangles - Q (kJcm^-2); rhomboids - U_max (knot); crosses - regular forecast (issued 3:00 (UT) 22.09 and 9:00 (UT) 23.09.2005); squares - N_al; horizontal lines - the range N_al=25±30%; the point 0 corresponds to 9:00 (UT) 20.09. 2005.

Overlooking of alignment effect by numerical models serving as a basis for regular predictions is more clearly demonstrated in the cases of Charley and Wilma. In contrast to them alignment number was favorable for development of Katrina and Rita during almost all life cycle. In this connection the role of HHP naturally has became decisive that clearly is reflected by similarity of TH intensity and HHP curves. Correspondingly, forecasting slips also are comparatively insignificant (for instance, overlooking of real preconditions for rapid intensification of Katrina in the period 48-64 hours, overlooking of absence of preconditions for further intensification of Rita at 42nd and 72nd hours).

 

 

 

Fig. 5. Correlation of the field data on TH Wilma (North West Atlantic,  2005):  triangles - Q (kJcm^-2); rhomboids - U_max (knot); crosses - regular forecasts (issued 5:00 (UT) 19.10. 2005, 9:00 (UT) 21.10.2005, 3:00 (UT), 15:00 (UT) and 21:00 (UT) 24.10.2005); squares - N_al; horizontal lines - the range N_al=25±30%; the point 0 corresponds to 9:00 (UT) 18.10. 2005.

 

 

As a whole, the results of consideration reveal fundamental character of alignment effect. Real potential is created for qualitative refinement of numerical models. Initial articles on subject matter are displayed at web page http://gtu.ge/usr/ishekriladze/ (section - "Hurricane").