Evaluación del programa

The model has three layers of unequal depth with boundaries at σ = 1, σ4, σ2 and 0 as

depicted in Fig. 2.1. All dependent variables, such as horizontal velocity, potential temper- ature, specific humidity and geopotential, are defined in the middle of each layer (σ =σb, σ3,

and σ1) and the vertical velocity is staggered, i.e. it is defined at the boundaries between

the layers (σ =σ4 and σ2). In the radial direction, the horizontal velocity components, u

andv, are staggered also as indicated in Fig. 2.1. This is the so-called Lorenz-grid (L-grid). The advantage with the L-grid model is that total energy is conserved. In additon, the mean potential temperature and the variance of the potential temperature are conserved under adiabatic and frictionless processes (Arakawa and Suarez 1983). The equations are expressed in finite difference form in both the radial and vertical and integrated using the Adams-Bashforth third-order method with an integration timestep of 6 s. The initial pressure, temperature, specific humdity and geopotential height in the middle of each layer and at the boundaries between the layers are listed in Appendix A.

Figure 2.1: Configuration of σ-levels in the model showing locations where the dependent variables are stored. The horizontal velocity components, geopotential, temperature, spe- cific humidity are calculated in the middle of each layer. These are the layers 1, 3 and b. The vertical velocity ˙σ and the convective mass fluxes are stored at the two interface levels 2 and 4. From Nguyen et al. (2002).

Chapter 3

Control experiment

A control experiment is carried out on an f-plane to investigate the evolution of a weak baroclinic initial vortex to a mature tropical cyclone. The Coriolis parameter, f, is set to a constant value that corresponds to a reference latitude of 20◦N and is denoted as f0.

The model has a 10 km radial grid spacing and the radial domain size extends to 1000 km. Deep cumulus convection is parameterized by a scheme proposed by Arakawa (1969). This scheme is complemented by a simple explicit scheme that is implemented at grid points where supersaturation occurs. The initial and boundary conditions are given in section 2.6. The results of this control experiment serve as a reference with which to compare the results presented in Chapter 6 that examines the sensitvity of the model to certain parameters and physical processes.

The initial radial profile of tangential wind in the lower layer is shown in Fig. 3.1. The profiles in the middle and upper layers are the same, but their amplitudes are multiplied by factors of 0.9 and 0.3, respectively.

26 3. Control experiment

3.1

Overview of vortex evolution

Figure 3.2 shows time series of the minimum surface pressure and the maximum tangential wind speed in the lower layer. It shows also the radius,rgales, at which the tangential wind

speed in the lower layer reaches gale force (17 m s−1_{). The vortex evolution can be divided}

into three successive stages:

• a gestation period during which the vortex first decays and then gradually intensifies and the minimum surface pressure slowly falls,

• a short period that lasts for only ten hours, where the vortex undergoes rapid inten- sification and deepening, and

• a mature stage during which the maximum tangential wind speed inreases only slightly and eventually reaches an approximate steady state.

During the first four hours of the gestation period, the vortex slows down due to surface friction before it gradually intensifies. It was shown in section 1.4, that significant vortex spin-up can occur within the boundary layer due to the frictionally-induced convergence of absolute angular momentum. However, a closer inspection of the magnitude of the terms of the tangential momentum equation reveals that the frictional drag is the dominant term during the first four hours of development. Above the boundary layer, the vortex spins down due to frictionally-induced divergence. The onset of rapid intensification can best be discerned from the maximum tangential wind speed and occurs after approximately one and a half days. The physical reason for the intensification is the release of latent heat in the inner-core region. The associated radial gradient of diabatic heating leads to convergence in the lower troposphere that more than offsets the frictionally-induced divergence (see Eq. (1.5) in section 1.2). This offset is a necessary requirement for the intensification of the vortex (e.g. Ooyama 1969, 1982, Smith 2000). As will be shown in section 3.2, the onset of rapid intensification occurs when there is saturation on the grid-scale in the middle layer. However, the inclusion of a parameterization scheme for convection also leads to latent heat release that gives rise to the gradual increase in intensity just before the vortex ultimately spins up rapidly. After the period of rapid intensification, the vortex reaches an approximate steady-state. The maximum tangential wind speed at twelve days is 56.8 m s−1.

The occurrence of rapid intensification is a typical feature during the development of tropical storms to a mature hurricane. According to Willoughby et al. (2007), rapid intensification may increase the maximum winds by more than 20 m s−1 in twelve to 24 hours. In the control calculation described here, the maximum tangential wind speed increases from 29.4 m s−1 _{at 39 hours to 48.7 m s}−1 _{only 10 hours later. Willoughby et al.}

(2007) state that nearly all major hurricanes, i.e. those that reach Category 3, 4 or 5 on the Saffir-Simpson scale, become major through rapid intensification. Still, rapid intensity changes remain almost unpredictable (NOAA 2006).

3.1 Overview of vortex evolution 27

(a) (b)

(c)

Figure 3.2: Time-series of (a) the minimum surface pressure, (b) the maximum tangential wind speed in the lower layer, and (c) the radius of gale-force tangential winds in the lower layer.

Interestingly, the evolution of the vortex size, as characterized by the radius of gale- force tangential winds, is not obviously related to the evolution of the intensity. The vortex reaches gale-force wind speed for the first time after half a day at r= 120 km and subsequently increases only slightly in size until two and a half days, whereas it intensifies rapidly during the same period. After the period of rapid intensification, the intensity increases only slightly, whereas the vortex size increases steadily from 160 km to 320 km over a time period of four days. A shorter period follows, where the vortex becomes smaller in size, before the radius of gales increases again a little bit and eventually reaches a steady state of about 310 km. This behaviour matches the observations of typhoons described by Weatherford and Gray (1988), mentioned in section 1.4, that inner-core changes in the azimuthal-mean tangential wind speed often occur independently from those in the outer core. A physical explanation for this behaviour has been provided recently by Smith et al. (2009). As described in section 1.4, these authors described two (sic) independent mechanisms that account for the spin-up of the inner core and outer core, respectively. However, the statement made by Smith et al. that the two mechanisms are independent is too strong. There must be a degree of coupling between them through boundary layer dynamics as discussed by Montgomery and Smith (2011). Even though the vortex size and the intensity develop largely independently, as noted above, both the maximum tangential wind speed and the radius of gales in the lower layer reveal a slight decrease between six and eight days before they eventually level out. A physical reason, why the vortex size

28 3. Control experiment

starts to decrease after reaching its maximum is given in section 3.4. More insight on the two mechanims that govern the intensification of the inner and outer core, respectively, is offered in section 3.3.