Numerical Simulation

Another important application that the turbulence model in the HBL has great in- fluence on is numerical simulations of hurricanes. As illustrated in the analytical model studies, the turbulence diffusivity plays a key role in the vertical mixing term that appears in the governing equations. It is also true when numerical simulations are in the play. More specifically, the turbulence model within the HBL, referred as the PBL scheme in various numerical simulation software, partially determines the vertical transportation of both the sensible heat and latent heat, and therefore determines the intensity of simu- lated tropical cyclones sine the warm, moist air at low altitudes is the energy source for the whole hurricane.

Many studies revealed the importance of correctly modelling the turbulence within the HBL, such as that of Bryan and Rotunno (2009). By conducting a sensitivity analysis of the hurricane intensity numerical prediction to different turbulence parametrization schemes, this study showed that it is critical to find an appropriate boundary layer turbulence model. In addition, it found that the radial turbulence weakens the radial gradient of angular momentum and entropy, which prevents the hurricane intensity from increasing. As argued by Bryan and Rotunno (2009), the simulated tropical cyclone is sensitive to the turbulence intensity in the HBL, which is, unfortunately, the most uncertain part in a numerical simulation. This study also discovered that one important factor in predicting hurricane intensity is a correct model of surface exchange processes, including momentum exchanges and moist exchanges between the atmosphere and the sea. However, it seems that the hurricane intensity is less sensitive to surface exchanges in an intense tropical cyclone than several previous studies have suggested.

Figure 2.3: The potential temperature profile from the observation and numerical simula- tions with different PBL schemes, reproducing Fig.5 in Nolan et al. (2009a). cAmerican Meteorological Society. Reprinted with permission.

A high resolution numerical simulation of Hurricane Bob (1991) conducted by Braun and Tao (2000) also analyzed the sensitivity of the simulated hurricane wind field to the

boundary layer turbulence parametrization. In this study, four different parametrization schemes are tested, and the sensitivity is seen. The pressure drop difference among differ- ent parametrization schemes is up to 16mband the difference among the maximum wind velocity is up to 15m/s. Besides the difference seen in the simulated wind fields, the precipitation distributions generated from different parametrization schemes also con- tained a substantial difference. By isolating the effect of vertical mixing, which is the major job of the turbulence parametrization in a numerical simulation software, from the surface flux parametrization, this study found that the simulated hurricane is more sensitive to surface fluxes than to vertical mixing, except for the Medium Range Forecast Model (MRF) model. This ”non-local” turbulent mixing which transport humidity more rapidly gives a drier lower boundary layer which reduces the intensity of simulated hurri- canes. Using the CBLAST data as a validation criteria, Nolan et al. (2009b) and Nolan et al. (2009a) simulated Hurricane Isabel (2003) using a series of ”local” and ”non-local” turbulence mixing schemes. Although neither turbulent mixing scheme is designed spe- cially for simulating the HBL turbulence, they both produced reasonable result. ”Local” schemes consistently produce larger frictional tendencies in the boundary layer than the ”non-local” schemes, leading to a stronger low-level inflow and a stronger azimuthal wind maximum at the top of the boundary layer. The vertical profile of the potential temper- ature produced by the numerical simulations with different boundary layer turbulence schemes are repeated here for the purpose of illustration, as in Fig. 2.3.

The study of Davis and Bostart (2002) also analyzed the sensitivity of a hurricane simulation to the boundary layer turbulence modelling, but it focused on the genesis of a tropical cyclone rather than the simulation of its wind field. The sensitivity analysis is done by doing numerous numerical simulations using different cumulus parametrization, boundary layer treatments, sea surface temperatures and grid spacing. In the discussion, they came to the same conclusion as in the study of Braun and Tao (2000), which is that the ”non-local” model gives a too dry and too deep boundary layer as the simulated hurricane is intensifying. Although this study did not favour the use of ”non-local” schemes in simulating the genesis of hurricanes, it focused primarily on the hurricane

development rate rather than the hurricane wind field, and therefore did not preclude the use of ”non-local” schemes in simulating a hurricane which is already in the mature stage.

Due to the importance of the turbulence parametrization on tropical cyclone simula- tions, endeavours are continuously being made to propose a more accurate and realistic turbulence model. One recent study of Zhu (2008) enlightened the thought of modelling the turbulence transportation based on large eddies. Using the Large Eddy Simulation (LES) within the framework of Weather Research and Forecast Model (WRF), this study is able to derive some coherent structure of large eddies within the HBL. The simula- tion results supported the idea that large eddies exist in the stable environment and is able to be represented by large scale up-drafts and down-drafts. It is found that the organized up-drafts and down-drafts, or large eddies, interact with the sea surface and the entrainment at the boundary layer top, which makes the main vortex more intense than that produced by the current turbulence parametrization. This finding illustrated the need to devise a new parametrization taking into account the large eddy effect. As a beginning, it proposed a conceptual model, using statistical distribution of organized up-drafts and down-drafts revealed by the LES, which can be potentially implemented in any widely used numerical simulation package. Another pioneer study using the LES to simulate the hurricane wind is that of Rotunno et al. (2009). It described a LES simulation of an idealized tropical cyclone in a favourable environment. They discovered that the resolved turbulence exchanges with a length scale of∼100m has a great impact on the simulated hurricane wind field. It increases the simulated turbulence gust while decreasing the mean maximum wind. Furthermore, this simulation showed noticeable differences between the resolved and parametrized turbulence, and therefore called for a further study on the small scale turbulence characteristics of the hurricane wind. It should be noted that this simulation focused on the horizontal turbulence diffusion rather than turbulent vertical mixing in the HBL, but the finding should be equally applicable in describing turbulent mixing in the HBL due to the similarity of small scale turbulence processes.

Chapter 3

Simulations of GPS Dropwindsonde

Motions

Since the dropwindsonde is only able to report its own velocity, rather than the real local wind velocity, in its fall through the measured wind field, the measurement is taken in neither a conventional Eulerian framework, which requires that the measurement is taken at a fixed point, nor a perfect Lagrangian framework, which requires that the measurement is taken smoothly following the flow. The dropwindsonde motion is close to the local wind velocity, but they are not the same since the dropwindsonde is not instantaneously responsive due to its mass.

Thus, it is necessary to introduce the wind finding equations to derive wind veloci- ties from dropwindsonde motions. Hock and Franklin (1999) introduced the currently used wind finding equations based on a brief analysis of the equations governing the dropwindsonde motion. Their equations have been widely adopted in processing drop- windsonde measurements as it is embedded in one standard processing software package named EDITSONDE. Their validity, however, has not been thoroughly evaluated. In addition, Hock and Franklin (1999) only briefly discussed the performance of their wind finding equations in reproducing the mean wind profile, but no follow-up studies have been conducted to evaluate their performance in reproducing a turbulent variable profile, such as the turbulent flux profile.

Based on a simulation of the dropwindsonde motion in a pseudo-stochastic wind field with known statistics, this study analyzed dropwindsonde motion characteristics. We focus on evaluating the wind finding equations introduced by Hock and Franklin (1999) in reproducing the vertical structure of both the mean and turbulence variables in the measured wind field. From the simulation and following analyses, the currently used wind finding equations are validated in a more thorough and systematical way. In addition, the numerical simulation also provided an opportunity to investigate various aspects of post- processing and compositing dropwindsonde measurements, which lays the foundation for revising the post-processing and composition techniques currently used to improve the interpretation of actual dropwindsonde measurements.

In order to conduct the numerical simulation described above, the dropwindsonde mo- tion governing equations and their numerical discretization need to be analyzed. More- over, the methodology of generating a pseudo-stochastic wind field based on given statis- tics also needs to be reviewed for preparing the driving wind field in the simulation. These two topics are discussed in sections 3.1 and 3.2. With these prerequisites formu- lated properly, the dropwindsonde motion simulation is conducted and its results are presented and discussed in section 3.3. At this point, the simulation is based on a un- validated assumption that the dropwindsonde can be treated as a point object with a constant drag coefficient regardless of the angle of attack. To improve the dropwindsonde motion model, wind tunnel tests are then conducted to measure dropwindsonde aerody- namics and their variation with angles of attack. The wind tunnel test results, along with their configurations, are presented and discussed in section 3.4. Using the wind tunnel test results, an alternative motion model which separates the parachute from the dropwindsonde body and explicitly includes the dropwindsonde body orientation is pre- sented in section 3.5. A numerical simulation of the dropwindsonde motion in the same pseudo-stochastic wind field, using the alternative model, is then carried out to further validate the wind finding equations and to investigate the calculation of the vertical wind from raw dropwindsonde measurements. The simulation results and a discussion on both the horizontal and vertical wind retrieval from raw dropwindsonde measurements are

presented in section 3.6.

3.1

Simple Motion Model

To fully utilize its measurements, it is necessary to gain a better understanding of dropwindsonde motion characteristics which helps improve post-processing techniques used to retrieve wind velocities from raw dropwindsonde measurements. Naturally, an analysis of the dropwindsonde motion governing equations is the starting point, like in the study of Hock and Franklin (1999). Methodologies used in studies analyzing motion characteristics and measurement interpretations of rising, or falling, wind sensors are followed here. Fichtl (1971) derived a set of differential equations governing the motion of vertically moving sensors. Using a set of equations similar to those used by Fichtl (1971), Nastrom and Vanzandt (1982) investigated the rising process of a wind sensor in the atmosphere by seeking the analytical solution to the governing equations. The advanced part of this study is that the analytical solution discussed includes nonlinear responses. Although the aerodynamics of wind sensors are different from those of the dropwindsonde, their derivation and analysis shed lights on the analysis of dropwindsonde motion characteristics.

As described in the beginning of this chapter, this section covers the analysis of the dropwindsonde motion governing equations and its numerical discretization based on which a numerical integration approach can be employed to solve for dropwindsonde motion variables. Therefore, this section is divided into two subsections, the first shows the derivation of the dropwindsonde motion governing equation and the second shows the numerical approach simulating dropwindsonde motions and measurements.