Data and Processing Technique

As described by Hock and Franklin (1999), the dropwindsonde is released by recon- naissance flights penetrating through tropical cyclones, and it is able to report the wind velocity, air temperature, humidity, etc. every 0.5s. The accuracy of its measurement for the wind speed is about 1m/s, for the temperature is about 0.2◦_{C, and for the relative} humidity is about 5%. Its falling speed decreases as it moves downwards due to the increase of the air density and eventually researches its terminal velocity, which is about 12m/s.

As maintained by the HRD of NOAA, a considerable dropwindsonde measurement database has been built up which allows a derivation of turbulence characteristic within the HBL. To get statistically meaningful results, a database much larger than that used in previous studies is adopted here. More specifically, dropwindsonde measurements gath- ered from the earliest publicly available time, the year 1997 to the year 2010, constitute the measurement database utilized here. The total number of dropwindsonde profiles processed is more than 10000. However, many profiles are eliminated from the database due to the failure in calculating the reliable storm center and RMW for those particular profiles. As a result, the total number of the profiles composited is around 4000, and is

different for different composition strategies. The necessity and details of calculating the storm track and RMW are given in the following paragraphs.

Before compositing dropwindsonde measurements to produce the desired statistics of the measured wind field, dropwindsonde measured profiles need to be post-processed, which includes a quality control process, dynamic corrections of the wind and other thermodynamic variables and low-pass filtering of dropwindsonde profiles. The quality control process is either an automatic or a human-intervention process to eliminate erro- neous and questionable measurements from an individual dropwindsonde profile. Drop- windsonde wind measurements are then dynamically corrected using the wind finding equations, which have been found important in deriving not only the mean but also tur- bulent wind structure of the measured wind field. Finally, dropwindsonde profiles are low-pass filtered to eliminate high-frequency measurement noise. As mentioned above, a package of specially designed code, named PostSonde, is employed to complete the post-processing described above. Following the functions provided and procedures uti- lized by EDITSONDE (J. L. Franklin 2010, personal communication), PostSonde is able to conduct a fairly comprehensive quality control, and PostSonde gives users the control over the selection of the differentiation scheme to calculate the dropwindsonde acceler- ation, which is required in the wind finding equations. In addition, the design of the low-pass filter is also adjustable in PostSonde. To justify the use of PostSonde, several selected post-processed dropwindsonde profiles, produced by PostSonde and other popu- lar dropwindsonde measurements processing systems, namely EDITSONDE and Aspen, are compared. One of the comparisons is shown in Fig. 4.1. Although the compari- son indicates processed profiles from three different programs are not identical for all the heights, they are nearly indistinguishable for a large portion of the comparison, and those noticeable differences can be explained by the different criteria used in the quality control process. It should be noted that the post-processing scheme is not fully retrievable for EDITSONDE and Aspen, since EDITSONDE processing results are taken directly from the database maintained by the HRD, and Aspen is a total ”black-box” software from which no internal processing scheme can be uncovered. Thus, the quality control criteria

and dynamic correction procedures are inevitably different for three different processing systems. Nevertheless, the obvious agreement shown in the figure supports the use of PostSonde in post-processing dropwindsonde measurements. As for the configuration of the post-processing, the second-order central difference is used to calculate the dropwind- sonde accelerations, and a moving average filer with a cut-off time scale of 3s is used to smooth the curve.

0 2000 4000 6000 8000 10000 12000 14000 16000 -8 -6 -4 -2 0 2 4 6 8 Height (m) WindX (m/s) Aspen EditSonde PostSonde

(a) Longitudinal Wind Comparison

0 2000 4000 6000 8000 10000 12000 14000 16000 0 200 400 600 800 1000 1200 Height (m) AirPress (mb) Aspen EditSonde PostSonde

(b) Air Pressure Comparison

0 2000 4000 6000 8000 10000 12000 14000 16000 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 Height (m) AirTemp (deg) Aspen EditSonde PostSonde

(c) Air Temperature Comparison

0 2000 4000 6000 8000 10000 12000 14000 0 10 20 30 40 50 60 70 80 Height (m) RelHumid (%) Aspen EditSonde PostSonde

(d) Relative Humidity Comparison

Figure 4.1: Comparison between dropwindsonde profiles processed by PostSonde, EDIT- SONDE and Aspen, the wind velocity shown is decomposed from the total wind velocity according to its orientation relative to the longitude circle.

After the post-processing procedures articulated above, dropwindsonde profiles are composited to produces desired statistics of the measured wind field. Following the same methodology proposed by Powell et al. (2003), dropwindsonde profiles are composited according the mean wind velocity measured in lowest 500m, or the MBL wind velocity. Given that the current database is much larger than that used in previous studies, the resolution of the MBL wind speed based composition can be increased. In detail, drop-

windsonde profiles are divided into 18 groups, corresponding to the MBL wind velocity from 20m/sto 74m/sincreasing at a 3m/s step. Since the gradient wind velocity is also an important velocity scale in the HBL (Kepert, 2001; Foster, 2009), the mean of the wind velocities measured from 1500m to 2000m is also used as a grouping indicator. In addition, considering that the wind field measured by dropwindsondes obviously varies horizontally, the combination of the MBL wind velocity and dropwindsonde splash down location, defined as where the dropwindsonde hits the sea surface, is also used to group processed dropwindsonde profiles. In order to keep the composition size large enough to produce statistically meaningful results for each group in the combined composition, the MBL wind velocity step is increased to 10m/s. As mentioned above, the dropwindsonde splash down location is categorized into three regions, the inner core region, the eye-wall region and the out-skirt region based on its normalized radius to the storm center, which is defined as the actual radius divided by the storm RMW. Moreover, to validate the composition part of PostSonde, the exactly same composition strategy, as in the study of Vickery et al. (2009), is adopted. Then, the composition results are compared to the calculations results of their empirical profile function.

Since the grouping scheme combining the MBL wind speed and dropwindsonde splash down location requires the center location and RMW of storms to be found before the composition, the track and size of tropical cyclones are calculated first. Following the technique proposed by Kepert (2005), the track and RMW of a storm are determined by fitting the sea level pressure observed by the dropwindsonde, and sometimes the geopo- tential height observed by concurrent reconnaissance flights, to an idealized pressure, or geopotential, horizontal profile. The fitting results are then subjectively reviewed and compared to the BestTrack data from HRD. Those results giving unrealistic tracks, mo- tions, or RMWs of storms are thrown away, which leads to eliminating the corresponding dropwindsonde profiles from the composition database. In addition to the combined grouping scheme, the storm track is also required to decompose measured wind velocities into tangential and radial components, and the storm motion is required in dividing the reconstructed wind field into four quadrants since the north direction of the storm relative

coordinate system used in setting up quadrants is the direction of the storm motion.

As dropwindsonde profiles are appropriately grouped according to various schemes, the composition is applied to every groups to calculate desired statistics of the measured wind field. The calculation is done in three steps. First, the processed dropwindsonde profile is segmented into several bins according to the measurement height in a profile. Each of bins contains measurement points with height differences less than 30m. In this case, the height of the measured wind field, which is assumed to be 3000mas in the study of Powell et al. (2003), is divided into 100 bins. Second, measurement points within one height bin from numerous different processed profiles constitute the sampling database to cal- culate the desired statistics. The calculation process is essentially a weighted-averaging process. This process can be applied to raw dropwindsonde measurements, which pro- duces a mean wind profile, or remains left by eliminating the mean wind profile, which produces the turbulence statistics. In the weighted-averaging, the weight is assigned to each measurement point according to the distance from the measurement height to the height bin center. A weight of 1 is assigned if the measurement is coincidently located at the height bin center while a weight of 0 is assigned if the measurement is taken at the boundary of the height bin. Any measurements taken in the region between the height bin center and boundary has a weight linearly interpolated between 1 and 0. Therefore, the calculated value represents the desired statistic at the height bin center. Third, val- ues for all height bins are assembled to produce the profile of the desired statistics. The actual number of measurement points used in the composition is presented in Fig. 4.2, which illustrates the number of measurements within each group in the MBL wind based composition. The number for a single group is calculated as the mean of all height bin sampling databases.