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Comparison of Planetary Boundary Layer Model Winds with Dropsonde Observations in Tropical Cyclones ROBERT A. BROWN

AND

LIXIN ZENG

Department of Atmospheric Sciences, University of Washington, Seattle, Washington (Manuscript received 17 March 2000, in final form 6 March 2001) ABSTRACT The values of surface winds simulated by the University of Washington (UW) two-layer similarity planetary boundary layer (PBL) model are compared with National Oceanic and Atmospheric Administration Hurricane Research Division global positioning system dropsonde observations and the surface wind analyses of a numerical weather prediction model. These three wind products compare fairly well at moderate wind speeds, away from the center of the storms where the coarse resolution of the numerical model is not a major factor. In the very high wind regime, the UW PBL model winds match the dropsonde observations fairly well, which is consistent with the unique characteristic of the PBL model being able to account for the nonlinear effects of organized large eddies. These eddies transport momentum and heat fluxes more efficiently than the smaller-scale, local turbulence can, leading to simulations of higher winds with mesoscale variability.

1. Introduction It has always been a major challenge to model the surface winds in the planetary boundary layer (PBL) over the ocean, especially at high wind speeds. This task has recently been brought to the forefront by two different surface wind analysis schemes. One is a higherresolution numerical model; the other is a model function for the ‘‘QuickSCAT’’ satellite microwave quick scatterometer (http://www.ssmi.com/qscatinfo.html). Because a crucial ingredient in the verification of both of these methods is a good PBL model, we examine the capability of the University of Washington PBL (UWPBL) model in simulating very high winds. This PBL model currently simulates higher winds than are obtained from other mesoscale PBL models. In a study of midlatitude Pacific Ocean storms, it simulated large regions of winds over 35 m s 21 where the European Centre for Medium-Range Weather Forecasts (ECMWF) model produced 23 m s 21 winds (Dickinson and Brown 1996). This result is primarily because the computing power available to the general circulation numerical models is insufficient to allow them to resolve fully the turbulent PBL eddies. In practice, most numerical weather prediction (NWP) PBL models employ an eddy-viscosity model that parameterizes the turbulent transport as a down-gradient diffusion. In these models, it is assumed that the turbulent flow at subgrid scales Corresponding author address: Robert A. Brown, University of Washington, Department of Atmospheric Sciences, Box 351640, Seattle, WA 98195. E-mail: [email protected] q 2001 American Meteorological Society

is homogeneous. A grid-scale eddy-flux parameter can then be used to represent the average turbulent transport over the region. However, theoretical and observational studies (Brown 1980, 2000; Etling and Brown 1993) show that persistent PBL-scale turbulent structures, known as organized large eddies (OLEs), are frequently present in unstable to near-neutral (stable) stratification. Recent observations in hurricanes have revealed evidence of frequent OLE presence in the PBL (P. Black and K. Katsaros, 2001, personal communication). The OLEs impart a significant mesoscale (500 m–5 km) twodimensional variability predicted by the PBL solution and observed by satellite remote sensing (Brown 2000). This horizontal variation in wind speed and flux has an impact on point surface measurements used as surface truth to determine wind and flux parameterizations. The OLEs transport momentum to the surface more efficiently than does the local down-gradient diffusion so that surface winds from the nonlinear solution are larger on the average than those of linear diffusion models. Although increasing the diffusivity coefficient in an ad hoc manner to account for the OLE can increase surface winds in the numerical model, it is not physically sound and may cause other ramifications. Usually the absence of OLE effects in PBL models leads to an underestimate of surface winds. Also contributing to the difficulty in modeling high winds is the lack of reliable observations. It has been shown (e.g., Zeng and Brown 1998; Large et al 1995) that oceanic buoy observations systematically underestimate wind speeds for speeds greater than 20 m s 21 . For the purposes of establishing the model function for

OCTOBER 2001

BROWN AND ZENG

satellite scatterometers, correlations with buoys were first tried. In over 70 000 hits there were no winds greater than 22 m s 21 . In a comparison study by Freilich and Dunbar (1999) there were only 186 out of 56 000 buoy winds above 18 m s 21 . Given that the buoys and numerical surface wind analyses have been the basic source of ‘‘surface truth’’ for the scatterometer model functions, it is likely that in general there has been no surface truth for high winds. However, there have been some indications of more frequent very high winds than are represented in the climatological record, model output, or satellite records. A survey of weather station ship data revealed that sustained winds in midlatitude storms exceeded 30 m s 21 many times and 45 m s 21 once every winter (Dickinson and Brown 1996). A study using surface pressure fields as surface truth showed a systematic underevaluation of about 10% for the National Aeronautics and Space Administration scatterometer, version 1 (NSCAT-1) model function (Zeng and Brown 1998). Based on sparse but compelling data in hurricanes (including the dropsonde data discussed here), a new model function for QuikSCAT recently has been made available that yields winds over 60 m s 21 for a 25-km footprint. This value is attained only in typhoons and at least one singular event off France in 1999. This ability to predict the extremely rare very high wind without changing the model function for the rest of the wind spectrum demonstrates the capability (in terms of continuous backscatter response in the horizontal polarization return) to include very high winds in the scatterometer model function. What is missing is correlating surface truth data. Here, we discuss an example of measurements that come closer to surface truth in high winds than any previous measurements. The global positioning system (GPS) dropsonde data are collected, archived, and quality controlled by the National Oceanic and Atmospheric Administration (NOAA) Hurricane Research Division (HRD). They are the first set of reliable wind measurements with abundant high-wind records near the sea surface (Hock and Franklin 1999). The goal of this study is to use these data to examine the validity and accuracy of the UWPBL model at high wind speeds. The model has been calibrated only under low to moderate wind speed conditions because of the lack of reliable high-wind observations. Although the higher winds are supported by a valid PBL turbulence theory summarized in the next section, there had not been any validation using direct wind observations until the GPS data became available. We first briefly introduce the UWPBL model (section 2), followed by a description of the data used in the study (section 3). Comparisons of the dropsonde observations and the UWPBL model winds are presented in section 4. A summary concludes the study in section 5.

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2. The PBL model The UWPBL model (Brown and Liu 1982) is a twolayer similarity model with parameterizations for stratification, variable surface roughness and humidity, gradient wind, isallobaric wind, thermal wind, and OLE effects. The OLE is a horizontal nonhomogeneity on the scale of the PBL height. The unique feature of the UWPBL model is that it includes a parameterization of the OLE effects on wind profile, momentum, and heat fluxes. When the advective flux of the large eddies is explicitly included, the high-momentum flow is brought to the surface much more efficiently. This is an analytic solution of the matching of an Ekman solution to a loglayer solution (Brown 1974b). The latter is corrected for interfacial layer effects according to Liu et al. (1979). The ratio of characteristic wind speeds in the two layers (u*/G, where u* is the surface frictional velocity and G is the scale of surface gradient wind speed) is related to a single similarity parameter l, the ratio of surface layer to Ekman layer characteristic heights. Given that the model has been published (Brown 1970, 1974a,b, 1978; Brown and Liu 1982; Brown and Foster 1994), is available online at pbl.atmos.washington.edu, and has seen considerable usage and verification in the community, we shall not expand the details here. The theory of the model, the effect of the OLE parameterization, and comparisons with a general circulation model PBL were thoroughly reviewed in Brown and Foster (1994) and Foster and Brown (1994a,b). The key similarity parameter of the UWPBL model, l, has been shown to be approximately a constant for variable stratification under low to moderate wind conditions (Brown 1982). However, there have been no observations to determine whether l remains the same constant for high winds. In this study, we keep l the same constant and compare the surface winds calculated by the model to collocated and coincident GPS dropsonde observations. 3. Data sources, preprocessing, and screening Quality-controlled observations from 891 GPS dropsondes are obtained from NOAA HRD. They cover selected tropical cyclones that occurred in the Atlantic basin during 1997 and 1998. In each of the dropsonde vertical data profiles, there are usually two observations located at ;7 and ;15 m from the surface, respectively. The component-based average wind observations at these two levels are interpolated to approximate the dropsonde wind at 10 m, the height at which the UWPBL model then calculates the winds. The upper boundary condition of the UWPBL model is initially calculated based on the sea level pressure (SLP) analyses from ECMWF. However, it is known that in the vicinity of storms the numerical model pressures can be in error (Brown and Zeng 1994) because of the model’s coarse resolution and inadequate PBL

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JOURNAL OF APPLIED METEOROLOGY

VOLUME 40

FIG. 1. The (left) NWP SLP analysis, (right) corrected SLP field, and the SLP observations from the dropsondes (shown in both panels). The SLP contours are labeled in bold italic fonts. The SLP observations from the dropsondes are marked with asterisks, and their values are marked below the asterisks.

modeling (e.g., Fig. 1, left panel). Thus, the NWP pressure analyses are corrected with the surface pressure observations from the dropsondes. The correction is based on an objective analysis based on a simple direct minimization approach (appendix A). A sample corrected SLP field is shown in Fig. 1 (right panel). The corrected pressure field, which is on a 0.258 by 0.258 grid, is then used to derive the surface geostrophic wind. In regions of high curvature of the flow, the geostrophic winds are converted to the gradient winds that serve as the upper boundary condition of the UWPBL model. For the geostrophic–gradient wind conversion, the radius of curvature of the streamline is calculated using the sonde-modified SLP analysis. The radius of curvature of the wind trajectory is estimated assuming the tropical cyclone wind fields are moving systems (Holton 1992). Mathematical details are discussed in appendix B. Given the surface gradient wind field as the upper boundary condition, the UWPBL model produces the surface wind field on the same grid. The ECMWF surface wind analyses are also included for comparison. Because they correspond to an approximately 100-km resolution, these represent only a largescale average of the winds and are used mainly as a reference. A two-step data screening is conducted to ensure that

the dropsonde observations and the UWPBL model winds are comparable. First, because the ECMWF analyses are available only at 0000, 0600, 1200 and 1800 UTC, only those dropsonde observations within an hour from the ECMWF analysis times are included in the comparison. Next, only those ECMWF SLP analyses that adequately capture the locations of the cyclones are selected. The criterion is that the low center of the SLP analysis must be within 50 km of the storm center determined by the HRD hurricane best-track data. Six ECMWF analyses corresponding to 46 GPS dropsondes pass both steps of the data screening. In addition, to account for the time lag or lead (up to 1 h) of dropsonde deployment relative to the analysis time, the locations of the dropsondes are adjusted based on the velocity of the storm center derived from the HRD hurricane best-track data. Thus, the adjusted positions of the dropsondes are their relative displacements from the center of the storm at the time of deployment. 4. Wind comparisons The UWPBL and NWP surface wind fields are linearly interpolated to the locations of the dropsonde observations. The surface wind speeds and directions are compared with the corresponding dropsonde observa-

OCTOBER 2001

BROWN AND ZENG

FIG. 2. The surface wind observations from the dropsondes (thick arrows) and calculated by the UWPBL model (thin arrows). The speed of the wind is proportional to the length of the arrow. A 20 m s 21 benchmark is plotted at the lower-left corner of the figure.

tions (Figs. 2 and 3). The NWP surface wind analyses and the UWPBL winds compare well with the dropsonde observations for low and moderate wind speeds, for which the dropsondes are deployed away from the center of the storms and coarse resolution of the numerical model is not a major factor. The UWPBL model winds are also in agreement with the dropsonde observations at the high wind speeds. This result is surprising because the dropsonde wind is nearly an instantaneous measurement of the mean wind in the bottom of the PBL. The UWPBL wind boundary condition represents an average corresponding to the NWP pressure field corrected with the dropsonde instantaneous pressures.

1721

Therefore the OLE are averaged in the UWPBL winds, implying an inherent error of 1–2 m s 21 in the comparison with a point value because of the organized turbulence. Apparently the fluctuations are sufficiently averaged to yield a good comparison. In the regions of highest curvature of the isobars, the gradient wind correction is necessary and has the effect of reducing the UWPBL winds in the vicinity of the dropsonde winds. In the center of the storms it is clear that the results are sensitive to isobar curvature and storm movement. This results in an increased error in the PBL winds. The comparisons are summarized in Table 1. The wind direction differences are defined as the directions of the UWPBL model (and the coarse-resolution NWP surface winds for reference), relative to the corresponding dropsonde observations, increasing counterclockwise. It is shown that they are comparable for all speed ranges with minimal bias (approximately 28) and a root-mean-square error of approximately 258. 5. Summary This study briefly summarizes the theoretical background of the UWPBL model and discusses the effects of nonlocal transport of momentum by OLEs in the boundary layer. The core of the study is a comparison of collocated and coincident HRD dropsonde winds and UWPBL model surface winds to investigate the validity of the model at very high winds. The results demonstrate that the UWPBL model with a constant similarity parameter adequately reproduces both surface wind speed and direction at these high winds with expected random

FIG. 3. The surface wind speeds from the NWP analysis (1) and the UWPBL model (*) vs the dropsonde observations.

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VOLUME 40

TABLE 1. Differences between UWPBL model and dropsonde surface winds. Low to moderate wind speeds (dropsonde wind , 20 m s21 )

High wind speeds (dropsonde wind $ 20 m s21 )

Mean difference

Root-mean-square difference

Mean difference

Root-mean-square difference

20.7

4.1

0.8

6.5

UWPBL minus dropsonde (m s21 )

errors. The results are consistent with the fact that the UWPBL model explicitly parameterizes the boundary layer OLE effects whereas most other PBL models, including the one used by NWP, do not explicitly include OLE. Acknowledgments. We thank the National Oceanic and Atmospheric Administration Hurricane Laboratory of Miami, Florida, for their cooperation. This work was supported by NASA QuikSCAT Grant NSO33A-01, administered through Oregon State University. APPENDIX A Correcting the NWP SLP Analyses with the Dropsonde SLP Observations Because of the coarse resolution of the NWP SLP analysis, it cannot be used directly to calculate the upper boundary condition of the UWPBL model. This appendix described a simple variational approach that corrects the SLP analysis based on SLP observations from dropsondes. At first, the initial NWP SLP analysis is interpolated to a 0.258 3 0.258 grid. Let X, Y, and Z be vectors representing the NWP SLP field, the dropsonde SLP observations, and the corrected SLP field, respectively. The goal is to solve for Z such that the following objective function F is minimized: F 5 w0 (Z 2 X) 2 /M 1 (HZ 2 Y) 2 /N 1 w s

O ¹ Z/M,

should be within a hurricane. Experiments show that 0.05 is a reasonable compromise of not generating too much noise (e.g., unrealistic local circulation), but letting the corrected SLP reflect the dropsonde value reasonably well overall. However, because the spatial change of SLP near the center of a hurricane can be extreme, the corrected SLP field from the objective analysis above cannot reproduce the steep pressure gradient observed by the dropsondes. For example, in Fig. 1 (left panel), the SLP observations from dropsondes A and B are 981 and 962 hPa, respectively. However, the SLP values interpolated from the corrected SLP fields are 980 and 976 hPa, respectively. This result implies that, near the center of the storm, the pressure gradient can be underestimated by approximately 4 times. This problem cannot be solved by using extremely small w 0 and w s values, because it would introduce unrealistic circulation patterns. To alleviate this problem, we further manually adjusted the pressure gradient for six dropsondes that are close to the storm centers in our comparison. For example, the UWPBL surface wind for dropsonde A is adjusted assuming the input pressure gradient is 4 times as great as that suggested by the SLP field. APPENDIX B Calculating the Radius of Curvature of the Trajectory

2

where H is the interpolation operator that interpolates the corrected SLP fields to the locations of dropsonde observations. Variables M and N are the number of grid points in the SLP field and the number of dropsonde observations, respectively. The first term on the right-hand side lets the corrected SLP field resemble the initial NWP SLP analysis. This is necessary because the dropsonde observations are not even distributed throughout the domain of interests. The second term forces the corrected SLP values to be close to the dropsonde observations. The third terms enables the corrected SLP field to be relatively smooth. The factors w 0 and w s control the relative importance of terms 1 and 3 versus that of term 2. In the vicinity of hurricanes, the typical SLP analysis error can be an order of magnitude greater than that of the dropsonde observations, as observed in this study. Thus, we let w 0 be 0.1. The choice of w s is fairly arbitrary because there is no prior knowledge of how smooth the SLP field

a. Calculating the radius of curvature of the streamline Because the streamline is parallel to the pressure contour, the radius of curvature of the streamline is equal to that of the pressure contour. Let the sea level pressure p 5 f (x, y), where x and y are the longitude and latitude in a local Cartesian coordinate. The equation of a pressure contour is then f (x, y) 5 const. Locally, it can be written as y 5 y(x). In a local polar coordinate (uˆ ,sˆ), the radius of curvature R is defined as R 5 ds/du.

(B1)

In addition, ds 5 Ï(dx) 2 1 (dy) 2 ,

and

du 5 d[tg 21 (dy/dx)]. Combining Eqs. (B1), (B2a), and (B2b) gives

(B2a) (B2b)

OCTOBER 2001

R5

[1 1 (dy/dx) 2 ] 3/ 2 . d 2 y/dx 2

(B3)

Now we need to calculate dy/dx and d 2 y/dx 2 from p 5 f (x, y), which is the known pressure field. We start from dp 5

]p ]p dx 1 dy. ]x ]y

1dx2 dy

52 p5const

@

]p ]x

]p y 5 g, ]y ug

]p

2

]p

2

]p

2

2

2

2

2

2

]2p ]2p ]2p 2 (dx) 1 2 dxdy 1 (dy) 2 ]x 2 ]x]y ]y 2 1

]p 2 ]p d x 1 d 2 y. ]x ]y

(B6)

Along a pressure contour, d(dp) 5 0. Thus,

1 2

]2p ] 2 p dy ] 2 p dy 12 1 2 2 ]x ]x]y dx ]y dx

2

1

]p d 2 y 5 0. ]y dx 2

(B7)

]

(B8)

Then,

[

1 2 @]y .

d2y ]2p ] 2 p dy ] 2 p dy 5 1 2 1 dx 2 ]x 2 ]x]y dx ]y 2 dx

2

]p

Combining Eqs. (B5) and (B8) and replacing the first and second derivatives of p with u g , y g , and their first derivatives gives

[

]

1 2 @u .

d2y ]y g ]u g y g ] 2 ug y g 5 2 2 2 dx 2 ]x ]x u g ]y u g

2

g

2

C cosg , V

(B10)

REFERENCES

2

2

12

(B5)

1]x2 dx 1 ]x d x 1 d 1]y2 dy 1 ]y d y ] p ] p ]p 5 1 dx 1 dy dx 1 d x ]x ]x]y 2 ]x ] p ] p ]p 11 dx 1 dy2 dx 1 d y ]x]y ]y ]y ]p

@1

Rt 5 R

where C is the speed at which the system moves, V is the wind speed, and g is the angle between the directions of the streamline and motion of the system.

where u g and y g are the east–west and north–south components of the surface geostrophic wind, respectively. From Eq. (B4), d(dp) 5 d

is used to estimate the radius of curvature of the trajectory R t :

(B4)

We have

5

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BROWN AND ZENG

(B9)

Combining Eqs. (B3), (B5), and (B9) gives R. b. Calculating the radius of curvature of the trajectory Assuming the tropical cyclone is a moving system, the equation used in the main text (from Holton 1992)

Brown, R. A., 1970: A secondary flow model for the planetary boundary layer. J. Atmos. Sci., 27, 742–757. ——, 1974a: Matching classical boundary layer solutions toward a geostrophic drag coefficient relation. Bound.-Layer Meteor., 7, 489–500. ——, 1974b: Analytic Methods in Planetary Boundary Layer Modeling. John Wiley and Sons, 150 pp. ——, 1978: Similarity parameters from first-order closure. Bound.Layer Meteor., 14, 3381–3096. ——, 1980: Longitudinal instabilities and secondary flows in the planetary boundary layer. Rev. Geophys. Space Phys., 18, 683– 697. ——, 1982: On two-layer models and the similarity functions for the planetary boundary layer. Bound.-Layer Meteor., 24, 451–463. ——, 2000: Serendipity in the use of satellite scatterometer, SAR and other sensor data. Johns Hopkins APL Tech. Dig., 21 (1), 21–26. ——, and R. Foster, 1974: On PBL models for general circulation models. Global Atmos.–Ocean Syst., 2, 163–183. ——, and W. T. Liu, 1982: An operational large-scale marine planetary boundary layer model. J. Appl. Meteor., 21, 261–269. ——, and L. Zeng, 1994: Estimating central pressures of oceanic midlatitude cyclones. J. Appl. Meteor., 33, 1088–1095. Dickinson, S., and R. A. Brown, 1996: Using SSMI/WETNET and ERS-1 data to analyze mid-latitude storms systems. J. Appl. Meteor., 35, 769–781. Etling, D., and R. A. Brown, 1993: A review of large-eddy dynamics in the planetary boundary layer. Bound.-Layer Meteor., 65, 215– 248. Foster, R., and R. A. Brown, 1994a: On large-scale PBL modelling: Surface wind and latent heat flux comparisons. Global Atmos.– Ocean Syst., 2, 199–219. ——, and ——, 1994b: On large-scale PBL modelling: Surface layer models. Global Atmos.–Ocean Syst., 2, 185–198. Freilich, M. H., and R. S. Dunbar, 1999: The accuracy of the NSCAT 1 vector winds: Comparisons with National Data Buoy Center buoys. J. Geophys. Res., 104, 11 231–11 246. Hock, T. F., and J. L. Franklin, 1999: The NCAR GPS dropsonde. Bull. Amer. Meteor. Soc., 80, 407–420. Holton, J., 1972: An Introduction to Dynamic Meteorology. Academic Press, 319 pp. Large, W. G., J. Morzel, and G. B. Crawford, 1995: Accounting for surface wave distortion of the marine wind profile in low-level ocean storm wind measurements. J. Phys. Oceanogr., 25, 2959– 2971. Liu, W. T., K. B. Katsaros, and J. A. Businger, 1979: Bulk parameterization of air–sea exchanges of heat and water vapor including the molecular constraints at the interface. J. Atmos. Sci., 36, 1722–1735. Zeng, L., and R. A. Brown, 1998: Scatterometer observations at high wind speeds. J. Appl. Meteor., 37, 1412–1420.

Comparison of Planetary Boundary Layer Model Winds with ...

with the unique characteristic of the PBL model being able to account for the nonlinear effects of organized large eddies. .... event off France in 1999. This ability to predict .... sure analyses are corrected with the surface pressure observations ...

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