A gust-factor criterion for rapid determination of atmospheric stability and mixing height for overwater dispersion estimates.

Abstract

In order to estimate atmospheric pollution concentration downwind from its source, meteorological models (numerical, analytical, or graphical) are usually employed. Included in the model inputs are atmospheric stability and mixing height, which are not routinely measured in the marine environment. On the basis of relationships amongst gust factor, turbulence intensity, and stability parameter, methods are developed for rapid estimation of these two inputs. It is found that, based on the stability classification of the Offshore and Coastal Dispersion Model, when the gust factor (G, which is the ratio of peak gust to the sustained wind speed) is between 1.15 and 1.45, the stability is near-neutral. When G is less than 1.15, it is stable, and for G greater than 1.45, unstable. Using routine buoy measurements as a composite characteristic, equations for the mixing height under various stability classes are also formulated.

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1. Introduction

Numerous waterways, marinas, ports, and coastal and offshore facilities (such as oil platforms) are vulnerable if an incidental release of hazardous material occurs. There is a definite need in the component of our homeland security to have a quick response plan to better estimate the concentration downwind from the point of release. In this regard, meteorologists will be inevitably called upon to assist.

The dispersion of atmospheric pollutants, whether chemical, biological, or nuclear, depends principally on the information of emission and meteorology. Estimates of air pollutant concentrations at receptors can be made using dispersion models. The purpose of a dispersion model is to simulate atmospheric chemistry and physics. According to Turner (1994), the primary inputs to a dispersion model consist of emission information, meteorological data, and receptor information. The meteorological parameters that are required for input to a dispersion model are hourly Pasquill stability class, wind direction, wind speed, temperature, and mixing height.

The purpose of this study is to provide information for rapid estimation of both stability class and mixing height using routine meteorological measurements from buoys. Specifically, in order to estimate the stability class, the routinely measured gust factor is used.

2. Estimating Overwater Stability Categories

Atmospheric stability in the surface boundary layer is broadly classified into three categories. When the sea-surface temperature, [T.sub.sea], is higher than the air temperature, [T.sub.air], (i.e., [T.sub.sea] > [T.sub.air]), we say it is under unstable conditions. When [T.sub.air] [approximately] [T.sub.sea], near-neutral condition prevails. When [T.sub.air] > [T.sub.sea], stable conditions exist. On the basis of an offshore and coastal dispersion model (Hanna et al. 1985), Hsu (1992) provided a criterion which is further simplified for this study as follows:

[z/L] [less than or equal to] -0.4 Unstable (1)

-0.4 < [z/L] < 0.4 Near Neutral (2)

0.4 [less than or equal to] [z/L] Stable (3)

where z is the height above the sea surface and is conventionally set to 10 m. Parameter L is called the Monin-Obukhov Stability length (Panofsky and Dutton 1984). The value of L is as follows (Hanna et al. 1985): for unstable, -25 m [less than or equal to] L; neutral, |L| > 25 m; and stable, L [less than or equal to] 25 m.

In the marine environment, Smith (1980) found that

[[sigma].sub.U]/U = 0.101 - 0.12[z/L] (4)

where [[sigma].sub.U] is the standard deviation of the sustained horizontal wind speed (downwind direction) U and [[sigma].sub.U]/U is termed the horizontal turbulence intensity. On the other hand, Hsu (2001) proposed that [[sigma].sub.U]/U and the gust factor (G) are related such that

G = [U.sub.gust]/U = 1 + 3[[[sigma].sub.U]/U] (5)

where [U.sub.gust] is the peak gust. Substituting Eq. (4) into (5), we have

G = 1.30 - 0.36[z/L] (6)

Verification of this concept was accomplished using a 5-year hurricane data set (see Table 1) of buoy measurements of peak gusts and sustained winds, which included one tropical storm and 11 hurricanes. This data set was used to be certain strong winds prevailed (Pasch and Avila 1999; Rappaport 1999; Pasch et al. 2001; Lawrence et al. 2001; and Franklin et al. 2001).

The statistical analysis of this data set yielded a coefficient of variation of less than 5% and a grand mean of 1.3. This agrees with the analysis of a 10-year hurricane data set where the grand mean was also 1.3 (Hsu 2002). Therefore, Eq. (6) is verified when z/L = 0. Now, substituting Eq. (2) into (6), G = 1.16 for z/L = 0.4 and G = 1.44 for z/L = -0.4. Hence, the following stability criteria are proposed based on overwater gust factor measurements:

G [greater than or equal to] 1.45 Unstable (7)

1.16 < G < 1.44 Near Neutral (8)

G [less than or equal to] 1.15 Stable (9)

3. Estimating Mixing Height

a. Under near neutral conditions (Eq. (8))

According to Geer (1996), the mixing height (or depth) is the vertical distance between the earth's surface and the altitude to which convective currents can uniformly disperse pollutants. This upper limit is usually a temperature inversion. Due to potential evaporation, the air over the water is usually moister than that over land, and the top of the marine layer is oftentimes capped by clouds. According to Garratt (1992), the cloud-topped boundary layer can be broadly identified with a turbulent region in which patterns and ensembles of stratus, stratocumulus and cumulus clouds reside beneath a capping inversion. It is a dominant feature of the weather of the lower atmosphere and the climate conditions of many areas of the globe, particularly over the sea. On the basis of analysis of vertical soundings taken by research aircraft, rawinsondes, radar wind profilers and Radio Acoustic Sounding Systems, it has been shown by Garratt (1992) that the mixing height (h) equals the lifting condensation level (LCL) under cumulus cloud conditions (where LCL = cloud base). The height of the LCL ([H.sub.LCL]) may be estimated by (Hsu 1998)

[H.sub.LCL] = 125([T.sub.air] - [T.sub.dew]) (10)

where [H.sub.LCL] is in meters and the dewpoint depression (difference between air and dewpoint temperatures) at the sea surface is in degrees Celsius.

Eq. (10) is recommended for estimating the mixing height under near neutral conditions. Note that in this mixing layer, the vertical distribution of potential temperature is nearly constant (Garratt 1992), meaning the atmosphere is nearly neutral. For example, under hurricane conditions the dewpoint depression is generally within 4[degrees]C (see NOAA/National Data Buoy Center Web site: seaboard.ndbc.noaa.gov during Hurricane Lili from 1-3 October 2002, at buoy 42001), hence the mixing height is approximately 500 m. This same value is used as the height of the habitation layer by Simpson and Riehl (1981) and as the boundary layer depth during a hurricane by Anthes (1982). According to Turner (1994), the neutral category should also be used when the wind speed at the standard 10 m height is higher than 6 m [s.sup.-1] or 12 kt.

If [T.sub.dew] for Eq. (10) is not available, it may be estimated by (Hsu 1988)

[T.sub.dew] = [237.3[log.sub.10]([e.sub.air]/6.1078)]/[7.5 - [log.sub.10]([e.sub.air]/6.1078)] (11)

and

[e.sub.air] = [1/0.62]P [q.sub.air] (12)

where [e.sub.air] is the vapor pressure (mb), P is air pressure (mb), and [q.sub.air] the specific humidity (g [kg.sup.-1]), respectively. For operational applications (Hsu 1998, Fig. 3 with a correlation coefficient = 0.96)

([q.sub.sea] - [q.sub.air]) = 5.68 + 0.37 ([T.sub.sea] - [T.sub.air]) (13)

and

[q.sub.sea] = 0.62[[e.sub.sea]/P] (14)

where

[e.sub.sea] = 6.1078 X [10.sup.[7.5[T.sub.sea]/(237.3 + [T.sub.sea])]] (15)

b. Under stable conditions (Eq. (9))

According to Venkatram (1980) for mid-latitude applications and the WAMDI Group (1988),

[H.sub.stable] = 2.4 * [10.sup.3][u.sub.*.sup.3/2] (16)

[u.sub.*] = [square root of [C.sub.d]]U (17)

[C.sub.d] = 1.2875 * [10.sup.-3], when U < 7.5 m/s (18)

where [u.sub.*] is the friction velocity and [C.sub.d] is the drag coefficient.

From Eqs. (16) through (18), we have

[H.sub.stable] = 16.3 [U.sup.3/2] (19)

where [H.sub.stable] is in meters and U in m [s.sup.-1].

c. Under unstable conditions (Eq. (7))

According to Hsu (1997),

[H.sub.unstable] = 369 + 6004[C.sub.T]U([T.sub.sea] - [T.sub.air])(1 + [0.07/B]) (20)

From Smith (1980),

[C.sub.T] = 1.10 * [10.sup.-3] (21)

and from Hsu (1999),

B = 0.146([T.sub.sea] - [T.sub.air])[.sup.0.49] (22)

[C.sub.T] is the coefficient for sensible heat flux, and B is the Bowen ratio. Substituting Eq. (21) into (20), we have

[H.sub.unstable] = 369 + 6.6U([T.sub.sea] - [T.sub.air])(1 + [0.07/B]) (23)

For example, if ([T.sub.sea] - [T.sub.air]) = 10[degrees]C and U = 3 m [s.sup.-1], [H.sub.unstable] = 598 m or 1962 ft.

4. Concluding Remarks

In order to facilitate rapid determination of atmospheric dispersion characteristics, the concept of gust factor is employed. Although all equations used in this study are based on those already available in the "open literature", further refinement may be needed by providing some cases which address systems over the Atlantic and Pacific in higher latitudes, or even for strong systems over the Great Lakes.

Table 1. Overwater measurements of sustained wind and peak gust during
hurricanes for a 5-year period from 1996 through 2000. The gust factor,
G, is the ratio of peak gust to sustained wind. (Data sources: Pasch and
Avila (1999), Rappaport (1999), Pasch et al. (2001), Lawrence et al.
(2001), and Franklin et al. (2001))

                          Peak Gust  Sustained Wind          SST*
Year  Hurricane  Buoy        (kt)          (kt)      G       [degrees]C

1996  Fran       41004        64            49        1.31   26.8
1997  Danny      42007        46            35        1.31   26.8
                 42040        42            33        1.27   28.4
                 44004        42            32        1.31   23.7
                 44008        37            30        1.23   17.2
                 44014        54            42        1.29   25.3
1998  Bonnie     41002        57            42        1.36   27.4
                 41004        49            38        1.29   27.4
                 44004        46            36        1.28   24.2
                 44014        47            37        1.27   24.6
                 Georges
                   Bank       45            35        1.29   NA
      Earl       42040        55            41        1.34   29.7
                 42039        63            45        1.40   26.9
                 42036        47            35        1.34   27.6
                 42002        34            26        1.31   30.2
                 42001        52            37        1.41   NA
                 42007        37            30        1.23   29.2
      Georges    42003        66            51        1.29   28.5
                 42039        56            43        1.30   28.2
                 42036        48            34        1.41   27.6
                 42040        68            54        1.26   26.8
                 42007        54            44        1.23   26.9
      Mitch      42003        44            37        1.19   26.7
                 41010        45            37        1.22   26.8
1999  Bret       42020        73            58        1.26   NA
      Dennis     41001        63            48        1.31   26.9
                 41002        59            43        1.37   27.6
                 41004        72            54        1.33   26.1
                 41008        43            31        1.39   28.9
                 41009        37            29        1.28   27.9
                 41010        72            57        1.26   28.2
                 44014        53            43        1.23   NA
      Floyd      41004        72            54        1.33   NA
                 41009        70            52        1.35   28.9
                 41008        31            24        1.29   26.8
                 41010        91            72        1.26   NA
                 44009        52            39        1.33   22.6
                 44014        66            50        1.32   NA
                 44025        43            33        1.30   21.2
      Irene      41009        60            45        1.33   27.6
2000  Gordon     42003        57            43        1.33   29.4
                 42036        41            31        1.11   29.0
      T.S.
        Helene   42003        39            32        1.22   28.9
                 42039        41            31        1.32   28.9
                 Grand Mean                           1.30   26.9
                 Standard Deviation                   0.059   2.5
                 Coefficient of Variation (or
                   Dispersion)                        4.5%    9.3%
                 Number of Measurements              44      37

*SST stands for Sea-Surface Temperature and NA is Not Available. These
SST data were obtained from the Web site of the NOAA/National Data Buoy
Center (seaboard.ndbc.noaa.gov)

Acknowledgments

This study was partially supported by the Minerals Management Service, U.S. Department of the Interior, through the Coastal Marine Institute of Louisiana State University under a Cooperative Agreement with Louisiana State University. The contents of this paper do not necessarily reflect the views or policies of the MMS. The author also gratefully acknowledges the support of Chevron-Texaco in the form of an Endowed Professorship at LSU. Comments to improve this paper from Cynthia Ann Nelson and Michael J. Bodner are also appreciated.

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S. A. Hsu

Coastal Studies Institute

Louisiana State University

Baton Rouge, Louisiana

Author

Dr. S. A. Hsu has been a Professor of Meteorology at Louisiana State University since 1969, after he earned his Ph.D. in Meteorology from the University of Texas at Austin. He is the author of Coastal Meteorology (Academic Press, 1988) and numerous papers on coastal and marine meteorology and air-sea interaction. Dr. Hsu is also an AMS Certified Consulting Meteorologist. Dr. Hsu can be contacted at the LSU Coastal Studies Institute, 308 Howe-Russell Geoscience Building, Baton Rouge, Louisiana 70803-7527; e-mail: [e-mail].