*z*

_{p}is the height of a given parcel,

*E*is the TKE, g is gravitational acceleration, Θ

_{υ}(

*z*) is the mean virtual potential temperature, and Δ

*θ*

_{υ}(

*z*) is the change in virtual potential temperature over a given layer. The integrals are meant to extend only over the depth of the boundary layer (BL); that is, the height

*z*

_{p}should lie within the BL. As B01 states in relation to Eq. (1): “Estimating wind gusts is done assuming a parcel flowing at a given height will be able to reach the surface if the mean turbulent kinetic energy of large turbulent eddies is greater than the buoyant energy between the surface and the height of the parcel.” Such parcels are assumed to bring their momentum to the surface as gusts.

*θ*

_{υ}(

*z*) in Eq. (1) be replaced with

*θ*

_{υ}

*z*

*α*

*θ*

_{l}

*z*

*β*

*q*

_{w}

*z*

*θ*

_{l}is liquid water potential temperature and

*q*

_{w}is total moisture. The coefficients

*α*and

*β,*which alter the relative weighting of Δ

*θ*

_{l}(

*z*) and Δ

*q*

_{w}(

*z*) inside and outside of a cloud, may be formulated as described by Yamada (1979) or Smith (1990) if cloud fraction,

*R,*is an available model variable. In the absence of

*R,*one can use the “all-or-nothing” assumption in which at any given time a grid volume is considered either fully saturated (

*R*= 1) or clear (

*R*= 0), yielding

*T*is temperature,

*T*

_{l}is liquid water temperature,

*q*

_{l}is liquid water content,

*q*

_{sl}is saturation vapor pressure at temperature

*T*

_{l},

*L*

_{υ}is latent heat of vaporization,

*C*

_{p}is specific heat at constant pressure, and

*R*

_{d}is the dry gas constant.

*z*

_{p}to reach the surface. For example, consider the case of a decoupling cloud layer in which a slightly stable layer develops just beneath cloud base and separates a subcloud region that may be driven primarily by surface fluxes from a cloud layer where radiative forcing may dominate (Bretherton and Wyant 1997). The mean TKE from the surface to a level

*z*

_{p}within the cloud layer may satisfy the inequality in Eq. (1); however, the mean TKE from

*z*

_{p}to cloud base may be insufficient to overcome the potential energy of buoyancy associated with the cloud-base stability. In this case the BL may not be filled with large eddies as depicted in Fig. 4 of B01, but rather may conform more to the sketch here in Fig. 1 wherein the subcloud and cloud-layer circulations have become distinct. This situation in which the TKE distribution contains a minimum at cloud base, with local maxima in the subcloud layer and the cloud layer, is common in trade wind and stratocumulus-topped BLs. Thus, we suggest that the criterion,

*at all levels*

*z*′

*beneath*

*z*

_{p}. Equation (1) then becomes a special case of Eq. (3) where

*z*′ = 0. Although our two proposed alterations to Eq. (1) are designed to make this expression more physically correct, we recognize that they may not routinely impact the computed gust velocity in a substantial manner.

*w**, is often used either to scale turbulence variables or as part of a BL parameterization. This scaling velocity derives from dimensional analysis that yields

*w*

^{3}

*B*

_{s}

*z*

_{i}

*B*

_{s}is the surface buoyancy flux and

*z*

_{i}the inversion height. The fact that

*w** is defined in terms of

*B*

_{s}, and yet

*w** is often needed to compute

*B*

_{s}, can be troublesome.

*ω̂*

*w** for clear, convectively mixed layers. Note, however, that because

*z*

_{i}is not predicted explicitly in most NWP models, it can be difficult to diagnose

*z*

_{i}[which appears in both Eqs. (4) and (5)] in an accurate and robust manner for the myriad of BL structures that can arise.

*ω̃*

*z*

_{i}. As described by Eq. (3), we again find all levels wherein parcels are capable of reaching the surface. But, rather than selecting the maximum wind speed from among these parcels as in the WGE approach, we select the square root of the maximum turbulent velocity variance (maximum standard deviation) at those levels. Thus,

*ω̃*

*E*

*z*

^{1/2}

*q*

*where the max is selected from among levels where parcels are capable of reaching the surface*and

*E*=

*q*

^{2}/2. In this application, it is expected to be important that the buoyancy flux in the model TKE equation, as well as

*α*and

*β*in Eq. (2), account for fractional cloudiness rather the using the all-or-nothing assumption that was discussed earlier.

To better discriminate coupled from decoupled BLs, one may compute 〈*ω̃**α**ω̃*_{cld} + (1 − *ε*)*ω̃*_{clr}, where, of parcels capable of reaching the surface according to Eq. (3), *ε* is the fraction coming from the cloud layer, (1 − *ε*) is the fraction from the subcloud layer, *ω̃*_{cld} is the maximum in-cloud turbulent velocity, and *ω̃*_{clr} is the maximum subcloud turbulent velocity. When the BL is fully decoupled *ε* = 0 and 〈*ω̃**ω̂**ω̃*

Observations of a well-mixed *clear* convective boundary layer (e.g., Caughey and Palmer 1979) show that the sum of the turbulent velocity variances, *q*^{2}, attains a maximum value of ∼*w**^{2} near mid-BL, thus, our choice of the maximum in Eq. (6). That is, *ω̃**ω̃*_{clr} ∼ *w**. Therefore, in such conditions, we do not expect *ω̃**w**, but *ω̃**z*_{i} or surface flux. We have already outlined the potential advantages of *ω̃*

We have coded the B01 WGE approach as well as our two modifications for testing in the navy's Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS). Working with colleagues, we intend to perform extensive tests comparing model forecasts with surface station wind gust observations.^{1} Also, we intend to conduct comparative tests of the alternative choices for convective scaling velocity, *w**, *ω̂**ω̃*

## Acknowledgments

Discussions with Dr. W. S. Lewellen of West Virginia University and Dr. J. W. Glendening of the Naval Research Laboratory were very helpful. This work was supported by the Office of Naval Research, Program Element 0602435N.

## REFERENCES

Brasseur, O., 2001: Development and application of a physical approach to estimating wind gusts.

,*Mon. Wea. Rev.***129****,**5–25.Brasseur, O., H. Gallée, H. Boyer, and C. Tricot, 2002: Reply.

,*Mon. Wea. Rev.***130****,**1936–1942.Bretherton, C. S., and M. C. Wyant, 1997: Moisture transport, lower-tropospheric stability, and the decoupling of cloud-topped boundary layers.

,*J. Atmos. Sci.***54****,**148–167.Caughey, S. J., and S. G. Palmer, 1979: Some aspects of turbulence structure through the depth of the convective boundary layer.

,*Quart. J. Roy. Meteor. Soc.***105****,**811–827.Deardorff, J. W., 1980: Cloud top entrainment instability.

,*J. Atmos. Sci.***37****,**131–147.Smith, R. N. B., 1990: A scheme for predicting layer clouds and their water content in a general circulation model.

,*Quart. J. Roy. Meteor. Soc.***116****,**435–460.Yamada, T., 1979: An application of a three-dimensional, simplified second-moment closure numerical model to study atmospheric effects of a large cooling-pond.

,*Atmos. Environ.***13****,**693–704.

^{1}

When we originally wrote this comment, we did not anticipate that initial publication of tests of our proposed new formulations would occur in a group reply by Brasseur et al. (2002).