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Reply to Arya, S. P., 1999: Comments on “Wind and temperature profiles in the radix layer: The bottom… Santoso, Edi; Stull, Roland B. Apr 30, 1999

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APRIL 1999  NOTES AND CORRESPONDENCE  495  Reply EDI SANTOSO  AND  ROLAND STULL  Atmospheric Science Programme, Department of Geography, University of British Columbia, Vancouver, British Columbia, Canada 1 August 1998 and 24 September 1998  We thank Arya (1999) for his comments regarding the radix layer (RxL) wind profile equation. Surfacelayer power laws (SLPLs) of the form of Arya’s Eq. (1) have indeed enjoyed a long and successful history in engineering applications. As Arya mentions, these SLPLs have not had the strong theoretical underpinning associated with the Monin–Obukhov similarity theory, which also works best in only a shallow region at the bottom of the boundary layer. Our radix layer paper (Santoso and Stull 1998) was a first step in creating a stronger theoretical basis for a profile that would work over a deeper portion of the boundary layer for the special case of quasi-barotropic and quasi-free-convection. The functional form of our profile, the product of a power times an exponential, fell out naturally from the theoretical requirement that the profile must become tangent to the uniform layer wind at a finite height and from the empirical constraint that it fit the observed data well. We had no particular bias to try to create a power law, exponential law, logarithmic law, or any other function. While Arya is correct in noting that the difference between our RxL profile equation and Arya’s Eq. (1) is an exponential factor that varies between 1.1 and 1.0, this small additional factor makes an important contribution to the profile shape. Namely, it forces the RxL profile to become tangent to the uniform layer profile at a specific height, as is observed in nature, rather than crossing through the uniform layer wind speed somewhere in the bottom fifth of the boundary layer as SLPLs are prone to do. Also, this exponential factor means that our RxL profile equation should not be categorized specifically as a power law relationship. One difference between the RxL profile and classical SLPLs is that the RxL profile is based on reference heights at the surface skin and the middle mixed layer (i.e., the uniform layer), rather than on a reference height  Corresponding author address: Dr. Roland Stull, Department of Geography, Atmospheric Science Programme, University of British Columbia, 1984 West Mall Vancouver, BC V6T 1Z2 Canada. E-mail: rstull@geog.ubc.ca  ᭧ 1999 American Meteorological Society  (z r ) within the surface layer. The reference height z r (ϭ10 m usually) in SLPLs is not at any ‘‘theoretically magical’’ height; namely, it is not at a height where any boundary layer or turbulence characteristic ends or begins. Arya points out that SLPLs have also used reference heights corresponding to relative wind maxima (which would not be appropriate for a well-mixed layer with no interior maximum) or the top of the boundary layer (which would give an unrealistic profile shape). We agree with Arya that an SLPL could be used with radix layer depth as a reference, and probably would give a better fit to the actual wind profile than an SLPL that uses z r ϭ 10 m, but in our opinion it would not be as good a fit as our radix layer equations. While Arya suggests from his review of the older surface-layer literature that there is no subgeostrophic uniform layer within the convective boundary layer, the more recent literature (e.g., from BOREAS and BLX96) utilizing aircraft soundings across the whole boundary layer shows many examples of such a uniform layer during quasibarotropic conditions. The advantage of using the base of the uniform layer as one of the RxL reference heights is that it is a theoretically magical height. Namely, it is the height where wind shear becomes zero. From this, we have inferred that it is the height above which the profile is less affected by surface aerodynamic roughness and mechanically driven eddies (Stull 1997). Regardless of whether this inference is proved right or wrong, our choice of base of the uniform layer as a reference height remains wellfounded theoretically. Our other reference height is the surface, which is also a strong constraint on the flow and thus a natural choice. Otherwise we agree with Arya that the radix layer profile must depend on roughness length. However, this dependence appears in the radix layer depth, not in the universal constant A. As we show in a new paper soon to be submitted, the radix layer depth depends on the friction velocity, which, in turn, depends on surface roughness. We will also show that the hilliness of the region also affects another parameter. However, neither the hilliness nor the aerodynamic roughness appear to control the universal constant A. Finally, this new profile approach is found to tie in well with convective transport  496  JOURNAL OF APPLIED METEOROLOGY  theory for surface fluxes (Stull 1994), suggesting the possibility of a new flux–profile relationship. We are grateful to the editors and referees of our first paper for tolerating publication of research that still had some unexplained components. It allowed some new ideas to reach the scientific community, which will hopefully trigger other ideas by other investigators. It also encouraged interesting and appropriate responses such as Arya’s.  VOLUME 38  REFERENCES Arya, S. P., 1999: Comments on ‘‘Wind and temperature profiles in the radix layer: The bottom fifth of the convective boundary layer.’’ J. Appl. Meteor., 38, 493–494. Santoso, E., and R. Stull, 1998: Wind and temperature profiles in the radix layer: The bottom fifth of the convective boundary layer. J. Appl. Meteor., 37, 545–558. Stull, R. B., 1994: A convective transport theory for surface fluxes. J. Atmos. Sci., 51, 3–22. , 1997: Reply. J. Atmos. Sci., 54, 579.  

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