REPLY J. WIERINGA Royal Netherlands Meteorological Instihtte, De Silt, Netherlandr

(Received 27 May, 1981)

I thank Wyngaard, Businger, Kaimal, and Larsen for jointly commenting on my analysis of published information from their Kansas 1968 experiment. A discussion of the critical arguments given by these investigators (hereafter called WBKL) must necessarily commence with a synopsis of the arguments that were actually given in my paper (hereafter called W’SO).In particular, the phrases ‘using a 2.4 m diameter sphere to represent the boxes’ and ‘choice of sphere size’ are an excessively short description of an analysis of experimental data. Having noticed that the anemometer comparisons from Kansas as reported by Izumi and Barad (1970) had too large an azimuthal variation to be compatible with the absence of significant mast interference, I tried to quantify the effect. To that purpose, I represented the obstacles in the mast by a single block of 0.8 m height and 1.0m width, which at that time was agreed by Kansas investigators to be an ‘essentially correct’ description Modelling the flow around such a compact block by potential flow upwind of an unspecified sphere, I found that model spheres of - 1.1 to 1.3 m radius at simultaneously computed locations gave satisfactory simulations of Izumi and Barad’s data In other words, the size of ‘Wieringa’s sphere’ was not a choice but an analytical result. If it looks large with respect to the size of mast and obstacles, this is because a spherical (model) obstacle is rather streamlined and harmless to flow. It can only produce the azimuthal variation and the flow stagnation observed by Izumi and Barad, if it is relatively large and nearby. A sphere with 0.9 m radius, as suggested by WBKL, is incompatible with those observations. A first conclusion from the analysis was that the overspeeding of cup anemometers at Kansas was at least 4% less than the 10% originally claimed by Izumi and Barad. This conclusion is supported by Gill (198l), and it agrees with evaluations from the ITCE experiment (Francey and Garratt, 1981).A second conclusion was that the horizontal flow was retarded by - 6 % at the sonic anemometer location If there is such stagnation, there should be flow deflection - even enhanced deflection in unstable atmospheric flow. For quantification of that deflection, it was a logical step to use the same model sphere resulting from the Izumi and Barad evaluation because of the compactness of the alleged obstacle. However, I stated explicitly that the probable occurrence of upflow was not exclusively linked to the applicability of a spherical flow model. In their comments, WBKL provide an improved description of the mast and its Boundary Layer Meteorology 22 (1982) 251-255. 0006-8314/82/0222-0251$00.75. Copyright 0 1982 by D. Reidel Publishing Co., Dordrecht, Holland. and Boston, U.S.A.

252

1. WIERINGA

contents, the latter being a row of three boxes. From the text specifications (in the WBKL Figure 1 the right-hand box looks significantly smaller than is indicated in the text), the aggregate obstacle can be described as a wall of 0.6 m height and 1.8 m width, ranged perpendicular to an azimuth of - 200” at -3.8 m distance from the sonic anemometer. An obstacle of this type induces a worse upflow than the compact obstacle pictured in Figure 2 of W’80. A step-like obstruction enhances upward flow deflection at relatively large distance, as shown e.g. by Taulbee and Robertson (1972). The improved description suggests as an improved flow model, a horizontal cylinder of such a size, that it produces - 6 % flow stagnation at the sonic location, i.e., with a radius of -0.95 m. The factor 1.5 between the actual barrier height and the radius of the equivalent cylinder agrees with the findings of Kondo and Naito (1972).At the sonic location, -4 radii away from the centre, such a cylinder induces an upward flow deflection of - 1.3”. This agrees with the - 1.4” upflow estimate from the spherical obstacle model, which suggests that this amount of upflow is a logical corollary to the observed stagnation, irrespective of the estimation model used It remains to discuss what the modelled effects do to turbulence and its measurement, since up to this point only average flow has been considered. For the estimation of flow distortion effects on turbulence parameters, the original W’80 analysis used the tilt error approach, assuming equivalence of the effects of flow direction change and instrument alignment deviation. In a separately published analysis, Wyngaard (1981) shows that this approach is incorrect in principle because it violates vorticity conservation, and that the difference between his conceptually superior analysis results and a simple tilt-error estimate becomes more apparent as the streamlines deviate more from parallelism Also, the degree of difference of results from these two approaches does vary with the turbulence parameter under consideration and depends on whether the mean flow distortion is two- or three-dimensional. The question is whether the use of Wyngaard’s principally superior method of estimating flow distortion effects for the Kansas situation does result in changed error estimates of practical significance. For stress measurement errors due to flow distortion, WBKL show that application of the Wyngaard approach to a 1.2m radius sphere as specified in W’80 will result in an error factor 0.85. Application of the Wyngaard approach to the 0.95 m radius cylinder discussed above gives an error factor 0.75 to 0.85, depending on the stability situation (seeWyngaard, 1981).The W’80 evaluation of the spherical model by combination of tilt error and stagnation effects gave an error factor 0.78 for stress.In view of the uncertainties inherent in such simple models, the three factors are rather compatible, and none of them supports the original claim that ‘no uncertainty of exposure existed for the sonic anemometers’ (Businger et al., 1971). However, these are only model results, and what the real Kansas mast did to the sonic measurements might well have been greater, particularly in unstable flow - the models can only estimate the order of magnitude of the incurred error. I still see no reason to retract my conclusion, that the drag-plate stress measurements

REPLY

253

should not have been decreased by a factor 0.67. No additional evidence has been forwarded by WBKL that the carefully executed drag measurements were so much in error. For the vertical heat flux measurement, WBKL show that for the spherical model evaluation according to Wyngaard (1981) the error is negligible, because at the sonic location the distortion effects on the vertical wind fluctuation are almost canceled by crosstalk of the turbulence components. In the case of cylinder blockage, however, such cancellation does not occur, and application of the Wyngaard approach to the discussed 0.95 m radius horizontal cylinder for the vertical velocity variance results in an error factor of 1.12 for this variance, i.e., of -6% for the vertical heat flux. The resulting error is comparable to the error factor, which was derived in W’80 by tilt error evaluation of the spherical model. Combination of the improved Wyngaard evaluation of flow distortion effects with the improved WBKL mast structure description thus still indicates that the eddy diffusion coefficient ratio K,/K, was overestimated at Kansas by the amount derived in W’80. This conclusion is supported by the ITCE experimental results (Francey and Garratt, 1981). Concerning the possible variation in 0,+,/u*, the normalized standard deviation of the vertical velocity component, WBKL overstate their case.In W’80 it is clearly stated that acceptance of the tilt error approach implies a tilt error correction to or+,as well as to u*. Since both errors have the same sign, the net effect of tilt on oW/u, is much less than that on u* alone: in Figure 2 of Rayment and Readings (1971) one finds that a l° tilt would decreasecr,+* from 1.3to - 1.2,not to 1.0. The improved approach of estimating the a,-change for the spherical Kansas model by the Wyngaard approach (and finding it negligible) logically implies that the Wyngaard-estimate for the u,-change (1.17l”) should simultaneously be applied, not the (1.22)-u,-change of W’80 based on the drag plate data! For a consistent Wyngaard-evaluation of the spherical model, gw/u* changes to - 1.17. Finally, for application of Wyngaard’s distortion model to the horizontal cylinder model, c&u* changes by a factor 1.06 x (-0.85)- ‘I’, i.e., to - 1.13. Thus the various models for estimating the sonic measurement error transform c,,Ju* to values ranging between 1.2 and 1.1. This makes it probable that the quotient of the actual free-flow u,-value (slightly larger than any model-corrected sonic value, if we accept the drag-plate measurements as correct) and the actual free-flow c,-value (not measured) has an average value in the same range. A a&,-value between 1.1 and 1.2 looks quite acceptable in view of the observation results from other experimental projects (Merry and Panofsky, 1976). Dissipation rate values at Kansas were, as usual, derived from horizontal fluctuation change rates (Wyngaard and Cot&, 1971).The formula used for this is a synopsis of a bookkeeping exercise with a large number of terms, valid only in isotropic turbulence. At Kansas various isotropy criteria, such as a 4/3-ratio between the inertial subranges of the w and u spectra, were approximatively met (Larsen, personal communication), but the uncertainty in the actual agreement with these

254

I. WIERlNGA

criteria is large (Wyngaard and Cot& 1971). Moreover these criteria are of the necessary-but-not-sufficient type. In other words, when flow is isotropic, these component spectra should show a 4/3-ratio at high frequencies, but conversely the presence of such a 4/3-ratio does not guarantee isotropy. When the stress deviates by no less than 17% (spherical model estimate according to Wyngaard, 1981) isotropy is at least doubtful, and what happens then to the many terms involved in the dissipation calculation formula is anybody’s guess. The experiments by Britter et al. (1979) are not so clear about this issue as WBKL suggest. First, Britter et al. state in their abstract that dissipation increases near the cylinder, but in their discussion they mention that a straining distortion can inhibit the mechanism of inertial transfer to higher wavenumbers (italics by Britter et al., 1979).Second, their experimental data refer to the stagnation line and thus do not quite apply to the off-line Kansas case. Concluding, it seemsa very difficult feat to predict from the present information just how large a bias was present in the dissipation values calculated from the Kansas mast measurements. Two minor matters are blown up out of context in the comments of WBKL. The first concerns the formula used in calculation of speed ratios in potential flow around a sphere. The formula which I used applies in my opinion to the horizontal speeds measured, but I also considered the vector speed alternative which indeed differs by a factor cos2 /l sin2 B. However, I found that even at the short relative distance of two radii, the outcome did not vary by more than 0.3 to 0.1% between the two formulas. Therefore I considered the choice unimportant, in view of more serious uncertainties involved in the whole modelling procedure. The second matter concerns the use made of the experimental results of Castro and Robins (1977).In my paper, I used their photographic results solely to illustrate the analogy between flow around rectangular objects and flow about somewhat larger circular objects -just to provide a picture along with the formulas and graphs of Kondo and Naito (1972). Nowhere in my paper did I use any quantitative conclusions from this particular picture, whatever WBKL’s imputations may suggest - I only used the picture as a qualitative introduction to the quantitative analysis of Izumi and Barad’s data. A more solid reason is provided by WBKL for doubting the applicability of the spherical model, namely the explicit specification of actual obstacles in the mast. However, in my opinion this leads to the alternative horizontal cylinder model sketched above, which does not alter my conclusions essentially. By the way, I am well aware that the blockage is not actually caused by a horizontal cylinder, but in view of available information it seemsthe best model approximation for purposes of analytical flow calculations. Any improvements would require either a numerical model or a windtunnel-size or full-scale experiment. Further analysis of the Kansas data is not likely to shed new light - on that point I agree with WBKL. Indeed a comparison of the sonic data with the hot-wire data has produced similar results (even a consistent upflow estimateh but since these instruments were placed close together upwind of the same mast obstacles, this

REPLY

255

only testifies to the careful evaluation of both. The analyses were independent, but the locations certainly were not, and the disagreement of the results from the wholly independently located drag plates testifies to the degree of uncertainty in the experimental conclusions. However, while the mast measurements were dubious because of mast influence, there is no final guarantee that the drag plates were absolutely correct, because at Kansas no additional independent flux measurements were made. At the ITCE-1976 experiment a larger number of independent flux measurements were available, and the meticulous comparisons by Francey and Garratt (1981) show clearly how difficult it is to reduce the experimental uncertainty to an acceptable level. In fact, because of various circumstantial experimental problems, the ITCE data have too much scatter to decide accurately on the value of the von K&man constant (k). Both the original Kansas value of 0.35 given by Businger et al (1971) and the values of 0.41 ) 0.01 given by various others (including W’80) are compatible with the ITCE estimate of k = 0.38 + 0.04. Additional experimental evidence is desirable to decide on this particular issue. For other surface-layer parameters, however, there is essential agreement between the results of the W’80 Kansas revaluation and those of other experiments like ITCE. This makes a return to the ‘gold standard’ (k x 0.40) probable. References Britter, R E., Hunt, J. R. C., and Mumford, J. C.: 1979, ‘The Distortion of Turbulence by a Circular Cylinder’, J. Fluid Mech. 92,269-301. Businger, J. A., Wyngaard, J. C., Izumi, Y., and Bradley, E. F.: 1971, ‘Flux-Protile Relationships in the Atmospheric Surface Layer’, J. Atmos. Sci. 28, 181-189. Castro, I. P. and Robins, A. G.: 1977, ‘The Flow Around a Surface-Mounted Cube in Uniform and Turbulent Streams’, J. Fluid Mech. 79, 307-335. Francey, R J. and Garratt, J. R.: 1981, ‘Interpretation of Flux-Profile Observations at ITCE (1976)‘, J. Appl. Meteorol. 20, No. 6. Gill, G. C.: 1981, ‘Comments on “A revaluation of the Kansas Mast Influence on Measurements of Stress and Cup Anemometer Overspeeding” by J. Wieringa’, submitted to J. Appl. Meteorol. Izumi, Y. and Barad, M. L.: 1970, ‘Wind Speeds as Measured by Cup and Sonic Anemometers and Influenced by Tower Structure’, J. Appl. Meteorol. 9, 851-856. Kondo, J. and Naito, G.: 1972, ‘Disturbed Wind Fields Around the Obstacle in Sheared Flow Near the Ground Surface’, J. Meteorol. Sot. Japan 50, 346-354. Merry, M. and Panofsky, H. A.: 1976, Statistics of Vertical Motion over Land and Water’, Quart. J. Roy. Meteorol. Sot. 102, 255-260. Raymenf R. and Readings, C. J.: 1971, ‘The Importance of Instrumental Tilt on Measurements of Atmospheric Turbulence’, Quart. J. Roy. Meteorol. Sot. 97, 124130. Taulbee, D. B. and Robertson, J. M.: 1972 ‘Turbulent Separation Analysis Ahead of a Step’, Trans. Am. Sot. Mech. Eng., J. Basic Eng. 94, 544549. Wieringa, J.: 1980, ‘A Revaluation of the Kansas Mast Influence on Measurements of Stress and Cup Anemometer Overspeeding’, Boundary-Layer Meteorol. 18, 411430. Wyngaard, J. C.: 1981, ‘The Effects of Probe-Induced Flow Distortion on Atmospheric Turbulence Measurements’, submitted to J. Appl. Meteorol. Wyngaard, J. C. and Cot& 0. R.: 1971, ‘The Budgets of Turbulent Kinetic Energy and Temperature Variance in the Atmospheric Surface Layer’, J. Atmos. Sci. 28, 19&201.