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Edgar L. Andreas

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Surface-level meteorological observations and upper-air soundings in the Weddell Sea provide the first in situ look at conditions over the deep Antarctic ice pack in the spring. The surface‐level temperature and humidity were relatively high, and both were positively correlated with the northerly component of the 850 mb wind vector as far as 600 km from the ice edge. Since even at its maximum extent at least 60% of the Antarctic ice pack is within 600 km of the open ocean, long‐range atmospheric transport of heat and moisture from the ocean must play a key part in Antarctic sea ice heat and mass budgets. From one case study, the magnitude of the ocean's role is inferred: at this time of year the total turbulent surface heat loss can be 100 W m−2 greater under southerly winds than under northerly ones.

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Edgar L. Andreas

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Recent work on the turbulent transfer of scalar quantities following a step increase in the surface value of the scalar is directly applicable to the problem of estimating heat and mass transfer from Arctic leads in winter. If the turbulent flux is nondimensionalized as a Nusselt number N and the flow regime over the lead is parameterized by the fetch Reynolds number Rr, either the exponential transfer relation N = 0.08 × Rr 0.76 or the linear relation N = 1.8 × 10−3Rr + 1100 describes the available data. Because N can be the Nusselt number for sensible heat, latent heat or condensate flux, Nusselt numbers of these scalar fluxes are equal for a given lead—Rr. The transfer relations and this Nusselt number equality are powerful estimation tools. With the transfer relations, turbulent fluxes can be computed from standard meteorological observables; and from the Nusselt number equality, partitioning of the turbulent fluxes can be evaluated— in particular, the partitioning of the heat flux between sensible and latent components.

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Edgar L. Andreas

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Evaluating the profiles of wind speed, temperature, and humidity in the atmospheric surface layer or modeling the turbulent surface fluxes of sensible and latent heat over horizontally homogeneous surfaces of snow or ice requires five pieces of information. These are the roughness lengths for wind speed (z 0), temperature (z T ), and humidity (z Q ) and the stratification corrections for the wind speed and scalar profiles ψ m and ψ h , respectively. Because over snow and ice the atmospheric surface layer is often stably stratified, the discussion here focuses first on which of the many suggested ψ m and ψ h functions to use over snow and ice. On the basis of four profile metrics—the critical Richardson number, the Deacon numbers for wind speed and temperature, and the turbulent Prandtl number—the manuscript recommends the Holtslag and de Bruin ψ m and ψ h functions because these have the best properties in very stable stratification. Next, a reanalysis of five previously published datasets confirms the validity of a parameterization for z T /z 0 as a function of the roughness Reynolds number (R∗) that the author reported in 1987. The z T /z 0 data analyzed here and that parameterization are compatible for R∗ values between 10−4 and 100, which span the range from aerodynamically smooth through aerodynamically rough flow. Discussion of a z 0 parameterization is deffered and an insufficiency of data for evaluating z Q is reported, although some z Q data is presented.

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Edgar L. Andreas

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Several electro-optical methods exist for measuring a path-averaged value of the inner scale of turbulence l 0. By virtue of Monin–Obukhov similarity, in the atmospheric surface layer such l 0 measurements are related to the friction velocity u * or to the surface stress τ = &rhou * 2, where ρ is the air density. Because l 0 is a path-averaged quantity, u * is too. Here the question of how precisely u * can be measured is investigated by combining these inner-scale measurements with two-wavelength scintillation measurements that yield the sensible and latent heat fluxes and, thereby, facilitate stability collections. The analysis suggests that current path-averaging instruments can generally measure u * to ± 20%–30%.

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Edgar L. Andreas

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Edgar L. Andreas

Abstract

Uncertainty over how long to average turbulence variables to achieve some desired level of statistical stability is a common concern in boundary-layer meteorology. Several models exist that predict averaging times for measurements of variances and covariances, but often we are not interested in the low-frequency fluctuations that dominate variances and covariances. For example, we may want to look only at the inertial subrange. Therefore, a theoretical model is presented here to use in estimating the required averaging time for both point measurements and path-averaged electro-optical or acoustic measurements of the turbulence spectrum at arbitrary frequency f. The model is based on 1) the fact that spectral estimators and sample variances have chi-squared probability distributions; and 2) observations of the spectral coherence between horizontally separated turbulence sensors in the atmospheric boundary layer. This model is different from others that predict required averaging times because it yields not only the measurement uncertainty associated with the averaging time but also the confidence level of the measurement. Consequently, one important prediction of the model is that to make statistically equivalent point or path-averaged measurements of the refractive index spectrum at frequency f requires the same averaging time for both measurements.

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Edgar L. Andreas

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Because the Lyman-alpha hygrometer averages turbulent fluctuations in humidity over a right circular cylinder, the spectral response of the instrument degrades at higher wavenumbers. This paper contains a derivation of the three-dimensional spectral averaging function and uses this function, with a new model for the scalar spectrum, to numerically evaluate how this spatial averaging affects measured humidity spectra and humidity variance dissipation rates. In general, hygrometer parameters can be chosen that allow spectral measurements to moderately high wavenumbers; but with the size of source and detector tubes currently in use, an accurate measurement of the humidity variance dissipation rate appears impossible.

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Edgar L. Andreas

Abstract

The von Kármán constant k occurs throughout the mathematics that describe the atmospheric boundary layer. In particular, because k was originally included in the definition of the Obukhov length, its value has both explicit and implicit effects on the functions of Monin–Obukhov similarity theory. Although credible experimental evidence has appeared sporadically that the von Kármán constant is different than the canonical value of 0.40, the mathematics of boundary layer meteorology still retain k = 0.40—probably because the task of revising all of this math to implement a new value of k is so daunting. This study therefore outlines how to make these revisions in the nondimensional flux–gradient relations; in variance, covariance, and dissipation functions; and in structure parameters of Monin–Obukhov similarity theory. It also demonstrates how measured values of the drag coefficient (CD ), the transfer coefficients for sensible (CH ) and latent (CE ) heat, and the roughness lengths for wind speed (z 0), temperature (zT ), and humidity (zQ ) must be modified for a new value of the von Kármán constant. For the range of credible experimental values for k, 0.35–0.436, revised values of CD , CH , CE , z 0, zT , and zQ could be quite different from values obtained assuming k = 0.40, especially if the original measurements were made in stable stratification. However, for the value of k recommended here, 0.39, no revisions to the transfer coefficients and roughness lengths should be necessary. Henceforth, use the original measured values of transfer coefficients and roughness lengths but do use similarity functions modified to reflect k = 0.39.

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Edgar L. Andreas

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Conceptually, electro-optical measurements of the path-averaged refractive index structure parameter C n 2 at three wavelengths should yield measurements of the vertical fluxes of sensible (H s ) and latent (H L ) heat. With three independent C n 2 measurements we can compute—at least formally—the meteorologically relevant temperature, humidity, and temperature–humidity structure parameters C t 2, C q 2, and C tq , respectively. The heat fluxes H s and H L derive from these and a simultaneous electro-optical measurement of the path-averaged turbulent kinetic energy dissipation rate ε through inertial–dissipation calculations. A sensitivity analysis shows that, with the best current technology (wavelengths of 0.94 µm, 10.6 µm, and 3.33 mm), the three-wavelength method would yield measurements of C t 2 accurate to ±20% when the Rowen ratio, Bo=H s /H L , is in the range 0.1<|Bo|≤10. The measurement of C q 2 is potentially accurate to ±10%—but only when 0.01≤|Bo|<0.5; outside this range, the accuracy is much worse. And the accuracy of the C tq measurement is poor. The predicted uncertainty is no better than ±40%. This three-wavelength combination, however, can yield the sign of C tq —an important piece of information—when 0.015<|Bo|<0.5. If instead of the 10.6-µm wavelength, we substituted a wavelength of 18.8 µm, where laser measurements are more difficult, the Bowen ratio ranges over which we could measure both C q 2 and the sign of C tq expand. For C q 2, the useful Bowen ratio range is now 0.01≤|Bo|<1; and for the sign of C tq , it is roughly 0.02<|Bo|<2.

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Edgar L. Andreas

Abstract

Because few geophysical surfaces are horizontally homogeneous, point measurements of the turbulent surface fluxes can be unrepresentative. Path-averaging techniques are therefore desirable. This paper presents a method that yields path-averaged measurements of the sensible and latent heat fluxes with a potential accuracy as good as that for eddy-correlation measurements. The method relies on electro-optical measurements of the refractive index structure parameter Cn 2 at two wavelengths: one in the visible-to-mid-infrared region, where Cn 2 depends largely on turbulent temperature fluctuations, and a second in the near-millimeter-to-radio region, where Cn 2 depends more strongly on humidity fluctuations. A sensitivity analysis, the cornerstone of the study, provides quantitative guidelines for selecting wavelength pairs to use for the measurements. The sensitivity analysis also shows that the method is not uniformly accurate for all meteorological conditions; for limited ranges of the Bowen ratio, the sensitivity becomes so large that accurately measuring one or both heat fluxes is impossible.

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