Two Regimes of Turbulent Fluxes Above a Frozen Small Lake Surrounded by Forest

Abstract

We present experimental results of turbulent heat exchange between a small frozen lake surrounded by forest and the atmospheric boundary layer. Heat fluxes are measured at three levels using the eddy-covariance method and estimated by Monin–Obukhov similarity theory (MOST). In addition, we estimate the heat flux due to non-local turbulent transport of heat by coherent structures originating at the forest/lake transition, given the measured skewness of $w^{\prime }$ and $\overline{{w^{\prime } w^{\prime } T^{\prime } }}$, using a bimodal bottom-up–top-down model or the mass-flux models appropriate to the convective boundary layer. Two heat-flux-formation regimes in the surface layer are clearly distinguished. When the flow is from the vast forest, wind shear at the tree height leads to increased turbulent kinetic energy above the centre of the lake. Under conditions of simultaneous horizontal advection of warm air in the boundary layer above the canopy, a downward turbulent diffusion of negative heat flux leads to increased negative sensible heat flux in the surface layer, accompanied by an increasing third moment $\overline{{w^{\prime } w^{\prime } T^{\prime } }}$. Since MOST does not account for this mechanism, MOST-based fluxes poorly correspond to the eddy-covariance data in this case. At the same time the contribution of coherent structures increases. In contrast, when the flow is from the gap connecting the lake with the wide clearing, the effects of landscape inhomogeneity significantly reduce. In this case the turbulent transport of the heat flux from the upper part of the boundary layer vanishes, $\overline{{w^{\prime } w^{\prime } T^{\prime } }}$ is negligible, and the heat flux is now primarily determined by the wind speed and temperature differences between the surface and near-surface atmosphere. This is a surface-flow regime for which MOST has been developed, and MOST-based fluxes correlate well with eddy-covariance data.

Appendix: General Description of MOST

The gradient method assumes that all statistical characteristics of the temperature, humidity, and wind velocity fields are normalized to the corresponding scales of the temperature $T_{*}$, humidity $q_{*}$, and velocity $u_{*}$, and are described by universal functions of the dimensionless height ξ = z/L, where L is the Obukhov length and z is the height. Specifically, according to the Monin–Obukhov similarity theory (MOST) the deficits of averaged meteorological variables in the surface layer obey the following relations,

$$ U\left( {z_{2} } \right) - U\left( {z_{1} } \right) = \frac{{u_{*} }}{\kappa }\left( {\ln \left( {\frac{{z_{2} }}{{z_{1} }}} \right) - \varPsi_{M} \left( {\frac{{z_{2} }}{L}} \right) + \varPsi_{M} \left( {\frac{{z_{1} }}{L}} \right)} \right) $$

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$$ T\left( {z_{2} } \right) - T\left( {z_{1} } \right) = \frac{{T_{*} }}{\kappa }\left( {\ln \left( {\frac{{z_{2} }}{{z_{1} }}} \right) - \varPsi_{H} \left( {\frac{{z_{2} }}{L}} \right) + \varPsi_{H} \left( {\frac{{z_{1} }}{L}} \right)} \right) $$

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$$ q\left( {z_{2} } \right) - q\left( {z_{1} } \right) = \frac{{q_{*} }}{\kappa }\left( {\ln \left( {\frac{{z_{2} }}{{z_{1} }}} \right) - \varPsi_{q} \left( {\frac{{z_{2} }}{L}} \right) + \varPsi_{q} \left( {\frac{{z_{1} }}{L}} \right)} \right) $$

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where κ is the von Kármán constant, lower indices “2” and “1” denote the two levels of measurements, ψ_i (ξ), i  =  M, H, and q are dimensionless universal functions. We used the universal functions (Beljaars and Holtslag 1991) for stable stratification

$$ - \varPsi_{M} \left( \xi \right) = - \varPsi_{H} \left( \xi \right) = - \varPsi_{q} \left( \xi \right) = a\xi + b\left( {\xi - \frac{c}{d}} \right){ \exp }\left( { - d\xi } \right) + \frac{bc}{d}, $$

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where a = 0.7, b = 0.75, c = 5, d = 0.35. The Businger–Dyer form (Businger et al. 1971; Dyer 1974) is used for unstable stratification,

$$ \varPsi_{M} \left( \xi \right) = 2\ln \left[ {\frac{1 + x}{2}} \right] + \ln \left[ {\frac{{1 + x^{2} }}{2}} \right] - 2{\text{arctg}}\left( x \right) + \frac{\uppi }{2}, $$

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$$ \varPsi_{H,q} \left( \xi \right) = 2\ln \left[ {\frac{{1 + y^{2} }}{2}} \right], $$

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where $x = \left( {1 - 16\xi } \right)^{1/4}$, $y = \left( {1 - 16\xi } \right)^{1/2}$. The turbulent fluxes are calculated from

$$ \tau = \rho_{0} u_{*}^{2} , $$

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$$ H = - C_{p} \rho_{0} u_{*} T_{*} $$

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$$ L_{s} E = - \rho_{0} L_{s} u_{*} q_{*} . $$

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