The Impact of Surface Temperature Heterogeneity on Near-Surface Heat Transport

Abstract

Experimental closure of the surface energy balance during convective periods is a long-standing problem. With experimental data from the Idealized horizontal Planar Array experiment for Quantifying Surface heterogeneity, the terms of the temperature-tendency equation are computed, with an emphasis on the total derivative. The experiment occurred at the Surface Layer Turbulence and Environmental Science Test facility at the U.S. Army Dugway Proving Ground during the summer of 2019. The experimental layout contained an array of 21 flux stations over a 1 km$^2$ grid. Sensible heat fluxes show high spatial variability, with maximum variability occurring during convective periods. Maximum variability in the vertical heat flux is 50–80 W m$^{-2}$ (median variability of 40%), while in the horizontal flux, it is 200–500 W m$^{-2}$ (median variability of 48% for the streamwise and 40% for the spanwise fluxes). Ensemble averages computed during convective afternoon periods show large magnitudes of horizontal advection (48 W m$^{-3}$ or 172 K h$^{-1}$) and vertical flux divergence (13 W m$^{-3}$ or 47 K h$^{-1}$). Probability density functions of the total derivative from convective cases show mean volumetric heating rates of 43 W m$^{-3}$ (154 K h$^{-1}$) compared to 13 W m$^{-3}$ (47 K h$^{-1}$) on non-convective days. A conceptual model based on persistent mean flow structures from local-surface-temperature heterogeneities may explain the observed advection. The model describes the difference between locally-driven advection and advection driven by larger-scale forcings. Of the cases examined, 83% with streamwise and 81% with spanwise advection during unstable periods are classified as locally driven by nearby surface thermal heterogeneities.

Appendix 1: Temperature Correction

Given the anticipated errors during in situ temperature-data acquisition (panel temperature error, thermocouple error, thermocouple voltage measurement error, noise error, thermocouple polynomial error, and reference junction error), we have determined that an a posteriori temperature collocation manages these errors. Please see the Campbell Scientific CR1000 data-logger manual, pp. 343–352 for more information on these errors. Note that these are errors which arise from utilizing research-grade instruments and a temperature collocation should always be considered during future advection experiments. This methodology utilizes a second-order polynomial fit over two weeks of data between a set of truth measurements and a set of values needing correction. This method seeks to only correct systemic error to correct for temperature differences between stations and does not aid in finding the absolute temperatures. A second-order polynomial is selected for the correction since the errors are nonlinear across the temperatures observed during data acquisition. For our purposes, we utilized the central high-resolution-array tower as our truth tower due to its proximity to the towers utilized in the horizontal advection measurement. However, its temperature is not used in performing the temperature derivative. Thus the assumption is that over the 30 min, the towers should converge to the truth tower.

An example of the temperature correction is observed in Fig. 15, which presents the 30-min-averaged truth temperatures against the temperature from the southern tower at the high-resolution array (10-m south from the truth measurements). The black circles denote the raw data, where the nonlinear trend across temperatures shows the extremes converging and the mid-valued temperatures showing the worst agreement. The black line illustrates a one-to-one fit. Meanwhile, the red line shows the parabolic fit to the data. The minimum $R^2$ value across all towers is 0.994, suggesting the parabolic fit works well without a dataset. Finally, the blue stars show the corrected temperature used for the computation of Eq. 2b. Note that this correction does not change the turbulent quantities and only works under cases where the absolute temperature is not needed for the final solution. Furthermore, for future applications, if the truth temperature was validated over a range of values observed during the experiment, then the absolute temperature could be calculated.

Fig. 15

An example of the 30-min averaged fine-wire temperatures from the centre high-resolution array tower ($T_{truth}$) against the south high-resolution array tower ($T_{fit}$). The black circles correspond to the raw data, where errors compile with a temperature dependency to create non-linear differences between observations. The blue stars illustrate the data with the correction applied. Each tower used in this analysis underwent the correction with the centre high-resolution array tower