BMe Research Grant
In my doctoral research, I analyze the turbulent momentum, sensible and evaporative (or latent) heat fluxes of the air-water interface of lakes. I derived new formulas for these exchange processes based on the so-called eddy-covariance (EC) measurements. Momentum flux estimation formulas arise from oceanographic literature, which does not apply to lake conditions. Lakes are characterized by short fetches, small depths, and not developed, young waves. These characteristics suggest that the drag of the water surface is increased. Furthermore, in modeling, it is essential to quantify the errors of the different measurement methods when parameterizing the heat flux formulations. The energy balance (EB) and its closing failure are good tools. The available energy for a lake water column mainly consists of radiations, the heat stored in the water body, and the bed heat flux. These are balanced by turbulent heat fluxes at the water surface, and the EB should close (Figure 1). The EC is the most accurate heat flux measurement technique; however, it is known that it cannot measure the developing large-scale eddies in the atmosphere. It mainly underestimates the air-water fluxes resulting in significant closing failures . The EB closure arising from the methodology of the EC measurements has not been analyzed in the literature for lake environment, although it is essential for lake modeling.
Figure 1. Characteristic lake water temperatures and energy budget components during a wind event (left) and a typical summer day (right).
Figure 2. The location, photo, and instrumentation of the hydrometeorological station.
The eddy-covariance instrument measured the wind speed, temperature, and humidity at very high temporal frequency, from which the momentum flux and the sensible (H) and evaporative heat fluxes (LE) can be directly calculated. Besides these, for the energy balance analysis, the net radiative heat (Rn) from the longwave and shortwave radiation, the water temperatures along the depth to calculate the heat stored in the water (ΔS), and the bed heat flux (G) were measured. According to energy conservation, the available energy (Rn+ΔS+G) must be in balance with the exchange processes (H+LE) at the water surface. The closure of the energy balance can be shown by the ratio of the two sides using the Energy Balance Ratio (EBR):
In case of energy imbalance, a residual term is defined, which is distributed by the Bowen ratio (Bo=H/LE), resulting in EB-corrected heat fluxes. For the other heat flux estimation method, the knowledge of the water balance (WB) of Lake Balaton is necessary, which has been measured on a monthly scale by the Water Directorate for decades. From the water balance equation and the recorded data, the lake evaporation can be calculated:
using the change in water volume (ΔV), precipitation (P), inflow (I), water usage (W), and regulated outflow (O).
Using the EC, EB, and WB measured/calculated exchange processes, so-called drag (CD) and transfer coefficients (CH, Cq) can be derived according to the flux-gradient method; so, fluxes can directly be estimated later using them, and simple routine weather data (wind speed, temperature, humidity). Based on the MOST, these coefficients can be expressed using roughness lengths (z0, z0H, z0q) characterizing the resistance of the air-water interface and stability functions describing the atmospheric stratification.
Figure 3. The drag coefficient as a function of wind speed (a) and wave age (b) with literature functions [5-12], and the aerodynamic roughness length as a function of inverse wave age (c).
The synchronized measurement of energy budget components and the turbulent heat fluxes supported the assumed significant EB closure error in the case of a shallow lake. I analyzed the EB on different time scales, from a few hours to one month. I found that the EB closure can be somewhat higher for larger time resolution, and at least a daily scale analysis is suggested. However, even on a monthly scale, the EC-measured heat fluxes are as much as 25% underestimated compared to the available energy [S3, S4]. Besides, the EB closure showed seasonal variability, and the error was most prominent in the summer. I derived the transfer coefficients in the case of the heat fluxes based on the EC measurements. I found a large scatter, and as a result, they could be characterized by constant values as functions of meteorological variables. The derived constants are higher, and their ratio differs from measurements at other lakes. Because of the large scatter expected according to the literature, and the seasonality of the EB closure, I analyzed the roughness lengths for both heat and humidity, the key parameters of the MOST. While the roughness lengths for the sensible heat flux are nearly constant (z0H ~10-3 m), in the case of the evaporative heat flux, I found significant intra-seasonal variability of even two magnitudes (z0q ~10-6-10-4 m) during the analyzed five months (Figure 4a). Because of that, the evaporative heat transfer coefficient showed similar seasonality (Figure 4b) [S4]. On a monthly scale, the latent heat flux could be estimated using the WB calculation that is entirely independent of the other methods. The available ten-year-long WB data supported the complete intra-annual variability, where the summer transfer coefficient can be two and a half times higher than the winter one (Figure 5) [S3].
Figure 4. The monthly and daily cycle of heat flux roughness lengths (a) and the seasonal variability of the evaporative heat flux transfer coefficient (b).
Figure 5. The latent heat flux (a) and its transfer coefficient (b) as a function of shortwave radiation.
In the case of other lakes, the coefficients are generally considered constants, and their intra-seasonal variability is not analyzed. As expected, the coefficients were underestimated with the EC-based heat fluxes; thus, they were higher in the case of EB closure (Figure 4b). The coefficients from the WB method were located between the results of the EC and EB methods. The correlation analysis showed that the radiative heat is the primary driver of the evaporative transfer coefficient on larger (weekly and monthly) time scales. The latent heat flux and its transfer coefficient were correlated with the shortwave radiation, and we found well-defined hysteresis characteristics and annual cycles (Figure 5). When applying varying transfer coefficients, the accuracy of the heat flux estimation increased significantly compared to the use of a constant value [S3].
[S1] Lükő, G., Torma, P., Krámer, T., Weidinger, T., Vecenaj, Z., Grisogono, B. (2020), Observation of wave-driven air-water turbulent momentum exchange in a large but fetch-limited shallow lake, Advances in Science and Research 17, 175–182
[S2] Lükő, G., Torma, P., Krámer, T., Weidinger, T (2021). Hullámzás módosította turbulens impulzusáram mérése és becslése a Balaton légkör-víz határfelületén, Hidrológiai Közlöny 101, 52–60
[S3] Lükő, G., Torma, P., Weidinger, T (2022). Intra-seasonal and intra-annual variation of the latent heat flux transfer coefficient for a freshwater lake, Atmosphere 13, 352
[S4] Lükő, G., Torma, P., Krámer, T., Weidinger, T. (2022), Air-lake momentum and heat exchange in very young waves using energy and water budget closure, Journal of Geophysical Research: Atmospheres 127, e2021JD036099
● Wave age
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