This paper gives an overview of 20 years of research on the energy balance closure problem. It will be shown that former assumptions that measuring errors or storage terms are the reason for the ...unclosed energy balance do not stand up because even turbulent fluxes derived from documented methods and calibrated sensors, net radiation, and ground heat fluxes cannot close the energy balance. Instead, exchange processes on larger scales of the heterogeneous landscape have a significant influence. By including these fluxes, the energy balance can be approximately closed. Therefore, the problem is a scale problem and has important consequences to the measurement and modeling of turbulent fluxes.
This historical survey shows that Obukhov's 1946 fundamental paper on a universal length scale for exchange processes in the surface layer was the basis for the derivation of the similarity theory by ...Monin and Obukhov in 1954. A brief overview of the experiments and findings used to formulate the universal functions in the presently used form is given. Finally, the current status of the theory is described, covering topics such as the accuracy of the universal functions and the turbulent Prandtl number.PUBLICATION ABSTRACT
The flux contribution of coherent structures to the total exchange of energy and matter is investigated in a spruce canopy of moderate density in heterogeneous, complex terrain. The study deploys two ...methods of analysis to estimate the coherent exchange: conditional averages in combination with wavelet analysis, and quadrant analysis. The data were obtained by high-frequency single-point measurements using sonic anemometers and gas analysers at five observation heights above and within the canopy and subcanopy, and represent a period of up to 2.5 months. The study mainly addresses the momentum transfer and exchange of sensible heat throughout the roughness sublayer, while results are provided for the exchange of carbon dioxide and water vapour above the canopy. The magnitude of the flux contribution of coherent structures largely depends on the method of analysis, and it is demonstrated that these differences are attributed to differences in the sampling strategy between the two methods. Despite the differences, relational properties such as sweep and ejection ratios and the variation of the flux contribution with height were in agreement for both methods. The sweep phase of coherent structures is the dominant process close to and within the canopy, whereas the ejections gain importance with increasing distance to the canopy. The efficiency of the coherent exchange in transporting scalars exceeds that for momentum by a factor of two. The occurrence of coherent structures results in a flux error less than 4% for the eddy-covariance method. Based on the physical processes identified from the analysis of the ejection and sweep phases along the vertical profile in the roughness sublayer, a classification scheme for the identification of exchange regimes is developed. This scheme allows one to estimate the region of the canopy participating in the exchange of energy and matter with the above-canopy air under varying environmental conditions.
The Budyko framework elegantly reduces the complex spatial patterns of actual evapotranspiration and runoff to a general function of two variables: mean annual precipitation (MAP) and net radiation. ...While the methodology has first‐order skill, departures from a globally averaged curve can be significant and may be usefully attributed to additional controls such as vegetation type. This paper explores the magnitude of such departures as detected from flux tower measurements of ecosystem‐scale evapotranspiration, and investigates their attribution to site characteristics (biome, seasonal rainfall distribution, and frozen precipitation). The global synthesis (based on 167 sites with 764 tower‐years) shows smooth transition from water‐limited to energy‐limited control, broadly consistent with catchment‐scale relations and explaining 62% of the across site variation in evaporative index (the fraction of MAP consumed by evapotranspiration). Climate and vegetation types act as additional controls, combining to explain an additional 13% of the variation in evaporative index. Warm temperate winter wet sites (Mediterranean) exhibit a reduced evaporative index, 9% lower than the average value expected based on dryness index, implying elevated runoff. Seasonal hydrologic surplus explains a small but significant fraction of variance in departures of evaporative index from that expected for a given dryness index. Surprisingly, grasslands on average have a higher evaporative index than forested landscapes, with 9% more annual precipitation consumed by annual evapotranspiration compared to forests. In sum, the simple framework of supply‐ or demand‐limited evapotranspiration is supported by global FLUXNET observations but climate type and vegetation type are seen to exert sizeable additional controls.
Key Points
Global FLUXNET data support Budyko hypothesis of surface water balance controls
Climate type, vegetation type exert additional control on evapotranspiration
Grasslands exhibit higher evaporative index than forests
It is now accepted that large-scale turbulent eddies impact the widely reported non-closure of the surface energy balance when latent and sensible heat fluxes are measured using the eddy covariance ...method in the atmospheric surface layer (ASL). However, a mechanistic link between large eddies and non-closure of the surface energy balance remains a subject of inquiry. Here, measured 10 Hz time series of vertical velocity, air temperature, and water vapor density collected in the ASL are analyzed for conditions where entrainment and/or horizontal advection separately predominate. The series are decomposed into small- and large- eddies based on a frequency cutoff and their contributions to turbulent fluxes are analyzed. Phase difference between vertical velocity and water vapor density associated with large eddies reduces latent heat fluxes, especially in conditions where advection prevails. Enlarged phase difference of large eddies linked to entrainment or advection occurrence leads to increased residuals of the surface energy balance.
► Mean energy balance closure at 173 FLUXNET sites is 0.84. ► Mean forest and non-forest closure does not differ. ► Significant differences in closure were found among plant functional types. ► ...Landscape-level vegetation variability should not be excluded from the interpretation.
The energy balance at most surface-atmosphere flux research sites remains unclosed. The mechanisms underlying the discrepancy between measured energy inputs and outputs across the global FLUXNET tower network are still under debate. Recent reviews have identified exchange processes and turbulent motions at large spatial and temporal scales in heterogeneous landscapes as the primary cause of the lack of energy balance closure at some intensively-researched sites, while unmeasured storage terms cannot be ruled out as a dominant contributor to the lack of energy balance closure at many other sites. We analyzed energy balance closure across 173 ecosystems in the FLUXNET database and explored the relationship between energy balance closure and landscape heterogeneity using MODIS products and GLOBEstat elevation data. Energy balance closure per research site (CEB,s) averaged 0.84±0.20, with best average closures in evergreen broadleaf forests and savannas (0.91–0.94) and worst average closures in crops, deciduous broadleaf forests, mixed forests and wetlands (0.70–0.78). Half-hourly or hourly energy balance closure on a percent basis increased with friction velocity (u*) and was highest on average under near-neutral atmospheric conditions. CEB,s was significantly related to mean precipitation, gross primary productivity and landscape-level enhanced vegetation index (EVI) from MODIS, and the variability in elevation, MODIS plant functional type, and MODIS EVI. A linear model including landscape-level variability in both EVI and elevation, mean precipitation, and an interaction term between EVI variability and precipitation had the lowest Akaike's information criterion value. CEB,s in landscapes with uniform plant functional type approached 0.9 and CEB,s in landscapes with uniform EVI approached 1. These results suggest that landscape-level heterogeneity in vegetation and topography cannot be ignored as a contributor to incomplete energy balance closure at the flux network level, although net radiation measurements, biological energy assimilation, unmeasured storage terms, and the importance of good practice including site selection when making flux measurements should not be discounted. Our results suggest that future research should focus on the quantitative mechanistic relationships between energy balance closure and landscape-scale heterogeneity, and the consequences of mesoscale circulations for surface-atmosphere exchange measurements.
Strong temperature gradients with stable stratification immediately above the surface are typical for radiation cooling, but near-surface temperature inversions (hereinafter referred to as ...inversions) have hardly been studied. Both phenomena are examined in more detail by means of measurements in the Caspian Sea and Antarctica and compared with measurements made by other authors. For this purpose, tests for decoupling are applied in the first case. In the second case, the inversions can be explained in the context of counter-gradient fluxes and turbulent Prandtl numbers greater than one.
The eddy covariance method is commonly used to calculate vertical turbulent exchange fluxes between ecosystems and the atmosphere. Besides other assumptions, it requires steady-state flow conditions. ...If this requirement is not fulfilled over the averaging interval of, for example, 30 min, the fluxes might be miscalculated. Here two further calculation methods, conditional sampling and wavelet analysis, which do not need the steady-state assumption, were implemented and compared to eddy covariance. All fluxes were calculated for 30 min averaging periods, while the wavelet method – using both the Mexican hat and the Morlet wavelet – additionally allowed us to obtain a 1 min averaged flux. The results of all three methods were compared against each other for times with best steady-state conditions and well-developed turbulence. An excellent agreement of the wavelet results to the eddy covariance reference was found, where the deviations to eddy covariance were of the order of < 2 % for Morlet as well as < 7 % for Mexican hat and thus within the typical error range of eddy covariance measurements. The conditional sampling flux also showed a very good agreement to the eddy covariance reference, but the occurrence of outliers and the necessary condition of a zero mean vertical wind velocity reduced its general reliability. Using the Mexican hat wavelet flux in a case study, it was possible to locate a nightly short time turbulent event exactly in time, while the Morlet wavelet gave a trustworthy flux over a longer period, e.g. 30 min, under consideration of this short-time event. At a glance, the Mexican hat wavelet flux offers the possibility of a detailed analysis of non-stationary times, where the classical eddy covariance method fails. Additionally, the Morlet wavelet should be used to provide a trustworthy flux in those 30 min periods where the eddy covariance method provides low-quality data due to instationarities.
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