Figure 1. A clear-sky day at Cabauw, showing that the turbulent heat flux is smaller in magnitude than the available energy
Figure 1. A clear-sky day at Cabauw, showing that the turbulent heat flux is smaller in magnitude than the available energy
Here the radiation components are defined all positive and the heat fluxes are defined positive when directed away from the surface. The sum of the three heat fluxes is called the total heat flux. Many field studies(1) report a significant imbalance in the SEB with almost always more net radiation than total heat flux. Here we define the imbalance as the net radiation minus the total heat flux and the fractional imbalance as the imbalance divided by net radiation. Over the years observational techniques have improved and nowadays the conclusion is widely accepted that in general the observed imbalance is significantly larger then the estimated measurement error, which points to a fundamental problem in our understanding of surface fluxes and how to measure them.

There exist a few studies that show good closure of the SEB. For example Heusinkveld et al.(2) show closure for a desert site where latent heat flux is almost absent. Bosveld et al.(3) show closure of 5%, well within the measurement error, for a forest site with high aerodynamic roughness. Other studies show imbalances of typical 10-20% of the net radiation during daytime and up to 50% or more during night time.

At the Cabauw Experimental Site for Atmospheric Research (CESAR)(4) a long-term meteorological measurement programme over grassland is performed. The programme includes all surface radiation components, soil heat flux, profiles of temperature, humidity, wind and CO2 along the 200 m tower and the fluxes of sensible heat, latent heat, momentum and CO2 at (3), 60, 100 and 180 m. A windprofiler/RASS (Radio Acoustic Sounding System) is operated that gives boundary layer height estimates and wind profiles up to several kilometres height. A scintillometer is operated at 60 m height over a 10 km path from the Cabauw tower to the IJsselstein TV-tower.
Figure 2. Mean fractional imbalance as a function of local time at Cabauw 1995-1996.
Figure 2. Mean fractional imbalance as a function of local time at Cabauw 1995-1996.

At CESAR the same SEB imbalance is found as at many other sites over the world. Figure 1 shows a typical example. Kroon(5) analysed 2 years of observations. Figure 2 shows the averaged diurnal variation in fractional imbalance. Around sunrise and sunset fractional imbalance is uncertain and therefore excluded. During night time higher values are found then during day time and during daytime the magnitude of the imbalance decreases during the day. During night time a clear influence of wind speed was found with a reasonable closure at high wind speeds as shown in Figure 3. Here we will discuss observational issues of the various components of the SEB and in the final section show the relation with other research performed at CESAR.

Radiation
Net radiation observations have improved over the years. In the past specific net-radiation instruments were used. The drawback of these instruments is that they have to compromise on conflicting design specifications for longwave and shortwave radiation. Nowadays separate dedicated instruments for shortwave and longwave radiation are used. Main improvements in these separate instruments are a smaller sensitivity of shortwave instruments for longwave radiation and a more accurate measurement of longwave downward radiation under clear-sky conditions. Calibration of radiation observations is well established. For shortwave radiation there exist calibration standards (World Radiation Centre, Davos, Switzerland). For longwave radiation there is not a true standard but a reasonable one. Independent radiation transport models confirm the adequate accuracy of current state-of-the-art instruments as they are nowadays employed at the sites of the Baseline Surface Radiation Network of which Cabauw is one(6).

Surface soil heat flux
Soil heat flux is measured with soil heat flux plates. They are positioned typically at 5-10 cm depth. Special attention is needed with regard to horizontal representativeness and with regard to the large vertical gradients in flux in the top soil layer. An ingenious combination of soil heat flux plates at two depths and temperature sensors in the top soil tackles this issue(7). Part of the inhomogeneity problem is treated by measuring at three locations at the vertices of a 2 m wide triangle. Corrections are still needed for the disturbance of the soil heat flux by the soil heat flux plates. Further uncertainty arises from the heat transport associated with water vapour transport in the soil.

If the soil heat flux at Cabauw for some reason would be underestimated by a factor of two, a large part of the SEB problem would disappear. Underestimation of the soil heat flux would also explain the night time wind speed dependence of the imbalance. At high wind speeds the diurnal amplitude of the surface soil heat flux is much smaller than at low wind speeds. However, occasional observations with a snow cover at Cabauw reveal that the same problem in SEB-closure remains (Figure 4). This despite the very small soil heat fluxes and thus very small absolute errors in soil heat flux during snow cover. This shows that problems in soil heat flux observations alone cannot explain the observed SEB-imbalance. By using a soil heat transfer model and an assimilation system Ronda and Bosveld(8) were able to show that the observed soil heat fluxes were consistent with the observed thermal properties of the soil.
Figure 3. Mean night-time fractional imbalance for clear nights as a function of wind speed at Cabauw 1995-1996.
Figure 3. Mean night-time fractional imbalance for clear nights as a function of wind speed at Cabauw 1995-1996.

Atmospheric fluxes
The most direct way of measuring atmospheric transport of heat is by means of the eddy-correlation (EC) technique. This method assumes that turbulence is the dominating mechanism of transport. With well-established techniques (sonical anemometer/thermometers and open path optical hygrometers) the fluctuations of wind, temperature and humidity can be measured over a broad range of timescales. Many error sources are recognized, most of them related to the instrumental limits both on the small and on the long time scales. Reasonable estimates of these errors can be made as a function of atmospheric conditions and instrumental properties. Most of these error sources have already been known for a longer time in micro-meteorology. Recently a renewed interest is found in the field of greenhouse gas flux observations(9).
Figure 4. A night with a snow cover, showing that the turbulent heat flux is smaller in magnitude than the available energy.
Figure 4. A night with a snow cover, showing that the turbulent heat flux is smaller in magnitude than the available energy.

When combining the observations of radiation, soil heat flux and atmospheric fluxes to make up the SEB there is the issue of different footprints of the instruments. The instruments should all see a surface with the same properties with respect to the energy fluxes. At Cabauw the surface consists of reasonable homogeneous grassland on clay soil. Inhomogeneities on the local scale exist due to different maintenance regimes for the grass and the presence of ditches covering circa 10% of the surface.

Questioning the eddy-correlation technique
Here we will put forward arguments that at least the eddy correlation technique does not represent atmospheric transport properly. To judge the performance of this technique we need independent estimates of the atmospheric fluxes. Traditionally various profile estimates are used to estimate sensible and latent heat fluxes. For an overview of the applied methods at Cabauw see Beljaars and Bosveld(10). The Energy balance Bowen ratio technique uses an estimate of the available energy from net radiation and soil heat flux observations. The available energy flux is then partitioned over latent – and sensible heat flux by measuring the ratio of differences in the vertical profile of temperature and humidity. This technique is inadequate for our purpose since it assumes SEB closure. The aerodynamic method uses vertical differences of temperature and humidity in the lowest meters of the atmosphere and a model for the turbulent mixing efficiency of the atmosphere. The latter is a function of wind speed and static stability of the atmosphere. This method has been tuned on eddy-correlation measurements and is therefore not completely independent. Moreover this technique suffers from serious problems under non-uniform surface conditions in the upwind direction. It has been hypothesized that at very stable conditions the eddy-correlation instruments are not capable of measuring the small-scale fluctuations dominating the transport. This has been tested at Cabauw by comparing vertical wind speed observations of a sonic anemometer with a laser Doppler anemometer which is able to measure turbulence down to the smallest scales. No significant deviation was found from theoretical correction procedures for high-frequency loss by Kroon et al.(11). Here we discuss comparisons between eddy-correlation observations and some other independent estimates of atmospheric fluxes.

Night time CO2 respiration flux
At night no assimilation of CO2 takes place by the grass. Night time CO2 fluxes are a result of respiration in the soil. The magnitude of the respiration flux is mainly determined by soil temperature related to bacterial processes in the soil. We tuned a respiration model(12) on night time eddy-correlationCO2 flux observations under high wind speed situations and found a clear response to soil temperature. Then we applied this model with tuned soil temperature response to low wind speed cases. In Figure 5 the ratio of observed and modelled respiration flux is plotted in bins of friction velocity (u*). Friction velocity is a measure for turbulent intensity and is linearly related to wind speed and further depends on atmospheric stability. A clear decrease of observed flux is seen for friction velocities smaller than 0.1 m/s. This shows a similar behaviour as Figure 3 for total heat flux, where observations are plotted as function of wind speed. Assuming that the bacterial process that drives respiration is not dependent on the weather conditions above the soil, except for the indirect influence on the soil temperature, we must conclude that the eddy-correlation method underestimates CO2 flux under night time low wind speed conditions.
Figure 5. Mean ratio of observed and modelled night time respiration flux as a function of friction velocity.
Figure 5. Mean ratio of observed and modelled night time respiration flux as a function of friction velocity.

Night time dew formation
The long-term observations of temperature and humidity along the 200 m tower enable an independent estimate of night time sensible and latent heat flux by making up the atmospheric budget in the lowest 200 m. Estimating surface fluxes from atmospheric budgets are problematic due to the influence of horizontal differential advection. Roode et al.(13) analyzed many nights from the long observational record and found systematic a decrease of heat and water vapour content in the 200 m column, which most likely is due to a downward surface sensible and latent heat flux. Comparing with eddy-correlation measurements they found a reasonable correspondence for sensible heat but a significant underestimation of EC-based downward latent heat flux. Figure 6 shows the mean diurnal cycle of the budget method and of the eddy-correlation method for latent heat flux. Jacobs et al.(14) performed direct measurements of dew formation in Wageningen, the Netherlands. The typical values they found correspond reasonably to the mean values obtained at Cabauw from the atmospheric budget technique as is also shown in Figure 6.
Figure 6. Night time latent heat flux from eddy-correlation, atmospheric budget and dewfall estimates classified per month for the period 2001-2008 at Cabauw.
Figure 6. Night time latent heat flux from eddy-correlation, atmospheric budget and dewfall estimates classified per month for the period 2001-2008 at Cabauw.

Daytime
From observations and in Large Eddy Simulation (LES) studies(15) it is shown that considerable transport takes place at large scales in the convective boundary layer. These so-called Turbulent Organized Structures (TOS) are most apparent in the middle of the convective boundary layer. In the atmospheric surface layer the contributions of these structures to the total flux decreases linearly with height, because there is no space for a considerable spatial extended vertical wind structure close to the surface. A specific experiment has been performed by Kohsiek (unpublished) at Cabauw in 2003 with the hypothesis that the SEB-imbalance is caused by this TOS. The aim was to measure the difference in turbulent flux between 1.25 and 5 m. Despite precautions taken to avoid differences in spectral loss between the two sets of instruments the results were inconclusive.

Relation with other research at Cabauw
Although the TOS cannot explain the surface SEB problem it is of interest for the interpretation of flux observations higher up in the atmospheric boundary layer as are done at Cabauw. This elevated flux observations can also be used to study the SEB by incorporating the storage of heat and water vapour below the observation level and select on periods that advection is negligible. As a preparation for this kind of studies it is crucial to have a good understanding of the interaction between transport on the large spatial scales and time windows used in deriving eddy-correlation fluxes. In cooperation with the Delft University of Technology two studies has been performed. One(16) looks at the behaviour of vertical wind speed at the long time scales and finds that at elevated levels mean vertical wind speeds persist at considerably longer time scales than as expected from surface layer similarity theory. The other study(17) quantifies the long time scales contribution to the vertical flux at different levels and shows that this contribution can reasonably be described with surface layer theory. These findings are then confirmed by analysis of LES results. This paves the way to correct elevated fluxes for low-frequency loss. The results of this study are of direct significance for a study in cooperation with the Wageningen University(18) into the interpretation of scintillometer observations at 60 m height over a 10 km path between Cabauw and the IJsselstein TV-tower and for a study on atmospheric budgets of CO2 (19).

Conclusion
SEB-imbalance is a fundamental problem in micrometeorology. We have presented evidence that radiation observations are well-established and an order of magnitude more accurate then the magnitude of the SEB-imbalance. Soil heat flux observations remain problematic, but it is shown that uncertainties in soil heat flux alone cannot explain the SEB-imbalance. For night time conditions it is shown that serious inconsistencies exist between eddy-correlation measurements and independent estimates of surface fluxes of heat and CO2. For daytime it is shown that at higher levels in the boundary layer large-scale structures are not well captured by the EC-method. It is, however, unlikely that these structures play a significant role close tot the surface. Unclear at this stage is the role of ditches which cover approximately 10% of the surface at Cabauw and which always will give significant temperature contrasts at the surface. The problematic conclusion is that as long as we cannot pin-down which part of the observed SEB is erroneous we must prescribe an error of 10-20% of the net-radiation to all the components of the surface energy budget. This seriously hampers progress when for example comparing observations with models or with satellite products. One route that will be pursued is exploiting the eddy-correlation observations at higher levels in the tower. It will be interesting to learn whether energy balance closure can be obtained from these levels.


References


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