Atmosphere–Surface Fluxes of CO<Subscript>2</Subscript> using Spectral Techniques

Different flux estimation techniques are compared here in order to evaluate air–sea exchange measurement methods used on moving platforms. Techniques using power spectra and cospectra to estimate fluxes are presented and applied to measurements of wind speed and sensible heat, latent heat and CO₂ fluxes. Momentum and scalar fluxes are calculated from the dissipation technique utilizing the inertial subrange of the power spectra and from estimation of the cospectral amplitude, and both flux estimates are compared to covariance derived fluxes. It is shown how even data having a poor signal-to-noise ratio can be used for flux estimations.     

Intermittency and the Exchange of Scalars in the Nocturnal Surface Layer

The determination of nocturnal surface fluxes in low wind conditions is a major problem for micrometeorological studies. The eddy correlation technique, extensively used in field measurements, becomes inappropriate if not enough turbulent activity exists. At the same time, the phenomenon of turbulence intermittency is responsible for the existence of localized events of short duration within which a large fraction of the total nighttime scalar exchange occurs. The scalar flux within a certain intermittent event varies considerably depending on the window used for the flux calculation. In many cases, events with very different time durations occur in the same night, and therefore, the proper determination of the surface flux would require averaging within data windows of different sizes for each event. In this work, the surface exchanges of temperature, moisture and carbon dioxide are analysed at a micrometeorological tower at southern Brazil. Intermittent turbulence is a common occurrence at the location. The analysis shows that the fluxes vary with turbulence intensity and the estimation technique. A variable-window size method for flux estimation is suggested and shown to cause an increase in the magnitude of the nocturnal surface fluxes     

Deduction of the Sensible Heat Flux from SODAR Data

A new method for deduction of the sensible heat flux is validated with three sets of published SODAR （sound detection and ranging） data. Although the related expressions have previously been confirmed by the author with surface layer data, they have not yet been validated with observations from the boundary layer before this work. In the study, selected SODAR data are used to test the method for the convective boundary layer. The sensible heat flux （SHF） retrieved from SODAR data is found to decrease linearly with height in the mixed layer. The surface sensible heat fluxes derived from the deduced sensible heat flux profiles under convective conditions agree well with those measured by the eddy correlation method. The characteristics of SHF profiles deduced from SODAR data in different places reflect the background meteorology and terrain. The upper part of the SHF profile （SHFP） for a complicated terrain is found to have a different slope from the lower part. It is suggested that the former reflects the advective characteristic of turbulence in upwind topography. A similarity relationship for the estimation of SHFP in a well mixed layer with surface SHF and zero-heat-flux layer height is presented.     

Dry-air boundary conditions for correction of eddy flux measurements

For measurements of eddy fluxes in the atmospheric boundary layer of gases (such as CO₂) whose average concentration is very large compared to the fluctuations, corrections for air density fluctuations are required. With the boundary condition of no flux of dry air at the surface, the evaporation correction to eddy fluxes is 2.6 times larger than has been estimated with the boundary condition of no mass flux at all at the surface. The heat flux correction is also increased by a few per cent.     

Application of the Hilbert–Huang Transform to the Estimation of Air-Sea Turbulent Fluxes

The Hilbert–Huang transform (HHT) is applied to analyzing the turbulent time series obtained within the atmospheric boundary layer over the ocean. A method based on the HHT is introduced to reduce the influence of non-turbulent motions on the eddy-covariance based flux by removing non-turbulent modes from the time series. The scale dependence of the flux is examined and a gap mode is identified to distinguish between turbulent modes and non-turbulent modes. To examine the effectiveness of this method it is compared with three conventional methods (block average, moving-window average, and multi-resolution decomposition). The data used are from three sonic anemometers installed on a moored buoy at about 6, 4 and 2.7 m height above the sea surface. For each method, along-wind and cross-wind momentum fluxes and sensible heat fluxes at the three heights are calculated. According to the assumption of a constant-flux layer, there should be no significant difference between the fluxes at the three heights. The results show that the fluxes calculated using HHT exhibit a smaller difference and higher correlation than the other methods. These results support the successful application of HHT to the estimation of air-sea turbulent fluxes.     

Methods to Estimate Surface Fluxes of Momentum and Heat from Routine Weather Observations for Dispersion Applications under Stable Stratification

We examine the efficacy of two methods commonly used to estimate the vertical turbulent fluxes of momentum and sensible heat from routinely observed mean quantities in the surface layer under stable stratification. The single-level method uses mean wind speed and temperature measurements at a single height, whereas the two-level method uses mean wind speed measurements at a single height and mean temperature measurements at two heights. These methods are used in popular meteorological processors such as the U.S. Environmental Protection Agency approved AERMET and CALMET to generate inputs for dispersion simulations. We use data from a flux station of the U.K. Met Office at Cardington for comparison. It is found that the single-level method does not describe the flux variation in the weakly stable regime at all, because of its assumption that the temperature scale, i.e. the ratio of the kinematic sensible heat flux to the friction velocity, is constant, which is plausible only under strongly stable conditions. On the other hand, the two-level method provides a physically realistic variation of the fluxes with stability, but the required temperature measurements at two levels are usually not available on a routine basis. If measurements of the standard deviation of temperature are also available, in addition to the mean temperature at a single level, then they can be usefully employed in a third (single-level) method, with the consequence that the computed fluxes are very similar to those obtained from the two-level method. An improvement to the original single-level method is considered, and flux calculations under low wind conditions are also discussed.     

Testing of the bandpass eddy covariance method for a long-term measurement of water vapour flux over a forest

The bandpass eddy covariance method has been used to measure the turbulent flux of scalar quantities using a slow-responsescalar sensor. The method issimilar in principle to the traditional eddy correlation method but includes the estimation of high-frequency components of the flux on the basis of cospectral similarity in the atmospheric surface layer. In order to investigate the performance of the method, measurements of the water vapour flux over a forest with the bandpass eddy covariance method and the direct eddy correlation method were compared. The flux obtained by the bandpass eddy covariance method agreed with that by the eddy correlation method within ±20% for most cases, in spite of a rather slow sensor-response of the adopted hygrometer. This result supports its relevance to a long-term continuous operation, since a stable, low-maintenance,general-purpose sensor canbe utilized for scalar quantities. Oneweak point of the method isits difficulty in principle to measure the correct flux when the magnitude of the sensible heat flux is very small, because the method uses the sensible heat flux as a standard reference for the prediction of undetectable high-frequency components of the scalar flux. An advanced method is then presented to increase its robustness. In the new method, output signals from a slow-response sensor are corrected using empirical frequency-responsefunctions for the sensor,thereby extending the width of the bandpass frequency region where components of the flux are directly measured (not predicted). The advanced method produced correct fluxes for all cases including the cases of small sensible heat flux. The advanced bandpass eddy covariance method is thus appropriate for along-term measurement of the scalar fluxes.     

Regional turbulent statistics over contrasting natural surfaces

Summary Regional turbulent fluxes of momentum, sensible and latent heat collected over both agricultural and native vegetation in the south west of Australia are presented. Analysis of the energy spectrum illustrates that the most energetic eddies are between scales of 20 metres to 5 kilometres and highlights the spatial distance required to obtain representative regional fluxes. For the sensible heat flux, this distance is a function of measurement height whereas the latent flux is also influenced by surface variability. Statistics of these fluxes highlight that for the unstable surface layer, despite marked differences in the underlying vegetation and the corresponding sources of heat and moisture, heat is transported more efficiently than water vapour from the ground surface. Received October 9, 2000/Revised April 23, 2001     

Bivariate conditional sampling of buoyancy flux during an intense cold-air outbreak

Buoyancy fluxes in the marine atmospheric boundary layer (MABL) for the cloud street regime, observed during the Genesis of Atlantic Lows Experiment (GALE), have been analyzed using the technique of joint frequency distribution. For the lower half of the MABL, the results suggest that the buoyancy flux is mainly generated by the rising thermals and the sinking compensating ambient air, and is mainly consumed by the entrainment and detrainment of thermals, penetrative convection, and the entrainment from the MABL top.The results are compared to those from previous studies of mesoscale cellular convection (Air-Mass Transformation Experiment, AMTEX), the dry convective boundary layer, and the trade-wind MABL. For the lower MABL, the quadrant buoyancy fluxes, fractional coverages, and flux intensities are in good agreement with those of mesoscale cellular convection (AMTEX) and the dry convective boundary layer. The results suggest that, if the buoyancy flux is primarily driven by the temperature flux, the physical processes for generating buoyancy flux mentioned above are about the same for the lower boundary layers over land and ocean, even with different convective regimes. For the trade-wind MABL, the buoyancy flux is mainly driven by the moisture flux; the quadrant flux intensities are stronger than those of the other three studies except for the buoyant updrafts (thermals). These results suggest that the entrainment and detrainment of thermals are more effective in the trade-wind MABL than in the boundary layers driven by the temperature flux.Scale analysis of the buoyancy flux is in good agreement with that of AMTEX. For the lower half of the MABL, the buoyancy flux is mainly generated by the intermediate scale (200 m to 2 km), which includes the dominant convective thermals in the surface layer and the mixed layer. The scale smaller than 200 m is important only in the surface layer. The scale larger than 2 km, which includes the roll vortices, increases its significance upward. While most of the positive and negative fluxes are associated with the updrafts for the intermediate scale, the downdrafts are as important as updrafts for the larger scale.ST Systems Corporation, Lanham, MD, 20706, U.S.A.     

Water vapour flux profiles in the convective boundary layer

Summary Water vapour flux profiles in the atmospheric boundary layer have been derived from measurements of water vapour density fluctuations by a ground-based Differential Absorption Lidar (DIAL) and of vertical wind fluctuations by a ground-based Doppler lidar. The data were collected during the field experiment LITFASS-2003 in May/June 2003 in the area of Lindenberg, Germany. The eddy-correlation method was applied, and error estimates of ±50 W/m² for latent heat flux were found. Since the sampling error dominates the overall measurement accuracy, time intervals between 60 and 120 min were required for a reliable flux calculation, depending on wind speed. Rather large errors may occur with low wind speed because the diurnal cycle restricts the useful interval length. In the lower height range, these measurements are compared with DIAL/radar-RASS fluxes. The agreement is good when comparing covariance and error values. The lidar flux profiles are well complemented by tower measurements at 50 and 90 m above ground and by area-averaged near surface fluxes from a network of micrometeorological stations. Water vapour flux profiles in the convective boundary layer exhibit different structures mainly depending on the magnitude of the entrainment flux. In situations with dry air above the boundary layer a positive entrainment flux is observed which can even exceed the surface flux. Flux profiles which linearly increase from the surface to the top of the boundary layer are observed as well as profiles which decrease in the lower part and increase in the upper part of the boundary layer. In situations with humid air above the boundary layer the entrainment flux is about zero in the upper part of the boundary layer and the profiles in most cases show a linear decrease.     

Countergradient Fluxes of Conserved Variables in the Clear convective and Stratocumulus-topped Boundary Layer: The role of the Entrainment Flux

Large-eddy simulations of a clear convective boundary layer (CBL)and a stratocumulus-topped boundary layer are studied. Bottom-upand a top-down scalars were included in the simulations, and theprinciple of linear superposition of variables was applied toreconstruct the fields of any arbitrary conserved variable.This approach allows a systematic analysis of countergradient fluxesas a function of the flux ratio, which is defined as the ratio betweenthe entrainment flux and the surface flux of the conserved quantity.In general, the turbulent flux of an arbitrary conserved quantityis counter to the mean vertical gradient if the heights where thevertical flux and the mean vertical gradient change sign do notcoincide. The regime where the flux is countergradient is thereforebounded by the so-called zero-flux and zero-gradient heights. Becausethe vertical flux changes sign only if the entrainment flux has anopposite sign to the surface flux, countergradient fluxes arepredominantly found for negative flux ratios. In the CBL the fluxratio for the virtual potential temperature is, to a good approximation,constant, and equal to -0.2. Only if the moisture contribution to thevirtual potential temperature is negligibly small will the flux ratio forthe potential temperature be equal to this value. Otherwise, theflux ratio for the potential temperature can have any arbitrary(negative) value, and, as a consequence, the fluxes for thepotential temperature and the virtual potential temperature willbe countergradient at different heights. As a practical application ofthe results, vertical profiles of the countergradient correction termfor different entrainment-to-surface-flux ratios are discussed.     

Conditional Wavelet Technique Applied to Aircraft Data Measured in the Thermal Internal Boundary Layer During Sea-Breeze Events

We describe a wavelet-based technique to determine the spectral turbulentcontribution to the vertical flux of sensible heat in a position-wavelength representation. This technique combines awavelet transform (Morlet wavelet) with conditional sampling. We apply this methodto aircraft datacollected during a sea-breeze circulation (BEMA97 experiment) with heterogeneousturbulence conditions horizontally and vertically as well. The turbulent fluxes are analysed with the conditional wavelet techniqueas a function of the wavelength and the horizontal distance.The turbulent processes within the thermal internal boundary layer associatedwith the sea breeze are clearly identified. The results exhibit the wavelength bands through which the upward flux (originating fromthe surface) and the downward flux (originating from the top of theboundary layer) are important.     

Similarity studies of entrainment in convective mixed layers

A similarity study of entrainment at the top of convectively driven mixed layer is presented. The similarity framework is used for a comparison between various parameterized models of mixed-layer growth rate and between closely related models for the ratio of heat fluxes at ground and inversion levels. These various models are also tested, in dimensionless form, against data from laboratory, field experiments and numerical higher-order-modeling of the convective layer. It is concluded that a rather accurate prediction of mixed-layer growth can be achieved with the simple constant flux ratio model, but that more refined studies of entrainment are required to account for the decrease of the heat flux ratio with increasing convective intensity.List of acronyms CRPE Centre de Recherches en Physique de l'Environnement, Issy-les-Moulineaux, France - EERM Etablissement d'Etudes et de Recherches Météorologiques, Boulogne, France - INRA Institut National de la Recherche Agronomique, Versailles, France - LAMP Laboratoire Associé de Météorologie Physique, Clermont-Ferrand, France - NCAR National Center for Atmospheric Research, Boulder, U.S.A. - NOAA National Oceanic and Atmospheric Administration, Environmental Research Laboratories, Boulder, U.S.A.     

Tropical sea surface temperature: An interactive one-dimensional atmosphere-ocean model

Because the atmosphere and ocean are interacting systems, it is inappropriate to specify sea surface temperature when dealing with the atmosphere, or atmospheric anemometer level temperature and moisture when dealing with the ocean. All of these quantities should be determined interactively in terms of the external forcing: the solar constant.In the tropics, it is shown that the (cumulus) convective processes may be described by a one-dimensional cloud model. The near-surface ocean may similarly be described by a one-dimensional mixed-layer model. The coupling is achieved through a sea surface flux budget combined with the flux parameterizations implied by Monin-Obukhov similarity theory.The coupled one-dimensional atmosphere-ocean model is applied to the equilibrium situation in which all temperatures reach a steady state. Since the ocean, lacking an internal heating or cooling mechanism, can only be heated or cooled through sensibleheat fluxes through the sea surface, in equilibrium these fluxes must vanish. The atmosphere, however, maintains a stable lapse rate by balancing cumulonimbus heating against net radiative cooling. All water precipitated from cumulonimbus clouds must have evaporated from sea surface. It is shown that this equilibrium system is closed and determinable solely in terms of the solar constant.For various values of the solar constant, the sea surface temperature, the flux of latent and sensible heat from the surface, the height of the tropopause, mixed layer, and trade inversion layer, and generally, the entire vertical structure of the tropical atmosphere and near-surface ocean can be determined. The equilibrium sea surface temperature is shown to be relatively insensitive to changes in the solar constant, additional solar flux being compensated mainly by additional evaporation. Finally, the usefulness and limitations of the model are pointed out.     

A Simple Model for the Vertical Transport of Reactive Species in the Convective Atmospheric Boundary Layer

We have developed a simple, steady-state, one-dimensional second-order closure model to obtain continuous profiles of turbulent fluxes and mean concentrations of non-conserved scalars in a convective boundary layer without shear. As a basic tool we first set up a model for conserved species with standard parameterizations. This leads to formulations for profiles of the turbulent diffusivity and the ratio of temperature-scalar covariance to the flux of the passive scalar. The model is then extended to solving, in terms of profiles of mean concentrations and fluxes, the NO _x –O₃ triad problem. The chemical reactions involve one first-order reaction, the destruction of NO₂ with decay time τ, and one second-order reaction, the destruction of NO and O₃ with the reaction constant k. Since the fluxes of the sum concentrations of NO _x = NO + NO₂ and O₃ + NO₂ turn out to be constant throughout the boundary layer, the problem reduces to solving two differential equations for the concentration and the flux of NO₂. The boundary conditions are the three surface fluxes and the fluxes at the top of the boundary layer, the last obtained from the entrainment velocity, and the concentration differences between the free troposphere and the top of the boundary layer. The equations are solved in a dimensionless form by using 1/(kτ) as the concentration unit, the depth h of the boundary layer as the length unit, the convective velocity scale w _* as the velocity unit, and the surface temperature flux divided by w _* as the temperature unit. Special care has been devoted to the inclusion of the scalar–scalar covariance between the concentrations of O₃ and NO. Sample calculations show that the fluxes of the reactive species deviate significantly from those of non-reactive species. Further, the diffusivities, defined by minus the flux divided by the concentration gradient may become negative for reactive species in contrast to those of non-reactive species, which in the present model are never negative.     

Atmospheric turbulence within and above a douglas-fir stand. Part II: Eddy fluxes of sensible heat and water vapour

This is the second paper describing a study of the turbulence regimes and exchange processes within and above an extensive Douglas-fir stand. The experiment was conducted on Vancouver Island during a two-week rainless period in July and August 1990. Two eddy correlation units were operated in the daytime to measure the fluxes of sensible heat and water vapour and other turbulence statistics at various heights within and above the stand. Net radiation was measured above the overstory using a stationary net radiometer and beneath the overstory using a tram system. Supplementary measurements included soil heat flux, humidity above and beneath the overstory, profiles of wind speed and air temperature, and the spatial variation of sensible heat flux near the forest floor.The sum of sensible and latent heat fluxes above the stand accounted for, on average, 83% of the available energy flux. On some days, energy budget closure was far better than on others. The average value of the Bowen ratio was 2.1 above the stand and 1.4 beneath the overstory. The mid-morning value of the canopy resistance was 150–450 s/m during the experiment and mid-day value of the Omega factor was about 0.20. The daytime mean canopy resistance showed a strong dependence on the mean saturation deficit during the two-week experimental period.The sum of sensible and latent heat fluxes beneath the overstory accounted for 74% of the available energy flux beneath the overstory. One of the reasons for this energy imbalance was that the small number of soil heat flux plates and the short pathway of the radiometer tram system was unable to account for the large horizontal heterogeneity in the available energy flux beneath the overstory. On the other hand, good agreement was obtained among the measurements of sensible heat flux made near the forest floor at four positions 15 m apart.There was a constant flux layer in the trunk space, a large flux divergence in the canopy layer, and a constant flux layer above the stand. Counter-gradient flux of sensible heat constantly occurred at the base of the canopy.The transfer of sensible heat and water vapour was dominated by intermittent cool downdraft and warm updraft events and dry downdraft and moist updraft events, respectively, at all levels. For sensible heat flux, the ratio of the contribution of cool downdrafts to that of warm updrafts was greater than one in the canopy layer and less than one above the stand and near the forest floor.     

An Optimal Inverse Method Using Doppler Lidar Measurements to Estimate the Surface Sensible Heat Flux

Inverse methods are widely used in various fields of atmospheric science. However, such methods are not commonly used within the boundary-layer community, where robust observations of surface fluxes are a particular concern. We present a new technique for deriving surface sensible heat fluxes from boundary-layer turbulence observations using an inverse method. Doppler lidar observations of vertical velocity variance are combined with two well-known mixed-layer scaling forward models for a convective boundary layer (CBL). The inverse method is validated using large-eddy simulations of a CBL with increasing wind speed. The majority of the estimated heat fluxes agree within error with the proscribed heat flux, across all wind speeds tested. The method is then applied to Doppler lidar data from the Chilbolton Observatory, UK. Heat fluxes are compared with those from a mast-mounted sonic anemometer. Errors in estimated heat fluxes are on average 18 %, an improvement on previous techniques. However, a significant negative bias is observed (on average $-63\,\%$ ) that is more pronounced in the morning. Results are improved for the fully-developed CBL later in the day, which suggests that the bias is largely related to the choice of forward model, which is kept deliberately simple for this study. Overall, the inverse method provided reasonable flux estimates for the simple case of a CBL. Results shown here demonstrate that this method has promise in utilizing ground-based remote sensing to derive surface fluxes. Extension of the method is relatively straight-forward, and could include more complex forward models, or other measurements.     

Estimating the Random Error in Eddy-Covariance Based Fluxes and Other Turbulence Statistics: The Filtering Method

A spatially local decomposition of turbulent fluxes based on properties of spatial filters is used to develop a new method of estimating random error in turbulent moments of any order. The proposed error estimation method does not require an estimate of the integral time scale, which can be highly sensitive to the method used to calculate it. The error estimation method is validated using synthetic flux data with a known ensemble mean and intercompared with existing methods using data from the Advection Horizontal Array Turbulence Study (AHATS). Typical errors for a 27.3-min block of data collected at a height of 8 m are found to be approximately 10% for the heat flux and 7–15% for variances. The error in the momentum flux increases rapidly with increasing atmospheric instability, reaching values of 40% or greater for unstable conditions. A new method based on filtering is also proposed to estimate integral time scales of turbulent quantities.     

Methods for Estimating Air–Sea Fluxes of CO<Subscript>2</Subscript> Using High-Frequency Measurements

The most direct method for flux estimation uses eddy covariance, which is also the most commonly used method for land-based measurements of surface fluxes. Moving platforms are frequently used to make measurements over the sea, in which case motion can disturb the measurements. An alternative method for flux estimation should be considered if the effects of platform motion cannot be properly corrected for. Three methods for estimating CO₂ fluxes are studied here: the eddy-covariance, the inertial-dissipation, and the cospectral-peak methods. High-frequency measurements made at the land-based Östergarnsholm marine station in the Baltic Sea and measurements made from a ship during the Galathea 3 expedition are used. The Kolmogorov constant for CO₂, used in the inertial-dissipation method, is estimated to be 0.68 and is determined using direct flux measurements made at the Östergarnsholm site. The cospectral-peak method, originally developed for neutral stratification, is modified to be applicable in all stratifications. With these modifications, the CO₂ fluxes estimated using the three methods agree well. Using data from the Östergarnsholm site, the mean absolute error between the eddy-covariance and inertial-dissipation methods is 0.25 μmol  m^?2 s^?1. The corresponding mean absolute error between the eddy-covariance and cospectral-peak methods is 0.26 μmol m^?2 s^?1, while between the inertial-dissipation and cospectral-peak methods it is 0.14 μmol m^?2 s^?1.     

Momentum- and Heat-Flux Parametrization at Dome C,Antarctica: A Sensitivity Study

An extensive meteorological observational dataset at Dome C, East Antarctic Plateau, enabled estimation of the sensitivity of surface momentum and sensible heat fluxes to aerodynamic roughness length and atmospheric stability in this region. Our study reveals that (1) because of the preferential orientation of snow micro-reliefs (sastrugi), the aerodynamic roughness length \(z_{0}\) varies by more than two orders of magnitude depending on the wind direction; consequently, estimating the turbulent fluxes with a realistic but constant \(z_{0}\) of 1 mm leads to a mean friction velocity bias of \(24\,\%\) in near-neutral conditions; (2) the dependence of the ratio of the roughness length for heat \(z_{0t}\) to \(z_{0}\) on the roughness Reynolds number is shown to be in reasonable agreement with previous models; (3) the wide range of atmospheric stability at Dome C makes the flux very sensitive to the choice of the stability functions; stability function models presumed to be suitable for stable conditions were evaluated and shown to generally underestimate the dimensionless vertical temperature gradient; as these models differ increasingly with increases in the stability parameter z / L, heat flux and friction velocity relative differences reached \(100\,\%\) when \(z/L > 1\); (4) the shallowness of the stable boundary layer is responsible for significant sensitivity to the height of the observed temperature and wind data used to estimate the fluxes. Consistent flux results were obtained with atmospheric measurements at heights up to 2 m. Our sensitivity study revealed the need to include a dynamical parametrization of roughness length over Antarctica in climate models and to develop new parametrizations of the surface fluxes in very stable conditions, accounting, for instance, for the divergence in both radiative and turbulent fluxes in the first few metres of the boundary layer.