John Finnigan

A re-evaluation of long-term flux measurement techniques - Part I: Averaging and coordinate rotation

Experience of long term flux measurements over tall canopiesduring the last two decades has revealed that the eddy flux of sensible plus latentheat is typically 30% smaller than the available radiant energy flux. This failureto close the energy balance is less common close to the surface over short roughnessbut is still sometimes seen, especially in complex topography. These observationscast doubt on the results obtained from long term flux studies where daily and annualnet ecosystem exchange is usually the small difference between large positive andnegative fluxes over 24 h. In this paper we investigate this problem by examiningsome fundamental assumptions entailed in analysis of surface exchange by the eddyflux method.In particular, we clarify the form and use of the scalar conservation equation thatunderlies this analysis and we examine the links between averaging period androtation of coordinates in the situation where coordinates are aligned with thewind vector. We show that rotating coordinates so that the x axis is alignedwith the mean wind vector has the effect of high pass filtering the scalar covariance,¯wc, such that contributions to the aerodynamic flux from atmosphericmotions with periods longer than the averaging period are lost while those of shorterperiod are distorted.We compare the effect of computing surface exchange by averaging many shortperiods, in each of which the coordinates are rotated so that the mean verticalvelocity is zero (the method currently adopted in most long-term flux studies),with analysis in long-term coordinates and show a systematic underestimationof surface exchange in the former case. This is illustrated with data from threelong-term forest field sites where underestimations of sensible and latent heatfluxes of 10–15% averaged over many days are seen.Crucial factors determining the loss of flux are the averaging period T, themeasurement height and the content of the scalar cospectrum at periods longerthan T. The properties of this cospectrum over tall canopies in both homogeneousand complex terrain are illustrated by measurements at our three sites and we see thatover tall canopies on flat ground in convectiveconditions, or on hilly sites in near neutralflow, the scalar cospectra have much more low frequency contentthan classical surface-layerspectral forms would predict. We believe that the filtering of this low frequencycovariance by the averaging-rotation operations in common use is a large contributoryfactor to the failure to close the energy balance over tall canopies.

A wind tunnel study of air flow in waving wheat: Two-point velocity statistics

Two-point, space-time correlations of streamwise and vertical velocity were obtained from a wind tunnel simulation of an atmospheric surface layer with an underlying model wheat canopy constructed of flexible nylon stalks. Velocity data extend from 1/6 canopy height to several canopy heights, with in excess of 2000 three-dimensional vector separations of the two x-wire probes. Isocorrelation contours over anx, z slice show the streamwise velocity autocorrelation to be roughly circular, such that vertical velocities at the same horizontal position but different heights are closely in phase. Cross-correlations between the two velocity components reflect this difference to some extent. Lateral displacements of the probes revealed side lobes with correlations of reversed sign but we cannot positively link this pattern to particular vorticular structures. Integral length scales obtained directly from the spatial correlations match similar scales deduced from single-point time series with Taylors hypothesis at 2 to 3 times the canopy height but greatly exceed such scales at lower levels, particularly within the wheat. We conclude that the reversed sign lateral lobes are important components of the correlation field and that an integral length scale for the lateral direction must be defined such that they are included. Convective velocities obtained from the time lag to optimally restore correlation lost by physical separation of the probes change only slowly with height and greatly exceed the mean wind velocity within and immediately above the canopy. Thus, mean wind velocity is not a suitable proxy for convective velocity in the application of Taylors hypothesis in this situation. The ratio of vertical to longitudinal convective velocity for the streawise velocity signal yields a downwind tilt angle of about 39° which is probably a better estimate of the slope of the dominant fluid motions than the tilt of the major axis of the isocorrellation contours mentioned previously.

On measuring net ecosystem carbon exchange over tall vegetation on complex terrain.

To assess annual budgets of CO2 exchange betweenthe biosphere and atmosphere over representativeecosystems, long-term measurements must be made overecosystems that do not exist on ideal terrain. How tointerpret eddy covariance measurements correctlyremains a major task. At present, net ecosystemCO2 exchange is assessed, by members of themicrometeorological community, as the sum of eddycovariance measurements and the storage of CO2 inthe underlying air. This approach, however, seemsunsatisfactory as numerous investigators are reportingthat it may be causing nocturnal respiration fluxdensities to be underestimated.A new theory was recently published by Lee (1998, Agricultural and Forest Meteorology91: 39–50) for assessing net ecosystem-atmosphere CO2 exchange(Ne) over non-ideal terrain. Itincludes a vertical advection term. We apply thisequation over a temperate broadleaved forest growingin undulating terrain. Inclusion of the verticaladvection term yields hourly, daily and annual sums ofnet ecosystem CO2 exchange that are moreecologically correct during the growing season.During the winter dormant period, on the other hand,corrected CO2 flux density measurements of anactively respiring forest were near zero. Thisobservation is unrealistic compared to chambermeasurements and model calculations. Only duringmidday, when the atmosphere is well-mixed, domeasurements of Ne match estimatesbased on model calculations and chamber measurements. On an annual basis, sums of Newithout the advection correction were 40% too large,as compared with computations derived from a validatedand process-based model. With the inclusion of theadvection correction term, we observe convergencebetween measured and calculated values ofNe on hourly, daily and yearly time scales. We cannot, however, conclude that inclusion of aone-dimensional, vertical advection term into thecontinuity equation is sufficient for evaluatingCO2 exchange over tall forests in complexterrain. There is an indication that the neglected term,ū(∂ c¯/∂ x), isnon-zero and that CO2 may be leakingfrom the sides of the control volume during the winter. In this circumstance, forest floor CO2 effluxdensities exceed effluxes measured above the canopy.

Turbulence in Waving Wheat

The intermittent features of the turbulent velocity field within a wheat canopy were investigated by conditional sampling techniques and short-period space-time correlations. The velocity and shear-stress profiles had qualitatively quite different forms during periods of high and low winds. Analysis of the relative importance of shear-stress contributions from different quadrants of the uw plane revealed the dominant role of gusts in penetrating the canopy and transferring momentum to it from the boundary layer above. Short-period space-time correlations of velocity indicated that over a significant fraction of the time, periodic velocity fluctuations pervaded the canopy-air layer. It is surmised that while this has only a secondary effect on momentum transfer, it may be of overriding importance in heat and mass transport.

A comment on the paper by Lee (1998): “On micrometeorological observations of surface-air exchange over tall vegetation”

We examine the analysis by Lee (1998) of the scalar conservation budget in advective flows. Lee treated the budget in a one-dimensional framework, neglected horizontal derivatives of turbulent quantities and proposed that mean flow advection, simplified to its vertical component, can be used to improve budget closure, when data from only a single tower are available. We conclude: that the appropriate analysis framework for constructing such budgets is unavoidably two- or three-dimensional because 2D and 3D mean velocity fields always induce streamwise variation in the eddy fluxes of scalars. that in such flow fields it is generally incorrect to assume that the vertical component of advection w@ c=@z is everywhere much larger than the horizontal component u@ c=@x The vertical component can only provide a good measure of total advective flux divergence in the special circumstance where the tower is located beneath the vertical stagnation streamline of a recirculating flow. By referring to a linear model of scalar transport over a hill we show that the relationship between u@ c=@x and w@ c=@z is entirely dependent on particular flow conditions and that, in general, w@ c=@z cannot even be used to provide a bound on the magnitude of total advection. that for measurements at heights small compared to the horizontal scale of the advective flow, the horizontal gradient of turbulent flux @u0c0=@x can probably be neglected relative to its vertical equivalent @w0c0=@z and, by using simple hydrodynamic models of 2D flows it can be shown that the vertical gradient of mean vertical velocity is approximately constant over tower heights small compared to the horizontal scale of the advective flow.

Turbulent flow in a model plant canopy

An array of slender, vertical, cylindrical rods was used in a wind tunnel to simulate a plant canopy. Turbulence measurements were made with a cross hot wire, both inside and above the canopy. Measurements were also made inside the canopy when its top was covered by boards, leaving no space above the rods. This artificially confined canopy provided reference data.The results show an exponential wind profile and constant turbulence intensity, skewness and mixing length along the height of the (unconfined) canopy, the contribution of the eddies shed by the rods to the turbulence observed inside the canopy was small, but clearly apparent.

A Re-Evaluation of Long-Term Flux Measurement Techniques Part II: Coordinate Systems

To convert measurements of windspeed, eddy flux and scalar concentration into estimates of surface scalar exchange, we implicitly or explicitly assimilate the measurements into mathematical statements of the mass balance in a control volume on a representative patch of the surface. The form of this statement depends on the coordinate system in which it is written and the coordinate system should be chosen so that measurements can be used optimally. This requirement imposes a set of conditions on the coordinates. Here we perform a comparative analysis of some candidate coordinate systems, concentrating on the Cartesian and physical streamline systems. We show that over gentle topography there are definite advantages in working in streamline coordinates. Transforming measurements of vector and tensor quantities measured in the reference frame, si, of the anemometer into the reference frame, ei, of the chosen coordinate system involves using the measured statistics of the wind field to define three Euler rotation angles. We compare the method in most common use, which employs the components of the mean wind vector and the Reynolds stress tensor to define these angles, with the more recent ‘planar-fit’ method that uses instead an ensemble of mean wind vectors to define the rotations. We find that, in real flows, the standard method has a previously unrecognized closure problem that ensures that the third rotation angle defined using the stress tensor or scalar flux vector will always be in error and often give unphysical results. An alternative procedure is recommended. Finally, the relationships between measurements and model outputs are discussed.

A wind tunnel study of turbulent flow over a two-dimensional ridge

We present a wind-tunnel simulation of adiabatic atmospheric flow normal to a rough, two-dimensional ridge. The data are analyzed in physical streamline coordinates, which are described in some detail. The mean velocity speed-up on the hill top is adequately predicted by existing formulae while the behaviour of the wake flow fits into a pattern that emerges from other wind-tunnel experiments. The turbulent stresses evolve in response to the extra strain rates induced by the hill, streamline curvature and acceleration: % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWG1bWaaWbaaS% qabeaaceaIYaGbaebaaaaaaa!3456!\[u^{\bar 2}\]is coupled strongly to acceleration while % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaadaqdaaqaaiaadw% hacaWG3baaaaaa!3462!\[\overline {uw}\]and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWG3bWaaWbaaS% qabeaaceaIYaGbaebaaaaaaa!3458!\[w^{\bar 2}\]follow curvature. These differing responses lead to significant phase differences between the changes in the component stresses as the hill is traversed. An analogous response is seen in the components of turbulent stress divergence, which are computed as part of streamwise momentum budgets. Only very close to the surface is turbulent stress divergence comparable to the inertial and pressure terms in the momentum budget; over most of the flow regime, the mean flow response is approximately inviscid. Finally, we compare our results with data from other wind tunnel models and from real hills.

Turbulent flow over a very rough, random surface

A knowledge of the nature of turbulent flow over very rough surfaces is important for an understanding of the environment of crops, forests, and cities. For this reason, a wind-tunnel investigation was carried out on the variations in mean velocity, Reynolds shear-stress, and other turbulence quantities in a deep turbulent flow over a rough surface having a fair degree of randomness in the shapes, sizes, and positions of its elements.There was a layer close to the surface with considerable variations in both mean velocity and shear-stress, and the horizontal scale over which the mean velocity varied was much larger than the average distance between roughness elements. Above this layer, whose depth was of the order of the spacing between roughness elements, shear stress was constant with height, and the velocity profile had a logarithmic form. The usefulness of both mean profile and eddy-correlation methods for estimating fluxes above very rough terrain is discussed in the light of these findings.

Coordinate Systems and Flux Bias Error

This Chapter examines theoretical and operational aspects of coordinate systems. A distinction is made between the vector basis, a local property of a coordinate system, and the overall coordinate frame consisting of the vector basis and coordinate lines, a global property of the flow that is determined by the flow field in three dimensions. Point measurements can only define the vector basis. Because in field campaigns many components that enter into the mass balance in complex flows are severely under-sampled, a properly chosen coordinate frame for point measurements should optimize our estimates of the surface-air exchange and should maximize information for diagnostics purposes.