COMPARISON OF EDDY COVARIANCE FLUXES CALCULATED

15 downloads 0 Views 137KB Size Report
Use of coordinate rotation is vital before the eddy covariance measurements can be thought to represent the fluxes between surface and atmosphere. This is ...
COMPARISON OF EDDY COVARIANCE FLUXES CALCULATED WITH TWO DIFFERENT COORDINATE ROTATION METHODS O. PELTOLA1 , I. MAMMARELLA1 and T. VESALA1 1

Department of Physics, P.O. Box 64, 00014 University of Helsinki, Finland.

Keywords: coordinate rotation, surface fluxes, complex terrain, lateral momentum flux. INTRODUCTION Use of coordinate rotation is vital before the eddy covariance measurements can be thought to represent the fluxes between surface and atmosphere. This is because prior to rotation the fluxes are susceptible to errors caused by sensor tilt relative to the terrain surface or tower structure induced turbulent wakes (Aubinet et al. 2000). McMillen (1988) found out that coordinate rotation improves results significantly. Thus it is important to study the effects of different coordinate rotations to the fluxes. Usually coordinates are rotated to align the streamline coordinates. In the surface layer and over a homogeneous terrain the flow is one dimensional, meaning that the velocity and scalar concentration have only vertical gradient (e.g. Kaimal and Finnigan, 1994). Therefore horizontal scalar advection does not exist nor does flow divergence. Three coordinate rotations are required in order to transform the measurements from the instrument’s reference frame to the streamline reference frame (Kaimal and Finnigan, 1994). In this study the effect of the third coordinate rotation, which aligns the coordinates so that v 0 w 0 = 0, is studied. According to many studies (Finnigan, 2004; McMillen, 1988; Wilczak et al., 2001) this third rotation induces errors to the observed fluxes, especially in complex terrain. METHODS Eddy covariance measurements were done by using a micrometeorological mast at a forest site located in Hyyti¨ al¨ a, southern Finland (61◦ 51’ N, 24◦ 17’ E), situated 181 meters above sea level. A 13 m high Scots pine tree stand dominates the site. The forest is homogeneous about 200 m in all directions around the mast. Extensive site description can be found in Vesala et al. (1998). Three wind speed components and sonic temperature are measured with an ultrasonic anemometer (Solent 1012R, Gill Instruments Ltd., Lymington, UK). It is situated on the mast at 23.3 meters, approximately 10 meters above the forest canopy. A 10 Hz sampling frequency is used for collecting data. Water and carbon dioxide concentrations are measured with a closed-path infrared gas analyser (LI-COR 6262, Licor Inc., Lincoln, NE). This study is based on measurements done in years 2001-2008. There are gaps, i.e. missing values, in the time series, especially in winter. The gaps are caused by different instrument maintenance operations or problems with measurement system, among other things. Gap filling was done according to the next procedure: if less than eleven consecutive measurements are missing, the points are filled with linear interpolation. If more than 10 measurements are missing, the gap is filled with mean diurnal variation values calculated for that time of year. Year was divided into four seasons: winter (December-February), spring (March-May), summer (June-August) and autumn (September-November). However, the gap filled dataset was used only when the cumulative sums were calculated. All the other data analysis was done by using the original dataset.

The dataset was post-processed with two different coordinate rotation methods. The first coordinate rotation method consist of two rotations: the first turns the vectors so that v = 0 and the second so that w = 0 (Kaimal and Finnigan, 1994). Here u and v are horizontal and w is vertical wind component. The aim of these rotations is to minimize error caused by the sensor tilt relative ~ | = u. These two coordinate roto the terrain surface (Aubinet et al., 2000) and to ensure that |U tations are valid on an ideal measurement site where terrain is homogeneous. However, in complex terrain the mean value of the vertical wind speed is not necessarily zero. Therefore there can be vertical scalar advection and it cannot be measured by eddy covariance technique. This means that part of the surface exchange is neglected when w = 0 is assumed. These two coordinate rotations are called ”2D-coordinate rotation”. The second coordinate rotation method, called ”3D-coordinate rotation”, consist of three rotations. The first two are identical to the rotations presented before and the third rotation turns the coordinates so that v 0 w 0 = 0. This term is likely to be zero over plane surfaces (Aubinet et al., 2000), meaning that the flow in the direction of the mean wind speed produces most of the momentum flux. Wind components after the third coordinate rotation (Kaimal and Finnigan, 1994): u3 = u2 v3 = v2 cos ψ + w2 sin ψ

(1)

w3 = −v2 sin ψ + w2 cos ψ where





1 2 v 2 w2   ψ = tan−1   2 v 2 − w2 2

(2)

2

Third coordinate rotation angle ψ is obtained from the Reynolds stress tensor (Finnigan, 2004). u2 , v2 and w2 are the wind components after the first two coordinate rotations. If we consider the fact that w2 = v2 = 0, the equation above can be written as   0 0 1 2 v 2w 2   ψ = tan−1   (3) 2 v02 −w02 2

2

where v 0 22 and w 0 22 are variances of the cross-wind and vertical wind components. v 02 w 02 is the cross-wind component of momentum flux. Theoretical maximum and minimum values for ψ are 45◦ and −45◦ , respectively. According to Finnigan (2004), the third rotation often yields unphysical values for ψ, causing error to the flux. Therefore the differences between 2D- and 3D-coordinate rotations are investigated. The unphysical values for ψ are caused by the fact that non-zero values of measured v 0 w 0 are not only caused by the differences between the instrument’s reference frame and the streamline reference frame but there are also real physical phenomena causing lateral momentum flux. These phenomena originate from the non-stationarities of the fluxes and the horizontal heterogeneities in the terrain (Finnigan, 2004). If the angle ψ has too large values, the coordinates will be rotated too much and thus they differ from the streamline coordinates. Therefore the scalar flux w 0 c 0 will be contaminated by the cross-wind flux v 0 c 0 (Lee et al., 2004). This can be seen from Eq. (4). On the other hand, ignoring the third rotation would also lead to systematic errors in the measured flux because the coordinates differ from the expected streamline coordinates. However, Finnigan (2004) showed that the error caused by the third rotation is generally larger than the error caused by using only the first two rotations. Therefore they suggest that only two rotations should be used, in addition to orientating the sonic anemometer z-axis normal to the underlying surface.

The difference between scalar fluxes w 0 c 0 calculated with 2D- and 3D-coordinate rotations can be determined from (4) w3 0 c 0 = −v2 0 c 0 sin ψ + w2 0 c 0 cos ψ where w3 0 c 0 and w2 0 c 0 are the scalar fluxes calculated with 3D- and 2D-coordinate rotation, respectively. From now on they are referred to 3D- and 2D-fluxes. This dependence is determined from Eq. (1) by using Reynold decomposition and taking the time average. The horizontal fluxes are not necessarily zero in heterogeneous flow, meaning that v2 0 c 0 is not negligible. An equation for relative difference between 2D- and 3D-fluxes can be derived from the equation above w2 0 c 0 − w3 0 c 0 v2 0 c 0 = 1 − cos ψ + sin ψ w2 0 c 0 w2 0 c 0

(5)

In ideal conditions v2 0 c 0 = 0 and the relative difference between 3D- and 2D-fluxes depends only on the third coordinate rotation angle ψ. RESULTS The data from years 2001-2008 were post-processed with 2D- and 3D-coordinate rotation. The most common value for ψ, the third coordinate rotation angle, is approximately −1.9◦ . The values are distributed quite symmetrically around the most common value. The 2D-fluxes have systematically larger absolute values than the 3D-fluxes. The median of the relative differences between these two methods are 2.3 %, 1.5 %, 1.9 % and 1.8 % for sensible heat, latent heat, momentum and CO2 -fluxes, respectively. The median of the relative differences describes better the usual value than the mean because the mean values are affected by the large relative differences when the 2D-fluxes are near zero. In addition, it must be emphasised that Eq. (4) and Eq. (5) are not valid for the momentum flux. There is a clear difference between night time and daytime values. In night time the median values of the relative differences are 3.7 %, 2.4 %, 1.9 % and 2.5 % for sensible heat, latent heat, momentum and CO2 -fluxes and in daytime these percentages are 0.9 %, 1.0 %, 1.8 % and 1.1 %, respectively. Night time is defined as those moments when the sun’s declination angle is smaller than −3◦ and in daytime it is larger than 10◦ . The definition of night time is taken from Markkanen et al. (2001) and the definition of daytime is determined assuming turbulence to be stationary in daytime which is true on average when the angle is larger than 10◦ . This difference between night time and daytime in the percentages above is probably caused by the stability of the surface layer. In night time the stability is usually stable and therefore turbulence is non-stationary. Thus the cross-wind momentum flux, v 0 w 0 , is significant and there is a notable difference between 2D- and 3D-fluxes. When the stratification is unstable, turbulence is usually stationary and the horizontal fluxes, for instance v 0 c 0 , are small. The difference between 2D- and 3D-fluxes is plotted against surface layer stability in Figure 1. Cumulative sums of the fluxes were calculated from the gap filled data. Mean annual cumulative sum of CO2 -flux was calculated with 2D- and 3D-coordinate rotation and the results are −267 g C/m2 and −277 g C/m2 , respectively. The values are of the same order as in Markkanen et al. (2001). The cumulative sums of sensible heat and CO2 -fluxes calculated with 2D-rotation are on average 2.9 % and 3.6 % smaller than if they are calculated with 3D-rotation. Therefore if coordinates are rotated with 2D-coordinate rotation the underlying forest is not as effective sink of CO2 than with 3D-coordinate rotation. The cumulative sum of latent heat is 2.4 % larger if the coordinates are rotated with 2D-coordinate rotation than if they are rotated with 3D-rotation. Also the cumulative sums of the whole eight year measurement period were calculated. The cumulative sum of the CO2 -flux over the eight year period was −2137 g C/m2 and −2215 g C/m2 , when it was post-processed with 2D- and 3D-coordinate rotation, respectively.

Figure 1: Relative difference between 2D- and 3D-fluxes plotted against stability parameter z/L. Dashed line denotes 1 − cos ψ. Values are calculated for logarithmically evenly spaced bins. The relative difference of momentum flux behaves similarly whether the conditions are unstable or stable and thus the upper figure shows only percentages 0-10 %. In addition, the mean annual cumulative sum of the sum H+LE was calculated. This was done in order to study differences in the energy balance closure between data post-processed with 2Dand 3D-coordinate rotation. The energy balance closure describes how well the sensible heat and latent heat fluxes balance the net radiation and ground heat flux. It is described in more detail for instance in Aubinet et al. (2000). The mean annual cumulative sum of H+LE is 0.4 % larger with 2D- than with 3D-coordinate rotation. Therefore it can be said that the energy balance is closed slightly better with 2D-coordinate rotation but there is no major difference between these two methods. However, it must be kept in mind that the used gap filling method was not the best possible and with a more sophisticated method the results might be slightly different. From Figure 1 we can see that the relative difference of all the scalar fluxes (H, LE, Fc ) behave similarly. This is caused by the fact that they all follow the same Eq. (5). In unstable cases all the scalar fluxes follow the dashed line and the relative differences are fairly independent of stability. Consequently it can be said that the third term on the right in Eq. (5) does not play a major role and the values of relative difference are mainly determined by 1 − cos ψ. However, in stable situations the third term is significant because the curves related to the scalar fluxes do not meet with the dashed line. In addition, the relative differences increase when stability turns more stable. The relative difference of momentum flux increases when the absolute value of stability parameter increases. This may be caused by the fact that in extremely stable/unstable conditions momentum flux is small. Therefore the relative difference is calculated as a difference between two small numbers divided with a small number. This kind of calculation is susceptible to errors and it would cause the relative difference to have unusual values. In Figure 2 the relative differences are plotted against the angle ψ. In addition 1 − cos ψ is plotted. This is done in order to demonstrate the influence that the terms on the right side of Eq. (5) have on the relative differences of the 2D- and 3D-fluxes. In horizontally homogeneous flow all horizontal fluxes are negligible. In other words, v 0 c 0 is small and the measured value of v 0 w 0 is caused only by the differences between the instrument’s reference frame and the streamline reference frame. In this kind of situation the relative differences between the 2D- and 3D-fluxes would follow the 1 − cos ψ line and the third coordinate rotation would not cause any error to the flux. However, as

Figure 2: Relative difference between 2D- and 3D-fluxes plotted against the angle ψ. Dashed line denotes 1 − cos ψ. Over 89 % of the accepted values of the angle ψ are between angles −17◦ and 17◦ . we can see from Figure 2, this is not the case. The differences between 1 − cos ψ and the other lines defines the magnitude of the third term on the right in Eq. (5). The slope of 1 − cos ψ is smaller than the slopes of the other lines and therefore we can say that the magnitude of the third term increases when the absolute value of ψ increases. This is logical because large values of ψ would indicate that v 0 w 0 differs exceedingly from zero. The sign of the angle ψ can be derived from Eq. (3). It is the same as the sign of the vertical transport of lateral momentum, v 0 w 0 , because the variance of lateral wind component is almost always larger than the variance of vertical wind component. All the fluxes behave in a similar way when ψ < 0 (Figure 2). Therefore the differences between the effect that the third coordinate rotation has on the fluxes are mainly caused by rotations with positive ψ values. This is caused by the fact that the third term on right in Eq. (5) is different for different fluxes when ψ > 0. In other words, the fluxes react differently on the effects caused by the horizontal heterogeneities. When ψ > 0, the along-wind and the cross-wind momentum fluxes transport momentum in different directions. This is a consequence of the fact that the along-wind momentum flux is almost always directed downwards because the surface is a sink of momentum. Relative difference of sensible heat fluxes increases the most when ψ increases (Figure 2). In other words, the sensible heat flux is the most vulnerable of the fluxes to the effects of the third coordinate rotation. This indicates that the lateral turbulent sensible heat flux is the biggest of the lateral turbulent fluxes. It causes the difference between sensible heat flux calculated with 2D- and 3Dcoordinate rotation to be larger than the difference of other fluxes, as mentioned at the begin of this section. CONCLUSIONS Difficulties in aligning the sonic coordinates to streamlines can induce large errors to the fluxes, measured by EC technique. The problems in aligning the coordinates arise from the fact that measurements are done only at one point. Therefore they can only define the local vector basis and it does not necessarily describe the global streamline coordinates. Especially the third coordinate rotation is problematic because in complex terrain the lateral momentum flux is not only caused by the fact that the instrument’s reference frame and the streamline reference frame differ from each other but there are real physical phenomena producing lateral momentum flux. Thus nullifying

v 0 w 0 will cause the coordinates to differ from the streamline coordinates. On the other hand if the third rotation is neglected, the non-zero value of lateral momentum flux causes error to the fluxes. Generally the absolute value of 2D-fluxes is larger than the absolute value of 3D-fluxes. In other words the third coordinate rotation decreases downward and upward fluxes. This is actually what we might expect if we consider Eq. (4). The observed relative differences between 2D- and 3Dfluxes are not big, order of few percentages. However they seem to depend on the stability of the atmospheric surface layer, growing when stability increases. In addition, it was found out that sensible heat flux is most susceptible to errors induced by the third coordinate rotation. This can be seen from Figure 2. From this study it is difficult to say which one of these coordinate rotation methods is better in terms of producing fluxes that describe the real surface fluxes between surface and atmosphere. This is due to the fact that there is no information about the real surface fluxes, the measured fluxes always suffer from some kind of errors. However, the 2D-fluxes close the energy balance slightly better than 3D-fluxes and this might indicate that the 2D-coordinate rotation cause less error to the fluxes. ACKNOWLEDGEMENTS The financial support by the Academy of Finland Centre of Excellence program (project no 1118615) is gratefully acknowledged. REFERENCES ¨ Moncrieff, J., Foken, T., Kowalski, A.S., MarAubinet, M., Grelle, A., Ibrom, A., Rannik, U., tin, P.H., Berbigier, P., Bernhofer, Ch., Clement, R., Elbers, J., Granier, A., Gr¨ unwald, T., Morgenstern, K., Pilegaard, K., Rebmann, C., Snijders, W., Valentini, R. and Vesala, T. (2000). Estimates of the Annual Net Carbon and Water Exchange of Forests: The EUROFLUX Methodology. Advances in Ecological Research, 30, 113-175. Finnigan, J.J. (2004). A re-evaluation of long-term flux measurement techniques part II: coordinate systems. Boundary-Layer Meteorology, 113, 1-41. Kaimal, J.C. and Finnigan, J.J. (1994). Atmospheric Boundary Layer Flows, their structure and measurement. (Oxford University Press, New York, USA). 289 pp. Lee, X., Massman, W. and Law, B. (2004). Handbook of micrometeorology: a guide for surface flux measurement and analysis. (Kluwer Academic Publishers, Netherlands). 250 pp. ¨ Keronen, P., Suni, T. and Vesala, T. (2001). Eddy covariance fluxes Markkanen, T., Rannik, U., over a boreal Scots pine forest. Boreal environment research, 6, 65-78. McMillen, R.T. (1988). An eddy correlation technique with extended applicability to non-simple terrain Boundary-Layer Meteorology, 43, 231-245. Vesala, T., Haataja, J., Aalto, P., Altimir, N., Buzorius, G., Garam, E., H¨ameri, K., Ilvesniemi, H., Jokinen, V., Keronen, P., Lahti, T., Markkanen, T., M¨akel¨a, J.M., Nikinmaa, E., Palmroth, S., ¨ Siivola, E., Ylitalo, H., Hari, P. and Kulmala, Palva, L., Pohja, T., Pumpanen, J., Rannik, U., M. (1998). Long-term field measurements of atmosphere-surface interactions in boreal forest combining forest ecology, micrometeorology, aerosol physics and atmospheric chemistry. Trends in Heat, Mass and Momentum Transfer, 4, 17-35.