Estimating random errors of eddy covariance data: An extended two-tower approach

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Abstract

The incorporation of eddy covariance (EC) data in a land surface model (LSM) with help of data assimilation techniques requires a specification of the uncertainty of EC measurements. EC measurement uncertainty is composed of a systematic and random component. The systematic error is for example related to the energy balance (EB) closure, whereas the random error can be determined on the basis of differences between simultaneous flux measurements from two towers according to Hollinger and Richardson (2005) (Tree Physiol. 25, 873–885, here referred to as classical approach). The two-tower method, however, can be applied only where two towers share very similar environmental conditions. Here, we introduce an extended procedure to estimate the random error from EC data on the basis of the two-tower approach adapted for more heterogeneous environmental conditions. Our extended procedure consists of three main steps: (1) the EB deficit is corrected by distributing the deficit over the latent and sensible heat fluxes according to the evaporative fraction for each tower. This correction is based on the assumption that the EB deficit is due to an underestimation of the turbulent fluxes; (2) heterogeneity (e.g. different soil properties or vegetation characteristics and local variability in precipitation amounts) between two towers can introduce additional systematic flux differences. These differences can be corrected by normalizing turbulent fluxes at each tower according to the averaged evaporative fraction from two towers; (3) the random error can be determined following the two-tower approach using the normalized fluxes for the two towers. EC data from three different sites with different environmental conditions are used to test the classical and our extended approach: (1) three EC towers are placed at the Merken site, Germany and each of the three towers is surrounded by different vegetation types. This allows an evaluation on the basis of three different two-tower pairs. (2) two EC towers are located at the Roccarespampani site, Italy, with the same vegetation type around both towers. However, there are differences in vegetation age and density between these two towers; (3) for the Howland site, Maine, USA also data from two towers are available with very similar environmental conditions around the two towers. The random errors calculated by our extended approach are smaller than random errors from the classical approach, especially for larger net radiation (or large absolute fluxes). In addition, the random errors calculated by our extended approach result also in 9 out of 10 cases in less steep increases of the random error as function of flux magnitude (compared to the classical method). It was also found that atmospheric stability is an interesting alternative explanatory variable for random error of fluxes, which could be of special interest in the context of the extended two-tower approach. We conclude that our extended two-tower approach can be used to determine the random error of EC data for two towers located in more heterogeneous environmental conditions than aimed at by the original approach.

Highlights

► An extended two-tower approach for estimating random errors of EC data is proposed. ► Random errors are smaller for the extended approach compared to the classical one. ► The extended approach is applicable for two towers with different vegetation types.

Introduction

Errors in eddy covariance (EC) measurements are composed of a systematic and random part. For various applications, it is important to quantify EC measurement uncertainties. This is for example the case for the use of EC data in sequential data assimilation, where both model prediction errors and observation errors have to be quantified in order to properly weight the influence of observations to correct model predictions (e.g. Evensen, 1994, Reichle et al., 2002, Moradkhani et al., 2005, Liu and Gupta, 2007). Systematic EC errors are linked to the energy balance closure problem and an associated possible underestimation of sensible (H) and latent heat flux (LE). This underestimation could be related to advection and low frequency turbulence (Culf et al., 2004, Foken, 2008). The measurement of the radiation is not expected to be the cause since the sensors already were considerably precise when the EB closure problem was discovered almost two decades ago (Halldin and Lindroth, 1992, Foken, 2008). Neglecting heat storage terms in soil and canopy, on the other hand, may play an essential role. In particular, often the heat storage in the upper soil layer above the ground heat flux plate is not correctly characterized (Heusinkveld et al., 2004, Meyers and Hollinger, 2004). However, underestimation of the turbulent fluxes appears to be a major contribution to the closure problem (Foken et al., 2011). Numerous studies in the past (Doran et al., 1989, Fritschen et al., 1992, Lee, 1998, Twine et al., 2000, Brotzge and Crawford, 2003, Foken et al., 2006, Foken, 2008) assume that the energy balance can be closed by distributing the energy balance gap to the sensible and the latent heat fluxes according to the Bowen ratio. This, however, is still a topic which is controversially discussed as also storage terms might sometimes play a larger role in the energy balance gap, especially during nighttime.

Different factors contribute to the random error of eddy covariance measurements like instrumental errors, footprint heterogeneity, and turbulence. By integrating the eddy covariance measurements over a period of 30 min the random error due to high frequency turbulence is reduced. Hollinger et al. (2004) and Hollinger and Richardson (2005) determined random errors using simultaneous measurements from two towers which are separated far enough (∼775 m) to prevent a significant footprints overlap. They focus in their analysis on pairs of measurements, taken at the same time from the two towers. The two measurements from the towers are assumed to be independent random variables with the same statistical distribution. The random error of the measurements σ(δ) can then be quantified as follows:σδ=σ(x1x2)2where σ(δ) is the standard deviation of the differences between the two measurements (W m−2), δ is the random variable of interest, and x1 and x2 are the measurements from tower 1 and 2 (W m−2), respectively.

The number of established sites with two flux measurement towers separated by an appropriate distance is small. Therefore Hollinger and Richardson (2005) and Richardson et al. (2006) also developed a technique which used flux measurements at one tower on two consecutive days under similar environmental conditions to determine the random error. A comparison of the results from both approaches was conducted by Hollinger and Richardson (2005) which illustrated that the random errors determined with the two-tower approach were somewhat smaller than the ones estimated on the basis of one tower. Dragoni et al. (2007) found that the two-tower method is preferable as the one-tower approach strongly overestimates the random error. The studies from Hollinger et al. (2004), Hollinger and Richardson (2005), and Richardson et al. (2006) focused solely on the random error and systematic errors were not included in their analysis.

Dragoni et al. (2007) introduced a paired observations approach which was similar to the approaches from Hollinger et al. (2004) and Hollinger and Richardson (2005) and assumed also that the two measurements are independent. However, Dragoni et al. (2007) further decomposed the error so that the estimated random error is related to only uncertainty from the measurement equipment. In order to do so, the approach by Dragoni et al. (2007) also requires a model run and makes the important assumption that there are no systematic differences between the measurements from the two towers.

Recently a study by Billesbach (2011) proposed a method called random shuffle (RS) for estimating the random error and compared this method with other four existing methods: (1) by Mann and Lenschow (1994), (2) by Verma and Billesbach (Billesbach et al., 1998), (3) by Hollinger and Richardson (2005), and (4) by Meyers et al. (1998), which have been formerly and currently used to estimate the random error. The findings from Billesbach (2011) suggest that the random error estimated from the four existing methods is the total uncertainty but the random error estimated from the RS method represents only the instrumental uncertainty. In general, it should be noted that there is a number of ways to estimate random errors from the turbulence-resolving raw data produced by EC set-ups, which have received little attention in the past (e.g. Lenschow et al., 1994, Benedict and Gould, 1996, Finkelstein and Sims, 2001, van Dijk et al., 2004) but are likely to improve the value of future datasets (Mauder et al., 2013). However, as these methods are often not feasible to apply to past or third-party datasets, it is also important to continue to compare and improve methods such as the two-tower approach, which only require processed fluxes.

In this study, we propose a new procedure to determine random errors from EC data on the basis of the two-tower method. For data assimilation procedures, like the fusion of eddy covariance data e.g. by Ensemble Kalman Filter (Evensen, 1994) in high-resolution hydrological models or land surface models (LSM's), it is essential that the random error would include only the influence of measurement error and turbulence. The effect of land use type, vegetation or soil differences between the two towers, in contrast, should not be included as the hydrological or LSM model can reproduce such systematic differences in turbulent exchange fluxes. Therefore we will determine a random error that includes the effects of instrumental error, turbulence and any hypothetical unknown small-scale variability within the varying footprint of each single tower (Richardson et al., 2012), but excludes the influence of systematic site differences between the two towers. Our approach is therefore also different from the one introduced by Dragoni et al. (2007) because we include both instrumental error and stochasticity from turbulence in the random error term. An advantage is that no numerical model has to be run in our proposed methodology. We determine systematic differences in evaporative fraction between the two EC towers and attribute these to soil, vegetation and other heterogeneities around the flux towers. This allows also estimating the random error for a pair of two towers located in different environment conditions. This will be illustrated in this paper for pairs of towers with different land use types around the towers. On one hand we argue that such systematic differences always should be taken into consideration, for example because different soil types might exert an unknown influence; on the other hand we argue that by making the two-tower approach robust against systematic differences, also much more heterogeneous conditions (i.e., different land use types around the two towers) can be handled. The proposed methodology also excludes the systematic error component indicated by the energy balance closure problem.

The random error will be estimated as function of net radiation and flux magnitude, but also analyzed as function of atmospheric stability. It will be analyzed whether atmospheric stability, also routinely reported in processed EC-datasets, is a possible alternative explanatory variable for random error. As the two-tower approach will be extended for pairs of sites with more heterogeneous conditions, it is also possible that for these heterogeneous conditions random errors cannot be considered similar for the two towers. In order to analyze whether such heterogeneous conditions can be a problem, it is also analyzed how different the recorded atmospheric stability is for the two towers which are used to estimate the random errors.

Section 2 outlines the data and the methodology used for the analysis. Section 3 presents results followed by a discussion in Section 4. Section 5 resumes the main conclusions from this work.

Section snippets

Data

The classical two-tower method from Hollinger and Richardson and our extended two-tower approach have been tested for three sites: Merken (Nordrhine-Westphalia, Germany), Roccarespampani (Central Italy), and Howland (Maine, USA).

Three EC towers are operated at the Merken site (6° 24′E, 50° 50′N, 114 m a.s.l.) and these towers are located on different types of agricultural land: barley, sugar beet, and wheat. The climate of this region is temperate, with an annual rainfall of 700 mm and an average

The energy balance deficit

At the Merken site and for the daytime data, the energy balance deficit (ΔEB) was determined for each of the three vegetation types: 8.74% for barley, 23.55% for sugar beet, and 12.68% for wheat. For the two EC towers at the Roccarespampani site (Ro1 and 2), the EB deficit is 34.31% for Ro1 and 34.76% for Ro2. At the Howland site, neglecting the soil heat flux term (G), the EB deficit is 24.42% for Ho1 and 18.61% for Ho2 whereas the EB deficit is 17.62% for Ho1 and 17.11% for Ho2 when the soil

Discussion

The results for the Merken, Roccarespampani, and Howland sites clearly indicate the differences between the two methods. The extended two-tower approach results in general in smaller (relative) random errors for LE and H compared to the classical two-tower approach, especially for larger net radiation and larger fluxes. In some cases, for small net radiation and small fluxes, the extended two-tower approach does not give smaller errors than the classical two-tower approach. This is related to

Conclusion

The random error of latent and sensible heat fluxes, measured by the eddy covariance method, can be determined with the classical two-tower method proposed by Hollinger and Richardson (2005). According to this method, the random error is estimated on the basis of the differences between simultaneous turbulent flux measurements made at two neighboring towers. However, this method does not consider any systematic differences in energy balance closure and energy partitioning between the two

Acknowledgements

This research is supported by the Helmholtz Climate Initiative REKLIM (Regional Climate Changes). We truly thank the University of Bonn and SFB/Transregio 32 for contributing to the Merken site dataset, CarboEurope, Riccardo Valentini and Dario Papale for providing EC data of the Roccarespampani site, and AmeriFlux, David Hollinger for providing EC data of the Howland site. A. Graf would like to thank the Deutsche Forschungsgemeinschaft (DFG) for funding through the project GR2687/3-1.

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