A field study was undertaken to investigate the accuracy of two
micrometeorological flux footprint models for calculating the gas emission
rate from a synthetic 10

Micrometeorological techniques such as eddy covariance and flux–gradient methods measure a vertical flux of gas in the atmosphere, which can be used to deduce the flux from an underlying surface area of interest. If the underlying surface is expansive and horizontally homogenous, the measured atmospheric flux and the surface flux can be considered equivalent (Dyer, 1963). However, if the area of interest has a limited spatial extent or is located some distance from the atmospheric measurement, the relationship between the two fluxes can be complex, as the measured flux may be capturing a dynamic mixture of surface fluxes from both inside and outside the area of interest. In these cases, flux footprint modelling can be used to quantify the relationship between the measured atmospheric flux and the surface flux from the area of interest.

The analytical flux footprint model of Kormann and Meixner (2001), hereafter referred to as the KM model, is widely used to evaluate and interpret flux measurements taken over spatially limited surface sources. The KM model relies on a simplified representation of atmospheric transport (Schmid, 2002) to create an easily computable footprint. It has been used to help quantify ammonia fluxes from fertilized plots (Spirig et al., 2010), interpret methane fluxes from heterogeneous peatland areas (Budishchev et al., 2014), and to reject periods where the footprint extends outside the source of interest (Stevens et al., 2012). Other footprint models use a more realistic treatment of atmospheric transport (e.g., Kljun et al., 2002; Sogachev and Lloyd, 2004). Using a state-of-the-art Lagrangian stochastic (LS) footprint model, Wilson (2015) found a clear separation between the footprints computed with the LS and KM models, depending on atmospheric stability and the distance from the measurement location. While more rigorous footprint models are clearly more defensible, the simpler KM model has the advantage of rapid analysis and the existence of software tools that make its application more accessible to non-specialists (Neftel et al., 2008).

This field study compares the accuracy of the KM footprint model with a more rigorous LS model. The motivation for this study was the question of whether the accuracy of the LS model was sufficiently better than the KM model so as to justify a more complex LS application. In this experiment we released gas at a known rate from a small synthetic area source and measured the vertical gas flux at a downwind location using the eddy covariance technique. The KM and LS models were then used to calculate the source emission rate from the measured atmospheric flux. The accuracy of those calculations is examined in this report. This follows the approach of Heidbach et al. (2017) and Coates et al. (2017) in their experimental evaluation of footprint models.

The experiment took place on an extensive, flat agricultural field at the
University of Alberta's Breton research farm, in Alberta, Canada
(

A synthetic source of carbon dioxide (CO

The vertical CO^{®} open-source software (version 6.2.1, LI-COR
Biosciences, Lincoln, NE, USA) to obtain 10 min average fluxes of
CO

Gas releases took place over 9 d, with the center of the synthetic
source positioned (Fig. 1) at one of three nominal distances from the EC
system (fetches of 15, 30, and 50 m). Placement of the source relative to
the EC system depended on the expected wind direction. Because CO

Map of the synthetic-source locations used in the study (polygons). The eddy covariance system was located at position (0,0).

Our study consisted of more than 300 flux measurement periods of 10 min each and
included periods of gas release, background flux measurements, and
transitions when gas was released but a steady-state plume may not have been
established over the field site (we assumed this occurred 10 min after gas
was turned on). There was a total of 125 valid gas release periods. From
this total we excluded 66 periods from our analysis based on two broad
factors:

19 periods were excluded for having wind conditions associated with
unreliability in the EC measurements or the dispersion model calculations, that is,
light winds with a friction velocity

47 periods were excluded when the EC measurement location was not obviously
in the source plume. This included periods when the measured CO

The KM model is based on an analytical solution to the steady-state
advection–diffusion equation, assuming simplified power-law profiles for
wind speed and eddy diffusivity and a crosswind diffusion component (Kormann
and Meixner, 2001). We used the ART Footprint Tool software (Spirig et al.,
2007) based on the KM model to calculate the synthetic-source emission rate
(

A state-of-the-art LS model was also used to calculate the emission rate
from the synthetic source (

The accuracies of the footprint calculations are evaluated from the ratio of
the model-calculated emission rate to the actual release rate:

The synthetic emission rates calculated with both footprint models
underestimate the actual emissions by roughly 30 % on average. The overall
means of the footprint calculations, expressed as the ratio of the model-calculated emission rate to the actual emission rate, are

When examining the footprint agreements as a function of fetch (Fig. 2), we
find both models are accurate at the shorter fetch of 15 m, as the means of

Agreement ratio of the footprint-model-calculated emission rate
(

In Fig. 3 we show the

Agreement ratio of the
footprint-model-calculated emission rate
(

There are no clear patterns in terms of explaining the differences between
the two footprint models based on environmental factors. Whether we separate
the data by fetch or by stability, the results from the two models are not
statistically different from each other. Wind speed, roughness length, and
wind direction (deviation from a line between the EC system and the source)
were also factors considered to explain the model differences, but again,
no pattern was observed. The lack of model differences was unexpected given
the studies of Göckede et al. (2005), Wilson (2015), and Heidbach et al. (2017) showing large differences in the calculations between analytical and
LS models. This suggests that in our study, any systematic differences
between the models were obscured by the substantial period-to-period
variability in the

From an end-user's perspective, our results show that both the KM and the LS model returned reasonably accurate flux footprint estimates on average, particularly for the shorter measurement fetches. Our dataset does not consistently discriminate between the performance of the two models, despite the theoretical advantages of the LS model. Based on the results of this study, we conclude that the easy-to-use KM model can provide accurate footprint calculations that are accessible to non-specialists. It is clear that the KM and LS footprint models give systematically different results (as shown in Wilson, 2015), but we were unable to (statistically) observe these differences given the large period-to-period variability in the calculations and the relatively small number of field observations. The small area of our synthetic source likely contributed to the large variability, and a larger source may have allowed better differentiation between the models. However, period-to-period variability is the nature of footprint calculations based on simplified models of atmospheric transport like the KM and LS formulations. These model calculations, which at best approximate an ensemble average realization of the atmosphere, will not reflect the period-to-period fluctuations of actual measurement periods.

The data used in this analysis are available in the Supplement or by request to trevor.coates@canada.ca.

The supplement related to this article is available online at:

TWC analyzed the field data and helped write the manuscript. MA design the experiment and coordinated and collected the field data. TKF helped with the experimental design and data analysis and reviewed the manuscript. GHR helped with the experimental design and reviewed the manuscript.

The contact author has declared that neither they nor their co-authors have any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The authors gratefully acknowledge funding from sources listed in the “Financial support” section below, as well as assistance from Dick Puurveen and Sheilah Nolan.

This research has been supported by the Canada Foundation for Innovation (John R. Evans Leaders Fund (grant no. 32860)), the Natural Sciences and Engineering Research Council of Canada (Discovery Grant (grant no. 2018-05717)), and Agriculture and Agri-Food Canada (Agricultural Greenhouse Gas Program 2 (grant no. AGGP2-004)).

This paper was edited by Christof Ammann and reviewed by Albrecht Neftel and Thomas Foken.