The experiment was conducted on a pasture at the Agroscope research farm near Posieux on the western Swiss Plateau (46∘46′04′′ N, 7∘06′28′′ E). The pasture vegetation consists of a grass–clover mixture (mainly Lolium perenne and Trifolium repens) and the soil is classified as stagnic Anthrosol with a loam texture. The vegetation growth was retarded at the beginning of the grazing season due to the colder spring and the wetter conditions during April and May compared to long-term averages. The dry summer (June and July) also led to a shortage of fodder in the study field. Therefore additional neighboring pasture areas were needed to feed the animals.

The staff and facilities at the research farm provided the herd management and automated individual measurements of milk yield and body weight at each milking. Milk was sampled individually 1 day per week and analyzed for its main components. Monthly energy-corrected milk (ECM) yield of the cows was calculated from daily milk yield and the contents of fat, protein, and lactose (Arrigo et al., 1999). Monthly ECM yield decreased over the first 3 months but overall it was fairly constant in time with a mean value of 22.7 kg and a standard deviation (SD) of 5.5 kg. The average live weight of 640 kg (SD 70 kg) slightly increased by around 6 % over the grazing season.

The field (3.6 ha) was divided into six equal paddocks (PAD1 to PAD6) of 0.6 ha each (Fig. 1). The arrangement of the paddocks was chosen to create cases with the herd confined at differing distances to the EC tower. Two main distance classes are used in the following: near cows denotes cases with animals in PAD2 or PAD5, far cows denotes cases with animals in one of the other four paddocks. The present study covers one full grazing season 9 April–4 November 2013. Twenty dairy cows were managed in a rotational grazing system during day and night. Depending on initial herbage height the cows typically grazed for 1 to 2 days on a paddock. The herd consisted of Holstein and Red Holstein × Simmental crossbred dairy cows and was managed with the objective to keep the productivity of the herd relatively constant in time. The cows left the pasture twice a day for milking in the barn where they were also provided with concentrate supplement (usually < 10 % of total diet dry matter) according to their milk production level. The cows left the paddock around 04:00 and 15:00 LT each day but the exact times varied slightly depending on workload in the barn and air temperature. If there was a risk of frost, the cows stayed in the barn overnight (58 nights), and if the daytime air temperature exceeded about 28 ∘C before noon, the cows were moved into the barn for shade (19 days). Waterlogged soil condition entirely prohibited grazing on the pasture between 12 and 13 April. In total the cows were grazing on the study field for 198 half-days and for another 157 half-days on nearby pastures not measured by the EC tower.

The management of the neighboring fields is also indicated in Fig. 1. The pastures in the southwest are the additionally used areas due to fodder shortage of the experimental site (see above) and were only used with cows participating in the experiment. The feeding behavior of each cow was monitored by RumiWatch (Itin + Hoch GmbH, Switzerland) halters with a noseband sensor. From the pressure signal time series induced by the jaw movement of the cow (Zehner et al., 2012) the relative duration of three activity classes (eating, ruminating, and idling) was determined using the converter software V0.7.3.2.

To assess the reliability of EC flux measurements of CH4 emissions by cows on the pasture, the measured fluxes (FEC) had to be converted to average cow emissions (E) per animal and time. This was done using three different information levels about animal position and distribution on the pasture:

GPS method: use of time-resolved position for each animal from GPS cow sensors (this section),

To assess the effect of the precision of cow position information on the determination of the average cow emission, an option with less detailed but easier to obtain position information was also applied and compared to the GPS approach. In the PAD method, no individual cow position information is used, but it is assumed that the animal CH4 source is evenly distributed over the occupied paddock area. For this approach, an accurate paddock stocking time schedule is needed.

EC measurements are frequently performed over pastures, but usually no detailed information on the position and exact number of animals and specific occupation times are available. If at least the average stocking rate over the grazing period is available and under the assumption that the cows are uniformly distributed over the entire pasture, the time-averaged cow emissions can be calculated as 〈Ecow〉=〈FEC〉-〈Fsoil〉⋅Afield⋅1〈ncow〉, with 〈FEC〉 denoting the mean observed CH4 flux of the grazing period, Afield the total pasture area, and 〈ncow〉 the mean number of cows on the study field over the grazing season. 〈ncow〉=6.6 heads is calculated as the total number of cows of each 30 min interval with cows on the study field plus one-half of the number of cows when the cows were moved between barn and pasture divided by the total number of 30 min intervals of the grazing period. For comparability reasons, the same Fsoil results (selected based on GPS data) were used for all three methods. It should be noted that an appropriate determination of the soil flux may be difficult without any cow position information.

Observed 30 min CH4 fluxes varied between -150 and 2801 nmol m-2 s-1 during the grazing season. Cases with cows close to the sensor revealed strong fluxes (Fig. 5b and c). For cases with no cows in the FP (Fig. 5a) or with cows further away, measured fluxes were very small. For the cow emission calculations with FP consideration, fluxes were divided into cases with near cows (Fig. 5 white paddocks) and far cows (Fig. 5 gray paddocks).

For a systematic assessment of the relationship between CH4 flux and cow position and for the separation of cases representing pure soil fluxes, all quality selected fluxes were plotted against φ‾herd in Fig. 6. It shows a clear relationship with a strong increase of fluxes only in the highest φ‾herd range. Cases with near cows led to generally higher FP weights and fluxes than for the far cows cases. Based on Fig. 6, a threshold of 2 × 10-4 head m-2 (φcrit, herd) was determined as the lower cut off for cow-affected fluxes to be used for the calculation of Ecow. Cases with φ‾herd below φcrit, soil=2 × 10-6 head m-2 were classified as soil fluxes. The exclusion of cases with φ‾herd between the two critical limits ensured that fluxes with potential influence by the cows grazing on the neighboring pasture were removed.

The soil flux values were found to be generally small but mostly positive in sign (typically in the range 0 to 15 nmol m-2 s-1 Fig. 6), indicating continuous small emissions by the soil and surface processes. The accuracy of these fluxes was difficult to quantify because they mostly had no well-defined peak in the covariance function and thus 92 % had to be calculated at the fixed lag. Even though temporal variations in median diurnal and seasonal cycles were observed (in the range of 1 to 7 nmol m-2 s-1), it was unclear whether these can be attributed to effects of environmental drivers or they result from non-ideal statistics and selection procedures. Also, varying small contributions from cows on neighboring upwind fields could not be excluded. Therefore we used a conservative overall average estimate for the soil flux of 4 ± 3 nmol m-2 s-1 with the uncertainty range of ±50 % covering the temporal variation of medians indicated above.

Fluxes used for cow emission calculations were less than 3 % of the total number of 30 min intervals (Table 1). In average years, 3.6 ha of pasture is approximately sufficient to feed 20 dairy cows by rotational grazing during the early season. The cold and wet spring in 2013 negatively influenced the productivity of the pasture. Therefore, additional pasture time, more than expected, outside the study field was needed to feed the animals. These neighboring pastures were used for 44 % of the time but contributed typically less than 5 % to the EC footprint, which was too low for a sufficient cow emission signal. Hence the data coverage for measuring cow emissions was lower than expected. The selection of acceptable wind directions and the limited probability that the wind came from the direction where the cows were actually present further reduced the number of cases selected as cow fluxes. Cow emissions with sufficient FP contribution mostly induced well-defined peaks in the cross-covariance function (Fig. 3) and were well above the flux detection limit (similar to that found by Detto et al., 2011). Even when the cows were present in the far paddocks, 94 % of the fluxes already filtered by the other quality criteria were determined at dynamic lag times. This shows that further quality filtering with a stationarity test was not needed.

Individual soil exchange fluxes were mostly below the 3σ detection limit of 20 nmol m-2 s-1 and more than 92 % were determined at the fixed lag time. Detto et al. (2011) reported a detection limit of ±3.78 nmol m-2 s-1 for a similar setup. The higher detection limit in this study has to be attributed to a different setup but also to the stronger polluted region with various agricultural CH4 sources (farm facilities). The uncertainty of the soil flux was of minor importance for the calculations of the cow emissions (Eqs. 4, 6 and 7) because the selected cow fluxes with significant FP contribution were about 2 orders of magnitude higher than Fsoil= 4 ± 3 nmol m-2 s-1 (Fig. 6). Soil fluxes observed here are of similar magnitude to fluxes measured in other studies: CH4 fluxes in the order of 0 to 10 nmol m-2 s-1 are reported from a drained and grazed peatland pasture (Baldocchi et al., 2012), fluxes around zero seldom larger than 25 nmol m-2 s-1 for a grassland in Switzerland after renovation (Merbold et al., 2014), and fluxes between -1.3 and 9.6 nmol m-2 s-1 from a sheep grazed grassland measured by chambers (Dengel et al., 2011).

Methane fluxes from pasture always include fluxes from animal droppings (dung and urine). Therefore the soil fluxes referred to here are the combination of fluxes from the soil microbial community and fluxes from dung/urine which normally dominate the pure soil fluxes (Flessa et al., 1996). Emissions from cattle dung were estimated to be 0.778 g CH4 head-1 d-1 (Flessa et al., 1996) and from Finnish dairy cows to 470 g CH4 ha-1 over a 110 day grazing period (Maljanen et al., 2012). The soil flux in the present study (16 g ha-1 d-1) is around 3 times higher than the corresponding flux calculated with the literature numbers (Flessa et al. (1996): 5 g ha-1 d-1 and Maljanen et al. (2013): 4.3 g ha-1 d-1). Hence, the soil in the present study was a source of CH4. Factors which may explain differences in the present study and the literature are different animal breeds/types, soil and vegetation types, and soil and weather conditions. Additionally, the rotational grazing led to measurements of mixed fluxes from old and new dung patches.

In the GPS and PAD method, cow emissions were derived from the measured fluxes (corrected for soil exchange) with the help of the KM01 footprint model (Eqs. 4 and 6). Although it can be assumed that the cows emitted the same amount of CH4 whether they grazed in the far or near paddocks, a systematic effect of their distance from the EC tower was found (see near cows vs. far cows results in Table 2). The accuracy of the emissions depends on the accuracy of the flux measurement and on the accuracy of the FP model. The FP weight gets smaller and thus its relative accuracy decreases further away from the EC tower. This led to larger systematic uncertainties for calculations in the far cows cases compared to the near cows cases.

One potential error source in the FP calculation could be the choice of z0. The observed course of z0 over the year (Fig. 7) coincides with the herbage productivity during the season and corresponds to around 1/10 of the grass height. The presence of the cows (in near cows paddocks) only slightly increased z0 but the values remained in the expected range of 8 mm to 6 cm for short to long grass terrains (Wieringa, 1993). For occasional large obstacles (separated by at least 20 times the obstacle height) a value of 10 cm and larger is expected instead (WMO, 2008). Cows were moving obstacles in the FP, which obviously damped the enhancement of z0. For the FP calculation, we therefore generally limited z0 to a certain range around the mean seasonal course. For the majority of the cases, individually calculated z0 values lay within this range, but in a minor fraction (18 %) of the cases with cows, they exceeded the range (see Fig. 7) and were truncated to the upper range limit. We tested the effect of a doubling of the parameterized z0, as observed for the cow effect in Fig. 8, on ΦPAD for the near cows cases and found a moderate increase of around 17 % which would lower the calculated cow emissions proportionally. Because the truncation effect was small and only applied to few cases, we consider the uncertainty in z0 as not important for our cow emission results. In particular, it cannot explain the observed mean difference between near cows and far cows cases.

We chose the KM01 footprint model because the model uses an analytical solution and the calculation is fast compared to numerical particle models (e.g., backward Lagrangian stochastic models; bLS), which describe turbulence structure in a more complex way. Kljun et al. (2003) compared the KM01 model to a bLS model and found in general good agreements. However, the KM01 model underestimates the FP weight compared to the bLS model around the maximum of the FP function φmax and overestimates the FP weight further downwind (see figures in Kljun et al., 2003). Integration over larger parts of the FP extension may balance this over-/underestimation. In the present study, the position of φmax typically laid within 30 m of the EC tower (in PAD2 or PAD5). Thus for the near cows cases with animals typically within 60 m distance, such a balancing effect can be assumed. For the far cows cases, the KM01 model generally tends to overestimate the FP weights and thus the resulting emissions were underestimated on average. According to Kljun et al. (2003), the KM01 model also underestimates the FP weights in the direct vicinity of the EC tower (few meters). A detailed analysis of the cow positions (data not shown) revealed that in 68 % of the near cows cases, animals were present in distances < 2/3 φmax from the tower. But in less than 5 % of the cases, more than a tenth of the 30 min was affected. Hence the influence on the φ‾herd was generally small.

The analytical model solution by KM01 was developed for ground-level sources. However, while the cow's mouth and nose (respiration source) are close to the surface during grazing, they may be elevated up to ∼ 1 m during other activities. Unfortunately, this effect could not be evaluated with the KM01 model. However, very recently McGinn et al. (2015) investigated the effect of elevated cow emissions for a micrometeorological flux method that also uses turbulent dispersion modeling. They found no significant difference in their results between simulations with sources at the surface and at 0.5 m height. It needs to be investigated in the future whether or not this finding is also valid for the EC flux footprint weight.

While measured methane EC fluxes depend on site and environmental conditions and are therefore not directly comparable to other studies, this is much more feasible for the average cow emissions derived by the GPS method and the two alternative methods (PAD and FIELD) described in Sect. 2.3–2.5. It can be assumed that dairy cows of similar breed and weight and with comparable productivity (milk yield) have a similar gross energy consumption and CH4 emission. We therefore collected literature results from Swiss respiration chamber studies selected for a mean milk yield in the range of 20 to 25 kg d-1 around the mean milk yield of the present study (22.7 kg d-1). Most of those studies aimed to find diets that reduce CH4 emissions based on different forage types and supplements. Cow diets therefore varied among all studies but always fulfilled animal nutrient requirements. One value from van Dorland et al. (2006) which showed very low CH4 emissions due to special diet supplements was excluded from Table 3. Mean body weight of cows in the present study (640 kg) was in the upper range of body weight in the selected chamber measurements.

The mean CH4 emission over all selected studies of 404 g CH4 head-1 d-1 agrees very well with emissions measured by EC for the near cows cases of 423 g CH4 head-1 d-1 (difference of only 5 %, within uncertainty range, see Table 2). The deviation for the PAD near cows results is about twice as large. The far cows results for GPS and PAD methods show even larger but negative deviations from the literature mean. The result of the FIELD method applied to the entire grazing period also shows a good agreement but we consider that as rather coincidental because the estimated uncertainty of monthly values as well as the deviation of their mean and median is much larger.

Based on the FP uncertainty considerations in Sect. 4.2 and the agreement with the recent literature values, we consider the GPS near cows results as the most reliable in this study. They were derived from only large fluxes with relatively low uncertainty. Therefore, the following discussion focusses on the GPS near cows results and uses them as reference for the comparison with the other results.

Our result show only a moderate diel cycle (Fig. 10a) with highest emissions in the evening and lowest before noon (hourly means ± 30 % around overall mean). Although the timing of maximum emissions coincides with maximum grazing activity, the general diel variation cannot be explained satisfactorily by the observed cow activities (Fig. 10b). On the other hand, the emission pattern shows some correlation to the stability conditions, which were also subject to a distinct diel cycle (predominantly unstable conditions from daybreak until early evening and stable conditions during evening and night). Therefore the methodology-induced effect of stability (e.g., via FP calculation) on the observed diel emission cycle cannot be fully excluded.

Increasing emission fluxes during daytime hours were also found over a sheep pasture by Dengel et al. (2011). But their nighttime fluxes were much smaller (close to zero) compared to daytime. Laubach et al. (2013) observed maximum CH4 emissions within 2 h after maximum feeding activity of cattle. Those cattle were fed before noon with imported fodder (all animals fed at the same time), whereas the cows in the present study themselves determined their grazing activity time throughout the day. Obviously, this is reflected in the less pronounced diel cycle.

To assess and interpret potential systematic effects of variations in cow performance (among animals in the herd and with time over the grazing season) we used published emission models based on observed productivity parameters (see Ellis et al., 2010). Figure 11 compares the results of two models (Corré, 2002; Kirchgessner et al., 1995) estimating cow emissions from recorded milk yield and body weight with results of this study. Although milk yield showed a general decrease over the first 3 months and a considerable variability within the herd, the effect on CH4 emissions according to the models was relatively small. The observed monthly emissions showed a larger variability which cannot be explained by the variability of cow performance.

Although the mean emissions observed in this study agree well with literature values the variation of the individual 30 min emissions is large (relative SD of 41 % for GPS near cows, see Table 2). It is a combination of various effects with major contributions of the discussed diel variation, the stochastic uncertainty (short-term variability) of turbulence, and the changing source distribution (various numbers of cows in the FP and moving). Very similar relative variability of 30 min fluxes was reported in a study using the micrometeorological bLS method (Laubach et al., 2014). Similar to Laubach et al., the large scatter of our individual emission values showed a fairly random-like (normal) distribution (Fig. 12) with only a minor deviation between mean and median. This distribution is clearly more symmetric than the corresponding distribution of cow FP weights (Fig. 9a). Based on this behavior, the estimated uncertainty range of the overall mean cow emissions calculated according to Gaussian error propagation rules is considered as representative.

In an intensive rotational grazing system, the cows are expected to effectively graze the entire paddock area. On shorter timescales of 30 min (Fig. 5) this assumption is often not fulfilled. For a grazing rotation phase of 2 days, the example in Fig. 13a shows that the cows indeed visited the entire paddock, but their position distribution was not uniform with higher densities in the central part of the paddock. Even over the entire grazing season, some inhomogeneity in the cow density distribution persisted (Fig. 13b). Despite this inhomogeneity, the mean emission calculated with the PAD method (implicitly assuming homogeneous cow distribution within the paddock) was comparable to the emission based on GPS data (Table 2), yet with a larger uncertainty range. Thus the hypothesis that more detailed information leads to better results was not clearly verified in this case. Apparently the limited size and the geometric arrangement of the paddocks in relation to typical extension of the FP area in the main wind sectors limited the value of the more detailed GPS information.

The PAD method uses a similar level of cow position information as other micrometeorological experiments applying the bLS approach (Laubach et al., 2008, 2013; Laubach and Kelliher, 2005; McGinn et al., 2011). The bLS models use the geometry of the paddock area and perform a concentration FP calculation (instead of the flux FP used here). The size of the paddock in those experiments (0.1 to 2 ha) was of the same order of magnitude as the paddock size in this study. Although the density of grazing animals in Laubach et al. (2013) was 5 times higher than the average density of 33 heads ha-1 in this study, they reported systematic effects of uneven cow distribution within the paddock on derived mean cow emissions, which was associated to the location where the fodder was available. They found a discrepancy of up to +68 % between their reference SF6 technique and the bLS model using concentration profile measurements at a single mast. The bLS experiments with line-averaging concentration measurements yielded generally better results because they are less sensitive to the source distribution. The corresponding uncertainties were similar to uncertainties found in this study.

Although some inhomogeneity of the animal density was found within the paddocks, the rotational grazing system prevented major differences among them in the long term (Fig. 13b). This may not be the case for a free range grazing system without subdivision of the field into paddocks, like e.g., in the study by Dengel et al. (2011). In such a case, a larger-scale inhomogeneity may develop leading to a systematic under- or overrepresentation of the animals in the flux FP (in the main wind sectors), and the FIELD method without cow position information would yield biased results. As an alternative to the use of GPS sensors on individual animals, their position could be monitored by the use of digital cameras and animal detection software (Baldocchi et al., 2012).

The problem discussed so far for CH4 also exists for the investigation of CO2 flux measurements at pasture sites because of the considerable contribution of animal respiration to the net ecosystem exchange. If joint CO2 and CH4 fluxes are available at the site, CH4 can be used as a tracer for ruminant-induced CO2 fluxes by using typical CH4 / CO2 ratios of exhaled air found in respiration chamber measurements.