Sampling frequency affects estimates of annual nitrous oxide fluxes

Quantifying nitrous oxide (N2O) fluxes, a potent greenhouse gas, from soils is necessary to improve our knowledge of terrestrial N2O losses. Developing universal sampling frequencies for calculating annual N2O fluxes is difficult, as fluxes are renowned for their high temporal variability. We demonstrate daily sampling was largely required to achieve annual N2O fluxes within 10% of the ‘best’ estimate for 28 annual datasets collected from three continents—Australia, Europe and Asia. Decreasing the regularity of measurements either under- or overestimated annual N2O fluxes, with a maximum overestimation of 935%. Measurement frequency was lowered using a sampling strategy based on environmental factors known to affect temporal variability, but still required sampling more than once a week. Consequently, uncertainty in current global terrestrial N2O budgets associated with the upscaling of field-based datasets can be decreased significantly using adequate sampling frequencies.

Furthermore manual chambers are simple to use, relatively inexpensive, and can be deployed in small experimental plots so the effect of multiple treatments on soil N 2 O fluxes can be investigated simultaneously 6 . Temporal coverage is typically limited to weekly, bi-weekly or monthly measurements when using manual chambers 9 . However, manual chambers are likely to underestimate annual N 2 O fluxes if the frequency of measurements does not adequately characterize N 2 O emissions during the year, in particular peak emissions following N fertilizer applications, irrigation, soil re-wetting or spring-thaw events, which may contribute up to 70% of the total annual flux [10][11][12] .
Guidelines for sampling frequency to estimate annual N 2 O fluxes using manual chambers are not well defined for all land-uses and environments. Instead the approach often taken comes down to an "educated guess" and resource availability 13 . A number of studies have investigated the influence of sampling frequency on cumulative N 2 O fluxes, however with the exception of Liu et al. 14 these studies have mainly used short-term N 2 O flux data sets (< 1 year), and have been confined to a single study site in an agricultural setting 9,15-18 . These short-term studies have demonstrated that high frequency measurements should coincide with management practices likely to increase N 2 O fluxes, with less frequent measurements during the intervening periods. Yet, the effect of sampling frequency on annual N 2 O flux estimates requires investigation across a broader range of land-uses and climates.
The introduction of automated chambers has enabled researchers to better characterize temporal variation in N 2 O fluxes 6 . Although this technology is expensive and not available to all researchers, it does provide a unique opportunity to better assess how sampling frequency affects estimates of annual N 2 O fluxes. Such an analysis is particularly beneficial to those new to measuring in situ N 2 O fluxes from land and to those planning to investigate a previously unstudied land-use. Consequently, the objective of the following study was to investigate the effect of sampling frequency on estimates of annual soil N 2 O fluxes using 28 published datasets of subdaily N 2 O fluxes from a variety of different terrestrial ecosystems across the globe.

Results
Annual N 2 O fluxes calculated from the average daily fluxes, which is used here as the reference annual flux, varied from 0.03 kg N 2 O-N ha −1 yr −1 to 8.1 kg N 2 O-N ha −1 yr −1 ( Table 1). The smallest annual flux was recorded for a sandy soil cropped to a grain legume in a semiarid environment 11 , while the greatest was from a loam soil cropped to tree fruit in a subtropical climate 19 . Daily N 2 O fluxes were highly variable within each dataset, but more so for some; the coefficient of variation (CV) of the mean daily N 2 O flux ranged from 78% for a subtropical rainforest to 913% for a semiarid soil planted to a grain legume. The variation in daily means was not related to the magnitude of the annual N 2 O flux (Table 1), but instead reflected the episodic nature of the daily fluxes for a particular study site (Fig. 1). We subsequently classified the data sets as having either moderate (CV > 50-100%), high (CV > 100-200%) or extreme (CV > 200%) 'episodicity' based on the CV of the mean daily flux (Table 2).
Increasing the interval between sampling days increased the variance in the estimated annual N 2 O fluxes, and hence decreased the accuracy of the estimate (Fig. 1). As the sampling frequency decreased, the deviation from the 'best estimate' , or expected value obtained using all daily fluxes, increased and caused annual losses to be either over-or underestimated ( Fig. 2; Supplementary Table 1). Across all sites and sampling frequencies (n = 1568), 22% and 58% of annual emission values were more than 10% higher or lower, respectively, than the 'best estimate' annual flux. The extent that decreased sampling frequency increased the deviation from the reference annual N 2 O flux appeared to be largely related to the variability, or coefficient of variation, of the daily fluxes (Fig. 3). The greater the variation in daily N 2 O within a dataset, the greater the impact of decreasing the sampling frequency had on the accuracy of the estimated annual flux. For example, for a tropical rainforest (Bellenden Kerr) with a daily N 2 O flux CV of 98%, sampling every 28 days resulted in an annual N 2 O flux that was up to 1.2 times greater than the best estimate; whereas for cropped soil in a semiarid region with a daily N 2 O flux CV of 913%, sampling every 28 days resulted in an annual N 2 O flux that was up to 12 times greater than the best estimate ( Fig. 1; Supplementary Table 1).
The minimum sampling frequency required to robustly estimate an annual N 2 O flux varied depending upon the 'episodicity' of the dataset and the required accuracy ( Fig. 2; Table 2; Supplementary Table 1). Twenty, or 74%, of the datasets required daily sampling to achieve an annual N 2 O flux value within 10% of the best estimate (Fig. 4). In only one case (tropical rainforest, Bellenden Ker), and when the daily N 2 O flux CV was relatively low (98%), did weekly sampling result in annual N 2 O flux within 10% of the best estimate. Generally speaking, highly or extremely episodic data sets (CV > 100%) required sampling either daily or 3 days a week ( Table 2). Lowering the desired accuracy decreased the required frequency of sampling, however 89% of the data sets still needed to be sampled at least weekly to achieve ± 30% accuracy (Fig. 4). Lowering the level of accuracy to ± 40% meant two datasets could be sampled once every 4 weeks (Fig. 4).

Discussion
Nitrous oxide emissions need to be measured daily to accurately determine annual N 2 O flux in environments where data has not previously been collated. Measuring N 2 O fluxes on a daily basis ensured that annual N 2 O fluxes were estimated within 10% of the expected value for all datasets in the present study. Although a similar result could be achieved in some instances (25%, or 7 datasets) by sampling 3 days a week, this still represents a highly regularly sampling regime. Our findings are consistent with others who have investigated the effects of sampling frequency on estimates of annual N 2 O fluxes. For example, a relatively frequent sampling regime (once every 2 to 3 days) was required to estimate cumulative losses within 10% of the expected cumulative loss from N-fertilized crops in China and the United States of America 9,14 . Our findings further confirm the importance of deploying automated chamber systems when determining annual N 2 O fluxes in previously unstudied environments, and when the drivers of temporal variability are not well understood.
The frequency of sampling required to accurately calculate an annual N 2 O flux will depend on the episodic nature of the N 2 O flux at the study site of interest, rather than the magnitude of the annual flux. This was particularly well demonstrated by studies conducted in semiarid environments of Australia and Inner Mongolia, where relatively low annual N 2 O losses ( ≤ 0.21 kg N 2 O-N ha −1 yr −1 ) resulted from a limited number of elevated daily N 2 O fluxes during the year 11,12 . For example in a cropped soil in south-western Australia, 75 to 85% of the annual fluxes were attributed to isolated, short-lived summer rainfall events 11 . Understanding the underlying temporal variability of daily N 2 O fluxes is therefore likely to improve the efficacy of sampling regimes.
Sampling efficacy for determining annual N 2 O fluxes may be improved, and the regularity of sampling decreased, if N 2 O flux responses can be anticipated. This may occur if previous research has been conducted in a similar environment, or if preliminary work is undertaken to assess the temporal variability of N 2 O fluxes. In either case, refining the sampling regime will require some underlying understanding of temporal variation in the N 2 O flux and its regulation. Using this approach, we estimated annual N 2 O fluxes for three of our datasets (Fig. 1) based on the authors' informed understanding of the factors driving daily losses. While we found the annual N 2 O fluxes estimated by the authors' did not vary statistically from the 'best' estimate calculated using all daily fluxes, the informed sampling approach still required sampling to occur every 2 to 6 days depending on the dataset ( Barton et al. 10 Li et al. 26 Barton et al. 27 Barton et al. 28 Xilin  18 , and rainfed cereal crops in subtropical Australia 17 ; agricultural land use not captured in the present study. Interestingly, some of these authors recommended weekly sampling (with a higher frequency following anticipated N 2 O events), which is less frequent than our analysis would recommend for agricultural and non-agricultural study sites in the present study. The uncertainty of current global N 2 O estimates maybe partly attributed to the sampling frequency of the datasets selected for inclusion in the analysis. Modelling of global soil N 2 O emissions has been largely derived from manual chambers measurements covering more than 300 days in a year 20 . However, less than a third of the 464 studies included in the metadata analysis by Stehfest and Bouwman 20 measured N 2 O on at least a daily basis, with 50% of the data used collected 3 days a week, or less than weekly. Given the influence of sampling frequency on annual N 2 O fluxes in the present paper, it is likely that current global N 2 O values have not been accurately captured. Instead, we recommend that revision of global estimates using high frequency measurements (at least daily) or an 'informed' sampling approach for at least a year.  Table 4  Finally, we recommend data from automated chambers should be continuously used to build on existing guidelines for use of manual chambers 21 . While the present study included and discussed a large number of datasets from a variety of climates, soils and land uses, there were a number of environments not represented. For example, grazed soils outside temperate climate, a broader range of horticultural soils, and non-agricultural soils in semiarid environments. We therefore encourage researchers utilizing automated chamber systems to determine annual N 2 O fluxes from soils, to in turn also utilize the data to investigate the impacts of sampling frequency on these losses.

Methods
Study sites. The meta-analysis included datasets from published research studies, and where N 2 O fluxes had been measured on a subdaily basis for approximately one year using automated chambers. Annual data sets were sourced from measurements in Australia, Germany, and Inner Mongolia, representing a variety of climates, soil types and land uses (Table 1). Climates ranged from semiarid (including a Mediterranean-type climate) to tropical, soil textures varied from sands to heavy clays, while land use included various agricultural production and forest systems. A number of study sites also included different treatments (Table 1). Consequently our meta-analysis included 28 sub-daily N 2 O datasets.
Automated chamber system. Nitrous oxide fluxes were measured at each study location using soil chambers connected to a fully automated system that enabled in situ determination of N 2 O fluxes.  Table 2. The relationship between the 'episodicity' of each study location and the minimum sampling frequency needed to meet a given accuracy. † Episodicity determined using coefficient of the mean daily flux (Table 1) Table 4) was compared to the 'best estimate' flux calculated from the average daily fluxes (expressed as a %). The 'best estimate' was calculated using all daily fluxes. For each sampling frequency, the datasets are presented in the same order (from left to right in the above Figure) as that listed in Supplementary   Figure), the range in deviation was determined after comparing the annual N 2 O fluxes calculated from a sample interval of 4-weekly (every 28 days) with the 'best estimate' for each permutation (    Details of the design and operation of the automated gas sampling systems have been described by Breuer et al. 22 and Kiese et al. 23 . Briefly, the various systems consisted of a gas chromatograph (e.g., Texas Instruments, SRI 8610C) equipped with an electron capture detector (ECD) for N 2 O analysis, an automated sampling unit for collecting and distributing gas samples, and a series of chambers (three to five replicates depending on the study site). Chambers (0.5 m × 0.5 m or 0.7 m × 0.7 m) were placed on metal bases inserted into the ground (0.05-0.1 m), and fitted with a top (0.15 m or 0.3 m in height) that could be automatically opened and closed by means of pneumatic actuators. The height of the chambers was progressively increased to accommodate crop growth at some study sites, with a maximum height of 0.95 m. Furthermore, in some instances the chambers were programmed to open if the air temperature in the chamber exceeded a set value, or if rain fell while the chambers were closed. The automated gas sampling unit enabled N 2 O to be monitored continuously, providing up to eight (hourly) emission rates per day. Specific N 2 O measurement details for each study site are described in the associated published papers (Table 1).
Evaluating sample frequency effects. The effect of sampling frequency on estimates of annual N 2 O-N fluxes was assessed using a modified jackknife technique 24,25 . Average daily flux measurements were calculated for each replicate chamber in each dataset from the sub-daily flux measurements as we did not consistently observe diurnal flux variations at each location. Each site's daily flux population was subsequently subsampled daily, three times per week, weekly, bi-weekly and 4-weekly, and for each permutation of the time interval, for each dataset (Table 4). There were 7 to 28 jackknifed populations depending on the sampling frequency ( Table 4). Estimates of annual N 2 O-N flux for a given chamber, site and frequency permutation were then calculated by linear interpolation and integration of daily fluxes with time. Missing daily N 2 O flux data was not replaced. The average annual flux estimate (calculated from replicate chambers) from each sampling frequency, and for each of the dataset, was then compared to the 'best estimate' annual flux calculated from the average daily fluxes (expressed as a %) so as to assess the accuracy of each of the sampling frequencies. An annual flux determined using an informed sampling regime (based on the authors' understanding of the factors driving daily N 2 O fluxes) was also compared with the 'best estimate' annual flux using a general analysis of variance (Genstat for Windows, 14 th Edition, VSN International).