Estimating Net Carbon and Greenhouse Gas Balances of Potato and Pea Crops on a Conventional Farm in Western Canada

Quantifying the emissions of the three main biogenic greenhouse gases (GHGs), carbon dioxide (CO2), nitrous oxide (N2O) and methane (CH4), from agroecosystems is crucial. In this study continuous measurements of N2O, and CH4 emissions from potato and pea crops in southwest British Columbia, Canada were made using the eddy‐covariance (EC) technique. Flux footprint analysis, coupled with EC and manual nonsteady state chamber measurements, was used to address the spatial heterogeneity resulting from the field edge at the study site. Flux footprint corrections had a larger effect on N2O fluxes than CO2 fluxes because of a more pronounced difference in N2O fluxes between the crop and edge areas. After flux footprint corrections, the potato and pea crops were both weak CO2 sinks with annual net ecosystem exchange values of −57 ± 9 and −97 ± 16 g C m−2 yr−1, respectively. However, after taking carbon (C) export via crop harvest and C import via seeding into account, the potato crop shifted to being a moderate C source of 284 ± 55 g C m−2 yr−1, while the pea crop became near C neutral, sequestering only 30 ± 26 g C m−2 yr−1. Annual GHG balances, quantified by converting N2O and CH4 to CO2 equivalents as pulse emissions using respective global warming potentials on a 100‐year timescale, were 417 ± 88 and 152 ± 106 g CO2e m−2 yr−1 for the potato and pea crops, respectively, with N2O contributing the largest proportion to annual total GHG balances and outweighing the CO2 uptake from the atmosphere.


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Thus, quantification of the three main biogenic GHGs, carbon dioxide (CO 2 ), nitrous oxide (N 2 O), and methane (CH 4 ), from agroecosystems is crucial in providing knowledge for climate-change related policy making (Maier et al., 2022).
In 2020, Canadian agricultural sector accounted for 8.2% of total national GHG emissions releasing 55 Mt CO 2 eq to the atmosphere, with a large proportion of the emissions (∼40%) resulting from agricultural soils, and 75% of national N 2 O emissions (Environment and Climate Change Canada, 2022). One of the main drivers of these emissions, based on inventory data, is the application of inorganic nitrogen fertilizers to agricultural soils in the Prairie Provinces (Environment and Climate Change Canada, 2022). In May 2015, Canada announced its intentions to reduce GHG emissions by 30% below 2005 levels by 2030 confirming its commitments in its Nationally Determined Contribution (NDC) to the Paris Agreement. This resulted in a considerable research directed toward mitigating GHG emissions generated by agricultural systems, but these studies have been largely limited to Ontario (Wagner-Riddle et al., 2007) and the Canadian Prairies including the provinces of Manitoba, Saskatchewan, and Alberta (Asgedom & Kebreab, 2011;Liebig et al., 2005;Rochette et al., 2018). Such efforts are greatly needed in other parts of Canada to allow the development of strategies to mitigate GHG emissions, while developing climate-change related policies.
In British Columbia (BC), GHG emissions in forage grass and silage corn fields have been monitored periodically using manual chambers (e.g., Bhandral et al., 2009;Bittman & Hunt, 2015;D. E. Hunt et al., 2016), and, recently, in a highbush blueberry (Vacinium corymbosum L.) field year-round with automated chambers (Shabtai Bittman, personal communication). Yet, field-scale, continuous, year-round measurements, needed to reliably quantify annual emissions from local high-value cropping systems, have been lacking.
The fertile soils in the Lower Fraser Valley (LFV) in BC allow for intensive arable cropping such as field vegetables and berries. Potatoes (Solanum tuberosum L.), as one of the main crops in the LFV, account for about 50% of BC's total area in potato production (British Columbia Agriculture & Food Climate Action Initiative, 2013), while peas (Pisum sativum L.) account for 7.8% of the total area of vegetables grown for harvest in BC (Statistics Canada, 2016) and are often planted following a potato crop in a typical crop rotation. Even though potatoes and peas are important crops in BC, no continuous measurements of GHG fluxes are available for those two crops in this region.
The eddy-covariance (EC) technique, an effective and widely-used micrometeorological technique, is used to determine half-hourly GHG fluxes at the landscape scale by measuring high-frequency fluctuations of vertical wind velocity and GHG concentrations above the field (Baldocchi, 2014). While the requirements of homogeneous surfaces and stationary conditions need to be met to conduct EC flux measurements, it must be recognized that some degree of spatial variability and inhomogeneity are inevitable over vegetated surfaces in most cases (Levy et al., 2020;Molodovskaya et al., 2011;Nagy et al., 2006). In such situations, flux chambers, as an important supplementary technique, can be used to determine localized soil GHG emissions from each contributing landscape component and to verify EC-integrated fluxes (Famulari et al., 2010;Schrier-Uijl et al., 2010;Waldo et al., 2019). Flux footprint (upwind source area contributing to the EC flux measurement) models have been used to compare GHG fluxes measured by point-scale chamber and landscape-scale EC systems when upscaling chamber fluxes (Christensen et al., 1996;Levy et al., 2020;Molodovskaya et al., 2011;Schrier-Uijl et al., 2010). Additionally, flux footprint models can be employed to make corrections for the field edge effect and estimate surface flux of each landscape component of the source area (Schmid, 1994).
In this study, continuous EC measurements of CO 2 , N 2 O, and CH 4 emissions from potato and pea fields ( Figure 1) were made year-round in the LFV of BC, Canada. The EC flux footprint comprised cropped areas on both sides of the edge area comprising a farm road, machinery turn-around strip and a drainage ditch, so footprint analysis was combined with EC and chamber measurements of soil GHG fluxes to estimate the annual GHG budgets of the cropped areas. The objectives of this study were to: QUAN ET AL.

The Study Site
The study site was located on Reynelda Farm (49°05′25.0″N, 123°09′47.9″W), a conventionally managed farm located on Westham Island, which is on the southwest edge of the Fraser River delta (Figure 2). This farm is typical of cropland in the area and was planted with potatoes, peas and silage corn during the study period in 2018 and 2019. The soils on the farm are Crescent Orthic Gleysol and Westham Rego Humic Gleysol, both naturally poorly drained and prone to ponding in the winter (Luttmerding, 1981). Our soil bulk density measurements on the ridge and furrow in the potato crop at the 0-7-cm depth were 1.27 and 1.50 g cm −3 , respectively. The texture of the topsoil is silt loam and the average pH of the top 15 cm of soil is 4.7 (Pow et al., 2020). The 30-year (1981-2010) climate record of the nearby weather station at Vancouver International Airport (YVR) (49°11′42.0″N, 123°10′55.0″W), 12 km north of the study site, indicated an average annual air temperature of 10.4°C, rainfall of 1152.8 mm, and snowfall of 38.1 cm (Environment and Climate Change Canada). A large proportion (∼80%) of precipitation occurs between October and April, contributing to appreciable seasonal variability in the soil moisture conditions. The experimental site mainly comprised three landscape components: a narrow drainage ditch (north-south oriented) with grass on its sides, a relatively bare soil strip on both sides, serving as a farm road (west side) and farm machinery turn-around area (east side), and crop fields on both sides of the ditch. For simplicity, both the ditch (water filled in the non-growing season) and bare soil strips are referred to the "edge area" in this study ( Figure S1 in Supporting Information S1).
In 2018, potatoes (varieties Goldrush Russet and Satina) were grown in both west and east fields as fresh produce. Both fields were plowed using a John Deere 975 reversible plow to a depth of 0.40 m 14 days before planting. They were fertilized 2 days before and during planting (15 May 2018) with a total application of 110 kg N ha −1 as NH 4 NO 3 fertilizer. In 2019, peas (variety Serge) were grown in the east field, while corn was grown in the west field. The pea field was disc harrowed 7-10 days before planting and broadcast fertilized with 34 kg N ha −1 of NH 4 NO 3 . Potato and pea canopy heights were steady at 0.45 and 0.35 m, respectively, during most of the growing season. After crop harvest, the aboveground biomass was left on the ground for both potatoes and peas.  , the west and east fields were planted with corn and peas, respectively. Due to insufficient winds from the west field during the corn growing season and insufficient measurement height of EC tower (3 m) compared with the maximum height of corn (3.1 m), it was not possible to obtain a complete time series of GHG fluxes from the corn field and to make reliable estimates of GHG budgets. Therefore, the corn crop was not included in this study and the second production cycle is referred to as the pea year ( Figure 3).

Flux Tower Location
The EC mast was located on a wooden platform above the ditch (not always water-filled) in the middle of the edge area to avoid interference with regular farm operations. This had the benefit of having the EC tower between the two crop fields to receive upwind flux signals from both fields as wind direction changed from one field to the other during the crop growing season. The width of the edge area adjacent to the west and the east fields was 10 and 14 m, respectively. The width of the edge area adjacent to the east field was reduced to 6 m during the pea growing season since the farmer planted the peas without leaving a machinery turn around strip beside the ditch. All the soil and meteorological measurements were made in the edge area to avoid disturbance from farm operations.

Eddy-Covariance (EC) Measurements
Fluxes of CO 2 , N 2 O, and CH 4 were measured continuously from 20 June 2018 to 30 October 2019 at the field scale by the EC sensors installed on the mast at a fixed height of 3 m. It is important to note that GHG fluxes from the beginning of the potato growing season (15 May 2018) were not measured by the EC system due to delayed installation while chamber measurements were made. The EC system consisted of a three-dimensional sonic anemometer (R3-50, Gill Instruments Ltd., Lymington, UK), an enclosed-path infrared gas analyzer (IRGA) (LI-7200, LI-COR Inc., Lincoln, NE, USA) and an off-axis integrated cavity output spectrometer (model 913-1054, Los Gatos Research Inc., San Jose, CA, USA; hereafter "laser spectrometer") ( Figure 1). The sonic anemometer measured the magnitudes of the three wind velocity components (u, v, w) and sonic temperature (T sonic ) at 20 Hz. The IRGA measured CO 2 (ρ c ) and water vapor (H 2 O) densities in air (ρ v ) at 20 Hz. The laser spectrometer measured gas densities of N 2 O ( , and ρ v at 10 Hz. Both gas analyzers reported concentrations on a dry mole basis (i.e., mixing ratios) at the measurement frequency thus not requiring subsequent Webb-Pearman-Leuning (WPL) corrections (Webb et al., 1980). Sample air was drawn through two separate air sampling inlets, one for the IRGA and the other for the laser spectrometer, positioned 15 cm below the center of the sonic anemometer array to avoid disturbance to the sonic measurements. The IRGA was mounted 2.5 m above the ground on the measurement mast and connected to a 1.3-m long and 4-mm inner-diameter air-sampling tube (Synflex 1300 Metal-Plastic composite tubing) (Eaton Corp. Inc., Beachwood, OH, USA) (flow rate of 15 L min −1 ). A second Synflex air-sampling tube 3.8-m long and 4-mm inner diameter (flow rate of 20 L min −1 ) running parallel to the first one was connected to the laser spectrometer, which was in an insulated water-proof box (2 m wide × 3 m long × 0.8 m high) mounted on a trailer (trailer top was 1.8 m above the soil surface). Temperature in the box was maintained at 35-36°C to ensure that the temperature in the laser spectrometer optical bench remained at 44.5 ± 0.1°C as recommended by the manufacturer. The air was drawn through the laser spectrometer by a dry scroll vacuum pump (XDS35i, Edwards Ltd., Burgess Hill, UK) at flow rate of 20 L min −1 (Figure 1). The cell pressure of the IRGA was maintained at −2.8 to −3.4 kPa below atmospheric pressure, while that of the laser spectrometer was maintained at 18.7 kPa (140 Torr) (as recommended by the manufacturers). The two sampling tubes were insulated and heated to 5-10°C above the ambient air temperature to reduce condensation inside the tubes. Before the sample air entered the IRGA and laser spectrometer, particulates were removed with a reusable 2-μm mesh 316-stainless steel filter (Swagelok Co., Solon, OH, USA) on the inlet, and a weekly manual replacement of the filters (after sonic bath cleaning) was performed to ensure adequate air flow in the tubing. Calibrations of the IRGA and laser spectrometer using a reference gas of known CO 2 , N 2 O, and CH 4 mixing ratios supplied by Environment and Climate Change Canada were conducted when necessary, based on the performance of the instruments, to ensure quality measurements. The zero offsets were determined using high purity (>99.998%) nitrogen gas.
Half-hourly EC fluxes were automatically calculated on the site computer using Matlab (The MathWorks Inc.). The calculated flux values were then transferred to the lab via cellular modem (Sierra Wireless RV50) on a daily basis. The real-time high-frequency data were backed up on a USB stick and manually transferred to a computer at the Biometeorology and Soil Physics Lab at University of British Columbia every week in case recalculations of half-hourly flux data were required (i.e., calculation procedure changes or interruptions on the site computer).
All half-hourly values of the three GHG fluxes were filtered for spikes (Humphreys et al., 2006) and non-stationarity. We also manually checked the half-hourly fluxes to remove suspect measurements. The detailed calculations and quality control can be found in Pow et al. (2020). In addition, the data with the friction velocity (u * ) less than 0.10 m s −1 were discarded. This threshold was determined by observing that nighttime EC-measured CO 2 fluxes remained relatively constant after u * exceeded this value (Humphreys et al., 2006). To separate fluxes for the two crop fields, wind direction ranges of 210°-330° and 50°-130° were used to select flux data for the west and east crop fields, respectively (see Appendix A1 and Figure A1). These wind direction windows were based on the criteria that more than 60% of the total flux footprint contribution from the crop and the edge areas together should be met. This was intended not only to avoid effects of the area beyond the potato and pea crops but also to avoid too much data loss. During the 2019 growing season, peas were planted in the east field, so data were only selected for winds from 50° to 130°.

Climate and Energy Balance Measurements
A four-component net radiometer (CNR1, Kipp & Zonen, Delft, The Netherlands) mounted 0.7 m above the ground measured incoming shortwave (S d ), outgoing shortwave (S u ), incoming longwave (L d ) and outgoing longwave (L u ) radiation. One quantum sensor (LI-190, LI-COR Inc.) mounted at the 1-m height measured incoming photosynthetically active radiation (PAR). Precipitation (P) was measured using a tipping bucket rain gauge (TR-525M, Texas Electronics, Dallas, TX, USA) at the 1-m height. Air temperature (T a ) was measured at the 2.5-m height using a bare 75-μm type-E (chromel-constantan) thermocouple. Three copper-constantan thermocouples and three water content reflectometers (CS616, Campbell Scientific Inc. (CSI), Logan, UT, USA) were installed to measure soil temperature and soil volumetric water content, respectively, at depths of 5, 20 and 60 cm. Three soil heat flux plates (CN3, Middleton Solar, Melbourne, Australia) were installed at the 3-cm depth to measure the soil heat flux (G) on the edge area. Due to malfunctioning of the rain gauge at the site, P from January to March in 2019 was gap-filled using data from the nearby climate station at YVR. All the data were logged on the CR3000 datalogger (CSI) using a signal multiplexer (AM16/32B, CSI), and was output on a half-hourly average basis.

Chamber Measurements
Soil surface fluxes of CO 2 , N 2 O, and CH 4 from the edge area and the crop fields were measured manually every two weeks using a nonsteady state flux chamber from May 2018 to August 2019. The measurements had to be discontinued after August 2019 as the chamber gas analyzer failed and had to be sent back to the manufacturer 6 of 22 for repairs. Four opaque cylindrical PVC collars (i.d. 20 cm, height 15 cm) were installed on both sides of the EC tower, with the collars inserted approximately 5 cm into soil. Two of these collars were located in the edge area, with one collar in the edge of the east field and one in the edge of the west field. The other two were located in the crop field, with one being in the plant-row and the other being in the interrow. Existing vegetation that interfered with tight sealing of the chamber lid was cut to a level below the lid. Collars in the edge area were left in place for the entire study period while those in the field were temporarily removed for farm operations.
A portable Fourier Transform Infrared (FTIR) Spectrometer gas analyzer (Gasmet DX4040) (Gasmet Technologies Group, Helsinki, Finland) was paired with the chambers to measure soil surface fluxes of CO 2 , N 2 O, and CH 4 following the procedure described by Schiller and Hastie (1994). Teflon-® tubing (i.d. 4 mm; flow rate of 2-3 L min −1 ) connected the metal lid to a silica gel container to remove excess moisture from the air stream. Air then passed through a 7-μm stainless steel filter before being drawn into the gas analyzer and then returned to the chamber.
All chamber measurements were made between 9:00 a.m. and 5:00 p.m. (PST). To ensure accurate gas flux estimation, the Gasmet readings of all the gases were verified for zero concentration level by flushing nitrogen gas through the system before each sampling campaign. The system was also tested for leakage in the laboratory the day before each campaign. While making measurements in the field on each sampling day, the FTIR was turned on for 5 min to warm up the gas analyzer and to stabilize background atmospheric gas concentrations before making measurements. Then the opaque lid was placed on the PVC collar for 6 min with 9 measurements made per minute. Ancillary measurements included collar air temperature (measured at the beginning, middle, and end of each cycle) and soil temperature (measured once per cycle at the 10-cm depth outside the collar) using a thermometer. Soil volumetric water content (0-7.6 cm depth) was once per cycle at three locations outside of the collar (within 30 cm) using a Fieldscout TDR 150 (Spectrum Technologies, Inc. Plainfield, IL) soil moisture meter with 7.6-cm long rods. The height of the collar above the soil surface at four different locations was measured and averaged to determine the volume of the chamber head space. The fluxes were determined by developing a linear relationship between the measured GHG mixing ratios and time since lid placement following Equation 1 in Christen et al. (2016). The CO 2 flux (or soil respiration) was used to approximate ecosystem respiration for the edge area. In summary, the chamber measurements were made to (a) gap-fill flux data during the period before the EC system was installed (refer to Section 2.3.1), and (b) provide fluxes from the edge area and hence allow us to calculate the actual crop field GHG fluxes (refer to Section 2.4.2).

Flux Gap-Filling
After screening half-hourly EC data, valid half-hourly fluxes after all the quality controls for CO 2 , N 2 O, and CH 4 were 54%, 54%, and 56%, respectively, for the whole study period (i.e., including both potato and pea seasons). Gaps of an hour or less were filled by linear interpolation and longer gaps were filled using mean diurnal variation (MDV) over 5 to 14-day cycles (Falge et al., 2001;Nemitz et al., 2018).
To estimate net GHG balances of the crops using EC-measured fluxes, a complete time series of half-hourly chamber-measured GHG fluxes at the edge area was required (refer to Section 2.4). In the case of N 2 O fluxes, chamber-measured N 2 O fluxes from the edge area were gap-filled using a simple spline interpolation. The magnitude and fluctuations of the N 2 O fluxes for the edge area were very small compared to those from the crop field. Thus, when the chamber gas analyzer failed during the pea non-growing season (i.e., 24 September 2019), we assumed N 2 O emission from the edge area were the same as the previous year (i.e., 24 September 2018). Then we performed the same simple spline interpolation method between the two values (i.e., chamber-measured fluxes on 13 August 2019 and 24 September 2018) to obtain the complete time series of chamber-measured N 2 O fluxes from the edge area. In the case of chamber-measured CO 2 fluxes of the edge area, the complete time series was obtained using an empirical relationship between manual chamber-measured CO 2 fluxes and soil temperature expressed as a logarithmic transformation of Equation 2. In the case of chamber-measured CH 4 fluxes, no gap-filling was applied as the fluxes were close to minimum detectable levels, that is, negligible.
As explained in Section 2.2.2, EC-measurements of GHG fluxes from the beginning of the potato growing season (15 May to 20 June 2018) were not made. However, chamber measurements from late May and early June indicated the response of the field to the fertilizer application and enabled us to estimate the GHG emissions during that period using linear interpolation. 7 of 22

Partitioning of Eddy Covariance Data
Net ecosystem exchange (NEE) was partitioned into two components as: where NEE was equated to CO 2 as changes in CO 2 storage in the air column beneath the EC measurement height were negligible considering the low EC measurement height (Montagnani et al., 2018). NEP is net ecosystem production, GPP is gross primary production, and e is ecosystem respiration. A negative NEE value indicates CO 2 uptake by the ecosystem from the atmosphere and a positive value indicates CO 2 release from the ecosystem to the atmosphere. The NEE partitioning procedure followed the standard FLUXNET Canada Research network (FCRN) protocol (i.e., nighttime-based partitioning method) using a moving window approach (Barr et al., 2004;Chen et al., 2009).
To investigate the effect of environmental variables on e and its estimation during daytime as well as gap-filling, a logarithmic transformation, lnR e = A + BT s , which allows the assumption of normality and homoscedasticity to be met for linear least squares regression, was used to obtain the parameters in the exponential relationship between R e and soil temperature (Humphreys et al., 2005): where R 10 is the reference respiration rate at 10°C, Q 10 is the relative increase in e for a 10°C increase in temperature and s is the soil temperature at the 5-cm depth.

Net Ecosystem Carbon and Greenhouse Gas Balances
Because EC measurements during the non-growing season following pea harvest were not completed, measurements in part of the previous non-growing season (1 October 2018-14 May 2019) were used in the calculation of the annual net ecosystem carbon balances (NECB, g C area −1 time −1 ) and balances of GHGs (g CO 2 e area −1 time −1 ) of the pea crop. The timeline of the EC measurements and defined potato and pea years are shown in Figure 3. NECB was calculated using (Chapin et al., 2006;J. E. Hunt et al., 2016;Waldo et al., 2016): where C import and C export are C import as a result of seeding and organic fertilizer and export as a result of harvested biomass, respectively. Negative values of NECB indicate net loss of C from the field. As no organic fertilizer or amendments were applied, C import values were estimated from the seeding rates of the potatoes and peas (3,440 kg wet matter ha −1 and 220 kg dry matter ha −1 , respectively). Using 78% water content of the seed potatoes and C content of 50% of the dry matter gave C import values of 38 ± 8 and 11 ± 2 g C m −2 yr −1 for the potatoes and pea, respectively, assuming an uncertainty of ±20%. C export was estimated using the fresh weight yields provided by the farmer and the typical C content in dry matter of potato tubers and peas (assumed to be 50%). The yield of potatoes (tubers) and peas (including pods) were 34.6 and 10.4 t wet matter ha −1 , respectively. Water contents of the tubers and peas were estimated to be 78% and 70%, respectively. The resulting values of C export were 379 ± 38 and 78 ± 8 g C m −2 yr −1 , respectively, assuming an uncertainty of ±10%.
The CO 2 equivalent flux of each non-CO 2 GHG was obtained by multiplying the cumulative flux by the respective value of the mass-based global warming potential (GWP). The GWPs of N 2 O and CH 4 (i.e., GWPN 2 O and GWPCH 4 ) for a 100-year time scale are 273 and 27 (Forster et al., 2021), respectively. The annual GHG balance of each crop was obtained by summing the CO 2 equivalent fluxes of the GHGs over the year as follows (Lee et al., 2017): where CO 2 is the sum of the CO 2 equivalent mass fluxes of CO 2 , CH 4 , and N 2 O (i.e., the balance of GHGs). 2 (i.e., ∼NEE), 4 and 2 are the study-period total molar fluxes, and 2 , 4 , and 2 are the molar masses of the respective GHGs.
Uncertainties in CO 2 , CH 4 , and N 2 O fluxes were determined following Pow et al. (2020) and included respective values of the measurement error, gap-filling error, and systematic error in the selection of the u * threshold. 8 of 22

Flux Footprint Model
To determine the source area of fluxes, the Flux Footprint Prediction model (FFP) proposed by Kljun et al. (2015) was used. Indicated by the annual flux footprint climatology ( Figure S2 in Supporting Information S1), the 80% contour line, the source area determined by the model to account for 80% of the measured flux, was within the west and east crop fields. The EC-measured fluxes at this site are the result of surface fluxes from two parts of the field: the crop area and the edge area. Although the edge area is small compared to the crop area, its proximity to the EC mast can greatly affect the EC fluxes. Thus FFP was further used to correct for this edge effect and to obtain the surface fluxes from the crop area of interest. For each half hour, we calculated the flux footprint over the whole domain around the tower at 1-m resolution. The EC flux over the integrated area can be expressed as follows (Kljun et al., 2015): where F EC is the flux measured by the EC system, Q(x,y) is the surface flux at location (x,y), f(x,y) is the footprint contribution to the EC flux at location (x,y) and dxdy is the unit size of the source area, which is 1 m 2 in this case.
When the surface fluxes from each landscape component (the crop and edge areas) are available, the fluxes measured by EC can be expressed as follows: where the subscript c denotes the crop area and e denotes the edge area adjacent to the crop area. To simplify the computation of the footprint contributions, Q c and Q e were assumed to be uniform within the crop and edge areas, respectively, since both landscape components were relatively homogeneous. Therefore, F EC can be expressed as follows: where ∑f c (x,y) and ∑f e (x,y) are the summations of the footprint contributions over the crop and edge areas, respectively, according to the actual sizes of these two landscape components. The two summations will now be referred to as f c and f e , respectively. They were calculated for each half hour using an online Matlab program created by N. Kljun (Kljun et al., 2015).

N 2 O
Using Equation 8, the N 2 O flux measured by the EC system ( N 2 O ) from the crop and the edge areas can be expressed as follows:

CO 2
The entire data analysis procedure for the CO 2 flux is shown as a flowchart in Figure S3 of Supporting Information S1. First, the net ecosystem exchange measured by the EC system (i.e., NEE) can be expressed as follows: where c_nee and e_nee are the values of NEE of the crop and the edge areas, respectively. An equation similar to Equation 10 can be written for R e (= NEE measured by the EC system during nighttime) as follows: where c_gpp = c_re − c_nee and e_gpp = e_re − e_nee which are the GPP values for the crop and the edge areas, respectively. Rearranging Equation 12 provides an expression for c_gpp as follows: where k is the ratio of e_gpp to c_gpp . Based on typical GPP ( c_gpp ) values of a grass crop reported in the literature (e.g., Sheehy & Peacock, 1975) and our estimated Qc gpp (Appendix A2), we considered three values of k (0.8, 1.0, and 1.2) in this analysis. A short experiment aimed at roughly estimating the sink strength of the grass by using tarpaulins to cover grass along the edge just north-west of the flux tower conducted in May 2019 confirmed this range of k values (see Appendix A2).
Nighttime e_re was obtained using the logarithmic relationship (ln e_re = + ) between daytime e_re measured using the chamber and T s . Nighttime c_re was calculated using Equation 11 for each half hour. Then c_re during the daytime was obtained by developing a relationship between c_re and corresponding T s during the nighttime but using daytime T s . Therefore, daytime R e was calculated using Equation 11, and with NEE directly measured by the EC system, GPP was obtained using Equation 1. Then c_gpp was obtained using Equation 13. Finally, c_nee was determined using:

CH 4
Chamber-measured CH 4 fluxes from the crop and the edge areas were generally negligible with very small emissions occasionally occurring possibly from the ditch. Therefore, no flux footprint correction was applied to the EC-measured CH 4 fluxes.

Meteorological and Soil Variables
Meteorological variables during the study period ( . While values of monthly and annual mean T a at the site were very close to the long-term mean values at YVR, annual P at the site was lower than the long-term mean at YVR, with the growing season (May to August) of 2019 being drier and December 2018 appreciably wetter. Average daytime vapor pressure deficit ( day ) was generally <0.5 kPa during the non-growing season but slightly exceeded 1 kPa during the growing season.
Daily average s at the 5-cm depth followed the same pattern as a , with a larger difference between the two during the summer months (Figure 4a). Daily mean s was always >0°C while daily mean a dropped slightly below 0°C during early February in 2019. Soil volumetric water content measured at the 5-cm depth (

Comparison of EC-Measured and Flux-Footprint-Corrected N 2 O Fluxes
There was a strong linear relationship between half-hourly EC-measured fluxes ( N 2 O) and footprint-corrected fluxes ( c_N 2 O) with the latter being 40% and 51% higher than the former for the west and east fields, respectively ( Figure 5). For the combined data for both fields, half-hourly c_N 2 O was 43% higher than N 2 O (R 2 of 0.97, RMSE = 0.23 nmol m −2 s −1 ). A strong linear relationship was also found between monthly c_N 2 O and N 2 O (R 2 = 0.95; results not shown). This suggests that it would be possible to apply a conversion coefficient to the fluxes measured by the EC system to correct for the effect of the edge area. This coefficient would likely be site specific but applicable with a proportional footprint contribution from the edge area being relatively constant. EC-measured total N 2 O values for the potato growing season (west and east fields as a whole), the potato non-growing season, the pea growing season (east field only), and the pea non-growing season were 0.37, 0.59, 0.07, and 0.67 g N 2 O-N m −2 , respectively. After applying footprint correction, we found the respective c_N 2 O totals were 0.51, 0.86, 0.11, and 0.98 g N 2 O-N m −2 , respectively (Table S1 in Supporting Information S1). Measured annual N 2 O emissions from potato fields have been found to be about 2.0 and 0.5 kg N 2 O-N ha −1 in southern Germany (mean temperature at 7.4°C and mean annual precipitation at 803 mm) and northern China (mean temperature at 3.2°C and mean annual precipitation at 343 mm), respectively (Flessa et al., 2002;Wang et al., 2017). These values are very low compared to ours (5.1 kg N 2 O-N ha −1 ). The potential reason could be the higher temperature and precipitation at our site. A pea field in Switzerland with a mean annual temperature of 8.8°C and mean annual precipitation of 1,088 mm emitted 1.4 kg N 2 O-N ha −1 over the growing season in 2019 (Maier et al., 2022), which was close to our results (1.1 kg N 2 O-N ha −1 ). Pattey et al. (2008) also measured similar N 2 O emissions (1.7 kg N 2 O-N ha −1 ) in eastern Canada even though their field experienced lower temperature. Much lower N 2 O emissions over three consecutive pea cropping seasons (0.03-0.9 kg N 2 O-N ha −1 ) were observed in France (Jeuffroy et al., 2013). It is noteworthy that except for Maier et al. (2022) and Pattey et al. (2008), the other studies used the flux chamber technique to quantify N 2 O emissions, and that lower emissions could likely be due to missing large peaks of highly episodic N 2 O emissions with much lower chamber measurement frequency (Merbold et al., 2021).
We found that the chamber-measured N 2 O fluxes from the edge area were between 0 and 1 nmol m −2 s −1 , similar to the background (i.e., before N fertilizer application) N 2 O measured by the EC system. However, while the edge area was a weak source, much higher EC-measured N 2 O flux pulses (>1.5 nmol m −2 s −1 ) were constantly observed during the study period.

Temporal Variation of N 2 O Flux
The potato field (east and west) and pea field (east) were N 2 O sources during the entire study period ( Figure 6). After the fertilization in mid-May 2018, c_N 2 O of the potato field peaked at approximately 3.8 nmol m −2 s −1 likely due to the increased NO3 − in the soil enhancing the denitrification process (Gillam et al., 2008). Relatively high soil temperatures during the summer months of June and July favored soil microbial activity, resulting in higher c_N 2 O which remained elevated for about 8 weeks. Then it declined to less than 0.2 nmol m −2 s −1 for the rest of the potato growing season, likely due to nitrogen uptake by the crop. After tuber harvest (18 September 2018), N 2 O production was stimulated by frequent rainfall events and multiple c_N 2 O pulses were observed with the highest value being approximately 4.2 nmol m −2 s −1 near the end of September 2018. It has been found that precipitation can greatly affect N 2 O emissions from agricultural soils (Nielsen & Ball, 2015;Pihlatie et al., 2004;Saarnio et al., 2013;Schaufler et al., 2010). By using EC measurements, Huang et al. (2014) found that N 2 O emissions from a corn field in Tennessee USA responded quickly to rainfall events and increased within 30 min. This was also observed on a silage farm in Australia (Phillips et al., 2013). In addition, the presence of organic matter from potato crop residues can promote sufficient heterotrophic respiration to create or enlarge anaerobic microsites in which denitrification can take place (Smith et al., 1997;Tiedje et al., 1984). Surprisingly, similar N 2 O emission pulses after fertilizer application in the pea field did not occur,   (Table S1 in Supporting Information S1). Based on the footprint-corrected fluxes, the growing season N 2 O emissions total for the pea crop was only 22% of that for the potato crop (Table S1 in Supporting Information S1). Large emissions during the non-growing season accounted for approximately 61% and 90% of the annual emissions for the potato year and the pea year, respectively. This emphasizes the importance of mitigating the N 2 O emissions especially during the non-growing season in a region where the weather during that period is characterized by heavy precipitation. According to Drever et al. (2021), it is critical to decrease GHG emissions from agricultural soils by growing cover crops during non-growing season. Cover cropping has been found to successfully reduce GHG emissions with no negative effects on cash crop yields in different crop fields (Bavin et al., 2009;Behnke & Villamil, 2019). By using data from five contrasting sites, Tribouillois et al. (2018) predicted that cover crops have the potential to lower the GHG balance by 315 kg CO 2 e ha −1 year −1 over 45 years compared to that of bare soil in France. Globally, cover crops, through their effect on GHG fluxes, are estimated to mitigate warming by between 1.00 and 2.06 Mg CO 2 e ha −1 year −1 (Abdalla et al., 2019;Kaye & Quemada, 2017). It is interesting to note that daily average c_N 2 O values were higher than those from a nearby blueberry field (∼1 km away) fertilized with a similar amount of fertilizer as that for the potato field (∼110 kg N ha −1 ). Although blueberry is a perennial crop, we suspect that this is likely due to the fertilizer being applied to the blueberry field 4 times during the growing season, resulting in higher N use efficiency and thus lower N 2 O emissions (Pow et al., 2020). However, the relationship between N fertilization (i.e., different type and mixed composition) and N 2 O fluxes can be complex (Ma et al., 2022). It has been found that N 2 O emissions increased substantially when N inputs exceeded crop needs (Shcherbak et al., 2014). Replacing 25% of mineral fertilizer with organic manure can greatly decrease N 2 O emissions (Lv et al., 2020). Chizen et al. (2022) concluded that lower N fertilizer rates (<100 kg N ha −1 ), especially in fields with degraded soils, can lower N 2 O emissions from potato production in British Columbia. Recently, Thilakarathna et al. (2023) evaluated different nitrogen management practices and found application of nitrification inhibitors has substantial potential to reduce N 2 O emissions in Canada.

CH 4 Flux
Over the entire study period, CH 4 values were generally very small, with evidence of both production and consumption of small amounts of CH 4 ( Figure S4 in Supporting Information S1). Overall the potato and pea fields were very weak sources of CH 4 . Daily average CH 4 was between 0 and 5 nmol m −2 s −1 for most of the observation period while some relatively high values larger than 5 nmol m −2 s −1 were occasionally observed. The possible reason could be that decomposition mainly happened in aerobic conditions that would only allow small CH 4 fluxes (Saunois et al., 2020). Low CH 4 emissions were also measured in a pea-maize field in Switzerland (Maier et al., 2022). Some high CH 4 values likely resulted from the CH 4 emissions from the ditch, similar to those observed by Needelman et al. (2007) and Peacock et al. (2021). However, the magnitude of CH 4 from the ditch could not be determined without careful and regular chamber measurements taken above the water surface of the ditch. In addition, the bare soil after the crop harvest experienced poorly drained periods of time after frequent rainfall events, which could also contribute to CH 4 emissions due to anaerobic soil conditions favoring CH 4 production (Conrad, 2020;Ehhalt & Schmidt, 1978). However, these emissions are difficult to partition from the fluxes measured by the EC system without confirmed surface fluxes from the ditch. CH 4 totals for the potato growing season (west and east fields as a whole), the potato non-growing season, the pea growing season (east field only), and the pea non-growing season were 0.46, 0.59, 0.40, and 0.71 g CH 4 -C m −2 , respectively (Table S2 in Supporting Information S1).

Comparison of EC-Measured and Flux-Footprint-Corrected CO 2 Flux Components
Flux footprint corrections for the CO 2 flux components were, in general, small. The largest corrections were to R e (Figure 7) which was due to the differences between soil respiration of the edge and R e of the crop. It is important to note that we used soil respiration from chamber measurements to approximate R e of the edge area. It is likely that this may have resulted in an underestimation of Q e_re by 20%-30% (Lohila et al., 2003). During the QUAN ET AL.

10.1029/2022JG007113
13 of 22 potato growing season, footprint-corrected R e was about 15% higher than uncorrected R e (or ∼0.4 μmol m −2 s −1 higher). It remained higher during the non-growing season between the potato and the pea crop growing seasons. Footprint-corrected GPP using k = 1 was very similar to EC-derived GPP thereby supporting our hypothesis that the photosynthesis of the grass component of the edge area was quite similar to that of the crop. Finally, as a result of the edge effect on R e , footprint-corrected NEE deviated slightly from EC measurements particularly during the latter half of the pea growing season when the magnitude of EC-measured NEE was underestimated by on average 0.7 μmol m −2 s −1 .
GPP increased gradually after each crop emerged and developed, reaching the highest daily mean values (k = 1) of 11 and 10 μmol m −2 s −1 during the potato and pea growing seasons, respectively. After the first half of the potato growing season, potato growth transitioned from vegetative growth to tuber bulking, and then to maturation, and GPP decreased until harvest as the vines senesced and lost leaves. Unlike the potato crop, the pea vine remained green until harvest, so the steep drop of GPP occurred outside the defined pea growing season. The highest monthly GPP was observed in July 2018 (302 g C m −2 month −1 ) for the potato crop, and in August 2019 (250 g C m −2 month −1 ) for the pea crop (Table S3 in Supporting Information S1, k = 1). In contrast to other studies (Gilmanov et al., 2013;Patel et al., 2021), we did not observe a decrease in GPP under high VPD conditions, which can decrease stomatal conductance and limit crop photosynthetic rate (Song et al., 2022). Potential reasons are that the study crop fields did not experience very high VPD (peak half-hourly value being about 1.5 kPa) and the soil moisture content maintained at a level much higher than the wilting point value.
Compared to the temporal patterns of GPP, crop-specific seasonal differences in R e were less pronounced. Maximum R e was very similar (∼4 μmol m −2 s −1 ) in the growing season of the two crops. After potato harvest, R e declined slowly, likely due to slower decomposition of the fresh residues left on the field at lower soil temperatures in September. Subsequently, non-growing season R e remained relatively low at approximately 0.5 μmol m −2 s −1 14 of 22 throughout the winter and increased to 2 μmol m −2 s −1 when soil temperature started to increase prior to the pea growing season. The difference between growing season and non-growing season R e is due to both the difference in soil temperature as well as the absence of autotrophic respiration (R a ) during the non-growing season as R a can account for 60%-90% of total R e during the growing season (Suleau et al., 2011). Non-growing season R e which is mainly heterotrophic respiration was 50% and 62% of annual R e during the potato and pea years, respectively, partly as a result of the period without active vegetation cover being very long (8 and 10 months for the potatoes and peas, respectively). Unlike the pea growing season, average footprint-corrected R e values were higher during the potato growing season (Table S4 in Supporting Information S1), likely due to higher autotrophic and heterotrophic respiration, which can be attributed to higher biomass and intensive pre-planting tillage, respectively.
Overall, the ecosystem-stored C from June to July 2018 for the potato crop and from July to August 2019 for the pea crop, with GPP being higher than R e . Similar to the results reported by Ceschia et al. (2010), we found that the length of time when there was photosynthetically active vegetation cover closely corresponded to the number of days that C was stored by the ecosystem (i.e., NEE <0), which were 56 and 64 days, for potato and pea crops, respectively. The growing season footprint-corrected NEE values for k = 1 were −144 and −208 g C m −2 for the potato and pea crops, respectively, while the non-growing season values were 87 and 111 g C m −2 , respectively (obtained from the Q c_gpp and Q c_er values in Tables S3 and S4 in Supporting Information S1, respectively). The corresponding EC-measured values are shown in Table S5 of Supporting Information S1 while Table S6 in Supporting Information S1 shows annual GPP, R e , and NEE values for the two crops for different k values.

Annual Net Ecosystem Exchange and Net Ecosystem Carbon Balance
For both the potato and the pea fields, annual CO 2 uptake exceeded CO 2 release, resulting in a net uptake of 57 ± 9 g C m −2 yr −1 (i.e., NEE = −57 g C m −2 yr −1 ranging from −101 to −21 g C m −2 yr −1 when k varied from 0.8 to 1.2, respectively) and 97 ± 16 g C m −2 yr −1 (i.e., NEE = −97 g C m −2 yr −1 ranging from −122 to −76 g C m −2 yr −1 when k varied from 0.8 to 1.2, respectively) for the potato and pea fields, respectively (Table 1 and Table S6 in Supporting Information S1). The corresponding uncorrected EC values for the potato and pea fields were −70 ± 11 and −30 ± 5 g C m −2 yr −1 , respectively (Table S5 in Supporting Information S1). The annual EC and footprint-corrected values were similar for potatoes but much different for peas. This is because the footprint-corrected values of NEE during the pea growing season were approximately 1 μmol m −2 s −1 more negative than the EC values. Anthoni et al. (2004) found that the annual NEE for a potato crop in Germany with reduced tillage was −34 g C m −2 yr −1 (ranging from −49 to 29 g C m −2 yr −1 ), which is comparable to that for the potato crop in this study. Gilmanov et al. (2014) reported that year-round annual legume crops at 17 flux tower sites in North America and three sites in Europe demonstrated a wide range of NEP (i.e., -NEE) values, with an average of −90 g C m −2 yr −1 (ranging from C sinks of 207 g C m −2 yr −1 to C sources of 573 g C m −2 yr −1 ). The average value of annual NEP in their study indicated overall tendency for legume crops to be C sources, while the pea crop in this study was a moderate C sink.
The annual footprint-corrected GPP for the potato crop with a 4-month growing season (793 ± 131 g C m −2 yr −1 , ranging from 837 to 757 g C m −2 yr −1 for k = 0.8 and 1.2, respectively) was similar to that for the pea crop with a shorter 2-month growing season (749 ± 124 g C m −2 yr −1 , ranging from 775 to 728 g C m −2 yr −1 for k = 0.8 and Table 1 Annual Ecosystem Respiration (R e

), Gross Primary Production (GPP), Net Ecosystem Exchange (NEE) Measured by Eddy Covariance (EC), Carbon Removal From Crop Harvest, Carbon Addition From Seeding, and Net Ecosystem Carbon Balance (NECB) for the Potato and Pea Crops Without Flux Footprint Correction (EC-Measured) and With Flux Footprint Correction Using k = 1 (k = Q e_gpp /Q c_gpp )
Potatoes Peas 1.2, respectively), as a result of the differences in the intensity and pattern of photosynthetic assimilation between the two crops (Table 1 and Table  S6 in Supporting Information S1). The corresponding EC values of GPP for the potato and pea fields were 671 ± 111 and 672 ± 111 g C m −2 yr −1 , respectively. The annual value of the footprint-corrected R e for the pea crop (652 ± 108 g C m −2 yr −1 ) was much less than that for the potato crop (736 ± 122 g C m −2 yr −1 ). Overall, values in Table 1 suggest that the potato and pea fields in this study were weak C sinks with the pea field being slightly stronger.
To obtain the NECB, NEE was combined with estimates of C export and C import (Equation 3). Based on the NECB values, the potato field shifted from being a weak C sink to being a moderately strong C source (−284 ± 55 g C m −2 yr −1 ), while the pea field shifted from being a weak C sink to being a very weak C sink (30 ± 26 g C m −2 yr −1 ) ( Table 1). This was the result of the large C export from the potato field and small C export from the pea field. Similar results that a large proportion of the C accumulation is exported from the site has been reported and discussed widely for cropland ecosystems (Ceschia et al., 2010;Ciais et al., 2001;Gilmanov et al., 2010). Ceschia et al. (2010) reported an average NECB of −138 ± 239 g C m −2 yr −1 for European croplands representing an annual loss of 2.6% of soil organic carbon. Their corresponding value of NEE was −284 ± 228 g C m −2 yr −1 pointing to the importance of C exports in the NECB. As pointed out by Gilmanov et al. (2010), the ability of managed agroecosystems to serve as sinks of CO 2 from the atmosphere depends on the ultimate fate of the harvested biomass. Wiesner et al. (2022) observed that an intermediate wheatgrass monoculture accumulated more C with an NECB of 306 ± 88 g C m −2 than a biculture with red clover being C neutral (NECB = 7 g ± 131 g C m −2 ) on a dairy farm in Wisconsin, USA. Kim et al. (2022) found that the two perennial crop fields in the Canadian prairies had NECB values of −60 (weak C source) and 448 (strong C sink) g C m −2 , respectively. However, another two annual crop fields were both C sources (−263 and −336 g C m −2 , respectively). They suggested the perennial crop enhanced the atmospheric C sink compared to the annual crop but also noted their assessment did not account for non-CO 2 C (e.g., CH 4 ) emissions.
When estimating the NECB, a large uncertainty associated with calculating C input and C output is often expected given that the information provided by farmers may be approximate. Given that NEE and C export have the greatest impact on the annual C balance of croplands (Ceschia et al., 2010), the importance of more accurate C export estimates should be stressed in future studies.

GHG Balances
Summation of footprint-corrected CO 2 e values of the three GHGs yielded (k = 1) a net GHG balance of 417 ± 88 g CO 2 e m −2 yr −1 (ranging from 256 to 574 g CO 2 e m −2 yr −1 for k = 0.8 and 1.2, respectively) for the potato field, and 152 ± 106 g CO 2 e m −2 yr −1 (ranging from 61 to 251 g CO 2 e m −2 yr −1 for k = 0.8 and 1.2, respectively), for the pea field (Table 2 and Table S7 in Supporting Information S1), indicating that both fields acted as net sources of GHGs on an annual basis. The corresponding EC values of annual GHG balances for the potato and pea fields were 193 ± 86 and 248 ± 57 g CO 2 e m −2 yr −1 , respectively. The former value was much smaller than the footprint-corrected value (k = 1) mainly because the footprint-corrected N 2 O CO 2 e was about 200 g CO 2 e m −2 yr −1 larger than the EC-measured N 2 O CO 2 e value ( Figure 6 and Table S7 in Supporting Information S1). In the case of the pea field, the EC-measured GHG balance was larger than the footprint-corrected value mainly because footprint correction resulted in an appreciably more negative NEE (i.e., −356 ± 59 g CO 2 m −2 y −1 ) as mentioned in Section 3.4.2. Recently, Maier et al. (2022) used a similar setup (i.e., sonic anemometer with a laser spectrometer) to measure GHG fluxes from a pea field in Switzerland, and found the GHG balance for the pea crop to be about −450 g CO 2 e m −2 over 55 days. This value is smaller than our footprint-corrected GHG balance for the pea crop over the growing season (i.e., about −700 g CO 2 e m −2 ) considering our pea growing season was 9 days more than theirs and their pea crop was not fertilized.
Similar patterns of the contribution of different GHGs to the annual GHG balances were observed for both crop fields. Uptake of CO 2 was offset by relatively large N 2 O emissions (588 ± 32 and 468 ± 25 g N 2 O-CO 2 e m −2 yr −1 , k = 1, for the potato and pea crops, respectively), with the N 2 O emissions strongly contributing to 16 of 22 global warming. The substantial contribution of N 2 O emissions (i.e., up to 66%) to the GHG balance was also observed from a fertilized sugar beet field in Belgium (Lognoul et al., 2019). This again highlights how critical it is to include N 2 O emissions when assessing the GHG budget from a fertilized crop. CH 4 accounted for a small proportion of the annual GHG balances (10% and 25%, k = 1, for the potato and pea fields, respectively) ( Table 2). Caution should be taken when comparing these two crop years as they share a common non-growing season, as a considerable proportion (63% and 90% for the potato and pea crops, respectively) of N 2 O emissions occurred outside the growing season. It is possible that the time period following pea harvest may have exhibited a different pattern of N 2 O emissions under different climate conditions from that of the common non-growing season in this study. Under similar climate conditions (P, s , and s ; see Figure 4) in the months of September and October in both 2018 and 2019, a lower rate of N 2 O emissions following pea harvest likely resulted from a lower N application rate to the pea crop. Furthermore, after harvest the standing pea crop was sequestering CO 2 (see Figure 7) so that (a) some soil N was likely still being taken up by the crop and (b) the pea biomass was not yet in a state of active decomposition as was the case following potato harvest thereby minimizing N 2 O emissions during the beginning of the pea NGS. In the case of CO 2 , given that R e was constantly low and did not exhibit an obvious temporal variation responding to changing weather during the winter, it likely did not contribute much to the non-growing season R e in the pea year ( Figure 7). However, it should be noted that the period (approximately 2 weeks) following the preparation of the potato field for planting was not included in the potato year in our study. It is recognized that tillage used in field preparation, which is always intensive for potatoes in this region, might have resulted in a notable increase in R e and consequently a more positive NEE for the potato year. For example, Abdalla et al. (2016) synthesized 46 peer-reviewed publications and found tilled soils significantly emitted 21% more CO 2 on average than untilled soils. A wheat-maize rotation crop field in the North China Plain has been found to emit more CO 2 under conventional tillage (65 g CO 2 -C m −2 y −1 ) than with no tillage (39 g CO 2 -C m −2 y −1 ) (Wu et al., 2017). Similarly, deep tillage has been observed to increase total CO 2 emissions by between 4.9% and 37.7% in another wheat field in North China (Gong et al., 2022). Figure 8 summarizes the contributions of the GHG fluxes and C imports and exports to the annual GHG balances for the two crops. Estimation of CO 2 e of C imports and exports assumes all C is released as CO 2 . The annual GHG balance for the potato crop was particularly high with a value of 1,669 ± 255 g CO 2 e m −2 yr −1 , which was almost 4 times higher than the value of 401 ± 143 g CO 2 e m −2 yr −1 for the pea crop. Results show that the export of potato tubers and peas accounted for a large proportion of the annual GHG balances (83% and 71%, respectively) ( Table 1 and Figure 8). It has been found that a managed highbush blueberry field in the LFV was a net GHG source of 840 ± 126 g CO 2 e m −2 yr −1 , primarily controlled by the application of sawdust mulch (Pow et al., 2020). Ceschia et al. (2010) found that for European croplands, the NEE (through uptake of CO 2 ), on average, represented 88% of the negative GHG balance, and exported C represented 88% of the positive GHG balance of 203 ± 253 g CO 2 e m −2 yr −1 . Figure 8. The greenhouse gas (GHG) balances (g CO 2 e m −2 yr −1 ) of CO 2 , N 2 O, and CH 4 with the difference between export of potato tubers and peas (C export ) and import of seed potatoes and pea seeds (C import ) from the field for the potato and pea years using flux footprint correction with k = 1 and accounting for the global warming potentials.

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It is important to note that we assumed annual GHG emissions for each crop as pulse emissions to estimate the GHG balances of the three GHGs, and C imports and exports. While we are aware that using values of GWP as opposed to sustained GWP (SGWP) of different GHGs does not provide the actual radiative forcing (Neubauer, 2021), it provides valid information as to whether an ecosystem is a net CO 2 e source or sink and compares GHG balances of two different crops.
We would also like to emphasize that impacts of some agricultural management practices and other environmental conditions were not assessed in this study. First, as the need of food is rapidly increasing, herbicides are expected to be used more in crop production globally (Gianessi, 2013). Besides serving as an effective tool to increase crop yield, applying herbicides can change vegetation-soil interactions and consequently alter soil GHG fluxes (Crouzet et al., 2010;Jiang et al., 2015;Oyeogbe et al., 2017). The application of herbicides to an agricultural field (alfalfa) led to largely increased CO 2 emissions which contributed to greater GHG emissions (Shi et al., 2020). Second, the phenological stage of crops can play an important role in GHG fluxes. Vegetation height showed a strong relationship with N 2 O fluxes for both peas and maize in a farm in Switzerland, likely because of plant-microorganism competition (Maier et al., 2022).

Conclusions
Due to frequent agricultural operations (e.g., herbicide spraying), the field instrumentation system in this study had to be deployed at the edge of the study agricultural field. We combined EC and manual flux chamber measurements with the flux footprint approach to make corrections for the edge effect resulting from the presence of a farm road and a machinery turn-round strip adjacent to the EC tower, and the resultant inhomogeneity of the footprint area, and hence to obtain GHG fluxes for the crop areas. The key findings are summarized as follows: 1. After the flux footprint correction, the potato and pea crops were both weak CO 2 sinks with annual NEE values of −57 ± 9 and −97 ± 16 g C m −2 yr −1 (k = 1), respectively. After taking C export via crop harvest and C import via seeding into account, the potato crop became a C source (NECB = −284 ± 55 g C m −2 yr −1 ), while the pea crop became a weak C sink (NECB = 30 ± 26 g C m −2 yr −1 ). 2. The annual footprint-corrected GHG balances for the potato and pea crops were 417 ± 88 and 152 ± 106 g CO 2 e m −2 yr −1 (k = 1), but when including C import and C export , the values were 1,699 ± 255 and 401 ± 143 g CO 2 e m −2 yr −1 , respectively. For both the potato and the pea crops, N 2 O contributed the largest proportion to the annual GHG balances and offset CO 2 uptake from the atmosphere, making both crop fields net GHG sources. 3. R e and N 2 O fluxes after flux footprint corrections were generally higher than those directly measured by EC due to smaller R e and N 2 O fluxes in the edge area compared with the cropped area. 4. Substantial N 2 O emissions were triggered by rainfall events during the non-growing season. CH 4 emissions were low and made a small contribution to the GHG balances. The magnitude of R e mainly followed seasonal changes in T s . Temporal variations in GPP were closely associated with crop development.
These results highlight the importance of future research into management practices that decrease N 2 O emissions and increase C sequestration in agricultural systems. This includes questions about how much can nitrogen fertilizer rates be decreased while maintaining acceptable yields, and the benefits of adding organic amendments such as poultry manure. In agricultural systems like those in this study where the non-growing season is relatively mild and rainfall is high, it will be useful to consider and evaluate how cover crops can be successfully grown during this period and their impacts on C and GHG balances.

Appendix A A1. Wind Direction Analysis
As shown in Figure A1, f for each landscape component generally followed a uniquely shaped curve closely related to wind direction. However, the f curves varied within a small range for a specific wind direction, which was due to varying atmospheric conditions. It is also apparent that the f curves for the west and the east fields (the left and right panels in Figure A1) exhibited mirror image symmetry due to the EC system being located between the two fields. The highest value of f c + f e (0.95) was observed when the wind direction was between 240° and 300°, with f c (0.6-0.85) being higher and f e (0-0.35) being lower than those for wind directions outside this range. A similar pattern was observed for the east field with the maximum value of f c + f e being approximately 0.92 18 of 22 when the wind direction was between 60° and 100°. This suggested that the west-east spans of the crop and the edge areas, both in the west (218 m) and in the east (177 m), were long enough to cover more than 90% of f c + f e . However, the wind direction range within which the maximum value of f c + f e remained high was narrower for the east field than for the west field due to the north-south span of the east field (125 m) being much less than the west field (600 m). In addition, due to the fact that the edge area in the east (14 m) was wider than that in the west (10 m), f c of the east field was slightly lower (0.5-0.78) while its f e (0.1-0.4) was higher. Mauder et al. (2013) recommended that a minimum percentage of 70% originating from the target area is required to enable the calculation of flux footprint contributions originating from one or more target areas, and indicated that this threshold can vary depending on the user's requirements. To avoid losing too much data, the threshold was selected as 60% for f c + f e . Based on this criterion, we decided to filter the data according to the wind direction ranges which are highlighted in pink in Figure A1.

A2. Tarpaulin Experiment
Due to the fact that CO 2 uptake was observed during the non-growing season with the crop field being completely bare soil and the grass in the edge area growing actively, the significant effect of the grass photosynthesis during the non-growing season was confirmed by covering the grass in the edge area near the EC system. In order to provide further insight into the sink strength of the grass during the non-growing season, a 5-day experiment was conducted from 21 to 25 May 2019. The grass immediately to the northwest of the EC system was completely covered by tarpaulins in order to eliminate the effect of grass photosynthesis on EC-measured NEE. Therefore, the sink strength of the grass could be roughly determined by comparing the NEE before and after the tarpaulins were in place using Equation 10. The GPP value of grass was estimated to be between 25 and 40 μmol m −2 s −1 .

Data Availability Statement
The data set of eddy-covariance, flux-chamber, and biometeorological variables used in this study is available in Zenodo at https://doi.org/10.5281/zenodo.7241474. Figure A1. Half-hourly flux footprint contributions (f c and f e ) during the study period calculated using the two-dimensional Flux Footprint Prediction (FFP) model (Kljun et al., 2015) for the crop area (a and b), edge area (c and d), and the total of the two areas (e and f) for the west and east fields, respectively. The pink colored bars are the two wind-direction ranges selected for filtering the data (CO 2 , N 2 O, and CH 4 fluxes) for the east and west fields (50-130° and 210-330° for the east and west fields, respectively). In the case of the CH 4 fluxes, it was to minimize the impact from the ditch even though no flux footprint correction was made.