The effect of Static Chamber’s Base on N 2 O Flux in Drip Irrigation

Static chambers are commonly used to provide in-situ quantification of N 2 O fluxes. Despite their 10 benefits, when left in the field, the physicochemical conditions inside the chamber’s base may differ from the ambient, especially in drip-irrigated systems. This research aimed to study the effects of static chambers’ bases on water and N distribution and the subsequent impact on N 2 O fluxes under. N 2 O emissions were measured in a drip-irrigated avocado orchard for two years, using bases with a dripper at their center (In) and bases installed adjacent to the dripper (adjacent). During the irrigation/fertigation 15 season, the measured N 2 O In fluxes were greater than the N 2 O Adjecent fluxes (0.015 ± 0.003 vs. 0.006 ± 0.001 g m -2 d -1 ). In contrast, during the winter, when the orchard is not irrigated or fertilized, insignificant differences were observed between the measured N 2 O Adjecent and N 2 O In fluxes. Three-dimensional simulations of water flow, N transport, and N transformations showed two opposing phenomena (a) increased water contents, N concentrations, and downward flushing when the dripper is placed inside the 20 base, and (b) hampering of the lateral distribution of water and solutes into the most bio-active part of the soil inside the base when the base is placed adjacent to the dripper. It also showed that both “In” and “adjacent” practices underestimate the “true” cumulative flux from a dripper with no base by ~25% and ~50%, respectively. A nomogram in a non-dimensional form corresponding to all soil textures, emitter spacings and discharge rates, was developed to determine the optimal diameter of an equivalent 25 cylindrical base to be used along a single dripline. Further studies under variable conditions (soil types, wetting patterns, nutrient availabilities), rather than a single study, are needed to test the constructiveness of the suggested methodologies. and ammonium), and N 2 O emissions, we concluded that static chamber methodology, which requires the insertion of bases into the soil, underestimates N 2 O emissions when used in drip irrigation. This is an outcome of: (a) increased water contents and N concentrations, and downward flushing when the dripper is placed inside the base, and (b) hampering of the lateral distribution of water and solutes into the most bio-active part of the soil inside the base when the base is placed adjacent to the dripper. These effects can be mitigated by optimizing the chamber design. A nomogram is proposed to determine the optimal diameter of a cylindrical base to be used along a single dripline. Further study is suggested to determin the validity of the developed nomogram and the optimal insertion depth of bases based on the enclosure period. An alternative option is to develop a static chamber that does not need a base. It will take many users in many conditions (soil types, wetting patterns, variable N carbon (C) and O regimes), rather than a single study, to tell whether these methodologies are constructive.


Introduction
Static chambers are commonly used to provide in-situ quantification of N2O fluxes from soil-plant 30 systems (Clough et al., 2020). Ideally, such cambers should be as large as feasibly possible in order to capture spatial variation, where most chambers cover a surface area of 0.03 -0.25 m -2 . Commonly, static chambers are built from two separate parts: (i) bases (also known as collars or anchors) that are pushed into the ground, and (ii) chambers that are placed and sealed onto the bases during flux measurements. results mainly from nitrification and denitrification reactions, which in turn are affected by the following parameters in the soil: (a) mineral N concentration [namely, nitrate (NO3 -) and ammonium (NH4 + )], (b) WFPS as a proxy for soil aeration and gas diffusion coefficient, (c) temperature, (d) pH, (e) redox potential, and (f) carbon availability (Rabot et al., 2015;Hénault et al., 2019;Wu and Zhang, 2014). This research aimed to study the effects of static chambers' bases on water and N-forms distribution inside it 80 and the impact it has on N2O emission measurements during drip irrigation. We used both field measurements and three-dimensional (3-D) simulations of flow and transport in order to test the effect of the base diameter and its location relative to the dripper lateral on N2O emissions.

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Nitrous oxide (N2O) fluxes were measured over a two-year period in a drip-irrigated avocado orchard.
The orchard is located near Kibbutz-Yasur in Western Galilee, Israel. The soil at the site is a Vertisol (58% clay dominated by montmorillonite) (Nemera et al., 2020). The climate at the site is Mediterranean, characterized by a relatively long dry season (April -October) requiring irrigation and a distinct rainy period during the winter (November -March). The trees are planted 3.5m apart on ridges (1.6m wide, 90 0.4m high), with 6m between rows. Each row of trees was irrigated with a set of two driplines (laterals), located 0.9m apart along both sides of the trees, with 0.5m spaced 1.6 L h -1 drippers (UNIRAM, Netafim).
From April through November, the orchard was fertigated every other day, using treated wastewater enriched with an ammonium sulfate nitrate solution (NH4:NO3 = 3:1), maintaining 50 -70 mg-N L -1 in the fertigation solution.

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From June 2018 through June 2020, N2O fluxes were measured at mid-morning using accumulation static chambers that were installed at 12 random locations in the avocado orchard. At each location, two chamber bases were inserted, one with a dripper at its center (In) and one adjacent to the dripper (adjacent) (Fig. 1). The bases were made from opaque polyvinylchloride (PVC) rings, 10 cm high and 19 cm internal diameter (ID, surface area of 283.5 cm 2 ). The rings were inserted to a depth of 6-8 100 cm two weeks prior to the start of the sampling campaign and remained in the soil for the duration of the experiment. The chambers were built from a 20 cm sewer PVC cup (volume of 3119 cm 3 ), equipped with a vent (3 mm Swagelok bulkhead union with a 12 cm long coiled copper tube, 1.5 mm i.d.), covered with a bubble reflective foil and a rubber skirt to ensure sealing with the base. Fluxes were measured in realtime by circulating the headspace in the static gas chamber via Teflon tubes into a Fourier-transform 105 infrared spectrometer (FTIR; Gasmet DX4000, Gasmet Technologies, Finland). During the enclosure period, N2O concentrations were recorded every five seconds, each measuring point represents an average of 50 reads. Nitrous oxide fluxes (q) [g cm -2 sec -1 ] were calculated based on the linear slope, representing the increase in N2O concentration throughout a 4 to 8 min enclosure time (Eq. 1). The Pearson's correlation coefficient (r 2 ) was calculated for the linearity of the slope, and readings were 110 accepted when r 2 was >0.70. [

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saturated conductivity, Ks, shape parameters, α and n, the saturated, θs, and residual, θr, values of water content, θ), was implemented here for the local description of the constitutive relationships for unsaturated flow. Based on previous studies (e.g., Russo et al., 1997;Russo and Bouton, 1992), it is assumed here that each of the VG parameters is a second-order stationary, statistically anisotropic, random space function, characterized by a constant mean, and a two-point covariance. Parameters of the 130 latter, the variance and the correlation length-scales, were adopted from Russo and Bouton (1992). Grainsize distribution data was obtained by the laser diffraction method (Eshel et al., 2004) from 0.3 m-segments of five soil cores extending to a depth of 1.2 m. The data were used to estimate the local-scale VG parameters by an optimization procedure. For more details see Russo et al. (2020). Mean values of the VG parameters were estimated using the soil texture-based procedure suggested by Mishra et al. (1989). Details of the 135 generation of the 3-D, cross-correlated realizations of the spatially heterogeneous VG parameters are given in Russo et al. (2006). Mean values and coefficients of variation (CV) of the resultant VG parameters are given in Table 1 of Russo et al. (2020). The numerical grid used for the generation of the 3-D VG parameters' field, was modified in order to account for the application of water by the drip irrigation system and for the geometry of the ridges. For more details, see Russo et al. ( 2020).

Quantification of the flow and the transport
Considering water and N extraction by plant roots, water flow and solute (NH4 + , NO3 -, and Cl -) transport in the 3-D, unsaturated, spatially heterogeneous flow system were simulated employing numerical solutions of the 3-D Richards equation and the 3-D single-region, advection-dispersion equation (ADE), 155 respectively. Following Russo et al. (2015), the flow model was modified to account for irrigation by drippers. The iterative procedure described in Russo et al. (2006) was employed in order to determine the size of the time-dependent ponding area that may develop around the drippers at the soil surface during an irrigation event. Furthermore, following Russo et al. (2020), the sink term representing water uptake by the plant roots, which appears on the right-hand side of the Richards equation, was modified to 160 account for the effect of the oxygen availability on water uptake. The maximization iterative (MI) approach proposed by Neuman et al. (1975) was adopted here in order to calculate water uptake by the plant roots and, concurrently, actual transpiration rate, τa(t).
Following Russo et al. (2013), the ADE was modified to account for N transformations and uptake by plants' roots in the soil-water-plant-atmosphere system. In addition, the competition between Cland 165 NO3and its effect on the extraction of N by the plant roots, and the inhibition of nitrification induced by Clwere taken into account. For more details, see Russo and Kurtzman (2019). The uptake of NO3and NH4 + by the plants' roots was also calculated by a MI approach described by Eq. 6 in Russo et al. (2013).
Where z is the proportion of nitrified nitrogen emitted as N2O (in this study z = 0.006), and NA is the actual areal nitrification rate (mg-N m -2 d -1 ).

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Details of the flow and the transport equations and the numerical schemes employed to solve them are given elsewhere (Russo and Kurtzman, 2019;Russo et al., 2013).

Implementation
Meteorological data collected in the Yasur orchard were used to estimate the reference evapotranspiration, ET0(t), using Penman-Monteith method. Potential evapotranspiration rates, εtp(t) = εp(t) + τp(t) (where ε: evaporation, τ -transpiration), were estimated from the ET0(t) data using the timedependent crop coefficients actually used in the Yasur site. Assuming that the wetted soil surface area of the ridge is completely covered by the trees' canopy, a negligibly low soil evaporation rate was adopted for the surface area of the ridges, i.e., τp(t)=ετp(t). For the soil surface area between the ridges outside the rooted zone, a negligibly small transpiration rate was assumed, i.e., εp(t)=ετp(t). Actual rates of water loss 190 by evaporation, εa(t), were implemented by a MI approach described in Russo et al. (2006).
The chamber base was modeled as a cuboid whose axes coincide with the coordinates of the flow system. The center of a given chamber base is located at a given, user-controlled point, p=p(x2,x3), in the x2x3-horizontal plane; it extends vertically from the soil surface, x1=0, to the depth of x1=Zbot, and horizontally from xc21=p-δx2 to xc22=p+δx2 and from xc31=p-δx3 to xc32=p+δx3, where Zbot=0.10 m and 195 δx2=δx3 vary between 0.1 m to 0.2 m. Unit-head-gradient is specified at x1=Zbot, and no-flow is specified at x1=0 and at the vertical planes of the chamber located at xc21 and xc22 and at xc31 and xc32.
Appropriate initial conditions for the present analyses were created by considering measured  at all depths from ~5 mg L -1 at the start of the simulation to ~25 mg L -1 following 20 days. After 20 days, the concentrations remained high with minor changes. In contrast, the concentrations under a normal representative dripper with no base (NH4 + -NNo) slightly increased during the 60 days of simulation (from 5 to 8 mg L -1 ) (Fig. 3B). Unlike with the NH4 + -N concentration, nitrate-N (NO3 --N) concentrations showed a clear oscillating trend over time that corresponded to the N concentration in the fertigation solution (Fig. 3C). The amplitude of change was higher when the dripper was placed inside the base.

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Simulations with bases of variable sizes (i.e., no-base, 20, 30, and 40 cm ID) showed a clear size impact on the average NH4 + -N and NO3 --N concentrations in the top 10 cm of the soil (Fig. 5). For NO3 --N, the smaller the base ID is, the higher the deviation from ambient (no-base) concentrations.
During fertigation events, NO3 --N concentrations inside the 20, 30, and 40 cm bases increased by up to 212%, 159%, and 137%, respectively, relative to a dripper with no base around it. In contrast, between Simulated N2O emissions showed a clear oscillating trend over time, which was affected by the irrigation and fertigation regime (Fig. 6). During fertigation events, N2O fluxes from the 20 cm ID base were on average higher by 14±6% (p = 0.0345) than the fluxes from a dripper with no base, with higher fluxes from deeper parts (< 10 cm) of the soil (Fig. 4C). However, the fluxes from the 30 and 40 cm ID 280 bases were lower by 10±5% and 26±4%, respectively (p < 0.001, both). A day after a fertigation event, the fluxes from the 20, 30, and 40 cm ID chambers were -4±10%, -14±5%, and -26±3% lower than the fluxes from a dripper with no base (p < 0.008, all). More than one day after fertigation, the fluxes from the 20, 30, and 40 cm ID chambers were significantly lower than from a dripper with no base, with the greatest reduction in the 20 cm ID base (-69±3%, -42±4%, and -24±3%). Irrigation events a day or two 285 days following fertigations drastically reduced the N2O fluxes, leading to fluxes that equaled 33±6%, 67±8%, and 85±5% of the fluxes measured from a dripper with no base.
Under a dripper with no-base and a 40 cm ID base, simulated N2O emission was significantly (p < 0.05) affected by the simulated WFPS, NH4 + -N, and NO3 --N concentrations at depths of 10, 20, and 30 cm below the surface, with R 2 regression of 0.10, 0.20 and 0.99, respectively (Table SI-2 and Table   290 SI-3). In contrast, under bases with a 20 and 30 cm ID, simulated N2O emissions were significantly affected only by the simulated NO3 --N concentrations (Table SI-1, and Table SI-2, Table SI-3).
Integration of the daily simulation fluxes for a period of 60 days showed the cumulative N2O emissions from the 20 cm ID base (N2OIn) to be ~47% higher than under a base placed adjacent to a dripper (9.53 vs. 6.48 g N2O-N m -2 ) (Fig. 7B). The highest cumulative flux was measured under a dripper 295 with no-base (12.67 g N2O-N m -2 ).
Computations with the DIDAS code are summarized as reference water potential (Fig. 8A) and cylindrical base nomogram (Fig. 8B). Both are presented in a non-dimensional form corresponding to all soil textures, inter-emitter spacing, and discharge. The dimensionless matric flux potential (ref= 8ref/q, K, or water content or pressure head (h) for a given soil () and dripper discharge rate 300 (q)) decreases sharply with increasing distance between emitters (demit) or with coarsening (increasing ) of the soil texture, what counts is only their product demit, and with increasing reference depth (dref) below the emitter (Fig. 8A). At a dimensionless inter-emitter distance (demit) of about 2, the refdemit) lines flatten as the effect of the neighboring emitters weakens and the potentials converge to those generated by a single emitter (not in a dripline, dash-dotted lines, Eq. [10] in Communar and Friedman the base, NO3 -In concentrations in the top 30 cm may be 50 -64 % higher during fertigation events and up to 67% lower following irrigation or in the days following fertigation events. Inspection of the trend over time shows that, on average, NO3 -In concentrations are decreased by -19%±5% (p = 0.017) relative to a dripper with no base. This phenomenon results from the higher WFPS and the geometry of the base that limits lateral flow. As such, the water flow in the base is essentially 1D in the vertical direction, which expedites downward water flow and N transport into the subsurface. Ammonium, unlike NO3 -, is positively charged, hence readily adsorbs to the clays in the soil. Accordingly, the NH4 + In concentrations in the top 30 cm increased by 280% relative to a dripper with no base and remained higher throughout the season (p < 0.001) (Fig. 3).
Inspection of the correlations between the simulated N2O fluxes and the NH4 + and NO3 -345 concentrations show that N2O emissions were mainly influenced by the NH4 + and NO3concentrations (Table SI-2 and Table SI-3). These, in turn, were affected by the base's ID, with higher ID leading to less biases. It is known that N2O emission fluxes vary from one fertilizer event to another, even at the same site with the same fertilizer type under similar environmental conditions (Cowan et al., 2020). Here we show that an additional factor that must be accounted for is the location of the chamber's base relative 350 to the water source and the perturbation that the base has on water and N-species distribution. Simulation results show that placing the dripper inside the base may increase the N2O flux during a fertigation event by up to 52% relative to a dripper without a base. In tandem, N2O fluxes following irrigation events or in the days following fertigation may be up to 91% lower when the dripper is placed inside the base (Fig.   7A). A similar effect is observed when the chamber's base is positioned adjacent to the dripper (i.e., up 355 to 23% increase during fertigation and up to 97% decrease following irrigation events or in the days following fertigation). One should note that the modeled N2O fluxes resulted mainly from denitrification, as suggested by Eq. 3 and its relation to the WFPS (Fig. 3A, Table SI-2, and Table SI Comparison of cumulative N2O emission measured in 2018, 2019, and 2020 and the simulated cumulative emissions (over 60 days) showed the N2OIn flux to be 40% -70% higher than the N2OAdjecent 365 (Fig. 7B). It also shows that both methods underestimate the "true" cumulative flux from a dripper with no base by ~25% and ~50%, respectively. These values suggest that in addition to measurement errors due to suppression of the gas concentration gradient at the soil-atmosphere in static chambers (e.g., Venterea et al., 2020;Venterea, 2010), the impact of the camber's base on the water and N distribution provides an additional level of complexity, leading to an erroneous estimate of the true N2O flux.
The degree to which the location of the chamber's base relative to the dripper affects the N2O flux will depend on the soil properties and on the chamber's ID. Overall, an increase in the chamber's ID will decrease the above-mentioned biases by reducing the lateral flow constraints posed by the chamber's base. An indication of this process can be seen in Figure 5 for the clayey soil used in this study. Such clayey soils have a large capillary length (i.e., tens of cm long), which supports high lateral capillary flow. Accordingly, the use of a chamber with a larger ID (i.e., the simulated 40 cm or even larger) is required to reduce the negative effects of the base on the water distribution near the surface and to provide 380 a more reliable representation of the ambient fluxes around drippers.
The upper limit of the dimensionless inter-emitter distance (demit) in the depicted cylindrical base nomogram (Fig. 8B) is 2, as larger spacings are not recommended to assure overlap between the wetted bulbs (Communar and Friedman, 2010b), and that of the dimensionless reference depth (demit) is 1, as the processes leading to N2O emission are occurring at shallow depths. The sharp decreases in the 385 diameter of the equivalent cylindrical base with increasing distance between emitters or for more sandy soils (demit), is because of the relative (dimensionless) effect of the parallel strip walls (i.e., of the neigboring emitters) increases with demit. However, the dependence of dcyl/demit on the reference depth (dref) is mild, a slight increase with depth of reference locations for small inter-emitter spacings (or for clayey soils), and virtually independence for large inter-emitter spacings (or for sandy soils). This is good 390 news, as it means that an equivalent cylindrical base of chosen diameter can provide similar water contents at a range of depths below the dripper. The diameter of the equivalent cylindrical base is larger than the inter-emitter spacing (dcyl/demit > 1) for smaller inter-emitter spacing, or for fine-texture soils, and slightly smaller than the inter-emitter spacing (dcyl/demit < 1) for larger inter-emitter spacing, or for coarse-texture soils (Fig. 8B). As written above, intuitively, it is expected that since an infinitly-deep 395 cylinder confines lateral water flow in all directions, while the symmetry vertical planes between drippers along the dripline confines it only in the direction of the dripline, dcyl should be larger than demit. These results agree with the simulation results discussed above, demonstrating mostly larger differences compared to undisturbed drippers for bases of smaller diametes (Figs. 5 and 6). As a sensible inter-emitter spacing is about one capillary length, i.e., demit = 1, the recommended dcyl/demit is about one (Fig. 8B), a 400 base diameter equal to the inter-emitter spacing. Notice that the dcyl/demit (demit, dref) nomogram is independent of the dripper discharge rate (q), since according to the linearized water flow equation used for the analysis (Eq. [5] in Communar and Friedman (2010), the matric flux potential generated by the drippers (point sources) is simply proportional to q, whatever is the geometry of the flow filed.
The use of the nomogram is very simple. Suppose we want to determine the diameter of a 405 cylindrical base (dcyl) that will optimally reproduce the wetting patterns under 50 cm-spaced drippers (demit) along a single dripline in a clayey soil with a capillary length ( -1 ) of 100 cm, by requiring that the water potential (content) at a depth (dref) of 25 cm below the dripper will be the same. The dimensional emitter spacing (demit) is thus 0.5, and the vertical arrow stops at the dimensionless reference depth (dref) of 0.25 (black solid line in Fig. 8B), from which the horizontal arrow stretches to approximately 410 dcyl/demit = 1.21, i.e., the cylindrical base diameter should be larger by 21% compared to the inter-emitter spacing, about 60 cm. The soil capillary lengths ( -1 ) of most agricultural soils vary between approximately 10 cm for sandy soils to 100 cm for structureless, clayey soils with common values of 20 to 40 cm for loams and fine sands (Friedman et al., 2016). If the value of the hydraulic conductivity at saturation is known, the soil capillary length can be evaluated with the universal relationship  = 415 0.04035Ks 1/2 (in which  is measured in cm -1 and Ks in cm h -1 ) (Fig. 12 in Communar and Friedman (2010), also used in DIDAS).
The analysis used for constructing the dcyl/demit(demit, dref) nomogram is based on addressing only water flow and applying multiple simplifying assumptions of steady flow, assuming an infinitely deep confining cylinder (as opposed to the just a few centimeters insertion of the chamber base, although       dash-dotted lines on (A) represent refat the given depth below a single emitter. ref= 8ref/q, is the soil's capillary lengths, q is the emitter discharge rate.