Study location and experimental design

All measurements were conducted in experimental agricultural fields located in the low elevation (−18 m ASL) University of California Desert Research and Extension Center (DREC), Holtville, Imperial County, CA (32°N 48′ 42.6″, 115°W 26′ 37.5″) characterized by deep alluvial soils (42% clay, 41% silt and 16% sand) with 2.34% C and 0.13% N, and a pH of 8.3. The field site experienced historically typical air temperatures during the experiments conducted in 2012 and 2013 (ref. 36). Two N-fertilization studies were conducted under cultivation of a forage cultivar of S. bicolor (cv. Photoperiod LS; Scott Seed Inc.) in adjacent fields. Seed of S. bicolor were planted at 90,000 plants per ha. High-biomass-producing grasses including sorghum, sudangrass and sugarcane are the 4th most common crop type in the Imperial Valley, behind Alfalfa, pasture and vegetables37. These high-biomass-producing grasses typically receive a large fertilizer application at planting (100–150 kg N ha−1) followed by smaller applications (50 kg N ha−1) throughout the growing season, typically following harvests38,39. Fertilizers are often applied by injecting anhydrous fertilizer into the sides of furrows or by broadcasting fertilizer on the soil surface. The cheapest form of fertilizer is dry urea, but ammonium nitrate and ammonia are also used40. The fields were gravity-fed flood irrigated as needed, usually every 10 days or when soil surface volumetric water content fell below 0.10 cm3 cm−3. Gravity-fed flood irrigation is the most prevalent irrigation practice in the Imperial Valley; 70% of irrigated crops using water from the Colorado River use flood irrigation41. Both fields had beds separated by 1.5 m with 20-cm-deep furrows, and have been used for agricultural production at least since the establishment of DREC in 1912. The first experiment was conducted in a large experimental field (5.3 ha) in 2012 and the second in a smaller field (0.4 ha) in 2013.

Large-field measurements

Seed of S. bicolor were planted on 16 February 2012. Urea fertilizer treatments of 90 kg N ha−1 were applied with a 3-m-wide fertilizer spreader on 10 February, 18 June and 16 August 2012, totalling to 270 kg N ha−1 per year. Pesticides were applied at 2.1 l ha−1 on 30 April 2012 (Lorsban insecticide, Dow AgroSciences, Indiana, USA) and herbicides were applied at 0.84 kg ha−1 on 27 March 2012 (Maestro, Nufarm Americas Inc., Illinois, USA). Three harvests were conducted in 2012 on 4 June, 14 August and 12 November (corresponding to DOY 156, 227 and 317, respectively). The second and third growth periods were ratoon crops. The field was left fallow in the winter and was re-seeded on 1 April 2013. Sorghum was planted later in the season in 2013 due to late rains. In 2013, only two harvests were conducted on 19 July and 18 September 2013. Fertilizer treatments were applied on 29 May 2013 at 52 kg N ha−1 (side dressed urea), 20 June at 66 kg N ha−1 (mixture of urea–ammonium nitrate solution (32%) and 8% ammonium nitrate organic solution), and 20 August 2013 as 96 kg N ha−1 (urea–ammonium nitrate 32%), totalling to 214 kg N ha−1 per year. No pesticides or herbicides were applied in 2013.

We installed 20 soil collars on 20 February 2012, split between the northwest and southeast quadrants. In each quadrant, 10 collars were divided between two rows separated by three furrows. Soil NO x measurements were conducted throughout the growing season to assess general trends in NO x emissions (21 March, 22 May, 27 June, 7 August and 20 August corresponding to DOY 81, 143, 179, 220 and 233, respectively) and again in 2013 (9 July, 30 July, 19 August, 22 August, 28 August and 2 September corresponding to DOY 190, 211, 231, 234, 240 and 245, respectively). Due to difficulties with instrumentation, not all collars were measured on every sampling occasion.

In the first N-fertilization experiment in 2012, 10 experimental collars received an irrigation and fertilizer treatment (dissolved 20 kg ammonium nitrate-N ha−1) on 18 September 2012, while 10 control collars received irrigation only (with five collars in the southeast quadrant and five in the northwest quadrant randomly receiving fertilization). Collars were fertilized concurrent with flood irrigation of the entire field. Before the experimental fertilization, the field had not received fertilization for 32 days (at 90 kg urea-N ha−1). During this experiment, each collar was measured on 18 September, 21 September, 25 September, 5 October and 13 October (corresponding to DOY 262, 265, 269, 279 and 287, respectively). Plant canopy height next to each collar was also measured on those dates.

Small-field measurements

A similar N-fertilization experiment was conducted in 2013 in an adjacent Sorghum field (planted on 1 April 2014). We installed soil collars on 23 July 2013 in a randomized block design where the field was split into three blocks each with six rows of control, six rows of low (50 kg urea-N ha−1) fertilizer treatment and six rows of high (100 kg urea-N ha−1) fertilizer treatment. One soil collar was established within each treatment per block (nine soil collars total with three replicates per treatment). Fertilizer granules (urea) were side-injected into the furrows using a tractor, immediately followed by flood irrigation on 29 July 2013 (DOY 210). Before the experimental fertilization, the crop had not received fertilization. Soils in this field had not been fertilized since the cultivation of a previous crop 5 months before. Measurements were collected on 30 July, 7 August, 13 August and 19 August 2013 (corresponding to DOY 211, 219, 225 and 231, respectively). Plant canopy height next to each collar was also measured on those dates.

Soil NO x flux measurements

NO x chamber measurements were conducted using the static chamber technique. Soil collars (made of polyvinyl chloride with a diameter of 20 cm and height of 10 cm) were inserted 4–6 cm into the soil on the top of furrows. A custom-built chamber was set on top of soil collars and set into place using a rubber seal. The chamber was also made from polyvinyl chloride with a mixing fan mounted on the inside and reflective tape covering the outside of the chamber42. Air was pulled from the top of the chamber at 1 l min−1 and routed to a portable NO monitor (Nitric Oxide Monitor Model 410 with NO 2 converter Model 401, 2B Technologies, Colorado, USA) where depletion of O 3 is measured using UV absorbance (detection range: 2–2,000 p.p.b.; precision: ±1.5 p.p.b.; measurement rate: 0.1 Hz). This system converts all NO 2 to NO using a molybdenum converter before sending sample air to the NO monitor, therefore measurements are expressed as NO x flux (NO+NO 2 ). This technique is similar to conventional chemiluminescence analyzers; however, we found our system to be better suited to high-emission environments compared with chemiluminescence instruments in preliminary studies conducted in both field and lab settings. Soil NO x flux was calculated using the rate of increase in NO x concentration within the first 3 min of placing the chamber onto the collar. We used linear regression to determine rates of change from an average of nine points in the regression or 1.5 min of data.

Ancillary soil sampling and inorganic soil N analysis

Each flux measurement was paired with soil temperature, moisture and inorganic N measurements. Soil temperature was measured next to each collar at 2 and 10 cm depth (Fluke 51 II Thermometer (Wilmingtion, NC, USA)). A soil core (1.5 cm diameter) was extracted next to each collar following the NO x measurement (0–10 cm). The core was homogenized in a bag before removing 15 g for measuring soil volumetric water content and 2.5 g for inorganic N extraction at a 1:10 soil weight-to-solution volume ratio using 2 M KCl. Extracts were put on ice until transported back to the lab, where they were processed within 24–48 h. Samples were shaken for 1 h at room temperature, centrifuged and filtered through Whatman no. 40 filter paper (11 μm) and frozen until further processing. Filtrates were acidified and analysed by automated cadmium coil reduction for nitrate/nitrite (Seal Analytical Inc., AQ2 Discrete Analyzer (Mequon, Wisconsin). NO 3 and NH 4 are expressed in μg N g−1 dry soil.

Statistical analyses

In a comprehensive analysis of all observed NO x fluxes, nonlinear generalized additive modelling was used to assess the influence of environmental parameters on NO x flux via the GAM function in R (v.3.1.1, Vienna, Austria). The model included explanatory variables NO 3 , NH 4 , soil temperature (averaged between 2 and 10 cm depth), soil volumetric water content (averaged across 0–10 cm depth) and days since fertilization. The best-fitting parsimonious model was selected using Akaike’s information criterion. For visualization, NO x fluxes were binned according to environmental variables (days since fertilization, soil volumetric water content and soil temperature). Third-order polynomials were fitted to the relationships between binned average NO x flux and soil volumetric water content and soil temperature. A Gaussian equation was fitted to the relationship between binned average NO x flux and days since fertilization. All fitting was performed in Matlab (v.R2014a, The Mathworks, Inc. USA). Repeated measures analyses of variance were conducted independently on each N-fertilization experiment to test for significant effects of treatment (fertilized or control) on NO x emissions. Pairwise comparisons using the Bonferroni adjustment were conducted to explore differences between treatments at specific time points. NO x emissions were log transformed to meet homogeneity of variance assumptions. Analysis of variance and Bonferroni tests were performed in R (v.3.1.1, Vienna, Austria). To estimate total N released as NO x in response to treatments, we performed numerical integration via the trapezoidal method in Matlab. These integrated values are only approximate and are most likely an underestimate of total flux, as peak fluxes may not have been captured with discontinuous measurement techniques.

Regional air quality modelling

We evaluated the influence of soil NO x emissions on regional air quality using the WRF-Chem (version 2.0). The WRF-Chem model29,43 is a regional air quality model that can be used for weather forecasting and simulating gas-phase chemistry, including NO x and ozone chemistry at an hourly time step. With its nested grid capability, WRF-Chem-simulated quantities can be more easily compared with a wide range of in situ and remote sensing data collected at different temporal and spatial resolutions. A nested grid configuration was used in this study with the centre in the Imperial Valley, CA. The resolution of fine grid was 12 × 12 km and the outer domain was 36 × 36 km. Table 1 lists the model configuration options employed in this study.

Table 1 WRF-Chem configuration. Full size table

The NARR (North American Regional Reanalysis) data at 0000, 0600, 1200 and 1800 UTC were used for initializing and specifying the temporally evolving lateral boundary conditions. The US National Emissions Inventory emissions data (NEI-05; version 2) was used in the simulation as background emission (US Environmental Protection Agency, 2010). The NEI-05 data are likely a high estimate for anthropogenic NO x sources in the Imperial Valley. Previous work in Los Angeles County has shown that anthropogenic NO x sources in NEI-05 are overestimated by 32% (ref. 30). The land-use data used in this study is the US Geological Survey land-use data. Biogenic emissions of volatile organic compounds and soil NO x emissions are calculated using the Model of Emissions of Gases and Aerosols from Nature (MEGAN v2.0 (refs 44, 45)). In MEGAN, gridded emission factors are based on global data sets of four functional plant types (broadleaf trees, needle-leaf tree, shrubs/bushes and herbs/crops/grasses), where the herbs/crops/grass category has a higher emission factor compared with the other plant types46. In this version of MEGAN, soil N (NO, NO 2 and NH 3 ) emissions are a function of temperature only; production and loss of NO x within the canopy is not considered. Previously reported canopy uptake rates are low, ranging up to 3 ng N-NO 2 m−2 s−1 under high light and high NO 2 concentrations (NO 2 =5 p.p.b.)47. However, canopy uptake rates in high-emission and high-temperature environments are uncertain and require further research36,47,48,49,50. Pulse NO x emissions following fertilization events are also not considered in the model. The emission factor for agricultural soils is 6 ng N m−2 s−1 at a standard temperature of 273.15 K (ref. 46). Due to assumptions made in the satellite observations, we apply an averaging kernel to the WRF-Chem simulations to allow comparison with the space-borne OMI (described below)51,52.

Modifications to a regional air quality model

To evaluate the sensitivity of air quality to soil NO 2 sources in the Imperial Valley, we modified the strength of soil NO x emissions from irrigated agricultural land. Other land types such as surrounding urban and dry native lands were not manipulated. We elevated WRF-Chem emission rates by a factor of 10 and 64.5, resulting in simulated soil NO x emissions in Imperial Valley croplands near 20 and 129 ng N m−2 s−1, which are representative of the range in mean and median flux values collected under both average and recently fertilized conditions in the field. It is important to note that this modelling exercise simply increases emission rates and does not account for the observed nonlinear pulse NO x emission events that occur in response to fertilization.

All simulations were run for 7 days in September 2012 (23–29 September 2012), with several days as spin-up time. These simulations were compared with measurements of surface and tropospheric NO 2 columns above the Imperial Valley.

Comparing modelled and measured NO 2

Evaluation of WRF-Chem model performance was assessed through comparisons with surface and satellite observations. First, we compared modelled with measured surface NO 2 in the Imperial Valley. Surface NO 2 concentrations are measured by the California Air Resources Board at an air quality-monitoring site located 11.3 km west of DREC on 9th Street, El Centro, CA (latitude: 32.79222; longitude: −115.563). This site is not near a point source and provides representative concentrations of pollutants for the Imperial Valley. Surface NO 2 measurements are made by first reducing all NO 2 to NO using heated molybdenum surfaces and then measuring the chemiluminescent reaction of NO with O 3 (ref. 53). Comparisons between modelled and measured surface NO 2 concentration were made for all WRF-Chem model simulations (default, 10 × and 64.5 × elevated soil NO x emission). WRF-Chem model performance was assessed using linear regression and the coefficient of determination (r2). Model bias was estimated using the absolute r.m.s.e. between modelled and observed surface NO 2 concentrations.

To evaluate the model’s ability to simulate local meteorology, we compared daily average wind speed (m s−1) and air temperature (°C) measured at the El Centro air quality monitoring station and simulated by the model. Model performance was assessed using the coefficient of determination (r2) and the absolute r.m.s.e.. We evaluated local sources of NO x from biomass-burning events using MODIS images. MODIS images are publically available and were assessed for 20–29 September 2012. We also analysed meteorological data from a weather station located at DREC (managed by the California Irrigation Management Information System, www.cimis.water.ca.gov) to investigate how rainfall (mm), air temperature (°C) and net radiation (W m−2) changed during the simulation period.