Modeling nitrous oxide emissions from digestate and slurry applied to three agricultural soils in the United Kingdom: Fluxes and emission factors

Accepted Manuscript Modeling nitrous oxide emissions from digestate and slurry applied to three agricultural soils in the United Kingdom: Fluxes and emission factors Jiacheng Shen, Roland Treu, Junye Wang, Fiona Nicholson, Anne Bhogal, Rachel Thorman PII:

S0269-7491(18)32202-4

DOI:

10.1016/j.envpol.2018.08.102

Reference:

ENPO 11540

To appear in:

Environmental Pollution

Received Date: 17 May 2018 Revised Date:

7 July 2018

Accepted Date: 31 August 2018

Please cite this article as: Shen, J., Treu, R., Wang, J., Nicholson, F., Bhogal, A., Thorman, R., Modeling nitrous oxide emissions from digestate and slurry applied to three agricultural soils in the United Kingdom: Fluxes and emission factors, Environmental Pollution (2018), doi: 10.1016/ j.envpol.2018.08.102. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Evapotranspiration

N2O Emission

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Biogas plant and digesters

Manure

CH4

Runoff Water table Leaching

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Digestate fertilizer

Soil Sorption &storage Groundwater

Biogas plant and digestate used as fertilizers at livestock farm

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Modeling Nitrous Oxide Emissions from Digestate and Slurry Applied to Three

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Agricultural Soils in the United Kingdom: Fluxes and Emission Factors

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Jiacheng Shen1, Roland Treu1, Junye Wang1*, Fiona Nicholson2, Anne Bhogal2, Rachel

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Thorman3 1

Faculty of Science and Technology, Athabasca University, 1 University Drive, Athabasca,

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Alberta T9S 3A3, Canada

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ADAS Gleadthorpe, Meden Vale, Mansfield, Nottinghamshire, NG20 9PF, UK 3

ADAS Boxworth, Battlegate Road, Boxworth, Cambridge, CB23 4NN, UK

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* Corresponding author Email: [email protected] Tel: +1 7803944883

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Highlights •

Modification of the UK-DNDC model to include application of digestate to soil

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Simulations of soil moisture and N2O fluxes using the Digestate UK-DNDC model

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Calculations of N2O emission factors (EFs) for two organic fertilizers

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Development of two-factor models for estimating N2O EFs

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Abstract Organic fertilizers, such as digestates and manure, are increasingly applied in agricultural

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systems because of the benefits they provide in terms of plant nutrients and soil quality.

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However, there are few investigations of N2O emissions following digestate application to

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agricultural soils using process-based models. In this study, we modified the UK-DNDC model

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to include digestate applications to soils by adding digestate properties to the model and

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considering the effect of organic fertilizer pH on soils. Using the modified model, N2O emissions

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were simulated from two organic fertilizers (digested food waste and livestock slurry) applied to

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three farms in the United Kingdom: one growing winter wheat at Wensum (WE) and two

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grasslands at Pwllpeiran (PW) and North Wyke (NW). The annual cumulative (not excluding

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control emission) N2O emissions were calculated using MATLAB trapezoidal numerical

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integration. The relative errors of the modeled annual cumulative emissions to the measured

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emissions ranged from -5.4% to 48%. Two-factor models, including linear, exponential and

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hyperbola responses, correlating total N loading and soil clay content to calculations of N2O

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emissions and N2O emission factors (EFs) were developed for calculations of emission fluxes

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and EFs. The squares of the correlation coefficients of the measured and two-factor linear

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modeled emissions were 0.998 and 0.999 for digestate and slurry, respectively, and the

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corresponding squares of correlation coefficients of EFs were 0.998 and 0.938. The two-factor

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linear model also predicted that the EFs increased linearly with decreasing clay content and the

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maximum EFs for digestate and slurry were 0.95 and 0.76% of total N applied, respectively. This

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demonstrates that the modified UK_DNDC is a good tool to simulate N2O emission from

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digestate fertilizers and to calculate the EFs in the way of a TIER 3 for the UK.

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Key words: Digestate; DNDC model; Emission factor; Linear model; Nitrous Oxide; Slurry.

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1. Introduction

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Global climate change with its atmospheric temperature increase caused by greenhouse gas

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emissions (GHG) is a widespread concern. The major greenhouse gases include nitrous oxide

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(N2O), methane (CH4), and carbon dioxide (CO2). Nitrous oxide has a higher global warming

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potential over 100 years of approximately 190-270 times that of CO2 (Zhang et al., 2016). It has

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been estimated that about 70% of the total N2O emitted in the UK originates from agriculture, of

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which 36% is directly emitted from agricultural soils following nitrogen (N) fertilizer addition,

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both synthetic and organic (Brown et al., 2016).

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Organic fertilizers, such as livestock manures, composts, digestates and food wastes, have

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been routinely applied to agricultural soils to supplement or replace manufactured fertilizers. In

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addition, organic fertilizers can improve soil physical properties (e.g. water-holding capacity)

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and reduce soil erosion (Bhogal et al., 2009; Bhogal et al., 2011; Chambers et al., 2003; Wang,

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2014). Food wastes and manure can be directly applied to agricultural soils or digested under

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anaerobic conditions to produce biogas and digestates as a by-product. This process can reduce

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up to 99% of pathogens and odors generated from the raw organic material. Since the ideal

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carbon/nitrogen (C/N) ratio for carbohydrate (glucose) conversion to CH4 is approximately 16:1

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(weight: weight), (Shen & Zhu, 2016a; Shen & Zhu, 2016b), it is often necessary to mix

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lignocellulosic material with a high C/N ratio, such as corn stover and wheat straw, with the low

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C/N ratio manure and food wastes (referred to as anaerobic co-digestion) in order to improve

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CH4 yield during digestion. However, since a high amount of C in the form of CH4 is removed

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from the process, the final digestates discharged from the co-digestion process still have a low

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C/N ratio (Shen & Zhu, 2017a; Shen & Zhu, 2017b). According to the National Society for Clean Air and Environmental Protection’s (NSCA,

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London, UK) report (NSCA, 2006), 30 million tons of dry wastes are generated annually in the

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UK, with the potential use as feedstock through anaerobic digestion (AD). The AD of source-

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segregated food waste is predicted to be an area of significant growth in the UK, with around 5

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Mt of the 7 Mt of food waste currently sent to landfill each year predicted to be available for

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digestion by 2020 (DECC, 2011). The number of AD plants in the UK increased by 34%

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between 2012 and 2013, and the corresponding treating capacity increased by 51% (WRAP,

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2014). This generated over 2 million tons of digestate, equivalent to a total of 92,000 tons of N

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entering UK soils in 2013. Compared to the numerous investigations of N2O emissions from

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manufactured fertilizers, such as urea (CH4N2O), ammonium nitrate NH NO

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sulfate (NH₄)₂SO₄, only a few experiments have been performed to estimate N2O emissions

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from agricultural soils where digestates are applied, particularly those derived from food waste

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feedstocks (Alburquerque et al., 2012; Baral et al., 2017; Nicholson et al., 2017). Moreover, few

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models have been developed which aim to predict N2O emissions following organic fertilizer

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and ammonium

addition, such as digestates, applied exclusively to agricultural soils (Wang, 2014).

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Due to the high cost of field and laboratory experiments, the simulation and prediction of

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GHG emissions

using mathematical models, such as the Denitrification-Decomposition

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(DNDC) model, has been undertaken for more than 20 years. The DNDC model was initially

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developed as a process-orientated simulation model for N2O, CH4, and CO2 emissions from

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agricultural soils in the U.S. A. (Li et al., 1992). The original DNDC model have been modified

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to various extension models such as PnET-N-DNDC (the photosynthesis-evapotranspiration), 5

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Crop-NDDC, Wetland-DNDC, Forest-DNDC, NZ-DNDC, Forest-NDNC Tropica, EFEM-

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DNDC (GIS-coupled economic-ecosystem), BE-DNDC, DNDC-Europe, DNDC-Rice, Mobile-

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DNDC, DNDC-CSW (Canadian Spring Wheat), Landscape-DNDC, NEST-DNDC (the Northern

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Ecosystem Soil Temperature), and Manure-DNDC (Gilhespy et al., 2014). While the DNDC

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simulates GHG emissions from crop soils, Manure-DNDC is to add a submodel to estimate GHG

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and ammonia emissions of the manure life cycle operations across livestock farm facilities

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including feedlot, compost, lagoon and anaerobic digester (Li et al., 2012). Therefore, Manure-

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DNDC has same functions of conventional fertilization as that in the DNDC, such as farmyard,

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slurry, and spread, but it does not include new organic fertilizers, such as digestates and bio char.

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The DNDC required parameters, such as soil properties, fertilizer properties and loading, crop

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types, types of agricultural management, and nitrogen concentration in the atmosphere etc,

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whereas the Manure-DNDC requires extra parameters of the manure life cycle operation, such as

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animal types and number, their age distribution, forage nutrients and, surface areas of each unit.

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In order to adapt it to the UK agricultural management, climate and soil conditions, the DNDC

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model has been modified by adjustment of the model parameters and formula, and it is termed

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the UK-DNDC model (Wang et al., 2012; Brown et al., 2002).

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The conversion efficiency of N fertilizers applied to agricultural soils to N2O is commonly

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evaluated using an emission factor (EF; g-N emitted (g-N applied)-1). The Intergovernmental

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Panel on Climate Change (IPCC) has a default Tier 1 EF of 0.01 (1%) for N2O emissions from

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agricultural soils following the application of organic fertilizers, such as livestock manure,

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compost, sewage sludge and digestates (Eggleston et al., 2006). However, some studies have

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shown EFs to vary greatly, depending on regional factors, as well as organic fertilizer types, soil

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types and application methods. For example, Burger et al. (Burger et al., 2016) observed that the

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IPCC Tier 1 approach underestimated the actual EFs by 74% in the 2nd year in alfalfa plantations

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and 90% in the 5th year calculated from the cumulative annual N2O fluxes, whereas Bell et al.

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(Bell et al., 2015) found that the UK EFs in most cases were much lower than 1%. Since the UK-

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DNDC model can simulate annual N2O emissions from a range of agricultural soils treated with

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various fertilizers, it provides an additional tool to estimate N2O EFs. Furthermore, the default

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IPCC Tier 1 EF is based on an assumption that the N2O fluxes increase linearly with increasing

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N input to soils regardless of spatial and temporal variability. However, recent investigations

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have shown that the responses of N2O fluxes to applied inorganic fertilizers may also be

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exponential (Cardenas et al., 2010) and hyperbolic (Breitenbeck & Bremner, 1986). Kim et. al.

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(Kim et al., 2013) developed three corresponding response models with respect to N loading,

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however, spatial variability was not considered in these models. Therefore, the IPCC have

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suggested that more complex process-based models should be developed for the Tier 3 approach,

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typically considering heterogeneously spatial and temporal variability of livestock and vegetation

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in local conditions (Eggleston et al., 2006).

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In this study, our objectives were (1) to simulate water filled pore space (WFPS) and N2O

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fluxes from two organic fertilizers (food-based digestate and slurry) applied to soils at three UK

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farms using the modified UK-DNDC model, called Digestate UK-DNDC model; (2) to calculate

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the N2O EFs of the two organic fertilizers applied to the soils using the simulated data; (3) to

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develop two-factor models of emission fluxes correlated to N loading and soil texture (i.e. clay

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content), and regress the measured data for the linear model constants; and (4) to predict N2O

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fluxes and EFs at three sites with increasing N loading.

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2. Materials and methods 7

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2.1. Field sites Three farms in the UK were selected for measurements of N2O emissions, located at:

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Pwllpeiran (PW), Ceredigionshire, Wales, North Wyke (NW), Devon, and Wensum (WE),

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Norfolk, England. The site locations, their soil characteristics, annual average climate data, and

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crop rotation are shown in Table S1. During the experiments the WE site was planted with

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winter wheat, whereas NW and PW were permanent grasslands. Two organic fertilizers in the

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form of food-based digestate and livestock slurry (cattle slurry at PW and NW, pig slurry at WE)

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were applied to the three sites WE, PW and NW on Feb. 22nd, May 2nd and April 18th,

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respectively (Table S1) by two methods: broadcast and bandspread. There were three replicates

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of each treatment. No synthetic N fertilizer was applied to the experimental soils. Due to

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abundant precipitation in the UK (Brown et al., 2002), no irrigation occurred at the three sites

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during the experimental period. The N contents of the two fertilizers used at the three sites are

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presented in Table S2. Full site characteristics, treatment and management details can be found

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in Nicholson et. al. (Nicholson et al., 2017).

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2.2. Experimental methods

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The N2O emissions were measured by Nicholson et al. (Nicholson et al., 2017) from the

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above field sites in the UK using the static chamber technique (5 chambers per plot). The gas

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samples were taken after the chamber headspace was closed for at least 40 min. At least 30

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measurement occasions took place over a year with sample timings weighted so that 50% of

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samples were taken in the 6 week period after digestate and slurry applications. Samples were

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analyzed by gas chromatography (GC) using an Electron Capture Detector and an automated

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sample injection system (Perkin Elmer Clarus 580 GC & TurboMatrix 110 auto headspace

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sampler). The measured daily fluxes were calculated using an assumption of linear gas

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accumulation within a chamber’s headspace (Chadwick et al., 2014). Linearity was checked on

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each sampling occasion using a time series of gas samples from 3 chambers.

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2.3. Modification of the UK-DNDC model

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primary

soil/climate,

crop

vegetation,

decomposition,

and

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denitrification/nitrification. The soil/climate sub-model calculates profiles of soil temperatures

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and WFPS. The crop vegetation sub-model simulates daily crop growth, N uptake by vegetation

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and root respiration driven by climate and soil conditions, and predicts biomass yields. The

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decomposition sub-model contains four soil C pools: litter, humus, humads, and microbial

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biomass. A fixed decomposition rate and a fixed ratio of C to N are given to each component in

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each pool. The denitrification/nitrification sub-model predicts the contents of nitrate, nitrite,

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ammonium, and organic residues in soils as well as the emissions of N2O, CH4, CO2 and

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ammonia (NH3). Input parameters required by the UK-DNDC model include daily climate data,

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soil properties (e.g., texture, pH, bulk density, microbial activities, etc.), vegetation (e.g., crop

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type) and management practices (e.g., tillage, irrigation, fertilizer applications, manure

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amendment, planting, harvest, etc.).

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sub-models:

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Similar to the DNDC model, the original UK-DNDC model also contains four interacting

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Nitrous oxide is predominantly generated from soil by the microbial processes of both

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nitrification and denitrification (Firestone and Davidson, 1989), which can be expressed by two

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sequential chemical reactions (Li, 2000):

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Nitrification

↓ NO

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NH 4+ → H 2 NOH → NOH → NO2− → NO3− ↓ N 2O

(1)

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Denitrification NO3− → NO2− → NO → N2O → N2

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(2)

The nitrification process requires oxygen. The oxygen requirements from NH4+ to

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can be expressed, respectively, as:

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3 O 2 → NO 2− + 2 H + + H 2 O 2

NO 2− +

1 O 2 → NO 3− 2

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and

When the oxygen availability is limited during nitrification,

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(3)

(4)

cannot be nitrified further

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NH 4+ +

via

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to

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Wrage et al., 2001). Denitrification is anaerobic. In addition to the oxygen free environment for

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denitrification, either the soluble nitrogen content (

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content in N-fertilized soils can influence denitrification (Firestone & Davidson, 1989).

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Therefore, nitrifying and denitrifying micro-organisms require soluble oxygen and soluble

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substrates of C and N to maintain their growth and metabolic activities.

) in non-fertilized soils or the soluble C

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in reactions (Equations 3 and 4), and a side pathway to N2O occurs (Goreau et al., 1980;

Activity of denitrification is driven by soil redox potential (Eh), temperature, moisture, pH and substrates, such as the dissolved oxygen, dissolved C and N oxides (i. e.

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and N2O). However, a part of total soil biomass is available for the denitrification. Therefore, the

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denitrification biomass in the UK-DNDC model needs to be modified to reflect the pH and

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organic matter content of digestate (Wang. 2014). The denitrification biomass in the top soil

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layer in the original UK-DNDC model is formulized as follows (Li et al., 2000):

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,

, NO,

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denitrifier = 0.02 * RBO * FD * ave_anvf * Fde * Fph * Fsm * SOC

(5)

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where denitrifier is the denitrification biomass, RBO (= 0.02) is the fraction of microbial biomass

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to total organic C (dimensionless), FD (= 0.05) is the ratio of denitrifier biomass to microbial 10

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biomass (dimensionless), ave_anvf is the average anaerobic volumetric fraction (dimensionless),

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SOC is the soil organic C (kg-C m-3), and Fde, Fph, and Fsm are the soil C, soil pH and soil

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moisture factors, respectively. Nitrogen oxides including

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partitioned into aerobic and anaerobic microsites. The changing rates of N oxides per hour in the

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DNDC model are expressed as:

)

(

)   

F pH * denitrifier * TE

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where

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− where d _ N j Ok ) is the conversion rate of an N oxide (kg-N hour-1),

(

and

− 3

+ NO

− 2

+ NO + N 2 0

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Nw = NO

, NO, and N2O are

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(

d _ N jO

 N j Ok− m N j Ok * N j Ok−  = Ff +  N j Ok max Nw 

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− k

and

(6)

(7) denotes N2O, NO,

, respectively, Ff is the water factor (dimensionless), which ranges greatly from

0.005 to 10, depending on the type of N oxides and soil water influences such as flooding and

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− irrigation, N j Ok max is the maximum specific growth yield of a N oxide (kg-C (kg-N)-1), mNjOk is

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the maintenance coefficient of an N oxide (kg-C (kg-C.hour)-1), FpH, and TE are the pH and

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temperature factors, respectively, and denitrifier is the denitrifier biomass (kg-C m-3). Digestate

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is a ‘new’ type of organic fertilizer with some specific properties which will influence the

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nitrification and denitrification processes described in the UK-DNDC model. For example,

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digestates possess a lower C/N ratio compared to undigested, raw feedstock. Therefore, a new

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function describing the C/N ratios was added to the UK-DNDC model. In this study, a C/N ratio

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of 3 for digestate was used (Shen & Zhu, 2017a; Shen & Zhu, 2016b). Thus, the C loadings from

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digestate and slurry were calculated based on the experimental N loading applied to the soils, and

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shown in Table S2. In addition, a factor Al was added to Equation (5) to describe the influence of

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digestate pH and C/N ratio to denitrification Equation (8):

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denitrifier = 0.02 * RBO * FD * ave_anvf * Fde * Fph * Fsm * SOC * Al

(8)

The Al is a linear function of digestate pH and C/N values, f (pH × C/N). The coefficient can be

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optimized from the calibration data sets of N2O emissions (the dataset measured by(Nicholson et

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al., 2017) at the three UK field sites) through statistical evaluations using the correlation

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coefficient (r) and RMSE. It should be mentioned that the digestate modification would not

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affect other functions of the original UK-DNDC since Al is the input parameter for digestates

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only. The UK-DNDC version is named as Digestate UK_DNDC.

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2.4. Model calibration and validation

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For the two organic fertilizers (food-based digestate and livestock slurry) and the two

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application methods (surface broadcast and bandspread) at the three sites, we used datasets with

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the higher N2O emissions for model calibration i.e. both digestate and slurry applied by surface

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bandspreading at WE, surface broadcasting of digestate and bandspreading of slurry at PW, and

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the bandspreading of digestate and surface broadcasting of slurry at NW. The three sites with the

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two types of fertilizers have a typical of features of soils, climate and vegetation in the UK. At

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each site and for each fertilizer type, the dataset not used for calibration was used for model

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validation i.e. if the surface broadcast data was used for calibration the bandspread data was used

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for validation and vice versa.

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The model was examined against the data measured by Nicholson et al. (2017) using three

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statistical parameters: the square of correlation coefficient (r2), root mean square error (RMSE)

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and average relative errors (RE) calculated by Equations (9 to 11), respectively: 2

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 n   ∑ (Pi − Pm ,i )(M i − M m,i )  r 2 =  ni =1 ∑ (Pi − Pm,i )2 (M i − M m,i )2

(9)

i =1

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n

RMSE =

n

∑ 262

RE =

i =1

i =1

i

2

i

(10)

n

(M i − Pi )

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∑ (P − M )

Mi n

(11)

where the subscripts i and m denote the index of experimental point and mean value,

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respectively, P is the value predicted by the model, M is the corresponding measured value, and n

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is the number of measured points.

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2.5. Emission factors of nitrous oxide

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The IPCC Tier 1 default EF is 0.01, i.e. 1% of the total N applied to soils (including organic fertilizers) is lost as N2O-N (IPCC, 2006). The EF is defined as ( %) =



!! "# !" $ !" %"

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× 100%

(12)

The definition and assumption of the IPCC suggest that the net emission flux is proportional to

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the N loading applied to soils )* )+ ,, - ./01 =

23× !! "# 455

(13)

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and that emission fluxes increase linearly with increasing N loading, in which the slope is the EF

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and the intercept is a controlling emission flux in the linear equation because the EF is constant.

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However, the IPCC method does not consider spatial and temporal variability, impact of climate

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(Kim et al., 2013; Laville et al., 2011; Wang et al., 2012) and potential differences in the N

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source e.g. different organic fertilizers.

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2.6. Development of the two-factor models of N2O flux and EF correlating N loading and soil

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texture It has been found that N2O fluxes can increase linearly or exponentially with increasing N

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loading (Cardenas et al., 2010), or exhibit hyperbolic change (Breitenbeck & Bremner, 1986).

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Kim et al. (Kim et al., 2013) summarized the corresponding equations of flux and EF as follows:

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Linear response:

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Flux

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EF

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Exponential response:

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Flux

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EF

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y (N ) − y (control ) =a N

y = a exp (bN

EF =

)

y (N ) − y (control N

) = a [exp (bN ) − 1)]

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EF =

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y = aN + b

N

(14)

(15)

(16)

(17)

and hyperbola response:

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Flux

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EF

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where y denotes the emission flux (g-N ha-1y-1), N denotes the experimental N loading (g-N ha-

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1 -1

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These equations only describe the relationships between N2O emission and N loading, and take

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no account of spatial and temporal variability e.g. due to soil type and climate (Laville et al.,

aN b+N

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y = y0 +

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EF =

y (N ) − y (control N

)=

(18)

a b+N

(19)

y ), and a and b are the regression constants (g-N ha-1y-1 and dimensionless), respectively.

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2011). We extended the above equations to include a variable of soil types, as an example proxy

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for spatial variability so that these two-factor equations have more widely applications for

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regression of experimental emission data, calculations of fluxes and EFs than one-factor models.

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Soil clay content was chosen as a representative soil characteristic because it is one of the main

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soil properties and its trend is monotonic changing as same as emissions (i.e. N2O emissions

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continuously increase with decreasing clay contents). Thus, the N2O emission from agricultural

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soils is a function of both N loading and soil clay content. For simplification, we assumed that

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the constants a and b in Equations (14-19) respond linearly to the clay contents:

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a = a1c + a 2

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b = b1 c + b 2

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(20) (21)

where a1, a2, b1, and b2 are the regressed constants (dimensionless in all), and c is the soil clay

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content (%). Substituting Equations (20 and 21) into Equations (14-19) produces

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Linear response:

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Flux

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EF

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Exponential response:

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Flux

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EF

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and hyperbola response:

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y = a 1 Nc + a 2 N + b1 c + b 2

EF = a 1 c + a 2

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(23)

y = (a 1 c + a 2 ) exp (b1 cN + b 2 N )

EF =

(22)

(24)

(a1c + a2 )[exp(b1cN + b2 N) −1]

(25)

N

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315

Flux

y = y(control) +

316

EF

EF =

(a1c + a2 )N

(26)

b1c + b2 + N

a1c +a 2 b1c + b2 + N

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(27)

317

3. Results and Discussion

319

3.1. Simulations of WFPS

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318

Moisture content is a key factor influencing N2O emissions from agricultural soils. Davidson

321

et al. (Davidson et al., 2000) found that nitrification was the main N2O production process at a

322

low WFPS, whereas at a higher WFPS, denitrification was predominant. The maximum N2O

323

emission occurred at a WFPS of 65%. However, Dobbie & Smith (Dobbie & Smith, 2001)

324

reported that in the UK the highest N2O emissions frequently occurred at a WFPS greater than

325

60%, as a result of denitrification.

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In addition to the prediction of GHG emissions, the Digestate UK-DNDC model also

327

simulates WFPS profiles in agricultural soils. The Digestate UK-DNDC model treats the soil as a

328

series of distinct horizontal layers. Each layer is assumed to be homogeneous so that soil

329

physical properties in each layer, such as porosity, bulk density and hydraulic parameters, as well

330

as the soil temperature and WFPS, are either volume-averaged or mass-averaged variable across

331

all layers. Thus, the UK-DNDC model calculates the WFPS values in layers of 5, 15, and 30 cm

332

from the soil surface. In the following text, only WFPS values from the 0-5 cm layer were used

333

to fit the measured WFPS data, as this was measured over 0-10 cm.

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Figure 1 shows the measured and modeled WFPSs at all three sites; WE, PW, and NW.

335

Generally, the simulated WFPS at all three sites were in reasonable agreement with the measured 16

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data according to RMSE.

The average measured WFPS values for three sites during the

337

experimental period were 0.67, 0.48, and 0.29 for NW, PW and NW, respectively. The

338

corresponding modeled WFPS values were 0.63, 0.46, and 0.30, and relative errors were 6.25%,

339

4.92%, and -3.61%. The average WFPS at WE was the lowest among those at the three sites

340

because (1) WE is a sandy loam soil texture (sand content 78% and clay content 11%), and both

341

PW and NW are clay loam textures (sand content 36% and clay content 28% for PW, and sand

342

content 32% and clay content 38% for NW), while sand has stronger water permeability than

343

clay so that WE had the lowest average WFPS; (2) WE had the lowest precipitation among three

344

sites (91 cm y-1, 203 cm y-1, and 147 cm y-1 for WE, PW, and NW, respectively). The largest

345

precipitation peaks at the three sites, such as March 4 in WE, June 8 in PW, and April 25, Sept.

346

25 and Nov. 25 in NW are consistent with the corresponding WFPS value peaks (Figure 1).

347

3.2. Simulations of N2O emissions following organic fertilizer applications

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The measured and simulated daily N2O emissions using the Digestate UK-DNDC model are

349

shown in Figure 2. The annual measured and modeled cumulative N2O fluxes (including the

350

control emissions) from the digestates and slurries applied to the three sites were calculated

351

(Figure 3). However, the measured N2O fluxes are not daily continuous over time. The measured

352

N2O fluxes were measured 1-3 times/week while the modeled N2O fluxes were calculated daily.

353

Thus, the different integration methods used for the measured fluxes can lead to some

354

differences in the annual cumulative emission. Here we used the MATLAB trapezoidal

355

numerical integration (Figure 3). All the N2O fluxes measured at WE were higher than modeled,

356

but the opposite trend was observed at PW and NW. This is because the Digestate UK-DNDC

357

model produced many sharp and narrow peaks of higher emission fluxes at WE, which

358

contributed to a smaller fraction of the total fluxes, whereas the measured points at WE formed

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several broad peaks when trapezoidal numerical integration was employed (Figure 2 a, b, c, and

360

d). In the lower emission flux situation at PW and NW, the model points produced either broader

361

peaks or higher peaks (Figure 2 e, f, g, h, i, j, k, and l). In the DNDC model, N2O emissions from

362

denitrification were driven by rainfall. The narrow peaks produced by the Digestate UK-DNDC

363

could be explained because WE has a much lower rainfall and a higher sand fraction in the soil

364

than at PW or NW.

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The average measured annual cumulative N2O emissions for the two fertilizer types were

366

2352 (N-g ha-1 y-1) for digestate and 1432 for slurry at WE, 944 for digestate and 842 for slurry

367

at PW, and 781 for digestate and 673 for slurry at NW. The corresponding average modeled

368

annual cumulative N2O emissions for the two application techniques were 1223 (relative error

369

48% of the measured value) for digestate and 1056 (N-g ha-1 y-1) (26%) for slurry at WE, 994 (-

370

5.4%) for digestate and 1055 (-25%) for slurry at PW, and 1064 (-36%) for digestate and 946 (-

371

41%) (N-g ha-1) for slurry at NW. The highest measured annual average cumulative fluxes of

372

N2O emissions (average of surface broadcast and bandspread) were: WE (2352 and 1432 g-N ha-

373

1

374

g-N ha-1 y-1) (Table 1). The reasons for highest emissions at WE among the three sites are likely

375

to be (1) the highest N loading (207 and 98 kg-N ha-1 y-1 occurred at WE for digestate and slurry

376

versus 107 and 67 kg-N ha-1 y-1 in PW and 160 and 77 kg-N ha-1 y-1 in NW) among the three

377

sites; (2) the soil pH value at WE was highest among the three sites (6.7 versus 5.1 and 5.5 of

378

PW and NW) because a higher soil pH favorites denitrification (Li et al., 1992) and a low pH

379

strongly inhibits soil microbial nitrification and denitrification activities (Wang et al., 2013).

380

Another possible explanation for the difference in emissions between the sites is the increase in

381

soil clay content (11, 28, and 38% for WE, PW, and NW). Because soil clay can adsorb N2O, the

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y-1 for digestate and slurry, respectively), PW (944 and 842 g-N ha-1 y-1), and NW (781 and 673

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increase in soil clay content may reduce the N2O emission (Li et al., 1992). This phenomenon

383

supports the one assumption in the DNDC model: increase of soil clay content will result in N2O

384

emission decrease. (Li et al., 1992).

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The square of the correlation coefficients (r2) between the measured and modeled values for

386

calibration were higher than those for validations (Table 1). The correlation coefficients of the

387

calibration datasets ranged from 0.403 (digestate bandspread at PW (Figure 2b)) to 0.779

388

(surface broadcast slurry at PW (Figure 2c)), whereas the validation datasets ranged from 0.185

389

(slurry bandspread at PW (Figure 2h)) to 0.615 (digestate bandspread at WE (Figure 2j)). The

390

average square of the correlation coefficient (0.549) at WE was higher than those at NW and PW

391

(0.388 and 0.305, respectively), which can be attributed to the higher average annual cumulative

392

N2O fluxes (2352 and 1432 g-N ha-1 y-1 for digestate and slurry, respectively) at WE than at PW

393

(944 and 842 g-N ha-1 y-1) and NW (781 and 673 g-N ha-1 y-1) (Table 1). Li (Li, 2000) also

394

observed the same phenomenon. This is because the capture of the higher flux peaks by the

395

model made a greater contribution to the correlation coefficients than the lower flux peaks.

396

However, some simulations indicated lower correlation coefficients, for example, 0.185 for

397

slurry bandspread at PW and 0.265 for digestate broadcast at NW. Validation cases usually have

398

lower correlation coefficients than calibration cases. In addition, daily N2O emissions are

399

statistically dependent (Giltrap et al., 2010). This means the daily emissions are related to events

400

of temperature and precipitation occurred around at the measured day, not only the measured

401

day. The emissions caused by microbial activity may be delayed by several days due to

402

precipitation and temperature events. For example, there is a lag period of bacteria from

403

dormancy to activity when they are stimulated by external factors such as an increase in

404

temperature. Thus, it is often difficult to accurately match daily emission peaks with

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precipitation and temperature events as the definition of correlation coefficient (data matched

406

day by day). Although the pattern of daily emissions, particularly the peak emissions, are

407

valuable in devising mitigation strategies (e.g. when and which fertilizer is applied to soils), the

408

seasonal or annual cumulative N2O emissions are important for the purposes of inventory

409

compilation and determination of EFs because many national statistical and census data are

410

based on annual amounts. For instance, the global C exchange trade is based on the annual

411

greenhouse gas emissions rather than the amount of emission peak.

412 413

3.3. Comparisons of the modified UK-NDNC model with the original UK-NDNC model for all calibration cases

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We also compared the simulated results of the Digestate UK-NDNC model of all calibration

415

cases with the original UK-NDNC model (Table 2). The statistical parameters, (r2) and average

416

relative error indicated that simulations of the Digestate UK-NDNC model are much better than

417

the original UK-DNDC model. The average squares of correlation coefficients for six cases are

418

0.548 for the modified UK-DNDC model and 0.095 for the original UK-DNDC model,

419

respectively. The corresponding REs based on absolute values are 23.8% for the Digestate UK-

420

DNDC model and 445% for the original UK-DNDC model. It is clear that the fitness of N2O

421

emissions from two fertilizers have been improved greatly due to introduction of pH to the

422

model. However, it should be noted that the N2O from the slurry was improved too. This is

423

because the pH value and C/N ratio of the slurry are inputted into only the soil pH and the C

424

pools in the original UK-DNDC. The soil becomes a buffer of the slurry influences. In this study,

425

although our modification was directed to the digestate, it could be useful for slurry applications.

426

It can be seen that the N2O emissions from the slurry at the grassland sites (PW and NW)

427

were better than that at the arable (WE) using the original UK_DNDC. This may be explained

428

that the original UK_DNDC was calibrated more at the grassland sites than at the arable (Brown

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et al., 2002; Wang et al., 2012). Therefore, a calibration should be taken when the UK-DNDC is

430

used for new soil, crop and weather conditions. It should be mentioned that the UK_DNDC

431

versions, including Digestate UK_DNDC, are based on the original DNDC framework.

432

Therefore, the Digestate UK_DNDC has similar functions as the original DNDC but was mainly

433

calibrated using in the UK climate conditions. However, the Digestate UK_DNDC is also used

434

for other countries after some modifications and calibrations (Yadav and Wang, 2017).

435

3.4. Estimates of N2O EFs using modeled data

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We also calculated the modeled EFs for the two organic fertilizers and application methods

437

using Equation (12) (Figure 3). The control modeled N2O emissions required in Equation (12)

438

were calculated to be 528 for WE, 461 for PW, and 749 (N-g ha-1 y-1) for NW using the

439

MATLAB trapezoidal numerical integration. The measured EFs were reported by (Nicholson et

440

al., 2017) (Figure 3). All the modeled EF data lie within the error bar ranges of the measured

441

EFs, except for digestate at WE and slurry broadcast at PW. Both the measured and modeled

442

EFs were less than 1% (Figure 3d-f), which suggests the IPCC Tier 1 default EF overestimates

443

the total emissions from the organic fertilizers

444

3.5. Applications of the two-factor model of N2O flux and EFs for the experimental data

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The annual cumulative N2O fluxes measured for two organic fertilizers applied by two

446

application techniques at three sites with respect to N loadings were regressed in Equation (22)

447

using the MATLAB multiple variable regression program. The regressed constants a1, a2, b1, b2,

448

R2 (0.999 and 0.877 for digestate and slurry, respectively), F-test, and p values (1.73x10-5 and

449

0.0111 for digestate and slurry, respectively) for the two organic fertilizers are shown in Table 3.

450

According to Equation (23) and the obtained constants a1 and a2, the EFs ranged from 0.72 to

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0.16 for digestate, and 0.61 to 0.23 for slurry when increasing the soil clay contents from 11% to

452

38%. Kim et. al. (Kim et al., 2013) proposed a three-phase model for N fertilizer applied to soils.

453

In their model, the first phase is the linear response of N2O emission to low N input in which the

454

N2O emissions are primarily controlled by competition between plants and microbes for the

455

available N; the second phase is the exponential response to medium N input in which N

456

additions exceed optimal N plant uptake rates, and microbes in soil quickly utilize excess N and

457

then generate a lot of N2O; the third phase is a steady-state in which N additions are beyond the

458

capacity of soil microbes to take up and utilize N, and the N2O emission becomes stable.

459

According to this model, the N loadings at all three sites were in the first phase because the

460

higher R2 and lower p values for N2O emissions linearly with increasing N loading for both

461

fertilizers. The three dimensional plots and their corresponding contour plots of N2O flux

462

against N loading and clay content are shown in Figure 5. The shapes of contour lines of

463

digestate in Figure 5 are the same as those of slurry. With increasing clay content, the N2O flux

464

decreased continuously for both organic fertilizers at the same N loading, but the N2O flux

465

increased with increasing N loading at the same clay content. A similar result was reported in

466

which N2O emissions increased with clay content occurred at an annual rainfall of about <750

467

mm, but at a rainfall >750 mm, N2O emissions decreased with clay content (Sylvester-Bradley et

468

al., 2015). Therefore, some combinations of these factors were not tested, and need to be studied

469

since statistical regressions are dependent on the selection of the parameters.

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470

Theoretically, the maximum or minimum value of the dependent variable in the two-factor

471

model can be obtained to solve the two first partial differential equations (Equations 28 and 29)

472

of the model (Equation 22):

22

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∂y = a 1 N + b1 ∂c

(28)

474

∂y = a1 c + a 2 ∂N

(29)

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473

Because the constants a1 and b1 obtained are negative (Table S3), while N is positive, Equation

476

(28) is negative. So the flux (y) will decrease with increasing clay content at the same N loading.

477

But the constant a2 and clay content are positive, Equation (29) is positive at lower clay contents,

478

so the N2O flux will increase with increasing N loading. Otherwise, the N2O flux will decrease at

479

higher clay contents because Equation (29) is negative. Letting Equation (29) equal to zero, the

480

transition points from N2O flux increase to N2O flux decrease are at 45.7% and 54.4% of clay

481

contents for digestate and slurry, respectively. At the two points (a = 0 (Equation 14)), there is no

482

net emission. At the clay content equal to zero, Equations (22 and 23) become

483

Flux

484

EF

485

where the maximum N2O fluxes will increase with increasing N loading and the maximum EFs

486

will be achieved to be 0.95% and 0.76% for digestate and slurry, respectively. This provides

487

further evidence that the IPCC Tier 1 default overestimates emissions from organic fertilizers. To

488

examine the regression effect, the modeled N fluxes and EFs were calculated using Equations

489

(22, 23) with the constants obtained in Table 3. The obtained data were compared with those

490

measured (Figure S1). The squares of correlation coefficients of the fluxes were 0.999 and 0.939

491

for digestate and slurry, respectively, and the corresponding squares of the correlation

492

coefficients of EFs were 0.992 and 0.686, which indicates that the two-factor linear models

493

(Equations 22 and 23 fitted the measured data very well.

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(30) (31)

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EF = a 2

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y = a 2 N + b2

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In addition to N oxides as nutrient required for soil microbes, carbon in soils is usually a

495

growth-limiting nutrient for microbes in soils because carbon is required for denitrification (Shen

496

et al., 2018). Although the two-factor model consider N loading and soil property, addition of C

497

in fertilizer to soils does not take account, which can be represented by the C/N ratio of a

498

fertilizer. Therefore, we further developed the three-factor linear model from the two-factor

499

linear model (Equation 22), which added three variable the ratio of C/N of an organic fertilizer.

500

Thus, the three-factor linear model can applied to the situation at different N loadings, soil types,

501

and types of organic fertilizers. In current studied situation, all the measured N2O emissions in

502

six sites and two organic fertilizers can be regressed with respect to N loading, soil clay content,

503

and C/N ratio of fertilizer in the three-factor model. Assuming the constants a1, a2, b1, and b2 in

504

Equation (22) are linearly related to the ratio of C/N of a fertilizer:

506

a 2 = f1c + f 2

507

b1 = g 1 r + g 2

508

b 2 = h1 c + h 2

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a1 = d 1r + d 2

(32) (33) (33) (34)

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where d1, d2, f1, f2, g1, g2, h1, and h2 are the regressed constants (dimensionless in all).

510

Substituting Equations (32-34) into Equations (22, 23) produce the three-factor linear model (35,

511

36):

512

Flux

513

EF

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y = d 1 Ncr + d 2 Nc + f 1 Nr + f 2 N + g 1 cr + g 2 c + h1 r + h 2 EF = d 1 cr + d 2 r + f 1 r + f 2

(35) (36)

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All the emission data with respect to N loadings, clay contents, and two ratios of C/N (3 and 2

515

for digestate and slurry, respectively) were fitted in Equation (35) using MATLAB multiple

516

variable regression program. The regressed constants d1, d2, f1, f2, g1, g2, h1, h2, and R2 were

517

showed in Table S4. It was expected that the squares of the correlation coefficients in the three

518

factor linear model should be those between digestate and slurry in the two-factor linear model,

519

i.e. higher than that of the two-factor linear model for slurry, but lower than the two-factor linear

520

model for digestate. Because four dimensional figure cannot be shown, we chosen the three-

521

dimensional plots of annual N2O fluxes (a and c), and their corresponding contour plots (b and d)

522

versus the N loading applied and soil clay contents for digestate (a, b) and slurry (c and d) at two

523

specific C/N ratios (C/N =3 (a, b) equal to the C/N ratio of digestate, and 2 (c, d) equal to the

524

C/N ratio of slurry). General speaking, the predicted emissions of the three-factor linear model

525

are somewhat lower than those of two-factor linear model comparing Figure 5 b, d with Figure 4

526

b and d. This may be attributed to combination of the lower emission data of slurry with the

527

higher emission data of digestate make the regressed results be biased toward the lower

528

emissions.

529

3.6. Predictions of N2O fluxes and EFs with increasing N loadings

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514

Agricultural management, such as optimizing fertilizer application rates to soils, can reduce

531

N2O emissions from agricultural soils. We carried out scenario analyses for two organic

532

fertilizers in three sites with respect to increasing the fertilizer loading from the experimental

533

loadings by 1.5 and 2 times (Table S2) although for digestate these were in excess of rates that

534

would be allowed in practice (the maximum permitted N loading rate in the UK is 250 kg-N ha-1

535

y-1). The predicted annual cumulative N2O fluxes increased with increasing loading rate for the

536

two fertilizers at the three sites (Figure 6). The lowest flux increase occurred for slurry applied at

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NW, and the next lowest flux increase for slurry applied at PW. The projected N2O fluxes with

538

respect to increasing N loading were fitted to the linear model (Equation 14). The fitted constants

539

a and b for scenario analysis and linear lines are shown in Table S5 and Figure 6, respectively.

540

All the squares of correlation coefficients were larger than 0.929 (Table 3), which indicates the

541

N2O emission increased linearly with increasing N loading according to the data projected by the

542

Digestate UK-DNDC model. All the projected constants (EFs) (Table S5) were much lower than

543

0.01 (1%), with the maximum EF of 0.66% for slurry applied at PW, and the minimum EF of

544

0.17% for digestate applied at NW.

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4. Conclusions

In this study, the UK-DNDC model was modified, called Digestate UK-DNDC model, with

548

properties of organic fertilizers including pH. It was then used for estimating N2O emissions

549

from food-based digestate and slurry applied to agricultural soils at the three UK sites. The

550

modeled results were in reasonable agreement with the measured data with the relative errors of

551

the UK-DNDC modeled emissions to the measured annual emissions ranging from -5.4% to

552

48%. The average squares of correlation coefficients for six cases calculated from the modified

553

UK-DNDC model (0.548) were much higher than those calculated from the original UK-DNDC

554

model (0.095), and the corresponding REs based on absolute values were 23.8% and 445%. The

555

corresponding modeled EFs for the food-based digestates and slurry were also estimated. The

556

modified model provides a method to calculate the N2O emissions and EFs of Tire 3. A two-

557

factor linear model correlating N loading and soil clay content for calculations of emissions

558

when the input data of the UK_DNDC may be limited or may not be available on a large scale.

559

EFs could fit the measured data well when input data for the Digestate UK-DNDC was lacking.

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The squares of the correlation coefficients of the measured and two-factor linear modeled

561

emissions were 0.999 and 0.938 for digestate and slurry, respectively, and the corresponding

562

squares of correlation coefficients of EFs were 0.992 and 0.686. According to the two-factor

563

model, the EFs ranged from 0.72 to 0.16 for digestate, and 0.61 to 0.23 for slurry when

564

increasing the soil clay contents from 11% to 38%. This demonstrates that the Digestate UK-

565

DNDC can estimate N2O emissions from digestate and slurry used as fertilizers and it also can be

566

used for calculation of country-specific EFs for agricultural fertilization management and Tier 3

567

GHG inventory methodology.

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Acknowledgements

This project was financially supported by Alberta Innovation and Advanced Education for

571

Campus Alberta Innovation Program (CAIP) Research Chair (No. RCP-12-001-BCAIP). We

572

thank the UK Waste and Resources Action Program (WRAP) for permission to use the

573

experimental data.

574

References

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Alburquerque, J.A., de la Fuente, C., Bernal, M.P. 2012. Chemical properties of anaerobic digestates affecting C and N dynamics in amended soils. Agriculture, ecosystems & environment, 160, 15-22. Baral, K.R., Labouriau, R., Olesen, J.E., Petersen, S.O. 2017. Nitrous oxide emissions and nitrogen use efficiency of manure and digestates applied to spring barley. Agriculture, Ecosystems & Environment, 239, 188-198. Bell, M., Hinton, N., Cloy, J., Topp, C., Rees, R., Cardenas, L., Scott, T., Webster, C., Ashton, R., Whitmore, A. 2015. Nitrous oxide emissions from fertilised UK arable soils: fluxes, emission factors and mitigation. Agriculture, Ecosystems & Environment, 212, 134-147. Bhogal, A., Nicholson, F., Chambers, B. 2009. Organic carbon additions: effects on soil bio‐ physical and physico‐chemical properties. European Journal of Soil Science, 60(2), 276-286.

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Gilhespy, S.L., Anthony, S., Cardenas, L., Chadwick, D., del Prado, A., Li, C., Misselbrook, T., Rees, R.M., Salas, W., Sanz-Cobena, A. 2014. First 20 years of DNDC (DeNitrification DeComposition): model evolution. Ecological Modelling, 292, 51-62. Giltrap, D.L., Li, C., Saggar, S. 2010. DNDC: A process-based model of greenhouse gas fluxes from agricultural soils. Agriculture, ecosystems & environment, 136(3), 292-300. Goreau, T.J., Kaplan, W.A., Wofsy, S.C., McElroy, M.B., Valois, F.W., Watson, S.W. 1980. Production of NO2- and N2O by nitrifying bacteria at reduced concentrations of oxygen. Applied and environmental microbiology, 40(3), 526-532. Kim, D.-G., Hernandez-Ramirez, G., Giltrap, D. 2013. Linear and nonlinear dependency of direct nitrous oxide emissions on fertilizer nitrogen input: A meta-analysis. Agriculture, Ecosystems & Environment, 168, 53-65. Laville, P., Lehuger, S., Loubet, B., Chaumartin, F., Cellier, P. 2011. Effect of management, climate and soil conditions on N2O and NO emissions from an arable crop rotation using high temporal resolution measurements. Agricultural and Forest Meteorology, 151(2), 228-240. Li, C., Salas, W., Zhang, R., Krauter, C., Rotz, A., Mitloehner, F., 2012. Manure-DNDC: a biogeochemical process model for quantifying greenhouse gas and ammonia emissions from livestock manure systems. Nutr Cycl Agroecosyst., 93, 163–200. Li, C. 2000. Modeling trace gas emissions from agricultural ecosystems. Nutrient Cycling in Agroecosystems, 58(1-3), 259-276. Li, C., Aber, J., Stange, F., Butterbach‐Bahl, K., Papen, H. 2000. A process‐oriented model of N2O and NO emissions from forest soils: 1. Model development. Journal of Geophysical Research: Atmospheres, 105(D4), 4369-4384. Li, C., Frolking, S., Frolking, T.A. 1992. A model of nitrous oxide evolution from soil driven by rainfall events: 1. Model structure and sensitivity. Journal of Geophysical Research: Atmospheres, 97(D9), 9759-9776. Nicholson, F., Bhogal, A., Cardenas, L., Chadwick, D., Misselbrook, T., Rollett, A., Taylor, M., Thorman, R., Williams, J. 2017. Nitrogen losses to the environment following food-based digestate and compost applications to agricultural land. Environmental Pollution. NSCA. 2006. Biogas as a Road Transport Fuel: An Assessment of the Potential Role of Biogas as a Renewable Transport Fuel, National Society for Clean Air and Environmental Protection, London, UK. Shen, J., Treu, R., Wang, J., Thorman, R., Nicholson, F., Bhogal, A. 2018. Modeling nitrous oxide emissions from three United Kingdom farms following application of farmyard manure and green compost. Science of The Total Environment, 637, 1566-1577. Shen, J., Zhu, J. 2016a. Kinetics of batch anaerobic co-digestion of poultry litter and wheat straw including a novel strategy of estimation of endogenous decay and yield coefficients using numerical integration. Bioprocess and biosystems engineering, 39(10), 1553-1565. Shen, J., Zhu, J. 2017a. Methane production in an upflow anaerobic biofilm digester from leachates derived from poultry litter at different organic loading rates and hydraulic retention times. Journal of Environmental Chemical Engineering. Shen, J., Zhu, J. 2017b. Modeling Kinetics of Anaerobic Co-Digestion of Poultry Litter and Wheat Straw Mixed with Municipal Wastewater in a Continuously Mixed Digester with Biological Solid Recycle Using Batch Experimental Data. Chemical Engineering Communications, 204(4), 501-511.

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Shen, J., Zhu, J. 2016b. Optimization of methane production in anaerobic co-digestion of poultry litter and wheat straw at different percentages of total solid and volatile solid using a developed response surface model. Journal of Environmental Science and Health, Part A, 51(4), 325-334. Sylvester-Bradley, R., Thorman, R., Kindred, D., Wynn, S., Smith, K., Rees, R., Topp, C., Pappa, V., Mortimer, N., Misselbrook, T. 2015. Minimising Nitrous Oxide Intensities of Arable Crop Products. AHDB Cereals & Oils Project Report (548). Wang, J. 2014. Decentralized biogas technology of anaerobic digestion and farm ecosystem: opportunities and challenges. Frontiers in Energy Research, 2, 10. Wang, J., Cardenas, L.M., Misselbrook, T.H., Cuttle, S., Thorman, R.E., Li, C. 2012. Modelling nitrous oxide emissions from grazed grassland systems. Environmental pollution, 162, 223-233. Wang, L., Du, H., Han, Z., Zhang, X. 2013. Nitrous oxide emissions from black soils with different pH. Journal of Environmental Sciences, 25(6), 1071-1076. Wrage, N., Velthof, G., Van Beusichem, M., Oenema, O. 2001. Role of nitrifier denitrification in the production of nitrous oxide. Soil biology and Biochemistry, 33(12-13), 1723-1732. WRAP, A. 2014. Survey of the UK Anaerobic Digestion Industry in 2013. Waste and Resources Action Programme. Zhang, Y., Niu, H., Wang, S., Xu, K., Wang, R. 2016. Application of the DNDC model to estimate N 2 O emissions under different types of irrigation in vineyards in Ningxia, China. Agricultural Water Management, 163, 295-304.

697

Table captions

698 699

Table 1 Correlation coefficients and RMSE of measured and Digestate UK-DNDC modeled values for WFPS and N2O emissions.

700 701 702 703

Table 2 Comparisons of annual N2O emissions, r2 and RE (%) of measured, Digestate UK_DNDC, and original UK_DNDC in all calibration cases

704

Table 3 Constants a1, a2, b1 b2, and statistical parameters in Equation (22)

705

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676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696

Figure captions

707 708 709

Fig. 1 The measured (symbol: square) and modeled (solid line) WFPS, and rainfall (red dot line) at WE (a), PW (b), and NW (c).

710 711 712 713 714

Fig. 2 The measured (symbol: square) and modeled (solid line) N2O emissions from in WE (a: digestate broadcast, b: digestate bandspread, c: slurry broadcast, and d: slurry bandspread), PW (e: digestate broadcast, f: digestate bandspread, g: slurry broadcast, and h: slurry bandspread), and NW (i: digestate broadcast, j: digestate bandspread, k: slurry broadcast, and l: slurry bandspread).

715 716

Fig. 3 The measured (white) and modeled (black) annual N2O fluxes and EFs at WE (a, d), PW (b, e), and NW (c, f).

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Fig. 4 Three-dimensional plots of annual N2O fluxes (a and c), and their corresponding contour plots (b and d) versus the N loading applied and soil clay contents for digestate (a, b) and slurry (c and d) using Equation (22). The data in (b) and (d) are the projected emission fluxes calculated from Equation (22).

721 722 723 724

Fig. 5 Three-dimensional plots of annual N2O fluxes (a and c), and their corresponding contour plots (b and d) versus the N loading applied and soil clay contents for digestate (a, b) and slurry (c and d) at C/N =3 (a, b) and 2 (c, d) using three-factor model (35). The data in (b) and (d) are the projected emission fluxes calculated from the three-factor model.

725 726 727 728

Fig. 6 Scenario analysis of annual cumulative N2O fluxes predicted by the Digestate UK-NDNC model (points) and linear regressions (lines) in WE (a), PW (b), and NW (c) with respect to increasing N loading. Symbol: the Digestate UK-NDNC model; Lines: linear regression. Digestate: square and regression solid line; Slurry: rhombus and regression dotted line.

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731 732

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Table 1 Correlation coefficients and RMSE of measured and Digestate UK-DNDC modeled values for WFPS and N2O emissions.

735 736

D. bandspread1 WE r2 0.773 0.615 0.692 RMSE 0.0008 16.2 15.5 A. E. 2 2276 2429 A. E. F3 2352 RE4 (%) -46.3 -49.6 PW WFPS D. broadcast1 D. bandspread r2 0.221 0.481 0.446 RMSE 0.0005 3.91 4.13 2 A. E. 936 952 A. E. F3 944 RE4 (%) 6.30 4.51 NW WFPS D. broadcast D. bandspread1 r2 0.554 0.265 0.403 RMSE 0.0004 3.3 2.94 2 A. E. 772 840 A. E. F3 781 RE4 (%) 37.8 13.2 1 Calibration dataset 2 Annual N2O emission flux (g-N ha-1 y-1)

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S. bandspread1

S. broadcast

0.392 10.2 1315

-19.7

0.495 11.2 1549 1432 -31.8

S. broadcast1 0.439 6.16 621 69.9 S. broadcast1 0.779 0.880 655 44.4

S. bandspread 0.185 13.2 1062 842 -0.66 S. bandspread 0.495 1.40 690 673 37.1

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Annual average N2O emission flux of two organic fertilizers (g-N ha-1 y-1) 4 Relative errors of modeled EFs to measured EFs

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Table 2 Comparisons of annual N2O emissions, and original DNDC in all calibration cases N2O emissions (g-N ha-1 y-1) Site Digestate Original Measured UKUKDNDC DNDC

r2 and RE (%) of measured, Digestate DNDC, r2

Digestate UKDNDC

RE (%)

Original UKDNDC

Digestate UKDNDC

Original UKDNDC

WE

D. bandspread

2429

1223

3801

0.615

0.172

-49.6

56.5

S. bandspread

1549

EP

739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757

3

2625

0.497

0.067

-31.8

69.5

1056

AC C

737 738

D. broadcast

S. bandspread

PW

936

995

4573

0.481

0.0065

4.51

388

1062

1055

6215

0.439

0.179

-0.66

485

NW

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D. bandspread

940

1064

6083

0.403

0.059

13.2

547

S. broadcast

655

946

7954

0.779

0.084

44.4

1114

759

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758

Table 3 Constants a1, a2, b1, b2, and statistical parameters in Equation (22)

a1 (%) a2 (-) b1 (%) b2 (-) r2 F value p value -4 -3 9.590x10 -13.22 966.7 0.991 176 1.73x10-5 Digestate -2.05x10 -4 -3 0.0111 -1.361x10 7.541x10 -13.16 979.5 0.873 11.5 Slurry

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769 770

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775 776 777

Fig. 1 The measured (symbol: square) and modeled (solid line) WFPS, and rainfall (red dot line) at WE (a), PW (b), and NW (c).

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Fig. 2 The measured (symbol: square) and modeled (solid line) N2O emissions from in WE (a: digestate broadcast, b: digestate bandspread, c: slurry broadcast, and d: slurry bandspread), PW (e: digestate broadcast, f: digestate bandspread, g: slurry broadcast, and h: slurry bandspread), and NW (i: digestate broadcast, j: digestate bandspread, k: slurry broadcast, and l: slurry bandspread).

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Fig. 3 The measured (white) and modeled (black) annual N2O fluxes and EFs at WE (a, d), PW (b, e), and NW (c, f).

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Fig. 4 Three-dimensional plots of annual N2O fluxes (a and c), and their corresponding contour plots (b and d) versus the N loading applied and soil clay contents for digestate (a, b) and slurry (c and d) using Equation (22). The data in (b) and (d) are the projected emission fluxes calculated from Equation (22).

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Fig. 5 Three-dimensional plots of annual N2O fluxes (a and c), and their corresponding contour plots (b and d) versus the N loading applied and soil clay contents for digestate (a, b) and slurry (c and d) at C/N =3 (a, b) and 2 (c, d) using three-factor model (35). The data in (b) and (d) are the projected emission fluxes calculated from the three-factor model.

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Fig. 6 Scenario analysis of annual cumulative N2O fluxes predicted by the Digestate UK-NDNC model (points) and linear regressions (lines) in WE (a), PW (b), and NW (c) with respect to increasing N loading. Symbol: the Digestate UK-NDNC model; Lines: linear regression. Digestate: square and regression solid line; Slurry: rhombus and regression dotted line.

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