Sampling took place on several days between 18 November and 11 December 2014 to allow processing of all samples within 24 h. Separate manual bilge pumps were used on each farm to collect 3-liter samples in 5-liter buckets from below slatted floors, pooling several subsamples from different positions to give the final sample. Air and slurry temperatures were registered at or close to the positions where slurry was sampled using a SAF-T-LOG^® HACCP ThermoMeter with a 1.4-meter probe and an accuracy of 0.4°C (ThermoWorks, Lindon, UT). Upon return to the laboratory slurry samples were stored outside until the following day (mean night temperatures between 0 and 7°C).

Slurry processing for determination of CH₄ production rates largely followed the procedure described by Elsgaard et al. [16]. Three-gram portions of each slurry material were transferred to eight 28 mL test tubes while flushing the headspace with N₂ following the Hungate approach [17]. Each test tube (subsample) was immediately closed with butyl rubber septum and crimp seal and placed on ice to temporarily arrest methanogenesis while completing sample preparation. Two subsamples were shaken vigorously for 1 min to release dissolved CH₄ and then sampled as described below for gas chromatographic analysis; this information was later used as background when calculating rates of CH₄ production during incubation. The other six subsamples were incubated at a temperature close to the temperatures recorded in slurry pits at the respective farm units.

The first batch of samples was incubated in a thermo-gradient incubator [18]; due to technical problems subsequent incubations were done using water baths operated at temperatures of approximately 10 and 20°C, respectively. The exact average temperature of water baths was certified with data from immersed temperature loggers (Hobo Pendant Temperature Data logger; Onset Computer Corp., Bourne, MA). An incubation time of 17 h was used based on the results of Elsgaard et al. [16].

Around 0.5 h before end of incubation up to 3 mL N₂ was added to the headspace to ensure sufficient gas volume for sampling. By the end of incubation samples were shaken to release dissolved gases, and then a 10 mL glass syringe was used to determine headspace volume at atmospheric pressure. Then a 3 mL sample of the headspace gas was transferred to a 6 mL Exetainer (Labco Inc., Lampeter, UK) pre-equilibrated to atmospheric pressure with N₂ (i.e., the vials were pressurised for analysis). Methane concentrations were determined on an Agilent 7890 gas chromatograph (GC) with CTC CombiPal autosampler (Agilent, Nærum, Denmark). For CH₄ analysis the GC had a 2 m backflushed pre-column with Hayesep P connected to a 2 m main column with Poropak Q. The main column was connected to a flame ionization detector (FID). The carrier gas was N₂ at a flow rate of 45 mL min⁻¹. The FID was supplied with 45 mL min⁻¹ H₂, 450 mL min⁻¹ air and 20 mL min⁻¹ N₂. Temperatures of injection port, columns and FID were 80, 80 and 200°C, respectively. The method detection limit for CH₄ was 0.2 μL L^-1. Observed concentrations ranged from 20 to 7000 μL L^-1; the detector response was linear over this range (r² = 0.999) as determined by standards prepared from a reference gas with 47,500 μL L^-1 CH₄ (AGA; Copenhagen, Denmark).

The measured CH₄ production rates were corrected to the exact temperature of slurry pit or ring channel at the time of sampling using the equation: ln(k2k1)=−(EaR)(1T2−1T1) (1) where k₁ and k₂ are the measured and corrected CH₄ production rate (mg CH₄ kg^-1 VS h^-1), respectively, E_a is activation energy (81 J mol^-1 [16]), R is the universal gas constant (8.314 J K^-1 mol^-1), and T₁ and T₂ are the temperatures (K) during laboratory incubation and in the slurry pit, respectively.

Slurry pH and electrical conductivity were measured using a pH/conductivity meter (CyberScan PC 300, EUTECH Instruments, Landsmeer, Netherlands). Slurry dry matter was determined by drying of approx. 10 g slurry fresh wt. subsamples at 105°C for 24 h. Slurry VS was determined by incineration of the dried material at 450°C for 5 h.

An estimate of degradable VS (VS_d) in the slurry materials was needed for model calculations (see below). Samples collected in slurry pits are characterised by an unknown degree of degradation, and therefore data from the literature representing fresh excreta, such as those derived by Sommer et al. [14], could not be used. Instead an aerobic assay was adopted in which VS_d was estimated from the ratio between short-term CO₂-C production during aerobic incubation and total organic carbon (TOC) in each slurry sample. Total organic carbon (g C kg^-1 fresh wt.) was analysed in triplicate by a cuvette test LCK 387 (DR 3900, HACH Lange; Düsseldorf, Germany) using a standard method (EN 1484). For determination of VS_d, 5 g slurry samples were surface-applied to sandy loam soil packed in 100-cm³ cylinders to a bulk density of 1.2 g cm^-3, and with soil moisture adjusted to 40% water-filled pore space. Preliminary tests showed that aerobic degradation of slurry VS would predominate under these assay conditions. The samples were incubated in a Respicond VI respirometer (Nordgren Innovation AB, Bygdeå, Sweden) at 20°C for 14 d where potential CO₂ evolution was determined by hourly measurements of conductivity in alkaline traps. The CO₂ accumulated over time (Y_t, g C kg^-1 fresh wt. slurry), corrected for background emissions from the soil, was used to estimate the asymptotic maximum (Y_max) with an exponential model: Yt=Ymax(1−e−kt)+y0 (2) where k is a rate constant (h^-1), t is time (h), and y₀ represents the offset on the y axis which may include degassing of carbonates dissolved in the slurry. Y_max (g C kg^-1 fresh wt. slurry) was determined by curve fitting in SigmaPlot 11.0 (Systat Software Inc.), but disregarding the 0–12 h period. Then VS_d (kg) was calculated from total VS (kg) and the ratio between maximum CO₂-C evolved and TOC in the slurry: VSd=YmaxTOCVS (3)

For comparison with experimental results, CH₄ production rates were calculated using the algorithm proposed by Sommer et al. [14]: Ft=(VSd+0.01VSnd)e(lnA−EaRT), (4) where F_t is CH₄ production rate (mg CH₄ kg^-1 VS h^-1), VS_nd (kg) is the remaining fraction of total VS which is virtually nondegradable during in-house storage, and E_a and lnA (mg kg^-1 VS h^-1) are Arrhenius parameters (units of E_a, R and T as in Eq 1). The model thus assumes that degradation of VS_nd is 100-fold slower than the degradation of VS_d. The model parameters (VS_d, E_a and lnA) used by Sommer et al. [14] to describe storage of fresh excreta are shown in Table 2, together with parameter estimates for slurry in pits derived from this study.

Methane production rates were also calculated using a new parameterisation based on experimental data. An activation energy (E_a) of 81 kJ mol^-1 was adopted from Elsgaard et al. [16] who found no significant difference in the temperature response of a cattle slurry, a pig slurry, fresh digestate and stored digestate over the temperature range 5–35°C. The frequency factor of the Arrhenius equation, A, is related to substrate quality and methanogenic potential and therefore unique to each material. Individual estimates of lnA for each slurry material were calculated by rearranging Eq 4: lnA=ln[Ft(VSd+0.01VSnd)]+EaRT, (5) hence estimates of lnA were not related to total VS, but only to the fraction of VS (i.e., VS_d + 0.01VS_nd) that was considered to be the substrate for methanogenesis.

Individual characteristics of pig and cattle slurry, including CH₄ production rate, were compared by t tests following transformation when required to achieve normal distribution and homogeneity of variance [19]. Model sensitivity to parameter estimates derived from experimental results was evaluated using a sensitivity ratio (SR), which calculates the relative change in model output, i.e., predicted CH₄ production rate, for a given deviation in parameter estimate [20]. Here, parameter ranges of lnA, VS_d and slurry temperature corresponding to 95% confidence limits were used: SR=(y+95%C.L.−y−95%C.L.x+95%C.L.−x−95%C.L.)∙(xobsyobs), (6) where y is CH₄ production rate in cattle or pig slurry, and x the parameter evaluated.

In eight of the 39 slurry samples collected for this study the DM content was less than 50%, or more than 200%, of the DM recorded in batches of slurry delivered to Thorsø Biogas Plant during the previous year (S3 Table). These eight samples were deemed unrepresentative and excluded from the estimation of CH₄ emissions from pits with pig and cattle slurry. Methane production rates of the remaining 31 samples (Table 4) were corrected to ambient temperature using Eq 1 (Materials and Methods). The difference between temperatures of slurry pits and incubations ranged between -3.9 and +3.3°C; the maximum relative correction of observed CH₄ production rates was 35%.

Histograms of the rate distributions for pig and cattle slurry are shown in Fig 1. Shapiro-Wilks tests for normality were accepted for both slurry types. Mean CH₄ production rates observed with cattle slurry were around five times lower than rates observed with pig slurry. This was partly explained by the lower storage temperature in cattle houses with passive ventilation, but degradability of VS in cattle excreta was probably also lower, as indicated by VS_d (Table 3). For pig slurry a negative relationship between time since the last emptying and CH₄ production rate was indicated, but it was not significant (p = 0.27, n = 18).

The laboratory-based CH₄ production rates observed in this study may be compared with rates derived from the national inventory of agricultural GHG emissions [23]. Here daily excretion of VS by pigs and cattle, and the emission of CH₄ from manure management per head per year, is reported (Table 5), and based on this information CH₄ emissions per kg VS of 0.032 and 0.015 kg CH₄ kg^-1 VS from pig and cattle slurry, respectively, can be estimated. In the present study daily CH₄ emission rates per kg VS were determined. Assuming a retention time in slurry pits of 15 and 30 d for pig and cattle slurry, respectively [14], total emissions from slurry pits of 0.030 and 0.011 kg CH₄ kg^-1 VS were estimated which are only sligthly lower than the estimates of total CH₄ emissions from manure management derived from the national inventory. This agreement suggests that the estimates of CH₄ emissions from manure management in the national inventory (including emissions from both confinements and storage facilities) are at a realistic level. The fact that CH₄ emissions from slurry pits observed here were only slightly lower than total estimated emissions from manure management is evidence that the proportion of CH₄ emitted from slurry pits is substantial, and that possibly total CH₄ emissions from pits and outside storage tanks are currently underestimated.

Sommer et al. [14] estimated the degradability of VS in fresh excreta at 0.89 and 0.46 kg VS_d kg^-1 VS in pig and cattle slurry, respectively. These values can be related to the default values for B₀ (i.e., the maximum CH₄ producing capacity of VS excreted; B₀ is also referred to as biochemical methane potential, BMP) proposed in the IPCC methodology ([5]; Annex 10A.2) which are 0.45 m³ CH₄ kg^-1 VS for pigs, and 0.24 m³ CH₄ kg^-1 VS for dairy cattle: At normal temperature and pressure (NTP), 1 m³ CH₄ gas is equivalent to 0.503 kg CH₄-C, and assuming a 60:40 molar ratio between produced CH₄ and CO₂ during B₀ measurement [24], this would correspond to a loss of 0.838 kg C m^-3 CH₄. Using the observed proportions of C in VS, i.e., 0.44 kg C kg^-1 in pig slurry and 0.42 kg C kg^-1 VS in cattle slurry, the B₀ of 0.45 m³ CH₄ kg^-1 VS for pigs corresponds to a VS degradability of 0.86 kg kg^-1 VS, and the B₀ of 0.24 m³ CH₄ kg^-1 VS for cattle corresponds to a VS degradability of 0.48 kg kg^-1 VS. Thus, pools of VS_d in pig and cattle slurry defined by Sommer et al. [14] are largely equivalent to B₀ values as defined in the IPCC methodology.

The slurry collected in pits was partly degraded at the time of collection, and therefore characteristics of fresh excreta did not apply. Instead an estimate of VS_d was obtained using a 14-day biodegradation assay to monitor CO₂-C evolution; results and curve fits are shown in the online Annex (S2 Fig, S3 Fig). Maximum CO₂-C (y_max in Eq 2, Materials and Methods) was related to TOC as an estimate of VS_d in individual slurry samples (Eq 3, Materials and Methods). The aerobic assay was preferred partly because of the shorter time required compared to anaerobic batch incubation for determination of B₀, and partly because of the complications associated with determination of B₀ [25–27]. It is well accepted that both aerobic degradation and anaerobic degradation of organic matter follow first-order degradation kinetics, but with different specific reaction constants [28]. Lesteur et al. [26] reviewed several methods for estimating anaerobic biodegradability of an organic substrate and concluded that VS degradation during a 5 d aerobic incubation as determined by oxygen (O₂) uptake and/or CO₂ evolution was in good agreement with a 21 d anaerobic incubation. Ponsa et al. [29] also found a strong correlation between aerobic and anaerobic stability indices for municipal solid waste materials. On the other hand, the current manure materials differed widely in DM content and soil infiltration after surface application in the VS_d assay, and further method development is probably needed to optimise the determination of VS_d.

The results of VS_d averaged 0.51 kg VS_d kg^-1 VS for pig slurry and 0.33 kg VS_d kg^-1 VS for cattle slurry (Table 3); this was, respectively, 43 and 28% lower than the VS_d concentrations in fresh excreta as defined by Sommer et al. [14] (cf. Table 2). These results suggested that significant VS degradation had already occurred during the short-term storage in slurry pits.

An E_a value of 81 kJ mol^-1 was adopted from Elsgaard et al. [16] which was much lower than the value of 112.7 kJ mol^-1 derived by Sommer et al. [14] from three different slurry storage experiments. The storage experiments used by Sommer et al. [14] ranged in duration from a few days and up to one year, and hence factors other than temperature could have influenced the relationship. For example, Petersen et al. [30] calculated tentative E_a values of only 21–25 kJ mol^-1 for CH₄ emissions across winter and summer storage experiments with pig slurry, and it was concluded that depletion of degradable VS during summer storage probably resulted in underestimation of the response to higher temperatures. Other models of CH₄ emissions from manure, e.g. [31,32], have used a value of 63 kJ mol^-1 derived from a number of different studies covering a temperature range from 15 to 60°C. In contrast, the E_a value reported by Elsgaard et al. [16] was derived from complete temperature response profiles of individual manure materials and digestates, and representing a temperature range (5 to 35°C) relevant for manure storage, which indicates that this is currently the most robust estimate available for the temperature response of CH₄ production in livestock slurry during storage.

The lnA values used by Sommer et al. [14] were also very different from those determined experimentally in this study. It should, however, be noted that Sommer et al. [14], due to limited availability of data for parameterization, fitted lnA to produce the same annual emission as the IPCC methodology. The parameter lnA reflects a potential for CH₄ production that is influenced by chemical and biological characteristics of the manure material (livestock category, age, and adaptation of the methanogenic microbial community). In the present study lnA was derived for each slurry sample using Eq 5 (cf. Materials and Methods), and the observed lnA averaged 31.3 and 31.2 g CH₄ kg^-1 VS h^-1 for pig and cattle slurry, respectively (Table 2). In comparison, the lnA values observed by Elsgaard et al. [16] in pig slurry and beef cattle slurry after storage for several months were 31.1 and 33.3 g CH₄ kg^-1 VS d^-1, corresponding to 27.9 and 30.1 g CH₄ kg^-1 VS h^-1. The pig and cattle slurry analysed by Elsgaard et al. [16] had been collected during at least six months, and so the lower values of lnA compared to samples from slurry pits probably reflected the more advanced stage of decomposition.

The response of predicted CH₄ production rates to uncertainties in parameter estimates were evaluated by calculation of sensitivity ratios (Eq 6, Materials and Methods) for each of the parameters lnA, VS_d and slurry temperature (Table 6). In each case the 95% confidence limits were selected as upper and lower boundaries of parameter uncertainty. Predicted CH₄ production rates were only moderately sensitive to uncertainties in the estimation of VS_d or slurry temperature, but dramatically affected by uncertainty in the estimation of lnA. This confirms that lnA must be determined experimentally for slurry representing a given livestock category and production system, whereas the precision required is smaller for VS_d. This is illustrated in Fig 2 where the observed lnA or VS_d for individual slurry samples were substituted by the average observed value for lnA (Fig 2A) or VS_d (Fig 2B). Clearly, deviations between predicted and observed values were large when using average values of lnA for pig and cattle slurry, whereas the adoption of average VS_d rather than individual values had little effect on the prediction. This suggests that adoption of a typical VS_d estimate for a given livestock category and production system may be acceptable if combined with observed CH₄ production rates, which allows calculation of lnA for individual slurry samples. This further implies that, with a representative set of slurry samples from a given livestock category and production system, it is possible to derive a robust estimate of mean lnA with confidence limits which can be used in scenario analyses.

The current IPCC methodology for estimating CH₄ emissions from slurry pits under animal confinements relies on very basic emission factors. On-farm verification of this source is extremely difficult, and an estimation method linking CH₄ production rates to quantifiable slurry properties would be an attractive alternative (Fig 1). The approach adopted in this study, corresponding to a Tier 3 method in the IPCC terminology, may represent such an alternative for estimating current CH₄ emissions from slurry below animal confinements. Furthermore, the method could help compare the mitigation potential of contrasting management practices, and effects of manure treatment technologies such as anaerobic digestion.

Observed CH₄ production rates were well described using the empirical model with experimentally derived parameters for VS_d, slurry temperature in the pit, an independent estimate of E_a [16], and lnA values calculated for individual slurry samples (Fig 2B). This is not a prediction model for estimating CH₄ emissions from a wider range of slurry materials, but rather a generalisation of observed CH₄ production rates that will represent a given livestock production system, as defined by livestock category, feeding, housing design, and manure management. The information required for individual slurry samples include CH₄ production rate, temperature of slurry in the pit at sampling, and total and degradable VS. Our results indicate that from this information a robust estimate of CH₄ emissions from a given source may be obtained. The number of slurry samples needed in each case will depend on the diversity of production systems and variability of slurry characteristics.

It was stated above that precise estimation of VS_d is less critical for the parameterisation of Eq 4 to characterise CH₄ emissions from slurry pits for a given livestock category. However, if model parameters are to be used for scenario analyses, the loss of VS and VS_d over time is still important, since prediction of CH₄ emissions on a daily basis also requires an estimate of daily VS loss. Carbon in VS is lost as both CH₄ and CO₂, and the proportions of CH₄ and CO₂ can vary depending on storage conditions. For example, significant aerobic degradation of carbon in VS to CO₂ may take place near the slurry-air interface, as demonstrated by Møller et al. [33]. Patni and Jui [34] also concluded that aerobic degradation was responsible for declining VS concentrations in the top layer during storage of cattle slurry. Significant degradation of carbon in VS to CO₂ may also be inferred from numerous slurry storage experiments reporting CH₄:CO₂ ratios of 0.1–0.3, e.g. [35–38]. Factors such as design of slurry pits, ventilation and retention time will all influence the exposure of slurry to atmospheric oxygen and, presumably, the balance between CO₂-C and CH₄-C emitted from slurry pits.

There is further evidence that the CH₄:CO₂ ratio of gases emitted from stored slurry declines with decreasing temperature [33,35]. This would be consistent with a recent report that temperature sensitivity of methanogenic communities is higher than that of ecosystem respiration, i.e., 0.93 and 0.65 eV, respectively, corresponding to E_a values of 89 and 63 kJ mol^-1, which implies that CH₄:CO₂ ratios will decline with temperature [39].

An attempt was made to assess proportions of CH₄ and CO₂ emitted assuming VS_d of 0.89 and 0.46 kg kg^-1 VS in fresh excreta from pigs and cattle, and retention times in the pit of 15 and 30 d for pig and cattle slurry, respectively [14]. Using the observed mean slurry temperatures in pig and cattle slurry with 95% confidence limits (Table 3), and the revised Arrhenius parameters from this study (Table 2), the daily loss of total VS and VS_d was calculated for different proportions of CH₄ and CO₂. Specifically, CH₄/(CH₄ + CO₂) ratios of 0.05, 0.1, 0.3 and 0.6 were used, corresponding to 5, 10, 30 or 60% of carbon in VS being emitted as CH₄, and the rest as CO₂.

Total residual VS calculated for each CH₄/(CH₄ + CO₂) ratio are shown in the top panel of Fig 3, and in the bottom panel residual concentrations of VS_d. Here, the gray hatched area represents the 95% confidence range of the experimentally determined residual VS_d, while the black and red lines represent, respectively, the average and 95% confidence limits of modeled residual VS_d. The overlapping confidence ranges then indicate the range of CH₄/(CH₄ + CO₂) ratios consistent with the observed residual VS_d concentrations. According to these plots 5–15% of carbon from pig slurry VS was emitted as CH₄, and 85–95% as CO₂. For cattle slurry 5–35% of carbon in VS degraded was emitted as CH₄, and 65–95% as CO₂. These ranges seem to confirm the results from storage experiments cited above, and it must be concluded that loss of VS as CO₂ are substantial and must be taken into account when estimating the loss of degradable VS in slurry pits. In this example, VS and VS_d in fresh excreta were not determined experimentally, and hence more work is needed to verify proportions of CH₄ and CO₂ in VS degradation products, as influenced by livestock category and storage conditions.