The United Nations Framework Convention on Climate Change (UNFCCC) kick-started an international political drive to reduce emissions of greenhouse gases (GHGs) and stabilise their midterm to long-term impact on the global climate. The focus of the international community over the past 2–3 decades has been on curbing emissions of carbon dioxide (CO2), the most abundant and well-understood GHG, but it is now recognised that emissions of other GHGs such as methane (CH4) and nitrous oxide (N2O) must also be addressed in order to fulfil the goal of limiting irreversible climate change set out under the 21st Convention of Parties (COP21). Reductions in CH4 emissions in particular would be effective in reducing GHGs more quickly, given its shorter lifetime. Annex 1 parties are required to report their GHG inventories annually to the UNFCCC following the guidelines set out by the Intergovernmental Panel on Climate Change (IPCC, 2006; UNFCCC, 2014). Emissions inventories are powerful tools but they intrinsically rely on detailed knowledge of source abundance and strength, and they can therefore carry significant uncertainties. For example, uncertainties on the fossil fuel emissions from Europe and North America have been estimated to be of the order of 2 % to 5 % (Marland, 2012); in contrast, a 1.4 Gt gap in CO2 emissions was reported in China in 2010, which was equivalent to ∼5 % of the global budget (Guan et al., 2012). Because much of its emission is directly linked to the amount of fossil fuel used, CO2 is the best-understood GHG but, despite this, regional and consequently global emissions budgets are thought to be underestimated and the uncertainties are increasing due to growing emissions from emerging economies (Gregg, 2008; Gregg et al., 2008; Peters et al., 2011). By contrast, relatively more CH4 emission is mediated by biological processes. After a period of stagnation in the first few years of the 21st century, atmospheric CH4 has been rising steadily since ca. 2007. This prompted renewed efforts by the international scientific community to identify the drivers of CH4 at local, regional, and global scales and reconcile bottom-up and top-down estimates (Kirschke et al., 2013; Saunois et al., 2016). At the global scale, total methane emissions from fossil fuels (from the fossil fuel industry and from geological seepage) have been relatively steady over the past 3 decades, but research indicates that the estimates must be revised upwards by as much as 60 %–110 % (Schwietzke et al., 2016). Several mechanisms have been proposed to explain the recent rise in atmospheric methane; these include increases in emissions from microbial sources, which are meteorologically driven and can therefore exhibit substantial inter-annual variability (Dlugokencky et al., 2011; Nisbet et al., 2016; Schwietzke et al., 2016), a weakening of the hydroxyl (OH) chemical sink strength (Rigby et al., 2017; Turner et al., 2017), and an increase in fossil fuel contributions in the context of a stable OH sink and a downward revision of the biomass burning budget term (Worden et al., 2017). Inventories are thought to overestimate global emissions, and a difference of 130 Tg CH4 yr-1 was found between bottom-up and top-down estimates (Kirschke et al., 2013). In this light, it is becoming increasingly clear that there is an urgent need to seek independent validation of the emissions inventories using an integrated range of measurements and modelling activities (Allen, 2016; Nisbet and Weiss, 2010).

The development in recent years of rugged, high-precision spectroscopic instruments (e.g. Peltola et al., 2014) has opened up new opportunities for continuous in situ measurements of methane at fine temporal resolution and at relatively large spatial scales. For example, such sensors have been used in airborne applications to study methane emissions from cities (Cambaliza et al., 2014, 2015; Mays et al., 2009; O'Shea et al., 2014) as well as anthropogenic and biogenic area sources (Hiller et al., 2014; Karion et al., 2013, 2015). Applications of eddy covariance to measure emission–deposition directly at the field scale are on the rise in a broad variety of environments ranging from agricultural and wetlands (Dengel et al., 2011; Erkkila et al., 2018; Felber et al., 2015; Meijide et al., 2011; Peltola et al., 2015; Podgrajsek et al., 2014; Nicolini et al., 2013) to urban (Gioli et al., 2012; Helfter et al., 2011, 2016; Pawlak and Fortuniak, 2016; Pawlak et al., 2016). Finally, networks of tall towers and networks thereof exist around the world to monitor and model methane emissions at spatial scales ranging from country to global (Bakwin et al., 1995; Bohnenstengel et al., 2015; Feng et al., 2009, 2011; Miller et al., 2013; Oney et al., 2015; Rigby et al., 2008; Stanley et al., 2018; Stavert et al., 2018).

The geography of the British Isles at the NE edge of Europe, with dominantly SW winds advecting clean Atlantic air masses, particularly lends itself to a further approach, namely boundary layer budget measurements of concentrations in the inflow and outflow. This has previously been utilised for airborne boundary layer budget measurements (Fowler et al., 1996; Gallagher et al., 1994; Polson et al., 2011), but these can only provide snapshots of the country emissions for a few individual days.

Extending the concept of these earlier studies, we present 3 years of continuous observations (2015–2017) of CO2 and CH4 concentrations measured on board a commercial freight ferry, which connects the ports of Rosyth (Scotland, UK) to Zeebrugge (Belgium) and tracks the east coast of most of Great Britain (Fig. 1). The route of the ferry transects the UK outflow with a time-dependent footprint (Fig. 2), which, combined with a typical west-to-east air mass travel time of 11 to 19 h across the domain (median values for winter and summer, respectively), allows for sub-daily emissions estimations. Furthermore, the three continuous years of measurements also provide an opportunity to study seasonal and inter-annual changes in emissions. This is to our knowledge the first example of country-scale emission budgets using a mobile platform measuring continuously over several years.

These shipborne measurements formed part of a larger observation and modelling programme – the Greenhouse gAs Uk and Global Emissions (GAUGE) project (Palmer et al., 2018) – aimed at determining the magnitude, spatial distribution, and uncertainties of the UK's GHG budgets of CO2, CH4, and N2O. In this paper we utilise shipborne observations at the outflow of the United Kingdom coupled with background measurements at the Mace Head site (Ireland) to estimate seasonal and annual budgets of CO2 and CH4 using a mass balance approach.

This section describes the measurement systems used at the two experimental sites (Mace Head and ferry) and provides details of the greenhouse gas budget calculations and mass balance approach.

The mass balance approach presented here relies on simplifying assumptions to derive GHG budgets for a large part of the British Isles. The main assumptions are that (a) the air masses travel west to east, (b) the PBL height is constant over the spatial domain for each nominal averaging period, (c) there is no loss or input of mass into the domain other than from land sinks–sources, and (d) the air is well-mixed over the entire PBL height.

The data were filtered for westerly flow based on air mass back trajectories obtained from the HYSPLIT Trajectory Model (NOAA Air Resources Laboratory, 2018) daily 72 h runs at two coordinates: the Mace Head reference site and one ferry position halfway along its route. The back trajectories were run daily, commencing at midnight, and the air mass histories were assumed to be valid for an entire 24 h period and for the entire spatial domain. Of the four main assumptions listed above, points (c) and (d) are the most subjective because they could not be verified nor quantified. Assumption (a) (air mass travel from west to east) can be considered to be reasonably well-constrained owing to the data screening procedure at the preprocessing stage. Violations of the stationarity assumption (point b) due to significant changes in the mean PBL height at a sub-hourly time step would either be captured, in part or entirely, during the next hourly averaging period or go unnoticed in the case of very transient non-stationary events. Whilst the temporal variability of the mean PBL height for the spatial domain considered can be quantified and propagated through the emissions budget calculations as measurement uncertainty, the potential bias between model output and observations is unknown. Recent studies have compared different WRF parametrisation schemes with observed PBL height and found that, in general, the YSU scheme used in this study performs reasonably well in terms of predicting PBL height with minimum bias typically observed before midday (Hu et al., 2010; Banks et al., 2016; Tyagi et al., 2018; Xu et al., 2018); however, these studies also highlighted the fact that model performance can vary significantly between sites and time of day and that YSU tends to underestimate the PBL height over the sea (Tyagi et al., 2018). Comparisons between observations and model outputs of wind speed profiles for different parametrisation schemes also found substantial variability, both intra- and inter-model, with the YSU scheme exhibiting a tendency to overestimate wind speeds (Balzarini et al., 2014; Tyagi et al., 2018). The formation of sea breezes adds another level of complexity to the modelling of PBL height and wind speed, in particular in the southern North Sea where the orientation of the coastlines and their proximity to one another have been shown to induce sea breeze formation and to influence sea breeze type and offshore extent (Steele et al., 2013, 2015). Furthermore, not all WRF parametrisation schemes are equal in performance with respect to sea breeze conditions; recent studies show that the YSU scheme used here exhibited the smallest bias for wind speeds measured onshore under complex sea breeze conditions (Steele et al., 2015) and that it also captured the temporal evolution of the atmospheric boundary layer height better than other schemes (Salvador et al., 2016).

Intrinsic, unquantifiable biases on the mixing layer heights and mean wind speeds derived from the WRF model are hence likely. Wind speed and enhancement above background concentration were found to be to dominant uncertainty terms, jointly accounting for over 80 % of the total uncertainty in all seasons (Table S2). In contrast, nudging the baseline concentrations measured at Mace Head by a time lag estimated from the mean air mass travel time had only a very modest impact on the final budgets (Table S2). The two measures of errors proposed in this paper (based on temporal variability and total uncertainty through error propagation) yield on the whole comparable results, with the main discrepancy found for the autumn budget (years used: 2015–2017) in which the total uncertainty was almost four-fold the value obtained by considering the temporal variability alone. The autumn uncertainty was brought in line with the temporal variability estimate for both gases when the day–night weighting was applied. Whilst the variability and the total uncertainty are useful as first approximations for the confidence in the emission budgets, they should be treated as potential lower limits because of the unquantified bias between WRF model outputs and actual values of the PBL height and wind speed.

The fluxes calculated under this data filtering regime were assumed to be representative of surface emissions and uptake over the land masses bounded by the spatial domain, and local influences (due to e.g. localised air recirculation) were assumed to be negligible. This assumption could not be tested on a point-per-point basis but the latitudinal trends for both CH4 and CO2 at the seasonal timescale (Figs. 7 and 8) are consistent with the demographics and the known spatial distributions of sources of GHGs over the latitudinal range considered. In particular, the emission peaks for CO2 observed around 52.5 and 54∘ N coincide with major urban centres in the British Midlands, namely Birmingham and Manchester, Liverpool, Leeds, and Sheffield, as well as Dublin further upwind in the Republic of Ireland. These conurbations are reported to be significant sources of CO2 by the UK's official National Atmospheric Emissions Inventory (NAEI, 2018a). The calculated CH4 emissions were elevated in the 52.5–54∘ N latitude band compared to the fringes of the domain. This agrees with the NAEI UK CH4 map (NAEI, 2018a), which shows large emissions from the western parts of England in that latitude band. The NAEI reports substantial CH4 emissions from the Cornwall area (SW England; latitudes < 51.3∘ N), which might not always have registered in their entirety by the measurement system on the ferry because the port of Zeebrugge – the starting and end point of the vessel's route – lies at 51.21∘ N.

The negative daytime fluxes of CO2 registered in summer for latitudes > 54.5∘ N are consistent with the demographics, topography, and land use of the northern parts of England and of Northern Ireland; these areas are less populated than the southern parts, host the hills and mountains of the Lake District and the North Pennines, and the land use consists largely of grasslands. The combination of these factors (lower density of anthropogenic sources and higher density of biogenic sinks compared to southern parts of the UK) can explain the net negative fluxes of CO2 measured during the daytime in spring and summer. Whilst the observed lower emissions of CO2 in the northern parts of the spatial domain are consistent with the spatial distribution of emissions from NAEI data (NAEI, 2018a), Polson et al. (2011) reported substantial summertime emissions from Ireland and Northern Ireland which should cancel out the sink terms in northern England when integrating along a latitude bin. The fact that negative and very low summer emissions were derived by the ferry mass balance approach could indicate that measurements on board the ferry were more sensitive to sources and sinks in the eastern parts of the domain sampled because of (a) violation of the simplifying assumption that there is no loss of mass out of the domain, (b) imperfect vertical mixing, or (c) local air circulation which would not have been resolved by the HYSPLIT air mass histories. Alternatively, the mass balance estimates are real and the high CO2 emissions assigned to Ireland in the aircraft inversion model are measurement artefacts caused by the venting of the nocturnal boundary layer as postulated by Polson et al. (2011).

There was no statistically significant difference between day and night fluxes for CH4, which could be because (a) the major sources of this gas in the British Isles (livestock, including enteric fermentation and manure management, and waste-treatment-related emissions, including landfills and waste water; 52.8 % and 39.1 % of the total CH4 budget for the UK, respectively; BEIS, 2017) do not have marked diurnal cycles, (b) the mass balance approach could not resolve them, (c) the transit time of the air masses over the spatial domain blurred the potential differences between day and night emissions, or (d) the CH4 signal measured on the ferry was contaminated and did not reflect emissions from the land surface. Due to the temporal and spatial averaging carried out to derive emission estimates from the ferry measurements, and due to the diffuse spatial distribution of the dominant land sources of CH4, it seems likely that relatively small diurnal variations (e.g. studies indicate diurnal cycles in CH4 emissions from dairy farms and from landfills sites; Van der Zaag et al., 2014, and Borjesson and Svensson, 1997, respectively) would not be resolved by the mass balance approach.

At the seasonal timescale, the fluxes of CH4 and CO2 were both strongly correlated with UK natural gas usage (Fig. 11; BEIS, 2018); this provides confidence that the fluxes calculated by the mass balance approach can be related to physical emissions within the spatial domain and that the data filtering and quality control criteria excluded data points potentially contaminated by emissions from the ship. The statistically significant linear correlations between derived CH4 and CO2 fluxes and natural gas usage do not demonstrate causality, but suggest that the sources of these two GHGs within the domain sampled have seasonal dynamics similar to those of natural gas usage. However, both CH4 and CO2 emissions exhibited a weaker correlation with mean seasonal air temperature than with natural gas usage (Fig. 12), and this may indicate that natural gas consumption is a causal driver rather than a proxy for another underlying variable. Whilst it is reasonable to infer that both CO2 and CH4 would increase in line with an increasing demand for natural gas during the colder months, the NAEI (NAEI, 2018b) attributes only 15 % of annual CH4 emissions to fuel-related sources (combustion and fugitive emissions); this does not tally with the ∼100 % increase in CH4 emissions between winter and summer, which is accompanied by a similar increase in natural gas usage. An unexpectedly large diurnal and seasonal variability in the CH4 flux was observed from direct flux measurements above London (Helfter et al., 2016), and this suggested that pressure variations in the gas supply network in response to gas demand may have a significant impact on urban emissions. Fugitive emissions from the network may be underestimated in the NAEI.

Seasonality in methane emissions from landfills has also been reported, with higher emissions sometimes observed in winter and autumn (Borjesson and Svensson, 1997; Chanton and Liptay, 2000). The explanation for this is that net CH4 emissions from landfill emissions can be largely regulated by methane oxidation in the top layer of the landfill cover soil: oxidation is limited by soil temperature and the methane-oxidising potential decreases in autumn and winter because of lower soil temperatures, which results in an increase in methane emissions during the colder seasons. Riddick et al. (2017) reported a 71 % winter-to-summer reduction in CH4 emissions from a waste treatment park near Haddenham, England. Central England has the largest densities of waste treatment and landfill sites, which might explain the statistically significant linear anti-correlation between seasonal CH4 emissions and mean air temperature found in this region (Fig. 13). This is a remarkable result, which demonstrates the merit of this simple mass balance approach. In the other two regions considered (N and S, i.e. north and south of the central region denoted as MID), there was no compelling correlation between CH4 emissions and mean air temperature. This suggests that the dominant sources of this GHG in the N and S regions differ from the ones in the central region.

For CO2, the seasonal emissions had statistically significant correlations with mean air temperature in the central and northern regions, whilst the linear correlation was only marginally non-significant in the southern region. This is consistent with (a) the seasonality of natural gas usage (the NAEI attributes ∼50 % of annual CO2 emissions to fuel combustion processes such as domestic and industrial gas usage; NAEI, 2018b) and (b) the seasonality of CO2 uptake by vegetation.

Contrary to our findings, the UK CH4 emissions derived by inverse modelling using concentration data from four tall tower sites distributed across the UK and Ireland did not exhibit any clear seasonality over the period August 2012–August 2014 (Ganesan et al., 2015), but the range of emissions (1.65 to 2.67 Tg) was consistent with the ferry measurements (1.52±1.0 to 3.56±0.32 Tg).

For CH4, all four annual budgets calculated using all the available data for the 2015–2017 period were consistent with the inventory values for the UK (excluding Scotland) and the Republic of Ireland, as well as with top-down modelling estimates (Table 3). Temporal data aggregation (i.e. not considering seasonality) increased the uncertainty on the final budget (36 % and 32 % uncertainty for annual budgets derived with and without considering differences in day and night emissions compared to 12 % and 19 % for the budgets into which seasonality was factored) and it therefore seems that this approach should be discarded. The difference between the annual CH4 budgets calculated with and without day–night segregation but with seasonality was within the uncertainty of the individual estimates, and since we found no compelling evidence of diurnal trends, we arrive at 2.55±0.48 Tg yr-1 as our final estimate of the methane emissions from the UK (excluding Scotland) and the Republic of Ireland for the period 2015–2017.

Following the same argument regarding temporal data aggregation, we derive an annual emission budget for CO2 of 881.0±125.8 Tg yr-1, which is the estimate obtained from seasonal budgets with day–night segregation because we found indications of diurnal trends in some parts of the spatial domain.

This value is more than twice the inventory estimate of 422.7 Tg, but contrarily to CH4, CO2 has significant biogenic sources (e.g. the CO2 exhaled by the 65 million-strong human population within the spatial domain considered is of the order of 18 Tg yr-1; Moriwaki and Kanda, 2004) and sinks (vegetation uptake) which are not accounted for by anthropogenic atmospheric emissions inventories; a direct comparison with the inventory is hence not possible. Polson et al. (2011) derived an annual budget for CO2 of 620±105 Tg yr-1 from a series of flights around Britain in the summer of 2005 and September 2006. Using only summer data, in order to emulate the temporal upscaling done by Polson, we arrive at an annual CO2 budget of 511±308 Tg yr-1, which agrees with the 2011 aircraft study within measurement uncertainty. Whilst the seasonality of CO2 emissions cannot be disregarded, comparing our summertime budgets with the aircraft study provides an independent validation of the ferry mass balance approach and gives us confidence in the method despite the simplifying assumptions that underpin it. Finally, we compared the ferry-derived summertime estimates for the southern region, filtered with a narrow 260–280∘ wind direction window, to the fluxes of CO2 and CH4 obtained in 2012 by airborne measurements in the greater London area (O'Shea et al., 2014). The ferry fluxes of both gases (CH4: 0.049±0.020; CO2: 24±15 Tg season-1) compared reasonably well with the ones from the airborne campaign (CH4: 0.034±0.002; CO2: 13.4±1.2 Tg season-1), but clearly also include sources upwind and downwind of the greater London area. The uncertainty was large for both gases, which is unsurprising considering the length of the averaging period (summers of 2015 and 2016), but this comparison with another independent measurement further consolidates the confidence in the method and in the overall annual budgets for CH4 and CO2.

Applying a mass balance approach to continuous measurements of CO2 and CH4 in the outflow and using a ship of opportunity, we estimated the net annual emissions of CH4 from the UK (excluding Scotland) and the Republic of Ireland, averaged over the 2015–2017 period, to be 2.55±0.48 Tg, which is consistent with the combined 2.29 Tg reported to the United Nations Framework Convention on Climate Change. The annual CO2 budget obtained by mass balance (881.0±125.8 Tg) was more than twice the inventory value (422.7 Tg), but a direct comparison is not possible for this gas because the atmospheric inventory only accounts for anthropogenic sources (BEIS, 2016). Instead we compared our CO2 budget estimate with previous airborne studies, one for the UK as a whole and the second one for the greater London area, and found good agreement with both. The mass balance approach presented here does not provide direct source apportionment information, but the latitudinal emission patterns observed for both CH4 and CO2 were generally consistent with known spatial distributions of sources and sinks. Assuming that the atmospheric emissions inventory captures all anthropogenic emissions, we estimate that the net biogenic component of the measured CO2 annual budget was 458.7 Tg, which corresponds to 52 % of the total emissions. We detected marked seasonality in the emissions of both gases with lower values in the summer, and the seasonal budgets had statistically significant correlations with natural gas and mean air temperature. We attribute the two-thirds decrease in CO2 emissions between winter and summer for CO2 to the superposition of the reduction in demand for fossil fuels and an increase in the biogenic sink during the summer. For CH4, we attribute the seasonal variability of the measured fluxes to natural gas consumption and to the waste management sector for which temperature has been shown to control the methane-oxidising potential of landfill cover soil and thereby the net emissions. With this study, we validated the atmospheric emissions inventory of CH4 for the UK (excluding Scotland) and Ireland, quantified the biogenic component of the annual CO2 budget, and derived seasonal emissions budgets for both gases. Finally, we demonstrated that CH4 emissions are strongly seasonal even at such a relatively large spatial scale, which highlights the importance of taking meteorological drivers such as air temperature into account in future bottom-up budgets.