Detectability of COVID-19 global emissions reductions in local CO2 concentration measurements

It is estimated that global anthropogenic carbon dioxide (CO2) emissions reduced by up to 12% at the start of 2020 compared to recent years due to the COVID-19 related downturn in economic activity. Despite the large decrease in CO2 emissions, no reduction in the trend in background atmospheric CO2 concentrations has been detected. So, how long would it take for sustained COVID-19 CO2 emission reductions to be detected in daily and monthly averaged local CO2 concentration measurements? CO2 concentration measurements for five measurement sites in the UK and Ireland are combined with meteorological numerical weather prediction data to build statistical models that can predict future CO2 concentrations. It is found that 75% of the observed daily variability can be explained by these simple models. Emission reduction scenario experiments using these simple models illustrate that large daily and seasonal variability in local CO2 concentrations precludes the rapid emergence of a detectable signal. COVID-19 magnitude emissions reductions would only be detectable in the daily CO2 concentrations after at least 38 months and in monthly CO2 concentrations after 11 months of sustained reductions. For monthly CO2 concentrations the time of emergence is similar for all sites since the seasonal variability is largely driven by non-local fluxes of CO2 between the terrestrial biosphere and the atmosphere. The COVID-19 CO2 anthropogenic emissions reductions are similar in magnitude to those that are required to meet the Paris Agreement target of keeping global temperatures below 2° C. This study demonstrates that, using measurements alone, there will be a considerable lag between changes in global anthropogenic emissions and a detected signal in local CO2 concentration trends. Thus, there is likely to be a delay of several years between changes in policy designed to meet CO2 anthropogenic emissions targets and our ability to detect the impact of these policies on CO2 concentrations using atmospheric measurements alone.


Introduction
Electricity production, transportation and industrial activity account for more than 80% of carbon dioxide (CO 2 ) emissions from fuel combustion (Quadrelli and Peterson 2007). Since the start of 2020, COVID-19 restrictions have significantly reduced these activities. Current estimates suggest that global fossil fuel CO 2 emissions in 2020 may have dropped by around 7%-8% (Friedlingstein et al 2020, Hale and Leduc 2020, Le Quéré et al 2020, Liu et al 2020. Andreoni (2021) estimates that in Europe more than 195 600 thousand tons of CO 2 have been avoided between January and June 2020, compared to the same period of the previous year, representing a −12.1% emissions change. A decline in annual CO 2 emissions of this size would exceed any decline since the end of World War II. The magnitude of these emissions reductions is similar to those required to meet the target of the Paris Agreement, which aims to keep the global temperature rise below 2 • C (hereafter 'Paris Agreement magnitude emissions reductions'). To meet the Paris Agreement temperature target, emissions from energy production and transport will have to peak almost immediately in the developed world (Annex I countries) and decline at about 10% each year until net-zero emissions are reached around 2030 (IPCC 2018). Thus the COVID-19 crisis presents a test bed for understanding these longerterm climate change policies on a more immediate time-scale.
While the recent reductions in CO 2 emissions are indeed substantial, they do not immediately equate to similar reductions in the trend of atmospheric CO 2 concentrations. Background CO 2 concentration measurements have not, so far, shown any changes as a result of COVID-19 emissions reductions (Liu et al 2020). This is consistent with previous situations when reductions in CO 2 associated with economic downturns did not significantly change the trend in CO 2 concentrations (Granados et al 2012). The lack of sensitivity to emissions reductions is due to the long atmospheric lifetime of CO 2 (50-200 years) which makes any perturbation in emission rate small compared to the reservoir of CO 2 currently present in the atmosphere. In addition, the large daily and seasonal variability of CO 2 concentrations makes changes in global CO 2 emissions difficult to detect (Samset et al 2020). Thus if we cannot expect immediately measurable impacts, how long would we need to wait to detect a change in the CO 2 concentration trend due to COVID-19 emission reductions?
In the climate change literature, many studies have investigated the response of the climate system to changes in greenhouse gases (Taylor and Penner 1994, Stainforth et al 2005, Sitch et al 2015. These studies typically involve running experiments with coupled atmosphere-ocean climate models with greenhouse gas forcing running over 50-100 year time periods. They may also be coupled to models of other processes in the Earth's atmosphere such as the carbon cycle, so as to better simulate climate feedbacks such as interaction with the terrestrial ecosystems or oceans. On decadal to centennial timescales changes in CO 2 emissions can alter the climate. Therefore, these long integrations are necessary so that the response of the climate to the changing greenhouse gas emissions can reach equilibrium (Tebaldi and Friedlingstein 2013). However, on shorter timescales (days to months) CO 2 behaves more like a passive tracer. The concentrations of CO 2 on these timescales is largely controlled by changes in the weather and terrestrial biospheric activity. Therefore complex climate models which represent interactions occurring over longer timescales (years to decades) are not needed to capture the near-term consequence of changes in CO 2 emissions on CO 2 concentrations.
The aim of this work is to determine how long it would take for COVID-19/Paris Agreement magnitude emissions reductions to be detected in local daily and monthly CO 2 concentration measurements. We have built multiple linear regression (MLR) models, similar to those used to predict short-lived air quality pollutants (e.g. Carslaw andBeevers 2005, Dacre et al 2020), to predict CO 2 concentrations using only meteorological data and recent local CO 2 measurements. These models will not capture the responses in the complex models because they are tuned using recent data and they do not include climate feedbacks. However, these reduced complexity models may nevertheless be used to gain insights into our ability to detect greenhouse gas emissions reductions. In addition, they are much less computationally expensive, making them very fast to run.

CO 2 data
The hourly atmospheric CO 2 measurements used in this study were taken from five in-situ observatories situated across the UK and Ireland (figure 1). Four of these stations, Tacolneston, Ridge Hill, Bilsdale and Heathfield, form the UK-based part of the UK Deriving Emissions linked to Climate Change (DECC 2020) network (Stanley et al 2018, Stavert et al 2019. Each of these sites makes use of a tall telecommunications tower to sample air from multiple height inlets (ranging from 42 to 248 m above ground level (magl) across the network). At each UK DECC site, we use data from the highest inlet only (table 1). The fifth site, Mace Head, is situated on the west coast of Ireland. This station is ideally positioned to intercept northern hemispheric background air from the North Atlantic. CO 2 measurements from Mace Head are made by Laboratoire des Sciences du Climat et de l'Environnement as part of the integrated carbon observation system (ICOS) network, from a 23 magl sample inlet (Vardag et al 2014). Note that lower-frequency CO 2 measurements are available from Mace Head data prior to 2011. Figure 1 shows the average footprint emissions sensitivity obtained from 30 day backwards simulations of the Met Office's numerical atmospheric dispersion modelling environment (NAME) model for the five sites for March 2020. The sensitivity is defined as the contribution per unit emission to the mole fraction measurement (Manning et al 2011). These footprints provide an indication of the location of the local emissions contributing to the measurements at each site in March 2020. At all five sites, continuous in-situ CO 2 measurements are made using cavity ring-down spectrometers (Picarro G2301 or G2401). At UK DECC sites, ambient measurements are corrected for linear instrumental drift via daily measurements of a standard gas. A small non-linear

Meteorological data
The meteorological data to build the statistical models in this study comes from the UK Met Office UKV model (Tang et al 2013). Hourly data covering the period 1 January 2015-31 May 2020 is used. Hourly 4D-Var assimilation allows the production of state-of-the-art weather forecasts for the UK, initialised every hour . The UKV has a high resolution inner domain (1.5 km grid spacing) over the UK, separated from a lower resolution grid (4 km grid spacing) near the boundaries by a variable resolution transition zone. The high resolution contains a better representation of land surface processes and orography than coarser resolution global models. Sub-grid scale processes such as, boundary layer turbulence, radiation, cloud, microphysics and orographic drag are represented by parameterizations. The UKV model has been shown to compare well against observations (Lean et al 2008, Roberts and Lean 2008, Clark et al 2016. Meteorological data for the 5-year period (1 January 2015-31 December 2019) is extracted from the UKV and interpolated to the location of the DECC sites to build the statistical models described in section 3. One advantage of using weather model output is that above surface variables, such as boundary layer height, can be extracted, although modelled boundary layer height has not been evaluated at many sites in the UK due to lack of climatological measurements (Harvey et al 2013(Harvey et al , 2015. One disadvantage of using weather model output is that the resolution of the model data is 1.5 km 2 , whereas the CO 2 concentration data are point measurements. If they were available, use of local meteorological measurements to build the statistical models would be more accurate.

MLR modelling
In order to predict daily and monthly average CO 2 concentrations during the ongoing COVID-19 restrictions, MLR models are built using up to 5-years of DECC and UKV data (2015-2019). MLR modelling is used since the concentration of CO 2 is likely to depend on more than one predictor variable. The technique enables the relative influences of the predictor variables to be analysed, which allows us to perform the simple CO 2 emission scenario experiments described in section 5. MLR modelling is commonly used for predicting the variability in shortlived pollutant concentrations such as NO 2 (Shi and Harrison 1997, Carslaw andBeevers 2005, Dacre et al 2020). The MLR models predict the daily average CO 2 concentrations we would expect, during the COVID-19 period, given no change in CO 2 emissions. Several meteorological and temporal explanatory variables (x i ) are used to predict CO 2 concentrations (y) at each DECC station. The regression coefficients (β i ) describe the size of the effect of the explanatory variable on the daily CO 2 concentrations and α is the value y is predicted to have when all the explanatory variables are equal to zero.
The Akaike information criterion (AIC) is used to determine which explanatory variables to include in the models. The model with the lowest AIC score is expected to have the best balance between its ability to fit the data set and its ability to avoid over-fitting the data set. The explanatory variables and regression coefficients used in this study are shown in table 2. Since wind direction is cyclic not linear (i.e. 0 and 360 degrees have the same direction) it is partitioned into its northerly (v-wind) and easterly (u-wind) components. Wind speed, wind direction and temperature are all extracted 10 m above ground level. Sensitivity studies using meteorological variables extracted at the height of the sample inlets for each site did not improve the MLR models.
Our aim in the design of the MLR models was to keep the number of explanatory variables to a minimum and to restrict the models to use local data only. This is desirable to ensure that others, with only local CO 2 concentration and meteorological measurements available to them, can build similar models for their site locations. Also, for simplicity, the same explanatory variables are used for each of five sites analysed. The importance of each variable in explaining the observed CO 2 concentrations varies for each site, but the variables in table 2 were found to contribute to a reduced AIC for all five sites.

Evaluation of predicted CO 2 concentrations
In this section the CO 2 concentrations predicted by the MLR models are compared to the observed CO 2 concentrations at all five DECC sites. The evaluation is performed for various temporal averaging periods. The aim is to determine whether the MLR models are a credible representation of reality and thus can be used to perform emission scenario experiments. Figure 2 shows the yearly averaged observed and predicted CO 2 concentrations between January 2015 and June 2020. At all sites there is a monotonic increase in yearly averaged CO 2 concentrations. CO 2 concentrations are primarily rising because of the increased amounts of fossil fuels that humans are burning for energy. The predicted CO 2 concentrations capture this annual increase in CO 2 concentrations due to the inclusion of the date in the MLR models with a coefficient of 0.007 ppm day −1 at all sites which is equivalent to 2.5 ppm year −1 (table 2). Figure 2 also shows the monthly averaged observed and predicted CO 2 concentrations between January 2015 and June 2020. At all sites there is a strong annual cycle in CO 2 concentrations, with highest CO 2 concentrations measured during the winter months and lowest CO 2 concentrations measured during the summer months. This annual cycle is the result of photosynthetic activity by plants. As plants begin to photosynthesize in the spring and summer, they absorb CO 2 from the atmosphere and eventually use it as a carbon source for growth and reproduction. Once winter arrives, plants save energy by decreasing photosynthesis. Without photosynthesis, the dominant process is the exhalation of CO 2 by the total ecosystem, including bacteria, plants, and animals. The modelled CO 2 concentrations capture the annual cycle in CO 2 concentrations fairly well due to the inclusion of monthly averaged temperature in the MLR models. The coefficients used in the MLR models for monthly averaged temperature are all negative indicating that CO 2 decreases as the temperature increases, and viceversa, with an average coefficient of −1.2 ppm K −1 (table 2).

Daily CO 2 concentration variability
In this section we focus on the daily variability in CO 2 concentrations, typically caused by the movement of synoptic-scale high and low pressure systems. To illustrate this we compare the daily averaged observed and predicted CO 2 concentrations between January 2020 and June 2020 (figure 3). Note that no data from 2020 was used to build the MLR models. The daily variability is largely driven by transport and mixing of CO 2 in the atmospheric boundary layer. High CO 2 concentrations occur when the boundary layer is shallow. During these conditions mixing is suppressed and emissions do not disperse rapidly away from sources but are trapped within the boundary layer where they can accumulate. The MLR models quantify this negative relationship with an average coefficient of −0.005 ppm m −1 . Since the daily averaged BLD can vary by several hundred metres this can result in CO 2 variability of 1-2 ppm day −1 . In addition, for certain wind directions, transport from regional CO 2 sources towards the measurement site occurs resulting in high CO 2 concentrations. The coefficients used in the MLR models for easterly wind speeds are all positive. This suggests that easterly winds, which advect air from mainland Europe, contain higher CO 2 concentrations than westerly winds which transport relatively low CO 2 concentration air from the North Atlantic. The coefficients for northerly wind speeds are more mixed. The Tacolneston and Bilsdale MLR models contain negative coefficients indicating that southerly winds increase CO 2 concentrations. This is consistent with their locations which have a long fetch of sea to their north. Conversely, the Heathfield and Mace Head MLR models contain positive coefficients indicating that northerly winds increase CO 2 at these sites. Heathfield is located south of several large urban areas so is potentially influenced by CO 2 emitted locally. Finally, Ridge Hill has no significant correlation with northerly wind direction since there are sources of CO 2 to both the north and south. Thus the modelled CO 2 concentrations capture the daily variability in CO 2 concentrations due to the inclusion of wind speed, wind direction and boundary layer depth in the MLR models.

MLR model evaluation
Over the training period (January 2015-December 2019), the MLR models capture 75% of the observed variability in daily averaged CO 2 concentrations with a root mean square error (RMSE) of 3.71 ppm (table 3). The RMSE in daily average CO 2 concentrations is relatively large due to an underestimation of the spikes in the observed daily CO 2 concentrations which are likely to be due to local emissions of CO 2 occurring within a few km's surrounding the tall towers. The normalised mean bias (NMB) is close to zero for all sites. The highest correlations (R 2 ) and lowest RMSE are found at Mace Head and Bilsdale. These sites have relatively small daily variability compared to the other sites suggesting that they are influenced less by local sources of pollution. Over the 2015-2019 training period the models explain more of the variability in the Spring/Summer (R 2 = 0.77) than in the Autumn/Winter periods (R 2 = 0.68) and the RMSE is lower (3.36 and 4.01 ppm respectively) (table 3). This is due to spikes in the observed daily CO 2 concentrations which occur predominantly during the winter and can reach 440 ppm (figure 2).
During 2020 the correlations are lower than during the training period but the MLR models still explain on average 67% of the observed variability in daily CO 2 (table 3). After the 16 March 2020 (UK lockdown) the RMSE increases at four out of the five sites ( figure 3). However, none of the MLR models systematically overestimate the observed CO 2 concentrations after the UK lockdown demonstrating that it will take longer than 2 months for any signal of reduced CO 2 emissions to be observed in the atmospheric CO 2 concentrations.

Global CO 2 emission scenarios
Since the MLR models describe so much of the observed daily CO 2 variability they provide a realistic substitute for the real world and thus can be used to perform emission scenario simulations. In particular, the MLR models are used in this section to determine how long it would take for COVID-19/Paris Agreement magnitude CO 2 emissions reductions to be detected in daily and monthly averaged CO 2 measurements. Since CO 2 has a lifetime much longer than 5 years, simple global emission scenario simulations can be performed by scaling the regression coefficient controlling the trend (i.e. the date) whilst maintaining the seasonal and daily variability. β 1 = 0.007 ppm day −1 represents 100% of the Table 3. Correlation (R 2 ), RMSE and normalised mean bias (NMB) statistics for daily model prediction of CO2 concentration at each measurement site. Statistics are calculated for the model training period (January 2015-December 2019), Autumn/Winter months (September-February) in the training period, Spring/Summer months (March-August) in the training period and for the prediction period (January-December 2020). annual CO 2 concentration increase due to increasing anthropogenic emissions and β 1 = 0.0 ppm day −1 represents net-zero anthropogenic emissions. Thus sensitivity to different global emission scenarios can be performed while keeping the seasonal and daily variability constant (i.e. the regression coefficients for wind speed and wind direction, boundary layer depth and monthly averaged temperature remain unchanged). The variability in daily CO 2 concentrations (daily noise) is estimated by the standard deviation of observed CO 2 concentrations over 30-day moving windows (figure 4). The variability in monthly CO 2 concentrations (monthly noise) is estimated by the standard deviation of the 2015-2019 de-trended observed CO 2 concentrations over moving 3 month periods. The difference in simulated CO 2 concentration between the 100% emissions and reduced global emissions scenarios (signal) increases with time and is proportional to the magnitude of the global emission reduction. The signal-to-noise ratio thus determines how reductions in CO 2 concentrations resulting from the emissions reduction scenarios compare to the estimated variability in CO 2 concentrations. The time of emergence is defined as the earliest time that the signal-to-noise ratio exceeds a value of 1. Since the time of emergence may depend on the initial conditions it is calculated for simulations initialised at varying weekly intervals between January 2015 and January 2020 to give a range of emergence times for each emission scenario. Figure 4(a) shows the evolution of daily CO 2 concentrations and daily noise for Ridge Hill assuming 100% emissions (plotted every 7 days). Different emission scenarios are also shown. For the Ridge Hill simulation initialised on 15 January 2015 (figure 4(a)) the time of emergence for the net-zero scenario simulation (−100%) occurs 10.3 months after the start of the simulation. The time of emergence for the −50%, −25% and −12% emissions scenarios occur 15.3, 27.3 and 50.6 months after the start of the simulation respectively. Figure 4( b) shows simulations initialised at the same time for the Mace Head site. The time of emergence for the netzero scenario is similar to that at Ridge Hill, for this initialisation time, but the time of emergence for the −50%, −25% and −12% emissions scenarios occurs earlier than the respective emission scenarios at Ridge Hill. Table 4 shows the range of time of emergence for multiple emission scenarios initialised at monthly intervals. If net-zero anthropogenic emissions are assumed (−100%) then a signal would be detectable in the daily CO 2 concentrations after an average of 8 months. The signal in daily CO 2 concentrations would likely emerge at Bilsdale and Mace Head 2-3 months earlier than the other DECC sites as the daily variability at these sites is smaller than at the other DECC measurement locations. The longest daily time of emergence for the net-zero emission scenario would likely be at the Heathfield site, which is a semi-rural UK site located 19 km south of Royal Tunbridge Wells (population 118 000), in East Sussex, UK. As the emission scenario reduces in magnitude, the daily time of emergence increases. If a 50% reduction in anthropogenic emissions is maintained indefinitely a reduction in the trend of daily CO 2 concentrations would be observable after an average of 15 months. For COVID-19/Paris Agreement like magnitude emissions reductions of −12% (Andreoni 2021) the daily time of emergence would be on average after 38 months. Thus we would be able to detect a reduction in daily CO 2 concentrations after 2-3 years  depending on the measurement site. Note that for the smallest emission reduction scenario (−12% emissions) there are large daily time of emergence interquartile ranges due to a decrease in the sample size. If we average the daily data to calculate monthly CO 2 concentrations then we smooth out the daily variability. Thus we can detect a reduction in the monthly CO 2 concentration trend due to COVID-19 like magnitude emissions reductions earlier, after about 11 months. Therefore, if current global lockdown restrictions continue we might detect a reduction in monthly averaged CO 2 concentration trend some time in 2021 at the earliest. When averaging over a month, the differences in the time of emergence between the measurement sites reduces as the CO 2 concentrations are less dependent on local emissions and are largely driven by non-local biogenic emissions.

Conclusions
In this paper, analysis of 5 CO 2 monitoring sites in the UK and Ireland has shown that after several months of CO 2 emissions reductions there are no detectable decreases in CO 2 concentrations exceeding the natural variations in measured CO 2 concentrations. Furthermore, global emission reduction scenario experiments show that it would take around 3 years of sustained global emissions reductions before any such signal could be detected in the local daily CO 2 concentration trend and 1 year before a reduction in CO 2 concentration trend would be detectable in the monthly averaged local CO 2 concentration trend. Future work could include performing the linear regression modelling using the fossil fuel contribution of CO 2 calculated from the measured 14 C content of CO 2 , instead of using total CO 2 concentrations. Since the method used to create the MLR models is generalizable, similar MLR models could be built for other locations with only local CO 2 and meteorological measurements available. It would be interesting to perform a similar study at a remote location, such as the Mauna Loa observatory, which is not affected by local CO 2 emissions in order to determine if the time of emergence appears earlier or later than those estimated for the sites in the UK and Ireland. The models used to make these estimates do not include climate feedbacks or processes determining plant growth which may make any detection of any signal even more difficult, hence these results should be seen as a lower limit. The results of this study show that the growth rate of CO 2 in the atmosphere will not decrease unless there is a substantial and persistent reduction in emissions over many decades.
Since CO 2 emissions are projected to eventually return to business-as-usual levels, the overall impact of COVID-19 CO 2 emission reductions on CO 2 concentrations in the atmosphere and therefore on climate change is likely to be small in the long run Forster et al (2020). The COVID-19 CO 2 emission reductions are similar in magnitude to those that are necessary to mitigate the worst effects of climate change. The COVID-19 crisis thus offers insights into the substantial changes in behaviour and infrastructure that are necessary if we are to achieve the temperature targets set out by the Paris Agreement. However, the measures deployed in response to the COVID-19 pandemic are not suitable or sustainable in the long term. These results support the need to create policies for recovering from the current economic downturn that do not further increase CO 2 emissions but which provide sustainable growth such as those outlined by Hepburn et al (2020).
The simple linear regression models used in this study could be used in the future to detect global scale emissions changes. However, the results of this study demonstrate that, using local measurements alone, there will be a significant delay between changes in global emissions and a detected signal in the local CO 2 concentrations.