#
Can We Measure a COVID-19-Related Slowdown in Atmospheric CO_{2} Growth? Sensitivity of Total Carbon Column Observations

^{*}

## Abstract

**:**

_{2}emission reductions up to −8% for 2020. This approximately matches the reductions required year on year to fulfill the Paris agreement. We pursue the question whether related atmospheric concentration changes may be detected by the Total Carbon Column Observing Network (TCCON), and brought into agreement with bottom-up emission-reduction estimates. We present a mathematical framework to derive annual growth rates from observed column-averaged carbon dioxide (XCO

_{2}) including uncertainties. The min–max range of TCCON growth rates for 2012–2019 was [2.00, 3.27] ppm/yr with a largest one-year increase of 1.07 ppm/yr for 2015/16 caused by El Niño. Uncertainties are 0.38 [0.28, 0.44] ppm/yr limited by synoptic variability, including a 0.05 ppm/yr contribution from single-measurement precision. TCCON growth rates are linked to a UK Met Office forecast of a COVID-19-related reduction of −0.32 ppm yr

^{−2}in 2020 for Mauna Loa. The separation of TCCON-measured growth rates vs. the reference forecast (without COVID-19) is discussed in terms of detection delay. A 0.6 [0.4, 0.7]-yr delay is caused by the impact of synoptic variability on XCO

_{2}, including a ≈1-month contribution from single-measurement precision. A hindrance for the detection of the COVID-19-related growth rate reduction in 2020 is the ±0.57 ppm/yr uncertainty for the forecasted reference case (without COVID-19). Only assuming the ongoing growth rate reductions increasing year-on-year by −0.32 ppm yr

^{−2}would allow a discrimination of TCCON measurements vs. the unperturbed forecast and its uncertainty—with a 2.4 [2.2, 2.5]-yr delay. Using no forecast but the max–min range of the TCCON-observed growth rates for discrimination only leads to a factor ≈2 longer delay. Therefore, the forecast uncertainties for annual growth rates must be reduced. This requires improved terrestrial ecosystem models and ocean observations to better quantify the land and ocean sinks dominating interannual variability.

_{2}growth; total carbon column observations; TCCON; column-averaged CO

_{2}; XCO

_{2}; annual growth rate; detection delay; ocean and land carbon sinks; interannual variability; climate variability; El Niño; intra-annual variability; synoptic variability; confidence; bootstrap resampling

## 1. Introduction

_{2}emissions reaching zero by 2055. This implies an urgent need to verify bottom-up emission estimates independently via atmospheric measurements. However, this is a demanding task, because the response of atmospheric concentrations to emission changes are masked by a much stronger effect from the interannual variability of the ocean and land sinks driven by climate variability, in particular El Niño [2]. Therefore, sink variability must be accurately taken into account by related measurements and models, in order to obtain closure between emissions, sinks, and measured atmospheric concentration changes [3]. This is a demanding task at the edge of the current state of the art in carbon cycle research [4].

_{2}) with an accuracy and precision of ≈0.8 ppm [8]. TCCON data have been exploited e.g., for satellite validation [9,10,11,12,13,14], investigations of sources and sinks [15,16,17], of the seasonality [18,19], or the north–south gradient [20]. Compared to in situ surface measurements, TCCON bares the disadvantage of less homogeneous sampling (solar absorption measurements with clear-sky and day-time limitations), but also the advantage that total column measurements are less impacted by boundary layer transport (“rectifier”) effects which are not easy to model, and thereby are more directly linked to the underlying emissions [21].

_{2}growth rates from TCCON observations along with their uncertainties in a rigorous mathematical way. The results on multiannual TCCON trends and annual growth rates and uncertainties are presented in Section 3. TCCON growth rates are then linked to a forecast of COVID-19-related growth rate reductions in 2020 based on a −8% annual emission reduction scenario [22]. The possible separation of TCCON-measured growth rate reductions vs. the reference forecast (without COVID-19 impact) is discussed in Section 4 in terms of the attainable detection delay, i.e., how much time it would take TCCON to measure the “true” growth rate until a significant difference vs. the reference forecast could be obtained given the TCCON confidence and forecast uncertainty. This is performed for varied cases giving insight into the differing mechanisms and magnitudes of the TCCON and forecast error contributions.

## 2. Data and Methods

#### 2.1. Total Carbon Column Observations

#### 2.1.1. XCO_{2} Data Set

_{2}, given in units of ppm) are recorded by ground-based solar absorption spectrometry in frame of TCCON. Briefly, TCCON observatories use Fourier-transform infrared spectrometers in the near infrared with a maximum optical path difference (OPD) of 45 cm (spectral resolution: = 1/OPD ≈ 0.02 cm

^{−1}). A profile scaling retrieval was used to determine the vertical columns of CO

_{2}, CO, CH

_{4}, H

_{2}O, and O

_{2}simultaneously from the observed spectra. Temperature, pressure, and water vapor profiles from NCEP (National Center for Environmental Prediction) were used as input. The CO

_{2}retrieval used two spectral windows centered at 6220 cm

^{−1}and 6339 cm

^{−1}. The retrieved column abundance (molecules m

^{−2}) was normalized by the column abundance of O

_{2}retrieved from the same spectrum to yield XCO

_{2}: = column (CO

_{2}) × 0.2095/column(O

_{2}). By this rationing approach, a variety of systematic measurement errors (correlated between CO

_{2}and O

_{2}) tend to cancel out to a good approximation; e.g., photometric errors or apodization effects due to solar intensity fluctuations by clouds. This is one major clue to achieve TCCON single-measurement precisions in the sub-per cent range (<0.2% or <0.8 ppm for XCO

_{2}). As in previous work [11,12], we performed TCCON routine data filtering for outliers. This comprised various parameter thresholds, in particular, a 5% threshold for fractional variation in solar intensity and a 10 ppm threshold for 1-sigma XCO

_{2}retrieval error.

_{2}accuracy of better than 0.2% (0.8 ppm) was achieved.

#### 2.1.2. TCCON Sites

_{2}trend representative of the northern hemisphere and derive the related annual growth rates, we used the time series of the mid-latitude TCCON station Garmisch (47°N, 0.74 km asl.). For the investigation of site-dependent effects, we compared and combined the results with the TCCON station on top of Mt. Zugspitze (2.96 km asl. [24]), located only ≈8 km in horizontal distance from Garmisch as well as with two more sites located at approximately the same (mid-)latitude (Karlsruhe, 49°N; Park Falls, 46°N, Table 1). It is worth noting that the atmospheric observations at other locations, i.e., close to the emission-reduction hot spots like locked-down power plants, obviously could be more sensitive to detect COVID-19-related reduction effects locally, while our site selection reflects the goal of our study to investigate the TCCON sensitivity and to detect COVID-19-related changes in hemispherically representative background levels.

#### 2.1.3. TCCON Time Series and Averaging

_{2}values M

_{i}of each time series were stored along with the time stamps t

_{i}of all individual column measurements. See Table 1 for the typical numbers for the integration durations of single XCO

_{2}measurements along with sampling statistics. It is worth noting that differing integration times in Table 1 are due to historic reasons: standard 40 kHz sampling (18 s duration, e.g., used in the early Zugspitze record) turned out to be not possible for other instruments using simultaneous dual-channel acquisition due to electronic sampling-speed limitations. Reduction to 20 kHz sampling (35 s integration used at Karlsruhe) was the fastest sampling rate allowing to eliminate the problem, but most sites reduced the speed to a more conservative standard of 7.5 kHz (95 s); averaging the spectra with a shorter integration time yielded a comparable precision as for the spectra with longer integration times.

_{2}retrievals: by simple arithmetic averaging, we also prepared daily-mean time series, weekly-mean time series, 2-weekly-mean time series, and monthly-mean time series.

#### 2.2. Mathematics to Derive Trends, Annual Growth Rates, and Related Confidence Intervals

#### 2.2.1. Model Fit

_{2}from the time series of a TCCON site, we used the model function:

_{2}measurements [4,29]. Here, t is the time axis, the multi-annual trend is a linear function with intercept and slope (a

_{0}, a

_{1}), while the average seasonality is parametrized as a fourth order Fourier series with parameters (b

_{1}, …, b

_{8}). The fit procedure is to minimize:

_{i}, M

_{i}) “initial-fit” parameter estimates (a

_{00}, a

_{10,}b

_{10}, …, b

_{80}) for trend and seasonality, respectively; all second parameter indexes “0” stand for “initial fit”. It is worth noting that we did not add a quadratic term a

_{2}t

^{2}to the linear trend model as used by the carbon project [29], because for the data of this work, a

_{20}turned out to not significantly deviate from zero. The decision on the order of the Fourier function used (fourth order) was drawn based on (i) the earlier experience with fitting CO

_{2}data [29] and (ii) an L-curve analysis of the root mean square of the fitting residuals of our data vs. the Fourier order. Remark: In consistency with previous CO

_{2}studies [29] we derived the trends from daily-mean time series.

#### 2.2.2. Confidence Intervals for Model Fit Parameters

_{00}, a

_{10}, b

_{10}, …, b

_{80}). This is because atmospheric parameters tend to be non-normally distributed. For such cases, the technique of bootstrap resampling [30] has been shown to be favorable for obtaining reliable confidence intervals [31]. This approach has been widely used for the uncertainty analysis of trends inferred from total column time series retrieved from mid-infrared solar FTIR measurements [32,33,34,35].

_{i}

_{,0}} with i = 1, …, m of the measurements relative to the initial fit:

_{i}

_{,0}= M

_{i}− F(t

_{i}, a

_{00}, a

_{10}, b

_{10}, …, b

_{80})

_{i}

_{,0}} are randomly resampled to other measurement time stamps t

_{i}(with replacement) to obtain a new set of residuals {R

_{i}

_{,q}} along with a first new (resampled) data set {t

_{i},M

_{i}

_{,q}} defined as

_{i}

_{,q}= F(t

_{i}, a

_{00}, a

_{10}, …, b

_{80}) + R

_{i}

_{,q}

_{01}, a

_{11}, …, b

_{81}), where all the second indexes “1” stand for the “first resampling”. This resampling was repeated typically N = 5000 times, yielding q = 1,..., N differing results for all the trend and seasonality parameters. This can be aggregated into a sample distribution matrix for each site:

_{11}… a

_{1N}) represents the distribution of the linear trend slope. The 2.5th and the 97.5th percentile can be read out to represent the 95% confidence interval associated with the trend slope obtained from the initial fit.

#### 2.2.3. Combined Trends from Multiple Sites

**D**

_{gm},

**D**

_{ka},

**D**

_{pa}by setting up a new matrix:

#### 2.2.4. Annual Growth Rates

_{2}with the unit (ppm/yr) and time stamp 1 January of a dedicated year, to be the difference between the annual mean of this very year and the year before. Unfortunately, the best way to calculate annual means from solar FTIR data is not straightforward. This is due to the non-homogeneous sampling during the year. Data gaps up to typically 2 weeks arise regularly due to the fact that clear-sky conditions are required for the measurements, or no operation during the holidays. This can lead to a non-equal weight of the measurements from the first vs. the second half of a year. This, along with the annual CO

_{2}increase, can alias into an error in the annual mean—if calculated via the arithmetic mean of all the measurements of a year. A lower boarder for such arithmetic-mean artifacts can be derived, e.g., from a shift of the 2 weeks from Christmas break either to the old or the new year. In combination with a typical annual growth rate of 2.5 ppm/year, this aliases into an ambiguity of the arithmetic annual mean of (2/53) yr × 2.5 ppm/yr = 0.1 ppm, and this would further alias as a 0.1/2.5 × 100 = 4% error into the derived annual growth rate. An upper boarder for such artifacts can be estimated, e.g., assuming a complete lack of measurements in one half of a year. This would lead to a 0.5 × 2.5 ppm = 1.25 ppm error in the arithmetic annual mean, which would alias as a 50% error into the annual growth rate.

_{j},M

_{j}} with j = 1, …. n and t

_{j}∈ (1 January, 31 December) of this year, which are not impacted by temporal sampling inhomogeneities. This is performed by using the five parameters (a

_{10}, b

_{10}, …, b

_{40}) obtained from the initial fit of the whole time series as constants, while fitting just one parameter to the data of this dedicated year (yr), namely the intercept a

_{0,yr}. Thus, we minimize:

_{0,yr}, yielding an initial fit result a

_{00,yr}for the intercept of this dedicated year. Note that:

_{00,yr}≠ a

_{00}

_{2}annual mean for the considered year is then calculated from:

#### 2.2.5. Confidence Intervals for Annual Growth Rates

_{2}values per day on ≈100–200 days per year from single spectra, and this implies an oversampling of natural variability. The dominant contribution to XCO

_{2}intra-annual variability (relative to the mean seasonal cycle) at a TCCON site originates from synoptic-scale horizontal transport in combination with the meridional gradient of CO

_{2}[20]; i.e., the dominant part of XCO

_{2}variability occurs on synoptic time scales which range from one day up to more than a week, and diurnal changes in XCO

_{2}are smaller on average. Performing e.g., n = 100 TCCON measurements per day, with a single-measurement precision of 0.8 ppm would mean that the 1-sigma standard error for a daily mean is reduced by sqrt(n) = 10 to be 0.08 ppm. This means that day-to-day changes in the order of up to 1 ppm can be measured practically without error. Even more, it is not daily means but annual means (calculated from ≈ 10,000 spectra) which are the basis for calculating annual growth rates. This gives qualitative insight as to why the confidence bands for case (i) are the smallest while confidence bands will become increasingly larger for longer sampling intervals (cases ii–v). We will present a quantitative analysis in the results Section.

#### 2.2.6. Combined Annual Growth Rates from Multiple Sites

#### 2.3. Forecast of 2020 Annual Growth Rate for Mauna Loa

^{−2}—given the confidence bands for the TCCON-derived growth rates (derived according to Section 2.2.5), and given the uncertainties of the forecast (2-sigma forecast uncertainty ±0.57 ppm/yr according to [22])?

_{2}) COVID-19-related emission reduction over 2020, provided by the International Energy Agency (IEA) at the end of April 2020 [6]. The authors used the IEA’s month-by-month projections of the reduced demand for oil and assumed the same profile for natural gas and coal, with an adjustment to account for the sharp reduction in coal use in China in February [22]. This emission estimate is in line with the high estimate of –7% [–3, –13%] given by [5]. Later in this paper, we will refer to the −8% scenario and the derived annual growth rate forecast [22] to illustrate the size of the potential effects in relation to the TCCON sensitivities.

## 3. Results

#### 3.1. TCCON Trend

_{2}time series from the Garmisch TCCON site. For the time period (January 2011, December 2019) a mean linear trend of 2.46 [2.44, 2.49] (95% confidence) ppm/yr was derived using the mathematics outlined in Section 2.2. In Table 2, we compared this trend with three further mid-latitude stations; Table 1 gives station details.

_{2}observations above Garmisch until the end of May 2020. The latest blue crosses are the highest values measured in the whole Garmisch time series: calculating the monthly mean for April 2020 from our daily observations yields a XCO

_{2}value of 413.4 [413.2, 413.6] (95% confidence) ppm.

^{−2}due to COVID-19. It is worth noting that we defined the 2020 annual growth rate as the annual mean 2020 minus the annual mean 2019. Therefore, assuming for simplicity a COVID-19-related trend changing point at the beginning of 2020 and a subsequent linear trend behavior, the −8% annual emissions reduction scenario [22] would result in a −6.4 ppm reduction towards the end of 2020, see orange line in insert of Figure 1. Note, this orange line is likely to be even steeper in the beginning, considering that daily global emissions decreased by –17% at their peak in early April [6].

#### 3.2. TCCON Annual Growth Rates

#### 3.2.1. Interannual Variability of TCCON Annual Growth Rates

_{2}annual growth rates covering the years (2012–2019) inferred from the TCCON time series. The analysis for the five sub-figures is based on the time series with differing temporal resolutions: a) using single-spectra time series, b) daily-mean time series, c) is based on weekly-means, d) on 2-weekly means, and e) on monthly means.

_{2}variability relative to the mean seasonal cycle is dominated by synoptic-scale horizontal advection along with the meridional CO

_{2}gradient [20]. A special example for the impact of differing circulation is that the annual growth rates for Zugspitze and Garmisch (sites separated only by ≈8 km horizontal distance) differ in Figure 2a, e.g., in 2018. The mechanism here is that synoptic horizontal advection dominates in the free troposphere relative to the boundary layer where there is less related activity. This is corroborated, e.g., via the observation of two CO

_{2}profiles above Park Falls, while a frontal system moved through the region: the profiles show an increase in free tropospheric CO

_{2}above 5 km by ≈5 ppm, but practically no change below (Figure 6 therein [20]). Due to the altitude difference, the column above Zugspitze (2.96 km asl.) is in the majority of cases fully located within the free troposphere, while the Garmisch column (0.74 km asl.) is not.

#### 3.2.2. Confidence Bands for the TCCON Annual Growth Rates

#### Oversampling with Single-Spectra Resolution

_{2}at a certain site over the year, relative to the mean seasonal cycle. As mentioned before, the XCO

_{2}variability relative to the mean seasonal cycle is dominated by the synoptic-scale horizontal advection along with the meridional CO

_{2}gradient and not by the local emission histories [20]. For example, free tropospheric CO

_{2}can vary by 5 ppm due to the overpass of a frontal system. This leads to an oversampling problem, when using fully resolved TCCON single measurements (time resolution ≈1 min).

_{2}values per day, and this implies the oversampling of natural variability. It is worth remembering that the dominant contribution to XCO

_{2}intra-annual variability (relative to the mean seasonal cycle) at a TCCON site originates from the synoptic-scale horizontal transport in combination with the meridional gradient of CO

_{2}[20]; i.e., the dominant part of XCO

_{2}variability occurs on synoptic time scales which range from one day up to more than a week.

#### Sampling with Synoptic-Scale Temporal Resolution

#### Undersampling with Monthly-Scale Temporal Resolution

_{2}variability, is exceeded. This goes along with an undersampling of the intra-annual evolution; this can be seen from Figure A1: while the 2019 late-summer XCO

_{2}minimum for Park Falls is well captured by all kinds of temporal samplings, it can be clearly seen that the 2018 late-summer minimum was extraordinarily sharp and this could not be captured by monthly-scale sampling resolution. Therefore, we consider the annual growth rates derived from TCCON time series with monthly-sampling resolution as not appropriate for the discussion of the TCCON sensitivity to the COVID-19 impact on CO

_{2}.

- The confidence bands in Figure 2a provide a measure for a contribution of ≈0.05 ppm/yr resulting from the propagation of single-measurement precision into TCCON-derived annual growth rates, but are no realistic measure for the total annual growth uncertainty (due to the oversampling/underrepresentation of the synoptic evolution).
- The black Figure 2b–d confidence bands from daily, weekly, and 2-weekly TCCON data (i.e., 0.38 [0.28, 0.44] ppm/yr) can be considered as the realistic total uncertainty estimate/range for the hemispherically representative annual growth rates attainable from the TCCON data; it is favorable to base the analysis of annual growth rates on the time series aggregated into synoptic-scale temporal resolution.
- For preferred synoptic-scale sampling, the annual growth rates from sites with differing sampling densities (see Table 1) become consistent (Figure 2). As a result, it makes sense to combine the annual growth rates of various sites to thereby reduce the confidence width as shown in Table 3 (i.e., not only use the site with the densest sampling).
- Aggregating TCCON time series into monthly means leads to an undersampling of the intra-annual XCO
_{2}evolution and thereby to unreliable annual growth rates and too large confidence bands.

#### 3.3. Synopsis of TCCON Annual Growth Rates with Mauna Loa 2020 Forecast

## 4. Discussion

#### 4.1. Discussion of Trend Results

_{2}growth down into a decrease compared to the year 2019. A step-forward working question would therefore be: what amount of reduction in the atmospheric XCO

_{2}increase do we expect from the estimated COVID-19-related emission reductions?

^{−2}reduction in the 2020 annual growth rate due to COVID-19? If not, what is the detection delay?

#### 4.2. Discussion of TCCON Annual Growth Rates

_{2}growth with units ppm/yr, we point here to the basic difference: the multi-annual trend can be considered as the multi-annual mean of the annual growth rates; and it is important to note that there is a significant interannual variability of the annual growth rates relative to the mean trend (Figure 4).

_{2}emissions from fossil fuel consumption and cement production, and the total emissions including deforestation, have been nearly constant between 2014 and 2016. This was caused by a large El Niño event leading to a drying and warming which caused tropical ecosystems to take up less carbon than in other years [2,3]. It is well understood that interannual variability in annual growth rates is dominated by the variability of the ocean and land-vegetation sinks driven by climate variability, while anthropogenic emissions (dominated by fossil fuel emissions) are driving the overall long-term growth of atmospheric CO

_{2}[4].

#### 4.3. Can TCCON Measure a COVID-19-Related Reduction of the Annual Growth Rate? Discussion of Five Cases

^{−2}—given the confidence bands for the TCCON-derived growth rates (red lines in Figure 4), and given the uncertainties of the forecast (blue vertical error bar in Figure 4)? We will elaborate answers to the question of TCCON sensitivity for the five cases summarized in Table 4.

#### 4.3.1. Case (i)

^{−2}, and further assumed that the forecast is true (i.e., zero forecast uncertainty). We used the synoptic scale hemispherically representative TCCON 95% confidence bands (0.38 [0.28, 0.44] ppm/yr from Table 3).

^{−1}/0.32 ppm yr

^{−2}= 0.6 [0.4, 0.7] yr. This number can be interpreted as a measure for the delay contribution of the synoptic variability of XCO

_{2}to the total attainable detection delay. We note that the delay in this case is not limited by the TCCON single-measurement precision (for details, see discussion in Section 3.2.2).

#### 4.3.2. Case (ii)

^{−1}/0.32 ppm yr

^{−2}= 0.08 yr which is ≈1 month. This number can be interpreted as a measure for the delay contribution of TCCON single-measurement precision to the total attainable detection delay.

#### 4.3.3. Case (iii)

^{−2}starting in 2020 and assumed to stay constant on this level during the subsequent years. We further assumed forecast uncertainties to apply in the full width of ±0.57 ppm/yr (±2 sigma), as given in [22], see vertical blue error bar indicated in Figure 4 for 2020.

^{−2}taken as truth and to be measured by TCCON (red lines). Therefore, it is obvious from Figure 4, that no significant growth rate reduction can be measured in this case. Of course, the same holds true if the growth rate reduction were limited to 2020 only. The mechanism limiting this (infinite) delay is the forecast uncertainty.

#### 4.3.4. Case (iv)

^{−2}starting in 2020 as in the cases before based on a −8% emissions reduction in 2020. However, here we additionally assumed a year-on-year increase in the growth rate reduction by −0.32 ppm yr

^{−2}. It is worth noting that this case describes a desirable progressive emission reduction over the years, which may or may not be COVID-19-related after 2020. This is comparable to the emission reductions needed year-on-year over the next decades to limit global warming to 1.5 °C [1]. We further assume a forecast error of ±0.57 ppm/yr and use the TCCON 95% confidence bands for synoptic-scale data samples (0.38 [0.28, 0.44] ppm/yr).

^{−2}(blue) and 2.48 ppm yr

^{−2}(red) until the blue minimum error bar matches the thick red (dashed red, thin red) maximum TCCON confidence line. This resulting detection delay is (0.57 ppm yr

^{−1}+ 0.5 × 0.38 [0.28, 0.44] ppm yr

^{−1})/0.32 ppm yr

^{−2}= 2.4 [2.2, 2.5] yr. The dominant mechanisms limiting this delay are the forecast uncertainty, plus an additional smaller contribution from synoptic variability. This detection delay can be interpreted as realistically achievable given the forecast uncertainty attained in [22].

#### 4.3.5. Case (v)

^{−1}+ 0.38 [0.28, 0.44] ppm/yr)/0.32 ppm yr

^{−2}= 5.2 [4.8, 5.3] yr. The dominant mechanisms limiting this delay were the max–min range of the previous observations with an additional smaller contribution from synoptic variability.

## 5. Summary and Conclusions

_{2}. The question of this paper was, whether we could still detect any reduction effects in the atmospheric column concentrations due to COVID-19?

_{2}for the reference case without the COVID-19 impact. There is also no point in referencing the growth rate measured the year before. This is because there are large year-to-year growth rate changes which are dominated by climate variability impacting the land and ocean sinks. Anthropogenic emissions and their changes over time, while driving the overall long-term growth of atmospheric CO

_{2}, are only a minor contributor to year-to-year changes in the atmospheric growth rate.

_{2}relative to a model forecast of the reference case without COVID-19. This included an in-depth analysis of the uncertainties inherent to the TCCON observations and the forecast.

_{2}.

_{2}growth rates are basically given by intra-annual synoptic scale variability, including non-uniform sampling effects (0.38 [0.28, 0.44] ppm/yr, 95% confidence), and by XCO

_{2}measurement precision (0.05 ppm/yr) as a minor contribution.

^{−2}for 2020 to be true and measured. We then calculated the attainable “detection delay”, i.e., how much time it would take TCCON to measure the “true” 2.48 ppm/yr growth rate until a significant difference vs. the forecasted 2.8 ppm reference case could be obtained given the TCCON confidence and the forecast uncertainty. We thereby obtained the following results:

- (i)
- There is a 0.6 [0.4, 0.7]-yr contribution to the detection delay due to the impact of synoptic variability on XCO
_{2}observations. This was inferred solely from the TCCON data analysis. The forecast-based verification of this result, however, was not feasible. This is because the forecast uncertainty for the forecasted reference case (without the COVID-19 impact) exceeds the forecasted (and to-be-measured) 2020 growth rate reduction. The currently attainable forecast confidence is only ≈10% narrower than the max–min range observed by TCCON during the last 10 years. - (ii)
- There is a ≈1-month (0.08-yr) contribution to the detection delay, originating from the (0.8 ppm) single-measurement precision of the TCCON measurements on the ≈1 min scale.
- (iii)
- Taking the reported forecast uncertainty of ±0.57 ppm/yr for the forecasted reference case (without the COVID-19 impact) fully into account, a one-time growth rate reduction of −0.32 ppm yr
^{−2}in 2020 cannot be detected. The same holds true if the growth rate reduction would stay constant on the same level during the subsequent years. - (iv)
- We assumed a growth rate reduction of −0.32 ppm yr
^{−2}starting in 2020, as in the cases before based on a −8 % emissions reduction in 2020. However, we then additionally assumed a year-on-year increase in the growth rate reduction by −0.32 ppm yr^{−2}. This describes a desirable progressive emission reduction over the years, which may or may not be COVID-19 related after 2020. This case is comparable to the rates of decrease needed over the next decades to limit climate change to a 1.5 °C warming. For this case, we derived an overall detection delay of 2.4 [2.2, 2.5] yr. This is limited by the forecast uncertainty with an additional contribution from synoptic variability. - (v)
- Finally, assuming the same type of progressive growth rate reduction, we investigated the case that no forecast for the reference case (without the COVID-19 impact) would be available. The idea to derive a detection delay was that due to the progressive growth rate reduction assumed, that the growth rate will leave at a certain point the max–min range of the previous observations. The resulting overall detection delay is 5.2 [4.8, 5.3] yr.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**Park Falls time series aggregated into five differing temporal resolutions, i.e., single-spectra (≈1 min), daily, weekly, 2-weekly, and monthly resolution.

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**Figure 1.**Daily-mean XCO

_{2}time series for the TCCON site Garmisch. The model fit (red) comprises a linear trend along with a fourth order Fourier series. The insert shows in addition in orange the forecasted trend reduction in 2020 due to COVID-19 [22] along with the tilted seasonal curve.

**Figure 2.**Annual XCO

_{2}growth rates for the TCCON sites Garmisch, Zugspitze, Park Falls, and Karlsruhe. The colored lines indicate the 95% confidence bands retrieved from the bootstrap resampling of the individual sites, and black is the multi-site combination: (

**a**) the analysis based on the single-spectra TCCON data; (

**b**) the analysis based on the daily-mean TCCON data; (

**c**) the analysis based on the weekly-mean TCCON data; (

**d**) the analysis based on the 2-weekly-mean TCCON data; and (

**e**) the analysis based on the monthly-mean TCCON data.

**Figure 3.**Width of the 95% confidence bands for the annual growth rates retrieved from the TCCON multi-site combination (gm, zs, pa, ka) as a function of the sampling resolution of the time series: single-spectra (≈1 min), daily, weekly, 2-weekly, and monthly resolution. Underlying data are the last row of Table 3.

**Figure 4.**Hemispherically representative annual growth rates derived from a combination of the TCCON sites Garmisch, Zugspitze, Karlsruhe, and Park Falls. The thick black lines give the 95% confidence band derived from the measured time series aggregated into weekly means, the thin black is from the 2-weekly sampling resolution, the dashed black is from daily sampling, the while grey is from using ≈1-min single-spectra sampling. The red and blue stars are the forecasts for Mauna Loa, Hawaii (MLO), with and without the COVID-19 impact [22]. The blue vertical error bars represent 2-sigma forecast uncertainty (±0.57 ppm/yr), and the red lines are the TCCON confidence bands.

**Table 1.**Total Carbon Colum Observing Network (TCCON) sites of this study and the sampling characteristics.

Site | Lat. | Lon. | Alt. (km) | Measurement Days per Year (Average) | Spectra per Day (Average) | Single Spectra Integration Time (s) | Data Set |
---|---|---|---|---|---|---|---|

Garmisch (gm ^{1}) | 47°N | 11°E | 0.74 | 127 | 79 | 95 | [25] |

Zugspitze (zs) | 47°N | 11°E | 2.96 | 110 | 37 | 18/97 ^{2} | [26] |

Karlsruhe (ka) | 49°N | 8°E | 0.12 | 120 | 46 | 35 | [27] |

Park Falls (pa) | 46°N | 90°W | 0.44 | 238 | 118 | 95 | [28] |

^{1}Site indexes used throughout the paper.

^{2}Before/after 17 Aug 2017.

Site | Fitted Period | Trend Slope [ppm/yr] | Confidence Interval [ppm/yr, 95%] |
---|---|---|---|

Garmisch | (Jan 2011–Dec 2019) | 2.46 | [2.44, 2.49] |

Karlsruhe | (Jan 2011–Dec 2019) | 2.46 | [2.43, 2.49] |

Park Falls | (Jan 2011–Dec 2019) | 2.44 | [2.42, 2.46] |

Zugspitze | (Jan 2016–Dec 2019) | 2.42 | [2.33, 2.50] |

Combined (gm, ka, pa) | (Jan 2011–Dec 2019) | 2.45 | [2.44, 2.47] |

Site | Monthly (ppm/yr) | 2-Weekly (ppm/yr) | Weekly (ppm/yr) | Daily (ppm/yr) | Single (ppm/yr) |
---|---|---|---|---|---|

Garmisch | 1.02 | 0.86 | 0.73 | 0.53 | 0.07 |

Karlsruhe | 1.03 | 0.91 | 0.82 | 0.60 | 0.10 |

Park Falls | 0.69 | 0.60 | 0.53 | 0.40 | 0.04 |

Zugspitze | 0.88 | 0.74 | 0.64 | 0.49 | 0.20 |

Combined (gm, ka, pa, zs) | 0.51 | 0.44 | 0.38 | 0.28 | 0.05 |

Case (i)−(v) Assumptions | Delay Type | Delay Time (yr) | Data Basis | Dominant Mechanism |
---|---|---|---|---|

(i) one-time growth rate reduction 2020 = −0.32 ppm yr^{−2}; forecast error = 0; TCCON confidence (weekly sampling) = 0.38 ppm/yr | delay contribution | 0.6 [0.4, 0.7] | weekly TCCON data | weekly-scale synoptic variability of XCO_{2} |

(ii) one-time growth rate reduction 2020 = −0.32 ppm yr^{−2}; forecast error = 0; TCCON confidence (single-spectra sampling) = 0.05 ppm/yr | delay contribution | 0.08 | single-spectra TCCON data | TCCON single-measurement precision |

(iii) growth rate reduction starting 2020 and constant afterwards = −0.32 ppm yr^{−2}; forecast error = ±0.57 ppm/yr | overall delay | ∞ | forecast error | forecast error |

(iv) growth rate reduction starting 2020 and linear annual increase afterwards = −0.32 ppm yr^{−2}; forecast error = ±0.57 ppm/yr; TCCON confidence (weekly sampling) = 0.38 ppm/yr | overall delay | 2.4 [2.2, 2.5] | forecast error and weekly TCCON data | forecast error |

(v) growth rate reduction starting 2020 and linear annual increase afterwards = −0.32 ppm yr^{−2}; no forecast error available; TCCON max–min range (weekly sampling) = 1.27 ppm/yr; TCCON confidence (weekly sampling) = 0.38 ppm/yr | overall delay | 5.2 [4.8, 5.3] | forecast error and weekly TCCON data | observed max–min range of growth rates |

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**MDPI and ACS Style**

Sussmann, R.; Rettinger, M.
Can We Measure a COVID-19-Related Slowdown in Atmospheric CO_{2} Growth? Sensitivity of Total Carbon Column Observations. *Remote Sens.* **2020**, *12*, 2387.
https://doi.org/10.3390/rs12152387

**AMA Style**

Sussmann R, Rettinger M.
Can We Measure a COVID-19-Related Slowdown in Atmospheric CO_{2} Growth? Sensitivity of Total Carbon Column Observations. *Remote Sensing*. 2020; 12(15):2387.
https://doi.org/10.3390/rs12152387

**Chicago/Turabian Style**

Sussmann, Ralf, and Markus Rettinger.
2020. "Can We Measure a COVID-19-Related Slowdown in Atmospheric CO_{2} Growth? Sensitivity of Total Carbon Column Observations" *Remote Sensing* 12, no. 15: 2387.
https://doi.org/10.3390/rs12152387