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\begin{document}
\title{The Fossil Fuel Emissions of Tokyo estimated directly from measurements of the Tsukuba TCCON site}
\runningtitle{Tokyo Emissions from TCCON}

\Author[1,*]{Arne}{Babenhauserheide}
\Author[1]{Frank}{Hase}
\Author[2]{Isamu}{Morino}
\affil[1]{IMK-ASF, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany}
\affil[2]{National Institute for Environmental Studies (NIES), Tsukuba, Japan}
\affil[*]{now at Disy Informationssysteme GmbH, Karlsruhe, Germany}

%% The [] brackets identify the author with the corresponding affiliation. 1, 2, 3, etc. should be inserted.

\runningauthor{A.~Babenhauserheide}

\correspondence{Arne Babenhauserheide (arne\_bab@web.de)}


\received{}
\pubdiscuss{} %% only important for two-stage journals
\revised{}
\accepted{}
\published{}

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\firstpage{1}

\maketitle



\begin{abstract}
  We present a simple approach for estimating the greenhouse gas
  emissions of large cities using accurate long-term data of
  column-averaged greenhouse gas abundances collected by a nearby FTIR
  (Fourier Transform InfraRed) spectrometer.

  We estimate the average yearly carbon emissions from the area of Tokyo to be
  \(86 \pm 33 \frac{MtC}{\text{year}}\) between 2011 and 2016, calculated using only
  measurements from the TCCON site in Tsukuba (north-east of Tokyo)
  and wind-speed data from nearby radiosondes.
\end{abstract}


\copyrightstatement{The article and all its materials are provided under the Creative Commons Attribution 4.0 License.}


\introduction  %% \introduction[modified heading if necessary]

Anthropogenic emissions of carbon dioxide are the strongest long-term
control on global climate \citep[Figure 12.3, page 1046]{IPCCLongtermProjectionsCollins2013}, 
and the Paris agreement
\citep{ParisAgreement2015} ``recognizes the important role of
providing incentives for emission reduction activities, including
tools such as domestic policies and carbon pricing``. Implementing
carbon pricing policies as an effective tool to reduce
emissions and stimulate research requires accurate measurements of
carbon emissions 
\citep[ch. 2.6.4 and 2.6.5, pp. 181ff]{IPCCWG3_2014_Ch2_RiskResponse}.

The carbon dioxide footprint of large scale fossil fuel burning emitters has been retrieved from satellite
\citep{Bovensmann2010,GRL:GRL55137,Hammerling2012,GRL:GRL55137,Ichii2017,Deng2014,Butz2016}
and via ground based differential measurements using multiple mobile
total column instruments \citep{Frey2015,Hase2015,Chen2016}. Inverse modelling
allows coupling in-situ measurements (which only capture enhancements
in mixing ratio close to the ground) with atmospheric transport for
similar investigations
\citep[i.e.][]{vanderLaanLuijkx2017,BasuHouwelingPeters2011,Babenhauserheide2015,vanderVelde2014b,Tolk2012},
but due to short mission times of satellites and differential
measurement campaigns and high uncertainties when using in-situ data,
long term changes in emissions are typically derived from economic
fossil fuel and energy consumption data
\citep[i.e.][]{Andres_2011,TokyoCapNTrade2010,CT_FossilFuel_Geocarbon,vanderVelde2014,LeQuere2015,LeQuere2016}.

The Total Carbon Column Observing Network \citep[TCCON,][]{Wunch2011,ToonBlavierWunch2009} provides highly
accurate and precise total column measurements of carbon dioxide
mixing ratios with multi-year
records of consistently derived data.

% TODO: include if it gets through peer review and modelling the
% spatial patterns of fossil fuel emissions suggests that
% surface-based networks are able to detect 30\% reductions in carbon
% emissions \citep{Liu2017}

The aim of our study is to provide an estimate of the Tokyo
\chem{CO_2} emissions by correlating measured X\chem{CO_2} with wind
speed and direction, resulting in a measurement-driven approach to derive the
annual carbon dioxide emissions of Tokyo city (Japan) using four years
of measurements (2011-08-04 -- 2016-03-30) by the TCCON site at
Tsukuba, Japan, along with radiosonde measurements of daily local wind
profiles. This method provides an inexpensive approach to estimate
city emissions which is easy to reproduce and to establish, and is
suitable for long-term monitoring.

\section{Observations}

The column data from TCCON provides the currently best measurements of
the column averaged \chem{CO_2} abundances. The average station-to-station bias is less
than 0.2~\unit{ppm} \citep{Wunch2011}.

The stations of the TCCON-network measure the absorption of CO\(_2\) in the solar spectrum \citep{Wunch2011}. Dividing this absorption by the absorption of O\(_2\) yields a pressure-independent measure for the concentration of carbon dioxide in the atmospheric column (XCO\(_2\)). The precision of these measurements is better than 0.2ppm (0.2\%) by \citet{Messerschmidt2011}. Since this study restricts itself to a single station it can ignore constant scaling factors.

This study uses the current 
dataset of column-averaged carbon dioxide abundances generated with 
GGG2014 from solar absorption spectra recorded at the Tsukuba TCCON station, Japan \citep{Ohyama2009,Morino2016}. Available data from Tsukuba at the TCCON data site\footnote{TCCON data is publicly available from \href{http://tccondata.org/}{tccondata.org}} station used in this study extends from 2011-08-04 to 2016-03-30. The coordinates of the Tsukuba TCCON site are 140.12\(^{\circ}\) East and 36.05\(^{\circ}\) North, the altitude is 31m.\footnote{Essential information about the TCCON site in Tsukuba is available from the TCCON wiki via \href{https://tccon-wiki.caltech.edu/Sites/Tsukuba}{https://tccon-wiki.caltech.edu/Sites/Tsukuba}} In addition to concentration data of trace gases, the station provides wind direction and speed measured at the rooftop of the observatory.

\clearpage

\section{Removing trend and natural cycles}
\label{sec:residuals}

\begin{figure}[t]
\includegraphics[width=8.3cm]{tk20110804-20160330-public-fit-xco2.pdf}
\caption{Detrending and deseasonalization of the XCO\(_2\) total column measurements in Tsukuba, Japan. The trend is removed with a linear fit to the full dataset (shown as a red ``trend'' line), the seasonal cycle from the signal due to photosynthesis, respiration and decay (shown as ``yearly cycle fit, degree 6'') is removed by fitting a polynomial of degree 6 to the combined yearly cycles of the detrended data. Degree 6 was chosen empirically.\label{fig:removetrendandseasonalcycle}}
\end{figure}

\begin{figure}[t]
\includegraphics[width=8.3cm]{tk20110804-20160330-public-fit-daily-xco2.pdf}
\caption{To remove a potential bias from correlation of wind direction and daytime which would couple the signal from photosynthesis and respiration, the daily cycle is removed by fitting and subtracting a polynomial of degree 4. Degree 4 was chosen empirically.\label{fig:removedailycycle}}
\end{figure}

To estimate the emissions of Tokyo directly from the measurements, they must be made accessible to a simple statistical analysis. Column averaged atmospheric CO\(_2\) abundances are subject to strong seasonal variations and a yearly rise of about 2.0 ppm per year \citep[][page 167 in section 2.2.1.1.1]{IPCCObservationsAtmosphereSurfaceHartmann2013}. Additionally there’s an average daily cycle of about 0.3 ppm in the densely measured daytime between 2:00 UTC and 7:00 UTC (local time between 11:00 and 16:00 GMT+9). To allow direct comparisons of values from different times of year and times of day, these cycles are removed by fitting and subtracting polynomials from the data: linear for the trend, degree 6 for the yearly cycle (roughly equivalent to bi-monthly granularity) and degree 3 (roughly 3-hour granularity) for the daily cycle. This daily cycle is fitted against measurements from all directions, so the fitting might remove a certain amount of the actual daily cycle of emissions, however the impact of this fitting in final estimates is limited to wind directions correlated with the time of day. Such a correlation exists, but mainly outside the densely measured daytime (a graph is available in the supplement of this paper). The programs are provided in the supplement of this paper. Figure \ref{fig:removetrendandseasonalcycle} and \ref{fig:removedailycycle} show the fits and residuals from the process. The calculations only use data provided directly from the TCCON network. The degrees of the fits were chosen empirically (by manual adjustment) to minimize the residuals over all TCCON sites available in 2016 \citep[][in preparation]{BabenhauserheideCTTCCON2018}.
% TODO: maybe fit only against wind from background directions.

\clearpage

\section{Directional dependence of remaining differences}

\begin{figure*}[t]
\includegraphics[width=16cm]{tk20110804-20160330-public-hexbin-wind-speed-xco2.pdf}
% need an optional argument to caption for the list of figures to be able to use a footnote.
\caption[The \textbf{left graph} shows a map of Tokyo and its surroundings, The \textbf{right graph} shows the positive half of the residuals from Figure \ref{fig:removedailycycle}, binned by wind direction and -strength.]{The \textbf{center graph} shows a map of Tokyo and its surroundings, retrieved from the ArcGIS REST service\footnotemark~with an overlay indicating the surface type. The colors in the overlay visualize land-use and settlement density \citep[taken from][]{Hasi2014}. It clearly shows decreasing population density with distance from Tokyo city, along with the long tail of Tokyo settlements towards the north west. Close by Tokyo Bay in the lower center of the map, at the south east perimeter of Tokyo and on the opposite shore, there are multiple coal and gas power plants. Tokyo city center and the position of the TCCON site in Tsukuba are marked along with white lines which form an opening angle for incoming wind at Tsukuba which is interpreted as coming from Tokyo Area, along with additional widening by 30\(^{\circ}\) as estimate of the actual origin of transported CO\(_2\) arriving at Tsukuba from the given wind direction. These white lines denoting the incoming wind angle limits are reproduced in the \textbf{right graph} and the \textbf{left graph} as delimiting directions in which the wind blows from west Tokyo area. The \textbf{right} graph shows the \textbf{positive} half of the residuals from Figure~\ref{fig:removedailycycle}, binned by wind direction and -strength. The color represents the mean value of the positive residuals within the bin. The \textbf{left} graph shows the \textbf{negative} half of the residuals from Figure~\ref{fig:removedailycycle}, binned by wind direction and -strength. The color represents the mean value of the negative residuals within the bin. The black arrow at the upper edge of the left graph indicates that values for wind speeds above 50 m/s have been left out to focus on the area between 5 and 15 m/s used in the later evaluation. Splitting the residuals into positive and negative values is done to simplify visual detection of emissions without interference from effective sinks. In the following, detailed treatment of the residuals uses both positive and negative residuals.\label{fig:binning}}
\end{figure*}
% Text for footnote in the figure.
\footnotetext{retrieved as EPSG:4301 using a ESRI\_Imagery\_World\_2D request to \href{http://server.arcgisonline.com/ArcGIS}{server.arcgisonline.com/ArcGIS} via the basemap library in matplotlib \citep{Hunter2007} as described at \href{http://basemaptutorial.readthedocs.io/en/latest/backgrounds.html\#arcgisimage}{basemaptutorial.readthedocs.io/en/latest/backgrounds.html\#arcgisimage}. Used by permission (Permission for publication of this graph under creativecommons attribution license granted by Esri). Copyright (c) (2017) Esri, ArcGIS.  All rights reserved.}

To calculate the carbon source of Tokyo, the residuals described in section \ref{sec:residuals} are binned by wind direction and speed, as shown in Figure \ref{fig:binning}. A major source of uncertainty in this endeavor is the actual extent of Tokyo. This extent was chosen as 170\(^{\circ}\) to 240\(^{\circ}\) as seen from the TCCON site in Tsukuba, following the 2D histogram shown in the right panel in Figure \ref{fig:binning}. Within these directional delimiters, the interval with wind speeds between 5 and 15 ms\(^{-1}\) contains only bins with an enhanced concentration of CO\(_2\). Perfect definition of these limits isn’t possible in the Scheme presented here, because the area can only be delimited orthogonal to the wind direction measured in Tsukuba. In parallel direction the only limit are changes in wind direction over time. This is indicated by the weaker enhancement seen for wind speeds below 5 ms\(^{-1}\).

Using \(\Delta\)XCO\(_2\), a measure proportional to the carbon dioxide column enhancement, and the effective wind speed ascribed to these enhancements from the direction of Tokyo allows estimating the source of Tokyo. However, the directly measured wind speed which is provided by the TCCON network only provides an approximate indication of the effective wind speed and direction in the altitude range carrying the enhanced carbon dioxide \citep[similar to the effects discussed by][for differential measurements of the emissions]{Chen2016}.

\subsection{Effective wind speed}
\label{sec:wind-speed}

Estimating the wind speed of air with enhanced carbon dioxide concentrations due to emissions from Tokyo requires taking the difference in height of the measured concentrations and the measured wind speed into account. To this end, the ground wind speed \(v_{wind}\) can be replaced by the density weighted average wind speed profile within the boundary layer.\footnote{Trajectories from Tokyo calculated with hysplit \citep{Rolph2017,Stein2015} show that most air parcels from Tokyo arriving at Tsukuba are contained within the lowest 2km of the atmosphere.} Radiosonde data from Tateno, Japan, situated close to Tsukuba station, provides 7 years of measurements from 2009 to 2016.\footnote{Data was retrieved from the Atmospheric Soundings site at University of Wyoming (\href{http://weather.uwyo.edu/upperair/sounding.html}{http://weather.uwyo.edu/upperair/sounding.html}). One example of these data sets is by \citet{ijima2016rmfs2015-12--858510}. Further details are available in the auxiliary material in the supplement of this paper.} Figure \ref{fig:tateno-wind-profiles} visualizes the variability of the profile by atmospheric pressure. The average wind speed in the profile is used to derive daily scaling factors from the ground wind speed to the average profile wind speed. These scaling factors are applied to the ground wind speed measured at the TCCON site in Tsukuba to estimate the effective wind speed of the volume of air with enhanced carbon dioxide concentration in the total column.

These scaling factors are provided in the auxiliary material but provide a significant source of uncertainty, since their use rests on the assumption on uniform mixing of the carbon emissions across the boundary layer. Forward trajectory calculations with HYSPLIT \citep{Stein2015} suggest that 50 km transport distance suffices for particles to reach the top of the boundary layer, but they do not prove that this suffices to generate a uniform \(CO_2\) mixing ratio. Therefore, as also seen by \citet{Chen2016}, the unknown actual transport pathway of emitted \(CO_2\) to the measurement location is a significant source of uncertainty.

\begin{figure*}[t]
\includegraphics[width=8.3cm]{tateno-sounding-profiles-boxplot.pdf}
\caption{Wind speed profile statistics up to 1000~m at Tateno, Japan using data from 2009 to 2016, including \citet{ijima2016rmfs2015-12--858510}. Values are calculated by dividing the wind speed at a given pressure by the wind speed at the lowest level. The boxplots show the median (red line) and the mean (green triangle). 50\% of values are within the box, the whiskers include 95\% of the values and the rest is shown as outliers (black circles). The notch in the box shows the uncertainty of the median calculated via resampling.\label{fig:tateno-wind-profiles}}
\end{figure*}


\clearpage

\section{Estimated carbon source of Tokyo}
\label{sec:source-of-tokyo}

\begin{figure*}[t]
\includegraphics[width=12cm]{tk20110804-20160330-public-tsukuba-residuals-xco2.pdf}
\caption{Residuals multiplied by wind speed plotted against the wind direction for scaled wind speeds between 5 ms\(^{-1}\) and 15 ms\(^{-1}\); measured by the TCCON site in Tsukuba, Japan. The mean enhancement \(\bar\Delta\), the mean Tokyo and median Tokyo and the std are calculated for the directions defined as from Tokyo in section \ref{fig:binning}. The median background is calculated from the residuals outside the background limits (drawn as vertical lines).\label{fig:residuals-times-windspeed}}
\end{figure*}

To calculate the source of Tokyo \(S_T\), the measured total column enhancement \(E_m\) (in \(\left [ g_{CO_2} \right ]\)) is multiplied with the \textit{area affected per second} by the emission source from within Tokyo area, \(At_{\textit{aff,Tokyo}}\) (in \(\left [ \frac{m^2}{s} \right ]\)):

\begin{equation}
  \label{eq:source-from-measurement}
  S_T = E_m \cdot At_{\textit{aff}}
\end{equation}

This affected area per second can be calculated from the wind speed of the volume of air with enhanced concentrations at the measurement location, approximately the average column wind speed \(v_{wind}\), and the spread of the Tokyo area perpendicular to the wind speed \(d_\perp\).

\begin{equation}
  \label{eq:affected-area}
  At_{\textit{aff}} = v_{\text{wind}} \cdot d_\perp
\end{equation}

The perpendicular spread \(d_\perp\) is calculated by assuming that total columns of carbon dioxide from Tokyo area are transported to the measurement location without effective divergence perpendicular to the wind direction and assuming approximately circular city structure. Therefore this spread can be approximated from the distance between Tokyo city center and the TCCON measurement site in Tsukuba:

\begin{equation}
  \label{eq:perpendicular-spread}
  d_\perp \approx 2 \pi \cdot d_{\text{Tsukuba--Tokyo}} \cdot \frac{\Delta\alpha}{360^{\circ}}
\end{equation}

with \(\Delta\alpha\) the opening angle of the limits of wind directions associated with Tokyo and \(d_{\text{Tsukuba--Tokyo}} \approx 65 \text{km}\)\footnote{The city center of Tokyo was chosen to be at the palace.}. Due to measuring total columns, vertical divergence only affects the height of the enhancement in the column and therefore the wind speed of air with enhanced concentrations at the measurement location. Treating 170\(^{\circ}\) to 240\(^{\circ}\) as wind direction coming from Tokyo, this yields a perpendicular spread of 79.4 km.

The angle-integrated \(E_m \Delta t_{\textit{aff}}\) is collected into contributions from different wind directions:

\begin{equation}
  \label{eq:separate-by-direction}
  E_m At_{\textit{aff}} = \int_\alpha E_{m,\alpha} At_{\textit{aff},\alpha} d\alpha = \frac{d_\perp}{\Delta \alpha} \cdot \int_\alpha E_{m,\alpha} v_{\text{wind},\alpha} d\alpha = d_\perp \bar \Delta_{CO_2}
\end{equation}

Here \(\bar{\Delta}_{CO_2}\) denotes the mean enhancement as depicted in Figure \ref{fig:residuals-times-windspeed}.

\(\bar{\Delta}_{CO_2}\) is calculated from the XCO\(_2\) residuals (described in section \ref{sec:residuals}). The median total column residual from background wind directions (chosen as 310° to 50°, using 0° as from north following meteorological conventions) is subtracted from the target direction residuals, then the result is multiplied with the wind speed during the time of measurement. Finally it is converted from measured total column concentration \(C_{CO_{2},t,\text{col}}\) to total column mass \(m_{CO_{2},\text{col}}\).

\begin{eqnarray}
\text{unit air column mass:}&m_{\text{air},\text{col}}&= ~ \frac{p_t}{g_{a_t,t}} \cdot 10^5 \left[ \frac{g}{m^{2}} \right] \\
\text{\(CO_{2}\) column mass:}&m_{CO_{2},\text{col}}&= ~ \frac{M_{CO_2}}{M_{\text{air}}} \frac{m_{\text{air},\text{col}}}{f_{col}} \cdot C_{CO_{2},t,\text{col}} \\
\text{total column residuum:}&R&= ~ m_{CO_{2},\text{col}} - m_{CO_{2},\text{col},\textbf{seasonal cycle fit}} - m_{CO_{2},\text{col},\textbf{daily cycle fit}} \text{; (described in section \ref{sec:residuals})} \\
\text{enhancement:}&E_m&= ~ R_{\text{from Tokyo area}} - \text{median}\left(R_{\text{from background}}\right)
\end{eqnarray}

at time \(t\), level \(l\) and daily apriori \(a_t\)\footnote{\(f_{col} = 0.9975\) is a column mass correction following \citet{Bannon_1997}} with

\begin{tabular}{p{3.5cm}l}
tracer mass & \(m_{\text{gas},\text{col}}\), \\
total column air mass & \(m_{\text{air},\text{col}}\), \\
column concentration & \(C_{CO_2,t,\text{col}}\), \\
molar masses & \(M_{CO_2} = 44.0 \frac{g}{mol}\) and \(M_{\text{air} = 28.9 \frac{g}{mol}}\), \\
gravity & \(g_{a_t,l}\) (from TCCON apriori), \\
pressure & \(p_t\). \\
\end{tabular}

From the mean enhancement \(\bar{\Delta}_{CO_2}\) the source of Tokyo is derived as

\begin{equation}
\label{eq:source-tokyo}
.S_T = \bar{\Delta}_{CO_2} \cdot d_\perp = 126 \pm 29 \frac{g_{CO_2}}{ms} \cdot 79400 m = 10.0 \pm 2.3 \frac{t_{CO_2}}{s}
\end{equation}

The given uncertainty is taken from the standard deviation as shown in Figure \ref{fig:residuals-times-windspeed}.

For comparison with city emission inventories, the \(CO_2\) source is scaled to yearly carbon emissions:
\begin{eqnarray}
\label{eq:scale-co2second-to-cyear}
S_{T,\text{C},\text{yearly}} &=& \bar{\Delta}_{CO_2} \frac{M_C}{M_{CO_2}} d_\perp \cdot \frac{s}{\text{year}} \\
 &=& 126 \pm 29 \left[\frac{g_{CO_2}}{ms}\right] \cdot \frac{12}{44} \left[\frac{g_C}{g_{CO_2}}\right] \cdot 79400 m \cdot 31557600 \frac{s}{\text{year}} \\
  &=& 86 \pm 20\frac{Mt_C}{\text{year}}
\end{eqnarray}

For comparison with gridded emission inventories, the \(CO_2\) emissions are scaled to average monthly carbon emissions per wind direction (in 1\(^{\circ}\) steps):
\begin{eqnarray}
\label{eq:scale-co2second-to-cmonthdeg}
S_{\tau,\text{CO\(_2\)},\text{average},\text{deg},\text{monthly}} &=& \bar{\Delta}_{CO_2} \frac{M_C}{M_{CO_2}} d_\perp \cdot \frac{s}{\text{month} \cdot \text{degree}} \\
 &=& 126 \pm 29 \left[\frac{g_{CO_2}}{ms}\right] \cdot \frac{12}{44} \left[\frac{g_C}{g_{CO_{2}}}\right] \cdot 1134 m \cdot 2592000 \frac{s}{\text{month} \cdot \text{degree}} \\
  &=& 101 \pm 23 \frac{kt_C}{\text{month} \cdot \text{degree}}
\end{eqnarray}


% TODO: integrate Notiz von Frank (plus Rechnung auf Zettel):
% ich habe jetzt das richtige Integral:
% s_quer = 1/arcsin(1/d) * integral[0 bis arcsin(1/d)] über 
% sqrt(1-(d*sin(alpha))^2)dalpha
% hier ist der Radius von Tokyo auf 1 normiert und s (die Sekantenlänge) und 
% s_quer (die winkelgemittelte Sekantenlänge) sind in Einheiten des 
% Kreisdurchmessers (also in absoluten Einheiten *2 zu nehmen). d, der Abstand 
% Kreismitte zum Beobachter ist also in Einheiten des Tokyo-Radius.
% Das Integral lässt sich mit irgendeinem CAS-Programm leicht auswerten, ich habe 
% mal mit dem TI89 ein paar Werte ausgerechnet (habe die Winkelausdehnung von 
% Tokyo leider nicht zur Hand)
% d   s_quer
% 10   0.7851
% 5   0.7841
% 3   0.7815
% 2   0.7760
% 1.5   0.7662
% 1   0.6366
% (Auf den Dir vorliegenden Zettel hatte ich mit 0.78 gerechnet, glaub ich)


% from bar Delta to yearly emissions:
% (/ (* 126 (/ 12.0 44.0) 79400 365.25 24 60 60) 1e12)
% => 87+-20MtC/year

% (* 78e3 0.04 60 60 24 365.25 1e-9)

\clearpage

\section{Estimating uncertainties}
\label{sec:uncertainties}
In addition to the statistical uncertainty and the uncertainty of the wind profile discussed in section \ref{sec:wind-speed}, the estimated emission depends on the selected extent of Tokyo area and is limited by the unknown actual distribution of distances of emission sources from the measurement site at Tsukuba.

Choosing different opening angles for air \emph{from Tokyo area} yields a yearly emission range from \(54.0 \pm 7.4 MtC \text{year}^{-1}\) when choosing air \emph{from Tokyo area} between 180\(^{\circ}\) and 220\(^{\circ}\) up to \(93 \pm 35 MtC \text{year}^{-1}\) when choosing air \emph{from Tokyo area} between 150\(^{\circ}\) and 260\(^{\circ}\). This uncertainty also plays a role in comparisons, if the actual wind direction higher up in the atmosphere is not distributed symmetrically around the wind direction at ground.

% xco2 column mass times wspd, sum of means minus median background from 180.0 to 220.0 : 4054.38067441
% xco2 column mass times wspd, mean of means minus median background from 180.0 to 220.0 : 138.32691209 +- 18.9780453491

% xco2 column mass times wspd, sum of means minus median background from 150.0 to 260.0 : 7515.41123606
% xco2 column mass times wspd, mean of means minus median background from 150.0 to 260.0 : 106.211466903 +- 39.8116552664

The distance of emission sources from the TCCON site in Tsukuba affects the estimated spread of the emission region perpendicular to the wind direction. This calculation assumes symmetric distribution of emission strengths parallel to the wind direction. This assumption is plausible, since the most densely populated region of Tokyo extends to the north west towards the prefecture of Saitama. However \citet{Hasi2014} and \citet{Oda2011} show a similar extension towards the south east, and the power plants are southward of the palace. If the ``center of mass'' of the emissions were located 10 km further away from the site, this would yield a 15\% increase of the estimate, in absolute numbers \(\color{blue}\pm 13\color{black} \frac{MtC}{\text{year}}\). This uncertainty always needs to be taken into account. Consequently the most robust estimate of the emissions of Tokyo is

\begin{eqnarray}
\label{eq:emission-uncertainties}
 \text{Yearly carbon emissions of Tokyo: }& S_{T,\text{C},\text{yearly}} &= 86 \pm 20 \color{blue}\pm 13\color{black} \frac{MtC}{\text{year}} \\
 \text{Monthly carbon dioxide emissions of Tokyo: }&   S_{\tau,\text{CO\(_2\)},\text{average},\text{deg},\text{monthly}} &= 101 \pm 23  \color{blue}\pm 15\color{black} \frac{kt_C}{\text{month} \cdot \text{degree}}
\end{eqnarray}


\clearpage
\section{Comparison with other Datasets}

\begin{figure*}[t]
\includegraphics[width=8.3cm]{plot-tokyo-2015-01.pdf}
\caption{Odiac carbon emissions per 1km\(\times\)1km in pixel for January 2015 in log\(_{10}\) scale. This graph is created directly from the 1km\(\times\)1km Odiac dataset \citep{Oda2011} to visualize its structure.\label{fig:odiac-emission-map}}
\end{figure*}

\begin{figure*}[t]
\includegraphics[width=8.3cm]{odiac-emissions-by-angle.pdf}
\caption{Sum of Odiac carbon emissions by direction as seen from Tsukuba, Japan. The ``aggregated odiac'' emissions show emissions per direction from beginning of 2011 to end 2016. The gaussian filter data uses a moving average with gaussian weight to estimate signals measured at a distance. The measured dataset shows the median residuals from figure \ref{fig:residuals-times-windspeed} for comparison.\label{fig:odiac-emissions-by-angle}}
\end{figure*}

To compare the results with the high-resolution Odiac emission inventory \citep{Oda2011},\footnote{Odiac data retrieved from \href{http://odiac.org/dataset.html}{http://odiac.org}} using the regional slice shown in Figure \ref{fig:odiac-emission-map}. Measurements are simulated from Odiac by summing over all emissions \emph{from Tokyo area} from 2011 to 2016 as (emissions by angle are shown in Figure \ref{fig:odiac-emissions-by-angle}), and then subtracting the sum of the emissions \emph{from background directions}:

\begin{equation}
\frac{1}{5}\sum_{t=2011-01}^{2015-12} \left( \sum_{\alpha}^{\text{Tokyo}} E_{odiac,t,\alpha} - \sum_{\beta}^{\text{bg}} E_{odiac,t,\beta} \right) = 40.4 \frac{MtC}{\text{year}},
\end{equation}

which is around half the emissions estimated in this paper from TCCON measurement data and within two standard deviations (\(2\sigma\)) of the estimated emissions.

The peak of the distribution of emissions (within ``from Tokyo area'') is shifted about 30° counterclockwise from model to measurements. This is within the expected shifts due to the typical shift in wind direction between measurements conducted close to the ground and measurements higher up in the planetary boundary layer. These discrepancies could be corrected for by using more complex atmospheric transport, but that would then require every reproduction to run such a transport, which would defeat the purpose of this study, namely to provide an easily reusable approach for estimating city emissions.

The economic data published by the \citet{TokyoCapNTrade2010} report emissions of \(57.7 \frac{MtCO_2}{\text{year}}\) in the fiscal year 2006 for the Tokyo Metropolitan Area. This is equivalent to \(15.7 \frac{MtC}{\text{year}}\) and shows a larger discrepancy to our results. This discrepancy which likely stems from different definitions for the source area. Part of this discrepancy cannot be reconciled, because the method shown in this paper cannot limit the emission aggregation parallel to the wind direction.

\clearpage


\conclusions[Conclusions and Outlook]  %% \conclusions[modified heading if necessary]

We find that a single multi-year dataset of precise column measurements provides valuable insights into the carbon emissions of city-scale emitters. The estimated emissions of \(86 \pm 33\) megatons carbon per year found for Tokyo has less than 40\% uncertainty despite our intentionally chosen constraint to use only a basic evaluation scheme which can be repeated on any personal computer with publicly available data. While the operation of a TCCON station is a major effort, a decade of CO\(_2\) column measurements of comparable quality can be conducted with affordable and easier to operate mobile spectrometers \citep[see for example][]{Frey2015} which opens an avenue for every country to measure and evaluate emissions of mega cities: Placing a single total column measurement site in the vicinity of a major city allows estimating its emissions. This can complement global source and sink estimates and improve acceptance of carbon trading programs by enabling independent verification of findings.

The uncertainties in these estimates could be further reduced by taking into account more detailed wind fields from meteorological models or by correcting for the wind direction at different altitudes. These corrections are already taken into account in source-sink estimates based on inverse modelling of atmospheric transport \citep[i.e.][]{vanderLaanLuijkx2017,Riddick2017,Massart_2014,Basu2013}, therefore we restrict ourselves to the simpler evaluation which allows us to stick closely to easily accessible data which keeps our findings easy to replicate.

Further uncertainty reductions can be achieved by establishing several observing sites within and around the source area. This approach also provides information about the spatial structure of emissions and can be used in focused measurement campaigns to obtain constraints for evaluation of measurements with lower spatial resolution as well as long term datasets.

To complete this outlook, we would like to suggest that the negative values seen on the left graph of Figure \ref{fig:binning} at a wind direction around 60\(^\circ\) indicate that it might also be possible to detect biospheric drawdown of CO\(_2\) by woodland with just a single total column instrument.

We conclude that long-term ground-based 
measurements of column-averaged greenhouse gas abundances with 
sufficient accuracy for detecting the signals of local emission sources 
are a cost-efficient approach to improve our knowledge about sources and 
sinks of greenhouse gases.

%% The following commands are for the statements about the availability of data sets and/or software code corresponding to the manuscript.
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\codedataavailability{All code used and pre-processed data in JSON format (as described in \href{https://tools.ietf.org/html/rfc7159}{RFC 7159}) are available in the supplementary material. See the README in the supplementary material for usage information.  The non-included data is publicly available from the TCCON data portal (\href{http://tccondata.org/}{tccondata.org}), from the Odiac project \href{http://odiac.org/dataset.html}{odiac.org}, and from the Atmospheric Soundings site at University of Wyoming (\href{http://weather.uwyo.edu/upperair/sounding.html}{weather.uwyo.edu/upperair/sounding.html}.} %% use this section when having data sets and software code available





% \appendix
% \section{}    %% Appendix A
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% \authorcontribution{TEXT} %% optional section

\competinginterests{The authors have no competing financial interests, but they are working on other projects with ground-based total column measurement instruments.} %% this section is mandatory even if you declare that no competing interests are present

% \disclaimer{TEXT} %% optional section

\begin{acknowledgements}
  Large parts of the inspiration for this method of evaluation and of
  the boldness to keep it simple are due to our treasured colleague
  Dr. Friedrich Klappenbach 
  \citep[especially his evaluation of CO\(_2\) in][]{Klappenbach2015}
  and the simple estimate of effective boundary layer wind speed from
  radiosonde data was suggested by Dr. Bernhard Vogel. Matthias Frey
  contributed insights into differential measurements of the Tokyo
  source using multiple portable spectrometers, as well as fruitful
  discussions about these evaluations. Support for this study was
  provided by the Bundesministerium für Bildung und Forschung (BMBF)
  through the ROMIC project, with funding for initial work provided by
  the Emmy-Noether program of the Deutsche Forschungsgemeinschaft
  (DFG) through grant BU2599/1-1 (RemoteC).

  The article processing charges for this open-access publication have
  been covered by a Research Centre of the Helmholtz Association.
\end{acknowledgements}


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\end{document}
