Network design for quantifying urban CO2 emissions: assessing trade-offs between precision and network density

Abstract

The majority of anthropogenic CO₂ emissions are attributable to urban areas. While the emissions from urban electricity generation often occur in locations remote from consumption, many of the other emissions occur within the city limits. Evaluating the effectiveness of strategies for controlling these emissions depends on our ability to observe urban CO₂ emissions and attribute them to specific activities. Cost-effective strategies for doing so have yet to be described. Here we characterize the ability of a prototype measurement network, modeled after the Berkeley Atmospheric CO₂ Observation Network (BEACO₂N) in California's Bay Area, in combination with an inverse model based on the coupled Weather Research and Forecasting/Stochastic Time-Inverted Lagrangian Transport (WRF-STILT) to improve our understanding of urban emissions. The pseudo-measurement network includes 34 sites at roughly 2km spacing covering an area of roughly 400km². The model uses an hourly 1 × 1km² emission inventory and 1 × 1km² meteorological calculations. We perform an ensemble of Bayesian atmospheric inversions to sample the combined effects of uncertainties of the pseudo-measurements and the model. We vary the estimates of the combined uncertainty of the pseudo-observations and model over a range of 20 to 0.005ppm and vary the number of sites from 1 to 34. We use these inversions to develop statistical models that estimate the efficacy of the combined model-observing system in reducing uncertainty in CO₂ emissions. We examine uncertainty in estimated CO₂ fluxes on the urban scale, as well as for sources embedded within the city such as a line source (e.g., a highway) or a point source (e.g., emissions from the stacks of small industrial facilities). Using our inversion framework, we find that a dense network with moderate precision is the preferred setup for estimating area, line, and point sources from a combined uncertainty and cost perspective. The dense network considered here (modeled after the BEACO₂N network with an assumed mismatch error of 1ppm at an hourly temporal resolution) could estimate weekly CO₂ emissions from an urban region with less than 5% error, given our characterization of the combined observation and model uncertainty.

Atmos. Chem. Phys., 16, 1346513475, 2016 www.atmos-chem-phys.net/16/13465/2016/ doi:10.5194/acp-16-13465-2016 Author(s) 2016. CC Attribution 3.0 License.

Alexander J. Turner1,2, Alexis A. Shusterman3, Brian C. McDonald4,a, Virginia Teige3, Robert A. Harley4, and Ronald C. Cohen3,5

1School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts, USA

2Environmental Energy and Technologies Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

3Department of Chemistry, University of California at Berkeley, Berkeley, CA, USA

4Department of Civil and Engineering, University of California at Berkeley, Berkeley, CA, USA

5Department of Earth and Planetary Sciences, University of California at Berkeley, Berkeley, CA, USA

anow at: Cooperative Institute for Research in Environmental Sciences, University of Colorado Boulder, Boulder, Colorado, USA

Correspondence to: Ronald C. Cohen ([email protected])

Received: 25 April 2016 Published in Atmos. Chem. Phys. Discuss.: 24 May 2016 Revised: 7 October 2016 Accepted: 13 October 2016 Published: 1 November 2016

Abstract. The majority of anthropogenic CO2 emissions are attributable to urban areas. While the emissions from urban electricity generation often occur in locations remote from consumption, many of the other emissions occur within the city limits. Evaluating the effectiveness of strategies for controlling these emissions depends on our ability to observe urban CO2 emissions and attribute them to specic activities. Cost-effective strategies for doing so have yet to be described. Here we characterize the ability of a prototype measurement network, modeled after the Berkeley Atmospheric CO2 Observation Network (BEACO2N) in Californias Bay

Area, in combination with an inverse model based on the coupled Weather Research and Forecasting/Stochastic Time-Inverted Lagrangian Transport (WRF-STILT) to improve our understanding of urban emissions. The pseudo-measurement network includes 34 sites at roughly 2 km spacing covering an area of roughly 400 km2. The model uses an hourly 1 1 km2 emission inventory and 1 1 km2 meteorologi

cal calculations. We perform an ensemble of Bayesian atmospheric inversions to sample the combined effects of uncertainties of the pseudo-measurements and the model. We vary the estimates of the combined uncertainty of the pseudo-observations and model over a range of 20 to 0.005 ppm and vary the number of sites from 1 to 34. We use these inversions to develop statistical models that estimate the efcacy of the combined modelobserving system in reducing uncertainty

in CO2 emissions. We examine uncertainty in estimated CO2 uxes on the urban scale, as well as for sources embedded within the city such as a line source (e.g., a highway) or a point source (e.g., emissions from the stacks of small industrial facilities). Using our inversion framework, we nd that a dense network with moderate precision is the preferred setup for estimating area, line, and point sources from a combined uncertainty and cost perspective. The dense network considered here (modeled after the BEACO2N network with an assumed mismatch error of 1 ppm at an hourly temporal resolution) could estimate weekly CO2 emissions from an urban region with less than 5 % error, given our characterization of the combined observation and model uncertainty.

1 Introduction

Carbon dioxide (CO2) is an atmospheric trace gas and the single largest anthropogenic radiative forcer, with a radiative forcing of 1.82 W m2 in 2011 relative to preindustrial times (IPCC, 2013). CO2 has increased from 280 ppm in preindustrial times to greater than 400 ppm in the present, largely due to changes in fossil fuel emissions. Over 70 % of these fossil fuel CO2 emissions in the United States (US)

are attributable to urban areas (US EIA, 2015; Hutyra et al., 2014), yet current bottomup inventories still have large un-

Published by Copernicus Publications on behalf of the European Geosciences Union.

Network design for quantifying urban CO2 emissions: assessing trade-offs between precision and network density

ban CO2 uxes from highways. However, most of the existing CO2 anthropogenic inventories are not available at this resolution. For example, the Emissions Database for Global Atmospheric Research (EDGAR) (European Commission, 2011) and VULCAN (Gurney et al., 2009) are only available at 0.1 0.1 and 10 10 km2, respectively. A notable ex

ception is the Open-Data Inventory for Anthropogenic Carbon dioxide (ODIAC) fossil fuel CO2 (Oda and Maksyutov, 2011), which is based on satellite-observed nightlight data and available globally at 1 1 km2 resolution. High-

resolution fossil fuel CO2 emissions are available for select cities and sectors such as Paris through the AirParif inventory (Bron et al., 2015; http://www.airparif.asso.fr/en/index/index

Web End =http://www.airparif.asso.fr/en/index/ http://www.airparif.asso.fr/en/index/index

Web End =index ) and Indianapolis, Los Angeles, Salt Lake City, and Phoenix through the Hestia project (Gurney et al., 2012; http://hestia.project.asu.edu/

Web End =http: http://hestia.project.asu.edu/

Web End =//hestia.project.asu.edu/ ); three recent studies (Gately et al., 2013; McDonald et al., 2014; Gately et al., 2015) developed high-resolution CO2 emissions from vehicular trafc.

The Bay Area Air Quality Management District (BAAQMD) provides detailed annual county-level CO2 emissions information for San Francisco and Californias Bay Area (Mangat et al., 2010). The BAAQMD found that the transportation sector accounted for 36 % of the Bay Area anthropogenic emissions, industrial and commercial for 36 %, electricity for 16 %, residential fuel usage for 7 %, off-road equipment for 3 %, and agriculture for 1 %.The BAAQMD also reports CO2 emissions for 4375 point sources in the Bay Area. We geocode these point sources based on the addresses provided by the BAAQMD. These point sources capture the emissions from the industrial, commercial, and electricity sectors. We map residential fuel usage to population using block level population data from the 2010 US Census and apply a temporal temperature scaling based on Deschnes and Greenstone (2011); the resulting temporal scaling effect is small due to the temperate climate in the East Bay region of the SF Bay Area.

Here we use the trafc CO2 emissions from the fuel-based inventory for vehicle emissions (FIVE) developed by Mc-Donald et al. (2014). The FIVE trafc CO2 inventory provides a representative week of hourly CO2 emissions for San Francisco and other nearby Bay Area cities at 10, 4, 1 km, and 500 m resolution. This representative week can be scaled to different years based on the state fuel sales (see McDonald et al., 2014, for additional details). The FIVE inventory is constructed by partitioning CO2 emissions using state-level fuel data to individual roads with road-specic trafc count data and temporal patterns from weigh-in-motion data. In this manner, CO2 emissions from the FIVE inventory will be consistent with state and national CO2 budgets and can easily be scaled to different years.

Combining the industrial, commercial, electricity, residential, and trafc emissions account for 95.8 % of the anthropogenic CO2 emissions in the Bay Area. We do not have high-resolution proxy data for the off-road equipment or agriculture sectors in the Bay Area and have chosen to as-

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13466 A. J. Turner et al.: Urban CO2 measurement network design

certainties. For this reason, quantifying and monitoring the emissions from urban areas is crucial to strategies for reducing future increases in CO2.

Numerous studies have performed topdown estimations of CO2 emissions using observations from urban surface monitoring networks of various sizes (e.g., Gratani and Varone, 2005; McKain et al., 2012; Newman et al., 2013;Lauvaux et al., 2013; Bron et al., 2015; Turnbull et al., 2015). However, it is not immediately clear how many sites are necessary to monitor the emissions from an urban area.Kort et al. (2013) found that a surface monitoring network would need at least eight sites operating for 8 weeks to accurately estimate CO2 emissions in Los Angeles. Yet most current urban monitoring networks have fewer than eight sites but operate for much longer than 8 weeks. For example, Gratani and Varone (2005) used a single site in Rome, Newman et al. (2013) used a single site in Los Angeles, Lauvaux et al. (2013) used two sites in Davos, Switzerland, McKain et al. (2012) used a network of ve sites in Salt Lake City, and Bron et al. (2015) used ve sites in Paris. Recent work from Turnbull et al. (2015) employed a denser network of 12 sites in Indianapolis.

This issue is further complicated by bias and noise in both the measurements and the modeling framework. The combined model and measurement error is known as the model data mismatch error (hereafter referred to as the mismatch error). Current monitoring networks use a mix of instruments and approaches to calibration with resulting variations of capital and operating costs, network precision, and potential instrument bias. Monitoring networks located in regions with complex orography are challenging for atmospheric transport calculations, making it more difcult to determine the dispersion from sources.

The trade-off between measurement network density and mismatch error has yet to be characterized. Understanding these trade-offs is crucial to reducing the uncertainty in emissions from urban regions and to developing cost-effective urban monitoring networks. Here we present a high-resolution inventory of CO2 uxes and a numerical model that relates atmospheric observations to high-resolution surface uxes.We then use this inventory and model in a series of observing system simulation experiments (OSSEs) to investigate the trade-off between reductions in the mismatch error and increases in the measurement network density. We develop statistical models to characterize this relationship for different types of sources in the San Francisco (SF) Bay Area, identify limiting regimes, and recommend future observing strategies.

2 Constructing a high-resolution regional CO2 inventory

McDonald et al. (2014) demonstrated that 1 1 km2 spa

tial resolution is necessary to resolve the gradients in ur-

A. J. Turner et al.: Urban CO2 measurement network design 13467

08:00 PM

-0.5 0.0 0.5 1.0 1.5

-2 -1

Figure 1. September 2013 CO2 uxes from bottomup inventories. Top row shows the uxes in the Bay Area (122.0357122.7683 W,37.377138.2218 N) at four representative hours (hour in local time). Right panel shows the atemporal EDGAR v4.2 FT2010 CO2 ux in the Bay Area. Bottom panel shows the total Bay Area CO2 ux (black), trafc (orange), other anthropogenic (red), and natural (green)

sources. Vertical gray shading indicates the time slices plotted in the top and middle panels.

sume their contributions are smaller than the uncertainty in the total budget; therefore, we neglect these sectors in the construction of our inventory.

CarbonTracker CT2013B (http://www.esrl.noaa.gov/gmd/ccgg/carbontracker/

Web End =http://www.esrl.noaa.gov/gmd/ http://www.esrl.noaa.gov/gmd/ccgg/carbontracker/

Web End =ccgg/carbontracker/ ; Peters et al., 2007) provides 3-hourly fossil fuel, ocean, biogenic, and re CO2 uxes at 1 1

resolution. These uxes are optimized to agree with atmospheric CO2 observations. We regrid these uxes to 1 1 km2 spatial resolution (see Supplement Sect. S3) and

use the re, ocean, and biogenic sectors to account for our natural uxes.

Figure 1 shows snapshots of the CO2 uxes from our inventory at four different times of day and the atemporal uxes from EDGAR v4.2 FT2010 (European Commission, 2011). From Fig. 1 we can see that the inventory clearly resolves the large CO2 gradients from highways, conrming that 1 1 km2 spatial resolution is sufcient to resolve urban

CO2 uxes from highways. The bottom panel of Fig. 1 shows a time series of Bay Area CO2 uxes broken down by source. The diurnal cycle in our inventory is largely driven by the trafc emissions with modest uptake from the biosphere during the middle of the day. Other anthropogenic sources were assumed to have a negligible diurnal cycle (Nassar et al., 2013). In what follows, we use EDGAR as the prior and the high spatio-temporal resolution inventory as the truth.

3 The Berkeley Atmospheric CO2 Observation

Network (BEACO2N)

The Berkeley Atmospheric CO2 Observation Network (BEACO2N; see http://beacon.berkeley.edu

Web End =http://beacon.berkeley.edu and Shusterman et al., 2016) was founded in 2012 as a web of approximately 25 carbon dioxide sensing nodes stationed atop schools and museums in the Oakland, CA, metropolitan area (see Table 1). With sensors installed on an approximately 2 km square grid, BEACO2N is the only surface-level (3 to 130 m a.g.l.) greenhouse gas monitoring system with roughly the same spatial resolution as the emissions inventories described above. Each node requires only a standard, 120 V power source and is sited on preexisting structures based on voluntary, no-cost partnerships. The BEACO2N conguration therefore represents a reasonable expectation and is one model for future monitoring networks aimed at constraining CO2 uxes on neighborhood scales within an urban dome.

BEACO2Ns unprecedented spatial density is achieved by exploiting lower-cost instrumentation than has traditionally been utilized for ambient CO2 detection. The nondispersive infrared (NDIR) absorption sensor used in each BEACO2N node (http://www.vaisala.com/en/products/carbondioxide/Pages/GMP343.aspx

Web End =http://www.vaisala.com/en/products/

http://www.vaisala.com/en/products/carbondioxide/Pages/GMP343.aspx

Web End =carbondioxide/Pages/GMP343.aspx ) has been seen to possess adequate sensitivity to resolve diurnal as well as seasonal phenomena relevant to urban environments (Rigby et al., 2008) and costs 1 to 2 orders of magnitude less than the commercial cavity ring-down instruments commonly used in other networks. However, the low-cost NDIR sensor is more susceptible to factors such as temporal drift and environmen-

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02:00 AM

1500

1250

11:00 AM

07:00 AM

EDGAR

Bay Area COflux (tC h)

1000

750

500

250

0

-250 15 Sept 16 Sept 17 Sept 18 Sept 19 Sept 20 Sept 21 Sept 22 Sept

Date (GMT)

CO flux (tC km h )

2

Total

Traffic Natural

Other anthro

13468 A. J. Turner et al.: Urban CO2 measurement network design

Table 1. The 34 sites in the network used in this study.

Site code Site name Latitude Longitude Height ( N) ( W) (m a.g.l.)

AHS Arroyo High School 37.680 122.139 3 BEL Burckhalter Elementary School 37.775 122.167 5 BFE Bayfarm Elementary School 37.744 122.251 3 BOD Bishop ODowd High School 37.753 122.155 3 CES Claremont Elementary School 37.846 122.252 3 CHA Chabot Space & Science Center (low) 37.819 122.181 3 CHB Chabot Space & Science Center (high) 37.819 122.181 9 COI Coit Tower 37.8030 122.406 5 CPS College Preparatory School 37.849 122.242 24 EBM W. Oakland EBMUD Monitoring Station 37.814 122.282 3 ELC El Cerrito High School 37.907 122.294 8 EXB Exploratorium (Bay) 37.803 122.397 6 EXE Exploratorium (Embarcadero) 37.801 122.399 3 FTK Fred T. Korematsu Discovery Academy 37.738 122.174 3 GLE Greenleaf Elementary School 37.765 122.194 3 HRS Head Royce School 37.809 122.204 7 ICS International Community School 37.779 122.231 3 KAI Kaiser Center 37.809 122.264 127 LAU Laurel Elementary School 37.792 122.197 12 LBL Lawrence Berkeley National Lab, Bldg. 70 37.876 122.252 3 LCC Lighthouse Community Charter School 37.736 122.196 3 MAR Berkeley Marina 37.863 122.314 3 MON Montclair Elementary School 37.830 122.212 3 NOC N. Oakland Community Charter School 37.833 122.277 3 OMC Oakland Museum of California 37.799 122.264 3 PAP PLACE at Prescott Elementary 37.809 122.298 3 PDS Park Day School 37.832 122.257 3 PHS Piedmont Middle & High School 37.824 122.233 3 POR Port of Oakland Headquarters 37.796 122.280 3 OHS Oakland High School 37.805 122.236 3 ROS Rosa Parks Elementary School 37.865 122.295 3 SHA Skyline High School (low) 37.798 122.162 3 SHB Skyline High School (high) 37.798 122.162 13 STL St. Elizabeth High School 37.779 122.222 3

This study uses both operational and proposed sites. See Shusterman et al. (2016) and http://beacon.berkeley.edu/

Web End =http://beacon.berkeley.edu/ for more information on the network.

tal instability that can negatively impact data quality. This trade-off between mismatch error and network density is explored below.

4 Observing system simulation experiments

CO2 concentrations were simulated at 34 sites in the BEACO2N network with the Stochastic Time-Inverted Lagrangian Transport (STILT) model (Lin et al., 2003), coupled to the Weather Research and Forecasting (WRF) mesoscale meteorological model run at 1 1 km2 grid res

olution (WRF-STILT; Nehrkorn et al., 2010). WRF-STILT computes footprints ([Delta1] CO2 per surface ux, or ppm per mol m2 s1; see Supplement Sect. S1 and Lin et al. (2003) for additional details) for each observation that relate the

hourly 1 km2 CO2 uxes (x; an m1 vector) to the observa

tions (y; an n 1 vector):y = Hx. (1)

Each row of the n m Jacobian matrix (H = @y/@x) is a re-

shaped footprint. Figure 2 shows the location of the sites and the average network footprint for 15 to 22 September. The spatial extent of the footprints found here is similar to those found in Bastien et al. (2015), who performed an adjoint-based sensitivity analysis of urban air pollution in the San Francisco Bay area (see their Fig. 2).

Our aim is to estimate hourly CO2 uxes at 1 km2 over a 1-week period. For this reason, the model domain is 88 km 101 km, and we solve for 240 h of uxes (1 week

plus 3 additional days of back trajectories). The resulting

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A. J. Turner et al.: Urban CO2 measurement network design 13469

[parenrightbig]

, (3)

where xp is an m1 vector of prior CO2 uxes, comprised of

a coarse (10 10 km2) atemporal EDGAR v4.2 FT2010 an

thropogenic CO2 inventory and natural uxes from Carbon-Tracker CT2013B, regridded to 1 1 km2. B is the m m

prior error covariance matrix. The prior error covariance matrix can be expressed as a Kroenecker product (cf. Meirink et al., 2008; Singh et al., 2011; Yadav and Michalak, 2013) of temporal and spatial covariance matrices: B = D E, where

D is the temporal covariance matrix and E is the spatial covariance matrix. The B matrix has an uncertainty of 100 % at the native resolution and the spatial and temporal covariance matrices are fully populated (see Supplement Sect. S2 for more details).

We do not explicitly represent the individual error terms contributing to the R matrix (instrument error, model error, and representation error). Instead, we have assumed that the

R matrix is diagonal and can be characterized by a single parameter: the total mismatch error (m; R = 2mI), which

represents the combined effects of the different error components.

Figure 3 shows an example of the estimated CO2 uxes. We can see that the posterior uxes capture more of the spatial variability in the CO2 uxes than the prior uxes in the region where the network is deployed. We nd substantial improvements in the diurnal cycle (see panel d). Previous work has used the posterior covariance matrix (Q = HT R1H + B1

1), averaging kernel matrix (A =

I QB1), and the degrees of freedom for signal (DOFs =

tr(A)) as metrics to evaluate the information content of different observing systems (e.g., Kort et al., 2013; Wu et al., 2016). However, it is computationally infeasible to construct these m m matrices for our application as m > 106, and

storing them would require 36 Tb of memory (assuming

double-precision, dense matrices).

Instead, we evaluate the efcacy of the posterior uxes by taking the norm of the difference between the posterior uxes and the true uxes:

[vextendsingle][vextendsingle][vextendsingle][vextendsingle]

x x[star]

Figure 2. Top panel shows the location of the sites (black circles), the area source (blue region), the line source (orange line), and point sources (red diamonds). Bottom panel shows the 15 to 22 September average footprint for the 34 sites in the network; see Table 1 for a list of the sites. The bottom panel is the full domain used for the inversion. Supplement Fig. S3 shows the footprint on a log scale.

state vector has 2 133 120 elements (m = mt mx my with

mt = 240, mx = 88, my = 101) and the posterior uxes will

have hourly temporal resolution and 1 km2 spatial resolution. The dimension of n will depend on the number of sites in the observational network.

Here we use our high-resolution CO2 inventory (x[star]; an m1 vector) to generate synthetic observations (y[star]; an n1

vector):

y[star] = Hx[star] + ", (2)

where " is an n 1 vector of normally distributed noise with

mean [epsilon1]b and diagonal covariance matrix R: " N ([epsilon1]b,R).

Using a diagonal R matrix means that we have assumed that our mismatch errors are uncorrelated. Our base case inversion assumes the mean bias is zero: [epsilon1]b = 0. We evaluate

the sensitivity to this assumption in Sect. 6 and Supplement

Sect. S6.2. These synthetic observations can then be used in a Bayesian inference framework to estimate the optimal CO2 uxes (cf. Rodgers, 2000). Assuming the prior and likelihood distributions are Gaussian gives us a closed-form solution for the posterior CO2 uxes:

x = xp + (HB)T [parenleftBig]

HBHT + R[parenrightBig]1[notdef][notdef]y[star]

Hxp

[vextendsingle][vextendsingle][vextendsingle][vextendsingle]

2. We express this as a relative improvement by comparing the norm of the difference between the prior uxes and the true uxes:

= 1

[vextendsingle][vextendsingle][vextendsingle][vextendsingle]

x x[star]

2 . (4)

This error metric, , was chosen as it has a similar form to the averaging kernel matrix, but it also allows us to directly compare the posterior uxes to the true uxes. This

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[vextendsingle][vextendsingle][vextendsingle][vextendsingle]x

p

[vextendsingle][vextendsingle][vextendsingle][vextendsingle]

x[star]

[vextendsingle][vextendsingle][vextendsingle][vextendsingle]

2

13470 A. J. Turner et al.: Urban CO2 measurement network design

Figure 3. Example of estimated CO2 uxes. Top row shows the average emissions from (a) the prior, (b) the posterior, and (c) the true emissions. Panel (d) shows a time series of the emissions from the area source with the prior (green), posterior (pink), and true emissions (black). Panel (e) shows the difference between the posterior and the prior. Panel (f) shows the difference between posterior and the truth. Posterior output is from the best-case scenario (ns = 34 and m = 0.005 ppm).

relative error metric can be related to the ux error (see

Supplement Sect. S5). Therefore, we can use the error metric to evaluate the ability of the observing system to resolve three types of emission sources (1) area, (2) line, and (3) point sources by examining a subset of grid cells in the domain (see Sect. S3 for more details). The area source (AS) examined here is the East Bay urban dome (147 55 tC h1; uncertainty is the 1 range of hourly uxes

from the high-resolution inventory), the line source (LS) is Interstate 880 and the Bay Bridge (45 20 tC h1), and

the point sources (PS) are 4 large CO2 sources in the East

Bay (9 4 tC h1). For comparison, Salt Lake City emits 300 50 tC h1 (McKain et al., 2012). The top panel of

Fig. 2 shows these three source types.

Figure 4 shows the error in the estimated CO2 uxes using the observations over a wide range of observing system scenarios. We vary the number of sites (ns = [1,2,...,34]) and the mismatch error (m =

[0.005,0.01,0.02,0.05,0.1,0.2,0.5,1,2,5,10,20] ppm) and perform an ensemble of 20 inversions for each combination to ensure the results are robust. Each ensemble member uses a unique observational network by randomly drawing ns sites from the population of 34 possible sites. In total, we perform 8160 inversions. Figure 4 shows the mean error in the estimated CO2 uxes for the area source, line source, and point source as a function of m and ns. This gure represents the uncertainty in the estimated emissions at a given hour.

5 Simplied statistical models of error reduction

We develop statistical models to predict the error reduction and quantify the importance of the different factors governing the error reduction. We tested all combinations of models with the following seven parameters (127 possible combinations): pm, pns, ln(m), ln(ns), m, ns, and a constant.

These statistical models were evaluated using the Akaike information criterion (AIC) and the Bayesian information criterion (BIC). The following statistical models were found to be best:

AS = 6pm + 5pns + 4 ln(m) + 3 ln(ns)

+ 2m + 0 (5)

LS = 6pm + 5pns + 4 ln(m) + 3 ln(ns)

+ 2m + 1ns (6)

PS = 6pm + 5pns + 4 ln(m) + 2m + 0. (7)

All the regression coefcients ( i) in the statistical models yielded statistically signicant (p < 0.001) parameters based on F tests (see the Supplement Sect. S7 for the regression coefcients and model selection criterion).

We nd the pm, pns, ln(m), and m parameters in all three statistical models (Eqs. 57). This dependence on pns

and pm logically follows from the assumption of Gaussian errors in the derivation of the posterior CO2 uxes (Eq. 3) and the basic properties of variance. These two parameters tend to be dominant and generally explain more than 50 % of the variance. For this reason, we suspect that these two

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A. J. Turner et al.: Urban CO2 measurement network design 13471

Figure 4. Left column shows the error in the posterior CO2 uxes. Right column shows the uxes being estimated. Top row is the area source, middle row is the line source, and bottom row is the point source. Inversions were performed using ns = [1,2,...,34] sites and

m = [0.005,0.01,0.02,0.05,0.1,0.2,0.5,1,2,10,20] ppm mismatch error. Results shown are the mean of a Monte Carlo analysis using 20

different combinations of sites for each (ns, m) pair. Contours are from the statistical models

(see Eqs. 57) converted to ux errors, and the red lines are the ridge lines that dene the cutoff between the noise-limited and site-limited regimes. Purple star shows an observing system with 25 sites and 1 ppm noise. Green star shows an observing system with three sites and 0.1 ppm noise. Note the log scale on the y axis.

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13472 A. J. Turner et al.: Urban CO2 measurement network design

parameters are the most important and that other terms are capturing higher-order effects.

These statistical models can also be used to dene the regimes where increasing the number of sites in the observing system is more important and those where reducing the mismatch error is more important. We estimate these regimes using the ridge line from the statistical models (Eqs. 57).From Fig. 4 we can see two distinct regimes: noise-limited and site-limited. Observing systems that lie above the ridge line are in the noise-limited regime where the error reduction is largely governed by the mismatch error in the observing system. Conversely, observing systems below the ridge line are in the site-limited regime where the error reduction is largely governed by the number of sites in the observing system.

The mismatch error is controlled by the instrument, representation, and model error. In the noise-limited regime, reducing these errors will provide the greatest benet, whereas, in the site-limited regime, the greatest benet will come from increasing the number of sites in the observing system and there will only be a marginal benet from reducing the instrument, representation, and model error.

6 Discussion

Three conclusions we can draw from Fig. 4 for Californias East Bay are the following:

1. Achieving m = 1 ppm adds value. There is relatively

little additional benet to reducing mismatch error to0.1 ppm, particularly for estimating line or point source emissions.

2. At m = 1 ppm there is a benet to increasing the num

ber of sites, but this benet increases more slowly than pns.

3. At m = 5 ppm there is little benet from increasing the

number of sites; reducing the noise would add more value.

Our work is primarily focused on estimating hourly uxes; however, we can further reduce the uncertainty in our estimates by considering temporally averaged uxes (e.g., what are the weekly or monthly emissions?). Figure 5 shows the error in our estimate of the area source emissions aggregated over various timescales. We nd the error in our estimate greatly decreases over the rst 72 h. The central limit theorem provides a lower bound on the error reduction we might expect, and the error reductions follow this limit reasonably well over the rst 72 h. This implies that our weekly-averaged emission estimate would be 10 times better than our hourly emission estimate.

20

Uncertainty aggregated in time

Mean

Range (1-)

Area source flux error (tC h)

-1

10

5

2

1

Central limit theorem

0.5

0 24 48 72 96 120 144 168

Number of hours used

Figure 5. Uncertainty aggregated in time for the best-case inversion (see Fig. 3). The CO2 ux estimate in this study has an hourly temporal resolution. The uncertainty in the emissions estimate declines as the estimate is averaged to longer temporal scales. Solid blue line is the mean uncertainty, shading is the 1 range, and the dashed black line is the uncertainty predicted by the central limit theorem. Note the log scale on the y axis.

6.1 Additional factors affecting observing system design

We considered three additional factors that could adversely impact an observing system: (1) inversion domain size,(2) site-specic systematic biases, and (3) using only daytime observations.

Our results are found to be largely insensitive to the inversion domain size (see Fig. S6). This is discerned through a set of sensitivity OSSEs with a reduced domain size. We nd that inversions on the reduced domain were only marginally worse at reducing the error ( 1 %) than inversions on the

full domain (see Supplement Sect. S6.1). This is due to the strong local signal in the footprint of the measurements (see bottom panel of Fig. 2). Therefore, the nonlocal emission sources do not adversely impact our ability to estimate urban emissions.

Biases can adversely impact the observing system (see Fig. S7). To test the impacts of biases in the modeling measurement framework, we repeated the OSSEs outlined in Sect. 4 but included a systematic bias. The bias was unique to each site and was drawn from a normal distribution ([epsilon1]b N 0,2bI

; b = 1 ppm). There are three major ndings from the OSSEs with systematic biases:

1. Systematic biases become particularly problematic when the spread of the potential biases (dened here as b) is larger than the mismatch error (b > m). This is because we have dened the observational error covariance matrix as R = 2mI. However, if b > m with

a dense observing system, then the site-specic biases

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A. J. Turner et al.: Urban CO2 measurement network design 13473

will articially inate the observational error covariance matrix R 2m + 2b

[parenrightbig]

The cost for these two networks is comparable. From Fig. 4, we nd that the sparse Network B is site-limited in all cases, whereas the dense Network A is in the noise-limited regime. Further, we nd that the dense Network A has less error in the estimate of all source types in San Franciscos East Bay. Networks sitting on the ridge line are at the optimal balance between precision and number of sites.

6.3 The relationship between network density and transport error

In this work we have treated transport error and the number of measurement sites as independent. However, in practice, there would be a relationship between the transport error and measurement network density. This can be understood with a thought experiment using two different observing systems to estimate emissions: a sparse network with a single site and an innitely dense network (sites at each grid cell in our domain). Estimating emissions with the sparse network would require us to simulate the atmospheric transport with high delity if we are to reliably say anything about emissions upwind of our site. This is especially true for point sources. Any errors in the simulated atmospheric transport would adversely impact the estimated emissions, whereas the innitely dense network could potentially neglect atmospheric transport and use data from only the local grid cell to estimate emissions. This is because the differential signal at each site would be largely governed by the local emissions.Explicitly quantifying this relationship between transport error and measurement network density should be the focus of future work.

7 Conclusions

Understanding the factors that govern our ability to estimate urban greenhouse gas emissions are crucial to improving an observing system and reducing the uncertainty in emission estimates. Here we have quantitatively mapped the errors in CO2 emission estimates from different observing systems for three different types of sources in Californias Bay Area: area sources, line sources, and point sources. Our results show that different observing systems may fall into noise or site-limited regimes where reducing the uncertainty in the estimated emissions is governed by a single factor; these regimes differ for the source types. Identifying the regime an observing system is in will help inform future improvements to the observing system. A number of prior urban CO2 experiments have dened as a goal, the understanding of emissions to less than 10 % (e.g., Kort et al., 2013; Wu et al., 2016). We nd that a BEACO2N-like network could achieve this accuracy and precision with 1 week of observations if the dominant source of error is instrument precision. This conclusion may motivate a re-examining of the conventional instrument

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I and the errors will be incorrectly characterized in the observing system. As long as b < m, then R = 2mI and the characterization of the

errors will be appropriate.

2. Observing systems with more sites are generally less affected by site-specic systematic biases. This is because observing systems with a small number of sites rely heavily on those few sites. An observing system with many sites is less reliant on a single site and the site-specic systematic biases act more like additional noise in the observing system.

3. Systematic biases have a greater impact when estimating an area source than line and point sources. This is because an air mass sensitive to a line or point source will have a greater enhancement relative to the background compared to a diffuse area source; thus, there is a larger signal-to-noise ratio for these sources, and a systematic bias is less important.

During the day, model calculations of the planetary boundary layer height are more reliable leading to a temptation to omit the nighttime data from the analysis. However, emissions at night can be as much as 30 % of the total, and ignoring them makes estimates of urban emissions strongly dependent on prior assumptions. Our observing system would be unable to correct the misrepresented nighttime emissions of our atemporal prior without using nighttime observations. As a result, even our most optimistic observing system would have a systematic 50 tC h1 error ( 30 %) in the estimated

area source emissions due to the misrepresented nighttime emissions.

6.2 Potential cost trade-offs

We consider two potential observing systems:

1. Network A (ns = 25, m = 1 ppm): a dense network

with moderate-precision instruments. This network is similar to BEACO2N, described in Sect. 3. We assume a cost of USD 5000 per instrument, giving a total cost of USD 125 000. This network is shown as a purple star in the left column of Fig. 4.

2. Network B (ns = 3, m = 0.1 ppm): a sparse net

work with high-precision instruments. This network uses cavity ring-down instruments. We assume a cost of USD 50 000 per instrument, giving a total cost of USD 150 000. This network is shown as a green star in the left column of Fig. 4.

We note that the assumed mismatch error for these two potential observing systems is dened as the instrument error and assumes there is no contribution from model or transport errors.

13474 A. J. Turner et al.: Urban CO2 measurement network design

quality-oriented design of CO2 observing systems, according to the stated goal of a given network.

The Supplement related to this article is available online at http://dx.doi.org/10.5194/acp-16-13465-2016-supplement

Web End =doi:10.5194/acp-16-13465-2016-supplement .

Acknowledgements. This work was supported by a Department of Energy (DOE) Computational Science Graduate Fellowship (CSGF) to Alexander J. Turner, a National Science Foundation (NSF) Grant 1035050 to Ronald C. Cohen, and a Bay Area Air Quality Management District (BAAQMD) Grant 2013.145 to Ronald C. Cohen. Alexis A. Shusterman was supported by a National Science Foundation Graduate Research Fellowship. This research used resources of the National Energy Research Scientic Computing Center, which is supported by the Ofce of Science of the US Department of Energy under Contract No. DE-AC02-05CH11231. We thank M. Sulprizio (Harvard University) for gridding the US Census population data and the UC Berkeley Academic Computing center for access to computing resources.

Edited by: T. ButlerReviewed by: two anonymous referees

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