1. Introduction
Although a majority of global anthropogenic carbon dioxide (CO2) emissions originate from urban areas (e.g., Satterthwaite 2008), few studies have investigated CO2 mixing ratios in the urban boundary layer (UBL). Observations are challenging because heights of tower platforms that could support in situ CO2 mixing ratio measurements in urban areas are often too low (located in the surface layer) and airborne measurements tend to be labor intensive and expensive. Satellite-based remote sensing techniques show promise, but instruments are not yet sensitive enough to resolve variations in CO2 mixing ratios that result from relatively small changes in surface emissions (Kort et al. 2012). Nevertheless, observations in the UBL are useful because CO2 mixing ratios here are representative of city-scale airsheds because of the spatial averaging properties of atmospheric turbulent mixing. Therefore, column-based measurements over urban areas are likely to yield more information about urban-scale fluxes than a near-surface measurement because they represent a larger source area of influence (McKain et al. 2012). This means there is potential to infer city-scale net CO2 emissions from mixing ratio time series in the UBL in order to monitor emissions and validate municipal emissions inventories and models.
Two general approaches have been commonly used to infer net emissions at city scales from concentration or mixing ratio measurements. The first uses mixing ratio observations together with inverse atmospheric transport modeling to derive upwind source areas and surface fluxes. Examples include the Stochastic Time-Inverted Lagrangian Transport (STILT) model (Lin et al. 2003) coupled with wind fields generated by a three-dimensional meteorological mesoscale model. An example study using this approach was conducted around Salt Lake City, Utah, where mixing ratio observations at several near-surface locations were used to detect changes in anthropogenic CO2 emissions of greater than 15% on monthly time scales (McKain et al. 2012). In Los Angeles, California, a similar inverse modeling approach was used to determine the minimum density of surface-based observation sites required to resolve anthropogenic CO2 emissions at 8-week and 10-km resolutions (Kort et al. 2013). In Heidelberg, Germany, atmospheric transport modeling was combined with a 5 min × 5 min–resolution CO2 emissions model to predict observations from a stationary network of CO2, CO, and radon sensors (Vogel et al. 2013). Another example of this approach was conducted in Paris, France, where a network of CO2 mixing ratio measurements was used to model surface CO2 fluxes on 6-h time scales. Bréon et al. (2015) concluded that inversion modeling techniques that rely on CO2 upwind-downwind gradients perform better than those that simply use raw CO2 mixing ratios. In Boston, Massachusetts, McKain et al. (2015) used an inverse modeling approach and tower-based measurements to quantify annual methane emissions from natural gas infrastructure.
Studies using a boundary layer budget approach in urban areas must take into account the unique ways that urban areas modify the overlying boundary layer structure. In idealized daytime conditions with clear skies and a regional background wind, an internal boundary layer grows downwind with distance from the upwind urban edge until it occupies the entire planetary boundary layer. This internal boundary layer is the UBL and strong heating of the urban surface relative to the surrounding nonurban areas (e.g., from the urban heat island effect and modification of the surface energy balance toward higher Bowen ratios) drives buoyant convection that propels the UBL higher than the surrounding nonurban boundary layer (Oke 1987). The lowest 10% depth of the UBL is classified as the surface layer and is characterized by steep vertical gradients of scalar atmospheric variables. In the overlying 90% of the UBL (the mixed layer), strong mixing from convective turbulence is expected to result in near-uniform vertical profiles of wind speed, water vapor, potential temperature, and suspended air pollutants (e.g., Oke and East 1971).
Overnight in nonurban areas, cooling of the urban surface after sunset creates a layer of stable air that acts to suppress vertical mixing and transport. Over urban areas, a shallow, slightly unstable surface layer (SL) has often been observed as a result of increased mixing from storage heat releases, anthropogenic heat emissions, and greater urban surface roughness (e.g., Oke and East 1971; Uno et al. 1988). Above the slightly unstable SL is an elevated temperature inversion and stable nocturnal boundary layer (NBL) along with an overlying residual mixed layer (RL). The RL is a near-neutrally stable layer of residual turbulence, heat, and pollutants from the previous day capped by a temperature inversion. Nocturnal profiles of potential air temperature are expected to be roughly constant from the surface through the SL, increase in the NBL, then become roughly uniform with height in the RL (e.g., Oke and East 1971). Vertical profiles of pollutants with active nocturnal surface sources, such as CO2, are expected to decrease with height above the nighttime SL as a result of near-surface buildup below the temperature inversion and lack of vertical mixing (e.g., Oke and East 1971).
Several studies have used aircraft-based measurements of CO2 mixing ratios to calculate the city-scale net CO2 flux using a box model formulation. In Indianapolis, Indiana, measurement flight paths were conducted through the depth of the boundary layer downwind of the city. A spatially interpolated vertical plane of CO2 mixing ratio values normal to the prevailing wind direction downwind of the city was then used to attribute net emissions to an upwind urban spatial area. Fluxes calculated using this method showed high temporal variability (mean 19.2 ± 15.4 μmol m−2 s−1), but mean values were not statistically significantly different from an independent spatial surface emissions model (Mays et al. 2009). In London, United Kingdom, a measurement campaign used aircraft-based observations to estimate urban CO2 fluxes and found daytime averages of 46–104 μmol m−2 s−1. These flux magnitudes are statistically similar to synchronous measurements from local-scale urban eddy covariance (EC) flux towers and emissions inventories (Font et al. 2015). In Rome, Italy, airborne measurements and mass budgeting techniques were used to estimate city-scale fluxes that ranged from 2.5 to 14.7 μmol m−2 s−1 (Gioli et al. 2014). These estimates were compared with concurrent CO2 emissions inventories and the largest differences between the model and inventories were associated with greater wind speed and direction variability during measurements.
Tower-based CO2 mixing ratio measurements have also been used in urban box model studies. In Vancouver, British Columbia, Canada, Reid and Steyn (1997) used a series of eight boxes describing UBL growth combined with a surface emissions model to predict CO2 mixing ratios at a single measurement location located 28 m above the urban surface. A similar approach was developed in Salt Lake City, Utah, using a total of 162 boxes and a near-surface CO2 monitoring network comprising seven stations (Strong et al. 2011). These studies rely on mixing ratios measured at a single tower height near the surface, rather than integrated measurements over the depth of the UBL.
To date, neither boundary layer budget approaches nor inverse modeling techniques are able to monitor emissions in near–real time nor resolve hourly scale urban-scale fluxes. Additionally, there is a lack of UBL CO2 mixing ratio data against which to test urban-scale emissions and atmospheric transport models. The primary objective of this work is to measure and describe vertically resolved CO2 mixing ratios observed in the UBL column over Vancouver and explain observations in terms of UBL dynamics. To our knowledge, no previous study has directly sampled CO2 mixing ratios in the urban environment through the depth of the UBL over the diurnal course. The second objective is to apply a box model to retrieve hourly city-scale CO2 surface fluxes from the UBL profile measurements. Results from the model are compared to local-scale eddy covariance measurements from a network of three flux towers within the metropolitan Vancouver area and to emission inventory data.
2. Methods
a. Observations of CO2 in the urban boundary layer
1) Study location and period
During 14–15 August 2008, vertical profiles of CO2 mixing ratios in the UBL were observed with a measurement system mounted on a tethered balloon. Measurements took place in Memorial Park cemetery (49.2362°N, 123.0392°W), located within the built-up metropolitan area of Vancouver (Fig. 1). The Vancouver metropolitan area includes a population of 2.37 million people with estimated annual greenhouse gas emissions from transportation, buildings, and solid waste sources of 10.35 Mt of CO2-equivalent per year (Metro Vancouver 2010).
Map of CO2 and wind measurements in Vancouver during July–August 2008. Mean wind vectors observed during selected afternoon (1200–1600 LST) and overnight (0200–0500 LST) during the balloon observation campaign are superimposed on the map. Metropolitan Vancouver land-use data are from 2006 (City of Vancouver 2006), and elevation contours are in 100-m intervals above sea level (MSL), with the 500- and 1000-m MSL contours thickened for reference.
Citation: Journal of Applied Meteorology and Climatology 55, 3; 10.1175/JAMC-D-15-0060.1
The tethered balloon launch site has an elevation of 80 m MSL and is located approximately 5.0 km from downtown (at a heading of 340°), 10 km away from the Strait of Georgia (270°), and 7.0 km away from Vancouver International Airport (YVR; 230°). The cemetery is approximately 0.5 km × 1 km in area and is bounded by arterial roads to the east (Fraser Street) and south (49th Avenue) with daily vehicle loads upward of 20 000 vehicles per day. Land cover in the cemetery is primarily clipped and irrigated grass. The cemetery is interspersed with individual trees of up to 25-m height, although no trees were within 100 m of the observation site.
Observations are representative of a synoptically calm situation characterized by weak horizontal pressure gradients (low regional wind speeds) and primarily clear skies (high solar radiation input during day, strong radiative cooling overnight). At the nearby “Vancouver-Sunset” flux tower (section 2b), the mean air temperature recorded during the 24-h period at 24.8 m AGL was 24.9°C, with a minimum of 21.0°C at 0800 LST (LST = Pacific standard time) and a maximum of 30.2°C at 1800 LST. The total solar irradiance measured at the flux tower was 23.49 MJ m−2 day−1 and the observed net radiation was 13.02 MJ m−2 day−1. A scattered layer of stratus clouds (~4500 m) and a thin, high layer of cirrus clouds (~7000 m) were observed on the morning of 15 August 2008 from 0000 to 1000 LST (Environment Canada 2013). Sunset on 14 August was at 1930 LST, and sunrise on 15 August was at 0505 LST.
This observation period was selected in order to sample a representative diurnal cycle of morning–afternoon convective boundary layer development, evening boundary layer collapse, and nocturnal development of a stable surface layer and residual layer aloft. Weekday conditions (Thursday–Friday) were selected to be representative of weekday CO2 emissions. Though this particular set of atmospheric conditions is not typical for this area (e.g., not representative of winter or during passage of synoptic-scale systems), these conditions make for a nearly ideal setting to observe specific processes operating at the city scale, such as the formation of a stable NBL, development of a daytime convective mixed layer, and onset of thermally driven land–sea breezes.
2) Instrumentation
UBL CO2 mixing ratios were measured with a GMM220 CO2 sensor (Vaisala, Inc.) and recorded on a CR1000 datalogger (Campbell Scientific, Inc.). A lightweight sensor (200 g) was required because of the payload restrictions of the balloon (<2 kg). Air temperature and relative humidity were measured with a HMP50 temperature–relative humidity (T–RH) sensor (Vaisala), and air pressure, wind velocity, and wind direction were measured using a Kestrel 4500 Weather Tracker (Nielsen-Kellerma Co.). The accuracy of air temperature measurements is ±0.4°C (at 20°C) and accuracy of relative humidity is ±3% (Campbell Scientific 2015). The Kestrel 4500 is factory calibrated and the wind speed accuracy is ±1.04%, wind direction is accurate within ±5°, and pressure accuracy is ±0.02%. All instruments were sampled at 5-s intervals. The measurement system was suspended 0.5 m below a 5-m3 volume meteorological balloon (Vaisala TTB series) inflated with helium. Wind direction measured by the Kestrel 4500 was determined by the balloon’s orientation (always aligned with the mean horizontal wind direction). The balloon’s altitude was controlled by an electric winch and the balloon was authorized to measure up to a height of 400 m AGL by air traffic control. During the 24-h period from 1100 UTC 14 August to 1100 UTC 15 August, 48 vertical profiles were measured in total. Each profile was completed in 30 min (i.e., two profiles per hour, one going up, one coming back down) and were timed to coincide with 30-min CO2 flux-averaging periods at three EC towers in operation in the region (see section 2b).
Voltage signals from the GMM220 CO2 sensor recorded by the CR1000 logger were converted to CO2 mixing ratios using results from an in-house calibration against an Li-7000 closed-path infrared gas analyzer (Li-Cor Biosciences). During the calibration, the GMM220 and Li-7000 intake valve were placed in a sealed chamber in which the CO2 mixing ratio was varied from 440 to 970 ppmv. Mixing ratios were kept constant at six different values and 10-min averages from the two sensors were compared.
Additional tests were performed on the GMM220 sensor under controlled laboratory conditions to quantify sensor drift, sensor precision, temperature dependence, and pressure dependence (Christen and Nesic 2015). For these tests, four GMM220 sensors, including the ones used in this study, were placed in a temperature- and pressure-controlled sealed container (0.35 m3) with the CO2 mixing ratio held constant. Temperature dependence was tested over the range of 28°–36°C and pressure dependence was tested from 900 to 1000 hPa. These tests showed that absolute sensor drift over a 24-h period is on average 0.34 (±0.40) ppm; the sensor responds linearly to pressure at a rate of 0.77 ppm hPa−1 and responds linearly to temperature changes at −5.44 ppm K−1 at ≈ 400 ppm. These results confirm the temperature and pressure dependences given by the manufacturer calibration (Campbell Scientific 2015). Sensor precision (defined as the standard deviation during the averaging period) is found to be dependent on the length of the averaging period. During the balloon observation period, the sensor sampled every 5 s and there were, on average, 12 individual samples per 10-m-height layer [section 2a(3)] resulting in a 60-s sample averaging period per ascent or descent. During the balloon observation campaign, the mean standard deviation of the sensor error during each 60-s sample period is 4.2 ppm. Sensor response time is 30 s.
Raw CO2 mixing ratios from the balloon observation system were corrected for air temperature and atmospheric pressure dependencies for each 10-m vertical increment [section 2a(3)] using the confirmed manufacturer supplied algorithms (Vaisala 2014). Before corrections were applied, the overall mean uncertainty during individual runs from temperature, pressure, precision, and drift was ±33.3 ppm (±8.5% of mean measured CO2). After temperature and pressure corrections were applied, the overall uncertainty was reduced to 4.2 ppm (±1% of the mean measured CO2).
3) Data processing
This procedure [Eqs. (4) and (5)] is also applied to potential air temperature θ and the horizontal components of the wind vector (u, υ) to retrieve profile-averaged values of potential air temperature 
b. Auxiliary measurements
During the tethered balloon observations, there were three micrometeorological towers within 20 km of the balloon launch site equipped with eddy-covariance instrumentation to measure local-scale CO2, energy, and water fluxes (Fig. 1; Table 1). The aforementioned Vancouver-Sunset tower was located 1.9-km distance to the southeast of the balloon launch site (143°) in a residential neighborhood, the “Vancouver-Oakridge” tower was located in a residential neighborhood 3.0 km to the west (250°), and the “Westham Island” site was established as a rural reference station located 18.5 km away to the southwest (200°). Additionally, CO2 mixing ratios were measured above the UBL at a forested offseason ski resort on Cypress Mountain at 1100-m elevation above sea level (“Cypress Mountain”; Fig. 1; Table 1)
Vancouver measurement network stations. WMO climate station identification numbers are given in parentheses for stations operated by Environment Canada, and hourly data were downloaded from the Environment Canada historical data archive (Environment Canada 2013). An Environment Canada identification number is given for the Vancouver-UBC station. Elevation refers to height of the station base above sea level (MSL), and height is the measurement height above ground level (AGL). Station surroundings are classified according the local climate zone (LCZ) scheme of Stewart and Oke (2012). CO2 measurements are of concentration.
At the Vancouver-Sunset flux tower, net mixing ratios and fluxes of CO2 (
A ceilometer (Vaisala CL31) was also in operation at Vancouver-Sunset during the balloon observations (McKendry et al. 2009) and is used to estimate daytime convective boundary layer heights (
The Vancouver-Oakridge tower was in operation from June to August 2008. EC instrumentation was mounted at 29 m on a guyed hydraulic mast located in the Oakridge neighborhood (LCZ-6, open lowrise). The tower is 0.5 km from arterial roads and a park composed of grass recreational fields (approximately 250 m × 250 m) is located immediately east of the tower. Based on analysis of satellite imagery, land cover fractions in a 1000-m radius about the tower are 23% building, 21% impervious, and 56% vegetation (both trees and lawn) (Tooke et al. 2009). Population density within 1000-m radius is 27.6 persons per hectare, and the built density is 8.0 buildings per hectare, with a mean roof height is 5.8 m. This location is structurally similar to Vancouver-Sunset (i.e., primarily detached two-story residential homes organized into city blocks and interspersed with mature vegetation), though the population and built density are lower than at Vancouver-Sunset and the vegetation density is higher (Table 2). Because of the lower population and built densities, greater vegetation coverage, and greater distance to arterial roads, the mean daily total 
Neighborhood characteristics for Vancouver-Sunset and Vancouver-Oakridge. Vancouver-Sunset values are for a 1900 m × 1900 m area centered on the flux tower, and Vancouver-Oakridge values are for an area with 1000-m radius around the tower.
A rural reference EC tower (Westham Island) was located in the Fraser River delta, 18 km south of the urban Vancouver-Sunset and Vancouver-Oakridge sites. The tripod tower was installed in a flat, unmanaged, nonirrigated grass field in a region characterized by intensive agriculture. The local-scale turbulent flux source area is classified as LCZ-D (low plant cover) and grass heights ranged from 10 cm in winter to 1.75 m in summer. Grass was 1.60 m high during August 2008 (Liss et al. 2010). EC instrumentation was mounted at 1.8 m AGL and the tower was located 300 m horizontally away from the Strait of Georgia.
All three flux sites measured CO2 fluxes using a sonic anemometer (CSAT 3-d; Campbell Scientific) and an open-path infrared gas analyzer (IRGA; Li-7500 from Li-Cor, Inc.). Each IRGA was calibrated in house every 6 months according to standardized procedures (Li-Cor 2015) against reference tanks from Environment Canada. The accuracy of the Li-7500 is ±1%, and its precision is 0.16 ppm (Li-Cor 2015). At all sites, three-dimensional wind velocities and CO2 mixing ratios were recorded at 20 Hz and subject to several quality control procedures (e.g., filtered for interference from precipitation, realistic maximum–minimum thresholds). Fluxes were then calculated from block-averaged means of 30-min periods and a 2D coordinate rotation was performed to align the coordinate system with the mean wind direction (Crawford et al. 2010).
Additional measurements of CO2 mixing ratios were taken during July–August 2008 at Cypress Mountain (Fig. 1). This station used a Vaisala GMM220 sensor that sampled every 5 s and recorded 10-min averages. This sensor was also included in the independent calibration and testing procedures described in section 2a(2), and sensor precision during the 10-min-averaging period is ±2.8 ppm. The sensor was located at the peak of a ski run at 1100-m elevation and was mounted at 2 m AGL above rocky soil with sparse vegetation, including mature coniferous trees within a 30-m radius. The station was 21-km horizontal distance (333° heading) away from the balloon launch site.
c. CO2 box model
Surface CO2 fluxes are inferred from UBL measurements using a boundary layer budget approach applied to a single-box model construct. This approach is chosen because of its relative simplicity in terms of data input requirements and for its potential to resolve fluxes at hourly time steps. To calculate the surface flux, the model uses observations of CO2 mixing ratios in the urban boundary layer and explicitly calculates values for vertical entrainment and horizontal advection fluxes. The remainder of this section describes the basic assumptions, develops the model framework, and discusses various inputs to the model, specifically CO2 mixing ratios outside of the model domain and urban boundary layer height.
This model construction assumes a column of air being advected along the surface at the mean wind speed and that CO2 emissions from the surface are evenly mixed throughout the boundary layer depth 
Profile averages from UBL measurements (0–400 m AGL) during the 24-h observation period. The upwind distance that air influencing measurements has traveled during each hour is given as 〈U〉t (km) (where t is the 3600-s temporal averaging period), the horizontal distance required for boundary layer adjustment to the surface during convective conditions is X (km) [Eq. (1)], and the convective time scale indicating the circulation time of the boundary layer scale eddies is t* (min) [Eq. (3)]. Hours without values (—) are the result of negative kinematic surface heat flux observations from Vancouver-Sunset (i.e., stable, nonconvective conditions).
Time–height contour plots of UBL (a) CO2 mixing ratio and (b) potential temperature.
Citation: Journal of Applied Meteorology and Climatology 55, 3; 10.1175/JAMC-D-15-0060.1
An upwind horizontal CO2 mixing ratio gradient is needed to calculate the advection term, along with 
The advection term is added to 
The entrainment flux term uses the two values of 
Measurements were limited to 400 m by air traffic control, but ceilometer measurements indicate UBL heights extend up to 540 m during the afternoon of 14 August. During hours when 
In summary, the box model uses measured values of hourly changes in CO2 mixing ratio and explicitly modeled values of vertical entrainment and horizontal advective fluxes to solve for 
3. Results and discussion
a. UBL dynamics and CO2 mixing ratios
During the 14–15 August observation period, the measured CO2 mixing ratios up to 400 m AGL range from 372 to 456 ppm. The lowest mixing ratios (372–384 ppm) at individual height layers in the UBL are observed during the late afternoon from 1600 to 1800 LST and the highest (420–456 ppm) are observed overnight and during the early morning (2000–0700 h) below 50 m AGL (Fig. 2; Table 3). Observed profile-averaged CO2 mixing ratios for the 0–400-m depth are 387.5 ppm during the initial profile from 1100 to 1200 LST, and fall to 376.2 ppm from 1700 to 1800 LST (see also Fig. 6). Overnight, the profile-averaged CO2 mixing ratio increases to 406.1 ppm at 0300–0400 LST.
During this time, the measured θ results range from 34.0°C at 400 m at 1900 LST to 19.0°C at 10 m at 0500 LST (Fig. 2). During the daytime (1100–1800 LST), potential air temperatures above 20 m are generally uniform with height and the 0–400-m profile-average 
Observed wind directions and velocities conform to a pattern of diurnally reversing land–sea-breeze thermal circulations typical in this area during summertime (Fig. 3; Table 3). During the afternoon (1100–1800 LST), wind directions above 10 m are from the west and southwest and profile-averaged wind speeds are 2.6 m s−1. Maximum daytime wind speeds are 4.2 m s−1 at 140 m AGL at 1600 LST. After sunset, the thermal circulation reverses and the observed wind directions shift to the northeast. From 1900 to 2000 LST, there is directional wind shear with height, with easterly winds observed at 100–250 m, and westerly winds from 250 to 400 m. By 2200 LST the flow at all heights up to 400 m was from the east, with a maximum velocity of 3.9 m s−1 at 140 m. Overnight, winds are light (<1.5 m s−1), with increases up to 2.5 m s−1 below 100 m at 0500 LST near sunrise. After sunrise, onset of the sea-breeze front is observed at 0700–0800 LST as wind directions shift back toward the southwest and velocity increases to 4.5 m s−1.
Time–height wind vector plots. Length and color of arrow indicate horizontal wind speed and direction of arrow indicates direction wind is coming from using meteorological conventions (e.g., 0° = north, 90° = east).
Citation: Journal of Applied Meteorology and Climatology 55, 3; 10.1175/JAMC-D-15-0060.1
Near-surface winds showed moderate regional spatial variability (Fig. 1). At YVR, Sandheads, Westham Island, and Vancouver-University of British Columbia (Vancouver-UBC), the mean afternoon winds from 1200 to 1600 LST are from the northwest and range from 2 to 4 m s−1. At the same time, Vancouver-Oakridge, Vancouver-Sunset, and the balloon system (20–30-m height) record wind directions from the southwest, west, and west, respectively. This backing is expected as winds slow down during the transition from ocean to land, increased surface roughness of the urban surface acts to reduce wind speeds, and the Coriolis force is reduced. During these hours (1200–1600 LST), the mean wind speeds at Vancouver-Sunset (24.8 m) are 2.8 m s−1 compared to 2.9 m s−1 measured by the balloon system at 20–30-m height during the same hours. Overnight (0200–0500 LST), the coastal and marine stations (YVR, Sandheads, Vancouver-UBC) record wind directions from the northwest while Vancouver-Oakridge, Vancouver-Sunset, and the balloon system (20–30-m height) indicate winds from the south, northeast, and northeast, respectively. Vancouver-Oakridge, Vancouver-Sunset, and the balloon launch site are located inland relative to the other stations, indicating possible topographic and thermal influences (i.e., sea–land-breeze circulation) that could account for observed differences. During these hours, the Vancouver-Sunset tower recorded a mean wind speed of 1.9 m s−1, compared to 1.2 m s−1 measured at 20–30 m by the balloon. These measurements provide a general overview of the spatial variability of the airflow, but station wind speeds are not expected to agree perfectly because measurements are taken at different elevations and heights (Table 1).
The observed UBL CO2 mixing ratios are strongly influenced by the thermal structure of the UBL. Initial backscatter measurements from the ceilometer show a UBL height of 540 m at 1100 LST (Fig. 4). This is the maximum UBL height measured during the observation period, and from 1100 to 1300 LST the UBL height fluctuates about 500 m before falling to 400 m by 1600 LST as a result of the reduced surface heating and less vigorous vertical mixing (Fig. 4). The observed pattern of convective UBL development and the magnitude of the UBL heights are consistent with long-term summertime measurements obtained from the ceilometer operated at this site from 2006 to 2008 (van der Kamp and McKendry 2010).
Measurements of the daytime convective UBL and estimates of the stable NBL height. The NBL height is estimated using three different methods. Daytime UBL measurements are from the ceilometer located at Vancouver-Sunset. The legend refers to the methods used to calculate the NBL height described in the text.
Citation: Journal of Applied Meteorology and Climatology 55, 3; 10.1175/JAMC-D-15-0060.1
Vertical profile measurements during the afternoon show a well-mixed UBL with nearly uniform potential temperatures and CO2 mixing ratios with height (Fig. 2). During late afternoon (1500–1800 LST), the profile-averaged CO2 mixing ratio up to 400 m AGL is 380.2 ppm and the mean vertical gradient is −0.1 ppm dam−1 (Fig. 5). The profile-averaged potential air temperature during the same period is 30.0°C, with a mean vertical gradient of 0.085 K dam−1. During this time, measurements by the EC system at Vancouver-Sunset indicate dynamically unstable conditions (mean 
The (left) CO2 mixing ratio and (right) potential air temperature in the UBL during afternoon unstable conditions (light blue) and overnight stable conditions (dark blue).
Citation: Journal of Applied Meteorology and Climatology 55, 3; 10.1175/JAMC-D-15-0060.1
Beginning before sunset, three methods were used to estimate the growth of the stable nocturnal boundary layer during the night of 14/15 August 2008 (Fig. 4). The cumulative cooling method [Eq. (14)] estimates an NBL height of 104 m at 2000 LST, approximately 30 min after sunset. This estimate rises to 212 m at by 0100 LST. This peak is explained by the increase in RL wind speeds from 2200 to 2300 LST (Fig. 3). After 0200 LST, the NBL height rises steadily to a maximum peak of 232 m by 0700 LST. The empirical estimate based on 10-m wind speeds fluctuates through the night between 15 m (2000 and 0300 LST) and 181 m (1800 LST). This estimate is directly scaled to thee observed fluctuations in nocturnal wind speeds at 10 m as measured by the tethered balloon system (Fig. 3). The NBL height estimate using the ad hoc method based on the θ gradient rises to 80 m by 1900 LST. The rest of the night shows a steady upward growth to 130 m at 0700 LST. The mean maximum NBL height of all three methods at midnight (3.5 h after sunset) is 123 m and at 0600 LST (9.5 h after sunset) is 158 m. Overall, the θ-gradient method appears to yield the most stable results throughout the night (i.e., no large fluctuations) relative to the other methods and also uses measurements directly related to the thermal structure of the NBL.
Vertical profile measurements overnight (0000–0400 LST) show that the profile-averaged potential air temperature has cooled to 25.7°C, with a mean vertical gradient of 0.2 K dam−1 and a maximum gradient of 1.0 K dam−1 from 20 to 40 m (Fig. 5). During these same hours, the profile-averaged CO2 has risen to 403.8 ppm and the mean vertical gradient is −1.6 ppm dam−1 with a steepest negative gradient of −15.0 ppm dam−1 from 20 to 40 m. Above the NBL, potential temperature profiles indicate the presence of a neutrally stable RL with roughly uniform CO2 mixing ratios with height.
In contrast to measurements of NBL structure over other urban neighborhoods [e.g., in Montreal, Québec, Canada (Oke and East 1971), and Sapporo, Japan (Uno et al. 1988)], there is no observed shallow thermally unstable layer at this site, though these studies are representative of different types of local-scale neighborhood surfaces. Instead, the nocturnal potential temperature inversion begins very near to the surface, presumably because of minimal storage and anthropogenic heat releases from the microscale park setting of the measurements and the surrounding low-density residential neighborhood. There is also a clear increase in CO2 mixing ratios in the NBL, which is evidence of vertical mixing of CO2 injected into the stable NBL from nocturnal canopy layer sources (e.g., human, soil, and vegetation respiration, as well as fossil fuel combustion from traffic and cooking). Because there is no indication of buoyant thermal turbulence production, this mixing must instead be dominated by mechanical processes (i.e., turbulence generated by wind shear and from flow over buildings and trees).
Beginning after sunrise (0505 LST), ceilometer backscatter measurements show the rise of the convective UBL up to a height of 350 m by 1000 LST. During this time, CO2 mixing ratios below 100 m show a decrease from 421.3 to 402.4 ppm. This indicates vertical flushing of accumulated CO2 in the NBL during growth of the convective UBL, in addition to entrainment of relatively low-CO2 content air from the overlying residual layer.
The pattern of overnight CO2 buildup and morning flushing of accumulated CO2 in the NBL observed by the balloon-based system is consistent with observations of CO2 mixing ratios and potential air temperatures measured in the urban canopy layer (UCL) in the Vancouver-Sunset neighborhood (Crawford and Christen 2014). In this study, there was an observed increase in UCL CO2 mixing ratios in the hour after sunset, followed by microscale horizontal advection along topographic gradients (i.e., cold-air pooling) during the night. Just after sunset, CO2 mixing ratios were observed to rapidly decrease throughout the UCL.
The diurnal course of the profile-averaged CO2 mixing ratio from 0 to 400 m is compared with CO2 mixing ratios measured at three locations in the metropolitan Vancouver area (Fig. 6). The highest CO2 mixing ratios throughout the study period are observed at Vancouver-Sunset (mean of 406.7 ppm, maximum of 444.6 ppm, and minimum of 375.8 ppm) and the lowest values are at Westham Island (mean of 375.8 ppm, maximum of 393.6 ppm, and minimum of 366.1 ppm). During the afternoon (1100–1800 LST), the mean UBL values measured by the balloon-based system are within 0.9 ppm (0.2%) of the measurements at Vancouver-Sunset and within 4.5 ppm (1.2%) of the measurements at Vancouver-Oakridge, measuring 24.8 and 29 m, respectively. Overnight (1800–0800 LST), the 0–400-m average is lower than at Vancouver-Sunset by −23.6 ppm (−5.5%) and lower by −8.0 ppm (−1.9%) at Vancouver-Oakridge, on average. This result suggests that urban tower-based measurements are representative of the entire UBL depth during unstable, well-mixed conditions. At night, however, the tower-based mixing ratio measurements diverge from the profile average, suggesting the decoupling of urban surface-layer conditions from the overlying RL (Crawford and Christen 2014).
Hourly mean CO2 mixing ratios measured by the observation network (Fig. 1) during the balloon campaign on 14–15 Aug 2008 (solid lines) and ensemble means during July–August 2008 (dashed lines). Values from Cypress Mountain are not available during the balloon observation period. The balloon measurement (dark blue) is a column-average value from 0 to 400 m (〈cm〉).
Citation: Journal of Applied Meteorology and Climatology 55, 3; 10.1175/JAMC-D-15-0060.1
Ensemble mean CO2 mixing ratios measured by the CO2 observation network during July–August 2008 indicate the CO2 content during the 24-h experimental period was unusually high overnight and during early morning (Fig. 6). At Vancouver-Sunset, the mean CO2 mixing ratio from 2000 to 0600 LST during the experiment was 429.5 ppm, as compared with the July–August ensemble mean of 387.4 ppm for the same hours (8.3% difference). Hourly CO2 mixing ratios from 2000 to 0500 LST at Vancouver-Sunset during the experiment were in the top 10th percentile of all July–August 2008 values for each hour. At the Vancouver-Oakridge tower, observed mixing ratios during the experiment were 3.8% higher than the July–August average. In contrast, overnight mixing ratios were −2.2% below average at the nonurban Westham Island site, although typically nighttime CO2 mixing ratios at Westham Island are higher than those at Vancouver-Sunset by 6.6 ppm (1.7%). During the daytime, all sites are within 2.2% of their respective July–August ensemble means.
The likely reasons for the above-average CO2 mixing ratios during this night are enhanced thermal stability and reduced mixing and advection from mean winds. This night was characterized by more negative sensible heat flux (
b. Modeled regional-scale 
Urban-scale CO2 fluxes were modeled using Eq. (12). Three variations of background CO2 mixing ratios were used to determine the sensitivity of the calculation to the choice of different vertical and horizontal gradients for entrainment and advection fluxes. Further, three variations of the stable NBL height were explored to estimate 
Boundary layer budget calculations of FC during 14–15 Aug 2008. The mean of all model variations is shown as the black line; error bars are maximum and minimum values of individual model runs with varying background CO2 and stable boundary layer height inputs. Also shown are observations from the Vancouver-Sunset (light blue), Vancouver-Oakridge (light brown), and Westham Island (light green) flux towers (Fig. 1) during the balloon observation period (dashed line) and for July–August 2008 (shaded areas; dotted lines). Note the x-axis hour range differs from previous plots.
Citation: Journal of Applied Meteorology and Climatology 55, 3; 10.1175/JAMC-D-15-0060.1
The box-model results are compared to EC observations and scaled greenhouse gas inventories; however, these methods are not expected to agree exactly. This is primarily because the box model, EC measurements, and scaled inventories are each representative of different spatial source areas with different surface CO2 source–sink configurations. Furthermore, the scaled inventory neglects biogenic CO2 processes (photosynthesis and respiration), while the reported CO2-equivalent emissions totals also include methane and nitrous oxide and are given for an entire year. Differences between methods are discussed in further detail throughout the following section. Though perfect agreement is not expected, a comparison between methods is still worthwhile as a check on the plausibility of the modeled results. We expect that although the magnitude of the hourly 
The total flux for the 24-h observation period calculated from the box model is 20.2 gC m−2 day−1, compared to local-scale EC measurements of 7.25 gC m−2 day−1 observed at Vancouver-Sunset, 1.07 gC m−2 day−1 measured at Vancouver-Oakridge, and −2.87 gC m−2 day−1 measured at Westham Island (Fig. 7; Table 5). Mean hourly uncertainty for the modeled fluxes is ±10.8 μmol m−2 s−1, compared with a mean hourly flux of 19.5 μmol m−2 s−1. For measured EC fluxes at Vancouver-Sunset, the mean hourly variability is ±10.80 μmol m−2 s−1, compared with the hourly mean of 15.54 μmol m−2 s−1.
Box-model results are also compared with spatially averaged EC fluxes. Spatial averaging of the EC measurements is necessary because spatial heterogeneity of the surface CO2 source and sinks can introduce location bias into the measured CO2 emissions when attempting to calculate long-term or spatially integrated emissions totals (Schmid and Lloyd 1999). In particular, the Vancouver-Sunset tower is affected by location bias as a result of a busy intersection located approximately 50 m to the SE (Crawford and Christen 2015). Two methods are used to spatially average EC measurements. The first uses directionally averaged fluxes calculated as the equal-weighted average of individual hourly mean 
A second method uses statistical models to calculate spatially averaged fluxes representative of an entire neighborhood at Vancouver-Sunset based on measured environmental variables (e.g., soil temperature, incoming solar radiation, time of day) and land cover characteristics of modeled turbulent flux source areas (e.g., plan area proportion of vegetation and busy roads). Using this method [described in detail in Crawford and Christen (2015)], the spatially averaged mean 
The modeled daily total of 20.2 gC m−2 day−1 is compared with the scaled greenhouse gas inventories for the city of Vancouver and its metropolitan region (Metro Vancouver 2010). “Metro” Vancouver (1672 km2) contains the city of Vancouver (100 km2). Comparison with both the city of Vancouver and the metro Vancouver inventories is useful because the box model is representative of areas that include both city and metropolitan areas. For both the city of Vancouver and metro Vancouver, inventories were conducted in 2007 and 2010 and provide annual total emissions totals, as well as the fraction from motor vehicle traffic sources, building sources, and solid waste sources (Table 4). Because of seasonal variations in the local emissions from natural gas combustion for building heating and traffic volume, and day of week variations in commuter traffic volume, annual emissions totals have been scaled to be representative of weekday emissions in August.
Summary of scaled community energy and emissions inventories for metro Vancouver and the city of Vancouver, 2007 and 2010.
Modeled boundary layer budget FC compared with values measured during the 24-h observation period by eddy covariance. ST is the Vancouver-Sunset flux tower, OR is the Vancouver-Oakridge flux tower, and WI is the Westham Island flux site (Fig. 1). Italicized values are data gaps that have been linearly interpolated. The overbar signifies the ensemble mean flux from July to August 2008 for each tower, and 〈ST〉 is the spatially modeled flux (section 3b) in the Vancouver-Sunset neighborhood using methods developed in Crawford and Christen (2014a). Units for all values are micromoles per meter squared per second. Note that the hour column is different than in Table 3.
For traffic, the monthly traffic emissions scaling factors are calculated based on modeled emissions from traffic counts and trip diaries for the Vancouver-Sunset neighborhood (Christen et al. 2011). These scaling factors are applied to the annual inventory traffic emissions totals to produce monthly traffic emissions totals. Weekday and weekend differences are then calculated based on EC observations at Vancouver-Sunset of reductions in weekend traffic emissions of 42% relative to weekdays (Christen et al. 2011). Although emissions factors are calculated specifically for the Vancouver-Sunset neighborhood, it is assumed that weekly and monthly patterns are representative of the entire city of Vancouver and metro Vancouver.
For building emissions, monthly scaling factors are determined for the Vancouver-Sunset neighborhood from building energy model (BEM) simulations and local climate data (Christen et al. 2011). The BEM results include local emissions due to natural gas combustion for both space-heating and water-heating purposes. Some uncertainty is introduced when these scaling factors are applied to the area of the city of Vancouver and the metro Vancouver area because BEM models are calibrated for the specific residential housing stock found in the Vancouver-Sunset neighborhood and may not be representative of all building types (e.g., high-density apartment blocks or commercial buildings). This uncertainty is expected to be minor because the emissions factors are monthly fractions of total annual emissions that are assumed to be similar across building types, rather than emissions totals, which are expected to vary. Additional error is introduced because this approach does not consider variations in emissions from industrial processes.
The emissions totals for August weekday conditions are then scaled to areal emissions rates based on population densities calculated for the city of Vancouver and metro Vancouver from population figures given from the inventory and land area from census tract data (Statistics Canada 2011). Total land area has been downscaled to exclude large uninhabited park areas that are not included in the model domain (e.g., the higher-elevation mountainous area north of the city of Vancouver) based on land-use fractions listed in the inventories. The city of Vancouver’s total land area is downscaled by 13% and metro Vancouver is downscaled by 42%. The box-model daily total of 20.2 gC m−2 day−1 is 32% higher than the scaled inventory from the city of Vancouver for 2007 (13.8 gC m−2 day−1) and 35% higher than 2010 (13.1 gC m−2 day−1). Possible reasons for the discrepancy between the box-model and inventory approaches are errors in building and traffic inventory scaling factors and biases in the balloon sampling area toward industrial areas and busy roadways. The metropolitan area scaled inventory daily total for 2007 is 3.9 gC m−2 day−1 and for 2010 it is 3.7 gC m−2 day−1, reflecting the much lower population density in the metropolitan area (13.4 persons per hectare in 2007 and 14.2 persons per hectare in 2010) relative to the city of Vancouver (61.0 persons per hectare in 2007 and 64.2 persons per hectare in 2010). Though the inventory provides context for the box-model results, it is emphasized that the box model and the scaled inventories are not expected to be in exact agreement. This is because the inventories are from different years than the balloon observations, and they neglect biogenic components of the carbon cycle (photosynthetic uptake, soil and vegetation respiration) that are implicitly included in the box model; they also include additional greenhouse gases besides CO2 (methane, nitrous oxide).
The model also simulates a realistic diurnal course of hourly 
Overnight (2100–0500 LST), the mean modeled 
For individual hours from 0000 to 0100 LST and 0400 LST, the 
After sunrise, the model predicts a rapid increase in 
On average, the magnitude of entrainment during 0700–1100 LST is −33.1 μmol m−2 s−1 (Fig. 8) as the height of the convective UBL rises rapidly after sunrise to 540 m by 1100 LST (Fig. 4). Mean uncertainty due to the different background CO2 mixing ratios used is ±25.2 μmol m−2 s−1 (Fig. 8). When observed CO2 values in the RL are used as the 
Modeled surface FC, entrainment, and advection during the 24-h observation period. Uncertainty ranges for entrainment and advection are plotted as error bars. The solid line is the observed profile-averaged UBL 
Citation: Journal of Applied Meteorology and Climatology 55, 3; 10.1175/JAMC-D-15-0060.1
Additional model uncertainties related to entrainment are generated because the single-box model construct used in this study assumes a spatially homogeneous rise in convective UBL height across the entire model domain. Though this is certainly a simplification, the assumption is supported by modeled mixed layer depths for eight individual boxes, each with an alongwind length of 1900 m (cumulative length is 15.2 km) extending westward from Vancouver-Sunset to the shoreline of the Strait of Georgia (Reid and Steyn 1997). This study modeled the mixed layer depth in June over each individual box using a parameterized surface sensible heat flux, inversion intensity, mixed layer temperature, and subsidence velocity (Reid and Steyn 1997; Steyn and Oke 1982). After sunrise, the mixed layer depths over all boxes are modeled to rise at the same rate up to nearly 600 m until 1100 LST.
From 0900 to 1700 LST, the mean modeled 
4. Conclusions and future directions
Vertical profiles of the CO2 mixing ratio, potential air temperature, wind speed, and wind direction were measured in the urban boundary layer of Vancouver, British Columbia, Canada, over a continuous 24-h period in August 2008. Observations were used to model integrated urban-scale surface CO2 fluxes at hourly time scales using a boundary layer budget calculation with a box-model construct. Model results were compared to observations from three local-scale EC towers in operation during the UBL observation period in the greater Vancouver region. The box-model 24-h emissions total of 20.2 gC m−2 day−1 is 35% higher than simultaneous spatially averaged local-scale fluxes from the Vancouver-Sunset neighborhood (15.0 gC m−2 day−1) and is higher by 32% of a scaled inventory total (13.8 gC m−2 day−1) from 2007 for the city of Vancouver. A possible reason the box model produces higher estimates of daily emissions totals is a bias toward busy roads and industrial areas in the balloon system measurement source area—although exact agreement between the box model, EC measurements, and scaled inventory is not expected. This is mainly because the EC measurements, the box model, and inventories are representative of different spatial scales and source areas. Additional discrepancies arise between methods because the inventory includes additional greenhouse gases (methane, nitrous oxide), neglects biogenic carbon processes (soil respiration, vegetation uptake), and uncertainties are introduced when annual inventories are scaled to be representative of the study period. The box-model output is also highly sensitive to entrainment and advection fluxes whose magnitudes are comparable to or exceed the magnitude of surface emissions.
This study also finds the vertical distribution of CO2 is regulated by the thermal structure of the UBL. Overnight, measured vertical profiles of potential air temperature show the development of a stable NBL with an overlying neutral RL beginning just after sunset. Measured vertical profiles of CO2 mixing ratio during this same time period show a clear buildup of CO2 in the stable NBL. Three estimates of NBL height were used and the average NBL 3.5 h after sunset is 123 m. Vertical potential temperature profiles and EC measurements from the nearby Vancouver-Sunset tower indicate vertical mixing CO2 in the NBL is dominated by mechanical processes. The model predicts positive hourly 
After sunrise from 0600 to 1100 LST, there is rapid growth in UBL height while the CO2 mixing ratios decrease in the NBL as a result of the flushing of accumulated overnight CO2 and entrainment from above. The modeled 
Throughout the afternoon (1100–1800 LST), the observed profile-averaged CO2 mixing ratios continue to decrease even though the surface is expected to be a net source of CO2. Measurements show a well-mixed UBL with roughly vertically uniform profiles of potential air temperature and CO2 mixing ratios. During this period, advection from upwind low-CO2 mixing ratio marine air is an important process (average 56% of the hourly CO2 budget). Though the modeled 
In summary, the model realistically simulates the diurnal course of city-scale 
Additional measurements, such as observations of carbon isotope ratios 
Given the complex coastal meteorology at this site (e.g., sea-breeze circulation, spatial heterogeneity of UBL dynamics, recirculation of CO2), a comparison of model performance using a high-resolution inverse atmospheric transport modeling approach would provide more detailed insights. Such a comparison would be especially interesting during the afternoon period when several meteorological processes (entrainment; advection) are interacting simultaneously with surface CO2 source–sink processes to influence CO2 mixing ratios in the UBL. A more sophisticated treatment of the upwind source area influencing the UBL measurements using an inverse modeling approach would also likely yield insights into urban-scale CO2 fluxes.
This work also has implications for the monitoring of urban-scale CO2 emissions using CO2 mixing ratio measurements. Tower-based CO2 mixing ratio observations in the surface layer are representative of the entire well-mixed UBL during convective situations and below the stable NBL height overnight during this 24-h observation period. This implies future research, using either a box-model approach or inverse atmospheric modeling, could take advantage of long-term (multiyear) mixing ratio measurements from towers to estimate urban-scale CO2 fluxes. Repeated measurements averaged over many days in varying atmospheric conditions would result in more robust emissions estimates.
Acknowledgments
The current research was funded by the Canadian Foundation for Climate and Atmospheric Sciences (CFCAS) as part of the Environmental Prediction in Canadian Cities (EPiCC) network [principal investigators (PIs): T. R. Oke, UBC, and J. Voogt, UWO] and by an NSERC discovery grant (“Direct measurement of greenhouse gas exchange in urban ecosystems”; PI: A. Christen, UBC). Research infrastructure was supported by NSERC, CFI, and BCKDF (PI: A. Christen). We acknowledge the support of the city of Vancouver and Environment Canada for providing additional data and BC Hydro and the city of Vancouver for granting access to the EC tower and balloon sites. We further acknowledge the significant scientific, technical, and administrative support of staff and students at the UBC, especially Rick Ketler, Eric Leinberger, Kate Liss, Zoran Nesic, Chad Siemens, and Derek van der Kamp.
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