The Berkeley Environmental Air-quality and CO2 Network (BEACO2N) Bay Area deployment currently consists of 73 nodes spaced at ∼ 2 km intervals with locations in Alameda, San Francisco, Contra Costa, Sonoma, Sacramento, and Solano counties. A full description of a BEACO2N node can be found in . Briefly, each node contains a nondispersive infrared Vaisala CarboCap GMP343 CO2 sensor, along with a Shinyei PPD42NS nephelometric particulate matter sensor and several Alphasense electrochemical sensors for measuring CO, NO, NO2, and O3 (CO-B4, NO-B4, either NO2-B42F or NO2-B43F, and either Ox-B421 or Ox-B431). The most recent version adds a Plantower PMS 5003 aerosol sensor. Sensors are assembled into compact, weatherproof enclosures with air flow through the enclosure provided by two 30 mm fans. Data are compiled with a Raspberry Pi microprocessor and an Adafruit Metro Mini microcontroller. Data are acquired every 5 or 10 s and are transferred to a central server via an Ethernet or Wi-Fi connection. Observations are posted on the BEACO2N website within a few hours of measurement time (http://beacon.berkeley.edu, last access: 14 June 2021).

The Vaisala CarboCap GMP343 instrument uses pulsed light from a filament lamp, which is reflected and refocused on an IR detector located behind a Fabry-Perot Interferometer (FPI). The FPI is electrically tuned so that its passband corresponds to either the absorption wavelength of CO2 or a reference band . The calibration procedure for the Vaisala CarboCap GMP343 CO2 sensor is as outlined in . Briefly, deployed Vaisala sensors operate with the internal relative humidity (RH), temperature, and pressure compensation set to “off” and the oxygen correction set to “on”, with oxygen input as 20.95 %. A post hoc multiplicative scale factor is applied to convert the raw CO2 outputs to the mole fraction of CO2 that would be measured if the observed air parcel were dried and brought to standard temperature and pressure (STP) ([CO2]STP). Raw CO2 data are adjusted using temperature (T) measured by the internal thermometer of the Vaisala. Water vapor pressure (PH2O) and air pressure (Ptot) are obtained from the pressure and dew point temperature measured inside each node enclosure by a Bosch Sensortec Adafruit BME280 sensor. The [CO2]STP is then adjusted to account for temporal drift in the instrument “zero” by comparing the background signal of the Vaisala CO2 measurement at each node to a reference Picarro G2301 system, located at the Richmond Field Station in Richmond, CA (Fig. ). A moving 3-week window of the 10th percentile of Vaisala CarboCap CO2 data Vaisala[CO2]10% is generated and compared with the 10th percentile of the reference Picarro instrument Picarro[CO2]10%. The difference between Vaisala[CO2]10% and Picarro[CO2]10% is used to define the offset of the Vaisala instrument [CO2]offsetdrift. A linear correlation between [CO2]offsetdrift and time is generated and used to calculate the drift-corrected CO2 data, [CO2]correcteddrift (Eqs. –): 1[CO2]offsetdrift=mt×days+b2[CO2]correcteddrift=[CO2]STP-mt×days-b, where mt is the temporal drift (ppm d-1) and b is a constant atemporal bias.

A “supersite” with reference grade instruments is operated within the BEACO2N Bay Area network to provide a reference for the network calibration. Instruments are installed within a temperature-controlled instrument shelter at the U.C. Berkeley Richmond Field Station. Measurements include basic meteorology, NOx (Thermo 42CTL with a molybdenum NO2 to NO converter), O3 (Teledyne/API T400), CO2, CH4, and CO (Picarro G2401 cavity ring down analyzer). Air is sampled through Teflon tubes mounted to a small tower affixed to the trailer roof, for a combined height of 6 meters above the ground. The colocated BEACO2N node is attached outside of the trailer to the same tower.

The NOx and Picarro analyzer calibrations are checked against reference gases every 2 to 3 weeks. The reference gas cylinders for NOx, CO, and CH4 are Certified Standard grade from Praxair, and for CO2 are from the NOAA Global Monitoring Laboratory (two levels: 403.61 and 687.47 ppm). The Picarro checks are made by flowing the sequence of references gases into a tee at the inlet of the instrument for 15 min per step. The sequence of steps is performed twice during a check. The flow rate is set to be larger than the instrument sample flow (0.4 L min-1) to overflow the inlet. The O3 analyzer is checked against a photometric calibrator (Teledyne/API 703E).

There exists an additional temperature dependence among the Vaisala CarboCap GMP343 instruments that varies between instruments. The temperature dependence was first identified from observations of CO2 diurnal cycles at certain Bay Area BEACO2N sites that were out of phase or larger in magnitude than the diurnal cycles at nearby nodes or measured by the Picarro. The presence of a temperature dependence in suspect Vaisala instruments was confirmed by examining the relationship between temperature in the node and the difference between baseline CO2 signals measured by the Vaisala and the Picarro reference instrument.

Diurnal cycles of urban CO2 typically exhibit a daily maximum at night or mid-morning (depending on influence from traffic emissions) due to mixing in a shallow nighttime planetary boundary layer (PBL), and reach a minimum during the day as PBL height increases and vegetation takes up CO2 . The presence of an additional temperature dependence in the Vaisala CO2 instrument is particularly pronounced and obvious in the measurements obtained with the sensor located at the East Bay Municipal Utility District (EBMUD) BEACO2N site during 2020 (Fig. ). The magnitude of the diurnal cycle at EBMUD is larger and out of phase with the Picarro reference instrument (Fig. a). The result of this temperature dependence at EBMUD (Fig. c) is a diurnal cycle that peaks midday (Fig. b). Figure b compares the CO2 diurnal cycle at EBMUD with the nearby urban site Laney College (Fig. ). In contrast to EBMUD, Laney College exhibits a daily maximum at mid-morning–a pattern more consistent with typical urban CO2 behavior .

The Vaisala temperature dependence varies in magnitude and sign. Figure  shows the CO2 mixing ratios and temperature dependence at the Montclair Elementary School site. Compared to the Picarro instrument, this site also demonstrates higher amplitude diurnal cycles (Fig. a), but these diurnal cycles are in phase with the reference instrument. Unlike EBMUD, the Montclair site exhibits a negative temperature dependence (Fig. c). Figure b shows the diurnal cycles at Montclair and the nearby node located at College Preparatory School (CPS). The comparison of these two sites suggests there may indeed be an amplification of the diurnal cycle at Montclair caused by a negative temperature dependence of the Vaisala instrument.

The goal of our approach to accounting for the temperature dependence of the Vaisala instruments is to rely exclusively on the network itself and, if available, supplementary reference instruments, such as a Picarro, for derivation of correction factors to null sensor temperature dependence.

The method we developed builds on our method for accounting for drift in the instrument zero. To derive a temperature factor, we use hourly averaged [CO2]STP and node measurements of temperature (T). It is important to note that a major factor contributing to the temperature inside the node is whether the node is placed in the sun or shade. As a result, direct correlation with meteorological temperature measured outside the node is not strong. For a moving three-week window, at each hour (h), the lowest 10th percentile of [CO2]STP within ±1 ∘C of T(h) is calculated. A running array of temperature-based 10th percentile data is created for both the Picarro supersite Picarro[CO2]10%T at the Richmond Field Station and each Vaisala instrument Vaisala[CO2]10%T using the temperature (T) of the Vaisala instrument. The Vaisala temperature is assumed to be the temperature that the instrument is responding to. Δ[CO2]10%T is then calculated, where 3Δ[CO2]10%T=Vaisala[CO2]10%T-Picarro[CO2]10%T.

A linear regression for Δ[CO2]10%T against T provides a slope (mT) and intercept (bT) for a moving three-week time window. We considered the possibility that the instrument response to temperature could be a zero shift and/or a change in the response to CO2. We were able to achieve similar results assuming the temperature effect is entirely due to one or the other of these possibilities. As there is already substantial drift in the instrument zero, we proceed under the assumption that the effect can be entirely attributed to the temperature dependence of the instrument zero. The median of mT (medmT)is calculated for the deployment period of the Vaisala sensor to determine the temperature-corrected offset and CO2 mixing ratios of Vaisala CO2 measurements, based on an additive error correction (Eqs. –). When it is observed that either the offset bias, the temperature-dependent slope, or the time-dependent drift in the instrument zero shifts dramatically during a deployment period, the deployment is manually separated into different periods that are calibrated separately. The occurrence and magnitude of this varies between instruments (0–3 times during a two-year-long deployment), and is typically identified by routine checks for agreement between neighboring sensors. Shifts in the offset bias, the temperature-dependent slope, or the time-dependent drift appear as sudden or gradual offsets in mixing ratios measured by a sensor and its neighbors. Typical identified shifts in the offset bias, the temperature-dependent slope, or the time-dependent drift are on the order of 10 ppm, 0.5 ppm ∘C-1, and 0.1 ppm d-1, respectively: 4[CO2]offsetT=Δ[CO2]10%T-medmT×T5[CO2]correctedT=[CO2]STP-medmT×T.

An example calibration, demonstrating mT and [CO2]offsetT over time at EBMUD 2020, is shown in Fig. S1 in the Supplement. Following calculation of the temperature-corrected offset, the temporal drift slope and intercept of this corrected offset are calculated and corrected using the methods described above, resulting in the generation of the temperature- and drift-corrected CO2 offset [CO2]offsetT,drift.

The final temperature- and drift-corrected CO2 [CO2]correctedT,drift is then calculated as 6[CO2]correctedT,drift=[CO2]STP-medmT×T-[CO2]offsetT,drift.

The majority of the BEACO2N nodes examined demonstrated a strong linear relationship between Δ[CO2]10%T and node temperature. However, the node at Elsa Widenmann Elementary School appeared to show a strong negative temperature dependence only on particularly warm days (Fig. a, c). The temperature dependence of Δ[CO2]10%T for this node better fit a quadratic than a linear relationship. To account for nodes with a nonlinear temperature dependence, in cases where a quadratic fit improves the R2 of the fit by more than 0.2, the [CO2]offsetT and [CO2]correctedT,drift are calculated via Eqs. ()–(): 7[CO2]offsetT=Δ[CO2]10%T-medmT1×T-medmT2×T28[CO2]correctedT,drift=[CO2]STP-medmT1×T-medmT2×T2-[CO2]offsetT,drift, where mT1 and mT2 are the first and second terms of the quadratic fit of Δ[CO2]10%T against T.

We attempted to determine a relationship between Vaisala sensor age and temperature-dependence slope, but mT was only weakly correlated with sensor age (r≈0.3). We did, however find some evidence that older sensors had a larger likelihood of having a larger temperature dependence. For sensors less than 3 years since their initial deployment, 90 % had mT<1 ppm ∘C-1 and 64 % had mT<0.5 ppm ∘C-1. For sensors older than 3 years, 75 % had mT<1 ppm ∘C-1. and 47 % had mT<0.5 ppm ∘C-1.

To assess the improvement in the network precision following application of the temperature-dependence correction, we combined observations from the entire Bay Area network using data from all of 2020. All sites with available data for more than one month of 2020 were included. Nearest neighbor pairs of each site were identified, where nearest neighbors to an individual site were considered as the closest BEACO2N sites within a 2 km radius of the site. There are 53 unique nearest neighbor pairs.

For each nearest neighbor pair X and Y, an array of the fractional differences between sites was calculated as: ([CO2]X-[CO2]Y)/[CO2]X. This was done using both the measurements before and after correction for temperature-dependent instrument zero [CO2]correcteddrift and [CO2]correctedT,drift. Figure a and d show the fractional differences of each nearest neighbor pair as a histogram calculated using [CO2]correcteddrift and [CO2]correctedT,drift, respectively. Most nearest neighbor site pairs exhibit a distribution of fractional differences centered close to zero, with both positive and negative tails (Fig. a, d). The temperature correction results in a clear improvement of agreement between nearest neighboring sites, with the mean of the absolute value of the average fractional differences of all nearest neighbor pairs decreasing by a factor of 2 from 0.025 to 0.013. For [CO2]correctedT,drift, this represents an average difference of 6.5 ppm at [CO2]=500 ppm. Figure b and e express the fractional differences of nearest neighbor pairs as a single distribution calculated using [CO2]correcteddrift and [CO2]correctedT,drift, respectively. Fit to a Lorentz distribution, the mean and scale parameter of the distribution of nearest neighbor pairs using [CO2]correcteddrift is 0.0026 and 0.014, respectively, without accounting for temperature dependence and there is a substantial narrowing of the distribution, resulting in a mean and scale parameter of 0.005 and 0.007, respectively, after accounting for the effect of a temperature-dependent offset.

Further analysis was performed to confirm that the temperature correction method eliminates any temperature-dependent disagreement between nearest neighboring sites. The nearest neighbor fractional differences of CO2 data were separated into 2 ∘C temperature bins. For each temperature bin, the absolute value of the mean fractional difference between each nearest neighbor pair, using either [CO2]correcteddrift or [CO2]correctedT,drift, was calculated. We then averaged the mean fractional difference in each temperature bin over all nearest neighbor pairs. A plot of the resulting network mean percent difference vs. temperature is shown in Fig. c and f, using [CO2]correcteddrift and [CO2]correctedT,drift data, respectively. In the original data, the mean percent differences were greatest at both high and low temperatures. In the temperature-corrected data, there is no clear dependence of nearest neighbor mean percent differences on temperature. The mean percent difference at all temperatures is also reduced.

To evaluate the network error, a semivariogram of γnn vs. distance was constructed for [CO2]correctedT,drift (Fig. ). Using data from all sites with more than three days of available data during the summer of 2020, we calculated the semivariance between CO2 measurements at each BEACO2N node, i, and all other sites in the Bay Area network (Eq. ) 9γnn=∑jN[CO2]i-[CO2]j22N. Summer months were chosen because the average and diurnal variability of CO2 mixing ratios are reduced, meaning that measured site variances are relatively more influenced by instrument error, rather than by “true” atmospheric variance, than in the winter. In Fig.  the square root of the semivariance is plotted against the distance separating the BEACO2N nodes and fitted with an exponential model. The Picarro reference instrument at the Richmond Field Station was included in this analysis.

Using the root semivariance as a correlation metric, in temperature-corrected data, the e-folding length scale for variation is 1.2 ± 0.3 km (1.7 ± 0.7 km using semivariance as a correlation metric, not shown), supporting the BEACO2N hypothesis that 2 km node spacing in a dense network will capture important elements of local variability. The temperature-correction results in a maximum root semivariance of 5.5 ± 2 ppm (reduced from 8 ppm in the uncorrected data). Extrapolated to a distance of zero, the temperature correction method has a predicted root semivariance of 1.3 ± 0.9 ppm, representing the network error. This analysis suggests that the temperature correction method provides a meaningful reduction of network measurement uncertainties toward our desired ∼ 1 ppm network error.

Length scales for correlations (r2) between sites calculated by during the summer 2017 were larger than the 1.2 km length scale identified here for root semivariance (1.7 km for semivariance). To more directly compare, we also performed the method of on the temperature-corrected CO2 data for the summer of 2020. We examined the correlation of CO2 concentrations for every pairing of Bay Area sites during this period for all hours, during the day, and during the night (Fig. S7). The e-folding distance for the decay of r2 correlation coefficients was 2.8 km for all times, 3.7 km during the day, and 2.8 km at night. This is in good agreement with the length scales of 2.9 km at all times, 3.6 km during the day, and 2.2 km at night found by . The base-line correlation for sites separated by more than 20 km was found to be 0.46, larger than the correlation background of ∼0.3 of . The temperature correction does not affect the characteristic length scale of BEACO2N sites, but improves the overall base-line correlations and variances.

We can represent the network instrument error also by examining the sources contributing to the semivariance between nearest neighboring sites. The semivariance (γnn) of nearest neighboring sites can be expected to have contributions from both “true” variations in emissions and meteorology and erroneous differences caused by instrument error. “True” variations in emissions and meteorology are reflected in temporal changes in CO2 concentrations due to emissions plumes and changes in wind speed and direction. Here we used temporal changes in CO2 concentrations at a certain site as a proxy for “true” atmospheric variations in CO2. To estimate the portion of the semivariance resulting from atmospheric phenomena, an analogous quantity for the hourly variations in CO2 was calculated for each site according to Eq. (): 10γhh=12N∑1N-1[CO2]h-[CO2]h+12, where N is the number of hours of data and [CO2]h , and [CO2]h+1 are the measured mixing ratios of CO2 at each hour and 1 h later, respectively. The individual instrument error was then calculated as: 11ϵinst=γnn-γhh. The resulting upper-bound instrument error from the median of individual instrument errors for the Bay Area network is 2.5 ± 0.5 ppm. (This estimate for nontemperature corrected data is 4.5 ± 0.9 ppm). We consider this an upper bound because hourly variations in the CO2 signal reflects the atmospheric changes at an individual site, which may not match with the atmospheric changes at the nearest neighbor sites. Variations in emissions or wind velocity may result in larger “true” differences between a site and its nearest neighbor than are represented by the site's hourly variability.

To reduce the influence from short-term atmospheric variations, the network error was also estimated using an individual site's root mean squared error (RMSEi) as a metric for “true” atmospheric variation (Eq. ) and a “paired” RMSE (RMSEpaired) using the mean CO2 signal of its nearest neighbor site (nn[CO2]‾) as a measure of total variation (Eq. ). The site error was then calculated according to Eq. : 12RMSEi=∑h=1N[CO2]h-[CO2]i‾N13RMSEpaired=∑h=1N[CO2]h-nn[CO2]‾N14ϵinst=RMSEpaired2-RMSEi2. The resulting network instrument errors were between 0.5 and 4 ppm, with a median of 1.6 ± 0.4 ppm, in good agreement with the error calculated from the semivariogram fit. Based on these analyses, we estimate the network error of the Bay Area BEACO2N network to be less than 1.6 ppm, close to our goal of 1 ppm network error.

We observe good agreement between the Picarro reference instrument during 2020 and [CO2]STPmed (Fig. ). The mean percent difference considering all 2020 data is 0.46 %, representing an accuracy error of 2 ppm at 420 ppm CO2 (Fig. d). We also do not see evidence of a temperature-dependent offset between the Picarro reference instrument and [CO2]STPmed.

The precision of the Bay Area network is negligibly affected when the network median is used as the reference, with the mean of the absolute value of the average fractional differences of all nearest neighbor pairs equal to 0.015 ± 0.008 (compared to 0.013 ± 0.007 with the Picarro as reference) (Fig. S8). The resulting maximum root semivariance is 5.5 ± 2 ppm and extrapolated root semivariance at 0 km separation is 0.8 ± 0.9 ppm, respectively, approximately equal to the values calculated when the Picarro is used as a reference. The network accuracy is however, more appreciably altered. Figure  shows the fractional difference between [CO2]correctedT,drift determined using the Picarro and [CO2]STPmed as a reference at each site. The resulting mean percent difference is 0.51 ± 0.02 %, representing a network accuracy error of 2 ppm at 420 ppm CO2. This accuracy error is mainly driven by small differences in the offsets (2 ppm on average) and mT (0.2 ppm ∘C-1 on average, see Supplement) between [CO2]correctedT,drift calculated using the Picarro and [CO2]STPmed as a reference. These results suggest that the network precision can be expected to remain near 1 ppm CO2 with the use of [CO2]STPmed as a reference, but additional accuracy error of 2 ppm may be introduced. The influence of a sea breeze in the Bay Area makes the median tenth percentile CO2 measured by Bay Area nodes a regional background. Although the median tenth percentile of other inland sensor networks may not represent a regional background, it can be expected to represent the overall network regional average baseline.

Analysis of the Bay Area network was performed on the 36 nodes with sufficient data availability for 2020. However, the newly established networks have fewer nodes than in the Bay Area. To use [CO2]STPmed as a reference, we must have sufficient nodes from which to calculate the network median. To evaluate this, for n=1–26, a random subset of n Bay Area nodes was selected 100 times. For each of the 100 random subsets of n nodes, the mean fraction difference was calculated between the network median CO2 and the median calculated using the subset. The average and standard error of the 100 mean fraction differences was then calculated. The results of this analysis are presented in Fig. . We suggest that a minimum of 7 nodes with mT less than 1 ppm ∘C-1 is required for the accuracy error to be lower than 2 %. For less than 1 % error, at least 12 nodes are required.

Data from the Houston network were subsequently calibrated using [CO2]STPmed as a reference for determining temperature dependence, drift, and offset. Temperature dependence calibration of each site in the Houston network was performed twice. All sites were first included in [CO2]STPmed and sites with mT greater than 1 ppm ∘C-1 were identified. These sites were then excluded from [CO2]STPmed and each site was recalibrated. Histograms of the fraction differences between nearest neighbor sites are shown in Fig. . The average mean percent difference between nearest neighbors was 2 ± 1 %. Though considerably larger than the differences between nearest neighbors in the Bay Area network, it is not immediately clear whether this difference is caused by greater precision error in Houston or differing meteorology and CO2 sources that cause greater differences between CO2 mixing ratios at adjacent sites. We attempted to perform a similar instrumental error analysis, but there are currently insufficient overlapping CO2 data in Houston for uncertainty analysis. However, we do not have reason to expect the instrument errors would be any larger in the Houston network.