Detecting long-term changes in point-source fossil CO 2 emissions with tree ring archives

. We examine the utility of tree ring 14 C archives for detecting long-term changes in fossil CO 2 emissions from a point source. Trees assimilate carbon from the atmosphere during photosynthesis, in the process faithfully recording the average atmospheric 14 C content in each new annual tree ring. Using 14 C as a proxy for fossil CO 2 , we examine inter-annual variability over six years of fossil CO 2 observations between 2004–2005 and 2011–2012 from two trees growing near the Kapuni Gas Treatment Plant in rural Taranaki, New Zealand. We quantify the amount of variability that can be attributed to transport and meteorology by simulating constant point-source fossil CO 2 emissions over the observation period with the atmospheric transport model WindTrax. We compare model simulation results to observations and calculate the amount of change in emissions that we can detect with new observations over annual or multi-year time periods, given both the measurement uncertainty of 1ppm and the modelled variation in transport. In particular, we ask, what is the minimum amount of change in emissions that we can detect using this method, given a reference period of six years? We ﬁnd that changes of 42 % or more could be detected in a new sample from one year at the same observation location or


Introduction
Carbon dioxide (CO 2 ) emitted by anthropogenic activity is the largest single contributor to the radiative forcing causing climate change (Pachauri et al., 2014). It thus plays a crucial role in any attempt to prevent or mitigate further warming. Large point sources (mainly from electricity generation and industry) contribute around a third of the total fossilfuel derived CO 2 (CO 2 ff) emissions (Pachauri et al., 2014) and in many places are included in government regulatory schemes that aim to reduce emissions (e.g. European Union ETS, South Korea, Switzerland, and others at the city/state level; Serre et al., 2015). Emissions are typically reported on an annual basis, and commonly agreed-upon reduction targets are annual or multi-year caps, often requiring changes in emissions relative to a baseline year (e.g. the Kyoto Protocol and the new intended nationally determined contributions, INDCs; UNFCCC, 2015a, b).
Emissions are currently known from bottom-up techniques such as self-reported data from fuel-usage statistics (Boden et al., 2015) and/or continuous stack monitoring (U.S. Environmental Protection Agency, 2005;eGRID, 2014) and are subject to significant uncertainties (Ackerman and Sundquist, 2008;Gurney et al., 2009Gurney et al., , 2012. This uncertainty might include not only methodological biases and possible deliberate underreporting but also simple error in compiling statistics. The integrity of regulation schemes and their effectiveness at limiting future climate change will require independent methods of evaluating reported emissions and improvement in the accuracy of emissions inventories (Tans and Wallace, 1999;Nisbet and Weiss, 2010;National Research Council, 2010;Gurney, 2013). Top-down atmospheric observations can provide an independent method for evaluating emissions. This involves taking observations of atmospheric gas mole fractions in combination with atmospheric transport modelling to infer the magnitude of emissions from a source or region over a particular time period (e.g. McKain et al., 2012;Lindenmaier et al., 2014;Brioude et al., 2013). It can be quite challenging to quantify absolute values of emissions and CO 2 fluxes in general because of the large errors and biases typically encountered in transport models (e.g. Stephens et al., 2007;Lin and Gerbig, 2005;Gerbig et al., 2008;Prather et al., 2008;Geels et al., 2007;Liu et al., 2011;Kretschmer et al., 2012). However, relative changes in emissions are usually easier to determine, since any consistent bias in the model will cancel out. By establishing a baseline measurement over a reference period, we can compare future observations to this reference and calculate relative changes that occur. In this manner, we can potentially verify relative emission reduction targets without requiring precise knowledge of the absolute levels of emissions.
One of the biggest challenges of atmospheric observations of CO 2 ff is distinguishing the fossil component from the considerable background level of CO 2 that occurs naturally in the atmosphere, currently about 400 parts per million (ppm; Mauna Loa observation record; re3data.org, 2015). In addition, there are large diurnally and seasonally varying CO 2 fluxes from the biosphere, which may result in changes in CO 2 mole fraction of tens of ppm within a single day at near-surface sites (e.g. Miles et al., 2012). This problem can be avoided by using the 14 C isotopic content as a tracer for CO 2 ff. CO 2 ff contains no 14 C: the half-life of 14 C is 5730 years (Karlen et al., 1968) and all of the 14 C has decayed away from fossil fuels. Other sources of CO 2 have roughly the same 14 C content as the atmosphere. By measuring the 14 C content of CO 2 or a proxy for CO 2 , we can calculate the portion of observed CO 2 that comes from recently added fossil fuel emissions (Levin et al., 2003;Meijer et al., 1996;Turnbull et al., 2006).
Plant material can be used as a proxy for atmospheric CO 2 ff because plants assimilate carbon from the atmosphere during photosynthesis, in the process faithfully recording the 14 C content in new plant material. Tree rings represent an integrated average of daytime CO 2 atmospheric mole fractions and 14 C content over the tree's annual growth period, and can be independently dated using dendrochronology methods. This allows for a retroactive analysis of CO 2 ff mole fractions over many years, including any trends in emissions that occurred during the life of the tree. The radiocarbon content in tree rings has been well established as a tracer for fossil CO 2 emissions (Suess, 1955;Tans et al., 1979;Djuricin et al., 2012;Rakowski et al., 2013) and as a method to detect leaks from CO 2 geosequestration (Donders et al., 2013).
In this study, we evaluate whether we can detect changes in CO 2 ff emission rates from a point source on an annual timescale using the CO 2 ff mole fraction derived from the 14 C content of tree ring archives. Variations in the observed CO 2 ff mole fraction at a given location are dependent on not only the emission rate but also on atmospheric transport, which in turn is subject to naturally varying meteorological conditions (e.g. wind speed and direction, temperature, pressure, etc.). Detecting a change in the emission rate requires disentangling this change from the natural variability in transport and meteorology as well as from measurement uncertainty in the observations. The question we ask in this paper is: can we use tree ring archives to detect changes in CO 2 ff emissions from a point source, and if so, what is the minimum change in annual emissions that we can detect given the typical measurement uncertainty of 1ppm and natural variability in transport? A similar analysis was carried out by Levin and Rödenbeck (2007) at the regional scale, using a 20-year time series of 14 C observations over Germany. McKain et al. (2012) also assessed the ability of an observation-model framework to detect changes in regional urban CO 2 emissions on a monthly timescale. We re-examine this question on the scale of an individual point source with mean annual observations.
We calculate interannual variability in observations from tree ring archives of annual (growing season) CO 2 ff between 2004-2005 and 2011-2012 1 , taken from two different trees growing south of the Kapuni Gas Treatment Plant in rural New Zealand (Norris, 2015). We then use an atmospheric transport model, WindTrax, with local meteorological data to quantify the interannual variability that can be expected due to measurement uncertainty, transport, and meteorology at different distances and orientations from the source, including the locations of the trees. Finally, we look at what this implies for detection limits in the context of emissions monitoring or verification and practical considerations in the presence of multiple sources of uncertainty.

Site
The site of our study is the Kapuni Gas Treatment Plant in rural Taranaki, New Zealand (39.477 • S, 174.1725 • E, 170 m a.s.l.; Fig. 1). This site was chosen because it is located in flat terrain and is relatively isolated from other sources of CO 2 ff, considerably simplifying measurement and analysis. The gas treatment plant, owned and operated by Vector, processes natural gas extracted from natural gas wells in the Taranaki Basin. The gas contains around 40 % CO 2 , which is removed during processing and vented to the atmosphere at a rate of ∼ 0.1 Tg C yr −1 (NZMED, 2010). In addition, there is an ammonia urea manufacturing plant 500 m to the west of the gas plant (Fig. 1a), operated by Ballance Agri-Nutrients, which also releases CO 2 ff to the atmosphere during the manufacturing process. This site emits roughly a third of the amount of the Vector gas plant (∼ 0.03 Tg C yr −1 ; Taranaki Regional Council, 2013). Although the signal from the Vector plant is much stronger, especially to the east (downwind from the dominant westerly winds), emissions from the Ballance plant are potentially large enough to detect at some locations and are included in our simulations unless otherwise specified.
The surrounding terrain is flat and mostly free of obstructions, with elevation varying no more than 10 m within 2 km of the plant. The largest nearby topographic feature is a dip of ∼ 5 m into the Kapuni Stream immediately east of the Vector emission source. The landscape is dominated by highly productive pasture grazed by dairy cows, with large and diurnally varying CO 2 fluxes. The prevailing wind direction is from the west, with a smaller proportion from the south-east and north (Figs. 2 and 3).

CO 2 emissions
Emissions data were supplied by Vector as monthly totals (P. Stephenson, personal communication, 2014), which we have converted to average daily rates for the purpose of modelling. Mean annual daily emissions for each year between 2004 and 2011 from 1 September to 30 April are shown in Fig. 4; data are listed in Table S1 in the Supplement. The long-term mean is 5341 g C s −1 , with a standard deviation in annual means of 388 (7.3 %). There are annual fluctuations but no long-term trend over the modelled period 2004-2011. The largest change during a single year occurred in 2007, when the emissions dropped by 14 % relative to the mean. On a longer timescale, there are more significant changes, including the start of operations at the Vector plant in 1971. However, we focus on the 2004-2011 period during which high-resolution local meteorological data are available. There are no significant seasonal or diurnal variations in the emissions of which we are aware.
The Ballance Agri-Nutrients plant emissions are reported on an annual basis (Taranaki Regional Council, 2013). Average daily rates in each growing season are depicted in Fig. 4. The mean daily rate of emissions over the period 2004-2011 is 1512 g C s −1 with a standard deviation in annual means of 88 (18 %), which is more variable than the emissions from the Vector plant, but smaller in absolute terms. Emissions vary somewhat from day to day according to production levels, but more detailed daily or monthly information is unavailable; for simplicity we assume a constant emissions rate in each year. We note that emissions are much lower in 2011, which is due to downtime after both a fire and scheduled maintenance (Taranaki Regional Council, 2013).

Tree ring observations
Tree rings faithfully record the 14 C content of assimilated CO 2 , so when the rings are independently dated by dendrochronology, we can determine an average 14 C content and recently added CO 2 ff in the local atmosphere for the period during which the tree ring was laid down. We use core samples from two individual trees located south of the plant: one pine tree, Pinus radiata, and one chestnut tree, Castanea sativa ( Fig. 1a; Norris, 2015). The pine tree is located in a stand of trees within 5 m of the Kapuni Stream, with the crown reaching 10 m above the associated terrain dip. The chestnut is isolated in a flat paddock.
Each tree ring is assumed to represent the Southern Hemisphere summer growth period from 1 September to 30 April, as this is when the majority of plant photosynthesis occurs and new plant material is produced. The sample preparation, measurement, and determination of CO 2 ff are described in detail by Norris (2015). In summary, wood was sampled from the trees using a Haglöff incremental borer. Four cores were extracted per tree at equidistant points at a height of approximately 1.2 m from the base of the tree. One core from 5484 E. D. Keller et al.: Detecting long-term changes in point-source fossil CO 2 emissions each tree was used to create a historic record of CO 2 emissions from the commission of the Kapuni plant in 1971 to the outermost ring at the time of sampling in 2012. Replicates were taken from a second core to validate ring counting and 14 C results. Alpha cellulose was extracted from individual rings using a method modified from Hua et al. (2000), combusted with a Europa ANCA elemental analyser (EA), reduced to graphite and measured by accelerator mass spectrometry at GNS Science laboratories in Lower Hutt, New Zealand (Baisden et al., 2013;Zondervan et al., 2015;Turnbull et al., 2015).
CO 2 ff was determined following Turnbull et al. (2014) from the isotopic difference between the measured tree ring and clean air background CO 2 measured at Baring Head, Wellington (41.4167 • S, 174.8667 • E; Currie et al., 2011;extended with unpublished data). Baring Head, located at the southern end of New Zealand's North Island and approximately 300 km south of Kapuni, was chosen as the background for this study over more local sites because it provides a long-term record of background CO 2 and 14 C, dating back to the early 1970s. The following equation was used: where C ff is CO 2 ff, C obs is the CO 2 mole fraction in the observed sample, obs and bg are the 14 C of the observed sample and background sample respectively. ff is the 14 C of CO 2 ff, and is assigned to be −1000 ‰, and bg is from the summer seasonal average from the long-term Wellington 14 CO 2 record at Baring Head. Comparison of this record with tree rings collected 3 km upwind of our source showed no difference from the Wellington record. A small correction, β, accounts for the fact that the 14 C of CO 2 from other sources may be slightly different from that of the atmosphere; in our case we set β to zero since the proximity to the coast and consistent winds suggest that other CO 2 is negligible in this location (Turnbull et al., 2014). Uncertainty in CO 2 ff is dominated by 14 C measurement uncertainty in both background and the observed sample and is typically ∼ 1 ppm for this data set. The process of CO 2 adsorption in plants is extremely complex. For simplicity, we assume a constant assimilation rate over all daylight hours. In reality, CO 2 adsorption varies with plant species and photosynthesis rates, being weighted towards sunny periods and midday (Bozhinova et al., 2013). There are also many different climatic and nutrient limitations that can only be properly accounted for with a full process-based biogeochemical model of plant growth, which is beyond the scope of this study. We do, however, take into consideration the fact that plant material will tend to underestimate mean CO 2 ff when CO 2 ff is variable, as in the case of a plume from a point source (see Sect. 2.7).

WindTrax model
WindTrax (WindTrax 2.0; Thunder Beach Scientific, Nanaimo, Canada, www.thunderbeachscientific.com) is a Lagrangian particle dispersion model used to estimate unknown trace gas concentrations or emission rates from a source over short distances (∼ 1 km). WindTrax has been applied to agricultural emissions from area sources, such as methane, ammonia, and other gasses from grazing dairy cows, cattle feedlots, and farm waste (e.g. Flesch et al., 2005;Laubach and Kelliher, 2005;Bonifacio et al., 2013;Rhoades et al., 2010;Wilson et al., 2012;McBain and Desjardins, 2005). It has also been assessed in the context of CO 2 sequestration leakage detection (Leuning et al., 2008;Loh et al., 2009). Modelling integrated averages of CO 2 ff in plant material is a relatively new application. WindTrax was chosen for this study because it is easy to use and the distance scale is appropriate for our site. We previously used WindTrax to estimate CO 2 ff in grass samples at the Kapuni site (Turnbull et al., 2014), demonstrating that the model is capable of providing reasonable estimates of observed CO 2 ff. Here, we take the same approach to model CO 2 ff measured in tree rings. We note that WindTrax is not applicable to complex terrain or larger distance scales and caution is urged when applying our methodology to other sites.
WindTrax simulates the transport of trace gases by releasing a set number of particles at each time step and following each particle's trajectory downwind. Based on Monin-Obukhov similarity theory (MOST), the physics underlying the model is described in detail in Flesch et al. (2004) and Wilson and Sawford (1996). The model equations are valid in the atmospheric surface layer. It assumes wind and other meteorological observations are averaged over a suitable time interval, representing a stable mean atmospheric state (model relationships are built from wind statistics over 15-60 min intervals; using model time steps greatly outside of this range is not recommended). Intervals longer than 1 h can be problematic (Flesch et al., 2004) because at these time intervals, large-scale fluctuations not described by MOST statistics become important. In this study, we use 1 h time steps to match the resolution of our meteorological data set (see Sect. 2.5).
The model can be run in forward (fLS) or inverse/backward (bLS) mode, depending on whether the emissions or the trace gas mole fractions are unknown. In all simulations described here we start with known emission rates and use the fLS mode to estimate the CO 2 ff mole fraction at locations surrounding the plant. Model "concentration sensors" represent simulated measurements of mole fractions at designated locations and supply the main model output.
The model is stochastic, meaning that it introduces random turbulence into particle trajectories, and no two runs are identical, even with the same parameters and meteorological input. There is, therefore, inherent error in the model predictions due to the randomness introduced in the transport process. Only the average behaviour of a group of particles E. D. Keller et al.: Detecting long-term changes in point-source fossil CO 2 emissions 5485 can be determined and releasing more particles at each time step will tend to reduce the degree of uncertainty. Statistical error (or the standard deviation within each set of trajectories) is calculated and output by the model at each time step. However, any biases in the modelled transport or the meteorological input data used to drive the model are not accounted for.

Meteorology
Modelling with WindTrax requires at a minimum measurements of wind speed, wind direction, air temperature, and atmospheric pressure at each time step. We use hourly meteorological data from the Hawera Automatic Weather Station (AWS) (39.6117 • S, 174.2917 • E, 98 m a.s.l), downloaded from the New Zealand National Climate Database (CliFlo, 2014). Hawera, approximately 20km distance to the southwest of Kapuni, is the nearest location with a nearly complete long-term data set of hourly wind direction and speed. Eight years of data (2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011) were available at the time of our study. We only use data from the growing season (1 September to 30 April) and daylight hours (08:00-18:00 local daylight savings time) in the model simulations to correspond to the time period during which trees assimilate CO 2 . A wind rose for all eight growing seasons is shown in Fig. 2a.
The area to the north-west of Hawera and Kapuni is dominated by Mount Taranaki, a 2518 m volcanic cone that rises steeply from relatively flat surrounding terrain. Wind direction and speed can be very different at sites only a few kilometres apart because of the local impact of the mountain on atmospheric flow. Thus we compared Hawera and Kapuni meteorological data sets to ensure that Hawera is representative of Kapuni over long (∼ 1-year) time periods and the wind speed and direction distributions as a whole are similar at both locations. Daily mean wind speeds were compared using the Virtual Climate Station Network (VCSN; Tait et al., 2006). This is a set of virtual weather stations that uses reanalysis interpolation techniques to provide historical daily weather variables on a 5 × 5 km grid across New Zealand. The mean wind speed at Hawera over the modelled time period, 5.0 m s −1 , is only slightly higher than that at Kapuni, 4.6 m s −1 . Histograms comparing the wind speed distributions at both sites are in Fig. S1.
Only one overlapping data set with sub-daily time intervals was available for direct comparison at the time of our study. We collected data at a temporary meteorological station situated in a paddock at Kapuni at 10 min intervals during the period 14 August to 26 October 2012, with some data gaps (Turnbull et al., 2014). These were averaged to hourly intervals and compared with the corresponding set of measurements at the Hawera AWS. Only daylight hours were included for consistency with the model simulations. Wind roses for the Kapuni data set and the corresponding time period at Hawera are shown in Fig. 2b and c. The distribution in direction is similar to the north, but there are more southerlies and fewer westerlies at Hawera. Using these data sets, correlation in wind speed is good, with R 2 = 0.82, and correlation in wind direction is moderate (R 2 = 0.61). Because wind direction is an angular measurement, correlation in wind direction was performed using the circular package v0.4-7 in R v3.0.2 (Lund and Agostinelli, 2013;R Core Team, 2013) rather than the standard linear correlation function. Scatter plots comparing wind speed and direction at Kapuni and Hawera directly at each time step are in Fig. S2. Wind speed is a good match, with Hawera on average having slightly higher speeds than Kapuni. When wind speed at Hawera is linearly regressed against wind speed at Kapuni, the resulting equation is y = 0.90x − 0.32. (Model II regression was performed with the lmodel2 v1.7-2 package in R v3.0.2; Legendre, 2014). With wind direction, most points are close to the 1 : 1 line or slightly below, indicating a small rotation in direction between the sites. Approximately 67 % of data points (one sigma) are within 30 • of each other, and 85 % are within 45 • . For the purpose of our simulation, in which we focus on integrated averages rather than particular points in time, the Hawera data set is sufficiently representative of typical conditions at Kapuni. We note, however, that the data set from Kapuni spans a very limited time period, and this is a potential source of error in our results.
We expect variability in CO 2 ff mole fraction to be strongly related to variability in wind speed and direction, and consequently sampling location. Annual mean wind speed does not vary by much; the mean hourly wind speed over all eight years is 6.3 m s −1 , and the standard deviation in annual mean is 0.11 m s −1 , which is only 2 % of the mean. Mean wind direction is 273 • (from the west), but there is also a significant amount of wind from the south-east and north-north-east ( Figs. 2 and 3). This general pattern did not change from year to year over the eight years of the simulation but relative proportions in each direction did sometimes vary considerably (Fig. 3). In particular, northerlies (the direction most relevant to our observations) range from 21 to 28 % of the total, a 30 % change in the northerly fraction. While always the largest category, the percentage of westerlies varies between 38 and 52 %. It is notable that there are very few periods with calm winds; the region is in general very windy.

Model parameters
Several model parameters are held constant throughout all simulations. The modelled surface is short grass (surface roughness z o = 2.3 cm), since the majority of the surrounding area is grazed dairy pasture. The heights of the two emissions stacks are set to their known values: 35 m above ground level for Vector and 36 m for Ballance. The model's atmospheric stability parameter is also held constant using the general class of "moderately unstable". While this is not true for all modelled time periods, in the absence of measurements from a 3-D sonic anemometer or other reliable indicators of atmospheric stability, a general stability class is a first approximation. We tested the model at a different constant stability class (slightly unstable) and found no significant difference in the amount of variability (results not shown). We note, however, that atmospheric stability is a potential source of error; others have found that stability is an important parameter that can bias results and model estimates are generally improved with input from a sonic anemometer or vertical profiles of wind speed and temperature (Flesch et al., 2004;Gao et al., 2009;Koehn et al., 2013).
Model concentration sensors at the locations of the pine and chestnut trees are placed at heights of 15.0 and 5.0 m respectively, reflecting the approximate height of the canopy. A single height at each tree was chosen to reduce model complexity and runtime; however, we recognize that in reality CO 2 is assimilated over a range of heights at each tree, corresponding to the vertical spread of the canopy. Some previous studies have indicated that concentrations modelled with WindTrax are sensitive to sampling height and/or the ratio of sampling height to distance from the source (e.g. McBain and Desjardins, 2005;Laubach and Kelliher, 2005;Laubach, 2010). To test for dependence on height, we simulated CO 2 ff along a 20 m vertical profile at the location of the pine and chestnut trees (results not shown). Results vary somewhat according to height, and averaging over a 5m height range slightly reduces the mean and interannual standard deviation, but not enough to change our results significantly.

Simulations
We ran a "constant emissions, variable meteorology" simulation at an hourly time step with all eight years of available meteorological data from Hawera (excluding night-time and winter months), concentration sensors placed at the locations of the trees, and both the Vector and Ballance plants as CO 2 ff point sources (Fig. 1). Because emissions are held constant, this simulation enables us to isolate contributions to variability from meteorology and transport. For each tree, four concentration sensors were placed on the vertices of a square, with sides of length 30 m, centred on the location of the trees and averaged to reduce model transport error. The emission rate at each source was the reported mean rate over the entire modelled period.
In addition to the model sensors at the locations of the trees, we placed sensors at hypothetical locations in four directions and two horizontal distances from the emissions source to examine more general model sensitivity and variability due to meteorological conditions at our site without being tied to the locations of specific observations. Eight additional sensors were placed 1.5 m above the ground in the four cardinal directions relative to the Vector plant; one each at 300 and 600 m horizontal distance from the source. Only one point source, the Vector plant, was included in the results at these sensors to simplify analysis. Emissions are constant at the Vector mean rate over the eight years.
We also ran a "constant meteorology, variable emissions" simulation in which we repeat the meteorology from one year (2004) and allow emissions rates to vary according to the reported values. This allows us to examine model annual variability due to emissions, independent of transport.
We subsequently generated a "variable emissions, variable meteorology" simulation by scaling modelled mole fractions at the tree rings from the constant emissions, variable meteorology simulation according to reported emissions levels in each year (Fig. 4). This is valid because the relationship between source strength and concentration flux passing through a location downwind is linear (Leuning et al., 2008). In addition, under unstable atmospheric conditions the emissions leave the model domain within 1 h and do not return, so data in a given year are not affected by the emissions from previous years. This simulation is used to compare the model to observations.
Because plant material will underestimate mean CO 2 ff when CO 2 ff is variable, rather than comparing the tree ring measurements to the raw model output of CO 2 mole fractions, we calculate a modelled "CO 2 ff tree ". This is the CO 2 ff that the model would predict from the plant material, given measured background levels and the equations governing 14 C. We use the following equations: where = 14 C, C ff i is the modelled CO 2 ff at the ith time step, N is the total number of model time steps, C bg and bg are measured (Norris, 2015), and ff = −1000. The basic derivation of this equation can be found in Turnbull et al. (2006). This accounts for the fact that plant material will assimilate roughly the same amount of CO 2 at each time step, regardless of the variability in atmospheric CO 2 mole fraction induced by the emission plume, and thus the 14 C of the plant material represents a simple mean of the 14 C in the assimilated CO 2 at each time step. In contrast, sampling of whole air across the same time period would collect more CO 2 during times of high CO 2 mole fraction, weighting the resultant 14 C towards these periods. This results in a CO 2 ff tree that is lower than would be obtained by determining the simple mean CO 2 ff from the modelled mole fractions. Model results from the variable emissions simulation reported in Fig. 4 and Sect. 3 were derived using these equations. Bottom panel (c) shows the average emissions rate in g C s −1 for Vector and Ballance in each year for comparison.

Observation and model comparison
We first compare modelled CO 2 ff tree to the observed tree ring CO 2 ff to evaluate the model's ability to estimate annual integrated averages in this context and to identify possible bias and error in the model. Our observations from tree rings consist of six annual measurements of CO 2 ff from both the pine tree and the chestnut tree between 2004 and 2011 (2008 and 2010 are missing; Fig. 4). The means over this period are 5.4 ppm (pine) and 2.1 ppm (chestnut; Table 1). Mean modelled CO 2 ff tree over the same six years (excluding the two years without observations, 2008 and 2010) are 6.1 and 2.2 ppm for the pine and chestnut trees respectively. The modelled mean is almost an exact match for the chestnut tree (difference of 0.1 ppm) and within error for the pine tree (difference of 0.7 ppm). Figure 4 shows a direct compar- ison between measured and modelled CO 2 ff for each year. At the pine tree, model performance is very good: four of the six (66 %) annual observed values are within one sigma of the modelled values and the remaining two are within two sigma. The agreement for individual years at the chestnut tree is poorer, but with large errors in the observations and the distance from the source close to the limit of model capabilities, this is expected. The model is able to simulate both the long-term mean and the annual variation in CO 2 ff tree with a reasonable degree of accuracy, and there are no significant biases apparent. Thus we can be confident that the model is representative of relative interannual variability in transport, which is the focus for the remainder of this paper.

Drivers of interannual variability in CO 2 ff
Detecting changes in emissions requires disentangling the changes in CO 2 ff due to emissions from other sources of interannual variability. We now examine the variability in our observations and turn to our model simulations to determine the relative contributions from emissions, transport, and measurement uncertainty.
The observed standard deviations of the six annual CO 2 ff values from the tree rings are 0.8 ppm (14 % of the 6-year mean) and 1.1 ppm (51 %) for the pine and chestnut trees respectively (Table 1). This includes not only variability in emissions but other sources of uncertainty such as meteorology and transport, variable 14 C assimilation rates in the trees, precision of measurements, and background corrections. Measurement uncertainty in particular is important at these relatively small concentrations. Given that the standard deviations are very close to the typical measurement uncertainty of ∼ 1 ppm, the scatter in annual means can be attributed in large part to this factor alone. For example, at the pine tree, we would expect at least four out of six measurements to be within 1ppm (one sigma) of the long-term mean, all other factors being constant. This is indeed true of four of the six observations. Measurement uncertainty is proportionally much higher in the case of the chestnut tree, which is ∼ 1 km from the Vector plant and where the average signal is only ∼ 2 ppm. At this distance, measurement uncertainty would seemingly dominate other sources of variability. In contrast, the pine tree is much closer to the source (∼ 400 m) and the signal is two to three times larger. Variations in emissions will make up a larger proportion of the total variation and are more likely to be detectable at current measurement precision.
The standard deviations of modelled CO 2 ff tree in the variable emissions, variable meteorology simulation are 0.5 ppm (7.8 %) and 0.3 ppm (15 %) at the pine and chestnut tree respectively (Table 1). Adding measurement uncertainty of 1ppm in quadrature, we would predict the standard deviations of the annual means in observed CO 2 ff to be 1.1 ppm (18 %) and 1.0 ppm (47 %) for the pine and chestnut, if variability in emissions, atmospheric transport, and measurement uncertainty explain all of the interannual variability. In comparison, the observed standard deviations of the an-Atmos. Chem. Phys., 16, 5481-5495 nual means are 14 % of the long-term mean at the pine tree and 51 % at the chestnut tree. Thus emissions, transport, and measurement uncertainty are able to explain the interannual variability in the observations within error. We can estimate the relative proportion of interannual variability that is due to atmospheric transport using the constant emissions model simulation, in which the only source of variability is meteorology. The modelled mean CO 2 ff over the six years with observations are 7.4 and 2.7 ppm for the pine and chestnut and modelled standard deviations are both 0.5 ppm (6.6 and 19 % of the respective means; Table 1). Over the full eight years of the model simulation, the means and standard deviations are 7.7/0.9 ppm (12 %) and 2.7/0.5 ppm (19 %) respectively.
Examining more general patterns of meteorological and transport variability at the Kapuni site, apart from the locations of the trees, reveals that the variation is highly dependent on the direction of the observation location relative to the source. The results at the eight hypothetical sensors averaged in each individual year and means for the entire eight years of simulation are compared in Fig. 5, and the long-term means and standard deviations are given in Table 2. The variation to the south of the plant (10-11 % of the mean) is the lowest of any direction and consistent with the variation found at the pine tree in the constant emissions simulation over the full eight years (12 %). Absolute CO 2 ff mole fractions are highest in the east (westerlies being dominant), but standard deviations are slightly higher at 14 % of the mean. Concentrations in the west are low (∼ 2 ppm) and highly variable -the result of the low percentage of easterlies in any given year (Fig. 3). Variation is relatively insensitive to the distance from the source.
It is apparent that wind direction drives a large part of the variation in transport. Annual modelled CO 2 ff at the trees in the constant emissions simulation is correlated with the annual percentage of wind in the direction ±30 • of the direct line between the source and the tree, corresponding to the plume trajectories that are most likely to pass through the tree locations ( Fig. S3; R 2 = 0.56 and 0.72 for the pine and chestnut tree respectively). The same correlation between wind direction and modelled CO 2 ff at all eight hypothetical sensors combined gives an R 2 of 0.58. Over half of the transport variability is thus explained solely by variation in the percentage of wind in each direction. However, other meteorological variables and model parameters (e.g. wind speed, temperature, pressure, etc.) still play a non-negligible role, as the annual variation in wind direction is not equivalent to the interannual variability in modelled CO 2 ff.
In the same manner, we can determine the contribution of changes in emission rates to the overall interannual variability with the constant meteorology simulation in which emissions vary but transport is the same in each year. This results in interannual variability in CO 2 ff similar to the variability in the emissions themselves, with the magnitude roughly scaled to the distance from the emission source: the standard devi- Figure 5. Constant emissions, variable meteorology simulation results for hypothetical sensors: CO 2 ff mole fraction averaged over all eight years of simulation (squares) and individual annual averages (circles). Sensors are labelled on the x axis by direction (N, E, S or W) and distance (300 or 600 m) from the source. ations are 0.5 ppm (7.4 %) and 0.2 ppm (7.6 %) for the pine and chestnut tree respectively. In comparison, the standard deviation of the average daily emissions rate over the six years with observations is 7.9 % of the mean for the Vector plant and 21 % for the Ballance plant, with a standard deviation of 8.1 % for the combined total (over the full eight years between 2004 and 2011, the standard deviations are 7.3 and 18 % of the 8-year mean for Vector and Ballance emissions respectively, and the variation in the combined emissions is 7.7 %). The variation due to emissions is thus of similar magnitude as the variability due to transport at the pine tree but is only about half of the transport variability at the chestnut tree.
Looking at all of the factors together (Table 1), variations in emissions and transport contribute about equally to total variation at the pine tree. At the chestnut tree, transport makes up a larger proportion of the total, which likely reflects the greater variability in meteorology in that particular direction. The variability in emissions somewhat counter-balances the variability in transport, particularly at the chestnut tree, where the standard deviation with both variable emissions and meteorology (0.3 ppm/15 %) is lower than that with constant emissions (0.5 ppm/19 %). This is most likely coincidental with the particular years of observations, as there is no correlation between variations in emissions and variations in transport (not shown). Meteorological variation happens to be lowest in the south, where the trees are located, even though the largest signal occurs to the east (Table 2 and Fig. 5). In this respect, the trees are fortuitously located for our study. This underscores the benefit of analysing transport variability at a particular location before collecting observations, as the quality of results can be greatly influenced by meteorological patterns. Table 2. Modelled mean CO 2 ff and standard deviation (SD) of eight hypothetical sensors simulated over the eight years 2004-2011 with constant emissions. Measurement uncertainty (MU) of 1.0 ppm is added to the standard deviation in the fourth column. Columns 5-10 show the detection limits calculated at the 2-sigma (95 %) and 1-sigma (68 %) confidence level (CL) for samples representing an average of one, two, or four years. Measurement uncertainty (MU) of 1.0 ppm is added in quadrature to the standard deviation of modelled CO 2 ff before limits are calculated.

Detection limits
Given the amount of interannual variation in meteorology and transport that we can infer from the model and typical measurement uncertainty of 1ppm, what is the minimum change in emissions that it is possible to detect in a tree ring sample taken at Kapuni, representing an integrated average of CO 2 ff over a year or more? We use a Student's t test to quantify the minimum amount of change in observations required (relative to the long-term average or reference period) that would allow us to conclude that there has been a change in emissions. The t test calculates the minimum difference between the long-term mean and a new annual tree ring sample (or samples) that would be statistically significant above scatter or noise from other factors. We make the assumption that our observations and simulated mole fractions are normally distributed. The results of the 2-sided test (representing change in either direction) at a 95 % confidence level are given in Table 3 for future samples representing one, two, and four years of integrated average CO 2 ff. All percentages are relative to the long-term mean over six years, which is our reference period for this study. We assume that the standard deviation in future samples due to interannual variability in meteorology is the same as the standard deviation over the reference period. Using the modelled means and standard deviations from the constant emissions simulation of tree ring CO 2 ff and measurement uncertainty of 1.0 ppm, the detection limits represent the minimum observed change that would indicate a driver of variability other than transport or measurement uncertainty, in this case CO 2 ff emissions. With a new observation representing one year (i.e. one tree ring), the difference between the long-term mean and the new sample would need to be more than 42 % at the pine tree and 115 % at the chestnut tree to have high confidence that the sample shows a change in emissions, rather than just natural variability or uncertainty. If we have four new annual observations at the new emission rate, the difference reduces by half to 22 and 62 % respectively. These detection thresholds are well above the reported annual changes in emission rates between 2004 and 2011 (Fig. 4). At the distance and location of the chestnut tree (∼ 1 km), it seems likely that the signal is too small and variable to be practical for detecting emission changes for a point source with emissions of this magnitude.
If we relax the condition to a 1-sigma (or 68 %) confidence level, would we be able to detect the largest change in emissions reported at the Vector plant between 2004 and 2011? The Student's t test at 68 % confidence level gives corresponding detection limits listed in Table 3. For a 1-year observation from the pine tree, this is 18 %; for the chestnut, it is 92 %. The largest change in emissions in any single year at the Vector plant is in 2007, with a decline of 14 % relative to the long-term mean, still below the detection limit. Indeed, looking at the results in Fig. 4, the decline (0.4 ppm, or 19 % of the mean) at the chestnut tree in 2007 is not significant; there is also a small decline (0.7 ppm, or 13 % of the mean) in CO 2 ff at the pine tree but it is again too small to conclude that emissions have changed. If we were able to achieve a reduction in measurement uncertainty to 0.5 ppm, however, the threshold for detection at the pine tree becomes an 11 % change in emissions, and we would expect to be able to observe a 14 % decline in emissions. In this case, the small decline in CO 2 ff at the pine tree in 2007 would be significant.
Would we be able to detect this change at a different location (in direction and/or distance) around the Kapuni plant? Our hypothetical concentration sensors 300 and 600 m from the source (Table 2) indicate that with a single 1-year CO 2 ff observation, only a change in emissions of at least 36 % would be detectable at 95 % confidence, a much larger change than occurs in our observational data set. The location of the pine tree (at 400 m south-east of the plant) appears to provide as good a detection capability as any of our Table 3. Detection limits for samples at the pine and chestnut trees, calculated with modelled CO 2 ff at constant emissions and six years of observations in reference period (2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011). Limits are given at the 2-sigma (95 %) and 1-sigma (68 %) confidence level (CL) for samples representing an average of one, two, or four years. Measurement uncertainty (MU) of 1.0 or 0.5 ppm is added in quadrature to the standard deviation of modelled CO 2 ff before limits are calculated. hypothetical sensors. However, if we have four years of observations (and the change in emissions was sustained over that time period) located either to the east or the south of the plant at a distance of 300 m, we would be able to detect a change of 10 % or more at the one-sigma confidence level. Changes of 20 % or more would be detectable at these same locations with one year of observations or alternately, four years of observations if we require high confidence. This analysis uses the actual meteorology only to determine the interannual variability in CO 2 ff that we might expect due to meteorological variations. If we also know the meteorology in the year or years of the new observations, we can quantify the change in emissions by modelling transport at constant emissions. For example, attributing 15 % of the 1-year variation at the pine tree to the combined factors of transport and measurement uncertainty (Table 1) and assuming that the rest of the variation is due to emissions translates to a change in emissions of 27 % over the one year. In this manner it is possible to get a more precise estimate of the long-term changes in emissions.
Additionally, if we have multiple measurements over the same period at different locations around the point source, measurement uncertainty reduces proportionally by 1/ √ n, where n is the number of independent measurements. The resulting reduction in detection thresholds is more complex and depends on the long-term mean and variation at each of the observation locations. One could, for example, use a paired t test to determine if the change detected in all of the measurements taken together is significant. This is beyond the scope of the current study, but the detection thresholds given in Tables 2 and 3, based on a single observation location, would overestimate the minimum change in emissions that it is possible to observe with multiple measurements designed to cover the area surrounding the point source.

Applicability to other point sources
The results presented here are specific to the meteorology and point sources at the Kapuni site, but the methodology can be extended to any point source with suitable trees growing nearby. Ideally, observations would be made as close to the source as possible in the direction where the signal is strongest and/or most consistent. If measurement uncertainty of 1ppm is to be relatively unimportant compared to the combined transport and emissions variability of 8 % at the pine tree (i.e. adding measurement uncertainty does not change the total variation in measured CO 2 ff by more than 1-2 %), we require a signal around 20-30 ppm, implying a required emission rate five times that of the Kapuni plant. Alternatively, if we were able to reduce measurement uncertainty to 0.5 ppm (for example, by increased measurement precision or taking measurements from multiple locations at the site), we would be able to detect changes with signals at around half the magnitude, and the method could be more feasible for emission sources the size of the Kapuni plant. Additionally, if we have multiple measurements from the same period at various locations surrounding the source, detection thresholds lower further and we can achieve the same sensitivity with a smaller point source.
Our case study involves point sources that are fairly small on an international scale; for comparison, the world's largest power plant, in Taiwan, emits about 300 000 g C s −1 or 9.5 Tg C yr −1 (Ummel, 2012), which is 95 times as much as the Vector plant at Kapuni. There are approximately 800 power plants worldwide that emit more than 10 times the annual total CO 2 ff at Kapuni (CARMA, 2009;Wheeler and Ummel, 2008;Ummel, 2012). The typical emission rates seen at these larger power plants would produce signals in which measurement uncertainty is only a small proportion of the total. With annual signals theoretically 10 times that observed at the Kapuni pine tree and the same amount of meteorological variation, all other things being equal, the de-5492 E. D. Keller et al.: Detecting long-term changes in point-source fossil CO 2 emissions tection threshold at the location of the pine tree would be 19 % for a 1-year measurement or 10 % with four years of measurements. This is a plausible reduction target and the method would be useful for verifying emissions changes in such cases.
The Kapuni site has several advantages that simplify the modelling component of this method: the terrain is flat and there are trees conveniently located close to the CO 2 ff sources. With larger distance scales and/or more complex terrain, WindTrax might not be an appropriate choice of model. Alternative atmospheric transport models that are applicable to larger distances (hundreds of kilometres and/or regional scales) and more complicated geographic features include CALPUFF (Scire et al., 2000), WRF-CHEM (Grell et al., 2005), and AERMOD (Cimorelli et al., 2005). While these models would need to be tested in the context of our method, the same general principles would apply.

Conclusions
We have examined sources of interannual variability in CO 2 ff in samples from tree ring archives representing integrated averages over one year. We used the atmospheric transport model WindTrax to separate variability in meteorology and transport from other sources of variation in our observations. At the location of the pine tree, modelled variation in transport is 7 % of the 6-year reference mean. This is about the same magnitude as the variation in emissions that were recorded over the same time period. At the chestnut tree, variation due to atmospheric transport is larger, at 19 % of the mean, and is about twice the magnitude of the variation in emissions. Taking into account typical measurement uncertainty of 1ppm for radiocarbon samples, in order to conclude with high confidence that there has been a change in emissions and not just natural variation in meteorology, we would require an observed change of 42 % from the mean in a new 1-year sample from the pine tree. If we take a 2-year or 4-year sample average, this reduces to 30 and 22 % respectively. This is well above the largest single-year change in emissions at the Vector plant, which is 14 %. However, if we are able to reduce measurement uncertainty by half, to 0.5 ppm, or if the point source doubles in strength, detection thresholds are closer to the actual level of variation in emissions. If we only require confidence at the one-sigma level, we would in this case be able to detect a 14 % change in a single year.
Detection limits are highly dependent on the location of the observations and specific meteorology of the site. Wind patterns should be carefully considered before deciding where to take samples in any study, preferably in an area where the signal will be strongest and where wind patterns will be most consistent through time. A model analysis such as we have performed can give an idea of the baseline variability in transport and the size of the signal needed to ob-serve changes in emissions. This makes it theoretically possible to separate the uncertainty in transport from other sources of uncertainty.
In general, this method will be most effective when observations are made in the dominant wind direction and/or in a direction with consistent winds, close enough to the point source so that natural variability in meteorological conditions and measurement uncertainty does not overwhelm the signal from the emissions. The larger the point source (the higher the emission rate) and the signal from CO 2 ff, the more able integrated averages from plant material will be to detect changes in emissions. For larger power plants or other point sources of a more typical size worldwide, detecting changes with this method could be feasible; with signals 10 times or more the size of Kapuni, measurement uncertainty is relatively insignificant and sustained changes in emissions on the order of 10 % can be detected from a single sampling location given suitable meteorological conditions and observations.

Data availability
The Mauna Loa CO 2 observation record, Hawera hourly meteorological observations, and the CARMA power plant emissions data are freely available to the public at the links and references provided.