A methodology for estimating seasonal cycles of atmospheric CO 2 resulting from terrestrial net ecosystem exchange ( NEE ) fluxes using the Transcom T 3 L 2 pulse-response functions

Abstract. We present a method for translating modeled terrestrial net ecosystem exchange (NEE) fluxes of carbon into the corresponding seasonal cycles in atmospheric CO2. The method is based on the pulse-response functions from the Transcom 3 Level 2 (T3L2) atmospheric tracer transport model (ATM) intercomparison. The new pulse-response method is considerably faster than a full forward ATM simulation, allowing CO2 seasonal cycles to be computed in seconds, rather than the days or weeks required for a forward simulation. Further, the results provide an estimate of the range of transport uncertainty across 13 different ATMs associated with the translation of surface NEE fluxes into an atmospheric signal. We evaluate the method against the results of archived forward ATM simulations from T3L2. The latter are also used to estimate the uncertainties associated with oceanic and fossil fuel influences. We present a regional breakdown at selected monitoring sites of the contribution to the atmospheric CO2 cycle from the 11 different T3L2 land regions. A test case of the pulse-response code, forced by NEE fluxes from the Community Land Model, suggests that for many terrestrial models, discrepancies between model results and observed atmospheric CO2 cycles will be large enough to clearly transcend ATM uncertainties.


Introduction
Net uptake of CO 2 on land and in the ocean has absorbed on average more than half of the total anthropogenic carbon input from fossil fuel combustion, cement manufacture and deforestation over the last 50 yr (Forster et al., 2007).Future increases in atmospheric CO 2 therefore depend not only on fossil fuel consumption but also on future CO 2 uptake by land and ocean sinks.However, predictions of these future sinks by ocean biogeochemistry and terrestrial ecosystem models vary dramatically (Friedlingstein et al., 2006).To improve confidence in projected atmospheric CO 2 levels, it is Introduction

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Full critical that the land and ocean sinks be quantified as accurately as possible using mechanistic models that have been rigorously tested against present-day metrics.
The mean seasonal cycle in atmospheric CO 2 is a logical present-day metric since the changes in land or ocean biogeochemistry expected due to anthropogenic forcing over the next century are generally small compared to changes that occur naturally over a seasonal cycle.Furthermore, the seasonal cycles in atmospheric CO 2 are well documented and reflect the integrated effects of surface carbon fluxes over large regions.The seasonal cycle in atmospheric CO 2 occurs mainly due to a seasonal imbalance between terrestrial net primary production and heterotrophic respiration known as net ecosystem exchange (NEE) (Fung et al., 1987;Keeling et al., 1996).In contrast, fossil fuel emissions are thought to have only a small seasonality (Rotty, 1987;Blasing et al., 2005) and air-sea CO 2 fluxes are strongly damped on seasonal time scales by ocean carbonate chemistry (Takahashi et al., 2002).
Use of the atmospheric CO 2 seasonal cycle to evaluate surface carbon fluxes has the drawback that atmospheric tracer transport models (ATMs) are needed to translate the surface fluxes into an atmospheric signal.Transport differences among ATMs unavoidably create uncertainty, making it difficult to distinguish whether discrepancies between modeled and observed CO 2 cycles are due to problems with the surface fluxes themselves or with atmospheric transport (Gurney et al., 2002;Baker et al. 2006;Stephens et al., 2007).Furthermore, ATM simulations driven by multiple years of surface fluxes are time consuming to set up and run.Here, we present a new methodology that allows the atmospheric seasonal cycle in CO 2 resulting from terrestrial NEE to be quickly and efficiently estimated, while providing an estimate of the range of uncertainty in the signal predicted by 13 different ATMs.

Methodology
Our method is based on the archived "pulse-response" functions from the Transcom 3 Level 2 experiment (T3L2) (Gurney et al., 2004).T3L2 was designed to examine the Introduction

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Full influence of ATM uncertainty on atmospheric CO 2 inversions, with emphasis on the mean seasonal cycle.As part of T3L2, each of 13 participating ATMs conducted forward simulations in which a pre-specified flux pattern, normalized to 1 Pg C yr −1 , was released from each of 22 regions (11 land, 11 ocean) for each of 12 "emission months," i.e.January-December.For the 11 land regions, the pre-specified spatial flux distributions were set to the annual mean Net Primary Productivity (NPP) patterns of the CASA Neutral Biosphere Model (Randerson et al., 1997).The simulations were run for 36 "measurement months," in which the pulses were turned on for the first month and shut off for the remaining 35 months, during which time the initial pulse became increasingly well mixed throughout the atmosphere.For each ATM, region, emission month and measurement month, the model atmospheric fields were sampled at each of 253 latitude/longitude/height coordinates corresponding to the locations of atmospheric monitoring sites.The resulting "pulse-response" functions, in units of ppm (Pg C yr −1 ) −1 , are footprints that represent the atmospheric signal corresponding to a unit surface pulse of CO 2 .
We used the pulse-response functions to construct a matrix H (Fig. 1, Table 1).H is similar to the matrix used in Bayesian atmospheric inversions (Baker, 1999(Baker, , 2001;;Baker et al., 2006).Here we perform a simple matrix multiplication (Eq. 1) that estimates the atmospheric CO 2 time series resulting from a set of Net Ecosystem Exchange (NEE) fluxes: where f is a vector of monthly mean NEE fluxes in Pg C yr −1 , aggregated over a given land region and c is the corresponding atmospheric CO 2 time series in ppm.As described below, f is 3 yr longer than c to account for the influence of fluxes predating the N − 3 years.N must be at least 4 to yield c of at least 1 yr, and ideally should be longer to permit easier detrending of c (we use N = 13 in this study).
The time series c can be analyzed using standard methods to derive the mean seasonal cycle in atmospheric CO 2 .Here, the raw monthly mean time series c first was detrended with a 3rd order polynomial, then a monthly mean seasonal cycle was constructed by taking the average of the detrended data for all Januaries, Februaries, etc.In principle, c can also be analyzed for interannual variability (IAV), but it will only reflect IAV due to f, rather than a combination of f and transport, since H uses an annually repeating cycle of meteorology.At each monitoring site, c is computed separately for each land flux region.The region-specific time series can either be aggregated over all regions to give the net atmospheric CO 2 signal or treated separately to estimate the contribution of each individual region to the CO 2 seasonal cycle.
To validate the results of our pulse response code, we used the forward "presubtracted tracer" simulations computed by each of the thirteen T3L2 ATMs (Gurney et al., 2004;Baker et al., 2006).These forward simulations were forced by fine-scale (0.5 × 0.5 deg) monthly mean net ecosystem exchange (NEE = heterotrophic respiration -NPP) fluxes from the CASA land biosphere model (Randerson et al., 1997).The simulations were run with the fluxes turned on for the first year and turned off for the last two years.The resulting ATM atmospheric CO 2 fields were sampled in each of the 36 months of the simulations at each of the 253 monitoring sites discussed above.The steady-state response, i.e. the mean seasonal cycle, was computed by summing all Januaries, Februaries, etc., for the three years.Conceptually, this calculation assumes that the ATM behaves linearly and that the steady-state response can be represented as the sum of the response to the fluxes from the present year, the past year, and two years previously, which correspond to the first, second, and third years of the simulations, respectively.Using the same methodology, we calculated the mean seasonal cycle due to fossil fuel and oceanic influences using the T3L2 "pre-subtracted tracer" forward simulations forced by oceanic net air-sea CO 2 fluxes and 1990 fossil fluxes (Andres et al., 1996;Takahashi et al., 1999;Gurney et al., 2004).These ocean and Introduction

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Full fossil cycles were used to "correct" the observed atmospheric CO 2 cycle, as described below.
We used our pulse-response code, forced with the same 0.5 • ×0.5 • CASA NEE fluxes used in the T3L2 forward simulations, to estimate the mean seasonal cycles at a subset of 60 of the T3L2 monitoring sites.As a validation exercise, these were compared to the mean seasonal cycle computed from the forward simulations of the NEE pre-subtracted tracer runs for each model.The comparison is presented for a single model (GCTM) at 16 selected stations (Fig. 2), while the comparisons for all 13 models, as well as the mean of all 13 models, at all 60 stations are summarized in a set of Taylor-type diagrams (Taylor, 2001) (Fig. 3).
Finally, as a test case of our model, we forced our pulse-response code with 13 yr of NEE fluxes corresponding to 1993-2005 from an online run of the Community Land Model (CLM4) with realistic transient forcing from increasing atmospheric CO 2 and nitrogen deposition (Bonan and Levis, 2010).We derived the corresponding mean seasonal cycle in atmospheric CO 2 as described above.

Results
The pulse-response code (PRC) forced with CASA NEE fluxes successfully captures the general shape and amplitude of the mean CO 2 seasonal cycle from the archived T3L2 forward simulations (FS) across a range of surface monitoring stations, spanning from the South Pole to Alert, Greenland (Fig. 2).The GCTM model is chosen to illustrate this validation exercise, but similar results are obtained for the other twelve T3L2 ATMs.As shown in the summary Taylor diagrams (Fig. 3), the PRC performs best in the Northern Hemisphere, where the correlation coefficient (polar axis) for PRC vs. FS at most stations is R = 0.95 or better, and the amplitude ratio (represented by the ratio of standard deviations: σ prc /σ fs on the radial axis) typically centers around 1. In the Southern Hemisphere, the PRC performance is generally weaker, although some models (e.g.TM2, CSU) still reproduce the FS seasonal cycles well.Introduction

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Full The pulse-response code is also useful for estimating which land regions contribute to the total NEE-driven seasonal cycle in atmospheric CO 2 at different monitoring sites (Fig. 4).Boreal Eurasia and Boreal North America both make important contributions to the seasonal cycle at Barrow, Alaska, with lesser contributions from Europe and Temperate North America.At Park Falls, Wisconsin, the contribution from Temperate North America dominates that from Boreal North America in a ∼ 2 : 1 ratio.Europe strongly dominates the seasonal cycle at Schauinsland, Germany, while many different land regions make small contributions to the cycle at Mauna Loa. Figure 4 also shows a comparison to the observed seasonal cycle from GLOBALVIEW-CO2, with and without an estimated correction for fossil and oceanic influences based on T3L2 model mean archived "pre-subtracted tracer" simulations.This comparison indicates that the CASA model matches the observed cycle reasonably well at these stations, consistent with Gurney et al. (2004).
In contrast, when NEE fluxes from the CLM4 are used as a test case for the PRC, there are clear discrepancies with GLOBALVIEW-CO2 at most stations that transcend ATM uncertainty, even though the range of that uncertainty is large (Fig. 5).At many Northern Hemisphere stations, the CLM4 seasonal cycle is too small in amplitude by about a factor of two, and, at a number of sites, reaches its minimum 1-2 months too early in the summer.

Discussion
The validation exercises shown in Figs.2-3 would only provide results from a single ATM.Thus, the PRC involves a relatively small sacrifice in accuracy in exchange for a large improvement in speed, convenience and information about ATM uncertainty.Since the same NEE fluxes were used for both the PRC and FS calculations, the differences shown in Figs. 2 and 3 reflect the impact of using approximate annual NPP spatial patterns for each month in the PRC, instead of the proper average NEE pattern across that month used in the forward runs.In addition, since the forward simulations were only run out for 2 yr after the 1-yr pulse was turned off, the later FS months were only run out for closer to 24 than 36 months, introducing a time difference in the PRC vs. FS comparison.The difference between the two curves in Fig. 2 should primarily reflect a combination of these 2 factors, assuming that the ATMs behave linearly and that regional results can be added accurately.
As discussed above, an important uncertainty in the PRC predictions is the influence of the spatio-temporal distribution of the unit flux pulse within each land region on the archived T3L2 pulse-response functions.The validation exercises presented above reflect a nearly optimal case with respect to this uncertainty, since the unit pulses in T3L2 were patterned after annual mean CASA NPP, which has a similar distribution to the CASA NEE fluxes used in the validation.As a test of the uncertainty introduced when the spatial pattern of the land fluxes to be evaluated diverges strongly from the CASA NPP distributions, we forced the PRC with the 1990 fossil fuel fluxes used in T3L2 (Andres et al., 1996).This is an extreme test in that fossil fluxes have very dissimilar spatial patterns to NPP.It also has the advantage that the results can be validated against archived T3L2 forward simulations using these same fossil fluxes.
The fossil fuel results are surprisingly good, with PRC v. FS correlations coefficients of R = 0.80 or better, and amplitude ratios falling around 1 ± 0.5.Predictably, the PRC performs best at island and remote coastal sites, where local land distributions matter least, and is weakest at sites in continental interiors, where local patterns have greater influence.This extreme test with fossil fuel inputs shows that the PRC results are indeed sensitive to the spatial pattern of the fluxes, and that continental interior sites will Introduction

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Full be the least faithfully represented by the PRC when forced with NEE fluxes that depart sharply from the CASA NPP spatial patterns.The CLM4 results (Fig. 5) are presented primarily as a test case to illustrate the benefit the PRC can provide to land modelers.A detailed assessment of the processes in the CLM4 that lead to discrepancies with observations is beyond the scope of this paper.An earlier application of the PRC code found similar large discrepancies for two other terrestrial ecosystem model NEE fluxes (one of which was an earlier version of the CLM4) (Randerson et al., 2009), suggesting that other process-based terrestrial ecosystem models also may have trouble reproducing the atmospheric CO 2 seasonal cycle.In contrast, the CASA NPP fluxes are not process-based but rather are scaled to agree with empirical satellite data, perhaps explaining why CASA NEE reproduces the observed CO 2 cycle relatively well (Randerson et al., 1997;Gurney et al., 2004).
While earlier terrestrial models focused on NPP, today's more sophisticated mechanistic models simulate the more fundamental processes of gross primary production (GPP).NEE is then the small residual of the two large and opposing fluxes of GPP and total ecosystem respiration.Since process-based models are focused on resolving the physiological processes contributing to the gross fluxes, it is perhaps not surprising that the models have difficulty simulating the NEE balance well enough to accurately reproduce the atmospheric CO 2 cycle.
We have compared PRC results mainly to observations in the Northern Hemisphere rather than the Southern Hemisphere for two principal reasons.First, in the validation exercises above, the PRC performance was weaker at southern sites.This may be due in part to the pulses only being carried out for 36 months in the PRC and for 25 to 36 months in the T3L2 forward simulations.Since Southern Hemisphere sites are far removed from major land regions, the importance of atmospheric mixing and dilution is particularly important at these sites.For some models, even a 36-month simulation may not be adequate to fully capture the smoothing of the atmospheric CO 2 gradient between hemispheres.Notably, full forward simulations with combinations of CASA NEE, ocean and fossil fuel fluxes have also resulted in generally poorer agreement with

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Full observations in the Southern Hemisphere (Randerson et al., 1997;Dargaville et al., 2002;Nevison et al., 2008), which may indicate additional problems with interhemispheric mixing in ATMs.
A second complication in comparing PRC results to observations at southern sites is that oceanic and fossil fuel influences contribute substantially to the (relatively small) CO 2 seasonal cycles in the Southern Hemisphere, making it inappropriate to compare observed CO 2 to modeled atmospheric cycles driven only by NEE influences (Randerson et al., 1997;Nevison et al., 2008).Although one can estimate and add in these contributions as we have done, the comparison of (NEE-driven) modeled and observed CO 2 is heavily influenced by uncertainties in the oceanic and fossil signals (Fig. 5c).
In the Northern Hemisphere, the CO 2 seasonal cycle is dominated by NEE, although even there the neglect of fossil fuel and oceanic influences introduces small errors.Forward ATM simulations suggest that the oceanic component of the atmospheric CO 2 accounts typically for ∼ 10 ± 10 % the magnitude of the observed cycle and tends to be out of phase with observations (Randerson et al., 1997;Nevison et al., 2008).Fossil fuel generally makes an even smaller contribution than the ocean to the overall seasonal amplitude in atmospheric CO 2 , but its importance could be underestimated (although probably only slightly) due to the lack of seasonality in prescribed fossil fluxes (Blasing et al., 2005;Nevison et al., 2008).
Based on the above discussion, we recommend to either (1) directly compare the NEE-driven cycles estimated with the PRC to observed atmospheric CO 2 seasonal cycle in the Northern Hemisphere, ignoring the fossil and oceanic contributions, or (2) estimate the fossil and oceanic influences and subtract them from observed CO 2 before comparing to the NEE-driven PRC results.Approach 2 in principle allows the PRC to be used in either hemisphere, although the relatively large uncertainty associated with Table 1.Expanded view of the structure of H (for a given ATM, region and sampling site) spanning 48 "measurement" months and 12 "emission" months (red rectangle in Fig. 1).The pulseresponse functions comprise a repeating 47-month band of measurement years, because the January pulse is released in month 1 of year 1 and allowed to decay through month 12 of year 3, while the December pulse is released in month 12 of year 1 and allowed to decay through month 11 of year 4, etc. Full Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | measurement month by up to 3 yr.In cases where only a single year of fluxes is available, a vector f spanning N flux years can be constructed, in which the cyclostationary fluxes are repeated year to year.Applying Eq. (1) then yields a time series c of length Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , which compare the results of the pulseresponse code driven by CASA NEE fluxes to archived forward simulations with the same fluxes, show that the PRC provides a reasonably faithful representation of the true FS results, especially in the Northern Hemisphere.The main advantages of the PRC are that it runs in seconds and provides an estimate of the spread of results across 13 ATMs.In contrast, a forward simulation with, e.g. a thirteen-year time series of NEE fluxes could take days to weeks, depending on the computer platform, and then Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | fossil and oceanic influences in the Southern Hemisphere undermines the usefulness of the exercise there as a test of model NEE fluxes.Discussion Paper | Discussion Paper | Discussion Paper |

Fig. 1 .Fig. 2 .Fig. 3 .Fig. 4 .Fig. 5 .Fig. 7 .
Fig. 1.Structure of H and the corresponding matrix multiplication Hf = c.H ∞ is the atmospheric signature of an infinitely well-mixed 1 Pg C pulse of atmospheric CO 2 .In this example, the input fluxes f span 10 emission years, 3 of which precede but still influence the first measurement year, but could extend over any number of years if H were expanded accordingly.