Using in situ measurements, we find a semiannual oscillation (SAO) in the midtropospheric and surface CO2. Chemistry transport models (2-D Caltech/JPL model, 3-D GEOS-Chem, and 3-D MOZART-2) are used to investigate possible sources for the SAO signal in the midtropospheric and surface CO2. From model sensitivity studies, it is revealed that the SAO signal in the midtropospheric CO2 originates mainly from surface CO2 with a small contribution from transport fields. It is also found that the source for the SAO signal in surface CO2 is mostly related to the CO2 exchange between the biosphere and the atmosphere. By comparing model CO2 with in situ CO2 measurements at the surface, we find that models are able to capture both annual and semiannual cycles well at the surface. Model simulations of the annual and semiannual cycles of CO2 in the tropical middle troposphere agree reasonably well with aircraft measurements.
 Atmospheric CO2 has a trend of ∼2 ppm/yr based on measurements from Mauna Loa covering from 1958 to 1994 [Keeling et al., 1995]. The increasing atmospheric CO2 has a significant impact on the global climate system [Dickinson and Cicerone, 1986]. Superimposed upon this trend is an annual cycle resulting from the uptake and release of CO2 by vegetation whose amplitude is greatest in the northern hemisphere (NH). Using CO2 measurements at Mauna Loa, Buermann et al.  found that variations of CO2 seasonal cycle amplitudes are closely related to carbon sequestration in the biosphere, and are influenced by precipitation and circulation. In addition to the trend and annual cycle, atmospheric CO2 also demonstrates intraseasonal and interannual variabilities.
 El Niño is the most important tropical interannual variability that can influence the CO2 concentrations. During El Niño (La Niña) events, the atmospheric CO2 growth rate increases (decreases) at tropical surface stations [Keeling et al., 1995; Jones et al., 2001; Nevison et al., 2008]. Using midtropospheric CO2 data from the Atmospheric Infrared Sounder, Jiang et al.  found that El Niño can influence the midtropospheric CO2 concentrations. Midtropospheric CO2 is enhanced in the central Pacific Ocean and diminished in the western Pacific Ocean during El Niño [Jiang et al., 2010]. In the high latitudes, midtropospheric CO2 concentration can be influenced by the strength of the polar vortex. Polar midtropospheric CO2 is reduced (enhanced) when the polar vortex is strong (weak) [Jiang et al., 2010]. Recently, Li et al.  demonstrated that midtropospheric CO2 concentrations are also modulated by the Madden-Julian oscillation.
 In this paper, we will focus on investigating the intraseasonal variability of midtropospheric CO2, especially on the CO2 semiannual oscillation (SAO) and its possible causes. This work will yield a quantitative study of how SAO influences the midtropospheric CO2. It also offers an opportunity to investigate the possible cause for the SAO signal in the midtropospheric CO2.
 To investigate the possible causes of the semiannual oscillation of midtropospheric and surface CO2, we use three different chemistry transport models. These models are the Caltech/JPL 2-D chemistry transport model (CTM) [Shia et al., 2006], 3-D GEOS-Chem [Suntharalingam et al., 2004], and 3-D MOZART-2 [Horowitz et al., 2003]. The 2-D CTM has 18 latitudes, equally spaced from pole to pole. It has 40 vertical layers, equally spaced in log scale of pressure from the surface to the upper boundary at 0.01 hPa. Transport in the model is by the stream function and the horizontal and vertical diffusivities taken from Jiang et al. . The stream function is derived from the National Center for Climate Prediction (NCEP) Reanalysis 2 data [Jiang et al., 2004]. An important feature of the 2-D CTM is its ability to reproduce the age of air in the stratosphere [Morgan et al., 2004].
 GEOS-Chem (v7.3.3) is driven by the Goddard Earth Observing System (GEOS-4) assimilated meteorological data from the NASA Global Modeling Assimilation Office (GMAO). Spatial resolution for GEOS-Chem is 2° (latitude) × 2.5° (longitude). There are 30 levels in the vertical from the surface to about 0.01 hPa (∼70 km). Advection is computed every 15 min with a flux form semi-Lagrangian method [Lin and Rood, 1996]. Moist convection is computed using the GEOS convective, entrainment, and detrainment mass fluxes described by Allen et al. [1996a, 1996b]. The physics in the GEOS-4 analysis system is adopted from the National Center for Atmospheric Research (NCAR) Community Climate Model, Version 3 (CCM3) and Whole Atmosphere Community Climate Model (WACCM) with important modifications to make it suitable for data assimilation [Bloom et al., 2005].
 MOZART-2 is driven by the meteorological inputs every 6 h from the NCEP Reanalysis 1 [Kalnay et al., 1996]. Advection is computed every 20 min with a flux form semi-Lagrangian method [Lin and Rood, 1996]. The horizontal resolution is 2.8° (latitude) × 2.8° (longitude) with 28 vertical levels extending up to approximately 40 km altitude [Horowitz et al., 2003]. MOZART-2 is built on the framework of the Model of Atmospheric Transport and Chemistry (MATCH). MATCH includes representations of advection, convective transport, boundary layer mixing, and wet and dry deposition.
 Surface emissions and vertical transport in CTMs are both crucial for CO2 simulation in the free troposphere. We will use two different boundary conditions to investigate how boundary conditions affect the midtropospheric CO2. The GLOBALVIEW-CO2 mixing ratio data [Tans et al. 1998; ESRL, 2007] are used as the lower boundary condition for the Caltech/JPL CTM, GEOS-Chem, and MOZART-2. For convenience, we refer to this hereforth as the GLOBALVIEW-CO2 boundary condition [Jiang et al., 2008]. Since the GLOBALVIEW-CO2 data are limited in space, especially over the oceans, we used the GLOBALVIEW-CO2 to rescale the monthly mean CO2 mixing ratios at the surface for the GLOBALVIEW-CO2 boundary condition. First, we use seasonal varying CO2 source and sink flux boundary condition to drive the model. We also interpolate monthly mean GLOBALVIEW-CO2 measurements to the model resolution. Then, we rescale the zonal mean CO2 mixing ratio in the boundary by the monthly mean GLOBALVIEW-CO2 measurements for each month and for each latitudinal band. The monthly mean GLOBALVIEW-CO2 flask data are close to the colocated GLOBALVIEW-CO2 boundary condition.
 We will also use prescribed CO2 sources and sinks as the boundary condition for GEOS-Chem and MOZART-2. The exchange of CO2 between the terrestrial biosphere and atmosphere is based on net primary productivity and respiration fluxes from the Carnegie-Ames-Stanford (CASA) ecosystem model [Randerson et al., 1997]. Monthly mean biospheric CO2 fluxes from 2000 to 2004 are used in the models, which includes interannual variability as that used in Feng et al. . Air-sea exchange of CO2 is taken from Takahashi et al. , which is an annual mean ocean CO2 flux. Estimates of fossil fuel emissions are from G. Marland et al. (Global, Regional, and National Fossil-Fuel CO2 Emissions, 2007, http://cdiac.ornl.gov/trends/emis/overview_2007.html), which is also an annual mean CO2 flux. Monthly mean biomass burning emissions of CO2 are based on Duncan et al. . Since there is an unbalanced CO2 budget associated with the prescribed source and sink boundary condition [Suntharalingam et al., 2003, 2004], we regress surface CO2 mixing ratio in the GEOS-Chem restart file against the GLOBALVIEW-CO2 surface flask measurements. As a result, the unbalanced CO2 budget is resolved to some degree [Jiang et al., 2008]. Discrepancies between the model CO2 simulations (driven by the same meteorological fields) with the above mentioned two boundary conditions would help identify potential issues with the surface sources and/or sinks on simulating CO2 annual and semiannual cycles.
Figure 1 presents a comparison between Matsueda's aircraft CO2 (red dots) and model CO2 mixing ratios averaged between 9 km and 13 km (solid lines) from 2000 to 2004. Figures 1a–1f show 25°S, 15°S, 5°S, 5°N, 15°N, and 25°N, respectively. Different color lines are for different model simulations. There are two GEOS-Chem model outputs. One is forced by the GLOBALVIEW-CO2 boundary condition (green line). The other is forced by the prescribed CO2 sources and sinks boundary condition (orange line). GEOS-Chem CO2 forced by the prescribed CO2 source/sink boundary condition (orange line) have higher CO2 concentrations in the summer seasons than that forced by GLOBALVIEW-CO2 boundary condition (green line). It suggests that there might be a missing sink in the prescribed CO2 source/sink boundary condition in the summer season. The purple line is CO2 from Caltech 2D model. The blue line is CO2 from MOZART2 forced by NCEP1 meteorology. The model results match the high-precision aircraft measurements of CO2 in the middle troposphere remarkably well. Seasonal cycle and trend for CO2 are simulated well by different models. The amplitude of CO2 seasonal cycle increases with latitudes, with larger seasonal cycle in the northern hemisphere compared with that in the southern hemisphere. In addition to the annual cycle, there is a 6 month signal appearing in the CO2 from both aircraft and model simulations. To investigate the 6 month signal in more detail, power spectral analysis is applied to the detrended CO2 from aircraft and model simulations. Linear trends have been removed from CO2 time series. Power spectra for the detrended CO2 are shown in Figure 2. In addition to the spectral peak at 12 months, there are 6 month signals appearing in the power spectra of Matsueda's CO2 and model CO2.
 To investigate the causes of the semiannual oscillations in the midtropospheric CO2, we first apply sensitivity studies to the 2-D Caltech/JPL chemistry and transport model. Averaged CO2 at 9–13 km forced by the GLOBALVIEW-CO2 boundary condition and NCEP2 meteorology is shown by the solid line in Figure 3. To investigate the annual cycle and semiannual cycle amplitudes in the midtropospheric CO2, we fit the data by a series of Legendre polynomials and harmonic functions [Jiang et al., 2008]. We use the sum of the first, second, and third Legendre polynomials to remove the trend from the data. The harmonic functions represent annual and semiannual cycles. Annual cycle, calculated by e cos(2πt) + f sin(2πt), is shown in Figure 3b, where e and f are the amplitudes of the annual cycle. The amplitude for the annual cycle of 2-D model CO2 at 25°N is about 2.3 ppm. The semiannual cycle, calculated by g cos(4πt) + h sin(4πt), is shown in Figure 3c, where g and h are the amplitudes of the semiannual cycle. The amplitude for the semiannual cycle of 2-D model CO2 at 25°N is about 0.8 ppm.
 In a sensitivity test, we remove the annual and semiannual oscillations from surface CO2 and use linear trends as the boundary condition at the model surface. As such, there is no semiannual cycle and annual cycle source originating from surface in this model run. This results in the reduction of the amplitude of semiannual cycle for midtropospheric CO2 to 0.09 ppm (black dotted line in Figure 3c), which is about 11% of the total amplitude of the semiannual oscillation in the midtropospheric CO2. It clearly suggests that the dominant cause of the semiannual cycle in the middle troposphere is from the surface sources. Weak semiannual and annual cycles in the midtropospheric CO2 shown by black dotted lines in Figures 3b and 3c originate from transport fields. The phase of the CO2 seasonal cycle due to the transport (black dotted line in Figure 3b) is shifted relative to that forced by the GLOBALVIEW-CO2 boundary condition and NCEP2 reanalysis meteorology field (black solid line in Figure 3b). The CO2 seasonal signal due to the transport (black dotted line in Figure 3b) is related to the strength of the vertical velocity in the 2D CTM. The vertical velocity is stronger in the summer season and weaker in the winter season. More CO2 can be lifted to the middle troposphere during the summer than in the winter season. Thus the midtropospheric CO2 (black dotted line in Figure 3b) reaches maximum value in the summer season at 25°N. Although the vertical velocity peaks in summer, the CO2 seasonal cycle (forced by the GLOBALVIEW-CO2 boundary condition and NCEP2 reanalysis meteorology field; black solid line in Figure 3b) reaches maximum in April as a result of summertime drawdown by the biosphere. In another sensitivity test, we force the model with linear CO2 trend boundary condition and climatological transport fields. Climatological transport fields are the average of the transport fields from 2000 to 2004. There is no semiannual oscillation originating from either the surface or the transport fields. As a result, the semiannual oscillation disappears in midtropospheric CO2 as shown by the black dashed line in Figure 3c.
 To further reveal how the surface annual cycle and semiannual cycle relate to the semiannual oscillation in the midtropospheric CO2, we decompose the net exchange between the biosphere and atmosphere (NEP) into the annual cycle and the semiannual cycle using the multiple regression method. Then, we use the combined CO2 linear trend and annual cycle from the NEP as the boundary condition for the model. Result from this sensitivity study is shown by the green dotted line in Figure 3. We also use combined CO2 linear trend and semiannual cycle from NEP as the boundary condition for the model, and result is shown by the red dotted line in Figure 3. As shown in Figure 3, the semiannual oscillation signal in the midtropospheric CO2 is mainly from the surface semiannual cycle instead of the surface annual cycle. From Figure 3c, we also find that the NEP is the major contribution to the SAO signal in the midtropospheric CO2 and counts about 60% of the total SAO signal. In addition to the contribution from transport and the biosphere, CO2 fluxes from biomass burning and exchange with the ocean can also contribute to the SAO signal in the middle troposphere. When we have better ocean CO2 surface emissions in the future, we can decompose the contributions to the SAO signal into different components in a future paper.
 Annual and semiannual oscillations in surface CO2 are also examined. Similar spectral analysis is applied to the GLOBALVIEW-CO2 and GEOS-Chem model CO2 at the surface. In addition to the annual cycle, semiannual oscillation signals are also present in the surface CO2 from GLOBALVIEW-CO2 and model CO2. To compare the annual cycle and semiannual cycle amplitudes in surface CO2 from observations and model results, we calculate the annual cycle amplitude ( ) and semiannual cycle amplitude ( ) for surface CO2 from GLOBALVIEW network and GEOS-Chem model output. Results are shown in Figure 4. The amplitudes for annual and semiannual cycles from GEOS-Chem CO2 are very close to those from GLOBALVIEW-CO2 at the surface. The amplitudes of annual and semiannual cycles are larger in the northern hemisphere compared with those in the southern hemisphere. The maximum amplitude for the annual cycle of surface CO2 is about ∼10 ppm. The maximum amplitude is about ∼3.5 ppm for the semiannual cycle of surface CO2. Scatterplots of the observed and model simulated amplitudes for semiannual cycle and annual cycle of surface CO2 are shown in Figure 5. As shown in Figure 5, the GEOS-Chem model seems to overestimate the semiannual oscillation amplitudes at some stations. This might relate to the relatively coarse spatial resolution in the model. The latitudinal distributions of the amplitudes for the semiannual and annual cycles are shown in Figure 6. The amplitude increases with latitude, which is consistent from both surface GLOBALVIEW-CO2 data and models. Semiannual and annual cycle amplitudes are larger in the northern hemisphere than in the southern hemisphere. This is because the semiannual and annual cycles in surface CO2 sources (e.g., the net exchange between biosphere and atmosphere) are larger in the northern hemisphere than those in the southern hemisphere.
 To investigate possible causes for the semiannual oscillation of CO2 at the surface, we examine the signals from different CO2 surface sources, which include biomass burning, fossil fuel emission, ocean, and biosphere. Fossil fuel emission contributes to the positive trend in CO2. CO2 semiannual cycle and annual cycle are mainly from exchange between the atmosphere and the biosphere. Biomass burning also contributes to the semiannual cycle of CO2. In the current model, the CO2 flux from ocean is an annual mean data. When we have better CO2 fluxes from ocean in the future, we can explore the SAO signal from the ocean in an independent paper. Gross primary production, respiration, and net ecosystem production at 30°N and 110°E, shown in Figure 7, are an example to illustrate the semiannual oscillation in CO2 source from the biosphere. Gross primary production (Figure 7a) is related to carbon uptake by plants during photosynthesis. The values are negative since CO2 is taken up by vegetation from the atmosphere. Ecosystem respiration (Figure 7b) is related to the autotrophic and heterotrophic respirations from biosphere. In the winter season, photosynthesis is largely reduced. The peak for gross primary production (Figure 7a) is relatively flat in winter. However, there are still CO2 emitted to the atmosphere by respirations from the biosphere in winter, which has a relatively sharp peak compared with the photosynthesis term. The sum of the two terms, gross primary production and ecosystem respiration, leads to the double peaks in each year in the net ecosystem production, as shown in Figure 7c. Thus, phase differences in the gross primary production (photosynthesis) and ecosystem respiration lead to the semiannual oscillation in CO2 at the surface. Surface semiannual oscillation can propagate to the middle troposphere, where it produces the semiannual oscillation in the midtropospheric CO2.
 In addition to the annual cycle, the semiannual oscillation of midtropospheric and surface CO2 is discussed in this paper by combining the in situ measurements with chemistry transport models. Chemistry and transport models, driven by different transport schemes, are used to simulate the middle tropospheric CO2. We also apply different boundary conditions to force the 3-D CTMs. The seasonal cycle and semiannual oscillation of surface CO2 are well simulated by chemistry transport model with the prescribed CO2 sources and sinks boundary condition. The semiannual oscillation is also found in the midtropospheric CO2. From the sensitivity study, we found that the semiannual oscillation in the midtropospheric CO2 originates mainly from sources at the surface. A possible reason for the semiannual oscillation of surface CO2 is the CO2 surface source due to net ecosystem production.
 We thank two anonymous reviewers and the Associate Editor for the helpful comments. X. Jiang is supported by JPL grant G99694. M. Liang is supported by NSC grant 98-2111-M-001-014-MY3 to Academia Sinica. Y. L. Yung is supported by JPL grant P765982 to the California Institute of Technology.