Assessing the regional surface influence through Backward Lagrangian Dispersion Models for aircraft CO 2 vertical profiles observations in NE Spain

In this study the differences in the measured atmospheric CO2 mixing ratio at three aircraft profiling sites in NE Spain separated by 60 km are analyzed in regard to the variability of the surface fluxes in the regional surface influence area. First, the Regional Potential Surface Influence (RPSI) for fifty-one days in 2006 is calculated to assess the vertical, horizontal and temporal extent of the surface influence for the three sites at the regional scale (104 km2) at different altitudes of the profile (600, 1200, 2500 and 4000 meters above the sea level, m a.s.l.). Second, three flights carried out in 2006 (7 February, 24 August and 29 November) following the Crown Atmospheric Sampling (CAS) design are presented to study the relation between the measured CO2 variability and the Potential Surface Influence (PSI) and RPSI concepts. At 600 and 1200 m a.s.l. the regional signal is confined up to 50 h before the measurements whereas at higher altitudes (2500 and 4000 m a.s.l.) the regional surface influence is only recovered during spring and summer months. The RPSI from sites separated by ∼60 km overlap by up to 70% of the regional surface influence at 600 and 1200 m a.s.l., while the overlap decreases to 10–40% at higher altitudes (2500 and 4000 m a.s.l.). The scale of the RPSI area is suitable to understand the differences in the measured CO2 concentration in the three vertices of the CAS, as CO2 differences are attributed to local surrounding fluxes (February) or to the variability of regional surface influence as for the August and November flights. For these two flights, Correspondence to: A. Font (afont@ic3.cat) the variability in the regional scale influences the variability measured in the local scale. The CAS sampling design for aircraft measurements appears to be a suitable method to cope with the variability of a typical grid for inversion models as measurements are intensified within the PBL and the background concentration is measured every ∼ 102 km.


Introduction
Atmospheric measurements show that the CO 2 concentration in the atmosphere is currently ∼387 ppmv; but this global average must be downscaled to understand the regional distribution of CO 2 emissions (Marquis and Tans, 2008).Improving our understanding of the carbon cycle at various spatial and temporal scales will require the integration of multiple, complementary and independent methods used by different research communities (Canadell et al., 2000;Gerbig et al., 2009).The assessment of CO 2 surface fluxes has been traditionally studied at two spatial scales: the local and the global (Lafont et al., 2002).Bottom-up approaches process local fluxes inferred for example by eddy covariance systems placed mainly on forests and/or grass lands (e.g.Baldocchi et al., 2001) which provide estimates of carbon fluxes at fine spatial scales (10 1 -10 2 km), and scale them up to the global or regional scale using oriented or diagnostic models (e.g.Papale and Valentini, 2003) or by satellite information (Running et al., 2004).Top-down approaches are based instead on atmospheric inverse transport studies and use CO 2 measurements on remote sites, inverse numerical methods and satellite data (e.g.Ciais et al., 1995;Fan et al., 1998;Bousquet A. Font et al.: Assessing the regional surface influence for CO 2 vertical profiles et al., 1999;Gurney et al., 2002Gurney et al., , 2008;;Peters et al., 2009).However, global inversions do not provide much spatial resolution nor do they have the potential to increase the current understanding of the terrestrial processes at the regional scale responsible for the future control of fluxes (Canadell et al., 2000).The CO 2 concentration over continents shows large variability resulting from surface fluxes which vary both spatially across the landscape in close relation to vegetation types and conditions (Gerbig et al., 2003a;Sarrat et al., 2007a;Choi et al., 2008); and temporally due to signal reversal of biospheric fluxes between night (respiration) and day (photosynthesis) combined with strong daily mixing within the planetary boundary layer (Gloor et al., 2001;Lafont et al., 2002;Gerbig et al., 2008;Denning et al., 2008).In addition, CO 2 variability over continents is also linked to synoptic and mesoscale changes in meteorological conditions (Sidorov et al., 2002;Shashkov et al., 2007;Ahmadov et al., 2009).The interpretation of these mixing ratios is therefore linked to the knowledge of surface fluxes around the measurement site and at a regional scale (Lin et al., 2004).
Regional fluxes are estimated by analyzing vertical profiles of concentration collected at one location from tall towers (i.e.Bakwin et al., 2003), from aircraft vertical sampling (Wofsy et al., 1988;Lloyd et al., 2001;Font et al., 2010) or by performing Lagrangian boundary layer budget campaigns (Schmitgen et al., 2004;Martins et al., 2009;Sarrat et al., 2009).The estimation of the regional surface fluxes based on a single tall tower is restrained by the influence of local fluxes (of up to 50 km distance) (Gerbig et al., 2009).Aircraft profiling characterizes the vertical distribution of the CO 2 concentration from the near surface up to the free troposphere.The further from the ground measurements are taken, the less they are influenced by local processes.Therefore, measurements obtained at higher altitude are more representative of a mean regional surface flux.
Mesoscale models have been developed in recent years to assess regional CO 2 variability that encompass the distribution of sources and sinks of carbon at this relevant scale.Inverse methods to infer regional surface fluxes are limited by the resolution of atmospheric transport models and by the availability of mixing ratios (Lin and Gerbig, 2005).However, the number of mesoscale campaigns to measure the CO 2 concentration and its variability at the regional scale has increased in the latest years (Dolman et al., 2006(Dolman et al., , 2009;;Sarrat et al., 2009;Sun et al., 2010).These campaigns are used to validate mesoscale models but uncertainties are still large (Sarrat et al., 2007b) mainly due to mesoscale flows (i.e.topography, sea-land breezes) and representation errors.Representation error is introduced by the assumption that a point observation can be represented by the mean CO 2 mixing ratio of a model grid box (Tolk et al., 2008) and is associated with the strong CO 2 horizontal gradient over the continents due to the variation of land use and topography.Previous studies have quantified the scales of variability of atmospheric CO 2 and the related representation error in coarse resolution mod-els, starting with statistical analysis of spatially distributed CO 2 aircraft data (Gerbig et al., 2003b;Lin et al., 2004), sensitivity analysis using different scales of variability of surface fluxes (Gerbig et al., 2003b) and statistical analysis of high resolution simulations of atmospheric CO 2 (van der Molen and Dolman, 2007;Corbin et al., 2008;Tolk et al., 2008).
The Crown Atmospheric Sampling (CAS, previously described in Font et al., 2008) was designed to provide a good characterization of the mean CO 2 concentration and its variability within the boundary layer in the central part of the Ebre watershed related to regional surface fluxes, as well as the characterization of the free troposphere concentration as a background value in a grid of 60 km × 60 km.In addition to vertical profiles in the vertices of a prism, horizontal transects at 600 and 1200 m a.s.l.complement the study of the spatial variability in the area.The aim of this paper is to study the vertical, horizontal and temporal extent of the regional surface influence area (10 4 km 2 ) that would have an impact on the CO 2 measurements carried out in vertical profiles using the CAS, examined through the concept of the footprint area.The footprint concept around a measurement site has been widely used to quantify from where and to what extent fluxes within the surrounding areas influence trace gas observations (Gloor et al., 2001).It is therefore a representation of the sensitivity of mixing ratios at measurement locations to upstream fluxes at prior times (Gerbig et al., 2009).It varies with height, but also with the wind direction, meteorological conditions (stability) and the magnitude of the CO 2 fluxes (Rannik et al., 2000;Aubinet et al., 2001).
The present study is organized as follows: the vertical, horizontal and temporal extent of the footprint area or the Potential Surface Influence (PSI) and the Regional Potential Surface Influence (RPSI) for a set of fifty-one days in 2006 for the three aircraft sites at four altitudes (600, 1200, 2500 and 4000 m a.s.l.) are examined in Sect.3.1, 3.2 and 3.3 respectively.The extent of the regional surface influence area and its variability between sites for the flights done on 7 February, 24 August and 29 November 2006 is discussed in Sect. 4. Abbreviations used on this manuscript are: DJF for December, January and February; MAM for March, April and May; JJA for June, July and August; and SON for September, October and November.

Aircraft surveys
The aircraft sites measuring atmospheric CO 2 concentrations belong to the Spanish network ICARO and are sampled following the Crown Aircraft Sampling (CAS) previously described in Font et al. (2008).CAS samples CO 2 mixing ratios continuously in the vertices of an approximate 60 km × 60 km × 60 km prism, integrating vertical profiles from 600 to 2500 and 4000 m a.s.l. with horizontal transects Atmos.Chem. Phys., 11, 1659-1670, 2011 www.atmos-chem-phys.net/11/1659/2011/The CAS location was chosen as being representative of intensively irrigated land in the Ebre watershed.

Potential Surface Influence (PSI) and Regional Potential Surface Influence (RPSI)
The Lagrangian Particle Dispersion Models (LPDMs) are well-suited to delineate contributions from upwind source regions (Blanchard, 1999) at different spatial scales.The calculation of the PSI in this study is derived from the FLEX-PART model.It simulates long-range and mesoscale transport, diffusion, dry and wet deposition, and radioactive decay of tracers released from point, line, area or volume sources (Stohl et al., 2005).The model parameterizes turbulence in the boundary layer and in the free troposphere by solving Langevin equations (Stohl and Thompson, 1999).LPDM backward simulations replace the traditional backward trajectory calculations as they account not only advection but also turbulence, convection and large-scale advection (Stohl et al., 2002;Seibert and Frank, 2004).FLEX-PART is driven by global model-level data from the National Oceanic and Atmospheric Administration -National Centers for Environmental Prediction -Global Forecast System (NOAA-NCEP-GFS ) with a horizontal resolution of 1 • × 1 • and 26 vertical layers and a time resolution of 3 h (analyses at 00:00, 06:00, 12:00, 18:00 UT; forecasts at 03:00, 09:00, 15:00 and 21:00 UT).Ten thousand particles are released at 12:00 UT and transported four days back in time by the resolved winds and by parameterized subgrid and convection motions.The majority of studies aiming the characterization of the source areas of CO 2 measurements are based on backtrajectories analysis of 2 days (Taubman et al., 2006), 5 days (Aalto et al., 2002;Apadaula et al., 2003) or 7 days (Lloyd et al., 2002(Lloyd et al., , 2007)).Jorba et al. (2004) chose backtrajectories of 4 days to describe the tropospheric circulation at Barcelona as they were representative enough of the longrange transport and their error remained controlled.Here, as the objective is the assessment of the regional influence on CO 2 measurements rather than the long-range transport, we have also chosen 4 days as representative of this scale.The release points are defined as small boxes round the measurement sites with dimensions 0.01 • × 0.01 • × 10 m.The size of the release box is chosen in accordance with the dimensions of the spiral drawn by the aircraft around the site (vertex of the CAS) when doing the vertical profiles.The model output (120 × 110 × 16 grids with a horizontal resolution of 0.5 • × 0.5 • ; 16 vertical levels from ground up to 3000 m above ground level (m a.g.l.); temporal resolution of 3 h) consists of a response function related to the particles residence time (R t ) in each grid.The horizontal resolution of the grid cells in the output files (0.5 • × 0.5 • ) is chosen based on the distance between two aircraft measurement sites.It is assumed that the R t in one grid cell is proportional to the source contribution to the mixing ratio at the measurement site.
The LPDM FLEXPART is used to assess the upwind source region of the three CO 2 vertical profiling sites (Linyola (LIN), Mequinensa (MEQ) and Binèfar (BIN); see Fig. 1) at four different altitudes (release altitudes at 600, 1200, 2500 and 4000 m a.s.l.) for 51 days in 2006.For each individual simulation the Potential Surface Influence (PSI) region is calculated to assess the upwind surface source region.The PSI is defined as the layer adjacent to the surface (0-300 m a.g.l.) where air masses reside before arriving at the measurement site, expressed in seconds.The thickness of the PSI is chosen as it is within the Planetary Boundary Layer (PBL) most of the time and it is high enough to allow large number of particles to be sampled (Stohl et al., 2003).Although the PBL height could be lower than 300 m a.g.l. in the region, especially in winter nights, the thickness of the PSI is a commitment threshold between the aforementioned factors.In this study, the PSI is a property function of the transport of air masses and it is independent of the intensity of surface fluxes.
A residence time threshold criteria is applied with the aim to assess the regional scale (10 4 km 2 ) of upwind surface source regions (RPSI) for the aircraft sites.Surface fluxes in the RPSI area are expected to create a detectable change www.atmos-chem-phys.net/11/1659/2011/Atmos.Chem.Phys., 11, 1659-1670, 2011 A. Font et al.: Assessing the regional surface influence for CO 2 vertical profiles in the measured CO 2 concentration at the receptor site.The RPSI concept is similar to the "catchment area" exposed in Henne et al. (2010).Taking the maximum and the minimum surface fluxes values (diurnal and 3-hourly values) from the European assimilation system CarbonTracker for 2006 (Peters et al., 2007(Peters et al., , 2009)), the time required to detect a change in the measured concentration of 1ppmv (4σ the noise of the instrument used in this study) is ∼500 s.The grid cells with R t greater than 500 s are expected to be those which potentially contribute the most to the variability at the measurements sites.
The ratio between mixing ratio and residence time in the PSI used in this study (1 ppmv/500 s = 2 × 10 −3 ppmv s −1 ) is situated in the range of values reported by Paris et al. (2010) that were obtained from direct regressions of CO 2 aircraft measurements over Siberia against residence time in the surface layer.That study reported values between 5 × 10 −5 ppmv s −1 and 5 × 10 −2 ppmv s −1 depending on the origin of air masses (local versus air masses advected from China) and the season in which the flight took place.The approach used here lies within the large range of values reported in Paris et al. (2010) found when air masses carried out the signal from areas with large surface fluxes (i.e.China).As the RPSI area for the measurements reported in this study is Europe, large ppmv s −1 ratios are also expected.
Considering this residence time threshold value and selecting those surface grid cells having a mean residence time greater than 500 s, the PSI area shrinks by 99.2% of its original value.The order of magnitude of the PSI area is the European continent (∼ 1 × 10 7 km 2 ) and the RPSI is the Ebre watershed (8.6 × 10 4 km 2 ).Therefore, the application of this residence time threshold criteria is a valid method to assess the regional surface influence of atmospheric observations.From this point, the term PSI represents the Potential Surface Influence without applying any residence time threshold and RPSI represents the surface influence area defined by the grid cells with a residence time greater or equal to 500 s.

Vertical range of the surface upwind sources for aircraft measurement sites
The residence time at different altitudes of the lower troposphere for air masses travelling to the receptor sites is studied by dividing the vertical model output in five levels: from 0 to 300 m (L1), from 301 to 800 (L2), from 801 to 1200 (L3), from 1201 to 3000 (L4), and above 3000 m a.g.l.(L5; out of the model output domain).The first layer (L1) is the same as defined by the PSI and is considered to be within the planetary boundary layer (PBL), and hence closely influenced by terrestrial or marine surface carbon fluxes.Conversely, the last two layers (L4 and L5) are considered to belong mostly to the free troposphere (FT).L2 and L3 are situated in a mid-dle zone situated either in the PBL, the Entrainment Zone (EZ) or the FT, depending on the time of the day and on the weather conditions.Figure 2a summarizes the mean percentage of the residence time of air masses in each of the five layers considered at every 3 h time step for the three aircraft sites.Air masses reside more time in L1 (PSI) as lower release points are situated at the very beginning of simulations.
For releases at 600 m a.s.l., the residence time in L1 (PSI) is ∼30% of the simulation time (3 h) at the very first time step of the model output (3 h back), decreasing to 10% at 96 h back.For releases at high altitudes, the residence time in the PSI is very short: ∼5% at 2500 m a.s.l. and less than 1.5% at 4000 m a.s.l.all along the 96 h simulation.For releases started at 4000 m a.s.l., air masses are encountered outside the output domain (L5) most of the simulation time (∼85%).Seasonally, the percentage of R t in the PSI for simulations starting at 600 m a.s.l. is higher during DJF and SON.For the first three hours of simulation, air masses remain more than 40% of the simulation time (DJF) and 35% (SON) in L1 and this value decreases to ∼20% for MAM and JJA.For simulations starting at 2500 and at 4000 m a.s.l., the percentage of R t in L1 is higher during MAM and JJA (reaching percentages of 10% and 5%, respectively) rather than DJF and SON (less than 5% and 2%, respectively).
The distribution of the percentage of R t in the PSI (L1) is related to the seasonality of atmospheric stability.During warm months, the convective boundary layer enhances intensive downward and upward motions leading to a well-mixed PBL.Convection acts as a scattering factor for particles, distributing them randomly in the PBL whereas during DJF and SON, inversions occur more often, suppressing the vertical transport near the surface and within the PBL.The vertical transfer of air masses in summer is faster than in winter more than a factor of 5 (Liu et al., 1984).During DJF and SON, the higher frequency of fronts and the uplift motions associated with them enhances the transfer of particles from lower layers up to higher ones.The transfer of particles from L5 or L4 to lower layers during warm months is associated to subsidence processes associated to anticyclonic weather.Therefore, gradients observed above the PBL might be attributed to surface fluxes over continental areas in MAM and JJA.
On average, the ground influence is almost lost at 2500 m a.s.l., confining the local, regional and elsewhere surface influence to below that altitude.CO 2 measurements at higher altitudes belong to a well-mixed latitudinal concentration not influenced by the short-term local and regional surface processes.Therefore, measurements taken at this altitude (or higher) are frequently used as boundary conditions (Gerbig et al., 2003b) even if continental-scale surface fluxes signals could be detected at high altitudes.
Those PSI grid cells having R t <500 s are attributed to the outside regional domain (horizontal scale larger than 10 4 km 2 ).If CO 2 fluxes (both regional and elsewhere) were spatially homogenous, the regional part of the PSI (that is, the RPSI) would explain ∼40% of the variability of CO 2 Vertical distribution of the percentage of the regional surface influence (10 4 km 2 ) and outside the regional domain for the CO 2 vertical profiles belonging to the Linyola's CAS.observed at the receptor; ∼30% at 1200 m a.s.l.; ∼9.5% at 2500 m a.s.l. and ∼1.5% at 4000 m a.s.l.(Fig. 2b).As expected, going up in the vertical profile, the CO 2 contribution from external sources is larger than at low levels.Measurements carried out below 2500 m a.s.l. are required for a good characterization of the surface fluxes and their spatial and temporal variability in the immediate proximity of observatories measuring atmospheric concentrations.
The fact that the RPSI influence accounts for 40% of the total variability of the entire PSI has an impact when modeling CO 2 mixing ratios: a bias in the fluxes from the RPSI area would have almost the same effect as the bias caused by the fluxes from the outside the domain.

Horizontal extent of the regional upwind sources for aircraft measurement sites
A classification of the grid cells to configure the regional surface influence area of a single atmospheric site is assessed by Principal Component Analysis (PCA).PCA, similar to eigenvector analysis or empirical orthogonal function analysis, has been used in studies to determine the spatial pattern of meteorological variables (Overland and Preisendorfer, 1982) and air pollution (Ashbaugh et al., 1984).PCA is a quantitative method that aims to reduce the number of variables describing a data set with several observations.The method generates a new set of variables or principal compo-nents (PC).Each PC is a linear combination of the original variables and all PCs are orthogonal to each other, so there is no redundant information.Here, the original variables are the set of 51 LPDM backward simulations for 2006 calculated using FLEPXART (j , from 1 to 51); the observations are the residence time (R t ) in each of the grid cells defining the RPSI (i-grid cells).The original matrix is composed by (R t ) i,j .The application of the PCA to the original data thereby classifies the grid cells that compose the RPSI for each of the three aircraft sites keeping the maximum of variability without redundant information.The first (PC1) and second principal component (PC2) combined explain 75% of the original variance of the entire data set.Furthermore, the scree plot (not shown) indicates a sharp decrease of the variance explained by the following PCs.The variability explained by PC1 varies for each site, from 44% for MEQ; to 74% for BIN.The variability explained by PC2 is approximately 15% for LIN and MEQ; and approximately 6% for BIN.
The classification of the RPSI grid cells as a function of the new variables (or PCs) is shown in Fig. 3.The unit of the color scale is minutes; negative values for PC2 indicate that a number of RPSI grid cells are incompatible with others.PC1 separates the very local grid cells from the regional ones.PC2 classifies the RPSI grid cells depending on the synoptic situations linked to the main wind directions for each site.PC2 separates those grid cells from the E weather patterns against those one from W directions for BIN and LIN; and those from NE against SW for MEQ.
Similar patterns are retrieved when checking the altitude influence when PCA was carried out for the RPSI for simulations centered at 1200 m a.s.l.However, no spatial patterns are seen when carrying out the same analysis for the RPSI at 2500 and 4000 m a.s.l. as the surface influence is scattered (as discussed in Sect.3.1).
Figure 3 represents the mean sensitivity surface area for each site.The different modes of variability classify the RPSI grid cells into local ones (PC1) or grid cells associated with a weather pattern (PC2).It presents the advantage of classifying the RPSI grid cells (local against regional; and different regional RPSI grid cells associated with some weather patterns).The PCA method highlights that there are combinations of RPSI grid cells which are disjointed in space, that is, there are impossible RPSI grid cell configurations.The classification of the RPSI grid cells enhances the contribution of CO 2 differences between sites to local or regional surface fluxes (see Sect.A classification of the RPSI grid cells is obtained from PCA: local versus regional (identified by PC1); and regional ones depending on the weather pattern (identified by PC2).

Temporal range of the regional surface influence
The mean annual residence time of air masses in the surface layer (0-300 m) are 14%, 11%, 4.3% and 1.1% of the total simulation time (96 h) for the release points centered at 600, 1200, 2500 and 4000 m a.s.l., respectively.The RPSI temporal influence is confined during the first 57 h of simulation (600 m a.s.l.) and 21 h (1200 m a.s.l.), that is, double and single diurnal cycles respectively before arriving at the measurement site.At 2500 and 4000 m a.s.l., regional influence is scarcely recovered.These results highlight that simulation times up to 50 h are enough for studies assessing the upwind surface regional influence.This result is in accordance with that reported in Gloor et al. (2001) who found that the timescale over which the imprint of surface fluxes on air masses before arriving at the Wisconsin tower was the order of 1.5 days.This finding also suggests that the choice of 4 days for the backward simulations is adequate to capture the regional surface influence of CO 2 measurements in vertical profiles in NE Spain.

Overlap of footprints and application to data
The analysis of the main RPSI for the three aircraft sites belonging to the CAS shows that all vertices have similar foot- prints (see Sect. 3.2 and Fig. 3) although some differences are visible.Such redundant surface information is important as it allows a better constraint of surface fluxes (Folini et al., 2009) as each measurement is a weighted combination of similar local and regional surface fluxes.
In order to assess the degree of similarity of the surface influence between sites, the pair-by-pair Sorensen's Quotient of Similarity (Kobayashi, 1987) for the PSI and RPSI is calculated as: where a and b are the PSI (RPSI) area for each of the compared sites, and j is the common PSI (RPSI) area shared by both.
Averaging for the three pair-by-pair comparisons, sites belonging to the same CAS share more than 90% of the PSI area at all altitudes (Table 1).With regards to the RPSI comparison, the shared information decreases to 70% at both 600 m and 1200 m; to 35% at 2500 m and to ∼10% at 4000 m a.s.l.As a whole the 30% unshared RPSI area would introduce the largest variability when comparing measurements carried out in the boundary layer at different sites.
Three aircraft campaigns carried out in 2006 in the Linyola's CAS are shown  in order to analyze the differences in the measured CO 2 concentration between the three vertices in relation to the PSI and RPSI areas of each site.Two of the three flights (February and November) are chosen as they were carried out during cold months and under similar weather conditions (anticyclonic weather).In February the anticyclonic conditions were settled a week before the campaign whereas in November the passage of a cold front occurred the previous day with the wind blowing from S Spain preceding the establishment of a high pressure center in the Iberian Peninsula.Light surface winds (less than 5 m s −1 ) and mild temperatures (6.6 • C and 12.8 • C, respectively), were registered for the February and November flight campaigns.The altitude of the PBL determined from radiosounding data at Zaragoza's airport (180 km east of Linyola within the same geographical unit located in the centre of the Ebre watershed) using the Bulk Richardson Number method (Grimsdell and Angevine, 1998;Menut et al., 1999;Eresmaa et al., 2006;Sicard et al., 2006;Morille et al., 2007) was 830 m (February) and 1250 m (November).The third campaign shown in this study took place on 24 August 2006 also under anticyclonic weather but characterized by the passage of a cold front in N Spain and the presence of relatively low pressure centres in the central part of the Iberian Peninsula forcing air masses to spin anticlockwise.Warm temperatures were registered in the Zaragoza airport at 12:00 UTC (∼ 22 • C) with northerly winds of ∼9 m s −1 .The PBL height, also determined from the radiosounding data in Zaragoza by the Bulk Richardson Number method, was 1490 m.
The vertical distribution of CO 2 concentrations for the flight in February (Fig. 4a) showed high concentrations at the 600 m level (mean concentration of 397.5 ppmv), and lower concentrations at 1200 m (385.7 ppmv) and 2100 m (383.4 ppmv).The spatial variability of the CO 2 concentration (expressed in terms of one standard deviation) was larger at 600 m (±2.0 ppmv) than at 1200 m and 2200 m (±0.7 ppmv and ±0.2 ppmv respectively).
Similar vertical distribution was observed during the November flight (Fig. 5a): high CO 2 values were recorded at the 600 m level (399.2 ppmv) while values decreased in altitude (385.0 ppmv at 1200 m and 385.6 ppmv at 2100 m).The spatial variability was also larger in the lowest sampled levels (±4.7 ppmv at 600 m and ±1.6 ppmv at 1200 m) whereas the dispersion at 2200 m was lower (±0.6 ppmv).
For the campaign in August, the mean concentration at 600 m was 377.6 ppmv; 378.6 ppmv at 1200 m and 379.7 ppmv at 2200 m.The variability of measurements was similar at the first two levels (±1.3 ppmv) whereas it was ±0.5 ppmv at the highest.The vertical distribution of CO 2 responds to the fact that the signal of the surface fluxes is vertically confined within the PBL.This is also shown by the total residence time in the PSI at different altitudes of the profile.At 600 m a.s.l., the total residence time in the PSI was 18.1 h (February), 12.1 h (August) and 19.8 h (November) whereas at 2200 m a.s.l., it was 0 h (February), 7.9 h (August) and 2.7 h (November).In winter, anthropogenic emissions and respiration fluxes from terrestrial ecosystems caused large CO 2 concentrations near the surface, thus higher concentrations were recorded within  the PBL compared to those above it.Conversely, larger concentrations were measured above the PBL in summer due to photosynthetic uptake CO 2 from the PBL.The spatial variability was larger in the levels within the PBL as concentrations were more influenced by the variability of local and regional surface fluxes (and also by local turbulent processes, convection and updrafts), than concentrations measured above it.The RPSI was null at 2200 m a.s.l. for the February and November flights, and reduced to 11.6% for the August flight.Conversely, the RPSI at 600 m a.s.l. was 35% (February), 25.8% (August) and 78.0%(November) of the total residence time in the PSI.
The horizontal distribution of the CO 2 mixing ratios at 600 m was different for the three flights.Large CO 2 concentrations (up to 400 ppmv) were detected in the E and NE part of the CAS during the February flight (Fig. 4a) whereas the largest CO 2 concentrations were measured in the N part of the CAS during the November flight, with values up to 410 ppmv (Fig. 5a).For the August flight, the largest CO 2 In order to explain the CO 2 differences observed in the CAS for three campaigns, the PSI (and RPSI) for the three vertices of the CAS are calculated.The PSI (RPSI) areas for the three vertices of the Linyola's CAS for 7 February 2006, 12:00 UTC at 600 m a.s.l. are displayed in Fig. 4b  and c.Even though the three vertices shared 91% of the overall PSI (Fig. 4b), each site had different regional information (RPSI shared area was ∼11%).Air masses contained a northerly component but they crossed the Pyrenees by separate transversal valleys before arriving at each measurement site.Air masses arriving at LIN crossed the Pallaresa valley while those arriving at MEQ crossed the Pyrenees by a more westerly valley, gathering the influence from the upper Ebre watershed.Conversely, BIN showed a very local RPSI influence.The mean RPSI Q/S index value was 11%, the highest being the LIN-BIN comparison (14%) and the lowest, LIN-MEQ (6%).The CO 2 difference measured at LIN was higher by 0.73 ppmv relative to MEQ; and only 0.05 ppmv lower than BIN.Given that the PSI areas were similar between the three sites and the RPSI regions were located in the Pyrenees (where small CO 2 surface fluxes are expected at that time of the year), the large CO 2 concentrations measured at 600 m a.s.l. are attributed to more local CO 2 fluxes that the meteorological model cannot resolve.
Conversely, for the campaign carried out on the 29 2006, sites separated by 60 km shared about 98% (65%) of the PSI (RPSI) area.The PSI area was located in the Iberian Peninsula and the Atlantic Ocean but the RPSI was the central part of the Iberian Peninsula and SW of the Ebre watershed.Despite the large PSI and RPSI similarity index values between vertices, the large surface fluxes caused measured CO 2 differences in the unshared RPSI area belonging to the central part of the Iberian Peninsula containing big cities and industrial areas around the Madrid region.The variability of the surface fluxes at the regional scale (10 4 km 2 ) influenced the measured CO 2 variability in the lower scale (10 2 km 2 ).
For the August flight, the PSI area of BIN was the Atlantic Ocean and W-SW of the Iberian Peninsula whereas the southern sites of the CAS (LIN and MEQ) also had influence from the Mediterranean Sea.Looking at the RPSI area, BIN and MEQ were mostly influenced by the central part of the Ebre watershed up to the Cantabria range in the north; and LIN the influence of the Meseta area.The large CO 2 concentrations at LIN compared to MEQ (3.4 ppmv higher) and BIN (5.6 ppmv higher) might be due to the influence from the Meseta region as the western sites of the CAS didn't gather.The smallest CO 2 difference between vertices was between MEQ and BIN (2.2 ppmv), related to the largest RPSI coincidence value (28.7%), rather than that between MEQ and LIN (3.4 ppmv) which exhibited the largest PSI coincidence (92%) but the lowest RPSI Q/S index value (21%).

Conclusions
The Potential Surface Influence (PSI) for three sites in NE Spain within the Linyola's Crown Atmospheric Sampling (CAS), separated by 60 km, at four different altitudes (600, 1200, 2500 and 4000 m a.s.l.) for 51 days in 2006, are examined in order analyze the horizontal, vertical and temporal extent of the regional potential surface influence (RPSI) for atmospheric CO 2 mixing ratios to explain measured variability.The application of a residence time threshold criteria in the PSI delimitate the regional surface influence (10 4 km 2 ) of atmospheric observations and improves the interpretation of the measured differences.The main regional footprint area for these three sites at 600 and 1200 m a.s.l.assures a good spatial coverage of the main land uses in the central part of the Ebre watershed.
Intensive sampling within the boundary layer is needed to cope with spatial CO 2 variability in relation to different land use coverage and vegetation conditions at the regional scale.The measurements carried out on low levels of vertical profiles contain most of the regional CO 2 surface flux signal whilst at high altitudes (2500 m and 4000 m a.s.l.) the regional surface influence is almost reduced to zero.CO 2 mixing ratios above the PBL adhere to a well-mixed latitudinal concentration not influenced by the short-term (hourly to diurnal) regional surface fluxes.Therefore, a single measurement point at 4000 m a.s.l.every 10 2 -10 3 km is enough to capture the free troposphere or background CO 2 concentration needed to quantify the enhancements due to regionalscale surface emissions (Folini et al., 2009).
Approximately 40% of the surface influence for measurements done 2200 m a.s.l. is confined in the 10 4 km 2 regional scale up to ∼50 h before the sampling.Measurements within the PBL are influenced by two complete diurnal cycles of terrestrial fluxes in the regional field (photosynthesis/respiration diurnal cycle) and by the boundary layer diurnal evolution.
The differences in the measured CO 2 concentration between vertices of the CAS could be assessed by differences on the RPSI area.Although sites that are separated by 60 km are sensible to similar surface fluxes (PSI Sorensen's Quotient Similarity index reach values up to 90%) differences in the CO 2 concentration appeared attributable to differences in the unshared RPSI regions.Dissimilant, in the measured CO 2 concentration between the vertices of the CAS are due to very local surface fluxes (as in the February flight) or due to the variability of the RPSI area with large surface fluxes (as in the November and August flights).
The dominance of the surrounding field contributions over daytime mixing ratios of CO 2 has an impact on inversion studies as a small bias in the assumed flux in the near field can bring a large bias in the modelled mixing ratio when only one measurement site is considered (Gerbig et al., 2009).A compensatory effect arises when using multiple sites in a network: a local bias in fluxes at one measurement location represents a small bias for another measurement site some distance away.A dense network of tower and aircraft observations with overlapping footprints in both surface area and vegetation class are needed to provide reliable regional CO 2 budgets.Overlapping coincidences within a network of measurement sites (as presented in this study) represent independent observations containing the same CO 2 regional surface flux information.The vertices of the CAS at 600 and 1200 m a.s.l.show an average overlapping value of 90% for the PSI and 70% for the RPSI.This configuration will increase the ability to assess the CO 2 regional carbon budget in NE Spain.The CAS design also brings information of the representation error in inversion models as it handles with the variability of a typical grid cell.The representation error could reach values of ∼5 ppmv as shown in the November flight at 600 m a.s.l.

Fig. 2 .
Fig. 2. (a)Temporal distribution of the percentage of Residence Time (R t ) at each 3 h time step at different layers of the low troposphere (0-300 or L1, 301-800 or L2, 801-1200 or L3, 1201-3000 or L4 and above 3000 m a.g.l., L5) for simulations started at 600, 1200, 2500 and 4000 m a.s.l.(b) Vertical distribution of the percentage of the regional surface influence (10 4 km 2 ) and outside the regional domain for the CO 2 vertical profiles belonging to the Linyola's CAS.

Fig. 3 .
Fig. 3. Maps resulting from Principal Component Analysis (PCA) applied to an original matrix composed by the residence time in the RPSI grid cells (observations) for 51 backward simulations for 2006 (variables) for each of the three sites belonging to the Linyola's CAS.The classification of the RPSI grid cells as a function of the new variables (PC1 and PC2) is shown, expressed in minutes.Negative values in PC2 values indicate that a number of RPSI grid cells are incompatible with others.A classification of the RPSI grid cells is obtained from PCA: local versus regional (identified by PC1); and regional ones depending on the weather pattern (identified by PC2).

Fig. 4 .
Fig. 4. (a) CO 2 mixing ratios measured during the flight on 7 February 2006 superimposed to the topography of the region extracted from GTOPO30 global digital elevation model (DEM) from the US Geological Survey's EROS Data Center in Sioux Falls, South Dakota (http://edc.usgs.gov/).(b) Pair-by-pair qualitative differences of the Potential Surface Influence (PSI) between LIN, MEQ and BIN for the simulation started at 7 February 2006 12:00:00 UTC.(c) Pair-by-pair qualitative differences of the Regional Potential Surface Influence (RPSI) between LIN, MEQ and BIN for the simulation started at 7 February 2006, 12:00:00 UTC.

Table 1 .
Annual and seasonal average (±1 standard deviation) of the Sorensen's Quotient of Similarity (Q/S) for the PSI and the RPSI areas for the three sites belonging to the Linyola's CAS for the set of 51 simulations for 2006.