We present a methodology for deriving emissions of volatile organic compounds (VOC) using space-based column observations of formaldehyde (HCHO) and apply it to data from the Global Ozone Monitoring Experiment (GOME) satellite instrument over North America during July 1996. The HCHO column is related to local VOC emissions, with a spatial smearing that increases with the VOC lifetime. Isoprene is the dominant HCHO precursor over North America in summer, and its lifetime (≃1 hour) is sufficiently short that the smearing can be neglected. We use the Goddard Earth Observing System global 3-D model of tropospheric chemistry (GEOS-CHEM) to derive the relationship between isoprene emissions and HCHO columns over North America and use these relationships to convert the GOME HCHO columns to isoprene emissions. We also use the GEOS-CHEM model as an intermediary to validate the GOME HCHO column measurements by comparison with in situ observations. The GEOS-CHEM model including the Global Emissions Inventory Activity (GEIA) isoprene emission inventory provides a good simulation of both the GOME data (r2 = 0.69, n = 756, bias = +11%) and the in situ summertime HCHO measurements over North America (r2 = 0.47, n = 10, bias = −3%). The GOME observations show high values over regions of known high isoprene emissions and a day-to-day variability that is consistent with the temperature dependence of isoprene emission. Isoprene emissions inferred from the GOME data are 20% less than GEIA on average over North America and twice those from the U.S. EPA Biogenic Emissions Inventory System (BEIS2) inventory. The GOME isoprene inventory when implemented in the GEOS-CHEM model provides a better simulation of the HCHO in situ measurements than either GEIA or BEIS2 (r2 = 0.71, n = 10, bias = −10%).
 Formaldehyde (HCHO) columns measured from space by the Global Ozone Monitoring Experiment (GOME) have been reported by Chance et al.  and Palmer et al. . As pointed out by Palmer et al. , these observations provide a proxy for mapping emissions of volatile organic compounds (VOCs) which are critical for understanding radical chemistry in the troposphere. For this purpose it is essential to (1) evaluate the accuracy of the GOME observations of HCHO columns by comparison with in situ observations and (2) derive the relationship between HCHO columns and VOC emissions. We address here these issues and go on to derive an isoprene emission inventory for North America which we compare to previous estimates from the Global Emissions Inventory Activity (GEIA) [Guenther et al., 1995] and from the second version of the Biogenic Emissions Inventory System (BEIS2) [Pierce et al., 1998].
 HCHO is produced in the atmosphere by VOC oxidation. Oxidation of methane (CH4) provides a global background. In continental boundary layers, oxidation of short-lived VOCs dominates over the source from CH4 and results in a major enhancement of the total HCHO column. Anthropogenic sources of VOCs are important in urban environments but biogenic sources usually dominate elsewhere, at least during the growing season. The most important biogenic VOC is isoprene (CH2=CH-C(CH3)=CH2), which has a lifetime of less than an hour against atmospheric oxidation and produces HCHO with a high yield [Sprengnether et al., 2002].
 The atmospheric lifetime of HCHO, determined by losses from photolysis and reaction with the hydroxyl radical (OH), is of the order of a few hours. Correlation of the HCHO column distribution measured by GOME with the emission field of the parent VOCs thus depends on the VOC lifetime, on the HCHO yield from VOC oxidation, and on the HCHO lifetime. Non-zero lifetimes for both the parent VOCs and for HCHO result in smearing and displacement of the correlation, as discussed below.
 GOME is a nadir-viewing UV/Vis solar backscatter instrument aboard the European Remote-Sensing-2 satellite, launched in 1995 [Burrows et al., 1999]. The satellite is in a Sun-synchronous orbit, crossing the equator at about 10:30 local solar time (LT) in the descending node. Spectra are collected for three forward scans of the Earth: east, center, and west, each with a pixel size (“footprint”) of 40 × 320 km2. Full mapping of the globe is achieved in 3 days. The backscattered spectra include a major HCHO absorption region (337–356 nm), whose features have been fitted to reference spectra to retrieve slant columns [Chance et al., 2000]. The slant columns have been converted to vertical columns with an air mass factor (AMF) formulation, constrained for the Rayleigh scattering atmosphere with information on the local shape of the HCHO vertical profile from the Goddard Earth Observing System global 3-D model of tropospheric chemistry (GEOS-CHEM) driven by assimilated meteorological observations [Palmer et al., 2001]. In continental atmospheres most of the HCHO column is in the boundary layer [Palmer et al., 2001].
 The GOME HCHO columns over North America in summer show a regional maximum over the southeastern United States, consistent with a major source from oxidation of isoprene [Lee et al., 1995]. Comparison of the GOME and GEOS-CHEM HCHO columns shows a high degree of correlation (r = 0.77) with a small positive bias in the model (≃10%).
 An important component of this paper is to assess the accuracy of the GOME HCHO column data. No specific validation experiments have been conducted for that purpose. In situ HCHO measurements from the ground, and, to a lesser extent, from aircraft are available but not coincident with GOME overpasses. We will use here the GEOS-CHEM model as an intermediary for testing the consistency between the in situ and satellite observations over North America in summer, where a large database of in situ measurements is available (Table 1).
Table 1. In Situ HCHO Measurements Between June and September Over North Americaa
Section 2 of this paper describes the theoretical basis for relating HCHO columns to VOC emissions and presents the transfer functions between the two from the GEOS-CHEM model. Section 3 assesses the validity of the GOME data by comparison with in situ observations, and section 4 derives the isoprene emission inventory constructed from the GOME data. Conclusions are in section 5.
2. Deriving VOC Emissions From HCHO Column Measurements
2.1. Production of HCHO From Atmospheric Oxidation of VOCs
 VOCs emitted to the atmosphere are oxidized photochemically by a succession of steps leading eventually to CO2 and H2O. HCHO is a high-yield intermediate of this oxidation chain. Laboratory chamber data are available for the HCHO yield from oxidation of many VOCs in atmospheres with high concentrations of nitrogen oxides (NOx = NO + NO2). In the general case of the oxidation of a hydrocarbon (RH) by OH, the organic peroxy radical (RO2) produced in the first stage of oxidation reacts with NO, producing HCHO or higher carbonyls that subsequently react to eventually yield HCHO [Atkinson, 1994]. In this manner one obtains ultimate HCHO yields per unit carbon of 1 for CH4 and typically 0.3–1 for C2–C6 VOCs [Altshuller, 1991]. Yields less than unity reflect mainly the formation of peroxyacyl radicals RC(O)OO for which further reaction with NO, followed by cleavage, converts the α carbon to CO2. The HCHO yield per unit carbon from the first stage of isoprene oxidation has been measured in several laboratory studies and found to be in the range 0.11–0.13 [Sprengnether et al., 2002]. Subsequent oxidation of short-lived isoprene oxidation intermediates results in an ultimate yield of about 0.4 per unit carbon from isoprene oxidation (Figure 1). For larger VOCs, including in particular terpenes, HCHO yields are expected to be lower due to formation of organic aerosols from low-volatility oxidation intermediates [Kamens et al., 1982; Hatakeyama et al., 1991; Orlando et al., 2000].
Table 2 lists summertime emission estimates E and HCHO oxidation yields Y for oxidation by OH under high NOx conditions of major VOCs emitted in North America. High NOx conditions, defined here by dominance of reaction with NO as a sink for RO2 radicals, typically require NOx concentrations in excess of a few hundred pptv; such conditions are typical of much of the United States but the complications associated with low NOx conditions will be discussed below. Unless otherwise indicated, the emissions are from the GEOS-CHEM model (Appendix A) and the yields are from the GEOS-CHEM chemical mechanism [Horowitz et al., 1998]. The yields are, in general, close or identical to the values given by Altshuller . The HCHO yield from oxidation of isoprene in the GEOS-CHEM mechanism is based largely on the study of Paulson and Seinfeld . The calculation of HCHO yields in Table 2 sums the contributions from successive stages of VOC oxidation until intermediates with lifetimes in excess of a few days are produced, because further HCHO production is not collocated with the loss of the parent VOC and therefore cannot be readily related to VOC emissions. This explains the low HCHO yield in Table 2 from oxidation of propane and methylbutenol (MBO), for which acetone (lifetime of weeks) represents the dominant first-stage oxidation product. Note also in Table 2 the low HCHO yields from pinenes due to formation of organic aerosol products [Griffin et al., 1999]. Although these compounds make an important contribution to biogenic VOC emissions, they make little contribution to HCHO columns.
Table 2. Emission of VOCs and Production of HCHO Over North America in Summer
Emissions are for the North American domain (10°–70°N, 60°–130°W). Values are from the GEOS-CHEM model for July 1996, unless otherwise stated.
VOC lifetimes against oxidation under midmorning summer conditions, assuming [OH] = 5 × 106 mol cm−3, [O3] = 40 ppb, and a temperature of 298 K. Oxidation by O3 contributes 25% of the total sink for α-pinene, 8% for propene, and less than 5% for the other VOCs in the table.
Yield from oxidation of VOC by OH under high NOx conditions (see text), calculated from the GEOS-CHEM chemical mechanism [Horowitz et al., 1998], unless otherwise stated. Ozonolysis represents a minor sink for the pinenes during the daytime [Atkinson, 1994] and the associated HCHO yield is expected to be very low [Orlando et al., 2000].
Relative contribution from the VOC to the total HCHO production from North American emissions as determined by YiEi/ΣjYjEj where the sum is over all emitted VOCs.
Alvarado et al.  report molar yields of 0.29 HCHO, 0.19 (CH3)C(OH)CHO, 0.61 CH2(OH)CHO, 0.58 acetone, and 0.05 organic nitrate in the first stage of methylbutenol oxidation by OH under high NOx conditions. Subsequent photolysis and oxidation of (CH3)C(OH)CHO and CH2(OH)CHO in our mechanism under high NOx conditions produce HCHO with molar yields of 0.25 and 0.50, respectively, resulting in an overall HCHO yield of 0.13 per atom C from the oxidation of MBO.
 The product YE measures the column production of HCHO from a given VOC. From Table 2, we see that this production from North America emissions in summer is largely dominated by isoprene, methane, and methanol. Methane is well mixed in the atmosphere because of its long lifetime and defines the HCHO background. Methanol has a lifetime of several days so that the resulting HCHO production is highly dispersed. Isoprene has a lifetime of the order of an hour and a large regional variability in emission [Guenther et al., 1995], so that we expect the variability of HCHO columns over North America in summer to reflect that of isoprene emissions. We elaborate on this point in section 2.2.
 One complication in quantifying the yield of HCHO from VOC oxidation is the fate of the RO2 radicals under low NOx conditions. Reaction of RO2 with HO2 can then compete with reaction of RO2 with NO and form organic hydroperoxides (ROOH). The main sinks for the simple alkylhydroperoxides are photolysis and reaction with OH on a timescale of hours to days, leading to carbonyl generation with no loss of carbon and not affecting the ultimate HCHO yield [Lurmann et al., 1986]. However, peroxides produced from the oxidation of isoprene by OH have a β-hydroxy group that may increase their solubility in water by several orders of magnitude [Betterton, 1992]. Scavenging of these peroxides from the atmosphere would greatly reduce the ultimate HCHO yield from isoprene oxidation under low NOx conditions (Figure 1) and also represent a major sink for HOx radicals [Horowitz et al., 1998]. A recent analysis of the HOx radical budget at an eastern U.S. site in summer indicates that the organic peroxides produced from isoprene oxidation do not represent major sinks of HOx [Thornton et al., 2002]. We therefore assume (following the study of Lurmann et al. ) that these peroxides photolyze and react with OH on a timescale similar to the alkylhydroperoxides, recycling the carbon. In that case, the HCHO yield from isoprene oxidation does not vary much with the NOx concentration or other variables (Figure 1).
 As shown in Figure 1, the ultimate HCHO yield per unit carbon from isoprene oxidation, determined in a photochemical steady-state calculation with the GEOS-CHEM model mechanism, is 0.3–0.45. Results from a time-dependent calculation with the same mechanism (Figure 2) provide insight into how the HCHO yield from isoprene oxidation increases with time. At high NOx concentrations (1 ppb), 90% of the ultimate HCHO yield (0.43 per C) is reached within the first 2 hours. At the low NOx concentrations (0.1 ppb) only 55% of the ultimate HCHO yield (0.29 per C) is reached in the same time period because of the formation of the peroxide reservoir; 2 days are required to reach 90% of the ultimate HCHO yield. Thus, we may expect a better correlation of HCHO columns with isoprene emissions in the high-NOx than in the low-NOx regime. This is further discussed in section 2.3 in the context of GEOS-CHEM model results.
2.2. Relating HCHO Columns to VOC Emissions
 Consider an atmospheric HCHO column Ω (molecules cm−2) produced from the oxidation of an ensemble of VOCs (VOCi, i = 1, …, n) with emission fluxes Ei (atoms C cm−2 s−1) and HCHO yields Yi per C atom. Let kHCHO (s−1) represent the loss rate constant for HCHO in the column from oxidation and photolysis. In the absence of horizontal transport, Ω at steady state would be given by
so that measurement of Ω would provide a proxy for the sum of local VOC emissions weighted by the HCHO yield. Horizontal transport displaces and smears this signal. Consider an air column (for all practical purposes the boundary layer) with mean column wind speed U in which a puff of VOCi with loss rate constant ki is injected at a certain location. Let us assume that HCHO is produced in the first stage of oxidation or quickly thereafter (i.e., from short-lived intermediates) so that we can write
 By solving the mass balance equations for VOCi and HCHO in the air column one finds that the maximum in the HCHO column produced from the VOCi emission puff is located downwind from the point of emission at a displacement length scale Ld,i given by
 One can further define a smearing length scale Ls,i as the distance where the integral of Ω downwind of the point of emission, ∫0Ls,iΩdx, reaches a fraction (1 − 1/e) of its asymptotic value ∫0∞Ωdx = [VOC]0/kHCHO, where [VOC]0 is the initial VOC column concentration at the point of emission. From solution to the mass balance equations one finds that Ls,i is the solution of the transcendental equation
with limiting values Ls,i → U/ki when ki ≪ kHCHO, and Ls,i → U/kHCHO when kHCHO ≪ ki.
 For isoprene, a typical lifetime against oxidation by OH in late morning is 0.5 hour, i.e., ki = 2 h−1. Further assuming typical values kHCHO = 0.5 h−1 and U = 20 km h−1 we obtain Ld,i = 20 km and Ls,i = 50 km. For methane (lifetime of several years) and methanol (lifetime of several days), Ls,i values are sufficiently large that there is no spatial resolution to the HCHO signal. We conclude that the HCHO column seen by GOME over North America in summer should map isoprene emissions with a spatial resolution of the order of 10–100 km. This resolution is comparable to the size of the GOME pixel (320 × 40 km2) so that for practical purposes we can view variability in the HCHO columns observed by GOME as reflecting local isoprene emission. In an alternate situation where VOCs with lifetimes of days made a major contribution to HCHO columns, as would be expected for example in winter, then the smearing length scale would be of the order of 1000 km. Relating the observed HCHO columns to VOC emissions would then require a complicated inversion.
2.3. 3-D Model Analysis
 The above ideas, including in particular the relationship between measured HCHO column and local isoprene emission, can be tested using the GEOS-CHEM global 3-D model of tropospheric chemistry (Appendix A). A general description of the model is given by Bey et al. , and specific applications to O3–NOx–VOC chemistry over North America in summertime are given by Palmer et al. , Fiore et al. , and Li et al. . This model includes emissions from anthropogenic alkanes, anthropogenic and biogenic alkenes, acetone, and isoprene (Table 2). Isoprene emission in our standard simulation is from the GEIA inventory [Guenther et al., 1995] but we will also show results from a sensitivity simulation using the BEIS2 inventory [Pierce et al., 1998]. The horizontal resolution is 2° × 2.5° (≃200 km), so that mesoscale displacement and smearing of the HCHO column resulting from isoprene emission are not resolved, as is the case also for GOME.
 We plot in Figure 3 the GEOS-CHEM relationship between HCHO columns and local isoprene emission in late morning (10–12 LT) for grid squares sampled along the GOME orbit tracks over the United States during July 1996. A strong linear relationship is found in the ensemble of data, confirming the dominance of isoprene over other model VOCs as source of HCHO and also confirming that Ld,i and Ls,i for isoprene are indeed small relative to the 2° × 2.5° resolution of the model. Also shown in Figure 3 are the contributions to the HCHO columns from sources other than isoprene, as determined from a simulation without isoprene emissions. We see that other VOCs make little contribution to HCHO enhancements over North America in the model and do not alias significantly the correlation of HCHO columns with isoprene emissions.
 It follows from the above arguments that the slope of the linear relationship between HCHO column and isoprene emission in Figure 3 should roughly equal Y/kHCHO (from (1)), where Y is the HCHO yield from isoprene oxidation. Mean values of the mean HCHO column lifetime (1/kHCHO) for each North American quadrant at 10–12 LT, as calculated in GEOS-CHEM, are given in Table 3. The values for the slopes imply HCHO yields in the range 0.24–0.39 (Table 3) from the oxidation of isoprene in the model, consistent with the values derived from the chemical mechanism (Table 2 and Figure 1), and confirming the robustness of the overall approach. The apparent low yield computed for the SW is due to the effect of smearing in a highly heterogeneous isoprene emission field. The definition of SW and SE quadrants dissects a region of relatively low isoprene emission (SW) and an extremely active isoprene emitting region (SE) (see Figure 4). The related manifestation of this smearing is apparent in the SE quadrant, as an occasional enhancement of the HCHO column over areas without isoprene emissions. In section 4, we will use the model slopes of Figure 3 as a transfer function to convert the HCHO columns observed by GOME into isoprene emission fluxes.
Table 3. HCHO Lifetimes and Yields From Isoprene Oxidation Over North America During Summer as Calculated From the Data Shown in Figure 3
Values are GEOS-CHEM model results sampled along GOME orbit tracks for North America (25°–60°N, 65°–130°W) at 10–12 LT in July 1996, partitioned by quadrants with latitudinal and longitudinal divides at 40°N and 100°W.
Slope, intercept, and coefficient of correlation r2 of the linear regression for the HCHO column versus isoprene emission relationships in Figure 3.
Apparent HCHO yield Y from isoprene oxidation in the model as determined from Y = SkHCHO, where S is the slope of the HCHO column versus isoprene emission relationship and kHCHO is the inverse of the mean HCHO column lifetime.
3. Consistency Between GOME and In Situ HCHO Observations
3.1. Updated GOME HCHO Column Data
 Since the works of Chance et al.  and Palmer et al.  we have improved several aspects of the retrieval of GOME HCHO vertical columns from the fitted slant columns. In particular, we have included AMF sensitivity to aerosol extinction by using local aerosol optical depths (AOD) from the GEOS-CHEM model [Fiore et al., 2002]. The AODs at 340 nm over the United States are typically in the range 0.1–1, and are assumed to be uniformly distributed over the depth of the local boundary layer. A single scattering albedo of 0.96 [Dickerson et al., 1997] is assumed. Palmer et al.  previously found that increasing the AOD of scattering aerosols from 0.1 to 1.0 (representing a typical AOD range at 340 nm over North America during summertime) increased the GOME sensitivity to the HCHO column by approximately 30% relative to an aerosol-free atmosphere.
 Clouds mask boundary layer HCHO from the GOME instrument, introducing a negative bias in the retrieval if not accounted for [Martin et al., 2002]. The GOME footprint (40 × 320 km2) is rarely cloud free. Palmer et al.  used cloud fraction information for each GOME scene from the Initial Cloud Fitting Algorithm (ICFA) [Kuze and Chance, 1994] to exclude data with cloud fraction >40%. This threshold value represents a trade-off between data quality and coverage; using alternative threshold values of 30% or 50% did not alter significantly the results. In this work we use an improved GOME cloud product, the GOME Cloud AlgoriThm (GOMECAT) [Kurosu et al., 1999] to remove scenes with cloud fraction >40%.
 Recent work has highlighted an artifact likely introduced by the solar diffuser plate onboard the GOME instrument [Richter and Wagner, 2001; Richter et al., 2002; Martin et al., 2002]. The artifact takes the form of a daily varying global bias in the retrieved column. Here we have estimated the effect of the diffuser plate on the HCHO slant column retrieval by first computing 3-day spatial means (GOME provides global coverage every 3 days) during July 1996 over the eastern Pacific (30°–50°N, 140°–180°W) where we would expect HCHO columns to be determined by CH4 oxidation and relatively constant. We assume the model chemistry to be correct in this remote region and calculate the mean HCHO column in the model for July 1996 to be 3.0 × 1015 molecules cm−2. Subtraction of this model-derived HCHO column from the GOME slant column yields a residual structure, with a mean value of 0.3 ± 2 × 1015 molecules cm−2 during July 1996. This structure is well within the spectral fitting precision of 4 × 1015 molecules cm−2 [Chance et al., 2000]. We remove it from the fitted slant columns by assuming that it is globally invariant [Martin et al., 2002].
Figure 5 shows the monthly mean GOME vertical columns computed with the above updates. As in the study of Palmer et al. , the AMF values for converting slant to vertical columns use local HCHO profiles from the GEOS-CHEM model for the position and time of each observation. The GEOS-CHEM model includes a number of minor improvements over the Palmer et al.  study, as described in Appendix A. Differences between the results shown here and those presented by Palmer et al.  are typically less than 10%. Subtraction of the diffuser plate artifact from the GOME slant columns is the most important effect. Agreement between GOME and GEOS-CHEM monthly mean HCHO columns is slightly improved relative to that shown by Palmer et al. . A scatterplot of the data (Figure 6) shows a Pearson correlation coefficient r of 0.83 (previously 0.77), with a model bias of +11%. We define the percent model bias, following the study of Balkanski et al. , as
where ΩiM and ΩiO represent the ith model and observed HCHO column, respectively. The variability of HCHO columns in the model is largely driven by emission of isoprene (Figure 3), implying the same for the GOME observations.
3.2. Daily Variability in GOME HCHO Columns
 To further diagnose the relationship between GOME columns and isoprene emissions, we examine data from individual GOME orbits. Isoprene emissions from a given location vary from day to day in response to changes in temperature and to a lesser extent solar radiation [Guenther et al., 1995]. The Ozarks Plateau in southeastern Missouri is expected to have unusually high isoprene emissions because of oak forest cover and high temperatures [Xu et al., 1997; A. Guenther, NCAR, personal communication, 2001]. The GOME data show frequent occurrences of very high HCHO columns in that area, with a strong day-to-day variability that is not captured by the model (Figure 7). We examined whether this daily variability observed by GOME over the Ozarks can be interpreted in terms of variability in the meteorological variables determining isoprene emission. Figure 8 shows the daily HCHO slant columns (used instead of vertical columns to avoid any model influence [Palmer et al., 2001]) as a function of surface air temperature. We find that the columns are significantly correlated to surface temperature in a manner that shows some consistency with the exponential temperature dependence of isoprene emission [Guenther et al., 1995]. However, the highest temperatures are not associated with particularly high HCHO columns.
3.3. Consistency With In Situ Observations
 Aircraft vertical profiles of HCHO concentrations are available from the Southern Oxidants Study (SOS) over Tennessee in summer 1995 [Lee et al., 1998]. These data were previously compared with simulated GEOS-CHEM profiles by Palmer et al.  to evaluate the ability of the model to reproduce the vertical shape factor for the AMF calculation. Here we compare the HCHO columns computed from the aircraft observations to the GOME column observations and to the corresponding GEOS-CHEM model values.
 The SOS aircraft data (19 June to 22 July) include 14 vertical profiles in the region 29.3°–40.5°N, 82.4°–105.4°W, extending from 0.1 to 8 km altitude. Model results indicate that HCHO above 8 km contributes less than 5% to the total column, reflecting the absence of short-lived VOCs at these altitudes and the temperature dependence of the oxidation of CH4. Thus, the aircraft observations (June and July 1995) provide a good approximation to the total HCHO column for comparison with the GOME observations (July 1996) on a statistical basis. The SOS aircraft observations have a mean column value of 2.0 ± 0.3 × 1016 molecules cm−2 (14 profiles), while the GEOS-CHEM modeled HCHO columns during July 1995 for the same geographic region have a mean column value of 1.4 ± 0.2 × 1016 molecules cm−2, representing a negative bias of 30%, consistent with previous results [Palmer et al., 2001; Fiore et al., 2002]. The spatial mean of the monthly mean GOME HCHO columns in 2° × 2.5° grid squares over the same geographic region (29.3°–40.5°N, 82.4°–105.4°W) for July 1996 is 1.3 ± 0.4 × 1016 molecules cm−2; whereas the same statistic in the GEOS-CHEM model is 1.4 ± 0.4 × 1016 molecules cm−2. The GOME and GEOS-CHEM HCHO columns are therefore consistent, and 30% lower than the aircraft observations. Most of the discrepancy between the model and the aircraft observations is in the lower free troposphere [Palmer et al., 2001] where photochemical models in general tend to yield values lower than observed [Frost et al., 2002].
 In situ measurements of HCHO at surface sites in North America (Table 1) bring additional information about the concentration and distribution of HCHO. We cannot compare them directly to the GOME column data, but through comparisons with the GEOS-CHEM model results we can determine whether they are consistent. The measured HCHO concentrations range from 0.1 to 12 ppb, largest in the Southeast United States. We compare in Figure 9 the observed HCHO concentrations from Table 1 with GEOS-CHEM model results using GEIA and BEIS2 inventories for July 1996. Note the large difference between the two inventories (Figure 4), although the spatial correlation between them is significant (r2 = 0.58). The model is unable to capture the two largest HCHO observations (>6 ppb), corresponding to points J and K. Riemer et al.  (point J, see Table 1) report a mean daytime HCHO concentration of 12 ppb in Tennessee during SOS, which they attribute largely to isoprene. Data from the Ozarks site (point K) indicate a range of 7–15 ppb, again reflecting high local isoprene emissions (A. Guenther, NCAR, personal communication, 2001). The Ozarks maximum of isoprene emission is apparent in the BEIS2 inventory [Pierce et al., 1998] but loses definition when averaged over the 2° × 2.5° GEOS-CHEM model grid (Figure 4). Aircraft measurements during the 1999 SOS showed a HCHO increase by more than a factor of 4 when passing over the Ozarks region at an altitude of 500 m (Y.-N. Lee, Brookhaven National Laboratory, personal communication, 2001).
 If points J and K are removed from the comparison we find that the model can reproduce most of the variance in the in situ surface air observations (Figure 9). In the standard simulation using the GEIA inventory the reduced major-axis linear regression [Hirsch and Gilroy, 1984] approaches the y = x line. When the BEIS2 inventory is used, the model underestimates observations by 30% on average, consistent with the difference in isoprene emissions relative to GEIA. The successful model simulation of both the in situ surface air observations (Figure 9) and the GOME observations (Figure 5) when the GEIA isoprene emissions are used suggests that the GOME data and the in situ observations are consistent.
4. Estimating Isoprene Emissions From GOME HCHO Data
 To estimate isoprene emissions from GOME HCHO column data we use the modeled relationships shown in Figure 3, which are discussed in detail in section 2. These linear relationships are transposed to construct a transfer function in which an isoprene emission can be calculated given a HCHO column measurement. The emissions are then regridded on the 2 × 2.5° GEOS-CHEM model grid and local diurnal factors from the GEOS-CHEM simulation are applied to convert the 10–12 LT values to 24-hour averages. Monthly mean emission estimates are then calculated (Figure 4). The spectral fitting uncertainty of 4 × 1015 molecules cm−2 on the HCHO columns corresponds to a mean uncertainty for the inferred isoprene emissions to be 1.1 × 1012 C cm−2 s−1. After monthly averaging we get slight negative isoprene emissions in three 2 × 2.5° grid squares over North America, reflecting HCHO columns well within the HCHO fitting uncertainty. For purposes of applying the GOME isoprene emission inventory to GEOS-CHEM, we set these negative isoprene emissions to zero.
Figure 4 shows that the GOME-derived isoprene emissions over North America in July (5.7 Tg C) are lower than the GEIA emissions (7.1 Tg C), and the spatial distribution shows some differences (r2 = 0.41). In particular, GOME emissions are higher in the midwest and the deep south. The BEIS2 inventory is lower than GOME by a factor of 2 with a spatial r2 of 0.35. The high GOME values over southern New England could possibly reflect anthropogenic hydrocarbons emitted in the Northeast metropolitan corridor.
 Discarding data with >40% cloud cover introduces a bias in the monthly mean isoprene emissions derived from GOME data. We estimated this bias using the model by excluding periods with cloud cover >40% from the monthly mean isoprene emissions computed with the GEIA inventory. The resulting bias range between −20% and −35% over North America during July 1996 and typically smaller than −25%.
 To provide closure on the consistency between the GOME HCHO columns and the in situ HCHO data, we conducted a GEOS-CHEM simulation using the GOME-derived isoprene emissions and compared the resulting HCHO concentrations in surface air to the observations in Table 1. Figure 9c shows the results. The GOME emission inventory for isoprene achieves a better simulation of the surface air observations than either GEIA or BEIS2, with less scatter in the comparison. Even with the GOME isoprene emission inventory we are still not able to reproduce the observations at points J and K, which as previously noted could reflect subgrid-scale variability.
5. Summary and Discussion
 Accurate VOC emission inventories are essential to understand radical chemistry in the troposphere. Conventional emission inventories for both anthropogenic and biogenic VOCs are highly uncertain. Here we documented a new methodology to obtain VOC emissions from space-based HCHO column observations and applied it to data from the GOME satellite instrument.
 HCHO is a high-yield product of VOC oxidation and its lifetime is short enough that a measure of its column abundance should correlate well with the emission field of its parent VOC. In regions with an active biosphere, isoprene is the dominant HCHO precursor. Anthropogenic VOCs could dominate over urban areas but would not be resolved with the GOME footprint (320 × 40 km2) Although emissions of terpenes can exceed those of isoprene for some ecosystems, the HCHO yield from terpenes is far less than from isoprene.
 We used the GEOS-CHEM global 3-D model of tropospheric chemistry to derive linear relationships between HCHO columns and isoprene emissions over North America in summer for application to GOME. The slope of the relationship in the model implies a HCHO yield of 0.24–0.39 per atom C of isoprene, consistent with a steady state analysis of the model photochemical mechanism, which is, in turn, constrained by laboratory studies of isoprene oxidation products. Smearing and displacement length scales are found to be of little importance when relating HCHO columns to isoprene emissions over the grid resolution of the model (2 × 2.5°).
 We presented updated GOME HCHO columns over North America in July 1996 including several minor improvements over the original retrievals of Chance et al.  and Palmer et al. . Results were compared to GEOS-CHEM model results with two different isoprene emission inventories, GEIA [Guenther et al., 1995] and BEIS2 [Pierce et al., 1998]. We find that these two inventories, although substantially different (GEIA emissions over North America are almost 3 times higher than BEIS2) both account for about 50% of the spatial variance in the GOME observations. Use of the GEIA isoprene inventory leads to a 3% negative bias in HCHO while the BEIS2 has a 33% negative bias. Summertime statistics of HCHO concentrations measured at surface sites in the United States and Canada are reproduced closely by the GEOS-CHEM model using GEIA emissions, implying consistency between these in situ observations and the GOME columns. Examination of individual GOME orbits reveals occurrences of extremely high HCHO columns over the Ozarks (southeastern Missouri) where isoprene emissions in current inventories are particularly high. The day-to-day variability of GOME HCHO columns over the Ozarks shows some consistency with the temperature dependence of isoprene emission.
 The GOME observations were used to construct an isoprene emission inventory for North America which was compared to GEIA and BEIS2 and applied within the GEOS-CHEM model to simulate in situ HCHO observations. This GOME-derived isoprene emission inventory (5.7 Tg C) is comparable to GEIA on the continental scale (7.1 Tg C) but the spatial distribution shows some differences (r2 = 0.41). GOME emission fluxes are higher in the midwest and the deep south. The BEIS2 inventory is lower than GOME by a factor of 2 with a spatial correlation r2 of 0.35. Applying the GOME-derived isoprene emissions to the GEOS-CHEM model provides a better simulation of the surface air HCHO observations than either the GEIA or BEIS2 inventories; the simulation captures 71% of the observed spatial variance in the observations with a −10% bias. This result further demonstrates the consistency between the GOME and in situ observations.
 Our analysis focused on North America during summer but it can be readily extended to the globe. It could be used to map isoprene emissions from tropical ecosystems or to determine the seasonal pattern of isoprene emissions at northern midlatitudes. Following on the approach in section 2, care has to be taken to identify any additional VOCs besides isoprene that could make a significant contribution to the HCHO column. Outside of the growing season, longer-lived anthropogenic VOCs may become important and a more detailed inversion analysis would be required to relate the sources to the observed HCHO columns.
Appendix A:: GEOS-CHEM Model Description
 The GEOS-CHEM global 3-D model of tropospheric chemistry is driven by assimilated meteorological data from the GEOS of the NASA Data Assimilation Office (DAO) [Schubert et al., 1993]. The 3-D meteorological data are updated every 6 hours; mixing depths and surface fields are updated every 3 hours. We use here GEOS fields for 1996 available with 2° × 2.5° (latitude/longitude) resolution and 40 sigma levels in the vertical, extending up to 0.1 hPa. We retain the original horizontal resolution but keep only 26 vertical levels by merging levels in the stratosphere which provide negligible information relevant to HCHO. The lowest model layers are centered at approximately 50, 250, 600, and 1100 m for a box at sea level. A comprehensive description and evaluation of the GEOS-CHEM model for tropospheric O3–NOx–VOC chemistry is given by Bey et al. , and improvements and application to regional air quality over North America during summer are given by Fiore et al. . We use here is version 4.4 of the GEOS-CHEM model. We initialize the GEOS-CHEM model in May 1996 with monthly mean values taken from another year [Bey et al., 2001] and run the model forward in time through July 1996.
 The chemical mechanism is that of Horowitz et al.  with minor updates [Bey et al., 2001; Fiore et al., 2002]. It includes detailed representation of oxidation pathways for five non-methane hydrocarbons (NMHCs) (ethane, propane, lumped >C3 alkanes, lumped >C2 alkenes, and isoprene). Numerical integration of the mechanism is done with a fast Gear solver [Jacobson and Turco, 1994]. In the present version we recycle by photolysis and reaction with OH the organic peroxides produced from isoprene oxidation, following the mechanism of Lurmann et al.  and as discussed in section 2.1. Photolysis rates are computed using the Fast-J radiative transfer algorithm [Wild et al., 2000] which includes Rayleigh scattering as well as Mie scattering by clouds. We use monthly averaged UV albedo fields from the study of Herman and Celarier . Aerosol scattering is included in the model by specifying AODs from a correlation with surface O3, as described by Fiore et al. .
 Gridded emission fields for anthropogenic NOx and NMHCs over North America in 1985 are taken from the study of Wang et al.  and are scaled to 1996 using national emission data. Biogenic hydrocarbon emissions include isoprene as discussed in the text plus small contributions from acetone and propene. Emissions of terpenes and methanol are not included; as discussed in the text, they are unlikely to make significant contributions to the HCHO column signal from GOME.
 For useful discussions of the ideas presented, we thank Alex Guenther (National Center for Atmospheric Research), Bryan Duncan (Harvard University, now at Ecole Polytechnique Federale de Lausanne, Switzerland), Yin-Nan Lee (Brookhaven National Laboratory), Tom Pierce and Robin Dennis (Environmental Protection Agency), and Robert Chatfield (NASA Ames). This work was supported by the NASA Atmospheric Chemistry Modeling and Analysis Program (ACMAP) and by the Atmospheric Chemistry Program of the U.S. National Science Foundation.