A simple scheme for the soil consumption of atmospheric methane, based on an exact solution of the one-dimensional diffusion-reaction equation in the near-surface soil layer, is described. The model includes a parameterization of biological oxidation that is sensitive to soil temperature, moisture content, and land cultivation fraction. The scheme was incorporated in the Canadian Land Surface Scheme (CLASS), with forcing provided by a 21-a, global land meteorological data set, and was calibrated using multiyear field measurements. Application of the scheme on the global scale gives an annual mean sink strength of 28 Tg CH4 a−1, with an estimated uncertainty range of 9–47 Tg CH4 a−1. A strong seasonality is present at Northern Hemisphere high latitudes, with enhanced uptake during the summer months. Under the specified surface forcings, the oxidation parameterization is more sensitive to soil moisture than to temperature. Compared to the previous work of Ridgwell et al. (1999), our empirically based water stress parameterization reduces uptake more rapidly with decreasing soil moisture, resulting in a decrease of ∼50% in the potential global sink strength. Analysis of the geographical distribution of methane consumption shows that subtropical and dry tropical ecosystems account for over half of the global uptake.
 Methane (CH4) is a potent greenhouse gas with both natural and anthropogenic sources. It is removed from the atmosphere largely by oxidation, mostly through reaction with OH in the troposphere, which accounts for 85–90% of the estimated annual mean sink of 570 Tg [Ehhalt and Prather, 2001]. The remaining sink (10–15%) is thought to be split roughly equally between the stratosphere (removal by OH and O1[D]) and biological consumption in near-surface soils [Smith et al., 2000]. The soil uptake has been estimated at 30 ± 15 Tg CH4 a−1 [Ehhalt and Prather, 2001], but statistical upscaling from the distribution of actual measurements leads to a much wider range of uncertainty, 7–120 Tg CH4 a−1 [Smith et al., 2000].
 The key factors controlling the rate of methane consumption are, first, the rate of diffusion of the substrates CH4 and O2 through the uppermost soil layer, as characterized by the diffusion coefficient Dsoil; and second, the rate of biological oxidation, usually well described by a first-order decay rate constant k. The diffusion rate depends strongly upon the soil properties (e.g., bulk density, porosity) and on hydrology, both of which determine the available pore space for gas exchange. The oxidation rate depends upon available soil water, soil temperature [Whalen and Reeburgh, 1996; Savage et al., 1997]), and land use (with farmed soils having a lower rate of consumption [Steudler et al., 1989; Mosier et al., 1996]).
 Because of uncertainties surrounding the exact nature of the oxidizers, explicit biological models are difficult to formulate (however, see Grant , who parameterized the growth of the methanotrophic population in a point-scale model). Here I provide a parametric description of the process, building on the work of Ridgwell et al.  (hereinafter referred to as R99), in which k and Dsoil are expressed as the product of several factors sensitive to local, time-dependent, environmental conditions. An empirically based procedure is used to optimize the model parameters. The consumption algorithm was implemented in the land surface model CLASS (Canadian Land Surface Scheme) version 2.7, first described by Verseghy  and Verseghy et al. . The model includes most relevant surface energy and hydrological processes and has been validated against time series measurements from sites representing a variety of land surface and soil types (see Atmosphere-Ocean special issue, 38(1), 2000). With the incorporation of two global data sets (the land cover of Wilson and Henderson-Sellers  and the soil texture/porosity of Zobler ) CLASS may be applied globally, and is the land scheme currently used in the coupled global general circulation model (GCM) at the Canadian Centre for Climate Modeling and Analysis [Verseghy et al., 1993; Verseghy, 1996]. In this paper, I present the results of offline calculations using a global meteorological data set with 6-hourly resolution, a considerable improvement over previous studies which used monthly forcing data. However, the methane consumption algorithm described in section 2 below was developed with applications to both equilibrium climate and climate change simulations in mind.
 In this study the possibility of methanogenesis in soil layers below the sink region, in the same layer under saturation conditions, or in permanent wetlands, is neglected. These situations require a considerably more sophisticated model than that described here [e.g., Walter et al., 2001; Zhuang et al., 2004]. Although wetlands are the principal natural source of CH4 (140–240 Tg a−1 [Ehhalt and Prather, 2001]), they constitute a small fraction (∼4–−6%) of the land surface, which is mostly covered by regions of net uptake, in the annual mean sense. While the influence of climate change on methanogenesis has been much discussed [Cao et al., 1998; Walter and Heimann, 2000; Christensen et al., 2003], with the positive feedback between temperature and anaerobic microbial activity identified as the dominant effect if sufficient moisture is retained, the corresponding changes in methane oxidation are still uncertain. This is in part due to the complex response of methanotrophs to soil drying, as inferred from relatively sparse field and laboratory measurements [Schnell and King, 1996; Horz et al., 2005]: Uptake may either increase or decrease depending upon prevailing moisture conditions [Torn and Harte, 1996]. This is an additional motivation for eventually incorporating the methane consumption scheme developed here into a comprehensive climate model.
 In section 2, a relationship between the modeled surface flux and the rates of diffusion and oxidation is established, followed by a description of how the latter two processes are linked to soil properties and climate. Section 3 covers model calibration and testing at a variety of sites, and sensitivity of the calculated uptake to soil texture, an exercise which reveals many of the key properties of the uptake scheme and how it differs from previous treatments. The application of the model at the global scale is described in section 4, where more a detailed comparison with previous schemes is conducted, followed by concluding remarks in section 5.
2. Model Description
2.1. Calculation of Methane Flux
 With the identification of the key controlling processes above, I begin with the one-dimensional diffusion-reaction equation,
depth, positive downward (z = 0 at surface);
CH4 concentration (cm−3; C ≡ C0 at surface);
diffusion coefficient in soil (cm2 s−1);
first-order oxidation rate constant (s−1).
The methane flux, or uptake, at a given depth is the first integral of equation (1):
In this paper, I shall be concerned exclusively with the flux at the surface, J0 ≡ J(z = 0), and make use of a particularly simple exact solution of equation (1) that holds when both Dsoil and k are constants:
The scale height zc ranges from a few cm under optimal conditions to 50 cm or more in moisture- or diffusion-limited soils (section 1). As mentioned by Dorr et al. , for z ≪ zc, the C(z) profile is not very sensitive to the exact distribution of the sink, which ameliorates somewhat the k = constant assumption at small depths. Our CH4 consumption scheme is applied only in the top (0–10 cm) layer of CLASS, where the above solution should be reasonably valid, and below which measured oxidation rates are usually small (section 1).
 Some previous treatments of J0 assumed a fixed value for the concentration gradient at the surface, (dC/dz)0. In this case, J0 depends only on the diffusion coefficient at the surface, Dsoil,0 [e.g., Potter et al., 1996] (hereinafter referred to as P96). However, this approach is unsuitable for the present study: first, because a single value of (dC/dz)0 is not representative of all locations; and second, because it is not easily adapted for use in climate change simulations, wherein (dC/dz)0 is not fixed in realistic scenarios. In addition, the fixed concentration gradient (FG) method presumes that oxidation is always limited by diffusion, irrespective of the oxidation rate, k. It will be demonstrated that this is not the case in many regions.
 The present formulation is most similar to that of R99, who also assumed constant Dsoil and k, but with k > 0 only in a layer of thickness ε at fixed depth zd (see equation (4) of R99). While this approach approximates the true situation of a strongly peaked k(z), it is inconsistent with the diffusion-reaction equation (1) since a solution of this type requires ε ≪ zd, whereas R99 chose ε such that zd = 6ε. Further, this formulation does not provide a realistic subsurface description (i.e., flux and concentration profiles), which may be desirable in some circumstances.
2.2. Parameterized Response to Climate and Soil Properties
 The quantities Dsoil and k are sensitive to soil type, porosity, ambient soil temperature, and hydrology. Following R99, Dsoil is expressed as the product of three factors:
total porosity (cm3 cm−3);
air-filled porosity (cm3 cm−3) = Φ − θ;
= θw + θi, where θw is fractional water content and θi is fractional ice content;
= 15.9 fclay + 2.91, where fclay is fraction of clay;
= 0.196 cm2 s−1 (STP).
The dimensionless functions defined in equation (5) represent the separate influences of soil temperature (GT) and texture, porosity, and moisture content (Gsoil), respectively. The above quantities are available in each of the three CLASS soil layers (0–10 cm, 10–35 cm, and 35–410 cm) from Zobler's  global data set. In this work, properties from the top layer only are used, since this is where the bulk of the oxidation activity is located. Note that decreasing soil moisture at a given site, for example, increases Φair and so increases Dsoil. In the FG scheme, this invariably increases the flux, with the maximum J0 determined by the texture and porosity of the soil. In the present scheme, equation (3) shows that J0 may or may not increase, depending on the behavior of k, which is now described.
 The oxidation rate parameterization takes a similar form to that used by R99, viz.
however, the right-hand side factors are somewhat different than in R99. In order to account for the small amount of uptake often observed at subzero soil temperatures [e.g., Del Grosso et al., 2000], the temperature factor was modified to
with rT = 0 outside this soil temperature range. The form of rT at Tsoil > 0 is identical to that used in R99 and ranges from unity to a maximum of 4.1 at Tsoil = 27.5°C.
 The soil moisture factor rSM describes the known decline of microbial oxidation at low fractional liquid water content θw (cm3 cm−3) due to biological stress. R99 assumed that rSM was proportional to the ratio of total moisture (precipitation plus soil moisture) to potential evapotranspiration when this ratio was less than unity, and rSM = 1 otherwise. Their parameterization implies that oxidation ceases only at zero soil moisture, which is unrealistic. Moreover, this form of rSM does not account for a common feature of experimental studies, namely the sharp decline of methane uptake as soil moisture decreases to small but finite values [Torn and Harte, 1996; Del Grosso et al., 2000]. In an attempt to capture this behavior, I adopt an approach previously used to model the dependence of microbial respiration on soil moisture [Griffin, 1981; Davidson et al., 2000], which utilizes the soil water potential ψ, a more sensitive measure of soil moisture under dry conditions [Clapp and Hornberger, 1978]:
Here ψsat ≡ /10 is the saturation soil water potential (kPa) and fsand is the fraction of sand in the topsoil layer. Note that while ψ is usually defined as a negative quantity, I consider its absolute value here. Following Schnell and King , rSM is assumed to be optimal (= 1) for ψ < 0.2 MPa, and to decrease smoothly to zero as ψ increases to 100 MPa, above which rSM = 0 [Davidson et al., 2000]. Specifically,
where β is an arbitrary constant specifying how rapidly rSM → 0 at low moisture content (high ψ). β is determined using empirical constraints in section 2.3. Under drier than normal conditions, J0 is therefore determined by the competing influences of increased diffusivity and decreased rSM. Note that rSM contains no corresponding limitation at high moisture content; it is assumed that this is adequately described by the decrease in Φair and Dsoil in equations (5) and (6) under conditions approaching saturation.
 Two further adjustments were made to the final flux calculation. Prescribed distributions of agricultural regions and wetlands were used to create spatially dependent scaling fields that were applied to J0. R99 included an empirically based factor rN = 1.0 − 0.75 fC, where fC is the local fractional area of cultivation, in equation (6) to account for the inhibition of CH4 uptake in cultivated soils. Since this factor should linearly multiply the uncorrected flux, it was moved outside the k parameterization in our formulation, since J0 ∝ k1/2 (equation (3)) versus J0 ∝ k in R99. fC was obtained from the global cropland data set of Ramankutty and Foley . As there seems to be little consensus on how much of the reduction in flux is due to land management (e.g., clearing, soil tilling), and how much to fertilizer application (area and/or amount) [e.g., Smith et al., 2000], I write this factor as rC rather than rN.
where g0 = 586.7 mg CH4 ppmv−1 s d−1 m2 cm is a factor that for C0 expressed in ppmv, gives J0 in mg CH4 m−2 d−1 (Dsoil in cm2 s−1, k in s−1), including a correction for temperature and density. While R99 adjusted to STP (100 kPa and T = 0°C) giving g0 = 616.9 mg CH4 s ppmv−1 d−1 m2 cm, I chose standard pressure and a more representative global mean temperature of 15°C. This change in the conversion factor corresponds to a 5% reduction in flux for our model compared to R99.
2.3. Model Calibration Using Observed Data
 In the formulation of R99, k0 was estimated from 13 surface measurements of J0, Dsoil and Tsoil, each of which was used in their equivalent of equations (3)–(9) to calculate a mean k0 value. In this procedure, both rSM and rC were set equal to unity. While the exclusion of agricultural sites justifies rC = 1, the use of rSM = 1 in this procedure is specious, since k0 is only a “base” value if regions where oxidation is limited by both temperature and soil moisture are included in its determination.
 In the absence of a unified data set for soil moisture at either the global or continental scale, I used a multiyear time series of methane uptake at a midlatitude continental site in order to determine the sensitivity of k to soil moisture and temperature as parameterized by rSM and rT. Methane flux measurements from several sites in the Colorado shortgrass steppe (40°40′23″N, 104°45′15″W) were taken from Mosier et al. , to which the reader is referred for a detailed description. A reasonably dry (time mean θw = 0.12) midslope site with sandy loam soil (76% sand, 13% clay; labeled MN by Mosier et al.) was selected for the calibration. Soil temperature, moisture, and CH4 flux were measured at a weekly sampling interval from April 1990 to January 1995, with only a few gaps in the record.
 The data were used to constrain the base oxidation constant k0 and the water stress exponent β as follows. Equation (10) was solved for k and then k0 (via equation (6)) in terms of the flux and other quantities obtainable from the data (e.g., air-filled porosity derived from soil porosity, texture, and liquid water content). Since the selected site is nonagricultural, rC = 1 is appropriate. A surface concentration of C0 = 1.753 ppmv (the 1990–1995 mean value from Niwot Ridge, Colorado, 40°03′N, 105°35′W, the nearest site in the NOAA/CMDL measurement network [Climate Monitoring Diagnostics Laboratory, 2001]) was used. The observed data were then used as input to the right-hand side of the expression for k0, excepting points with rSM = 0 (since k0 ∝ rSM−1), and assuming a range of β = 0–4.0.
 For each β, the mean of the resulting time series of k0 values was calculated, 〈k0〉, along with its variance. Each of these β, 〈k0〉 pairs is consistent with the mean observed flux, soil moisture, temperature, and soil texture/porosity at this site. An optimal β, 〈k0〉 was selected as that having the smallest relative variance (i.e., σ2/〈k0〉), with the result β = 0.8, 〈k0〉 = 5.0 × 10−5 s−1. Plotting rSM against θw using this β with the same input data (not shown) shows that rSM falls below unity at θw = 0.125, declining to zero at θw = 0.037. Both the shape of the (rSM, θw) curve and the threshold θw values resemble the J0 − θw relation for grassland-tropical-coniferous forests developed by Del Grosso et al. , which they derived from a beta function fit to flux data. Recall, however, that the current formulation has the advantage that it can be applied in simulated past and future climates, since k0 is ostensibly independent of both temperature and hydrological state.
 The mean k0 found by R99, 〈k0〉 = 8.7 × 10−4 s−1, is more than an order of magnitude larger than that obtained here. However, much of the difference can be ascribed to the different model formulations. In R99, all oxidation occurs in a thin 1 cm layer located at 6 cm depth, while in the present model, consumption is assumed to occur at all depths. Hence it is not surprising that our derived 〈k0〉 is much smaller than that of R99, since it represents the vertically averaged consumption over a much larger depth, according to equation (2).
3. Model Predictions and Time Series at Specific Sites
 CLASS was forced with meteorological fields from the 21-a (1979–1999) Global Land Surface Dataset (GOLD) of Dirmeyer and Tan  (available at http://www.iges.org/pubs/tech.html). These 6-hourly data, based on NCEP reanalysis but corrected for several known biases, were obtained at a grid resolution of 3.75° × 3.75°, in anticipation of eventual comparison with GCM runs at the same resolution. The data were disaggregated to half-hourly frequency to match the fixed time step of CLASS. Air temperatures were linearly interpolated, while the 6-hourly precipitation was used to estimate the number of wet half hours, assuming a lognormal distribution. The 6-hourly precipitation was then randomly distributed among these wet half hours [Arora, 1997]. These data represent a significant improvement over the monthly mean forcing data used by P96 and R99, insofar as brief (diurnal timescale) precipitation events are resolved. The associated response of CLASS to episodic wetting and drying of the soil may explain some of the differences found in sections 3.1–3.5 compared to these previous studies.
 Methane consumption was calculated at each CLASS time step from the current local values of Tsoil and θ. The results at a number of sites representing a variety of climatic and soil conditions are described below. Except at the Colorado site where more accurate measurements were available (section 2.3), the value C0 = 1.72 ppmv, representative of the global mean methane surface concentration circa 1994, was used in all calculations.
3.1. Colorado Site
 The CH4 uptake scheme, with the optimal values of k0 and β determined in section 2.3, was applied at the CLASS grid cell corresponding to the Mosier et al.  data (section 2.3; 38°58′N, 105°W). Figure 1 compares the observed and modeled time series at this site. Figure 1a shows the air temperature from Mosier et al. (data at point scale), the GOLD near-surface air temperature (reanalysis at grid scale), and the mean (0–10 cm) soil temperature of CLASS (at grid scale). The CLASS soil temperatures are generally cooler, due to the coupling of the topsoil layer with the more thermally inertial layers beneath [Verseghy, 1991], except when the air temperature falls below zero. Figure 1b shows the Mosier et al. volumetric water content θw and the corresponding CLASS-calculated quantity in the topsoil layer. The agreement between the model and observations is generally good, despite the slightly larger soil depth probed by the measurements (0–15 cm).
 The simulated and observed methane fluxes are shown in Figure 1c. The mean measured flux over the entire period, 1.29 mg CH4 m−2 d−1, is close to the simulated value, 1.28 mg CH4 m−2 d−1. Overall, a strong correlation is seen between modeled and measured flux over the observation period (linear correlation r = 0.47, P = 2.1 × 10−11, n = 182). However, the model flux seems to be systematically lower during the winter months, a result of high ice fraction in the soil pores, which reduces Φair and thus Dsoil. J0 falls to zero for several weeks during February–April 1993 and February 1994; unfortunately, there are no measurements during these intervals to corroborate this behavior. This may indicate deficiencies in the diffusivity parameterization (specifically, in Gsoil), although it should be kept in mind that the soil texture data are averaged over large scales. Indeed, it should be emphasized, as the model is applied below to sites with a less complete measurement record, that since the grid cell area is always much larger than the point scales represented by measurements, detailed quantitative agreement between model and observations is not to be expected.
 Finally, Figure 1d compares the present model time series with the predicted uptake from the other two schemes described in section 2.1. The similarity of the present and R99 schemes is evident at this site, with R99 giving a somewhat smaller time-mean uptake. The FG flux also displays an annual cycle similar to the other two models, but differences are evident on weekly/monthly time scales. For example, after a sudden moisture increase at day 210, uptake decreases in the FG model (because of decreased diffusivity) while J0 remains relatively unchanged in the other two models.
3.2. Amazon Site
 In order to examine the behavior of the model under conditions where neither moisture nor temperature is expected to be limiting (but where diffusion may be), a tropical humid site in the western Brazilian Amazon (1°51′S, 63°45′W) was selected. Figure 2 shows the annual cycle of soil temperature, water content, and CH4 uptake for the 21-a simulation. Variations in surface air temperature, and thus Tsoil, in this location are minimal (Figure 2a), with a mean annual range of <2°C. The annual range in soil moisture (0.38–0.41) is similarly narrow (Figure 2b). Figure 2c shows a maximum CH4 uptake of 0.95 mg CH4 m−2 d−1 (21-a mean) at day 281, coincident with the minimum in θw of 0.38 and just prior to the maximum Tsoil of 28.1°C at day 301. Despite the small amplitude of the variations, a clear anticorrelation of J0 with θw is seen in Figures 2b and 2c. Since rSM is never far from unity in the 21-a mean, this may be understood as a purely diffusive effect. During periods of relatively high water content, air-filled porosity is reduced, decreasing Dsoil and thus J0, with the opposite behavior occurring at low θw. While the maximum in J0 also approximately coincides with that in Tsoil, there is no correspondence at the secondary Tsoil maximum at day 80, indicating that Tsoil is not the primary influence on the uptake. At this site, J0 is always well above zero, with an average 21-a mean value of 0.75 mg CH4 m−2 d−1. This lies within the range 0.27–0.85 mg CH4 m−2 d−1 measured by Verchot et al.  in a variety of forest and pasture biomes in the eastern Amazon. For comparison, the uptakes calculated using the R99 and FG flux formulae are 0.40 and 0.06 mg CH4 m−2 d−1, respectively. The FG model gives especially low results in this diffusion-limited region.
3.3. Finland Site
 As an example of a northern continental site, time series results for a location in Finland (61°14′N, 30°E) are shown in Figure 3. Many differences from the tropical Amazon site described above are apparent. First, a strong annual cycle in surface air temperature is present, featuring an extended period of freezing temperatures in the topsoil layer. This results in a yearly (approximately January to April) low uptake interval seen in Figure 3c. Second, in contrast to the Amazon site, J0 is more strongly correlated with Tsoil than with θw. This is partly due to the subzero temperature response just noted, but is also evident between days 180 and 300 when the decrease in J0 tracks the corresponding decline in Tsoil more closely than the increase in θw over this period. Third, there is much more variability in soil moisture at this site than in the Amazon. This results not only from the annual spring thaw, but also from the episodic character of summer precipitation. The rise of soil water content spanning day 90–140, the result of spring thaw, is not immediately reflected in J0, which remains near zero until day 120. At day 120, J0 begins to rise sharply toward its maximum daily mean value of 2.1 mg CH4 m−2 d−1 at day 189, while θw drops abruptly from 0.25 to 0.10 over this period. This behavior reflects the effectiveness of diffusivity in aiding uptake under nonfreezing conditions. However, J0 is more sensitive to temperature at this northern continental site than near the equator, chiefly because of passage through the freezing point. The annual mean value of J0 at this site is 0.75 mg CH4 m−2 d−1, which may be compared to the value of 1.07 mg CH4 m−2 d−1 measured at a forested site near Liperi, Finland (62°31′N, 29°23′E) by Maljanen  (available at http://www.uku.fi/∼maljanen/publications.htm). The corresponding uptake values for the R99 and FG models are 0.57 and 0.26 mg CH4 m−2 d−1, respectively.
3.4. Central Australia Site
 As an example of a site where arid conditions are found to limit methane uptake via the parameterized moisture stress, results for a site in western Queensland, Australia (24°7′S, 138°45′E) are shown in Figure 4. Like the Finland site, this location has a strong seasonal variation in Tsoil, with a 21-a mean range of 23.8°C (Figure 4a). It is also one of the driest sites modeled, with an annual mean θw of only 0.076. The soil moisture time series is characterized by a succession of pronounced spikes (Figure 4b), the result of infrequent rainfall events (total annual precipitation = 211 mm). The 21-a mean θw is never very far from the minimum value enforced by CLASS (0.04–0.08, depending on available moisture in the second and third soil layers, which can replenish the top layer through capillary action; D. Verseghy, personal communication, 2006).
 The CH4 uptake time series (Figure 4c) closely tracks the available soil moisture. A similar response to rapid rainfall events was measured in a desert environment by Streigl et al.  and in short-grass prairie soils by Mosier et al. . Although the annual mean value of J0 at this site is only 0.12 mg CH4 m−2 d−1, among the lowest found anywhere in the model (section 4.1), the peak values are comparable to those seen at the Finland site in summer (Figure 3). It should be emphasized that J0 may be underestimated during the many dry, low uptake periods, when oxidation may shift to deeper layers (>10 cm, not included in the flux calculation), where adequate moisture to allow microbial activity is retained. In any event, it is interesting that even the large temperature variations at this location play essentially no role in methane uptake, a result noted previously in less extreme locations [Smith et al., 2000]. The corresponding uptake values for the R99 and FG models at this site are 0.080 and 1.05 mg CH4 m−2 d−1, respectively. In addition to its much larger mean value, the FG model time series (not shown) displays a clear anticorrelation with the other two models, a result of the opposite effect of moisture scarcity on uptake in the respective schemes.
3.5. Sensitivity of Methane Uptake to Soil Moisture and Texture
 The strong dependence of methane uptake on soil moisture is evident in the above examples, but the role of soil texture, another key determinant of gas diffusivity, remains to be examined. Figure 5 shows scatterplots of daily mean uptake versus liquid water fraction at three sites: the Amazon and Finland locations discussed above, and a third site in New Zealand (42°41′S, 172°30′E). There are several features here worth noting. First, the uptake has a maximum value, J0,max, at an intermediate value of the range in θw (≡ θ*w) at a given site. Second, J0,max is largest in coarse, sandy soils (e.g., Finland) and decreases as soils become finer (e.g., Amazon). This reflects the larger diffusivity of coarser soils. Third, the peak uptake shifts from low θ*w (≃0.08) at the Finland (sandy) site to relatively high θ*w (∼0.3) at the Amazon (predominantly clay) site. The location of θ*w coincides with, but is usually somewhat smaller than, the θw below which rSM decreases to less than unity (not shown); hence the decline in J0 at θw < θ*w is entirely due to the parameterized moisture stress at low θw (high ψ). At θw > θ*w, the air-filled porosity (and thus J0) decreases with increasing θw (assuming θi = constant, a valid assumption at the New Zealand and Amazon sites, where θi = 0). The shift to larger θ*w in fine-textured soils reflects the strong sensitivity of the soil water potential to the exponent b in equation (8). At fixed θw, ψ increases rapidly with increasing b (i.e., as soils become finer), so that rSM decreases below unity at larger θw, leading to the turnover in J0 at θ*w.
Figure 5 shows that the range of J0 at a given θw is highly variable from one site to the next. Particularly remarkable is the J0 − θw relation in the Amazon: almost all of the daily mean flux values lie on a single curve in the diagram (also note that since there are no θw < 0.30 at this location, the uptake is always nonzero; see Figures 2b and 2c). This is in contrast to the other two sites, where a single θw corresponds to a range of calculated uptake, from 0 up to a maximum value. This is a direct result of the different annual temperature ranges at tropical and temperate sites. At the Amazon and New Zealand sites, where freezing temperatures are not encountered, the air-filled porosity depends solely on water content, i.e., Φair = Φ − θw, so that a given θw corresponds to a unique Φair and Dsoil. This accounts for the nearly unique J0 − θw relation in the Amazon, where rSM ≃ 1 and rT≃ constant introduce only minor fluctuations over the year. In New Zealand, the departure of these factors from constant values introduces somewhat more variability in J0, while at higher latitudes, the occurrence of freezing temperatures means that ice takes up a significant volume of pore space in the winter months. This leads to a range of possible Φair values for a given θw, since Φair = Φ − (θw + θi), and a much wider range of J0 at the Finland site, for example. It follows that at a given location, the dispersion of J0 scales roughly with the annual temperature range.
 Finally, from equations (3), (4), and (5), J0 ∝ Φairα where α = 3/4 + 3/2b ranges from 0.83 (fclay = 1) to 1.27 (fclay = 0). Since the maximum J0 at any θw occurs when θi = 0, this explains the nearly linear decrease of the maximum J0 at large θw, a feature seen at all sites irrespective of texture.
4. Global Application
 Having explored the behavior of the CH4 consumption scheme at sites with widely varying climate and soil texture, the model was next applied globally at 3.75° × 3.75° resolution, using the same meteorological forcing data as described for individual sites above. Areas of permanent water, ice, and desert were masked out. Separate scalings were applied to the flux calculated at grid cells coincident with wetland and agricultural areas, as explained in section 2.2. Approximately 14% of eligible land points were affected by the wetland scaling, and 37% by the agricultural correction. Spatial maps of the mask and scaling fields are available as auxiliary material.
 The annual, January, and July mean distributions of CH4 uptake are displayed in Figures 6a, 6b, and 6c. In the annual mean map, one can see that the regions of largest uptake are in the bulk of South America, sub-Saharan Africa, and south central Australia. In the latter two regions, it is notable that some of the highest uptake cells border large deserts, where spatial variability is high due to low soil moisture and the associated threshold effect of rSM (see section 4.2). The annual mean flux ranges from 0 up to a maximum of 783 mg CH4 m−2 a−1 (Botswana), with an annual global uptake of 28.0 Tg CH4 a−1. The Northern and Southern hemispheric contributions to this total are 17.4 and 10.6 Tg CH4 a−1, respectively, values that closely reflect the respective land areas of the two hemispheres (omitting Greenland and Antarctica, which are both masked out). At the majority of locations outside of the tropics, methane consumption is largest in summer, with maxima of 762 mg CH4 m−2 a−1 in January (south Australia) and 852 mg CH4 m−2 a−1 in July (Pakistan). Globally, consumption in July (36.4 Tg CH4 a−1) is about 70% larger than that in January (21.1 Tg CH4 a−1), again in agreement with the ratio of available land area in the two hemispheres.
 The seasonality of CH4 consumption is shown in more detail in Figure 7, averaged by latitude zones of 30° width. In the extratropics, the variation in the annual amplitude of the flux may be explained on the basis of climatic considerations alone: as one approaches the equator, the amplitude decreases in concert with the annual cycle of temperature. The seasonal amplitude is much higher in the Northern Hemisphere than in the south, where climatic variations on land are moderated by ocean thermal inertia in many locations (e.g., coastal South America and South Africa). On the other hand, the seasonality of uptake in subtropical Africa and central Australia is significant. Interestingly, while peak consumption in the extratropics (30–90°) occurs in summer, the tropical-subtropical maxima appear in the fall. This is likely due to lower soil moisture and a more favorable diffusive regime during the dry season, as at the Amazon site (Figure 2), although the steep decline of rT at large Tsoil in equation (7) in summer may also play a role.
 The influence of the temperature, soil moisture, cultivation, and wetland factors rT, rSM, rC, and rW was explored by performing runs with each factor set separately equal to unity at all locations. It was found that rSM = 1 (no moisture limitation) gave the biggest change in global, annual mean flux: the total uptake of 55.3 Tg CH4 a−1 is almost twice as large as in the standard case with all three factors varying. This reduction in global sink strength is considerably larger than that estimated by both P96 and R99 employing their rSM parameterization. Setting rT = 1, the global annual uptake fell by 37% to 17.7 Tg CH4 a−1. Both results suggest that the model may be quite sensitive to regional increases in temperature associated with climate change. However, since the relationship of θw to Tsoil is complex, this is an issue that requires more careful study using GCM simulations. The inhibition of uptake by cultivation was responsible for a decrease of 3.4 Tg a−1 (11%) in the 21-a annual mean uptake, a value similar to those found by R99 and P96 (9% and 13%, respectively). The effect of rW was the smallest among these factors, with a reduction of only 3% in J0 due to prescribed wetlands.
 Methane consumption is a function of ecosystem type, and this is quantified in Table 1. I use the ecosystem classification of the International Institute for Applied Systems Analysis (available from http://iridl.ldeo.columbia.edu/SOURCES/.ECOSYSTEMS/.Holdridge/), an aggregation of the 38 Holdridge life zones [Leemans, 1992]. While all major ecosystem types are represented, this classification differs slightly from that used by P96 and R99, mainly insofar as distinctions are made between subtropical and tropical forests and deserts. Table 1 shows that subtropical forests are the dominant sink, in terms of both area-averaged (309 mg CH4 m−2 a−1) and area-integrated uptake (8.0 Tg CH4 a−1), followed by subtropical desert/scrub (4.1 Tg CH4 a−1) and tropical dry forest (2.7 Tg CH4 a−1). In both P96 and R99, tropical forests and grasslands were the dominant sinks, but as their tropical classes include the subtropics, this is likely a superficial difference between the respective model results. Note, however, that the difference in uptake between classes is generally larger in the present model and R99 than in P96.
Table 1. Annual Mean Methane Consumption Averaged by Aggregated Holdridge Life Zone
Mean Uptake, mg CH4 m−2 a−1
Area, 106 km2
Total Uptake, Tg CH4 a−1
cool temperate desert/scrub
cool temperate forest
warm temperate desert/scrub
warm temperate forest
tropical dry forest
tropical moist forest
4.2. Comparison With Other Uptake Schemes
 The spatial uptake pattern predicted by the R99 and FG methods (in the latter, the value [dC/dz]0 = 0.04 from P96 was used) is shown in Figure 8a and 8b, and results from all three models are compared at selected sites in Figure 8c. It is critical to note that these other consumption formulae were applied within the same land surface scheme (CLASS) as the present model, meaning that the corresponding results differ somewhat from those presented in the original papers. In particular, CLASS hydrology gives a different air-filled porosity, and thus Dsoil, than the moisture schemes used in the original application of the other two models. In addition, the surface climate data used to drive the models, and the particular land mask, wetland, and agricultural scalings applied to the raw fluxes lead to differences between the results presented here and those found in P96 and R99.
Figures 6a, 8a, and 8b show that among the three algorithms, the range of fluxes is largest in the present model, followed by the R99 and FG schemes, respectively. The three models give similar results in the NH extratropics where, for the most part, soil moisture is not limiting and uptake is mostly diffusion limited. Over the remainder of the globe, however, the present model results differ significantly from those of the other two schemes. Simply scaling the R99 flux by a uniform factor of ∼1.5 produces a map that looks much more like Figure 6a than the FG result, as might be expected from the commonality of the underlying parameterizations. However, neither the R99 nor the FG scheme produces an annual mean uptake exceeding 557 mg CH4 m−2 a−1 = 1.53 mg CH4 m−2 d−1, which places both in apparent conflict with a handful of observations of at least 1-a duration in tropical and temperate forest soils [P96; Smith et al., 2000; Keller et al., 1993].
 The annual mean integrated uptake using the FG approach is 21.1 Tg CH4 a−1, 25% smaller than that obtained using the present model formulation. The spatial variation of FG-calculated uptake closely reflects local soil texture/porosity, being largest in coarse, porous soils and smallest in fine, high clay content soils. The largest differences from the present and R99 schemes are in the tropics (10°S–10°N; Figure 8b), where the FG method produces a local minimum in uptake compared to adjacent latitudes due to high rainfall and low air-filled porosity year-round. However, in both the present model (Figure 6a) and that of R99 (Figure 8a), no such minimum is present, due to the additional (parameterized) dependence on biological oxidation. Indeed, in equatorial Africa, the latter two models display a local maximum in uptake, in stark contrast to the FG result. The annual mean uptake in the SH extratropics is also considerably higher in the present model calculation than in the R99 and FG schemes. The global FG uptake found here is 24% larger than the 17 Tg CH4 a−1 obtained by P96 using the same value of (dC/dz)0 but a different calculation for Dsoil (i.e., the model of Millington and Shearer  for gas diffusion in partially saturated and aggregated soils). This level of disagreement is not surprising, however, given the aforementioned differences in model setup.
 Regarding Dsoil, it is worth noting that despite using the same formulation as employed here, R99 found results very similar to P96 when they performed a global FG calculation. That is, R99 reported a globally integrated FG value of 38.0 Tg CH4 a−1 for (dC/dz)0 = 0.087, implying a value of 17.5 Tg CH4 a−1 for (dC/dz)0 = 0.04, versus P96's 17 Tg CH4 a−1. This suggests that the combination of R99'sDsoil formulation and hydrology are not significantly different, in a global mean sense, than that of P96. Yet our FG calculation (the same as R99) with CLASS hydrology gives a ∼20% larger global mean uptake than the other two models. This suggests that the CLASS diffusivity in the upper soil layer, in a global and time-averaged sense, is larger than in the other two schemes, implying generally drier soils in CLASS. This is consistent with the drainage of moisture from the bottom soil layer in CLASS, versus the single-layer “bucket” moisture schemes of the other two models.
 Differences in calculated uptake between the current and R99 schemes as presented here (i.e., both running under CLASS) arise entirely from the respective formulae used to calculate J0. It can be shown that for the respective values of the base oxidation constant employed in the two schemes, it is always the case that J0 (present model) >J0 (R99). This is easily illustrated in the diffusion and moisture-limited regimes: since the R99 formula is proportional to Dsoil or k in these respective limits, while our formula is proportional to the square root of these quantities, our J0 always exceeds that of R99 when Dsoil and/or k is small. The converse can only be true (and then only over a limited range of Dsoil and k) if the base oxidation constant of the R99 scheme were approximately doubled to a value of k0 ≃ 1.7 × 10−3 s−1 or higher.
 While the above elucidates the results obtained in the present model setup, it will be noted that the global total uptake according to the R99 formula, 18.6 Tg a−1, is less than half the value cited by R99 (37.8 Tg a−1). Since Dsoil is generally somewhat larger in CLASS, this discrepancy cannot originate with the diffusional part of the calculation. Further, since the rT parameterizations are the same in the two schemes except at Tsoil < 0 (where uptake is minimal in any case), the disagreement must originate with the different rSM parameterizations. Recall that our equation (9) ensures that rSM = 0 and thus J0 = 0 below some threshold θw > 0, while the R99-calculated rSM > 0 unless θw = 0 (section 3). At the central Australia site, for example, this threshold value of θw = 0.082 was exceeded only 9% of the time over the 21-a simulation, resulting in the very low annual mean J0 = 43 mg CH4 m−2 a−1. The value of J0 (R99) using our rSM formulation is only 29 mg CH4 m−2 a−1 at this location, compared to a value ≥≳250 mg CH4 m−2 a−1, seen in R99's Plate 1. Indeed, it is apparent from R99's map that CH4 uptake is not nearly as strongly limited in desert-bordering regions as it is in the present model; presumably this intermodel difference is present wherever very dry conditions are encountered. Since, in R99, tropical and subtropical dry regions account for 38% of the total uptake, this represents a critical point of difference between the two models.
 On a related note, it seems likely that the most sensitive factor in the oxidation parameterization of the original R99 model is not rSM, but rather rT. This can be deduced from the following: (1) According to R99, the use of rSM = 1 in their formulation gave a 16% decrease in the global flux. (2) Although R99 did not provide a similar figure for the effect of rT > 1, it can be diagnosed from the present calculations using the R99 formula, independent of the effect of rSM. The result is a 45% decrease in annual global uptake when rT = 1, much larger than the −16% change due to rSM. Hence the present model is distinguished from R99 also in this respect; that is, the oxidation and flux are more sensitive to the parameterized response to low soil moisture than to elevated soil temperature.
 A secondary factor is the sensitivity of the oxidation k in the present and R99 methods to the calculation frequency of the uptake. J0 was computed using both formulae every 30 min with new meteorological forcings, whereas R99 used monthly mean forcing data. Because more extreme values are sampled at higher frequency, and since rSM falls rapidly to zero at low θw, the time mean J0 will be systematically smaller at dry sites in the present computational method.
Figure 8c compares the annual CH4 flux at selected locations according to the three uptake schemes. Sites where the present model uptake exceeds that of the FG approach, sometimes by a large margin, are shown on the left-hand side of the chart. At those sites where the ratio of present-to-FG model flux is the largest, the annual mean air-filled porosity is limited, either by frequent rainfall (coastal Peru, Borneo, New Zealand, Amazon), or effective moisture retention due to high clay fraction (Borneo, Amazon), or both. All of the sites on the far right-hand side of the chart are dry (the extreme being West Africa, with a 21-a mean rSM = 0.013) and predominantly sandy in texture, explaining their high FG method uptake. All of these sites have a small time mean rSM, so moisture stress accounts for the low consumption using the present and R99 schemes.
 A simple model of methane consumption in unsaturated soils was presented. The consumption algorithm, which is sensitive to surface meteorology, subsurface hydrology and temperature, and soil texture/porosity, was incorporated into the land surface scheme CLASS. The model has two specifiable parameters: the base oxidation constant k0 and the soil moisture exponent β. Both were determined using multiyear flux measurements at a midlatitude continental site in Colorado. Application of the model at this and other varied locations appears to exhibit the correct qualitative, time-dependent behavior. In particular, the inhibition of uptake expected under both diffusion-limited and oxidation-limited conditions is well represented.
 The model was applied globally in order to ascertain the spatial distribution and seasonality of the methane uptake. As in previous studies (R99 and P96), tropical and subtropical forest and desert ecosystems are found to be the major consumers of atmospheric CH4; however, the present scheme allocates considerably more to subtropical forests (29%) and less to tropical forests (15%) than R99. The principal points of difference between the models are the larger mean diffusivity of CLASS, which increases uptake compared to the other schemes in the diffusion-limited regime, and the parameterized moisture factor rSM, typically much lower under dry conditions in the present model than in the model of R99, which decreases consumption in the moisture-limited regime.
 The current model could be improved by employing a variety of experimental data in the determination of the key parameters β and, especially, k0. While the latter is in principle location-independent, the variance about the mean value adopted here is still too large to justify a great deal of confidence. The 2σ limit on k0 gives a range of ≃0–1.4 × 10−4 s−1. Replacing the zero lower limit by a more reasonable (but still conservative) factor of 10 reduction and noting that J0 ∝ k01/2, I estimate an uncertainty range in the annual mean J0 = 28.0 Tg a−1 of 9–47 Tg a−1. While the rSM factor has been improved by linking soil moisture to observed microbial respiration thresholds, the latter may be somewhat different for methanotrophs specifically [e.g., Schnell and King, 1996; Torn and Harte, 1996]. Thus, further data on the response of methanotrophs to water stress may provide better estimates of these thresholds, to which the present model results are highly sensitive (section 4.1). Despite these caveats, however, the improved hydrological scheme and moisture parameterization of the present model represent an advance over previous work.
 The overall impact of greenhouse gas increases and subsequent global warming on soil methane consumption is a topic for future investigation using the present model. For a globally uniform temperature increment of 5°C, R99 found a modest change in annual mean uptake (≲8%), with the sign depending on the degree of soil moisture sensitivity to temperature. As mentioned in section 3, the counteracting effects of increased diffusion and decreased water potential that accompany decreasing soil moisture need to be modeled explicitly in order to determine the sign, much less the magnitude, of the change in methane consumption. The present scheme, which is readily adapted for use in a multiple component (atmosphere-ocean-biosphere) general circulation model, will allow a more definitive exploration of this issue.
 I am grateful to Derek van der Kamp for early work on this project, Vivek Arora for many helpful discussions and remarks on the manuscript, Diana Verseghy and Adam Draginda for help with CLASS and the meteorological data, respectively, and Steve Del Grosso for providing access to the Mosier et al.  methane uptake measurements. Comments by Jim Christian, Katrin Meissner, and two anonymous referees also improved the manuscript. The author is supported by the Canadian Foundation for Climate and Atmospheric Sciences, as part of the Canadian Global Coupled Carbon Climate Model (CGC3M) research network.