5.1. Spatial Variability of SOC Inventory and the Utility of Stratified Sampling
[14] Bird et al. [2001] has previously discussed the need for a relatively laborintensive stratified sampling regime for the purpose of obtaining reliable measurements of SOC inventory at large spatial scales necessary for global estimates and model validation. Previous work following this regime has demonstrated that the range of SOC_{TG} values obtained from single locations within one transect of five sampling locations can vary by nearly an order of magnitude [Bird et al., 2003]. Our measurements of average differences from the mean for five transects in each region shows that this error is reduced by using five transects, but there is still significant variation about the mean at these large regional scales (average of 18 and 24% of SOC_{TG} for 0 to 5 and 0 to 30cm intervals). Using bulked samples from 25 sampling locations, we have retained the accuracy and precision of the laborintensive sampling regime, but also reduced the analytical load that would otherwise be required for such large sample sets. We expect that the need for stratified sampling with a large number of sampling locations becomes more significant for the purpose of obtaining reliable measurements of stable and radiogenic isotopes at such large spatial scales (J. G. Wynn et al., A continentalscale measurement of the isotopic composition of soil organic carbon, Australia: Implications for modeling soil carbon dynamics, submitted to Global Biogeochemical Cycles, 2006) (hereinafter referred to as Wynn et al., submitted manuscript, 2006).
[15] Figure 5 shows the utility of stratifying the sample set across the distribution of vegetation physiognomy. The measured difference between SOC inventory at tree and grass locations is generally due to a higher SOC concentration in samples from tree locations, and occurs despite the fact that the mass concentration of solids (dry bulk density) is generally lower near trees. In cases where SOC_{G} exceeds SOC_{T}, this is generally due to a higher bulk density of the SOC_{G} samples rather than a higher concentration of SOC, and most likely reflects slightly better drained conditions at tree sites. A similar increase in variability between tree and grass locations with aridity is evident from the stable carbon isotopic composition (δ^{13}C) of SOC from this data set (Wynn et al., submitted manuscript, 2006). Veldkamp and Weitz [1994] similarly found δ^{13}C variance in tropical savanna systems to be greater by an order of magnitude compared with wetter and more homogenous ecosystems. Hence, by using a stratified sampling regime and f_{t} data to calculate regional SOC inventory weighted for the distribution of vegetation types (SOC_{TG}), we have removed the effects of biotic control by smallscale vegetation distribution and can examine the relationship of SOC_{TG} to climatic and edaphic controls over broad geographical regions. This methodology has provided more accurate representation of SOC inventory in arid climates, typical of most of Australia.
5.2. Climatic Controls SOC Inventory of Australian Sandy Soils
[16] Climatic controls on SOC inventory are commonly thought of in terms of mean annual precipitation and temperature because of their familiarity, data availability and ease of measurement [Amundson, 2001; Jobbágy and Jackson, 2000; Schimel et al., 1994]. However, we find that there is a much stronger correlation between our Australian SOC_{TG} data and W*, our index of water availability that is derived from annual measures of precipitation rate and global solar irradiance. This is because W* is a more accurate measure of the water potentially available to plants for photosynthesis. Climatic controls on SOC inventory are most fundamentally determined by the rate of input from biomass, and the rate of decomposition by heterotrophic microorganisms. The average annual rate of carbon fixation by vegetation, gross primary productivity (GPP), is very well correlated with the amount of water available to plants [Berry and Roderick, 2002, 2004; Roderick et al., 2001]. The availability of water in an environment (i.e., the soil store) is dependent on the rates of input (precipitation) and output (evaporation and net runoff). As solar irradiance increases, potential evaporation (E_{p}) increases, a factor that needs to be taken into account when considering the availability of water for plant growth, which is accomplished by use of W*. Operationally, a linear equation fit to W* explains much of the variance in the magnitude of SOC_{TG} (R^{2} = 0.73 and 0.82 for a linear fit). However, on the basis of theoretical constraints discussed below, we prefer to use a sigmoidal function,
to describe the relationship of SOC_{TG} to W*. The sigmoidal equation is a solution to the ordinary differential equation,
E_{SOC} is a term describing the efficiency of SOC storage per unit of water availability, and thus is related to water use efficiency of overlying plants (i.e., the water use efficiency of vegetation for assimilating organic carbon in soil). Λ is a term describing the density limitation to carbon assimilation as SOC (i.e., Λ is the slope of a linear equation between SOC decomposition rate to SOC_{TG}). This model is analogous to density limited growth of populations in time (logistic functions), and implies a density limitation of SOC inventory with respect to water availability. Using this parameter and equation, SOC_{TG} approaches a maximum SOC capacity of at some finite water availability. This sigmoidal equation provides a better fit to the data and is more appropriate to extension beyond the boundaries of the measured Australian data set because predicted SOC_{TG} can never be negative and reaches a maximum asymptote in soils with high W* (high precipitation, low solar radiation, or both). Also, as MAP approaches zero, GPP also approaches zero, as should the regional SOC inventory, SOC_{TG}. This parameter and equation provides more accurate estimates than other empirically based regressions based on global SOC data and MAP and MAT [e.g., Amundson, 2001], which under conditions near the boundaries of an observational data set can predict negative SOC inventory (for example at MAT = 25°C and MAP = 150 mm/yr), or fail to predict a value for SOC inventory (at MAT < 0). Least squares surface regressions for our relationship are shown in Figure 6, and are slightly better than other empirically based predictive equations. R^{2} values for least squares regression to the weighted data are relatively high: 0.83 and 0.86 for the 0 to 5 and 0 to 30cm depth intervals.
[17] Using the relationship to water availability alone, SOC_{TG} of welldrained sandy soils reaches a maximum of ∼110 mg/cm^{2} for the 0 to 5cmdepth interval and 335 mg/cm^{2} for the 0 to 30cmdepth interval, corresponding to maximum carbon densities of 0.022 and 0.011 g/cm^{3}, respectively. Both predictive equations reach a maximum decrease in the rate of change of change of slope (SOC‴_{TG}(W*) = 0, the “foldingvalue”) at 1835 mm/yr W*, and exhibit a maximum increase in the rate of change of change of slope at approximately 730 and 800 mm/yr W* for the 0 to 5 and 0 to 30cm intervals, respectively. The latter value is significant because it represents the limit to SOC inventory (below this point there is essentially zero SOC_{TG}). The threshold of 1835 mm/yr W* is most significant because it is the point above which the availability of water is no longer the dominant controlling variable of SOC_{TG}. A similar limitation by water availability on the mean fraction of photosynthetically active radiation (PAR) intercepted by the canopy over the annual period (_{v}) was observed by Berry and Roderick [2002] at W* of about 3000 mm/yr. _{v} is a primary determinant of mean annual GPP (i.e., the rate of photosynthesis [Berry and Roderick, 2004; Roderick et al., 2001]). The threshold of water availability on SOC_{TG} is somewhat lower than 3000 mm/yr most likely because of differences in the seasonal cycles of GPP and transfer of carbon from vegetation to soil, which are approximated by mean annual values here. Similar observations of precipitation limits to GPP and decomposition have been observed in the Great Plains of the United States by Sala et al. [1988] and Gholz et al. [2000], in which GPP increases more rapidly than decomposition between 300 and 800 mm/yr MAP.
[18] This model implies that in waterlimited environments (<1835 mm/yr W*), both production and decomposition rates of SOC increase linearly with respect to water availability, following the relationship described in equation (3). Above this threshold, environmental controls on photosynthesis are energy limited, and factors other than W* limit photosynthetic carbon fixation, such as availability of other nutrients, CO_{2}, inhibited decomposition and/or differences in radiative flux of PAR. Hence control of SOC_{TG} above this threshold is dominated by changes in nonhydrological factors which limit the rate of photosynthesis (GPP, such as nutrient status), or other factors driving the rate of SOC loss through decomposition or transport, such as energy control on SOC decomposition rate.
[19] The effect of temperature on the rate of decomposition is a known to be a primary climatic control on SOC inventory. It can be taken into account in equation (4) using the parameter Λ, which describes the density limitation on SOC loss through decomposition. In an analysis of the effect of temperature on soil respiration rate, Lloyd and Taylor [1994] describe an Arrhenius type equation in which respiration rate depends on temperature and SOC concentration,
where R is respiration rate (mol C/m^{2}/s), k_{R} is the temperaturedependent rate constant (s^{−1}), E is activation energy (J/mol), ℜ the universal gas constant (8.314 J/mol/K), T is absolute temperature (°K), and d is an empirical constant. We make the assumption that the density limitation to SOC decomposition is a similar function of temperature (due to the response of microbial activity) which can be described over the annual cycle as a function of MAT,
where d_{1} is another empirical constant. Using a constant value of 53,000 J/mol, a value which provides a reasonable fit to soil respiration data (Lloyd and Taylor [1994], and noting that E may vary somewhat with T), substitution into equation (3) yields
R^{2} values for least squares regression to this data increase slightly over the relationship to W* alone to 0.87 and 0.85 for the 0 to 5 and 0 to 30cmdepth intervals, although this relationship significantly reduces a trend in residuals above the threshold of 1835 mm/yr W* at which water availability is not the primary control on SOC inventory (Figure 7).
[20] Although we cannot directly compare the MAP and MATbased model of 1mdepth SOC inventory [Amundson, 2001] to our 5 and 30cmdepth intervals, a regression following the form of the equation of Amundson [2001] shows a somewhat worse fit to our data set (R^{2} = 0.80 for both the 0 to 5 and 0 to 30cmdepth intervals) than does our model based on water availability and temperature control of decomposition kinetics (W* and MAT with physically based model parameters and constants, R^{2} = 0.87 and 0.85). The predictions of our physically based regression model are reasonably comparable with the empirically based prediction of the 1mdepth SOC inventory from global data separated by ecosystems (SOC_{30cm}(W*, MAT) = 0.415[SOC_{1m}(MAP, MAT)], R^{2} = 0.71 [Amundson, 2001]). However, the simple MATMAP approach consistently underpredicts SOC_{TG} in our measured data for hot dry regions of Australia as compared to cool, wet regions. This may be due to the effect of preservation of a stable pool of SOC near trees in arid environments, a factor which is only accounted for by the stratified sampling regime used here. Our data show that in such arid climates, SOC is preferentially preserved at sampling locations near trees (SOC_{T}) as compared to locations away from trees (SOC_{G}, Figure 5).
[21] The regression equations presented here are good predictors of the magnitude of SOC_{TG} in welldrained sandy soils because variation in nutrient availability and nonclimatic factors controlling decomposition and transport losses are very limited in such soils. However, in the global range of soil types, decomposition and transport losses are additionally controlled by edaphic factors, which are addressed in this study in terms of soil texture in the following section. Other decomposition rate limiting factors include the hindrance of gas exchange (oxygen supply and CO_{2} release) by poor drainage in lowpermeability soils and chemical factors inhibiting decomposition rate. Factors controlling SOC loss through transport include loss of dissolved organic carbon to surface and groundwater discharge.
5.3. Extension to Soils of Other Textures
[22] Although edaphic controls on SOC_{TG} can be primarily attributed to a number of factors which control SOC decomposition and transport rates, we use a measure of soil texture (fraction of fine particles) to approximate the edaphic effects soil on SOC preservation. Fine textured soils can increase physical and hydrological protection of SOC by inhibiting decomposition, and physically protecting SOC, which increases both residence time and SOC content [Schimel et al., 1994]. We assume that the percent of soil that passes a 63μmdiameter sieve is the fraction active in retaining or stabilizing biomass decomposition products (soil in this study being defined as material that passes a 2mm sieve). This fraction is readily measurable and has been shown to contain the mineral fraction active in stabilizing the ^{13}Cenriched solid products of SOC decomposition [Šantrùčková et al., 2000; Wynn et al., 2005].
[23] We modify the relationships of SOC inventory to W* and MAT in order to separate the variance of measured SOC_{TG} that can be attributed to the role of soil texture, by calculating the degree to which a region is underpredicted (or “overmeasured”) by equation (7),
and attribute the magnitude of f_{SOC−underp.(W*, MAT)} to variation in the fraction of fine soil material, f_{<63μm} (Figure 8). Regions of variable soil with clustered W* and MAT values were sampled to examine variability in the nature of this relationship in several different climatic regions. Linear regression for specific climatic regions shows that much of the underpredicted values can be attributed to soil texture in some of the climatic regions sampled, but not in others. Table 1 shows regression values for an empirical linear fit to an equation,
for each of five climatic regions sampled in Australia for variation with soil texture (deserts, semiarid savannas, tropical rain forests, temperate rain forests). Although the correlation is mostly positive, R^{2} values vary from 0.03 to 0.62, and slopes vary from negative to 2.25. Some portion of this variability is likely in part due to the small number of regions used for each individual regression (n = 5–6), and variation of climate within the relatively large regions used (σ_{W*} = 23–408 mm/yr). However, from this data it appears that the role of SOC stabilization by fine mineral particles is diminished in cool, temperate environments (Tasmania), where other factors may play a more significant role in inhibiting SOC decomposition, particularly temperature control on respiration rates as discussed above.
Table 1. Regression Values for the Effect of Soil Texture on the Fraction of Underpredicted SOC^{a}  Climatic Region  0–5 cm  0–30 cm 

W*, mm/yr  σ_{W*}  MAT, °C  σ_{MAT}  A  B  R^{2}  A  B  R^{2} 


Deserts (BIR, INN, COR, ARR, NAP, DIA)  833  59  13.2  0.6  2.15  −0.413  0.6  1.33  −0.219  0.62 
Semiarid savannas (ANA, NEH, LAR, HAP, GRO, CRK)  1019  23  15.6  0.4  0.516  −0.239  0.03  1.10  −0.160  0.42 
Tropical rain forests (MUS, COE, BLE, KIR, KEN, HIN)  2334  143  17.2  1.3  2.25  −0.264  0.57  0.993  −0.439  0.49 
Temperate rain forests (STR, BRR, SCA, LOD, SCB)  4120  408  4.9  1.8  −0.817  −0.175  0.35  −0.59  −1.57  0.15 
[24] For the entire data set of both 0 to 5 and 0 to 30cm samples, correlation of the soil textural effect is generally very weak. The magnitude of the effect depends partially on temperature, and can be described by
The interrelationships between soil textural control and other potential factors that can inhibit decomposition are in need of further study, and here we use a simple linear empirical correlation. The effect of soil texture in the regions sampled can primarily be observed in climates above ∼10°C MAT, when the fine fraction exceeds ∼0.2, above which SOC_{TG} increases by a factor of about 50% of the predicted SOC_{TG} with respect to climatic variables alone.
[25] Using this equation and the previously described equations for the regression to W* and MAT, we find that SOC_{TG} variability with respect to two variables of climate and texture for the entire Australian soil data set can be defined by the function
In this analysis, adding soil texture to the regression analysis does not explain much more of the variance of SOC_{TG} than does the simple relationship to climate, although SOC_{TG} is very sensitive to f_{<63 μm}, especially in warmer regions. R^{2} values for least squares regression to this data increase slightly over the relationship to W* and MAT to 0.90 and 0.89 for the 0 to 5 and 0 to 30cmdepth intervals. In part, the poor fit is because the relative magnitude of the “noise” has been amplified by prior removal of the primary relationship to climate. However, poor correlation of SOC_{TG} with texture also stems from the oversimplification of using particle size to describe a variety of conditions that inhibit decomposition including interrelationships between climate and texture, variability of SOC_{TG} with clay mineralogy, specific surface area of clay minerals, and other soil textural factors not considered using the simple variable f_{<63μm}. Other factors which potentially attenuate decomposition rates such as soil nutrient chemistry [Cleveland et al., 2002; Neff et al., 2002] and hydrochemical factors [Freeman et al., 2001], need to be further considered and parameterized.
[26] Finally, to analyze the source of the remaining variance, we examine the degree to which a soil region is misfit by f(W*, MAT, f_{<63μm}), by using the residual from this modeled equation,
The residual variance can be attributed to factors attenuating SOC decomposition rates not taken into account by using soil texture as a variable, such as direct input of a stable pool of SOC from charcoal, or hydrochemical factors inhibiting decomposition which result in minimally decomposed particulate organic carbon (POC). Figure 9 shows that the regions with underpredicted, “excess” SOC_{TG} (SOC_{TG} > SOC_{TG}, commonly have either low ^{14}C activity (pM; Figure 9b), or high proportions of SOC attributable to charcoal (Figure 9a), or both. These factors indicate that some of the missed prediction is due to a relatively longterm stability of an “excess” pool of recalcitrant carbon, in the case of only a few outliers. Soil regions with high proportions of SOC attributable to charcoal include many of the finer textured soils of the savanna region of Queensland used in the textural analysis (CRK, GRO, LAR, not measured for ^{14}C activity), and other sandy soils in similar climatic regions (DAR, FIT). The accumulation of POC does not appear to be a factor causing any outliers to prediction of SOC_{TG} (Figure 9c), likely because most factors relating to slowed decomposition have been taken into account by climate and vegetation variables (MAT and stratified sampling). Overpredicted sites (where SOC_{TG} < are less significant and most commonly have ^{14}C activity (pM) similar to that of the modern atmosphere at the time of sampling, indicating a dominantly labile pool of recently assimilated SOC.