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Published online 28 September 2007
Published in Soil Sci Soc Am J 71:1719-1729 (2007)
DOI: 10.2136/sssaj2007.0051
© 2007 Soil Science Society of America
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PEDOLOGY

Applying a Quantitative Pedogenic Energy Model across a Range of Environmental Gradients

Craig Rasmussena,* and Neil J. Taborb

a Soil, Water and Environmental Science Dep., Univ. of Arizona, 1177 E. Fourth St., Shantz Bldg. Rm. 429, Tucson, AZ 85721-0038
b Dep. of Geological Sciences, 3225 Daniels Rd., Southern Methodist Univ., Dallas, TX 75275-0395

* Corresponding author (crasmuss{at}ag.arizona.edu).


   ABSTRACT
TOP
 NOTES
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Conceptual energy-based pedogenic models present a framework for quantitatively linking pedon energy throughflow to soil development. In this study, we utilized a quantitative pedogenic energy model (QPEM) based on rates of effective energy and mass transfer (EEMT, kJ m–2 yr–1) to the soil system to predict pedogenesis across a wide range of pedogenic environments. Our objectives were to: (i) derive a global equation for estimating EEMT; (ii) test the QPEM framework at the pedon scale across a series of environmental gradients on igneous rock residuum; and (iii) develop quantitative transfer functions between pedogenic indices and EEMT. We derived a simplified two-dimensional Gaussian expression for estimating EEMT from mean annual temperature (MAT) and mean annual precipitation (MAP) (R2 = 0.96, significant at P ≤ 0.001) using a global climate data set. Environmental gradient data indicated significant differences in EEMT between soil orders (i.e., Entisol = 14,586 vs. Ultisol = 36,521 kJ m–2 yr–1), whereas neither MAT nor MAP demonstrated significant differences among soil orders. Pedon data from the gradients were used to derive quantitative transfer functions between EEMT and pedogenic indices, including pedon depth, clay content, subsurface chemical index of alteration minus potassium (CIA–K), and the ratio of free Fe oxides to total Fe (Fed/FeT). Significant linear and nonlinear functions were derived between EEMT and all of the pedogenic indices, whereas no significant functions could be fit between pedogenic indices, MAT, or MAP. The favorable results from this study suggest that the QPEM framework and EEMT may provide a basis for quantitative pedogenic modeling and prediction of soil properties.

Abbreviations: AN, andesite • BS, basalt • CR, Cascade Range • CIA–K, chemical index of alteration minus potassium • EEMT, effective energy and mass transfer • ENPP, energy transfer from net primary production • ETp, potential evapotranspiration • Fed/FeT, ratio of free iron oxides to total elemental iron • GR, granite • IAEA, International Atomic Energy Administration • MAP, mean annual precipitation • MAT, mean annual temperature • NPP, net primary production • QPEM, quantitative pedogenic energy model • SN, Sierra Nevada Range • SSPM, Sierra San Pedro Martír


   INTRODUCTION
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Conceptual pedogenic models almost universally include climate parameters as implicit or explicit factors driving soil genesis (Dokuchaev, 1883; Jenny, 1941; Simonson, 1959; Runge, 1973; Johnson and Watson-Stegner, 1987). Soil "climofunctions" have been studied extensively in attempts to quantify the relationships between soil physicochemical characteristics and specific climate parameters (i.e., Jenny, 1941; Arkley, 1963; Yaalon, 1983; Alvarez and Lavado, 1998; Sheldon et al., 2002). The classic climofunction example of Jenny (1941) derived quantitative "transfer functions" between climate parameters and soil properties, such as organic N and clay content, based on data from a wide range of climate systems. Runge (1973) presented a conceptual pedogenic model modified from Jenny (1941) that focused on climatically derived energy input and flow through the pedon as the driving force of pedogenesis. In the Runge (1973) energy model, energy manifests as organic matter input (controlled by climate and nutrient supply) and the gravitational flux of water through the pedon. This model, while conceptual in nature, presents a framework for quantitatively linking climate or climofunctions, via energy flow through the pedon, to soil development. To date, only a few empirical studies have attempted to apply the Runge energy model or its derivatives to predict pedogenesis (Brye, 2004; Rasmussen et al., 2005; Schaetzl and Schwenner, 2006).

Brye (2004) used the Runge energy framework to correlate water flux and organic matter storage to degree of pedogenesis across a local-scale toposequence on a loess-covered, glaciated landscape in south-central Wisconsin. This study characterized pedon energy throughflow by estimating a kinetic energy flux from the amount and speed of water flux within a pedon, as well as the stored potential energy content of soil organic matter, estimated from its oxidation state. Schaetzl and Schwenner (2006) used the Runge energy model framework to characterize variation in soil development and podzolization in northern Michigan. They related soil morphologic and chemical properties to variability in drainage and water flux through the soil profile, highlighting the importance of water throughflow under the force of gravity for ordering and profile development. These studies demonstrated conceptually how the Runge energy model could be linked to quantitative profile data, but did not provide a soil-independent quantification of energy throughflow for predicting soil properties.

In contrast, Rasmussen et al. (2005) presented a general theory of quantitative energy transfer to soil systems based in part on the Runge energy framework. They used an estimated rate of energy input (EIN) that was derived independent of soil data to predict patterns of soil development across the continental USA. The EIN term presented in Rasmussen et al. (2005) represents the effective transfer of solar radiation to soil systems in the forms of energy and mass. To recognize the importance of energy and mass transfer, the term EIN will herein be referred to as the rate of effective energy and mass transfer (EEMT). The findings of Rasmussen et al. (2005) suggest that pedogenic indices related to soil development and mineral weathering may be quantitatively linked to the variation in EEMT and attendant changes in regional precipitation and temperature patterns, thereby providing a means to predict patterns in soil development from a common energy variable. The general framework presented in Rasmussen et al. (2005), and its refinement described here, is referred to as the quantitative pedogenic energy model (QPEM).

The objectives of this study were to: (i) derive a global equation for estimating EEMT based solely on mean annual temperature (MAT) and mean annual precipitation (MAP); (ii) test the QPEM framework at the pedon scale across a series of well-constrained environmental gradients; and (iii) develop quantitative transfer functions for predicting soil physical and chemical properties based on EEMT under the QPEM framework. Developing quantitative relationships between a common energy variable, such as EEMT, and soil physical and chemical properties is important for both modern and ancient soils (paleosols) to provide a quantitative means of assessing current and paleopedogenic environments.


   MATERIALS AND METHODS
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Quantitative Pedogenic Energy Model
Detailed derivation of the QPEM is given in Rasmussen et al. (2005) with a brief conceptual and methodological description presented here for context. Briefly, QPEM combines traditional conceptual models of ecosystem and soil formation with open-system thermodynamic concepts of system self-organization, entropy minimization, and free energy maximization (Dokuchaev, 1883; Jenny, 1941; Morowitz, 1968; Smeck et al., 1983; Schneider and Sagan, 2005). Open-system thermodynamic theory suggests that soil systems (pedons) will self-organize to optimize the use of energy flowing into and through the pedon as long as entropy is passed external to the pedon through dissipative processes (Odum, 1983; Addiscott, 1994; Anderson, 1995). It thus follows that a quantification of the rate of EEMT to a soil system should represent the pedogenic environment and the potential developmental state of that system (i.e., pedon depth, clay accumulation, degree of primary mineral weathering, or taxonomic class) (Rasmussen et al., 2005). The EEMT may be substituted into the generalized factorial model of Jenny (1961): S = f(Lo,Px,t), where S is the soil or system state, Lo is the initial state of the system, Px is external flux factors, and t is the age of the system. The initial state includes characteristics of the geologic substrate and topography, while the external flux factors are equivalent to EEMT derived from solar radiation and precipitation, such that the equation may be restated as: S = f(Lo,EEMT,t).

In the context of the QPEM framework, EEMT (that portion of solar radiation converted to a form important for pedogenesis) may be quantified in two forms: (i) heating of soil material and soil water; and (ii) reduction of C via photosynthesis. Heating of pedon water accelerates chemical and biological reaction rates, and transfers energy out of the pedon via the latent heat of evaporation and leaching. Net primary production (NPP) produces reduced C compounds that provide an energy source for microbial metabolism and drives mineral weathering via metabolic organic acids and CO2 production. The effective transfer of solar-radiation-derived energy to the pedon is dependent in large part on the presence and movement of water into and within the soil. Water is both a reactant in chemical and biological processes and a means to flux solar-radiation-derived energy through soil systems. In freely drained systems, water and energy will flow through the pedon following the gravitational potential.

Within the QPEM framework, the calculation of EEMT follows a traditional soil-water balance model (Arkley, 1963) and NPP estimate (Lieth, 1975a), and transforms the potential mass flux of water and reduced C into the soil to rates of energy transfer (kJ m–2 yr–1). Energy input from precipitation (P) and NPP are calculated from mean monthly temperature data and estimated effective precipitation (Peff = P – ETp, where ETp is potential evapotranspiration). The value of Peff (cm) is scaled to units of cm3 H2O cm–2 soil mo–1 assuming 1 cm is equivalent to 1 cm3 H2O cm–2 soil. Further, Peff is assumed to be heated from 0°C to the average temperature of air at the ground surface for each respective month ({Delta}T in K–1). The reference temperature of 0°C is selected under the assumptions that liquid water is the primary phase for soil chemical reactions and that the relative increase in temperature above 0°C corresponds to the increase in weathering potential of that liquid-phase water. The specific heat of water (4.18 kJ kg–1 K–1) is used to convert Peff (scaled to a mass of liquid H2O cm–2 of soil [unit time]–1 by assuming 1 cm3 H2O is equivalent to 1 g H2O) to an energy flux ({Delta}Q, referred to as EPPT), where EPPT = {Delta}T4.18Peff. Energy transfer to the system via EPPT is calculated for each month of positive Peff, and results summed for a total annual input of EPPT (kJ m–2 yr–1). The EPPT is assumed to be negligible and adjusted to a value of zero for months of negative Peff.

Net primary productivity is assumed to occur primarily when water is available in the soil profile (e.g., months with positive Peff) and light or solar irradiance is not limiting. Using the assumption that air temperature serves as a proxy for solar irradiance and plant physiological processes (Lieth, 1975a; Bonan, 1993), an empirical equation (Lieth, 1975a) is used to estimate monthly biomass production (g m–2 yr–1) from the mean monthly air temperature: NPPi = {3000/[1 + exp(1.315 – 0.119MATi)]}[daysi/(365 d)], where i is a month of positive Peff. Net primary productivity from all months with positive Peff is summed to provide an estimate of annual rates of NPP. Net primary productivity is converted to an energy flux (ENPP) assuming that 1 g of organic matter resulting from NPP is equivalent to 22 kJ (Lieth, 1975b): ENPP = 22NPP, and that all NPP is input to the soil system. The sum of ENPP and EPPT represents the total annual rate of EEMT (kJ m–2 yr–1) to the soil system: EEMT = ENPP + EPPT. Results from Rasmussen et al. (2005) indicated distinct spatial patterning of EEMT across the continental USA (Fig. 1 ; note that the term EEMT in the current study is equivalent to EIN in Rasmussen et al. [2005]).


Figure 1
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  		Fig. 1. Probability distribution of effective energy and mass transfer (EEMT) for the continental USA. The studied environmental gradients span a range of EEMT that represents >85% of the U.S. continental land mass. The inset shows the spatial distribution of EEMT for the USA derived from the PRISM climate data set (EEMT equivalent to EIN from Rasmussen et al., 2005).

 
Global Effective Energy and Mass Transfer Equation Derivation
The QPEM was originally developed using monthly precipitation and temperature data for the continental USA from the PRISM data set at a scale of 1:250,000, equivalent to 4-km pixel resolution (Daly et al., 1994). Using this data, a qualitative relationship was observed between MAP, MAT, and EEMT (Rasmussen et al., 2005), suggesting the potential to derive a quantitative estimate of EEMT based solely on MAP and MAT. For the current study, we utilized global weather station data compiled by the International Atomic Energy Administration (2004) to examine the relationship between MAP, MAT, and EEMT. The International Atomic Energy Administration (IAEA) data set consists of weather stations that occur at all longitudes, range from 76°N to 76°S latitude, and up to 3059 m above sea level, thereby describing climate-pattern variation from the vast majority of continental surface conditions. A quantitative relationship derived between MAP, MAT, and EEMT from this data should provide a general equation broadly applicable to estimation of effective energy and mass transfer into soil systems anywhere in the world. The QPEM framework was used to calculate Peff, EPPT, ENPP, and EEMT using monthly data from the IAEA data set. Various linear and nonlinear combinations of MAT and MAP were tested in an attempt to accurately quantify the MAT–MAP–EEMT relationship. The best-fit model was chosen based on minimization of model root mean square error and maximization of the regression coefficient between actual vs. predicted EEMT.

Field Setting for Pedon-Scale Application of the Model
A series of 21 well-drained soils from stable landscape positions on residual igneous bedrock was sampled across four elevation gradients between 40 and 30°N latitude along the west-facing slopes of the southern Cascade Range (CR; 121°37'W, 40°30'N) and Sierra Nevada Range (SN; 120°32'W, 38°34'N and 119°19'W, 37°1'N) of California, and the Sierra San Pedro Martír (SSPM; 115°36'W, 30°58'N) of Baja California, Mexico (Table 1 ). Transect parent materials encompassed three igneous rock types: granite (GR), andesite (AN), and basalt (BS). The CR transect included four sites developed on mid- to late-Pleistocene basalt flows (Jennings, 1977); the two SN soil transects included 14 sites derived from Miocene–Pliocene andesitic lahar deposits of the Mehrten Formation (seven sites; Piper et al., 1939), and Mesozoic granitic rocks that represent the plutonic core of the Sierra Nevada Range (seven sites; Jennings, 1977); the SSPM transect included three sites derived from granitic rocks (Minnich et al., 1997). The geomorphic age, while difficult to constrain, was assumed to be similar among sites, with the assumption that soil properties were in a relative steady state with mid- to late-Holocene climate conditions. The high-elevation CR and SN sites probably had permanent snowpack during glacial episodes, although there is no evidence of glaciers having reworked high-elevation materials among the study sites. While we recognize that eolian deposition may contribute to the mineral and cation assemblage at each site, it was assumed that the dominant parent material properties are inherited from the residual bedrock and that the observed variation in pedogenesis is dominantly attributable to variation in climate and EEMT.


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  		Table 1. Site characteristics for a series of environmental gradients from the southern Cascade, Sierra Nevada, and Sierra San Pedro Martir ranges on the west coast of North America.

 
Generally, along each transect, MAT decreased and MAP increased with elevation; the snowline (lower limit of winter snowfall) increased from roughly 1500 m at the higher latitude CR and SN transects (Alexander et al., 1993; Dahlgren et al., 1997; Rasmussen et al., 2007) to 2000 m toward the lower latitude SSPM (Minnich et al., 1997). All sites are characterized by a Mediterranean climate with hot, dry summers and cool, wet winters, and the primary source of moisture is derived from Pacific Ocean frontal systems. Data from the above-noted studies indicate that soil moisture regimes are dominantly xeric (i.e., winter wet), although higher elevation sites along the southern Cascades and Sierra Nevada transects may remain sufficiently moist during the summer months to classify as udic due to late melting of winter snowpack and summer thunderstorm activity. Soil temperature regimes progress from thermic (15–22°C) at low elevation to cryic (0–8°C) at high-elevation sites. Climate data (MAT and MAP) for the field sites represent a mix of local weather station data (i.e., data for SN granite sites from Dahlgren et al. [1997] and SSPM sites from Minnich et al. [1997]) and the 4-km-resolution PRISM data where local station data were not available. Field sites were separated by >4 km across the respective environmental gradients, such that the general trends in MAT and MAP presented in the PRISM data should represent gross climate patterns at each site. We recognize that local relief and landform attributes will modify local microclimate relative to the PRISM data; however, we specifically limited each site to similar landform and landscape position to minimize microclimatic variation among sites (see below for detail).

The dominant plant communities change along each environmental gradient in response to climatic variables. Along the higher latitude CR and SN transects, vegetation progresses from blue oak (Quercus douglasii Hook. & Arn.)-dominated oak woodlands at low elevation (150–700 m) through ponderosa pine (Pinus ponderosa C. Lawson), white fir [Abies concolor (Gordon & Glend.) Lindl. ex Hildebr.], and red fir (Abies magnifica A. Murray) mixed conifer communities at middle elevations (750–2300 m), to subalpine mixed conifer and alpine grassland communities at high-elevation (>2300-m) sites. Vegetation along the more arid, lower latitude SSPM transect progresses from a dominantly Adenostoma fasciculatum chaparral community at low elevation (900–1500 m), through a piñon (Pinus quadrifolia Parl. ex Sudw.) and A. fasciculatum (mixed piñon–chaparral) community at middle elevation (1500–2200 m), to a dominantly Jeffrey pine (Pinus jeffreyi Balf.) forest at high elevation (>2200 m).

The sites selected for this study allow relative control of geologic parent material composition and age of landscape, such that within each parent material, the generalized soil formation equation (Jenny, 1961) may be reduced to: S = f(Px)Lo,t or S = f(EEMT)Lo,t', where Lo (parent material) and t (time) are held constant, and EEMT varies between sites. For this study, we used four pedogenic indices as the S (soil state) parameter: (i) pedon depth (cm); (ii) pedon clay content (kg m–2); and two chemical weathering indices (iii) chemical index of alteration minus potassium (CIA–K) and (iv) the ratio of "free" Fe oxides to total elemental Fe (Fed/FeT). This approach allows development of quantitative transfer functions between S and EEMT both across the pooled data set and by individual parent materials. The impact of parent material on pedogenesis has long been recognized; however, a robust quantitative measure of the parent material effect is lacking, with parent material generally discussed in qualitative terms or through semiquantitative indices (Yaalon, 1975; Schaetzl and Anderson, 2005). The environmental gradients in this study span a parent material gradient from felsic, coarse-grained granitoid rocks to mafic, fine-grained basaltic rocks, and as such provide the opportunity to quantify how parent material moderates pedogenic response to EEMT, e.g., one may compare the parameters used to fit quantitative functions solving for S = f(EEMT)Lo,t among the parent materials (Lo).

As mentioned, the parent materials in this study span a compositional gradient from felsic granitoid to mafic basaltic and "intermediate" andesitic materials. A brief generalization of each rock type is provided for context. Briefly, granitic materials represent coarse-crystalline (phaneritic), intrusive, acid (low in base cation) igneous rocks with dominant minerals including quartz and feldspar (mainly orthoclase) associated with mica (biotite and muscovite) and minor mafic or ferromagnesian mineral components (amphibole and pyroxene). The dominance of these rocks by stable, silica-rich tectosilicates of large crystal size limits chemical weathering and favors physical weathering due to the relative ease of water infiltration into the rock matrix (Taylor and Eggleton, 2001). As such, soils derived from granitic parent materials generally exhibit deep profiles and saprolite layers with relatively low clay content (Schaetzl and Anderson, 2005). Formation of thick saprolite layers is further favored by the weathering of micas that includes hydration, oxidation of octahedral Fe2+ to free Fe3+ oxides, and the loss of interlayer K+ that allows interlayer expansion and physical degradation of the rock matrix (Nesbitt and Markovics, 1997).

Basaltic materials represent finely crystalline (aphanitic) extrusive igneous rocks rich in base cations (particularly Mg2+ and Ca2+) and ferromagnesian minerals, with mineral constituents including amphibole, pyroxene, olivine, and plagioclase feldspar, all of which are highly unstable in the weathering environment of the Earth's surface (Colman, 1982; Taylor and Eggleton, 2001). The extrusive character of these rocks promotes rapid mineral crystallization, resulting in a fine to very fine crystalline rock matrix that limits water infiltration. The combination of the fine-grained rock matrix with unstable minerals rich in Fe2+ and base cations favors formation of relatively shallow, clayey soil rich in Fe3+oxides and base cations (Schaetzl and Anderson, 2005).

Andesitic materials represent extrusive igneous rocks of fine to intermediate grain size, with a greater proportion of silica-rich minerals (sodic plagioclase feldspar, K feldspar, low-temperature quartz or cristobalite, and biotite) and less pyroxene and olivine relative to basaltic materials (Colman, 1982; Taylor and Eggleton, 2001). Andesitic-derived soils for this study were derived from a porous andesitic lahar representing a consolidated mix of volcanic ash, volcanic glass, and mudflow material. The nature of the andesitic material allows moderate ease of water infiltration into the rock matrix and an intermediate weathering pattern relative to granitic and basaltic materials.

Soil Physical and Chemical Characterization
Detailed soil physical properties for the CR and SN sample sites have been reported previously (Dahlgren et al., 1997; Rasmussen et al., 2006, 2007). Briefly, three pedons, separated horizontally by roughly 15 m, were sampled at each field site. Sampling sites were on summit positions, with a west to southwest aspect and slopes averaging 10 to 15% and did not exhibit evidence of human perturbation or accelerated erosion. Soil morphology was described in the field and samples collected by genetic horizon (Soil Survey Staff, 1999). All analyses were performed on the air-dried, <2-mm (fine-earth) fraction unless otherwise noted. Bulk density of surface soils (three replicates per horizon) was measured in the field using a hammer corer device (Blake and Hartge, 1986) for one pedon at each site. Sample weight and volume were corrected for coarse-fragment content (Soil Survey Staff, 2004). For subsurface horizons in the BS and AN parent materials, the high coarse fragment content made coring infeasible; therefore, we used bulk density data from field samples available from the NRCS Soil Survey Laboratory research database (ssldata.nrcs.usda.gov/ [verified 28 July 2007]) for the respective soil series located near our sampling sites.

Particle-size analysis was determined by the pipette method and wet sieving (Soil Survey Staff, 2004). Samples were pretreated with NaOCl at pH 9.5 to remove organic matter and dispersed by shaking with dilute sodium hexametaphosphate. Dispersed samples were wet sieved at 53 µm, and clay and silt (material <53 µm) collected for pipette analysis. Sands (>53 µm) were collected, dried at 105°C, and weighed. The data on the percentage of clay by weight from the particle-size analysis was converted to a mass per area (kg m–2) basis using bulk density, depth, and coarse fragment content for each horizon and summed for the entire pedon (Tan et al., 2004). Selective dissolution with citrate–dithionite was used to remove the "free" or "pedogenic" Fe oxides. Citrate–dithionite extraction consisted of shaking 4 g of soil for 15 h with 2 g of sodium dithionite and 100 mL of 0.3 mol L–1 sodium citrate to extract Fe (Fed) from organic complexes, some short-range-order aluminosilicates, and secondary forms of Fe oxyhydroxides (Parfitt and Childs, 1988; Dahlgren, 1994). Iron concentrations were determined by atomic absorption spectrophotometry (Weaver et al., 1968).

Total elemental analyses were performed on the fine-earth fraction of the first subsurface horizon sample from each soil profile, either a B, BC, or AC horizon, consistent with previous studies that have sought to relate soil chemical indices of alteration to ambient climate data (Sheldon et al., 2002; Sheldon and Retallak, 2004; Driese et al., 2005; Prochnow et al., 2006). Samples were analyzed for major element concentrations by x-ray fluorescence spectroscopy at the Center for Applied Isotope Studies (University of Georgia) and reported as weight percentage oxide components. Weight percentage oxide data (Table 2 ) were converted to molar ratios and used to calculate CIA–K (Maynard, 1992): CIA–K = [Al2O3/(Al2O3 + Na2O + CaO)]100. Large CIA–K values correspond to a greater degree of leaching and removal of base cations (Ca2+ and Na+), with a theoretical CIA–K of 100 for soils dominated by kaolinite [Al2Si2O5(OH)4] or gibbsite [Al(OH)3]. Furthermore, the molar ratio of free Fe oxides to total Fe oxide (Fed/FeT) was calculated as another index of chemical weathering.


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  		Table 2. Pedogenic indices for a range of soils from a series of environmental gradients in the Cascade, Sierra Nevada, and Sierra San Pedro Martir mountain ranges on the west coast of North America.

 
Statistical Analyses
Climate data (MAP and MAT), EEMT, and pedogenic indices (pedon depth, clay content, CIA–K, and Fed/FeT) from all transect sites were averaged by soil order and a one-way ANOVA performed by soil order to test for significant differences in pedogenic variables. The parameters pedon depth, clay content, CIA–K, and Fed/FeT were natural-log-transformed before ANOVA to meet assumptions of normality (Steel et al., 1997). Means were compared for significant differences using Tukey's honestly significant difference post hoc test at a 95% confidence interval. Mollisols were excluded from the ANOVA due to sample size (n = 1). Further, to derive transfer functions between EEMT and S (i.e., the soil state or pedogenic index), linear and nonlinear regression analyses were performed between EEMT and the pedogenic indices, with parameters fit through a least square means iterative process. Transfer functions were fit to the data set pooled across parent materials (n = 21) and by individual parent materials (n varies by parent material: BS, n = 4; AN, n = 7; GR, n = 10). All statistical analyses, curve fitting, and data manipulation were performed using JMP IN 5.1 (SAS Institute, Cary, NC) and SigmaPlot 8.0 (Systat Software, Point Richmond, CA).


   RESULTS AND DISCUSSION
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
CONCLUSIONS
 REFERENCES
 
Global Effective Energy Transfer Equation
Based on data from our previous study (Rasmussen et al., 2005), the distribution of EEMT varied substantially across the continental USA, with the majority of the land area receiving relatively low rates of effective energy and mass transfer (<15,000 kJ m–2 yr–1) (Fig. 1). In general, low EEMT was a function of a lack of effective precipitation, thereby limiting NPP and leaching of water through the soil. In the previous study, EEMT was derived from monthly temperature and precipitation data, thereby requiring an exhaustive climate data set. In the previous study, however, a qualitative relationship between EEMT, MAT, and MAP was observed, suggesting the potential to calculate EEMT solely from MAT and MAP. Deriving a quantitative relationship between EEMT, MAT, and MAP would preclude the necessity for monthly climate data and allow characterization of effective energy and mass transfer based on more commonly available annual estimates of climate properties.

For the current study, we used the monthly time scale IAEA global climate data set to calculate EEMT (as noted above) and derive a quantitative relationship between EEMT, MAT, and MAP. Calculated EEMT values exhibited a highly significant correlation (R2 = 0.96, P < 0.001) with MAT and MAP data when a two-dimensional Gaussian function was considered (Fig. 2 ). The Gaussian function provided the following equation describing the derivation of EEMT:

Formula 1[1]
where EEMT represents the estimated rate of effective energy and mass transfer into the soil system (kJ m–2 yr–1), and MAT and MAP represent mean annual temperature (°C) and mean annual precipitation (mm), respectively. The parameters of the equation represent the following: 347,134 kJ m–2 yr–1 is the maximum EEMT at the peak of the Gaussian function; 21.5°C and 4412 mm are the MAT and MAP where EEMT equals 347,134 kJ m–2 yr–1; and –10.1°C and 1704 mm are fitting parameters that describe the width of the Gaussian function.


Figure 2
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  		Fig. 2. Modeled relationship between mean annual precipitation (MAP), mean annual temperature (MAT), and effective energy and mass transfer (EEMT) derived from the global climate data set of the International Atomic Energy Administration (IAEA). The contour surface represents the best-fit two-dimensional Gaussian function. Symbols indicate the IAEA data used to derive the relationship.

 
As a test of the effectiveness of Eq. [1], we compared EEMT from the previous study (Rasmussen et al., 2005), which was calculated using monthly PRISM climate data and the data exhaustive monthly time step method (referred to as EEMTPRISM), with EEMT calculated using Eq. [1] and MAT and MAP data from the PRISM data set (referred as EEMTIAEA). Use of comparable data sets (monthly vs. annual PRISM temperature and precipitation data) allowed direct comparison of EEMT values on a pixel-by-pixel basis across the continental USA (Fig. 3 ). Comparison of EEMTIAEA and EEMTPRISM values indicated a highly significant relationship (R2 = 0.90, P < 0.001; slope = 1.2), suggesting that Eq. [1], derived from only two variables, accurately predicted the EEMT values across the continental USA derived from a monthly time step. The greatest difference between the two EEMT values was at high EEMT, where EEMTIAEA underestimated EEMTPRISM (Fig. 3). We consider the highly significant relationship between EEMT, MAT, and MAP obtained from the IAEA data set, in conjunction with the favorable comparison between EEMTIAEA and EEMTPRISM to indicate that Eq. [1] provides a reasonable estimate of EEMT across a range of climates based solely on MAT and MAP. As such, all following discussion of EEMT will apply to the relationship derived from the IAEA data set.


Figure 3
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  		Fig. 3. Comparison of effective energy and mass transfer (EEMT) derived from the PRISM data set using the data exhaustive monthly time series (EEMTPRISM) to EEMT calculated using the quantitative two-dimensional Gaussian relationship between mean annual precipitation (MAP), mean annual temperature (MAT), and EEMT derived from the global climate data set of the International Atomic Energy Administration (EEMTIAEA). The black line represents the 1:1 line.

 
Soil Taxonomy and Pedogenic Indices
The environmental gradients span a range of EEMT values that represent >85% of the modeled EEMT for the continental USA (Table 1, Fig. 1). As such, quantitative relationships derived between EEMT and pedogenic indices for these sites should apply across a wide geographic area. Observed patterns in pedogenesis and soil chemico-physical properties across the environmental gradients were reflected in soil taxonomic classification (Tables 1 and 2). Across the high-latitude (37–40°N) CR and SN gradients, indicators of soil development (pedon depth, reddening, subsurface clay accumulation) increased with increasing elevation, reaching a maximum in the mid-elevation (900–1400-m) ponderosa pine-dominated systems, and subsequently decreased at higher elevations. Soils graded from Mollisols, Inceptisols, and Alfisols at lower elevation sites to deep, well-developed clay- and free Fe oxide-rich Alfisols and Ultisols at mid-elevation sites, to weakly developed Andisols, Inceptisols, and Entisols at high-elevation sites. The latter, relatively weakly developed soils were found above 1600-m elevation, corresponding to the shift in precipitation type from dominantly rain to snow. Previous studies (Alexander et al., 1993; Dahlgren et al., 1997; Rasmussen et al., 2007) suggested a threshold in weathering processes related to the shift from rain- to snow-dominated climate systems. In contrast, all soils along the low-latitude (30°N) SSPM transect were classified as weakly developed Entisols, reflecting minor variation in soil morphology and development. The uniform and weak development of these soils corresponds to limited weathering resulting from the generally arid conditions at these sites (Table 1).

The ANOVA indicated distinct patterns in pedogenic indices and climate parameters by soil order (Table 3 ). Of particular interest was the lack of significant difference in climate parameters (MAP and MAT) among soil orders, whereas EEMT demonstrated distinct and significant differences by soil order. Average soil order EEMT values corroborate those observed in the continental-scale analysis of Rasmussen et al. (2005), and follow theoretical pedogenic trajectories (Smeck et al., 1983) where Ultisols exhibit significantly greater EEMT (an average of 36,500 kJ m–2 yr–1) than the other soil orders, followed by Alfisols, Andisols, Inceptisols, and Entisols in order of decreasing EEMT (Table 3). Pedogenic indices also demonstrated significant variation by soil order that corresponded well with the average soil order EEMT (Table 3). Ultisols possessed significantly greater values than the other soil orders for all reported indices (pedon depth, clay content, CIA–K, and Fed/FeT). Specifically, Ultisols were twice as deep (200 vs. 100 cm) and contained three times the total pedon clay content (1133 vs. 323 kg m–2) relative to Alfisols, and demonstrated substantial leaching of cations relative to Al (CIA–K of 98%) and near-complete transformation of elemental Fe to free Fe oxides (Fed/FeT of 82%).


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  		Table 3. Average of pedogenic indices (±SE) and effective energy and mass transfer (EEMT) by soil order across a series of environmental gradients along the west coast of North America.

 
Model-Derived Pedogenic Transfer Functions
Significant variation in EEMT, coupled with a lack of significant difference in MAP and MAT among soil orders (Table 3), indicates that EEMT and the QPEM framework better describes pedogenic regimes and soil development relative to MAT and MAP across the observed sites. Indeed, comparison of pedogenic indices to MAP and MAT across the environmental gradients indicated little to no relationship (Fig. 4 ). In contrast, all of the pedogenic indices demonstrated a significant relationship with EEMT, both on the pooled data set and by individual parent materials (Fig. 5 , Table 4 ). Variation in parent material significantly affected the observed relationships between pedogenic indices and EEMT. Derived quantitative EEMT transfer functions are discussed in detail below.


Figure 4
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  		Fig. 4. Pedogenic indicators plotted against mean annual precipitation (MAP): (A) pedon depth; (B) total pedon clay content; (C) free Fe oxide to total Fe oxide ratio (Fed/FeT) of the first subsurface genetic horizon; and (D) the chemical index of alteration minus potassium (CIA–K) of the first subsurface genetic horizon. Data derived from pedons sampled from stable landscape positions across four environmental gradients on basalt, andesite, and granite parent materials.

 

Figure 5
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  		Fig. 5. Pedogenic indicators regressed against effective energy and mass transfer (EEMT): (A) pedon depth; (B) total pedon clay content; (C) free Fe oxide to total Fe oxide ratio (Fed/FeT) of the first subsurface genetic horizon; and (D) the chemical index of alteration minus potassium (CIA–K) of the first subsurface genetic horizon. Plotted lines and equations represent the best-fit regression to the data. Data derived from pedons sampled from stable landscape positions across four environmental gradients on basalt, andesite and granite parent materials.

 

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  		Table 4. Equations and parameters for predicting pedogenic indices from effective energy and mass transfer (EEMT){dagger}.

 
Pedon Depth
Pedon depth exhibited positive and significant exponential relationships with EEMT across the pooled data set (R2 = 0.45, P < 0.001) and when considered by individual parent materials (Fig. 5, Table 4). The EEMT exhibited only a moderate and insignificant relationship (r2 = 0.44, P = 0.33) to pedon depth across the BS sites. The lack of predictive power for this parent material may be a function of the small data set for BS-derived pedons (n = 4). In contrast, EEMT exhibited a highly significant relationship with pedon depth in the andesitic and granitic parent materials (r2 = 0.90, P < 0.001 and r2 = 0.67, P < 0.01, respectively) (Table 4). Equation parameters quantify specific variation in parent material response to EEMT and profile deepening. Data for GR indicated the shallowest profiles at the y intercept, or zero EEMT (i.e., 7-cm depth relative to 14- and 12-cm depths in AN- and BS-derived soils, respectively). The inverse of the rate constant parameter (1/b), however, which approximates the EEMT required for a unit increase in pedon depth, was equal to 7800 kJ m–2 yr–1 in GR-derived soils relative to 14,300 and 13,300 kJ m–2 yr–1 in AN and BS soils, indicating less EEMT required to deepen GR profiles. The variation by parent material may well correspond to grain size and mineralogy control of weathering characteristics. Coarse-grained physical weathering dominates in granitic materials and may favor rapid profile deepening relative to the fine-grained chemical weathering that dominates in andesitic and basaltic materials.

Clay Content
Pedon clay content exhibited a positive and highly significant exponential relationship to EEMT both across the pooled data set (R2 = 0.75, P < 0.001) and by individual parent materials (Fig. 5, Table 4). In particular, the pooled data set indicated a threshold near an EEMT value of 20,000 kJ m–2 yr–1, below which clay content was minimal and above which clay content increased rapidly (Fig. 5). It should be noted that this EEMT threshold also corresponds with the observed difference in EEMT between Alfisols and Ultisols (Table 3). The clay content–EEMT transfer function explained >94% of the variance for each parent material, with highly significant exponential functions fit to each (Table 4). Pedon clay content at the y intercept, or zero EEMT, was greatest in AN (0.2 kg m–2) and least in GR (0.04 kg m–2) derived soils. Variation in the y intercept may be a function of parent material grain size and mineralogical composition, with AN-derived soils forming from a mix of consolidated volanic ash and mudflow material that inherently contains a greater fine-earth fraction (including volcanic glass and possibly hydrothermally altered materials consisting of clay-size material) on deposition relative to the coherent crystalline structure and mineralogy of BS and GR materials, respectively. The inverse of the rate constant parameter (1/b) suggested that GR-derived soils required less EEMT to produce an equivalent amount of total pedon clay (2600 kJ m–2 yr–1 relative to 3600 and 4500 kJ m–2 yr–1 in BS and AN soils) and appeared contradictory relative to the mineral assemblage of the respective parent materials. This result is probably related to the fact that pedon clay content (kg m–2) takes into account pedon depth, so while GR soils may have less clay on a mass percentage basis, greater pedon depth in GR soils results in a relatively low EEMT threshold for clay accumulation. Relative to AN soils, BS-derived soils demonstrated a lower EEMT threshold for clay accumulation that fits with the general weatherability of the dominant AN and BS primary minerals.

Subsurface Iron Oxide and Alteration Indices
The pedogenic indicators Fed/FeT and CIA–K of subsurface horizons exhibited highly significant linear relationships with EEMT (Table 4). The EEMT explained >80% of the variance in observed Fed/FeT values for the pooled data set and 70 to 96% of the variance among individual parent materials (Fig. 5, Table 4). The relative increase in Fed/FeT per unit of EEMT (1/a) indicated that BS-derived soils were the most sensitive to EEMT, i.e., an increase of one unit of Fed/FeT only required 324 kJ m–2 yr–1, whereas GR- and AN-derived soils required 431 and 446 kJ m–2 yr–1, respectively. This pattern fits with the mineral assemblage of the BS parent materials dominated by primary minerals rich in Fe2+ that rapidly weather to secondary minerals and Fe3+ oxides at the Earth's surface. Similarly, CIA–K values also exhibited a significant linear relationship with EEMT across pooled data (R2 = 0.76, P < 0.001) and among individual parent materials (Fig. 5, Table 4). The relative EEMT needed for a unit increase of CIA–K (1/a) followed expected patterns by parent material, i.e., BS-derived soils required greater EEMT (588 kJ m–2 yr–1) to increase CIA–K, whereas GR-derived soils required the least EEMT (500 kJ m–2 yr–1) to increase CIA–K by one unit (Table 4). Given the base-cation-rich nature of the BS primary mineral assemblage (particularly Ca2+ and Na+ present in pyroxenes, amphiboles, and plagioclase feldspars), it fits that greater EEMT was required to reduce the overall abundance of CaO and Na2O in the profile. Generally, granitic materials lack significant CaO or Na2O such that less EEMT was required to reduce the overall abundance of cations relative to Al2O3.

Given the theoretical end point values of 100% for CIA–K and Fed/FeT, it must be assumed that the linear relationships presented above probably do not represent pedogenic regimes with EEMT greater than ~40,000 kJ m–2 yr–1, where the values for each index would be estimated at or above 100%. We therefore posit that the relationship between EEMT and these variables assumes a sigmoidal function that rises to a maximum asymptote near or at 100%. Applying a sigmoidal function to EEMT and the CIA–K and Fed/FeT from the pooled data set derived significant relationships for each index (Fig. 6 ). The sigmoidal transfer functions suggest that the observed environmental gradients span the EEMT range of rapid and significant subsurface horizon mineral weathering. Beyond this EEMT range, it is likely that subsurface B horizons will be significantly depleted in base cations and dominated by free Fe oxides. Similar relationships may also be derived between EEMT, depth, and clay content, but it is difficult to constrain the upper limit of these parameters at this time.


Figure 6
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  		Fig. 6. Hypothesized sigmoidal transfer functions relating (A) the free Fe oxide to total Fe oxide ratio (Fed/FeT) of the first subsurface genetic horizon and (B) the chemical index of alteration minus potassium (CIA–K) of the first subsurface genetic horizon to effective energy and mass transfer (EEMT). Prediction equation, parameters, regression coefficient and P value inset in each figure. Data derived from pedons sampled from stable landscape positions across four environmental gradients on basalt, andesite and granite parent materials.

 
The sigmoidal transfer functions presented in Fig. 6 represent hypothesized relationships and provide testable hypotheses that may be vetted with further field data. Data mining of existing soil data sets and further field sampling of residual materials on stable Holocene-age landscapes would facilitate testing these hypotheses and provide a more robust set of quantitative transfer functions between EEMT and pedogenic indices. Furthermore, the current analysis focused on systems of assumed similar relative age, such that the rate of EEMT may be used as the prediction parameter. A more robust approach would be to sample landscapes of quantifiable age on Holocene landscapes where one can assume relatively constant climate patterns during the formation of that soil. This would allow the inclusion of time as an independent variable and calculation of an absolute EEMT (kJ m–2) that could be used as a prediction parameter rather than a rate, as presented here.


   CONCLUSIONS
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
REFERENCES
 
This study utilized and refined the QPEM framework for quantitatively modeling pedogenesis on residual igneous parent materials based on a predicted EEMT. We derived a simplified expression for estimating EEMT based solely on MAT and MAP using data from a global climate data set. The global climate data set encompassed climate systems from all areas of the Earth's surface and, as such, the derived equation should be applicable to the majority of Earth surface systems. We further used pedon data from a range of environmental gradients on residual igneous parent materials to derive quantitative transfer functions between EEMT and a suite of pedogenic indices (pedon depth, clay content, and subsurface CIA–K and Fed/FeT). The environmental gradients encompass >85% of the predicted rates of EEMT for the continental USA such that the derived transfer functions should be applicable to soils formed from residual igneous materials across a relatively large geographic area. Furthermore, we present a hypothetical sigmoidal relationship between EEMT and pedogenic indices that may be tested and refined with further field sampling or data acquisition. The favorable results from this study suggest that the QPEM framework may provide a basis for quantitative pedogenic modeling. Further extension of QPEM to a wider variety of parent materials and to landscapes of known absolute Holocene age will permit further refinement of the presented transfer functions and facilitate incorporation of time as an independent factor.


   ACKNOWLEDGMENTS
 
The conceptual nature of this work benefited from discussion amongst the University of Arizona Critical Zone Work Group.


   NOTES
TOP
 NOTES
ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Permission for printing and for reprinting the material contained herein has been obtained by the publisher.

Received for publication February 6, 2007.


   REFERENCES
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 




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