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

Applying a Quantitative Pedogenic Energy Model across a Range of Environmental Gradients Craig Rasmussen* Soil, Water and Environmental Science Dep. Univ. of Arizona 1177 E. Fourth St. Shantz Bldg. Rm. 429 Tucson, AZ 85721-0038

Neil J. Tabor Dep. of Geological Sciences 3225 Daniels Rd. Southern Methodist Univ. Dallas, TX 75275-0395

PEDOLOGY

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.

C

onceptual 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 cli-

Soil Sci. Soc. Am. J. 71:1719–1729 doi:10.2136/sssaj2007.0051 Received 6 Feb. 2007. *Corresponding author ([email protected]). © Soil Science Society of America 677 S. Segoe Rd. Madison WI 53711 USA 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.

SSSAJ: Volume 71: Number 6 • November–December 2007

matically 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, 1719

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 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 1720

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 (ΔT 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 (ΔQ, referred to as EPPT), where EPPT = ΔT4.18Peff. 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]).

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 SSSAJ: Volume 71: Number 6 • November–December 2007

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 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 quantify the MAT–MAP–EEMT relaU.S. continental land mass. The inset shows the spatial distribution of EEMT for the USA detionship. The best-fit model was chosen rived from the PRISM climate data set (EEMT equivalent to EIN from Rasmussen et al., 2005). based on minimization of model root and the primary source of moisture is derived from Pacific Ocean fronmean square error and maximization of tal systems. Data from the above-noted studies indicate that soil moisture the regression coefficient between actual vs. predicted EEMT. regimes are dominantly xeric (i.e., winter wet), although higher elevation Field Setting for Pedon-Scale Application sites along the southern Cascades and Sierra Nevada transects may remain sufficiently moist during the summer months to classify as udic due to of the Model late melting of winter snowpack and summer thunderstorm activity. Soil A series of 21 well-drained soils from stable landscape positions temperature regimes progress from thermic (15–22°C) at low elevation to on residual igneous bedrock was sampled across four elevation gradients cryic (0–8°C) at high-elevation sites. Climate data (MAT and MAP) for between 40 and 30°N latitude along the west-facing slopes of the southern the field sites represent a mix of local weather station data (i.e., data for SN Cascade Range (CR; 121°37′W, 40°30′N) and Sierra Nevada Range (SN; granite sites from Dahlgren et al. [1997] and SSPM sites from Minnich et 120°32′W, 38°34′N and 119°19′W, 37°1′N) of California, and the Sierra al. [1997]) and the 4-km-resolution PRISM data where local station data San Pedro Martír (SSPM; 115°36′W, 30°58′N) of Baja California, Mexico were not available. Field sites were separated by >4 km across the respective (Table 1). Transect parent materials encompassed three igneous rock types: environmental gradients, such that the general trends in MAT and MAP granite (GR), andesite (AN), and basalt (BS). The CR transect included presented in the PRISM data should represent gross climate patterns at each four sites developed on mid- to late-Pleistocene basalt flows (Jennings, site. We recognize that local relief and landform attributes will modify local 1977); the two SN soil transects included 14 sites derived from Miocene– microclimate relative to the PRISM data; however, we specifically limited Pliocene andesitic lahar deposits of the Mehrten Formation (seven sites; each site to similar landform and landscape position to minimize microcliPiper et al., 1939), and Mesozoic granitic rocks that represent the plutonic matic variation among sites (see below for detail). core of the Sierra Nevada Range (seven sites; Jennings, 1977); the SSPM The dominant plant communities change along each environmentransect included three sites derived from granitic rocks (Minnich et al., tal gradient in response to climatic variables. Along the higher latitude CR 1997). The geomorphic age, while difficult to constrain, was assumed to and SN transects, vegetation progresses from blue oak (Quercus douglasii be similar among sites, with the assumption that soil properties were in Hook. & Arn.)-dominated oak woodlands at low elevation (150–700 m) a relative steady state with mid- to late-Holocene climate conditions. The through ponderosa pine (Pinus ponderosa C. Lawson), white fir [Abies conhigh-elevation CR and SN sites probably had permanent snowpack during color (Gordon & Glend.) Lindl. ex Hildebr.], and red fir (Abies magnifica glacial episodes, although there is no evidence of glaciers having reworked A. Murray) mixed conifer communities at middle elevations (750–2300 high-elevation materials among the study sites. While we recognize that m), to subalpine mixed conifer and alpine grassland communities at higheolian deposition may contribute to the mineral and cation assemblage at elevation (>2300-m) sites. Vegetation along the more arid, lower latitude each site, it was assumed that the dominant parent material properties are SSPM transect progresses from a dominantly Adenostoma fasciculatum inherited from the residual bedrock and that the observed variation in pedochaparral community at low elevation (900–1500 m), through a piñon genesis is dominantly attributable to variation in climate and EEMT. (Pinus quadrifolia Parl. ex Sudw.) and A. fasciculatum (mixed piñon–chapGenerally, along each transect, MAT decreased and MAP increased arral) community at middle elevation (1500–2200 m), to a dominantly with elevation; the snowline (lower limit of winter snowfall) increased from Jeffrey pine (Pinus jeffreyi Balf.) forest at high elevation (>2200 m). roughly 1500 m at the higher latitude CR and SN transects (Alexander et The sites selected for this study allow relative control of geologic paral., 1993; Dahlgren et al., 1997; Rasmussen et al., 2007) to 2000 m toward ent material composition and age of landscape, such that within each parthe lower latitude SSPM (Minnich et al., 1997). All sites are characterized ent material, the generalized soil formation equation (Jenny, 1961) may be by a Mediterranean climate with hot, dry summers and cool, wet winters, SSSAJ: Volume 71: Number 6 • November–December 2007

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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. Parent material

Mountain range†

Soil taxonomy‡

Elevation§ m

BS-4

basalt

CR

Typic Xerorthent

2300

BS-3

basalt

CR

Typic Haploxerept

1600

BS-2

basalt

CR

Xeric Haplohumult

BS-1

basalt

CR

AN-7

andesite

AN-6

Sample

MAT¶

MAP¶

EEMTIAEA#

°C

mm

kJ m−2 yr−1

6.5

1340

12,889

8.3

1150

21,522

920

14.2

990

35,403

Typic Rhodoxeralf

280

16.7

780

31,120

SN

Humic Lithic Dystrocryept

2700

3.0

1520

14,854

andesite

SN

Vitrandic Dystrocryept

2450

4.5

1400

17,159

AN-5

andesite

SN

Humic Vitrixerand

2150

7.6

1350

20,779

AN-4

andesite

SN

Typic Melanoxerand

1700

11.3

1300

28,136

AN-3

andesite

SN

Andic Palehumult

1150

13.3

1250

37,638

AN-2

andesite

SN

Ultic Haploxeralf

520

15.6

780

28,989

AN-1

andesite

SN

Lithic Ultic Haploxeroll

160

17.0

460

21,306

GR-7

granite

SN

Entic Cryumbrept

2850

3.9

1270

13,476

GR-6

granite

SN

Dystric Xeropsamment

2300

7.2

1080

18,457

GR-5

granite

SN

Humic Dystroxerept

1800

9.1

1010

21,932

GR-4

granite

SN

Ultic Haploxeralf

1400

11.1

910

24,461

GR-3

granite

SN

Ultic Haploxeralf

670

14.4

620

22,682

GR-2

granite

SN

Ultic Haploxeralf

560

15.0

570

22,123

GR-1

granite

SN

Typic Xerorthent

200

16.7

330

17,553

BJ-3

granite

SSPM

Typic Xeropsamment

2424

7.4

626

10,942

BJ-2 granite SSPM Lithic Xeropsamment 1738 12.2 454 15,092 BJ-1 granite SSPM Typic Xerorthent 1021 17.1 275 16,658 † Mountain range and general location: CR, southern Cascade Range, California; SN, Sierra Nevada, California; SSPM, Sierra San Pedro Martir, Baja California, Mexico. ‡ Great group level of classification (Soil Survey Staff, 2003). § Elevation data reported from 7.5′ quadrangle map readings. ¶ MAT, mean annual temperature; MAP, mean annual precipitation. # Effective energy and mass transfer (EEMT) calculated using the quantitative two-dimensional Gaussian relationship between MAP, MAT, and EEMT derived from the global climate data set of the International Atomic Energy Administration.

reduced to: S = f(Px)L ,t or S = f(EEMT)L ,t, where Lo (parent material) and o o 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 1722

(amphibole and pyroxene). The dominance of these rocks by stable, silicarich 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 SSSAJ: Volume 71: Number 6 • November–December 2007

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. Sample

Pedon depth

Clay†

cm

kg m−2

Major oxides‡ Na2O

MgO

BS-4 76 46 2.3 6.0 BS-3 60 41 2.7 3.3 BS-2 200 1406 0.2 0.7 BS-1 50 424 0.6 1.3 AN-7 49 31 3.0 2.7 AN-6 62 30 2.7 2.7 AN-5 79 16 1.4 3.7 AN-4 83 15 1.1 3.8 AN-3 200 861 0.0 0.3 AN-2 90 187 0.2 0.4 AN-1 42 67 1.6 1.8 GR-7 71 32 ND†† ND GR-6 81 58 2.8 0.4 GR-5 173 175 2.1 3.1 GR-4 180 536 0.3 0.7 GR-3 119 302 2.6 1.3 GR-2 79 167 ND ND GR-1 57 79 ND ND BJ-3 60 67 4.1 1.7 BJ-2 30 31 3.0 2.4 BJ-1 36 78 3.5 2.6 † Sum of clay content for the entire pedon.

Al2O3

SiO2

P2O5

K2O

CaO

TiO2

MnO Fe2O3 LOI§

——————————— % (w/w) ——————————— 19.1 48.0 0.2 0.9 4.5 0.9 0.1 9.1 20.7 49.0 0.1 1.3 3.7 0.9 0.1 7.1 28.5 39.1 0.1 0.4 0.3 1.6 0.1 13.4 22.4 47.9 0.2 0.5 0.8 1.8 0.4 14.9 18.3 51.4 0.3 1.5 5.2 1.0 0.1 8.1 18.9 50.8 0.2 1.4 4.7 1.0 0.1 8.0 21.5 39.5 0.2 0.7 2.9 1.1 0.2 9.6 19.8 39.2 0.2 0.8 3.1 1.3 0.2 10.9 27.5 37.8 0.1 0.2 0.1 1.4 0.0 11.8 25.6 43.3 0.1 0.7 0.4 1.3 0.1 11.2 18.9 51.5 0.1 1.0 2.6 1.2 0.1 10.3 ND ND ND ND ND ND ND ND 15.2 70.4 0.1 4.3 1.3 0.2 0.1 2.1 17.6 55.5 0.4 2.0 5.0 1.0 0.1 7.9 18.1 65.1 0.0 2.8 0.2 0.6 0.1 4.3 18.0 63.6 0.1 2.2 3.2 0.5 0.1 4.2 ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND 18.0 62.4 0.1 1.4 4.5 0.8 0.1 4.3 17.3 60.7 0.1 2.0 4.2 0.8 0.1 5.4 17.9 58.0 0.1 0.7 5.1 0.9 0.1 6.3

9 12 16 10 8 9 19 19 21 17 11 ND 4 6 8 5 ND ND 3 4 5

Total 100 101 100 101 100 100 100 100 100 100 100 ND 101 101 100 101 ND ND 100 100 100

CIA–K¶

Fed/FeT#

— mol % — 61 20 65 33 97 85 90 74 56 34 59 26 74 19 73 33 99 80 96 59 72 34 ND ND 69 18 58 20 96 43 64 40 ND ND ND ND 55 12 58 10 54 17

‡ Major oxide percentage by weight values have an uncertainty of ±0.2%. § Loss on ignition. ¶ Chemical index of alteration minus K calculated as [Al2O3/(Al2O3 + Na2O + CaO)]100, where all values represent a molar mass. # Mole ratio of free Fe oxides (determined by citrate–dithionite extraction) to total elemental Fe. †† Data not available for these samples.

(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, 94% of the variance for each parent material, with highly signifiacross the observed sites. Indeed, comparison of pedogenic indices to cant exponential functions fit to each (Table 4). Pedon clay content MAP and MAT across the environmental gradients indicated little at the y intercept, or zero EEMT, was greatest in AN (0.2 kg m−2) to no relationship (Fig. 4). In contrast, all of the pedogenic indices and least in GR (0.04 kg m−2) derived soils. Variation in the y interdemonstrated a significant relationship with EEMT, both on the cept may be a function of parent material grain size and mineralogipooled data set and by individual parent materials (Fig. 5, Table 4). cal composition, with AN-derived soils forming from a mix of conVariation in parent material significantly affected the observed relasolidated volanic ash and mudflow material that inherently contains tionships between pedogenic indices and EEMT. Derived quantitaa greater fine-earth fraction (including volcanic glass and possibly tive EEMT transfer functions are discussed in detail below. hydrothermally altered materials consisting of clay-size material) on deposition relative to the coherent crystalline structure and mineralPedon Depth ogy of BS and GR materials, respectively. The inverse of the rate Pedon depth exhibited positive and significant exponential constant parameter (1/b) suggested that GR-derived soils required relationships with EEMT across the pooled data set (R2 = 0.45, P less EEMT to produce an equivalent amount of total pedon clay < 0.001) and when considered by individual parent materials (Fig. (2600 kJ m−2 yr−1 relative to 3600 and 4500 kJ m−2 yr−1 in BS 5, Table 4). The EEMT exhibited only a moderate and insignifiand AN soils) and appeared contradictory relative to the mineral cant relationship (r2 = 0.44, P = 0.33) to pedon depth across the assemblage of the respective parent materials. This result is probBS sites. The lack of predictive power for this parent material may ably related to the fact that pedon clay content (kg m−2) takes into be a function of the small data set for BS-derived pedons (n = 4). account pedon depth, so while GR soils may have less clay on a mass In contrast, EEMT exhibited a highly significant relationship with percentage basis, greater pedon depth in GR soils results in a rela1726

SSSAJ: Volume 71: Number 6 • November–December 2007

tively 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/ Fig. 5. Pedogenic indicators regressed against effective energy and mass transfer (EEMT): (A) pedon FeT only required 324 kJ m−2 yr−1, depth; (B) total pedon clay content; (C) free Fe oxide to total Fe oxide ratio (Fed/FeT) of the whereas GR- and AN-derived soils 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 bestrequired 431 and 446 kJ m−2 yr−1, fit regression to the data. Data derived from pedons sampled from stable landscape positions respectively. This pattern fits with the across four environmental gradients on basalt, andesite and granite parent materials. mineral assemblage of the BS parent materials dominated by primary minerals rich in Fe2+ that rapidly weather Table 4. Equations and parameters for predicting pedogenic indices from effective energy and mass transfer (EEMT)†. to secondary minerals and Fe3+ oxides at the Earth’s surface. Similarly, CIA−K Pedogenic index‡ Parent material a b r2 1/b§ 1/a¶ values also exhibited a significant linear Pedon depth, cm all sites 28.6 0.000046 0.45*** 21,739 NA# relationship with EEMT across pooled basalt 11.6 0.000075 0.44 NS 13,333 NA y = a exp(bx) data (R2 = 0.76, P < 0.001) and among andesite 13.5 0.000070 0.90*** 14,286 NA a = cm −2 −1 −1 individual parent materials (Fig. 5, granite 7.2 0.000129 0.67** 7,752 NA b = (kJ m yr ) Table 4). The relative EEMT needed Clay, kg m−2 all sites 7.59 0.000133 0.75*** 7,519 NA for a unit increase of CIA−K (1/a) basalt 0.076 0.000278 0.99*** 3,600 NA y = a exp(bx) followed expected patterns by parent andesite 0.199 0.000222 0.99*** 4,505 NA a = kg m−2 material, i.e., BS-derived soils required granite 0.041 0.000387 0.94*** 2,584 NA b = (kJ m−2 yr−1)−1 greater EEMT (588 kJ m−2 yr−1) to Fe /Fe , mol % all sites 0.00278 −25.4 0.81*** NA 360 d T increase CIA−K, whereas GR-derived basalt 0.00309 −25.2 0.96* NA 324 y = ax + b soils required the least EEMT (500 kJ andesite 0.00224 −13.5 0.70* NA 446 a = mol % (kJ m−2 yr−1)−1 m−2 yr−1) to increase CIA−K by one granite 0.00232 −21.7 0.81* NA 431 b = mol % unit (Table 4). Given the base-cation- CIA−K, mol % all sites 0.00188 30.3 0.76*** NA 532 rich nature of the BS primary mineral basalt 0.00170 35.4 0.93* NA 588 y = ax + b assemblage (particularly Ca2+ and Na+ andesite 0.00191 29.6 0.82** NA 524 a = % (kJ m−2 yr−1)−1 present in pyroxenes, amphiboles, and granite 0.00200 26.8 0.45 NS NA 500 b=% plagioclase feldspars), it fits that greater * Regression not significant at P < 0.05; NS = not significant. EEMT was required to reduce the ** Regression not significant at P < 0.01. overall abundance of CaO and Na2O *** Regression not significant at P < 0.001. in the profile. Generally, granitic mate- † y is the pedogenic index and x is EEMT in kJ m−2 yr−1. rials lack significant CaO or Na2O ‡ Pedon depth is depth to bedrock or minimally altered C horizon; clay is the sum of the clay content such that less EEMT was required to for the entire pedon; Fed/FeT is the mole ratio of free Fe oxides to total elemental Fe from the first reduce the overall abundance of catsubsurface genetic horizon (B or AC); and CIA−K is the chemical index of alteration minus K from the first subsurface genetic horizon. ions relative to Al2O3. Given the theoretical end point § Inverse of the rate constant (b) represents the EEMT rate needed to increase y by one unit. values of 100% for CIA−K and Fed/ ¶ Inverse of the slope (a) represents the rate of EEMT needed to increase y by one unit. FeT, it must be assumed that the lin- # Not applicable to applied equation. SSSAJ: Volume 71: Number 6 • November–December 2007

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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

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.

ear 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. 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 1728

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. ACKNOWLEDGEMENTS The conceptual nature of this work benefited from discussion amongst the University of Arizona Critical Zone Work Group. REFERENCES Addiscott, T.M. 1994. Simulation, prediction, foretelling or prophecy? Some thoughts on pedogenetic modeling. p. 1–17. In R.B. Bryant and R.W. Arnold (ed.) Quantitative modeling of soil forming processes. SSSA Spec. Publ. 39. SSSA, Madison, WI. Alexander, E.B., J.I. Mallory, and W.L. Colwell. 1993. Soil–elevation relationships on a volcanic plateau in the southern Cascade Range, northern California, USA. Catena 20:113–128. Alvarez, R., and R.S. Lavado. 1998. Climate, organic matter and clay content relationships in the Pampa and Chaco soils, Argentina. Geoderma 83:127–141. Anderson, D.W. 1995. Decomposition of organic matter and carbon emissions from soils. p. 165–175. In R. Lal et al. (ed.) Soils and global change. Lewis Publ., Boca Raton, FL. Arkley, R.J. 1963. Calculation of carbonate and water movement in soil from climate data. Soil Sci. 96:239–248. Blake, G.R., and K.H. Hartge. 1986. Bulk density. p. 363–375. In A. Klute (ed.) Methods of soil analysis. Part 1: Physical and mineralogical methods. 2nd ed. SSSA Book Ser. 5. SSSA, Madison, WI.

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Bonan, G.B. 1993. Physiological derivation of the observed relationship between net primary production and mean annual air temperature. Tellus Ser. B 45:397–408. Brye, K.R. 2004. Pedogenic interpretation of a loess-covered, Pleistoceneglaciated toposequence using the energy model. Soil Sci. 169:282–294. Colman, S.M. 1982. Chemical weathering of basalts and andesites: Evidence from weathering rinds. Geol. Surv. Prof. Pap. 1246. U.S. Gov. Print. Office, Washington, DC. Dahlgren, R.A. 1994. Quantification of allophane and imogolite. p. 430–451. In J.E. Amonette and L.W. Zelazny (ed.) Quantitative methods in soil mineralogy. SSSA, Madison, WI. Dahlgren, R.A., J.L. Boettinger, G.L. Huntington, and R.G. Amundson. 1997. Soil development along an elevational transect in the western Sierra Nevada, California. Geoderma 78:207–236. Daly, C., R.P. Neilson, and D.L. Phillips. 1994. A statistical–topographic model for mapping climatological precipitation over mountainous terrain. J. Appl. Meteorol. 33:140–158. Dokuchaev, V.V. 1883. Russian chernozems (Russkii chernozem). Israel Prog. Sci. Transl., Jerusalem, 1967. Transl. from Russian by N. Kraner. Natl. Tech. Inf. Serv., Springfield, VA. Driese, S.G., L.C. Nordt, W. Lynn, C.A. Stiles, C.I. Mora, and L.P. Wilding. 2005. Distinguishing climate in the soil record using chemical trends in a Vertisol climosequence from the Texas coast prairie, and application to interpreting paleozoic paleosols in the Appalachian basin, U.S.A. J. Sediment. Res. 75:340–353. International Atomic Energy Administration. 2004. Isotope hydrology information system: The ISOHIS database. Available at isohis.iaea.org (verified 27 July 2007). IAEA, Vienna. Jennings, C.W. 1977. Geologic map of California, scale 1:750,000. Div. of Mines and Geol., Calif. Dep. of Conserv., Sacramento. Jenny, H. 1941. Factors of soil formation. A system of quantitative pedology. McGraw-Hill, New York. Jenny, H. 1961. Derivation of state factor equations of soils and ecosystems. Soil Sci. Soc. Am. Proc. 25:385–388. Johnson, D.L., and D. Watson-Stegner. 1987. Evolution model of pedogenesis. Soil Sci. 143:349–366. Lieth, H. 1975a. Measurement of caloric values. p. 119–129. In H. Lieth and R.H. Whittaker (ed.) Primary productivity of the biosphere. SpringerVerlag, New York. Lieth, H. 1975b. Primary production of the major vegetation units of the world. p. 203–215. In H. Lieth and R.H. Whittaker (ed.) Primary productivity of the biosphere. Springer-Verlag, New York. Maynard, J.B. 1992. Chemistry of modern soils as a guide to interpreting Precambrian paleosols. J. Geol. 100:279–289. Minnich, R.A., E.F. Vizcaino, J.S. Ramirez, J.H. Burk, W.J. Barry, M.G. Barbour, and H.C. Salcedo. 1997. A land above: Protecting Baja California’s Sierra San Pedro Mártir within a biosphere reserve. J. Southw. 39:613–695. Morowitz, H.J. 1968. Energy flow in biology. Ox Bow Press, Woodbridge, CT. Nesbitt, H.W., and G. Markovics. 1997. Weathering of granodioritic crust, long-term storage of elements in weathering profiles, and petrogenesis of siliciclastic sediments. Geochim. Cosmochim. Acta 61:1653–1670. Odum, H.T. 1983. Systems ecology: An introduction. John Wiley & Sons, New York. Parfitt, R.L., and C.W. Childs. 1988. Estimation of forms of Fe and Al: A

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