A Quantitative Model of Magnetic Enhancement in Loessic Soils

Abstract

We present a quantitative model for the climatic dependence of magnetic enhancement in loessic soils. The model is based on the widely accepted hypothesis that ultrafine magnetite precipitates during alternating wetting and drying cycles in the soil micropores. The rate at which this occurs depends on the frequency of drying/wetting cycles, and on the average moisture of the soil. Both parameters are estimated using a statistical model for the soil water balance that depends on frequency and intensity of rainfall events and on water loss by evapotranspiration. Monthly climatic tables are used to calculate the average soil moisture and the rate of pedogenic magnetite production, which is proportional to a new parameter called magnetite enhancement proxy (MEP). Our model is tested by comparing MEP calculated for known present-day climates with the magnetic enhancement of modern soils. The magnetic enhancement factor, defined as the ratio between a given magnetic enhancement parameter and MEP, is expected to be a site-independent constant. We show that magnetic enhancement differences between soils from the Chinese Loess Plateau and from Midwestern U.S. are explained by our model, which yields similar magnetic enhancement factors for the two regions. Our model is also successful in predicting the mean annual rainfall threshold above which magnetic enhancement declines in a given type of climate.

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25.1 Introduction

Magnetic susceptibility records of loess/paleosol sequences have been used to reconstruct climatic changes during the Neogene (e.g. Liu et al. 1992, Heller et al. 1993, Banerjee et al. 1993, Maher et al. 1994, Liu et al. 1995, Maher 1998, Fang et al. 1999, Maher and Thompson 1999, Maher and Hu 2006). Climatic reconstructions are based on the observation that the magnetic susceptibility of the uppermost soil horizons (A and top of B) is higher than that of the underlying layers, as first discovered by Le Borgne (1955), provided that the soil parent material is not excessively magnetic. Magnetic enhancement is caused by superparamagnetic (SP) and single domain (SD) magnetite (Fe₃O₄) or maghemite (γ-Fe₂O₃) particles (Maher 1986, Evans and Heller 1994), commonly referred to as pedogenic magnetite, which are preserved in the loess/paleosol record (see Heller and Evans 1995, Maher and Thompson 1999, Evans and Heller 2003 for reviews). Even if pedogenic magnetite represents only a negligible fraction of pedogenic Fe minerals by mass (Cornell and Schwertmann 2003), its magnetization is much stronger and controls the bulk magnetic properties of the enhanced horizons.

The mechanism of pedogenic Fe minerals formation and the role of climate in it are not yet fully understood. Several hypotheses have been formulated to explain magnetic enhancement. Natural fires cause the partial reduction of weakly magnetic iron oxyhydroxides to magnetite or maghemite in the presence of organic matter (Le Borgne 1960, Kletetschka and Banerjee 1995); however, their effective role as systematic enhancement mechanism is not considered fundamental in most cases (Maher 1986). A widely accepted model for the precipitation of ultrafine magnetite in soils requires the oxidation of Fe²⁺(aq) at near-neutral pH, which has been shown experimentally to produce a magnetic material that is very similar in chemical composition, morphology and grain size (Taylor et al. 1987, Maher 1988). In a first step, Fe²⁺ ions are released by weathering of Fe-bearing silicates during repeated wetting and drying cycles. Fe²⁺ ions oxidize rapidly to Fe³⁺ in presence of oxygen, and Fe³⁺ hydrolysis induces the precipitation of poorly crystalline oxyhydroxides such as ferrihydrite (Fe₅HO₈·4H₂O) (Cornell and Schwertmann 2003). Ferrihydrite is easily reduced during episodic anaerobicity caused by organic matter respiration (Fischer 1988), leading to the precipitation of magnetite and other Fe(II) minerals (Tamaura et al. 1983, Tronc et al. 1992). This so-called “fermentation mechanism” has been proposed by Le Borgne (1955), Mullins (1977), and Dearing et al. (1996), and was later refined by Maher (1998). A similar redox mechanism involving direct precipitation of magnetite by metal dissimilatory reducing bacteria under anaerobic conditions (Lovley et al. 1987) has been considered as a possible alternative (Maher 1998, Dearing et al. 2001, Maher et al. 2003, Banerjee 2006). A completely different enhancement path recently proposed by Torrent et al. (2006, 2007) postulates the formation of an intermediate ferrimagnetic phase when ferrihydrite is converted to hematite (α-Fe₂O₃), in which case the reducing environment necessary for magnetite precipitation is not essential.

Heller and Liu (1984) found a significant correlation between magnetic susceptibility of a loess/paleosol profile from the Chinese Loess Plateau (CLP) and oceanic δ¹⁸O, providing the first continuous record of Pleistocene glacial/interglacial stages in a continental section. They proposed topsoil decalcification and down-profile carbonate reprecipitation as a means of iron oxide concentration. An alterative explanation of susceptibility variations by Kukla et al. (1988) postulated a constant atmospheric input of iron oxides which has been diluted by weakly magnetic dust at times of rapid loess accumulation. Maher and Thompson (1992) confirmed the correlation with oceanic climate records, which they attributed to the degree of soil formation as seen by the accumulation of secondary ferrimagnetic minerals (magnetic enhancement). The magnetic record is thus controlled by temperature and humidity of the regional climate, rather than variations in the deposition rate.

Magnetic susceptibility variations in loess/paleosol sections can be interpreted in terms of detrital and pedogenic mineral fluxes, expressed as accumulated mass per unit surface and time. If each group of minerals is characterized by specific, invariant magnetic properties, the mass fluxes can be converted to magnetic susceptibility fluxes, and vice-versa (Beer et al. 1993). Heller et al. (1993) used ¹⁰Be – which is supplied to the sediment through dust accumulation and rain – to calculate susceptibility fluxes, discovering large differences in pedogenic magnetite production rates between loess and paleosol layers. Furthermore, they found a clear match between present-day mean annual rainfall (MAR, see Table 25.1 for a list of symbols and abbreviations) and paleosol susceptibility at different sites on the CLP. Paleo-rainfall reconstructions based on susceptibility fluxes and susceptibility enhancements differ mainly by the underlying assumptions about the timing of pedogenic processes.

Table 25.1 Definition of important parameters used in the text, sorted by subject: (1) water balance, (2) iron content, and (3) magnetic measurements

The systematic study of large numbers of modern soils in warm temperate climates (Maher and Thompson 1995, Liu et al. 1995, Han et al. 1996, Porter et al. 2001, Maher et al. 2003, Geiss and Zanner 2007) confirmed the existence of a significant correlation between MAR and susceptibility enhancement. This evidence led to the proposal of a so-called soil climofunction (Jenny 1941) linking climate, expressed by MAR, with production of secondary ferrimagnetic minerals, quantified by pedogenic susceptibility (fluxes) (Heller et al. 1993, Maher et al. 1994). A soil climofunction is the key for reconstructing paleorainfall from magnetic measurements of loess/paleosol sections, under the assumption that the function is invariant over time (e.g. Heller et al. 1993, Maher et al. 1994, Florindo et al. 1999a, b, Evans et al. 2002).

The soil climofunction depends on additional parameters related to the climate itself (e.g. temperature, seasonality), and to soil forming factors such as chemistry, Fe supply, drainage, and time (Jenny 1941, Maher 1998, Hanesch and Scholger 2005). The evolution of soil-forming parameters with time is described by a so-called chronofunction (Jenny 1941, Bockheim 1980). The final onset of a stationary regime is known as the mature stage in soil evolution models (Jenny 1941). The time required for reaching this stage depends on the weathering intensity. Contrasting views exist on the rapidity of soil development, with estimates spanning from hundreds of years for particle size, pH, and organic matter content of Iowa loess deposits (Hallberg et al. 1978), to >0.5 Myr for the magnetic enhancement of Californian soils formed on stratified aeolian silt and sand terraces (Singer et al. 1992). Contradictory chronofunction reconstructions – expressed as peak magnetic susceptibility vs. paleosol development duration – have been obtained for the CLP. Vidic et al. (2004) report a positive correlation based on three different age models (r ² = 0.44–0.81), while no correlation is found when soil development duration estimates are calculated from ages measured with optically stimulated luminescence (Maher and Hu 2006). The caveat in reconstructing reliable chronofunctions is the age model used for calculating soil development durations: models based on correlation with reference curves (magnetic polarity or δ¹⁸O) (Grimley et al. 2003, Vidic et al. 2004) tend to overlook sedimentation rate discontinuities, overestimating the development duration of the most enhanced soils.

Fe supply is generally not a limiting factor for magnetic enhancement, since the typical Fe content of pedogenic ferrimagnetic minerals (<0.1 wt%) is much lower than the total iron concentration (Fe_t) of most parent materials (2–5 wt%) (Maher 1998). Secondary ferrimagnetic minerals also make an insignificant contribution to the citrate-bicarbonate-dithionite (CBD) extractable iron (Fe_d), which is a proxy for the Fe contained in fine-grained secondary minerals. Fine et al. (1995) found a linear correlation between magnetic susceptibility and Fe_d of loess/paleosol samples from the CLP, with magnetic enhancement starting at Fe_d = 7 g/kg and a slope of 2.6×10^–4 m³/kg(Fe_d), which can be interpreted as the susceptibility of Fe_d-bearing minerals normalized by their Fe content. For comparison, much higher values, in the order of 4.3×10^–3 m³/kg(Fe_d), would result if Fe_d is assumed to originate only from pedogenic magnetite (see the Appendix for a proof). This means that magnetic enhancement is caused by <6% Fe in secondary iron minerals.

The concentration of pedogenic minerals is controlled by several factors, such as production rate, dust inputs during soil formation, mineral dissolution, and vertical mass transport between horizons (Brimhall and Dietrich 1987, Begét et al. 1990, Anderson and Hallet 1996, Maher 1998, Porter et al. 2001). The interplay of all factors becomes important when pedogenic mineral production is slow compared to the other processes. In general, magnetic enhancement depends on soil type, vegetation, and climate (Maher 1986, Dearing et al. 1996, Hanesch and Scholger 2005). The formation of pedogenic magnetite is favored in well drained, not very acidic soils (pH ≈ 5.5–8.0), and is correlated with organic matter content and cation exchange capability (Maher 1998). Weathering of primary Fe minerals and precipitation/dissolution of secondary iron oxides is sensitive to pH and Eh. For example, Fe²⁺ is most rapidly removed from Fe-bearing silicates under reducing, acidic conditions (White et al. 1994). The alternation of strongly reducing and oxidizing conditions induced by water table oscillations leads to magnetite dissolution, and – ultimately – to a depletion of secondary ferrimagnetic oxides (Maher 1998, Dearing et al. 2001, Hanesch and Scholger 2005, Fischer et al. 2008). Magnetite dissolution is also promoted by a number of substances that might be present in the upper soil horizons, such as organic ligands (Appelo and Postma 2005), and pore water silica (Florindo et al. 2003).

Site-specific climofunction variations are minimal on the CLP, where loess has exceptionally uniform chemical and physical properties that promote rapid accumulation of pedogenic minerals. Maher et al. (1994) report following empirical relation:

$${\textrm{MAR}} = 222 + 199\;{\log _{10}}({\chi _{\textrm{B}}} - {\chi _{\textrm{C}}}),$$

((25.1))

between MAR, expressed in mm/yr, and the susceptibility enhancement $\Delta \chi = {\chi _{\textrm{B}}} - {\chi _{\textrm{C}}}$ where χ _B and χ _C are the susceptibilities of B and C horizons, respectively, in units of 10^–8 m³/kg. The climofunction in Eq. (25.1) has been successfully extended to loessic soils from the Russian steppe (Maher et al. 2003) and other areas of the northern hemisphere temperate zone (Maher and Thompson 1995). These results support the use of magnetic parameters as rainfall proxies for paleosols where chemical conditions and drainage favored the formation and preservation of ferrimagnetic iron oxides.

On the other hand, the implementation of a climofunction that is universally valid for a certain category of soils and soil forming conditions is faced with some unresolved problems. Limiting the discussion to loess as parent material, these are: (1) a large scatter of Δχ values (typically a factor of 2) for modern soils from sites with similar MAR; (2) systematic, yet unexplained geographic differences within the CLP (Guo et al. 2001, Bloemendal and Liu 2005) and between CLP and North America (Geiss and Zanner 2007, Geiss et al. 2008); (3) no correlation between Δχ and MAR above a cursive MAR threshold; and (4) apparent lack of magnetic enhancement in soils where the accumulation of pedogenic iron oxides is not suppressed by known causes such as gleyzation (Orgeira et al. 2008). Furthermore, Jahn et al. (2001) report inconsistencies between chemical and magnetic indicators of pedogenesis, which may be explained by selective sensitivity to different pedogenic processes.

Magnetic enhancement depends ultimately on the long-term balance between dissolution of primary and pedogenic Fe minerals on the one hand, and precipitation of magnetic iron oxides on the other. This balance is controlled by several environmental factors – the most important being soil moisture and the chain of chemical reactions related to it (Maher 1998). The importance of soil water balance is demonstrated in laboratory simulations of flooding and drying cycles, which produce a complex sequence of magnetic mineral accumulation and dissolution (Crockford and Willett 1995). MAR is only one of the parameters controlling soil moisture: it represents the water supply rate, which is counterbalanced by drainage – in which case soil porosity and thickness play an important role – and by evapotranspiration (ET). ET depends on the type of vegetation cover and on climatic parameters such as insolation, wind speed, and temperature. Aspects of Fe oxides accumulation and dissolution driven by the soil water balance, such as seasonal oscillations (Tite and Linington 1975) and excessive drainage (Schwertmann et al. 1982), have been recognized since a long time. One of the most systematic investigations of water balance effects on pedogenesis has been carried out on a sequence of soils located on the flanks of a volcano (Chadwick et al. 2003). While the parent volcanic rocks are identical at all sampling sites, rainfall and potential evapotranspiration (PET) vary strongly with altitude. Several geochemical parameters – such as pH, weathering rate, and effective cation exchange capacity – were shown to depend critically on the difference between MAR and PET, which is a measure of the net water balance. Dramatic changes occur at the point where MAR starts to exceed PET: therefore, MAR–PET = 0 was considered a sort of pedogenic threshold (Chadwick and Chorover 2001).

The idea of a pedogenic threshold driven by soil water balance was used by Orgeira and Compagnucci (2006) to explain magnetic enhancement differences in loessic soils from Russia, China and Argentina. They observed that soils from sites characterized by negative values of MAR – PET, such as the CLP, are magnetically enhanced, contrary to locations where this difference is ∼0 or positive. This trend is also valid for soils with no evidence of waterlogging or gleyzation, as in many Argentinean loess/paleosol profiles.

It is evident from the previous discussion that – even in case of a climofunction that does not depend on soil-specific parameters – MAR is not sufficient to fully describe the climatic control over pedogenic Fe oxides production and preservation. Furthermore, the empirical logarithmic expression for the susceptibility enhancement of loessic soils (Eq. (25.1)) is not of a form that can be obtained from the solution of mass balance and chemical reaction kinetic equations. In this article, we provide a quantitative frame for the magnetic enhancement model proposed by Maher and co-workers (Maher et al. 1994, Maher 1998), which is combined with a stochastic treatment of soil moisture derived from Rodriguez-Iturbe et al. (1999). The result is a physically-derived expression that fits published magnetic enhancement data on modern loessic soils worldwide. Our calculations are able to explain systematic differences between modern soils from the CLP and from North America in terms of climatic factors that are not completely expressed by MAR. Furthermore, pedogenic thresholds limiting the magnetic enhancement of soils formed in cold climates (Alaska and Siberia), or in climates with strong monsoons (Southern China) are correctly predicted. These results demonstrate that soil water balance is one of the most important parameters affecting the formation and dissolution of magnetic minerals – acting not only as a threshold, as originally postulated, but effectively as a regulating factor in a wide range of climates.

25.2 Soil Magnetic Properties in Different Regions of the World

In this section we provide a review of published data on soil magnetic enhancement according to geographical location and climate. Since the focus of this article is on the climatic control of pedogenesis, the variability of other soil forming factors – such as parent material composition and soil age – is minimized by limiting our dataset to modern loessic soils or Pleistocene/Holocene paleosols. The relatively homogeneous composition and texture of loess, its weatherability and pH buffering capability, as well as good drainage properties, provide adequate conditions for pedogenic magnetite accumulation and preservation (Evans and Heller 2003, Maher 1998). Soil development on loess is believed to occur rapidly (Hallberg et al. 1978, Maher and Hu 2006), in which case soil age effects do not need to be considered. For comparison reasons, we also discuss few examples of non-loessic soils. These include heamtitic “terre rosse” from the Mediterranean region (Torrent and Cabedo 1986), and a set of intensively studied Hawaiian volcanic soils (Chadwick et al. 2003).

Soil provenance is divided into five major regions, according to modern climate and magnetic enhancement characteristics. Susceptibility enhancement and annually averaged climatic data for representative soils from these regions are summarized in Table 25.2 and discussed in the following.

Table 25.2 Summary of magnetic and climatic properties of representative loessic soils. The moisture ratio W is calculated as the ratio between MAR and yearly PET

25.2.1 Central Asia

The Chinese Loess Plateau (CLP) provides the longest and most complete sequence of terrestrial wind-blown sediment (Heller and Liu 1984, 1986), which occur in form of extended and thick Pleistocene to Holocene loess/paleosols sequences overlaying tertiary red clays deposits (Ding et al. 2001). It represents an important terrestrial paleoclimatic archive that has been the subject of extensive research over the last ∼20 years (Evans and Heller 2003, Maher 2009). In wintertime, dust from arid regions, including sources beyond proximal deserts on the Siberian-Mongolian High, is transported to the plateau by northwesterly winter monsoon winds, while southeasterly winds dominate in summer (An 2000, Maher et al. 2009). Heavy rainfall (>1000 mm/yr) in the southern part of the CLP is caused by humid air brought by the Indian and the SW East Asian Monsoons (e.g. Han et al. 1996). As a result, the CLP is characterized by a strong climatic gradient between arid regions with large dust accumulation and low weathering rates in the N, and humid regions with opposite dust accumulation and weathering characteristics in the S (Derbyshire et al. 1995).

The high chemical and isotopic homogeneity of Chinese loess suggests that dust is supplied, mixed, and recycled from several source regions (Jahn et al. 2001, Maher et al. 2009). Further transformation of the deposited dust depends on the intensity of the two East Asian Monsoon systems. Increasing summer monsoon intensities raise temperature and rainfall, favoring vegetation, weathering and pedogenesis, as particularly evident in paleosols formed during interglacial stages. Paleosols contain a higher concentration of ultrafine (SP and SD) magnetite and/or maghemite grains (e.g. Maher 1986, Liu et al. 1992, Banerjee et al. 1993, Eyre and Shaw 1994, Evans and Heller 1994, Liu et al. 1995, Maher 1998, Jackson et al. 2006, Liu et al. 2007), which are the main responsible for magnetic enhancement, as recorded by magnetic susceptibility (χ, Δχ), its frequency dependence (χ _fd), and anhysteretic remanent magnetization (χ _ARM). The enhanced SD magnetite fraction has been initially attributed to fossil magnetosomes produced by magnetotactic bacteria (Evans and Heller 1994), a hypothesis supported by living magnetic bacteria findings in the Ah horizon of a low-moor soil (Fassbinder et al. 1990), and fossil magnetosome chains in paleosol samples from the CLP (Maher and Thompson 1995, Maher 1998). Magnetotactic bacteria, however, do not contribute significantly to the soil magnetic signature under conditions typical for the CLP (Egli 2004, Dearing et al. 2001).

Han et al. (1996) conducted a systematic magnetic survey of the top horizon (5–10 cm from the surface) of 160 modern soils over the CLP, finding a systematic magnetic enhancement with an increasing trend towards the southern limit of the Plateau. These results have been confirmed by N-S transects across the CLP (Florindo et al. 1999a, Deng et al. 2000, Evans et al. 2002). A positive and systematic correlation between magnetic enhancement parameters and MAR, as well as the mean annual temperature (MAT), exists for all sites where MAR does not exceed ∼1100 mm/yr. Above this limit, which occurs S of the Yangtze river (∼32°N), soils are magnetically enhanced, but susceptibility is not correlated with rainfall or temperature. Similar results for modern CLP soils have been obtained by Porter et al. (2001), who discuss the link between χ and several annually averaged climatic parameters, including PET. They found a good correlation with a soil water balance proxy given by MAR – PET; however, MAR × MAT was suggested to be a better proxy of “potential pedogenic activity”.

Homogeneous dust composition over the CLP and the weak magnetic susceptibility of loess in comparison to well developed soils provides an ideal situation for modeling the influence of climate on the magnetic record of loess/paleosol sequences (e.g. Heller et al. 1993, Maher et al. 1994, Balsam et al. 2004). On this basis, similar trends could be observed for the spatial distribution of χ during interglacial periods of the last 600 kyr and modern rainfall maps (Hao and Guo 2005). Discrepancies in the relationship between χ and MAR involve sections that are close to the S boundary of the CLP (Evans and Rokosh 2000, Guo et al. 2001, Bloemendal and Liu 2005). For example, S5-S8 paleosols from Duanjiapo (34.2°N, 109.2°E) are magnetically less enhanced than corresponding units from central parts of the CLP, while the opposite trend is observed for present-day MAR. In contrast to magnetic data, geochemical parameters clearly indicate a period of significantly higher weathering at Duanjiapo, which resulted in almost complete decalcification (Bloemendal and Liu 2005). Paleorainfall underestimation by magnetic proxies at the S boundary of the CLP has been attributed to a climatic threshold above which pedogenic magnetite is not preserved (Evans and Rokosh 2000, Guo et al. 2001).

Discrimination between low- and high-coercivity minerals indicates that parts of the Duanjiapo section affected by discrepancies between chemical and magnetic proxies of pedogenesis contain proportionally less ferrimagnetic and more antiferromagnetic iron oxides (Bloemendal and Liu 2005). This is also a typical feature of Tertiary red clays, whose low susceptibility contrasts with chemical indicators of pedogenesis, as for example Fe_d/Fe_t (Ding et al. 2001). Although substantial gleyzation in some portions of the red clay sequence is suggested by the occurrence of dark Fe-Mn films, the pedogenic magnetite/maghemite grain size distribution – expressed by the ratio between magnetic parameters sensitive to the SD and SP fractions, respectively – is not significantly different from that of ordinary paleosols (Nie et al. 2010). This observation is hardly compatible with magnetite dissolution, which is expected to selectively eliminate the smaller grain sizes (Smirnov and Tarduno 2000). Therefore, reduced magnetic enhancement on the S boundary of the CLP is probably caused by a diminished production of ferrimagnetic minerals, rather than by dissolution phenomena.

Outside the CLP, small loess deposits in the Kashmir valley (India) contain paleosol horizons that are magnetically enhanced with respect to loess layers. Mineral magnetic data correlate well with the global marine δ¹⁸O record (Gupta et al. 1991). The region is characterized by MAR ≈ 600 mm/yr and MAT ≈ 13°C.

25.2.2 North America

Magnetic data for North America (Rousseau and Kukla 1994, Grimley et al. 2003, Geiss et al. 2004, Geiss and Zanner 2006, 2007) refer to modern prairie soils formed mainly on the Peoria loess formation, which has been deposited during the Last Glacial period. The investigated sites are located in the centre of the Great Plains and in the Central Lowlands, following a strong east-west MAR gradient (400–1000 mm/yr). Lower Peoria loess sections show varying degrees of reworking after aeolian deposition. The great local relief in some areas fostered gravity-driven processes that complicate the stratigraphic interpretation of some sections (Bettis et al. 2003a). Early phases of deposition where marked by permafrost (Bettis et al. 2003b), which might have altered the loess deposits. Dust sources of the Peoria formation have been traditionally located in the river valleys that transported melt water from the Laurentide Ice sheet. Other contributions include non-glacial sources for some of these deposits (Bettis et al. 2003a, b). Peoria loess is less homogeneous than CLP loess, both geochemically and in terms of grain size, probably because of dust admixtures from different sources (Muhs and Bettis 2000), and later Holocene inputs (Muhs and Zárate 2001, Muhs et al. 2001, Muhs et al. 2004, Jacobs and Mason 2005). Dust heterogeneities are also reflected by the magnetic properties of modern soil parent material. For example, magnetic susceptibility of underlying loess (χ _C) ranges from 100 to 1000 mm³/kg, compared to 100–350 mm³/kg for Chinese loess (Geiss and Zanner 2007).

All modern soils are magnetically enhanced in the top horizons (Ap and A). Holocene loess deposition might contribute to the topsoil magnetization; however, magnetic enhancement is due to ultrafine ferrimagnetic minerals, similarly to Chinese soils, rather than to primary minerals brought by dust (Grimley et al. 2003, Geiss and Zanner 2006, Geiss et al. 2008). The maximum susceptibility enhancement is only 20–50% of χ _C, making pedogenic susceptibility estimates based on $\Delta \chi = {\chi _{\textrm{B}}} - {\chi _{\textrm{C}}}$ very sensitive to the alteration of primary minerals (weathering) and syn-pedogenic dust inputs. Grimley et al. (2003) observed that magnetic enhancement is best recorded by magnetic parameters that are less sensitive to multidomain (MD) primary minerals, such as χ _fd and χ _ARM.

A positive correlation exists between magnetic enhancement in the top horizons and MAR (Geiss and Zanner 2007). However, Δχ appears to be influenced by variations in parent material magnetic properties, and the correlation with modern rainfall data is not as good as on the CLP. Furthermore, Δχ is consistently ∼3.7 times lower than expected from CLP modern soils with similar MAR. Relative enhancement, defined as the ratio between topsoil and parent loess magnetic parameters, appears to provide a better degree of correlation with MAR than absolute enhancement, which is based on the difference between soil and parent material (Geiss and Zanner 2007). A possible explanation for the better performance of relative magnetic enhancement parameters is that the formation of pedogenic iron oxides is controlled by climate and by Fe supply from primary minerals. Relative enhancement parameters, however, define climofunctions that are even more strongly dependent on the geographic provenance of soils. Because primary ferrimagnetic minerals contain a negligible fraction of total wheatherable Fe, relative magnetic enhancement parameters should be calculated with respect to Fe_t. The total Fe contents of Peoria loess (2–4.5 wt% Fe₂O₃ (Muhs and Bettis 2000)) and of Chinese loess (4.5–5.5 wt% Fe₂O₃ (Jahn et al. 2001)) are too similar to explain the difference in magnetic enhancement of the two regions in terms of Fe availability. This is also the case for other geochemical parameters, which do not provide an obvious explanation for the observed magnetic enhancement differences between CLP and U.S.

25.2.3 South America

Loess deposits and reworked loess are widely distributed in the Pampean Plain (Argentina), including deposits at Pcias de San Luis, Córdoba, Santa Fe, La Pampa, and Buenos Aires (e.g. Teruggi 1957, Muhs and Zárate 2001). These deposits form sequences of Pleistocene loess and paleosols which extend to middle or late Holocene in some cases (Orgeira 1990). The loess outcrops considered in this article belongs to the “Pampeano” unit (former “Buenos Aires Formation” (Ameghino 1909)). They are characterized by a high textural and mineralogical homogeneity with increasing sand content toward SW (Zárate and Blasi 1993). Aeolian deposition during cold dry periods is combined with reworking and redeposition by fluvial processes. Dominant SW winds transported clastic particles mobilized by glacial and fluvial action from the Andes region (Teruggi 1957, Smith et al. 2003). Pampean loess contains high concentrations of volcano-pyroclastic particles, which can reach 60% in ashy horizons. The main constituents are volcanic glass shards and plagioclase, with minor quartz contributions (e.g. Teruggi 1957, Muhs and Zárate 2001). The glass shards appear relatively unweathered; however, trace elements such as As in shallow groundwater indicate ongoing dissolution (Nicolli et al. 2004). The magnetic susceptibility of Argentinean loess is comprised between 600 and 1300 mm³/kg, and reflects a relatively large concentration of MD low-Ti titanomagnetites (Orgeira et al. 2008), while the total Fe content of 3.6–5.6 wt% Fe₂O₃ is similar to that of other loesses (Gallet et al. 1998).

Here we discuss results relative to modern soils classified as Argiudolls from three sites in the Buenos Aires Province: (1) Verónica and (2) Zárate, both located on the Buenos Aires Formation (Orgeira et al. 2008), and (3) a transect located on sandy loess that is probably more recent than the Buenos Aires Formation (Bartel et al. 2006). Modern soils from Verónica are characterized by a marked depletion of magnetic minerals, while moderate magnetic enhancement characterizes the B and A horizons of modern soils from the other sites. This difference has been interpreted in terms of preservation of detrital and pedogenic magnetite in Zárate, as opposed to extensive dissolution in the other sites (Orgeira et al. 2008). On the other hand, Pleistocene and late Holocene paleosols from the Pampean Plain are characterized by an apparent lack of magnetic enhancement (Orgeira and Compagnucci 2006). Magnetite dissolution – even without waterlogging – could be promoted by volcanic glass weathering, which releases silica in the soil pore water. High silica concentrations have been found to dissolve magnetite in marine siliceous sediments (Florindo et al. 2003). On the other hand, lack of magnetic enhancement could be the result of a complex interplay between weathering of lithogenic magnetic minerals and the formation of secondary iron oxides through pedogenesis, with opposed magnetic signatures that compensate each other.

25.2.4 Northern Loess Boundaries: Alaska and Siberia

Loess from central Alaska has a different mineralogical composition with respect to Peoria loess. Quartz is a dominant mineral, accompanied by unusually high concentrations of Fe minerals and Al₂O₃. The total absence of carbonates and low clay content reflect its origin from granites, metabasalts, and schists (Muhs et al. 2003). Vegetation might have played an important role in modulating loess production, which is maximal during glacial periods, and loess accumulation, which is enhanced during interglacials, because of boreal forests acting like a dust trap (Muhs et al. 2003). Extremely thick loess sediments of aeolian origin, often reworked by secondary processes, cover a large area in southern Siberia. Reworking occurred during the development of a fluvial system, which was triggered by an uplift of the region during Late Pliocene/Early Pleistocene (Zhu et al. 2003). Alaskan loess susceptibilities of 1100 ± 300 mm³/kg (Lagroix and Banerjee 2002) are comparable with maximum values for North America, and are about one order of magnitude larger than those of Chinese loess. Even larger susceptibility values are characteristic for loesses from southern Siberia (Chlachula et al. 1998).

Loess/paleosols sequences in Alaska and Siberia have opposite magnetic susceptibility signatures with respect to China and North America, with paleosols being less magnetic than loesses (e.g. Begét et al. 1990, Chlachula et al. 1998). This trend has been explained by the so-called wind-vigor model with the greater efficiency of atmospheric entrainment and transport of dense (∼5000 kg/m³) magnetic Fe oxide grains during glacial times, when wind action is maximal, with respect to the less dense (e.g. quartz, ∼2600 kg/m³) non-magnetic minerals (Evans 1999, 2001). According to this model, glacial sediments contain higher concentrations of magnetic minerals and are more magnetic. This mechanism is likely active in all loess regions, including the CLP. The reason for the opposite trends of Alaska and Siberia with respect to the CLP is attributed to the different intensities of pedogenic mineral production on one hand, and wind-vigor-based dust sorting on the other. The wind-vigor effect is most evident in Alaska and Siberia because of the shorter distance to dust sources and higher concentrations of magnetic minerals in dust. On the other hand, Alaskan and Siberian soils are often assumed to be seasonally waterlogged, with chemical conditions that promote gleyzation and subsequent reductive dissolution of ultrafine iron oxides (Feng and Khosbayar 2004, Kravchinsky et al. 2008). In this case, magnetic minerals of pedogenic origin are not expected to accumulate, leaving wind-vigor sorting as the sole modulation mechanism for the magnetic properties of loess/paleosols sequences.

An evaluation of the relative importance of pedogenesis and wind-vigor dust sorting requires unmixing the magnetic signatures of lithogenic and pedogenic minerals. The frequency dependent magnetic susceptibility χ _fd is a suited parameter for this purpose, because of its highly selective response to magnetic minerals with grain sizes corresponding to the SP/SD boundary (Worm 1998), which happens to be within the grain size distribution of pedogenic magnetite (Liu et al. 2007). Measurements of χ _fd indicate that both Alaskan and Siberian soils/paleosols are enriched in ultrafine magnetic minerals with respect to the loess layers (Liu et al. 1999, Kravchinsky et al. 2008). Hydromorphic conditions with subsequent gleyzation might occur locally, mainly driven by local topography and poor drainage (e.g. Grimley et al. 2004), but cannot be considered a systematic characteristic of these soils.

25.2.5 Europe, Russian Steppe, North Africa

Unlike the CLP, European loess deposits are very heterogeneous, reflecting variations in dust provenance, accumulation conditions, post depositional alteration, and presence of tephra (Derbyshire 2001). Loess/paleosols sequences from the Czech Republic (Forster et al. 1996, Oches and Banerjee 1996), south-west Slovakia (Ďurža and Dlapa 2009), along the Danube River (Panaiotu et al. 2001), and in Alsace (France) (Rousseau et al. 1998) are characterized by a magnetic enhancement pattern similar to that of the CLP. On the other hand, the magnetic record of Polish and western Ukrainian sequences is complicated by gley paleosol horizons with susceptibility values lower than those of loess. These horizons indicate that loesses were accumulated in a more humid and cooler climate than the Chinese ones (Nawrocki et al. 1996). East European loess/paleosol sections cannot always be used as a direct climate indicator: spore and pollen analyses suggest that some paleosol horizons correspond to considerable cooling, while traces of warming-up could be revealed within loess horizons (Bolikhovskaya and Molodkov 2006).

A SW-NE climate transect across loess deposits on the Russian Steppe, with MAR ranging from 300 mm/yr (Volgograd) to 500 mm/yr (Stavropol), is characterized by a systematic magnetic enhancement of modern topsoils, with same correlation between susceptibility and MAR as in China (Maher et al. 2003). Present-day dust accumulation in the region is minimal, excluding significant dust flux contributions to magnetic enhancement.

Few data is available for Northern Africa. Loess/paleosols sequences on the Matma Plateau (Tunisia) are characterized by reddened fersillitic paleosols whose susceptibility is a factor 3–9 higher than loess layers. A collection of modern soils from the same area is characterized by a positive correlation with rainfall for MAR values <500 mm/yr, while modern soils formed at >700 mm/yr display the same magnetic enhancement as those with ∼250 mm/yr (Dearing et al. 2001).

25.2.6 Non-loessic Soils

Few magnetic studies exist on non-loessic modern soils formed under “aggressive” climates characterized by very high MAR and/or alternation of extremely wet and dry seasons. These soils can provide useful knowledge about magnetic enhancement limits. Torrent et al. (2010) proposed the ratio Hm/χ _fd between hematite content and frequency dependence of susceptibility as an indicator of weathering intensity, with values <5 × 10⁷ g/m³ for loessic soils in temperate areas, ∼10×10⁷ g/m³ for red Mediterranean soils, and >20×10⁷ g/m³ for well-drained Brazilian ferralsols. The variability of Hm/χ _fd could suggest that the total concentration of pedogenic Fe minerals is poorly reflected by magnetic parameters in certain cases. This problem is obvious if magnetic enhancement is assumed to be an intermediate product of ferrihydrite-to-hematite conversion (Torrent et al. 2006). On the other hand, pedogenic magnetite formation via redox cycling (e.g. Maher 1998) is not directly linked to pedogenic hematite, and its correlation with climate would not be affected by variations in Hm/χ _fd.

Torrent et al. (2010) report geochemical and magnetic parameters of two hematitic soil profiles from the Province of Córdoba (southern Spain). The parent rocks are calcarenite and calcareous orthoquarzite, respectively, containing 0.5–2% Fe_t and <0.3% silicate Fe (Torrent and Cabedo 1986). The present climate is of the warm Mediterranean type, with 600 mm/yr MAR and a long summer drought. A clear magnetic enhancement is observed in the upper horizons, although, on average, to a lesser extent than Chinese loessic soils with same MAR.

We also discuss a series of soils collected along a volcanic mountain transect (Kohala Peninsula, Hawaii) characterized by an altitude-driven climosequence with MAR varying from 160 mm/yr on the coast to 4500 mm/yr at the maximum altitude of 1254 m asl (Chadwick et al. 2003). Age and composition of lavas is homogeneous and rainfall varies to a much greater extent than temperature, making it an ideal site for studying the effect of rainfall on weathering and pedogenesis. Magnetic susceptibility has been measured on soil profiles taken across the climatic gradient, with sampling sites chosen in places with minimal erosion (Singer et al. 1996). Magnetic enhancement is evident in all sites with rainfall <1000 mm/y, while an opposed trend is seen above this limit.

We conclude our review with tropical soils collected across a strong MAR gradient in Ghana (Hendrickx et al. 2005), which are characterized by highly variable magnetic enhancements. These soils formed on a variety of bedrock types including sandstones, phyllites, quartzites, schists, clay shales, and volcanic andesites, schists and amphiboles. MAR values are comprised between 1000 and 2000 mm/yr. Topsoil χ does not correlate significantly with rainfall. One factor responsible for these variations is soil drainage: poorly drained soils on floodplains are one order of magnitude less enhanced than well drained soils with same MAR. On the other hand, strong magnetic enhancement in the uppermost 10 cm is likely produced by burning, which is a prevalent practice in Ghana. This example shows that drainage and human impact must be taken into account when measuring the magnetic properties of modern soils.

25.3 Modeling Soil Moisture and Magnetic Enhancement

One of the most important parameters controlling pedogenic processes is the soil moisture s, which is obviously related to the rainfall R (see Table 25.1 for a definition of all parameters used in this section). Additional factors determining the soil water budget are losses due to leakage L and evapotranspiration E (direct evaporation and transpiration from vegetation). Soil moisture s is defined as the ratio between the actual pore volume filled with water and the total pore volume, so that 0 ≤ s ≤ 1. The fraction of soil volume occupied by pores is the soil porosity φ. The water balance of a soil slab of thickness H and porosity φ is described by the differential equation

$$h\dfrac{{{\textrm{d}}s}}{{{\textrm{d}}t}} = I(t) - E(s,t) - L(s,t),$$

((25.2))

where I is the rate of water infiltration from rainfall, and h = φ H is the effective thickness of an equivalent slab with no porosity (Rodriguez-Iturbe et al. 1999). The individual terms of Eq. (25.2) depend in a complex manner on soil properties, vegetation, and climate. Here we use the statistical model of Rodriguez-Iturbe et al. (1999) to estimate the individual terms of Eq. (25.2) and isolate the most important factors controlling s.

25.3.1 Infiltration from Rainfall

Runoff can be neglected on a horizontal soil, and therefore we assume that infiltration equals rainfall: I = R. Rainfall is idealized as a series of point events described by a Poisson process with mean rate λ, thereby ignoring the temporal structure within each rain event. Furthermore, the intensity of a rain event is quantified by the rain depth Z, defined as the total volume of water per unit surface that reaches the soil during the event. The rain depth is a random variable assumed to have an exponential probability density function

$${p_Z}(z) = \dfrac{1}{\zeta }{e^{ - z{\textrm{/}}\zeta }},$$

((25.3))

where ζ is the average of Z in a given climate (Rodriguez-Iturbe et al. 1999). The rainfall expected over a fixed period of time (e.g. MAR) is thus given by $\left\langle R \right\rangle = \lambda \zeta$. Distinct climates might be characterized by same MAR and different rates and depths of the rain events (Fig. 25.1). For example, rare but strong storms (e.g. λ is small and ζ is large) occur in hot arid climates, while frequent, low-intensity rainfall events are common in cold, humid climates (e.g. λ is large and ζ is small). Both rate and depth of rainfall events display seasonal variations. Typical values for λ and ζ are 0.2–20 events/month and 5–20 mm/event, respectively. In most cases, rainfall depth is positively correlated with temperature (Fig. 25.1).

Fig. 25.1

Rainfall frequency λ and rainfall depth ζ at 4460 climate stations in the U.S. for (a) January, and (b) July, averaged between 1971 and 2000 (source: NOAA). The number of rain events during each month is identified with the number of rainy days with ζ > 2.5 mm. Each station is a point whose gray level is coded according to the mean monthly temperature. Circles are used for stations where temperature data is not available (NA)

25.3.2 Evapotranspiration

Evapotranspiration losses are accounted by a simplified but commonly accepted model where E is assumed to be proportional to soil moisture, until a threshold s _E is reached, above which evapotranspiration takes place at a maximum rate $\hat E$. This maximum rate is called potential evapotranspiration (PET), and depends on several factors such as temperature, wind speed, and vegetation. Evapotranspiration is thus given by:

$$E(s) = \left\{ \begin{array}{l} \,\hat E\,s{\textrm{/}}{s_E},{\textrm{ if }}0 < s \le {s_E} \\ \,\hat E,{\textrm{ }} \quad {\textrm{if }}{s_E} < s < 1 \\ \end{array} \right.$$

((25.4))

(Fig. 25.2). The threshold s _E depends on soil properties and type of vegetation cover; whereby it is assumed that vegetation is under water deficit stress as long as s < s _E . The typical range of s _E is 0.10–0.50, with higher values being characteristic for grasses and desert shrubs (Table 25.3).

Fig. 25.2

Modeled dependence of the total water loss on soil moisture. The contributions of evapotranspiration and deep infiltration are highlighted (shaded areas). The dashed line represents leakage according to Eq. (25.9)

Table 25.3 Dependence of water balance parameters on soil texture (data from (Laio et al. 2001a, b)). Regular numbers indicate typical average values, while cursive numbers refer to particular cases for specific vegetation types. Cursive abbreviations refer to following species: Bouteloua gracilis (short grass, steppe, north-central Colorado), Prosopis glendulos a (woody plant, savanna, Texas), Paspalum setaceum (grass, savanna, Texas), Burkea africana (woody plant, savanna, Nylsvley region, Africa), and Eragrostis pallen s (grass, savanna, Nylsvley region, Africa)

PET is a challenging parameter to estimate, and several empirical methods have been developed for this purpose. Here, we use following approximation valid for a short green crop that is completely shading the ground:

$$\hat E = 1.6 \times {(10\,\,\tau {} /{} J)^a},$$

((25.5))

where τ is the mean monthly temperature in °C, a is an appropriate exponent, and J is a so-called heat index given by the sum of the monthly values j (Thornthwaite 1948). The latter two parameters are given by:

$$\begin{array}{l} \,j = \left\{ \begin{array}{l} \;{(\tau /5)^{1.514}}{\textrm{,}} \quad {\textrm{if }}T > 0 \\ \;0, \quad\qquad\quad\; {\textrm{if }}T \le 0. \\ \end{array} \right. \\ a = 0.49 + 1.79 \times {10^{ - 2}}J - 7.71 \times {10^{ - 5}}{J^2} + 6.75 \\ \qquad \times {10^{ - 7}}{J^3} \end{array} $$

((25.6))

Equation (25.5) can be used for any location at which rainfall and daily maximum and minimum temperatures are recorded. It is based on the inherent assumption that a high correlation exists between mean temperature and some of the other pertinent parameters such as radiation, atmospheric moisture, and wind. Accurate PET estimates also take the latitude dependence of daylight time and the variable month length into account. A daylight-corrected PET estimate is therefore given by:

$${\hat E_{\textrm{c}}} = \hat E \times (D{\textrm{/}}12) \times (n{\textrm{/}}30),$$

((25.7))

where D is the monthly mean daylight duration (photoperiod) in hours, and n is the number of days in a month (Dunne and Leopold 1978). Various algorithms have been implemented for the calculation of the interval D between sunrise and sunset, defined as the times of the day when the sun has an altitude Q above (below if Q < 0) the horizon (Ligr et al. 1995). One of the simplest solutions is:

$$\begin{array}{l} D = \dfrac{2}{{15}}\arccos \left[ {\dfrac{{\cos (90^\circ + Q) - \sin \varphi \sin \eta \sin L}}{{\cos \varphi \sqrt {1 - {{(\sin \eta \sin L)}^2}} }}} \right] \\ \end{array}$$

((25.8))

$$\begin{aligned}[rl]L &= M + 1.916^\circ \sin M + 0.02^\circ \sin 2\,M + 282.565^\circ, \\ M &= (360^\circ {\textrm{/}}365.25)\,t - 3.251^\circ\end{aligned}$$

((25.8))

where ϕ is the latitude, η = 23.44° is the obliquity of the ecliptic, and t is the number of days from the beginning of the year (Keisling 1982). Estimates of D obtained using Eq. (25.8) have a maximum error of 0.33 h for latitudes <60°, which is sufficiently small for practical purposes.

25.3.3 Leakage

Leakage K is modeled as vertical percolation through the lowest active soil layer. Leakage of a saturated soil (i.e. s = 1) is equal to its saturated hydraulic conductivity $\hat K$. For s < 1, leakage is given by:

$$K(s) = \hat K{} {s^c},$$

((25.9))

where the exponent c depends on soil texture, ranging from c ≈ 11 for sand to c ≈ 25 for clay. Since $c \gg 1$, K can be assumed to be effectively zero below a critical moisture threshold s _K , and to vary linearly above it:

$$K(s) \cong \left\{ \begin{array}{l} \;0, \,\qquad\qquad {\textrm{if }}0 \le s \le {s_K} \\ \;\hat K\dfrac{{s - {s_K}}}{{1 - {s_K}}}, \quad {\textrm{if }}{s_K} < s \le 1 \\ \end{array} \right.$$

((25.10))

(Fig. 25.2). The saturated hydraulic conductivity can vary between 9 and 2000 cm/day, depending on soil texture (Table 25.3) (Clapp and Hornberger 1978). Compaction of deeper soil layers, especially below the root zone, produces an exponential-like decrease of the hydraulic conductivity with depth (Lind and Lundin 1990, Youngs and Goss 1988). Typical s _K values are comprised between 0.84 (sand) and 0.92 (clay).

25.3.4 Solution of the Water Balance Equation

A stochastic solution of Eq. (25.2) for the stationary case can be expressed in terms of a probability density function p _s of the soil moisture (Rodriguez-Iturbe et al. 1999). This function provides an estimate of the average soil moisture 〈s〉, as well as the probability of drought events, which is particularly important in agricultural science but not relevant here. The analytical expression for p _s is greatly simplified if normalization (obtained by ensuring that the integral of p _s over 0 ≤ s ≤ 1 is equal to 1) is neglected. In this case, p _s is given by:

$${p_s}(s) = \left\{ \begin{array}{ll} \;\dfrac{h}{{\hat E}}{\left( {\dfrac{s}{{{s_E}}}} \right)^{\lambda {s_E}h{\textrm{/}}\hat E - 1}}{e^{ - sh{\textrm{/}}\zeta }}, &\quad {\textrm{if }}0 < s \le {s_E} \\\\ \;\dfrac{h}{{\hat E}}{e^{\lambda (s - {s_E})h{\textrm{/}}\hat E}}{e^{ - sh{\textrm{/}}\zeta }}, &\quad {\textrm{if }}{s_E} < s \le {s_K} \\\\ \;\dfrac{h}{{\hat E}}{\left[ {\dfrac{{\hat K}}{{\hat E}}\dfrac{{s - {s_K}}}{{1 - {s_K}}} + 1} \right]^{\lambda (1 - {s_K})h{\textrm{/}}\hat K - 1}}{e^{\lambda ({s_K} - {s_E})h{\textrm{/}}\hat E - sh{\textrm{/}}\zeta }}, &\quad {\textrm{if }}{s_K} < s \le 1 \\ \end{array} \right..$$

((25.11))

The complex dependence of soil moisture on the parameters described in Sections 25.3.1, 25.3.2, and 25.3.3 is best illustrated by the examples shown in (Rodriguez-Iturbe et al. 1999) for typical climates specified in Table 25.4. Here, we are interested in the average moisture 〈s〉, which can be calculated from Eq. (25.11) using:

$$\langle s\rangle = \dfrac{{\int_{{} 0}^{{} 1} {{p_s}(u)\,u{} \,{\textrm{d}}u} }}{{\int_{{} 0}^{{} 1} {{p_s}(u)\,{\textrm{d}}u} }}.$$

((25.12))

Table 25.4 Water balance parameters for typical soils formed in four different climates: (1) deep soil in tropical climate with frequent rainfall of moderate intensity and high maximum evapotranspiration, (2) shallow, sandy soil in a hot arid climate, covered with a mixture of trees, shrubs, and grasses, (3) steppe soil in a cold, arid climate with low maximum evapotranspiration, and (4) forest soil in a humid temperate region (data from Rodriguez-Iturbe et al. 1999)

In principle, 〈s〉 depends on seven parameters describing climate, soil properties and vegetation. An important simplification is obtained by grouping the climatic parameters into a single number $W = \lambda \zeta {\textrm{/}}\hat E$, which we call moisture ratio, because it is the ratio between MAR = λζ and PET. This simplification is possible because different combinations of λ , ζ , and $\hat E$ corresponding to the same value of W result in very similar average moistures 〈s(W)〉 (Fig. 25.3). Analogous ratios have been proposed as soil moisture proxies (Jenny 1941).

Fig. 25.3

Right plot: dependence of the average soil moisture 〈s〉 on W for different climates, represented by weak (ζ = 5 mm/event) and intense (ζ = 20 mm/event) rainfall events. Soil properties used for the calculation are: s _E = 0.3, s _K = 0.85, h = 30 cm, $\hat K =$0.5 m/day. Left plot: probability distributions p _s of soil moisture during unsaturated (W = 0.4) and saturated (W = 1.2) conditions for the same parameters used to calculate 〈s〉. The effect of potential evapotranspiration on the curves is negligible and is not shown

The main parameter controlling the shape of the function 〈s(W)〉 is ζ  , which describes the intensity of rain events and therefore discriminates between climates that are more or less “stormy”. Figure 25.3 shows the largest climate-driven variations of 〈s(W)〉 obtained by choosing extreme values of ζ. The error introduced by grouping different parameters into a single number calculable from climatic tables is not larger than the uncertainties involved in estimating λ, ζ, and $\hat E$.

If W < 1, maximum evapotranspiration exceeds rainfall, and soil moisture remains relatively low on average. As W approaches 1, soil moisture increases until the threshold s _K is reached, above which water starts to percolate. If W > 1, soil moisture is maintained constantly near saturation and drainage becomes the main mechanism of water loss. Interestingly, a step-like increase of 〈s〉 to near-saturation values occurs in a narrow range around W = 1 in well-drained soils. Therefore, W = 1 is a threshold separating regimes of low/moderate soil moisture from saturation. The transition sharpness increases with soil thickness (Fig. 25.4a). Soils characterized by poor drainage (e.g. $\hat K \to 0$) experience the transition to a saturation regime when W is as low as 0.5 (Fig. 25.4b). Soil moisture in the saturation regime is mainly controlled by s _K (Fig. 25.4c), which in turn depends on soil texture. The importance of this threshold was recognized by Thornthwaite (1948), who defined a similar parameter, corresponding to W – 1, for which zero is the saturation threshold. Alternative parameters, such as the “effective rainfall” PET – MAR, have been defined with the same purpose (Chadwick et al. 2003, Orgeira and Compagnucci 2006).

Fig. 25.4

Dependence of 〈s(W)〉 curves on (a) soil thickness h, (b) drainage, which is mainly controlled by the saturated hydraulic conductivity$\hat K$, and (c, d) soil texture (s _K and s _E are small for sand and large for clay). The model parameters correspond to a temperate climate (ζ = 15 mm/event, $\hat E$ = 4 mm/day), and, unless otherwise specified in the plots, on typical average soil properties (s _E = 0.3, s _K = 0.85, h = 30 cm, $\hat K =$0.5 m/day)

As long as saturation is not reached, a direct proportionality exists between 〈s〉 and W, and we obtain:

$$\langle s\rangle = {s_E}\,W$$

((25.13))

from the λ → 0 limit of Eq. (25.11) (Fig. 25.4d). The proportionality factor s _E is controlled mainly by soil texture and by vegetation cover (Table 25.3). Equation (25.13) is valid over a range of s _E values typical of soils, and for h > 20 cm (Fig. 25.5). It can be used to estimate the average moisture of soils in the non-saturated regime (e.g. W < 1 in well drained soils and W < 0.5 in poorly drained soils) under typical climatic conditions, vegetation cover, and drainage, using data available from climatic tables. Therefore, W can be considered a climatic proxy for soil moisture, and thus an important parameter to take into account for constructing a climofunction.

Fig. 25.5

Validity range of Eq. (25.13) tested for (a) different values of s _E , and (b) different soil thicknesses. Solid lines represent the dependence of the initial slope of 〈s(W)〉 on s _E and h, compared with the approximation given by Eq. (25.13) (dotted lines)

25.3.5 Enhancement Proxy for Pedogenic Magnetite

Several studies demonstrated that soil magnetic enhancement and climate are correlated (e.g. Maher and Thompson 1992, 1995, Maher et al. 1994, Thompson and Maher 1995, Han et al. 1996, Maher 1998, Porter et al. 2001). Common parameters used to establish such correlation are log₁₀Δχ and MAR (Eq. (25.1)), as proposed by Maher et al. (1994). Attempts to improve this correlation led to proposing alternative magnetic proxies, such as ARM for loessic soils in the U.S. (Geiss and Zanner 2007), and to the consideration of additional climatic parameters, for example the mean annual temperature (Han et al. 1996). Porter et al. (2001) observed a negative correlation between susceptibility of modern soils on the CLP and the mean annual evapotranspiration, therefore recognizing the role of the latter parameter in the soil water balance. Beside the production of pedogenic minerals, climate-related processes such as weathering of parent magnetic minerals (Liu et al. 1999), syn-pedogenic dust inputs (Heller et al. 1993), and chemical collapse (Anderson and Hallet 1996) are additional factors that influence the magnetic properties of soils. A first model using these factors as a-priori parameters for glacial and interglacial periods was proposed by Anderson and Hallet (1996). The optimal choice of climatic proxies depends critically on understanding how pedogenic magnetite and other magnetic oxides are formed during pedogenesis. For example, the “fermentation process” proposed by Le Borgne (1955) and the ferrihydrite alteration model of Barrón and Torrent (2002) can be expected to have different climatic responses.

In the following, we refine the “fermentation” magnetic enhancement model of Maher (1998) by constructing a quantitative link between pedogenic magnetite and the soil water balance. In simple words, our work consists in replacing MAR with a climatic parameter that accounts for the effects of soil moisture dynamics on the formation of magnetite by redox cycling of Fe sources. The model can be subdivided into distinct processes described as follows (Fig. 25.6):

• (1) Weathering. Hydrolysis of primary Fe minerals releases Fe²⁺ ions, whose oxidation results in the production of poorly crystallized oxyhydroxides (ferrihydrite). Ferrihydrite is assumed to be the primary source of pedogenic minerals that contribute to the magnetic enhancement. As long as wheatherable Fe minerals exist or enter into the system, the total concentration of iron available for pedogenic minerals increases. Depending on the composition of primary minerals, weathering can be more or less rapid, leading to a variable time necessary for reaching the mature stage. In our model, along with Maher (1998), we assume that the production of pedogenic minerals responsible for magnetic enhancement is not limited by Fe availability, and that a stationary regime is reached in mature soils. Lack of Fe limitation in soils formed on most types of parent materials is supported by the fact that the concentration of pedogenic magnetite necessary to explain observed susceptibility enhancements is much smaller than typical Fe_d and Fe_t concentrations. The onset of a stationary regime without significant syn-pedogenic dust inputs implies that iron in pedogenic minerals is recycled.

• (2) Wetting phase 1 (Fig. 25.7). After each rain event, a number of soil pores become saturated with water. In the active soil horizon and in presence of organic matter, oxygen is consumed by microorganisms in wet pores. In some pores, higher initial nutrient concentration, after oxygen depletion, might consume all available electron acceptors until Fe³⁺ reduction becomes possible (Deming and Baross 1993, Maher 1998, Chadwick and Chorover 2001). Possible primary sources for Fe reduction are ferrihydrite – which supports much higher reduction rates than other Fe oxides (Roden and Zachara 1996) – and clay minerals (Kostka et al. 2002). The outward diffusion of Fe²⁺ ions in a microscale redox gradient around “reduction spots” is accompanied by re-oxidation and precipitation of a variety of iron oxides and oxyhydroxides, depending on pH and oxidation rate (Dearing et al. 1996, Maher et al. 2003). One of the oxidation products is ultrafine magnetite, which – although not relevant in terms of mass – is the main cause for magnetic enhancement. Because of the order of magnitude difference in concentration, magnetite can be neglected in the mass balance. The invariant grain size distribution of pedogenic magnetite in Chinese soils and paleosols formed at sites with different MAR (Liu et al. 2007) can be interpreted as a circumstantial evidence that pedogenic magnetite is formed under specific, well controlled geochemical conditions, as it is the case with biological mediation by dissimilatory iron reducing bacteria (Maher et al. 2003). Although rapid microscale iron redox cycling is actively sustained by communities of iron oxidizing and reducing bacteria (Sobolev and Roden 2002), the role of dissimilatory metal reducing bacteria in producing a magnetic enhancement could not be proven (Guyodo et al. 2006). Fully inorganic magnetite formation paths are possible, for example by reaction of ferrihydrite with low Fe²⁺ concentrations (Tamaura et al. 1983, Tronc et al. 1992). The invariant grain size distribution of the product might be explained with the specific formation mechanism requiring Fe²⁺ adsorption at pH > 5.0 and subsequent crystal growth by dissolution-recrystallization or solid state reaction. The exact mechanism of magnetite formation is not relevant in our model: we only assume that ultrafine magnetite precipitates during the wetting phase in minute amounts negligible for the Fe mass balance but sufficient produce a magnetic enhancement. Furthermore, we assume that the rate of pedogenic magnetite production depends only on the activity of reduction spots that can support Fe reduction.

• (3) Drying phase. As water is lost by evapotranspiration, an increasing number of reduction spots dry out and oxidizing conditions are re-established. Magnetite crystals produced during the wetting phase will start to oxidize from the surface towards the interior (Maher 1998). This process can be thought as the growth of a cation-deficient maghemite-like surface layer. The oxidation kinetics is controlled by the diffusion of Fe²⁺ ions in the crystal lattice (Gallagher et al. 1968). For example, magnetite particles with a diameter of 8.7 nm are half-way converted to maghemite after 6.7 days in aqueous solution at 24°C (Tang et al. 2003). Therefore, a significant amount of pedogenic magnetite oxidation can be expected during dry or well oxygenated time intervals (Murad and Schwertmann 1993).

• (4) Wetting phase 2. Soil pores are subjected to repeated wetting and drying cycles modulated by rain events and successive evapotranspiration (Laio et al. 2001a, b). It is therefore only a matter of time before a pedogenic magnetite particle – after one or more drying and wetting cycles under oxic conditions – experiences a new “reducing event” similar to that during which it was created. If this is the case, reducing conditions promote the dissolution of the oxidized layer, and eventually of the entire particle. Analogous dissolution of surface oxidation layers has been proposed to explain the appearance of the Verwey transition in pelagic sediments below the Fe redox boundary (Smirnov and Tarduno 2000). Simultaneous magnetite production and maghemite dissolution during wetting phases in the active soil horizon explains two important observations. The first is that – at least in certain types of soils – magnetic enhancement reaches a dynamic equilibrium with the environment and does not proceed indefinitely with time (Thompson and Maher 1995). The second observation is that maghemite in paleosols is preserved over geological times, implying that dissolution must be promoted by chemical conditions that occur only in active soils. A dynamic equilibrium governing the concentration of pedogenic ferrimagnetic minerals is essential for observing a reliable correlation between magnetic enhancement and climate when comparing soils of different ages.

Fig. 25.6

Conceptual model of soil magnetic enhancement

Fig. 25.7

Organic matter consumption by a sequence of reactions involving different electron acceptors, driven by the Eh potential decrease (modified from Chadwick and Chorover 2001). Pedogenic ferrimagnetic minerals are assumed to form by oxidation of Fe²⁺ ions released by iron reduction reactions

The conceptual enhancement mechanism described above, which is essentially the same proposed by Maher (1998), is used in the following to implement a semi-quantitative estimate of pedogenic magnetite concentrations at equilibrium with the average climatic parameters described in Sections 25.3.1, 25.3.2, 25.3.3, and 25.3.4. The production rate p is expected to be proportional to the number of reduction spots, which, on a long term, is proportional to the average soil moisture 〈s〉. Each reduction spot can produce magnetite during a limited amount of time, until it dries out or chemical conditions are no longer favorable. In order to sustain magnetite production over time, reduction spots must be “reset” during dry or oxygenated periods. Therefore, magnetic enhancement is ultimately driven by the alternation of wet and dry phases, whose pace is dictated by the frequency λ of rain events. The last factor to take into account is the onset of a saturation regime at W ≈ 1, as discussed in Section 25.3.4. During this regime, excess water is drained and evapotranspiration plays a minor rule. Drainage through the active soil layer decreases the chances that pores dry out, limiting the frequency of “reset” events and thus the capability of maintaining appropriate conditions for the production of pedogenic magnetite. Accordingly, we define the effective soil moisture, s _eff, as the fraction of pores that can sustain magnetite production. This parameter is calculated by multiplying the average fraction 〈s〉 of wet pores with a function θ (W−W ₀) that equals 1 when W is smaller than a critical threshold W ₀ ≈ 1 marking the onset of a saturated regime, and is 0 if W > W ₀. Since the onset of saturation occurs between W = 0.9 and 1.3 (Fig. 25.3), we assume θ  to express a similar, smooth transition (Fig. 25.8).

Fig. 25.8

Average fraction 〈s〉 of wet pores, fraction θ of wet pores that dry by evapotranspiration, and effective fraction s _eff of pores where magnetic enhancement occurs, as a function of the moisture ratio W

The instantaneous magnetite production rate is then given by:

$$p = \dfrac{{{\textrm{d}}m}}{{{\textrm{d}}t}} \propto \lambda {} {s_{{\textrm{eff}}}},$$

((25.14))

where m is the pedogenic magnetite mass, t is time, and ${s_{{\textrm{eff}}}} = \langle s\rangle \,\theta (W - {W_0})$. Since the calculation of 〈s〉 according to Eqs. (25.11 and 25.12) is elaborated, we approximate 〈s〉 with Eq. (25.13) and choose a suitable function θ such that s _eff has a similar dependence on W as in Fig. 25.8. This is the case when $\theta (x) = [1 - \tanh (5x)]/2$ and W ₀ = 1.0–1.2. Then, Eq. (25.14) simplifies to:

$$p \propto \lambda {} {s_E}\,W\,\theta (W - {W_0}).$$

((25.15))

The magnetite production rate expressed in Eq. (25.15) is only meaningful when evaluated over a time interval that is sufficiently long to overcome the statistical nature of λ and W.

On the other hand, low-temperature oxidation of pedogenic magnetite proceeds with a diffusion-controlled kinetics. The fraction δ of Fe²⁺ ions that diffuse out of a magnetite sphere with radius r is given by:

$$\delta = \dfrac{6}{{\sqrt \pi }}{\left( {\dfrac{{Dt}}{{{r^2}}}} \right)^{1{\textrm{/}}2}} - 3\dfrac{{Dt}}{{{r^2}}}$$

((25.16))

where D is a temperature-dependent diffusion constant (D ≈ 1.3×10^–24 m²s^–1 at 24°C), and t is time (Tang et al. 2003). Typical pedogenic magnetite particles have a radius of the order of 10 nm (Maher 1998), so that $Dt{} /{} {r^2} \ll 1$ over one month: in this case, the second term in Eq. (25.16) can be neglected, and $\delta \propto {(Dt)^{1{\textrm{/}}2}}{r^{ - 1}}$. The average time interval during which a particle is uninterruptedly exposed to oxygen can be assumed to be inversely proportional to R. Therefore, the mass of the oxidized layer will be proportional to δ, which is in turn proportional to ${(D{\textrm{/}}R)^{1{\textrm{/}}2}}{r^{ - 1}}$. This is the amount of pedogenic magnetite that is subsequently removed under reducing conditions. Because the frequency by which reduction spots are activated is λ, the rate q of pedogenic magnetite dissolution is:

$$q \propto \dfrac{\lambda }{r}\sqrt {\dfrac{D}{R}} \,m.$$

((25.17))

If we assume that the grain size distribution of pedogenic magnetite is climate-independent, the average grain size r in Eq. (25.17) is constant and can be neglected, along with D, which is a material property. The grain size distribution of pedogenic minerals can be estimated using the blocking temperature distribution obtained from the temperature dependence of the out-of-phase susceptibility ${\chi _{\textrm{q}}}(T)$ (Shcherbakov and Fabian 2005, Egli 2009). Measurements of ${\chi _{\textrm{q}}}(T)$ for a series of CLP paleosols with various magnetic enhancement degrees, supposedly formed under different rainfall regimes, confirm that the blocking temperature distribution does not vary significantly (Liu et al. 2005). Therefore, we will neglect grain size effects in Eq. (25.17).

At equilibrium, the production and dissolution rates given by Eq. (25.15) and Eq. (25.17) must equal each other. This is possible when

$$m \propto {s_E}{R^{1{\textrm{/}}2}}W\theta ({W_0} - W).$$

((25.18))

Equation (25.18) describes the equilibrium concentration of pedogenic magnetite in terms of rainfall (R), type of climate (W), and soil properties (s _E ). Monthly climatic tables can be used to evaluate Eq. (25.18) over the year. In analogy with the “rainfall effectiveness” introduced by Thornthwaite (1931), we define the magnetite enhancement proxy, MEP, as:

$${\textrm{MEP}} = \dfrac{{\hat E_0^{1{\textrm{/}}2}}}{{{s_0}}}{s_E}\sum\limits_{k \,=\, 1}^{12} {\dfrac{{R_k^{3{\textrm{/}}2}}}{{{{\hat E}_k}}}\;\theta \left( {{W_0} - \dfrac{{{R_k}}}{{{{\hat E}_k}}}} \right)},$$

((25.19))

where R _k and ${\hat E_k}$ are monthly values of rainfall and potential evapotranspiration, respectively, and W ₀ = 1.2. The constant ${\hat E_0}$ is an arbitrarily chosen PET value which ensures that MEP and its monthly values have the same unit as rainfall. Similarly, s ₀ is an arbitrarily chosen value of s _E . Normalization of Eq. (25.19) by ${\hat E_0}$ and s ₀ eases the comparison between rainfall and MEP, which can be regarded as the “effective rainfall” driving the production of pedogenic magnetite. Given the large number of publications on the magnetic enhancement of soils and paleosols from the CLP, we choose s ₀ = 0.3 as the typical s _E of those soils, and ${\hat E_0}$ = 100 mm/month, which is comparable with the maximum monthly PET of the region.

In order to understand the proxy defined by Eq. (25.19), we consider a set of similar soils collected from a region with a defined type of climate. We assume that these soils never experienced a water saturation regime, in which case θ = 1. A typical example is the CLP when MAR < 1000 mm/yr. In this case, magnetic enhancement is proportional to R ^3/2, providing a climofunction that fits the modern CLP soil data as well as Eq. (25.1) does. However, MEP also depends on the additional parameters $\hat E$ and s _E , which do not necessarily co-vary with MAR. This can explain the relatively large Δχ scatter (about a factor of 2) of modern loessic soils of the same region and similar MAR (e.g. Han et al. 1996, Porter et al. 2001, Maher et al. 2003, Geiss and Zanner 2007). Because age and parent material heterogeneities are negligible in this case, the scatter must originate from “hidden” climatic parameters that are taken into consideration by MEP. Therefore, we expect MEP, which can be calculated from climatic tables, to correlate much better with magnetic enhancement parameters. Furthermore, regional climofunction differences, such as those existing between loessic soils from China and from Midwestern U.S., should disappear if MAR is replaced by MEP.

25.4 Model Verification

In this section we test the magnetite enhancement proxy (MEP) defined in Eq. (25.19), by considering ratios of the form M/MEP, where M is a magnetic enhancement parameter (i.e. $\Delta \chi = {\chi _{\textrm{B}}} - {\chi _{\textrm{C}}}$, χ _fd, and χ _ARM), and comparing them with M/MAR. We expect M/MEP to be less scattered than M/MAR for any group of soils whose magnetic enhancement occurs as described in Section 25.3, with no regional differences. Since M/MEP is a constant in the ideal case, we call this ratio magnetic enhancement factor. Persisting regional differences would indicate that the magnetic enhancement mechanism assumed to calculate MEP is not universally valid, or that pedogenic magnetite has not been preserved, for example because of gleyzation. Magnetic enhancement factors of soils from the regions discussed in Section 25.2 are summarized in Tables 25.5 and 25.6 and discussed in the following.

Table 25.5 Magnetic enhancement factors of modern soils discussed in the text

Table 25.6 Comparison of soil magnetic enhancements (calculated from most reliable magnetic parameters), relative to the CLP

25.4.1 Modern Soils on the CLP

We begin our discussion with the magnetic enhancement threshold at MAR = 900–1100 mm/yr observed for modern soils on the CLP (Han et al. 1996, Porter et al. 2001). Monthly climatic data for two sites across this threshold (Duanjiapo, MAR = 578 mm/yr, and Nanling mountains, MAR = 1552 mm/yr) are shown if Fig. 25.9, together with MEP estimates obtained by assuming s _E = 0.3 for both soils. In Duanjiapo, monthly PET values are larger than rainfall during spring and summer and about equal in autumn. A different situation occurs in winter, when smaller PET values result from lower temperatures. Elevated W in December and January ensure that the soil is permanently wet, and no magnetite formation is expected during this time. Rainfall is low in December and January as well, meaning that pedogenic magnetite accumulation is not important during wintertime, regardless of PET. Therefore, both rainfall and MEP predict magnetic enhancement to occur mainly between March and November, with maximum values in summer (Fig. 25.9). Using Eq. (25.19) we calculate MEP = 514 mm/yr, which is 90% of MAR.

Fig. 25.9

Monthly values of rainfall R, potential evapotranspiration PET, and magnetite enhancement proxy MEP for two sites in China: Duanjiapo (MAR = 578 mm/yr, PET = 704 mm/yr, MEP = 514 mm/yr), and the Nanling mountains (MAR = 1550 mm/yr, PET = 792 mm/yr, MEP = 240 mm/yr). Dashed areas correspond to periods of water excess characterized by R > PET

In southern China, rainfall has a strong monsoonal character, with a maximum monthly value of 300 mm in May. This value corresponds to the total yearly rainfall at the Northern boundary of the CLP. PET is comparable with Duanjiapo; however, rainfall is larger than PET over the entire year, except for September. Maximum values of W are concentrated in winter and spring, and W < 1.4 between July and October, which is the only period of the year when pedogenic magnetite production is expected. The resulting MEP is 240 mm/yr, which is only 15% of MAR, and 46% of MEP calculated for Duanjiapo. The susceptibility enhancement expected for this site is Δχ ≈ 250 mm³/kg (Han et al. 1996), which is ∼1/3 of the susceptibility measured at Duanjiapo (Table 25.2). MEP estimates agree much better with susceptibility measurements than MAR, and correctly predict the non-monotonic dependence of Δχ on MAR. The residual differences in Δχ/MEP might reflect additional effects from mountain topography (runoff), or gleyzation, which are not accounted by Eq. (25.19).

25.4.2 Red Mediterranean Soils

Warm Mediterranean climates are characterized by an extended summer drought (June-September) with rainfall concentrated during the winter time, when PET is low and W > 1 (Fig. 25.10). Pedogenic magnetite is expected to accumulate only during few rainy months in spring and autumn. The area near Montilla sampled by Torrent and Cabedo (1986) is characterized by MAR = 600 mm/yr and a MEP of only 246 mm/yr, which explains the lower magnetic enhancement with respect to soils with similar MAR in China. Larger MAR values – obtained for example by multiplying the monthly R values with a constant factor >1 – would produce even lower MEP values. The same reasoning can be used to show that the maximum enhancement for this type of climate is expected to occur at MAR = 600 mm/yr.

Fig. 25.10

Monthly values of rainfall R, potential evapotranspiration PET, and magnetite enhancement proxy MEP for Montilla (Spain): MAR = 600 mm/yr, PET = 1056 mm/yr, MEP = 246 mm/yr. Dashed areas correspond to periods of water excess characterized by R > PET

The magnetic enhancements of the two soil profiles (Montilla and La Ramba) differ by a factor of two (Torrent et al. 2010), which cannot be explained by climatic differences between sites. Geochemistry and magnetic mineralogy of the two soils are similar as well. Interestingly, the product between the enhanced horizon thickness (∼60 cm in Montilla and ∼120 cm in La Ramba) and magnetic enhancement is constant. Nevertheless, Δχ/MEP, χ _fd/MEP and χ _ARM/MEP values obtained from the average of the two profiles are similar to the corresponding factors calculated for Chinese soils. Different magnetic enhancements at Montilla and La Ramba could arise from the extreme sensitivity of MEP to the onset of a saturation regime in this type of climate. A slight shift of the saturation threshold W ₀ – caused for example by different values of the hydraulic conductivity – is sufficient to change the duration of magnetite production and thus MEP. For example, a 15% MEP increase is obtained when W ₀ = 1.2 in Eq. (25.19) is replaced by W ₀ = 1.4. Hydraulic conductivity is strongly dependent on soil porosity, which decreases with depth (Lind and Lundin 1990, Youngs and Goss 1988). Therefore, the thinner active soil layer in Montilla is expected to have a larger hydraulic conductivity, a higher saturation threshold W ₀, and a larger magnetic enhancement, as indeed observed.

Modern loessic soils on the Matmata Plateau (Tunisia) have formed in a similar climate with rainfall concentrated between December and March, when W > 1, and a long summer drought (Dearing et al. 2001). MAR – PET values in excess of 200 mm/yr can be inferred from clay pervection and the development of blocky prismatic structures (Dearing et al. 2001). As for the case depicted in Fig. 25.10, pedogenic magnetite is expected to form during short periods just before and after summer drought. Interestingly, the maximum magnetic enhancement is observed at MAR ≅ 500 mm/yr (Dearing et al. 2001), close to 600 mm/yr limit calculated using the climatic data of Fig. 25.10. Magnetic enhancement of soils with similar MAR is highly variable, as seen by typical ratios of ∼5 between highest and lowest susceptibility values. The same scatter is observed for χ _fd, excluding parent material variability as a possible explanation. As discussed for the two soil profiles in Spain, highly variable magnetic enhancement are expected because of the sensitivity of MEP to small climatic differences and to soil drainage capability.

25.4.3 Volcanic Soils from the Kohala Peninsula, Hawaii

The case study of Hawaiian volcanic soils collected across a strong rainfall gradient provides an interesting test for our enhancement model. Although reliable magnetic enhancement estimates are complicated by the strong magnetic signature of the underlying lava rocks and possible weathering effects on primary magnetic minerals, a clear, non-monotonic dependence of magnetic susceptibility on rainfall can be recognized (Singer et al. 1996). Maximum magnetic enhancement occurs when MAR ≈ 1000 mm/yr: above this threshold, χ declines and becomes highly variable. The climatic gradient is primarily determined by altitude, with MAR values increasing from 160 mm/yr on the coast, to 3000 mm/yr at maximum altitude. Evapotranspiration decreases moderately with altitude along with temperature: measured values range from 2200 mm/yr at sea level to 1000 mm/yr at maximum altitude (Shade 1995). Because of opposed MAR and PET trends, the yearly mean soil moisture ratio W increases from ∼0.08 at sea level, to ∼3 at maximum altitude, with monthly peak values >10. Using the climatic data in (Shade 1995, Chadwick et al. 2003), we calculated MEP values for the sites measured by Singer et al. (1996). Although a direct comparison between χ and MEP should be interpreted with caution because of the strong magnetic signature of the parent material, a common trend can be recognized (Fig. 25.11). Interestingly, MEP estimates become highly variable at large MAR values, as seen also for χ measurements. The scatter can be explained by the “cutoff” effect occurring near W = 1, which makes the number of reduction spots subjected to wetting/drying cycles very sensitive to little changes of the soil moisture. The maximum susceptibility enhancement around MAR = 800 mm/yr coincides with maximum effective cation exchange capacity, and precedes the onset of strong leaching effects at larger MAR values (Chadwick et al. 2003).

Fig. 25.11

Mean annual rainfall vs. profile sum of magnetic susceptibility (squares) for nine soils from the Kohala peninsula, Hawaii (Singer et al. 1996), compared with MEP (circles) calculated for sites with available monthly climate data (Shade 1995). The dashed line is a guide for the eye

The rainfall vs. MEP curve predicted by our model is similar to the rainfall vs. pedogenic magnetite model postulated by Balsam et al. (2004), with a similar peak at MAR ≈ 700 mm/y. Poor soil drainage or low PET values can shift the position of this peak to much lower MAR values. It is important to notice that our model does not require reductive dissolution effects to explain the decline of magnetic enhancement for W > 1, although gleyzation, if occurring, will strengthen the existing trend.

25.4.4 Comparison Between Loessic Soils from China and North America

In previous sections, we discussed magnetic enhancement examples that were mainly controlled by the decline of pedogenic magnetite production as soils become saturated with water. Most paleorainfall reconstructions, however, are based on loess/paleosol sequences where saturation effects are not sufficient to reverse the positive correlation with MAR. Calibration of susceptibility measurements for paleorainfall reconstruction purposes is based on the study of modern soils collected from worldwide warm temperate regions (Maher 1998, Maher et al. 1994, Maher and Thompson 1995, Maher et al. 2003). The extension of this archive to loessic soils in North America, however, clearly disagrees with the susceptibility-rainfall trends obtained for Asia (Geiss and Zanner 2007). The definition of regional-based climofunctions overcomes this problem, yet the apparent lack of a universal enhancement law in soils with very similar geological settings casts a cloud on the reliability of magnetic enhancement models.

Modern soils on Peoria loess are systematically less enhanced than soils from Asia formed in climates with similar MAR: Δχ and χ _ARM are only ∼1/3 and ∼1/2 of those of Chinese soils, respectively (Fig. 25.12). Pedogenic ARM, defined as the difference between χ _ARM of the maximum enhanced horizon and the parent loess, correlates significantly with MAR (r ² = 0.84) while Δχ does not (r ² = 0.3). A reason for the discrepancy between these two magnetic enhancement parameters could be related to the fact that the assumption of a depth-independent contribution of primary minerals, which underlies the common definition of magnetic enhancement, is not valid. This hypothesis is supported by magnetic unmixing analyses of selected soil profiles, which shows that the magnetization of the coercivity component attributed to non-pedogenic minerals changes with depth (Geiss and Zanner 2006). A depth-dependent magnetic background can result from weathering effects and/or syn-pedogenic dust inputs (Bettis et al. 2003a, b). Because of its strong selectivity to SD particles, ARM is less affected by the parent material and should be considered, at least in this case, a more reliable indicator for the concentration of pedogenic magnetite. Geiss and Zanner (2007) observed that relative enhancement parameters (defined as the ratio between maximum enhancement horizon and parent loess) correlate systematically better with MAR that absolute enhancement parameters, and suggested that magnetic enhancement is limited by the Fe supply from the parent material. This hypothesis is in contradiction with our model, which assumes no Fe limitation.

Fig. 25.12

(a) Mean annual rainfall vs. susceptibility enhancement Δχ of modern soils in China (Porter et al. 2001), Russian Steppe (Maher et al. 2003), worldwide sites on the northern hemisphere with a warm temperate climate (Maher and Thompson 1995), and Midwestern U.S. (Geiss and Zanner 2007). Lines are least squares fits ∝ MAR^3/2 for China and Russian Steppe, and for Midwestern U.S., respectively. The difference between the two fits defines a ratio of 0.27 between susceptibility enhancements in Asia and Midwestern U.S. (b) Susceptibility enhancement Δχ vs. Δχ/χ _ARM for Chinese paleosols (Liu et al. 2004) and modern soils from Midwestern U.S. (Geiss and Zanner 2007). Because of highly magnetic parent material, ARM for the U.S. soils is calculated as the difference between maximum enhanced horizon and the parent loess. Lines are least squares fits for Midwestern U.S. and China, calculated over the susceptibility interval covered by the US soils. The Δχ/χ _ARM ratios of U.S. soils are 60% of those of Chinese paleosols

Monthly climatic data are shown in Fig. 25.13 for two sites: Arbor cemetery, Nebraska (MAR = 494 mm/yr), and Mt. Calvary cemetery, Iowa (MAR = 890 mm/yr). At Arbor cemetery, rainfall is > PET during winter and spring, and pedogenic magnetite is expected to form between May and October. The estimated MEP is 253 mm/yr, which is about 50% of MAR. For comparison, MEP in Duanjiapo is 90% of MAR. Climatic conditions are even less favorable to magnetite pedogenesis at Mt. Calvary cemetery, where rainfall is > PET over the entire year, except for three months in summer. Accordingly, MEP for this site is only 31% of MAR. All sites sampled by Geiss and Zanner (2007) are characterized by climatic parameters that are intermediate between the two examples of Fig. 25.13.

Fig. 25.13

Monthly values of rainfall R, potential evapotranspiration PET, and magnetite enhancement proxy MEP for two sites on Peoria loess (Midwestern US): Arbor cemetery (MAR = 494 mm/yr, PET = 577 mm/yr, MEP = 253 mm/yr), and Mt. Calvary cemetery (MAR = 890 mm/yr, PET = 611 mm/yr, MEP = 273 mm/yr). Dashed areas correspond to periods of water excess characterized by R > PET

To quantify differences with Chinese soils, we compare magnetic enhancement and MEP of Peoria soils with typical soils on the CLP. A typical Chinese soil is characterized by $\Delta \chi /{\textrm{MEP}} \approx {\textrm{0}}{\textrm{.18}}$ and ${\chi _{{\textrm{ARM}}}}/{\textrm{MEP}} \approx 1.1$, where Δχ and χ _ARM are expressed in 10^–8 m³/kg, and MEP in mm/yr (Table 25.5). On the other hand, Δχ and MEP/MAR of Peoria soils are ∼27% and ∼47% of the values for soils with same MAR on the CLP, respectively, as obtained from Fig. 25.12a and from climatic data of the sites listed in (Geiss and Zanner 2007). Using simple proportions for soils with same MAR, we estimate the magnetite enhancement factor of Midwestern U.S.:

$$\begin{aligned}&{}{\left( {\dfrac{{\Delta \chi }}{{{\textrm{MEP}}}}} \right)_{{\textrm{Peoria}}}} \\&{}\quad= \dfrac{{\Delta {\chi _{{\textrm{Peoria}}}}}}{{\Delta {\chi _{{\textrm{CLP}}}}}}\dfrac{{{{({\textrm{MEP/MAR}})}_{{\textrm{CLP}}}}}}{{{{({\textrm{MEP/MAR}})}_{{\textrm{Peoria}}}}}}{\left( {\dfrac{{\Delta \chi }}{{{\textrm{MEP}}}}} \right)_{{\textrm{CLP}}}} \\&{}\quad\approx 0.1 \pm 0.02.\end{aligned}$$

((25.20))

A similar reasoning can be applied to χ _ARM, knowing that $\Delta \chi /{\chi _{{\textrm{ARM}}}} \approx 0.091$ for Peoria soils on average (Fig. 25.12b), which is ∼60% of the typical values over the CLP. Then,

$$\begin{aligned}{\left( {\dfrac{{{\chi _{{\textrm{ARM}}}}}}{{{\textrm{MEP}}}}} \right)_{{\textrm{Peoria}}}} &{}= {\left( {\dfrac{{\Delta \chi }}{{{\textrm{MEP}}}}} \right)_{{\textrm{Peoria}}}}\left( {\dfrac{{\Delta \chi }}{{{\chi _{{\textrm{ARM}}}}}}} \right)_{{\textrm{Peoria}}}^{ - 1} \\ &{}\approx 1.1 \pm 0.2.\end{aligned}$$

((25.21))

The χ _ARM/MEP ratio of CLP and Peoria soils can be considered identical within the standard errors produced by the large scatter of individual sites in Fig. 25.12. A significant difference between the two regions persists if Δχ/MEP is considered; however, as discussed before, Δχ is not a reliable enhancement parameter on Peoria loess. Further investigation is needed to obtain unbiased estimates of the pedogenic susceptibility, for example by comparing measurements before and after selective CBD dissolution of pedogenic minerals (Vidic et al. 2000). From the preliminary results obtained with ARM measurements, we can reasonably conclude that a different magnetic enhancement mechanism is not required to explain magnetic data, and that the same model for pedogenic magnetite formation is valid for loessic soils in China and in the US, if climatic differences are taken into account.

25.4.5 Alaska

Loess/paleosol sequences from Alaska provide an interesting test for our model, due to extreme climatic conditions at high latitudes. There is a general agreement that pedogenic enhancement occurred in Alaskan paleosols, although not recognizable from susceptibility measurements, because of the strong opposite trend imposed by the wind-modulated, large concentration of primary magnetic minerals in loess. Nevertheless χ _fd is small compared to CLP soils (Table 25.2), suggesting that magnetic enhancement is weak, possibly because of magnetite dissolution due to gleyzation (Liu et al. 1999). The climatic parameters of Halfway House, the site where a loess/paleosol sequence has been characterized by magnetic measurements, are dominated by an extremely pronounced seasonality (Fig. 25.14). Evapotranspiration is absent during the winter months due to temperatures constantly below the freezing point and snow coverage, and rises to moderately large values during summer. Summer evapotranspiration is larger than expected from the relatively cool weather, because of the extended day length at high latitudes (Eq. 25.7). Rainfall is highest in summer, but much lower than evapotranspiration, and obviously occurs in form of snow during the wintertime. Pedogenic magnetite is therefore expected to accumulate during months with mean temperatures >0°C, when evapotranspiration is possible. An exception is given by May, when snow melts. Because a non-zero MEP is predicted for May by Eq. (25.19), while the soil is saturated with melt water, we ignore this month and estimate an annual MEP of 128 mm/yr, which is ∼49% of MAR.

Fig. 25.14

Monthly values of rainfall R, potential evapotranspiration PET, and magnetite enhancement proxy MEP for Halfway House (Alaska): MAR = 264 mm/yr, PET = 354 mm/yr, MEP = 128 mm/yr. Dashed areas correspond to periods of water excess characterized by R > PET. The calculated MEP contribution of May (dashed) was not taken into consideration because of snow melt

Magnetic enhancement estimates for Alaska rely on χ _fd, because susceptibility is dominated by the dust signal. Published χ _fd values refer to a paleosol from oxygen isotope stage 3 (Liu et al. 1999), which we compare with present day climate. Given these uncertainties, we obtain χ _fd/MEP ≈ 0.094, which is ∼60% of the value for China (Table 25.5). The residual discrepancy could arise from a different climate during oxygen isotope stage 3, or from an incipient dissolution of pedogenic magnetite due to gleyzation.

25.4.6 Argentina

The last case we discuss in detail deals with modern soils from two sites on Pampean loess: Verónica (MAR = 885 mm/yr) and Zárate (MAR = 1115 mm/yr). This case is interesting because one site is magnetically enhanced and the other is not, despite similar climates (Orgeira and Compagnucci 2006). Two soil profiles have been measured at each site, one located in the upper watersheds, and the other in a depression with poorer drainage (Orgeira et al. 2008). Besides the orographic differences between profiles of the same site, the Verónica and Zárate soils have distinct textures. Higher clay content in Zárate reduces the saturated hydraulic conductivity (Table 25.3), and thus drainage. Using hydraulic conductivity data of soils with various clay contents (Clapp and Hornberger 1978) and the textural data in (Orgeira et al. 2008), we obtain K _s ≈ 100 mm/day for both soils in Verónica, and K _s ≈ 380 mm/day for both soils in Zárate. Soils in Verónica are therefore systematically less drained in comparison with Zárate, regardless of the orographic setting. Only the soil profile with best water drainage (upper watershed in Zárate) is magnetically enhanced in the uppermost horizon.

The climatic data of Fig. 25.15 can be used to estimate the expected magnetic enhancement. Monthly rainfall values are constantly larger than PET at both sites, creating a stable saturation regime in the soil. At Verónica, the difference between PET and rainfall is less marked during the summer months, where most of the pedogenic magnetite is expected to form. Only little magnetic enhancement is expected at Zárate, as testified by MEP = 259 mm/yr, which is ∼1/4 of MAR. In analogy with the discussion about North America and Alaska, we compare the magnetite production expected from MEP with the actual enhancement of the soil profile in Zárate. Using the data of Table 25.2, we obtain Δχ/MEP ≈ 0.15 and χ _fd/MEP ≈ 0.17. These values are similar to our estimates for Chinese soils.

Fig. 25.15

Monthly values of rainfall R, potential evapotranspiration PET, and magnetite enhancement proxy MEP for two sites on Pampean loess (Argentina): Verónica (MAR = 961 mm/yr, PET = 741 mm/yr, MEP = 457 mm/yr), and Zárate (MAR = 1088 mm/yr, PET = 749 mm/yr, MEP = 259 mm/yr). Dashed areas correspond to periods of water excess characterized by R > PET

25.4.7 Brief Overview of Other Sites

Having discussed the most relevant soil sites in the previous sections, we conclude with a brief overview of other sites. A rapid assessment of the climatic conditions relevant for pedogenesis is provided by the annually averaged moisture ratio W = MAR/PET, which represents the net balance between water input by rainfall and loss by evapotranspiration. We recall that W ≈ 1 represent the threshold above which the production of pedogenic magnetite is expected to decline. Yearly averages obscure many of the previously discussed details, and do not provide a sufficient basis for a quantitative magnetic enhancement analysis. This is particularly the case for climates with very strong and opposed seasonal dependences of rainfall and evapotranspiration. For example, the warm Mediterranean climate discussed in Section 25.4.2 is characterized by MAR/PET = 0.568, but a monthly analysis shows that rainfall is larger than evapotranspiration during most part of the rainy season.

Nevertheless, W is useful to identify regions of the world where the use of soil magnetic properties as continental climatic proxies might be problematic. For this purpose we compiled maps of W for different regions of the World using the University of Delaware’s climatic database (Delaware University 2009). This database contains long-term monthly means of air temperature and rainfall obtained from land climatic station and interpolated on a 0.5° latitude/longitude global grid. These maps provide a rough climate classification based on criteria that are similar to those used by Thornthwaite (1931, 1948).

The dominant feature on the map of central Asia (Fig. 25.16) is a strong N-S gradient along which W increases from <0.4 on the central CLP to >1.4 in SE China, where the climate is controlled by the eastern summer monsoon and the Indian monsoon. The W = 1 isoline is located at ∼33°N, and coincides with the MAR = 1100 mm/yr isoline that Han et al. (1996) identified as the maximum enhancement limit. When moving from the central CLP towards Siberia, W increases again, this time because of the temperature dependence of PET. The magnetic enhancement of loess/paleosol sequences collected at two localities in Siberia, Lozhok (W = 0.87) and Novokuznetsk (W = 1.11), follow the trend predicted by W, with paleosols in Novokuznetsk being less enhanced than in Lozhok (Table 25.2).

Fig. 25.16

Map of annually averaged W = MAR/PET for Asia. Crosses are soil sample sites on the CLP (Han et al. 1996), and two sites in Siberia (Kravchinsky et al. 2008)

Europe (Fig. 25.17) is characterized by a complex pattern of W with overall minimum values towards SE, and W slightly >1 in spots centered over Austria and E of the Black Sea. This situation is reflected by the magnetic enhancement of loess/ paleosol profiles in the Czeck Republic and Romania, as well as modern soils from the Russian Steppe (Table 25.2). Parent material heterogeneities and W ≈ 1 are the main reason for susceptibility-MAR correlations that are not as high as over the CLP.

Fig. 25.17

Map of annually averaged W = MAR/PET for Central and Eastern Europe. Crosses are soil sample sites in the Czech Republic (Forster et al. 1996), Romania (Panaiotu et al. 2001), Russian Steppe (Maher and Thompson 1995), and Tunisia (Dearing et al. 2001)

Peoria loess in the Midwestern U.S. is characterized by a strong EW gradient of W, with W < 1 in Nebraska, W ≈ 1 along the Missouri river, and W > 1 over Missouri, Iowa, and Minnesota (Fig. 25.18). As discussed in Section 25.4.4, these values are characteristic of a climate that is less favorable to magnetic enhancement. A similar situation is encountered in Alaska, where W ≈ 1 on average.

Fig. 25.18

Map of annually averaged W = MAR/PET for North America. Crosses are soil sample sites on Peoria loess (Geiss and Zanner 2007), and Alaska (Liu et al. 1999, Lagroix and Banerjee 2002)

Pampean loess extends over regions where W is generally >1 with some exceptions in the S (Fig. 25.19). The case of two localities in the Buenos Aires province with W > 1 has been discussed in Section 25.4.6. The magnetic enhancement of Pampean soils seems to be more sensitive to water saturation than soils with similar W and MAR values in Asia. For example, a clear enhancement pattern is missing for both soil profiles in Verónica (W = 1.3), partially because of poor drainage (Orgeira and Compagnucci 2006). For comparison, magnetic enhancement is observed in soils from a third locality SE of the Buenos Aires Province, where W ≈ 1 (Bartel et al. 2006), and all soils with W ≈ 1.3 and MAR ≈ 1000 mm/yr in SE China are strongly enhanced (Han et al. 1996). We must conclude from these observations that magnetic enhancement in Argentina is completely suppressed above W = 1.1–1.3 – yet the magnetite enhancement proxy defined in Eq. (25.19) predicts a gradual decrease and values clearly above zero even for W = 1.4 (e.g. North America, Table 25.2).

Fig. 25.19

Map of annually averaged W = MAR/PET for South America. Crosses are the soil sample sites near Zárate and Verónica (Orgeira et al. 2008), and SE of the Buenos Aires Province (Bartel et al. 2006)

A possible reason for the elevated sensitivity of Argentinean soils to water saturation regimes is the high concentration of volcanic glass in the Pampean loess. Glass dissolution is expected to release silica in the soil pore water, as seen from the occurrence of trace elements present in the glass, such as As, in groundwater (Nicolli et al. 2004). High silica concentrations can have a twofold effect on magnetic enhancement, by promoting magnetite dissolution (Florindo et al. 2003), and by preventing the crystallization of Fe minerals, as observed in the case of ferrihydrite (Schwertmann and Cornell 2000).

25.5 Conclusions

We developed a quantitative description of the climatic modulation of soil magnetic enhancement that integrates Maher’s (1998) conceptual model of magnetite formation by pedogenesis with a statistical treatment of the soil water balance (Rodriguez-Iturbe et al. 1999). Our model is based on the following assumptions:

• (1) Magnetic enhancement is mainly caused by ultrafine magnetite and maghemite particles.

• (2) Pedogenic magnetite forms in “reduction spots” characterized by a microscale redox gradient. Magnetite precipitation is not limited by Fe availability, whose concentration in form of easily reducible minerals is much larger than the magnetite product.

• (3) The formation of pedogenic magnetite requires alternating drying and wetting phases. Wetting phases are necessary to support oxygen respiration by microorganisms and the formation of reduction spots. Drying phases are necessary for the precipitation of poorly crystalline Fe(III) minerals, such as ferrihydrite, that serve as a Fe source during the next wetting phase.

• (4) The rate of magnetite production is proportional to the frequency of drying/wetting cycles, and to the fraction of wet pores in the soil. The drying/wetting frequency is controlled by rainfall, while the fraction of wet pores, which is related to the soil moisture, is controlled by the balance between water input by rainfall, and water loss by evapotranspiration.

• (5) The moisture ratio W, defined as the ratio between rainfall and potential evapotranspiration, controls the average soil moisture. A threshold given by W ₀ ≈ 1 marks the transition from relatively dry conditions to water saturation. The onset of a saturation regime at W > W ₀ decreases the frequency of drying/wetting cycles and suppresses magnetite production. The saturation threshold is lower (0.5 < W ₀ < 1) in poorly drained soils.

• (6) During the drying phase, surface oxidation of pedogenic magnetite produces a maghemite shell whose growth is controlled by the outward diffusion of Fe²⁺ ions.

• (7) If a partially oxidized magnetite particle is exposed to reducing conditions during the wetting phase, the maghemite shell is dissolved. Maghemitization is thus responsible for the destruction of pedogenic magnetite in an active soil. The destruction rate is proportional to the maghemite shell mass, which depends on the average time interval between rain events, and to the frequency of drying/wetting cycles.

• (8) The concentration of pedogenic magnetite at equilibrium is obtained by solving a mass balance equation that includes production and destruction processes. The solution defines a climate-dependent proxy for magnetite concentration in soils, which we called magnetite enhancement parameter MEP (Eq. (25.19)). MEP has the same unit as MAR, and is identical to MAR for a reference case chosen to represent typical loessic soils on the CLP. MEP is proportional to the 3/2 power of rainfall, and inversely proportional to evapotranspiration. It also depends on soil properties and vegetation cover. Magnetic parameters used to describe pedogenic magnetite concentration, such as the susceptibility enhancement Δχ, the frequency dependence χ _fd of susceptibility, and the anhysteretic remanent magnetization ARM, are expected to be proportional to MEP. The proportionality factor is called magnetic enhancement factor.

• (9) MEP can be calculated from monthly rainfall and PET estimates available from climatic tables. A comparison between calculated MEP values and measured magnetic enhancement provides a test for our model. Site-independent enhancement constants are expected if the model is correct.

We tested our model using magnetic enhancement data for three main loess deposit regions: Asia (China and Siberia), North America (Peoria loess and Alaska), and South America (Pampean loess). In general, our model reduces or eliminates discrepancies observed when comparing magnetic parameters with MAR. It explains the differences between magnetic enhancements in North America and on the CLP in terms of climates characterized by a different ratio between rainfall and evapotranspiration. The estimated magnetic enhancement factors for the two regions agree within the confidence limit given by the variability of individual sites. The model also accounts for the enhancement pattern observed in SE China. On the other hand, results for South America suggest that Pampean soils are more sensitive to water saturation than loessic soils from other regions. In one site (Zárate, Buenos Aires Province), drainage is sufficient to guarantee a magnetic enhancement that is compatible with the prediction of our model. In the other cases, additional factors that prevent the formation of pedogenic magnetite or promote its dissolution must be invoked.

We conclude that our model for pedogenic magnetite formation is generally valid and is capable of accurate and quantitative magnetic enhancement predictions on the CLP and on Peoria loess. This result reinforces the reliability of continental paleoclimate reconstructions from loess/paleosol sequences, and provides the starting point for establishing a universal “climofunction” relating magnetic and climatic parameters. Our model takes some physical properties of soils related to water drainage into account, but it ignores geochemical parameters, such as pH, weathering rate, and cation exchange capacity, which might affect pedogenic magnetite production or promote dissolution. A comparison between model predictions and effective magnetic enhancement in cases where only a qualitative agreement can be obtained might provide the basis for incorporating important soil geochemical parameters, improving our understanding of magnetic mineral pedogenesis.

Appendix: The Susceptibility of Pedogenic Magnetite

Quantitative estimates of pedogenic magnetite concentrations are useful for evaluating the relative abundance of different pedogenic minerals. Because of typical mass concentrations <1%, pedogenic magnetite is not detected by X-ray diffraction and Mössbauer spectrometry on bulk samples. Estimates based on magnetic extracts are generally not reliable, because the extraction efficiency is grain size dependent. On the other hand, the concentration of pedogenic magnetite can be quantified from magnetic measurements if (1) its contribution is separable from that of other minerals, and (2) its properties are known and identical within a large set of soils, for example those from the CLP.

In the following, we assume pedogenic magnetite to be fully oxidized to maghemite, which has a spontaneous magnetization μ _s = 73 Am²/kg (Dunlop and Özdemir 1997) and contains n _Fe = 73% Fe by weight. Pedogenic magnetite from the CLP is a mixture of SD and SP particles with invariant magnetic properties and a fixed grain size distribution. Magnetic properties of the pedogenic ferrimagnetic phase are defined by following ratios: $\Delta \chi /{\chi _{{\textrm{ARM}}}} = 0.165 \pm 0.02$ (Liu et al. 2004), ${\chi _{{\textrm{ARM}}}}/{M_{{\textrm{rs}}}} = (1.3 \pm 0.2) \times {10^{ - 3}}\,{\textrm{m/A}}$ (Egli 2004, Liu et al. 2004), and ${M_{{\textrm{rs}}}}/{M_{\textrm{s}}} = 0.2 \pm 0.01$ (Liu et al. 2004). Assuming that maghemite is the only phase responsible for magnetic enhancement, the susceptibility of pedogenic ferrimagnetic minerals, normalized by their mass, is

$$\begin{aligned}{X_{\textrm{p}}} &{}= \dfrac{{\Delta \chi }}{{{\chi _{{\textrm{ARM}}}}}}\dfrac{{{\chi _{{\textrm{ARM}}}}}}{{{M_{{\textrm{rs}}}}}}\dfrac{{{M_{{\textrm{rs}}}}}}{{{M_{\textrm{s}}}}}{\mu _{\textrm{s}}} \\&{}= (3.1 \pm 0.6) \times {10^{ - 3}}{\textrm{ }}{{\textrm{m}}^{\textrm{3}}}{\textrm{/kg}}.\end{aligned}$$

((25.22))

If susceptibility is normalized by the Fe mass of pedogenic ferrimagnetic minerals, we obtain ${X_{{\textrm{p,Fe}}}} = (4.3 \pm 0.8) \times {10^{ - 3}}\,{{\textrm{m}}^3}/{\textrm{kg}}$. The mass concentration C _p in the bulk sample can be estimated using the ratio between the susceptibility enhancement Δχ of the bulk sample and ${X_{\textrm{p}}}:{C_{\textrm{p}}} = \Delta \chi /{X_{\textrm{p}}}$. For example, the strongest susceptibility enhancement on the CLP is $\Delta \chi \approx 2 \times {10^{ - 6}}\,{{\textrm{m}}^3}{\textrm{/kg}}$ which corresponds to a mass concentration ${C_{\textrm{p}}} \approx 6 \times {10^{ - 4}}$ or 0.06%.