Quantitative paleoenvironmental and paleoclimatic reconstruction ...

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42 N.D. Sheldon, N.J. Tabor / Earth-Science Reviews xxx (2009) xxx–xxx
Fig. 23 depicts the predicted pH values for a wide range of fractional
values between a hypothetical paleosol and its parent material.
Larger fractionations of δ 11 B between a paleosol and its parent
material correspond to more acidic pHs. It should be noted that at
lower temperatures, more typical of soil formation, more acidic pH
values would be predicted for the same magnitude fraction of δ 11 B.
25 °C was used primarily because it represents standard temperature
for thermodynamic data, but it is possible to solve for values appropriate
for lower temperatures, so this does not represent an impediment
to applying this method.
One potentially exciting application of pH values calculated from
δ 11 B values of pedogenic carbonates is to address the question of what
a reasonable value for S(z) is in calculations of paleoatmospheric CO 2
levels (see Section 7.4.3.1), because the pH at the time of formation
of the pedogenic carbonate nodules should be related to soil gas
composition. For the purposes of illustration, we will consider the
simplest possible case (again at 25 °C) for the formation of pedogenic
carbonate:
CO 2ðgÞ þ H 2 O þ Ca 2þ ¼ 2H þ þ CaCO 3 LogK calcite ¼ −9:634 ð66Þ
Assuming pure calcite and water (i.e., a=1), the equilibrium
relationship may be defined as follows:
h i
H + 2
h i
H + 2
=KZ = pCO
½pCO 2 Š Ca 2+ K 3 Ca 2+
2 ð67Þ
Because there is a 1:1 relationship between the number of moles
of Ca 2+ and CO 2 , the expression may be further simplified to the
following:
Sz ðÞ= pCO 2 =
sffiffiffiffiffiffiffiffiffiffiffiffiffi
½a H + Š 2
K calcite
ð68Þ
Using pH values derived from Fig. 23 for (δ ΣB −δ BA − ) values
ranging from 16 to 19 gives a range of pH from 8.05 to 7.04 (aH +
8.86×10 − 9 to 8.94×10 −8 ). Applying those values to Eq. (68) gives a
range of S(z) values of 581–5867 ppm, with the largest δ 11 B (and
lowest pH) values indicating the highest S(z) as would be expected.
For most calculations of paleatmospheric CO 2 levels, the predicted S(z)
using this method is similar to what is already being used, though
somewhat lower, as only relatively acidic pH conditions would predict
high S(z). Using lower S(z) values would predict lower atmospheric
CO 2 values (Section 7.4.3.1), so this is potentially important as an
additional check on those calculations.
Thus, there is considerable scope for development of new paleoproxies
for pH and potentially for S(z) using δ 11 B analyses obtained
from pedogenic carbonates. The main difficulties lie with δ 11 B analysis
Fig. 23. Boron isotope fractionation versus pH for 25 °C. At lower temperatures,
fractionation factors are smaller when boric acid is converted to borate (Kakihana et al.,
1977), which shifts the curve to the left.
itself, potentially poorly constrained parent material compositions,
and uncertainties about paleotemperature at the time that the carbonate
formed. Nonetheless, we feel that this is an area of research with
considerable scope for future growth.
8.2. Energy balance models
Another recent development is a model that relates energy input
into the soil system during weathering to mean annual precipitation
(MAP) and temperature (MAT). Rasmussen et al. (2005) defined a
new term for the energy input into a soil during pedogenesis (E in );
Rasmussen and Tabor (2007) refined the early framework, renaming
E in as effective energy and mass transfer (EEMT) and put forward a
quantitative pedogenic energy model (QPEM) that relates EEMT to
various quantitative measures of pedogenic properties including
pedon depth, clay content, CIA-K (Eq. (5)), and the ratio of free Feoxides
to total Fe (Fe d /Fe T ). EEMT represents the total amount of solar
energy that is available for pedogenesis and is represented by two
quantities: 1) heat available to warm soil material and water and
2) reduction of C due to photosynthesis (Rasmussen and Tabor, 2007).
Full derivation of the model may be found in Rasmussen et al. (2005)
and Rasmusen and Tabor (2007); at least one of the relationships
in the paper is potentially applicable to paleosols. Using empirical
data collected for soils with igneous parent materials in the Sierra
Nevadas, southern Cascades, and Sierra San Pedro Martir ranges,
EEMT (kJ m −2 yr −1 ) may be related to MAT and MAP as follows:
EEMT = 347; 134 exp − 0:5 MAT − 21:5
ð − 10:5 Þ 2 +
MAP − 4412
ð 1704 Þ 2 ð69Þ
Rasmussen and Tabor (2007) also found significant differences
in EEMT among different soil orders (UltisolsNAlfisols≈AndisolsN
MollisolsNInceptisolsNEntisols). In the form of Eq. (69), the relationship
is somewhat cumbersome to apply, because while calculation of
EEMT for a paleosol where MAT and MAP are known could be used to
confirm a taxonomic designation, those paleoclimatic values (in particular
MAT) are not that well-constrained typically. Alternatively,
Rasmussen and Tabor's (2007) relationship may be re-arranged to
solve for either MAT or MAP. As an example, here is the re-arranged
expression for MAT:
MAT = 21:5 +
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
½ − 2Ln EEMT MAP − 4412 2
347;134
+
1704
−10:1
ð70Þ
To give a concrete example, we will apply Eq. (70) to a series of
Miocene Alfisol-like paleosols (Argillisols; Sheldon, 2006d) used elsewhere
in this review. EEMT for Alfisols is 25,875±1781 kJ m −2 yr − 1
(Rasmussen and Tabor, 2007) and the reconstructed MAP using
Eq. (30) ranges from 540 to 854 mm/yr. Assuming a constant EEMT
and using the MAP figures published by Sheldon (2006d),MATfigures
ranging from ~12 to 20 °C are obtained (Fig. 24) and are plotted
against previously obtained MAT estimates using Eq. (25). Obviously,
the MAT estimates obtained using EEMT are very different than those
obtained using Eq. (25), so which estimate is more reasonable?
Both equations have upper limits to the temperatures that they can
predict, (17.3 °C for Eq. (25) and 21.5 °C for Eq. (70)), so Eq. (70) is
potentially viable over a larger range of paleotemperatures than
Eq. (25). The paleosols all correspond to the middle Miocene climatic
optimum, which lead Sheldon (2006d) to question the paleotemperature
results in his original study that used Eq. (25), because while
the MAP estimates that he obtained matched paleobotanical results,
the MAT values were only semi-consistent with estimates based
on paleobotanical proxies for MAT (i.e., the highest MAT values
with the full SE). Thus, based on independent lines of evidence the
values obtained using Eq. (70) are perhaps more in line with expected
middle Miocene MAT.
Please cite this article as: Sheldon, N.D., Tabor, N.J., Quantitative paleoenvironmental and paleoclimatic reconstruction using paleosols, Earth-
Science Reviews (2009), doi:10.1016/j.earscirev.2009.03.004