Quantifying the roles of bedrock damage and microclimate on potential soil production rates , erosion rates , and topographic steepness : A case study of the San Gabriel Mountains , California

Discerning how tectonic uplift rates, climate, soil production rates, erosion rates, and topography interact is essential for understanding the geomorphic evolution of mountain ranges. Perhaps the key independent variable in this interaction is the potential soil production rate, i.e., the upper limit at which bedrock can be converted into transportable 10 material. In this paper I document the controls on potential soil production rates using the San Gabriel Mountains (SGM) of California as a case study. The prevailing conceptual model for the geomorphic evolution of the SGM is that tectonic uplift rates control topographic steepness, erosion rates, and potential soil production rates. I test the alternative hypothesis that bedrock damage and microclimate also exert first-order controls on landscape evolution in the SGM via their influence on potential soil production rates. I develop an empirical equation that relates potential soil production rates in the SGM to a 15 bedrock damage index that depends on the local density of faults and a microclimatic index that relates to aspect-driven variations in vegetation cover and wildfire severity and frequency. Assuming a balance between soil production and erosion rates at the hillslope scale, I further show that observed trends in topographic steepness can be reproduced using the empirical equation for potential soil production rates. The results suggest that tectonic uplift rates, bedrock damage, and microclimate play co-equal and interacting roles in controlling landscape evolution in the SGM and perhaps other 20 tectonically active mountain ranges.


Introduction
The potential soil production rate (denoted herein by P 0 ) is the highest rate, achieved when soil cover is thin or absent, that bedrock or intact regolith can be converted into transportable material.Despite its fundamental importance, the geomorphic community has no widely accepted conceptual or mathematical model for potential soil production rates.Pelletier and Rasmussen (2009) took an initial step towards developing a model for potential soil production rates by relating P 0 values from granitic landscapes to mean annual precipitation and temperature values.The Pelletier and Rasmussen (2009) Earth Surf.Dynam. Discuss., doi:10.5194/esurf-2016-37, 2016 Manuscript under review for journal Earth Surf.Dynam.Published: 16 August 2016 c Author(s) 2016.CC-BY 3.0 License.model predicts P 0 values consistent with those reported in the literature from semi-arid climates, where P 0 values typically range from ~30-300 m/Myr.In humid climates, the Pelletier and Rasmussen (2009) model predicts P 0 values greater than 1000 m/Myr (Fig. 2A of Pelletier and Rasmussen, 2009), which is broadly consistent with measured soil production rates of up to 2500 m/Myr in the Southern Alps of New Zealand where mean annual precipitation (MAP) exceeds 10 m (Larsen et al., 2014).The Pelletier and Rasmussen (2009) model was a useful first step, but clearly not all granites are the same.In particular, variations in mineralogy (Hahm et al., 2014) and bedrock fracture density (Goodfellow et al., 2014) can result in large variations in soil production rates in granites of the same climate.This study seeks to test the hypothesis that P 0 values are controlled by bedrock damage and microclimate, and to explore how spatial variations in P 0 values drive variations in erosion rates and topographic steepness.
The San Gabriel Mountains (SGM) of California (Fig. 1) have been the focus of many studies of the relationships among tectonic uplift rates, climate, geology, topography, and erosion (e.g., Lifton and Chase, 1992;Spotila et al., 2002;DiBiase et al., 2010;2012;DiBiase and Whipple, 2011;Heimsath et al., 2012;Dixon et al., 2012).These studies take advantage of a significant west-to-east gradient in exhumation rates in this range.What controls this gradient is debated.Spotila et al. (2002) documented close associations among exhumation rates, mean annual precipitation (MAP) rates, and the locations and densities of active tectonic structures.Spotila et al. (2002) concluded that landscape evolution in the SGM was controlled by a combination of tectonics, climate, and bedrock characteristics.Heimsath et al. (2012) presented an alternative view based on millennial-scale soil production and erosion rates.Heimsath et al. (2012) demonstrated that soil production rates (P) and erosion rates (E) in rapidly eroding portions of the SGM greatly exceed P 0 values in slowly eroding portions of the range.Assuming that climate and lithology are similar throughout the SGM, Heimsath et al. (2012) concluded that high erosion rates, triggered by high tectonic uplift rates and the resulting steep topography, cause potential soil production rates to increase, via a higher frequency of disturbance for a given soil thickness, above any limit set by climate and bedrock characteristics.
Climate, lithology, and local fault density (which controls bedrock fracture density) vary greatly in the SGM (Fig. 1), however, with potentially important implications for potential soil production rates.Bedrock fracture density, which controls the rate of bedrock breakdown into transportable material (e.g., Molnar et al., 2004;Koons et al., 2012;Goodfellow Earth Surf. Dynam. Discuss., doi:10.5194/esurf-2016-37, 2016 Manuscript under review for journal Earth Surf.Dynam.Published: 16 August 2016 c Author(s) 2016.CC-BY 3.0 License. et al., 2014), varies inversely with distance to individual faults and directly with fault density in the SGM (Chester et al., 2005;Savage and Brodsky, 2011).As such, it is reasonable to hypothesize that P 0 values are higher in the eastern and southern portions of the SGM in part because local fault density, and hence bedrock fracture density, is higher there.Mean annual precipitation (MAP) rates vary by a factor of two across the elevation gradient and exhibit a strong correlation with exhumation rates (Spotila et al., 2002, Fig. 10).In addition to this range-scale climate variation, slope aspect variations create microclimates in which vegetation cover and wildfire severity and frequency vary.Many steep, south-facing slopes of the SGM, for example, are chaparral shrublands (Holland, 1986) that are prone to frequent, high-severity wildfires (Keeley and Zedler, 2009) that these plant communities have evolved to use as a seed germination mechanism (Keeley, 1987).More wildfire-prone hillslopes experience faster rates of rock weathering compared to less wildfire-prone hillslopes (Blackwelder, 1927;Goudie et al., 1992;Dorn, 2003;Shtober-Zisu et al., 2010).In this paper I test the hypothesis that bedrock damage and microclimate exert first-order controls on potential soil production rates in the SGM.Further, I quantify the implications of this control on erosion rates and topographic steepness.

Data analysis and mathematical modeling 2.1 A model for potential soil production rates in the SGM
Soil buffers the underlying bedrock or intact regolith from physical weathering processes.P 0 values are a natural place to begin quantifying the coupled soil production-erosion system because they do not depend on soil thickness and its controlling factors; hence, they isolate the effects, if present, of environmental factors (e.g., water availability, vegetation cover, wildfire severity and frequency) and material factors (e.g., bedrock fracture density and lithology/mineralogy) that influence soil production rates.Moreover, P 0 values are the rate-limiting step for erosion in areas where deep-seated bedrock landsliding is not a dominant process.Slope failure in bedrock or intact regolith is common in fine-grained sedimentary rocks (e.g., Griffiths et al., 2004;Roering et al., 2005)  where P 0,meas refers to values inferred from measurements of P, h is soil thickness, and h 0 = 0.32 m for locations with S ≤ 30° and h 0 = 0.37 m for locations with S > 30° based on the regressions reported in Figure 3 of Heimsath et al. (2012).Heimsath et al. (2012) did not include data points from locations with no soil cover in their regressions because these data points appear (especially for areas with S > 30°) to fit below the trend of equation ( 1).This implies that a humped production function may be at work in the SGM.The mean value of P from areas with S ≤ 30° that lack soil cover is 183 m/Myr, i.e., slightly higher than, but within 2σ uncertainty of, the 170 ± 10 m/Myr value expected based on the exponential soil production function fit by Heimsath et al. (2012).As such, it appears that for areas with S ≤ 30°, data from locations with and without soil cover are consistent with an exponential soil production function.The mean value of P from areas with S > 30° that lack soil cover is 207 m/Myr, i.e., significantly lower than the 370 ± 40 m/Myr expected based on the exponential soil production function.This suggests that a hump may exist in the soil production function for steep (S > 30°) slopes as they transition to a bare (no soil cover) condition.To account for this, I estimated P 0 to be equal to 1.78P (i.e., the ratio of 370 to 207) at locations with S > 30° that lack soil cover.This modification of equation ( 1) affects 4 of the 57 data points.
P 0 values estimated in this way can be modeled using the product of a coefficient c 1 (units of m/Myr) and dimensionless indices related to bedrock damage, D, and microclimate, A: where P 0,pred refers to model predictions of P 0 .The mathematical form of equation ( 2) honors trends between P 0,meas and the bedrock damage and microclimatic indices documented below.
The bedrock damage index D is based on the concept that soil production rates increase in bedrock that is more pervasively fractured, together with the fact that bedrock fracture densities are correlated with the density of local faults (Chester et al., 2005;Savage and Brodsky, 2011).Savage and Brodsky (2011) documented that bedrock fracture density decreases as a power-law function of distance from small isolated faults, i.e. as r -0.8 where r is the distance from the fault.
Fracture densities around larger faults and faults surrounded by secondary fault networks can be modeled as a superposition of r -0.8 decays from all fault strands (Savage and Brodsky, 2011).Chester et al. (2005)  index D (Fig. 2A) as the sum of the inverse distances, raised to an exponent 0.8, from the point where the D value is being computed to every pixel in the study area were a fault is located: where Δx is the pixel width (included to make D dimensionless), x is the map location where bedrock damage is being computed, and x' is the location of each mapped pixel in SGM where a fault exists.Equation (3) honors the roles of both the distance to, and the density of, local faults documented by Savage and Brodsky (2011) because longer faults and/or more mature fault zones with secondary fault zones have more pixels that contribute to the summation.A least-squares regression of the logarithms of P 0,meas to the logarithms of D (Fig. 3A) results in a p value of 0.014, indicating that the null hypothesis that P 0 is unrelated to D can be rejected with 98.6% confidence.
The correlation between P 0,meas and D values (Fig. 3A) is especially apparent at the extremes: 12 of 13 of the highest P 0,meas values come from locations where D is higher than the median value of 23, while the 7 lowest P 0,meas values come from areas where D is lower than the median value.The correlation between P 0,meas and D values may include some influence of lithology/mineralogy in addition to bedrock fracture density.For example, the high P 0,meas values observed in the Cloudburst summit and related monzogranites (Fig. 1) may be a function of their high biotite content in addition to their proximity to locally dense fault networks.I attempted to introduce lithology as an additional variable but I found the number of points in the dataset to be insufficient to objectively calibrate equation (2) separately to individual lithologies in addition to bedrock damage and microclimate.There are several clusters of data points that weaken the correlation of P 0,meas and D.
One such cluster is circled in Figures 1 and 3A.This cluster of five data points is located in an area with a relatively low density of active faults (hence D values are low) but which nevertheless have relatively high P 0 values (155-261 m/Myr) and thick soils (15-43 cm).These points are located in an area with an unusually high density of mapped landslides (Fig. 1).If these five points were removed, the statistical significance of the relationship between P 0 and D would increase to 99.9% (p = 0.001).
A natural starting point for evaluating the climatic control on P 0 values in the SGM is to plot P 0,meas values vs. elevation, which is strongly correlated with MAP (Spotila et al., 2002).No systematic relationship between P 0,meas values and elevation exists (Fig. 4A).However, a relationship does exist between P 0,meas values and cos(φ-φ 0 ), where φ is the slope aspect (azimuth) and φ 0 = π radians or 180° (included so that the value of cos(φ-φ 0 ) is maximized for south-facing slopes; φ 0 = 0 would maximize this function for north-facing slopes).As with the relationship between P 0,meas and D values, the relationship between P 0,meas and cos(φ-φ 0 ) is particularly apparent at the extremes, with the largest several values of P 0,meas occuring on south-facing hillslopes and the lowest several values occurring on north-facing hillslopes.Rather than using slope aspect alone, microclimate is traditionally quantified using S•cos(φ-φ 0 ), where S is the slope gradient (e.g., Callaway and Davis, 1983).The slope gradient is included in the standard microclimatic index to provide a continuous variation from steep south-facing slopes, where S•cos(φ-φ 0 ) is close to 1 (if S ≈ 1), to steep north-facing slopes, where S•cos(φ-φ 0 ) is close to -1.In the absence of a slope gradient term, the index would change stepwise from maximum and minimum values among slopes that vary by only a degree or less (i.e., from a slope that dips slightly to the south to one that dips slightly to the north).A least-squares regression of the logarithms of P 0,meas to A demonstrates that an approximately exponential relationship exists (i.e., a linear trend on a log-linear plot) for south-facing slopes (p = 0.0003 or >99.9% significance) (Fig. 3C): where c 2 = 1.7 ± 0.4 is the best-fit value from the regression.A similar fit of P 0,meas to S•cos(φ-φ 0 ) for north-facing slopes indicates no relationship (p = 0.5), hence I used a constant value of A = 1 to honor the absence of a dependence of P 0,meas on S•cos(φ-φ 0 ) for north-facing hillslopes.I propose that microclimate most likely controls P 0 values in the SGM as a result of the wildfire-prone nature of the chaparral shrublands (Keeley and Zedler, 2009), which tend to occur on steep, south-facing slopes (Holland, 1986), together with the fact that rock weathering rates tend to increase with wildfire severity and frequency (Blackwelder, 1927;Goudie et al., 1992;Dorn, 2003;Shtober-Zisu et al., 2010).
To constrain the mathematical form of the relationships among P 0 , D, and A, I performed a multivariate linear regression of the logarithms of P 0 to the logarithms of both D and A. Transformed in this way, the best-fit coeffcients obtained by the regression are equivalent to the exponents of power-law relationships of P 0 (the dependent variable) to D and A (the independent variables).This regression yielded exponents of 1.1 ± 0.4 and 1.1 ± 0.3 for the relationship of P 0 to D and A, respectively.These values are sufficiently close to 1 that I chose to fix the values of the exponents to 1 (i.e., eqn.( 2)) for simplicity and reanalyze the data to determine the value of c 1 that yields the best fit of equation ( 2 6.7 m/Myr.The regression metrics of ln(P 0,meas ) vs. ln(P 0,pred ) are R 2 = 0.24 and p = 10 -4 (Fig. 3D).Equation ( 2), with c 1 = 3.5 m/Myr, also predicts P values (Fig. 4C, R 2 = 0.41, p = 10 -7 ).

Relating potential soil production rates to erosion rates and topographic steepness in the SGM
Equation ( 2), in combination with modified versions of equations ( 9)&( 11) of Pelletier and Rasmussen (2009), i.e., predict spatial variations in erosion rates and topographic steepness associated with spatial variations in bedrock damage and microclimate predicted by equation ( 2).In equations ( 5)&( 6), κ is a sediment transport coefficient (m 2 /Myr) and L is a mean hillslope length (m).Equation ( 6) assumes a steady-state balance between soil production and erosion (modeled in eqn.( 6) via the nonlinear slope-dependent model of Roering et al., 1999) at the hillslope scale.
Spatial variations in erosion rates can be estimated using P 0 values predicted by equation (2) if spatial variations in soil thickness can also be determined.To do this, I developed an empirical relationship between soil thickness and slope gradient derived from the Heimsath et al. ( 2012) dataset (Fig. 4D) with best-fit coefficients of b = 1.0 and h 1 = 0.06 m (R 2 = 0.18, p = 0.001).For this regression I shifted the soil thickness in areas with no soil upward to a small finite value (0.03 m).Without some shift, the 10 data points with h = 0 cannot be used, biasing the analysis towards areas with soil cover.The 0.03 m value was chosen because this is the minimum finite soil thickness measured by Heimsath et al. (2012).
Using equation ( 7) as a substitution, equations ( 5)&( 6) can be combined to obtain a single equation that predicts topographic steepness, S: Given a map of steepness obtained by solving equation ( 8), soil thicknesses and erosion rates can be mapped using equations ( 5) and ( 6), respectively.Equations ( 5)&( 6) are the same as equations ( 9)&( 11) of Pelletier and Rasmussen (2009) except that their equation ( 9) included a term representing the bedrock-soil density contrast related to a slightly different definition of P 0 and their equation ( 11) assumed a depth-and slope-dependent transport relation.Here I use a slope-dependent relation because depthdependent models depend on the average soil depth when soil is present (because soil must be present for transport to occur), which cannot be determined for locations where soil thickness is currently zero.
The S values predicted by equation ( 8) (Fig. 2C) reproduce the observed first-order patterns of topographic steepness (Fig. 2D) if L/κ = 0.003 Myr/m and S c = 0.8 are used.The value S c = 0.8 was chosen because it is in the middle of the range of values (i.e., 0.78-0.83)that Grieve et al. (2016) obtained for steep landscapes in California and Oregon.With this value for S c , the best-fit value for L/κ was determined by minimizing the least-squares error between the model prediction (Fig. 2C) and observed variations in slope (Fig. 2D).Predicted and measured S values are lowest in the Western block and higher in the Sierra Madre, Tujunga, and Baldy blocks.The results in Figure 2 demonstrate that spatial variations in bedrock damage and microclimate can be directly associated with observed variations in topographic steepness in the SGM.Soil thicknesses predicted by the model correlate inversely with slopes and P 0 values (Fig. 2E).Erosion rates (Fig. 2F) closely follow P 0 values, but they are lower in absolute value, reflecting the buffering effect of soil on bedrock physical weathering.
The absence of a systematic relationship between P 0 values and elevation (Fig. 4A) is perhaps surprising given the strong correlation Spotila et al. (2002) documented between exhumation rates, elevation, and MAP.Spotila et al. (2002) cautioned, however, that this correlation could be coincidental as "prevailing winds happen to deliver the most precipitation along the southern range front where the most active structures are."The largest P 0,meas values increase and then decrease with elevation between 1.5 and 2.5 km elevation, as indicated by the dashed curve that defines the envelope of the data in Geological Survey, 2016), follows a similar pattern to that of P 0,meas (Fig. 4B), correlating positively with elevation below 1.8 km a.s.l. and negatively with elevation above 1.8 km due to limited energy availability, especially in the cold-season months when most precipitation falls in the SGM.Figures 4A&4B suggest that P 0 may have some dependence on range-scale climate or vegetation.However, it is difficult to tease apart this possible control from other factors given the relatively narrow range of elevations over which P 0,meas values are available, i.e., 80% of the data points are from 1.6 to 2.2 km a.s.l.

Discussion
The key result of this paper is that statistically significant relationships exist between P 0 and both bedrock damage (98.6% significance) and microclimate (>99.9%significance, for south-facing slopes).This result suggests that a revision to the standard conceptual model for the relationships among tectonics, climate, potential soil production rates, and erosion rates in the SGM may be necessary.I propose that the correlation between P 0 and E values documented by Heimsath et al. (2012) can partly be understood as a consequence of the fact that E values are limited by (i.e., cannot exceed) P 0 values in the relative absence of bedrock landsliding.This suggests that erosion rates in areas of thin or no soil are controlled by potential soil production rates, not vice-versa.In addition, P 0 and E values tend to be correlated because they have similar bioclimatic controls.The influence of wildfire on rock weathering rates, for example, has been documented in the field or established experimentally by many authors (Blackwelder, 1927;Goudie et al., 1992;Dorn, 2003;Shtober-Zisu et al., 2010).
Similarly, wildfires alter rainfall-runoff partitioning in a way that tends to increase erosion rates, both on an event basis (e.g., Wagenbrenner and Robichaud, 2014) and over geologic time scales (Orem and Pelletier, 2016).Tectonic uplift rates still exert significant control in this revised conceptual model, acting in concert with bedrock damage and microclimate, via their control on soil thickness.Soil thickness is set by the difference between P 0 and E values.This difference tends to be smaller, resulting in thinner soils and higher erosion rates, in areas of higher P 0 values because tectonic uplift tends be localized where erosion rates (which correlate with potential soil production rates for the reasons stated above) are higher (e.g., Willett, 1999).This hypothesis is consistent with the inverse relationship between soil thickness and slope gradient (the latter of which correlates with erosion rates, as documented by Heimsath et al. (2012), Figs.1E&1F) documented in Figure 4D together with the fact that the spatial variations in erosion rates predicted by the model (Fig. 2F) are similar to those Earth Surf.Dynam. Discuss., doi:10.5194/esurf-2016-37, 2016 Manuscript under review for journal Earth Surf.Dynam.Published: 16 August 2016 c Author(s) 2016.CC-BY 3.0 License.measured over million-year time scales (Spotila et al., 2002, Fig. 7B).The localization of tectonic uplift in areas of higher bedrock damage may also lead to enhanced localization of bedrock damage in a positive feedback.The higher variability of small-scale (i.e., 1-10 m) topographic curvature in areas of thin/patchy soil cover (Crouvi et al., 2013) may also be a factor in explaining the persistence of soil cover in rapidly eroding landscapes.Zones of locally high (positive) topographic curvature may promote temporary soil deposition/storage not yet accounted for in most models of hillslope evolution.Channel steepness, which varies from west to east in a manner similar to P 0 values in the SGM (DiBiase et al., 2010), likely correlates with increasing P 0 values because tectonic uplift is localized where P 0 and E values are highest and because channels must steepen in areas of higher P 0 simply to remain bedrock channels, i.e., to transport the larger sediment fluxes delivered from hillslopes.
To the extent that the correlations documented in this paper are not stronger, it should be noted that substantial scatter is expected due to the inherent variability in P 0 values, which vary at the hillslope scale due to factors such as smallscale variations in bedrock characteristics.Equation (2) correctly predicts P 0 values to within a factor of 2 (the inherent range of variability at the hillslope scale estimated by Heimsath et al. (2012) in their Fig.4A) for 72% of the dataset.Finally, the validity of this or any other model should not be judged exclusively on the strength of its correlations with data because factors besides model quality, including the accuracy with which the independent variables (e.g., bedrock damage) can be quantified and the range of variation in the controlling variables captured by the dataset, factor into such correlations.While the fault map illustrated in Figure 1 represents a best attempt to map the fault network of the San Gabriel Mountains, a single missing fault strand, if located close to a cluster of cosmogenic sample locations, could significantly alter the relationship plotted in Figure 3A.The model of this paper may also improve as additional information becomes available on how best to quantify the relationships among P 0 values, bedrock fracture density, and local fault density, and among P 0 values, vegetation cover, and wildfire severity and frequency.I also wish to stress that the mathematical forms of the relationships are not unique, and additional research in the SGM and elsewhere will almost certainly require a revision to the specific forms of the equations that relate P 0 values to bedrock damage and microclimate.My hope is that this paper stimulates the community to debate the factors that control potential soil production rates, better quantify the linkages among the potential soil production rate and its controlling factors, and add to the remarkable datasets that Heimsath and his colleagues have made available for studying the soil production problem.In particular, the analysis of this paper points to the need for measurements of soil production rates in the SCM and elsewhere across the broadest possible range of elevations, lithologies, and bedrock damage values.

Conclusions
In this paper I documented that bedrock damage (quantified using the local density of faults) and microclimate control potential soil production rates in the San Gabriel Mountains (SGM) of California.Assuming a balance between soil production and erosion rates at the hillslope scale, I further showed that observed trends in topographic steepness can be reproduced using the empirical equation for potential soil production rates based on bedrock damage and microclimate.The results suggest co-equal and interacting roles for tectonic uplift rates, bedrock damage, and microclimate in the geomorphic evolution of the SGM.In this conceptual model, erosion rates increase in areas of where bedrock damage, microclimate, and potentially additional factors not explicitly account for here (e.g., mineralogy, large-scale variations in climate) make bedrock conducive to rapid soil production.The localization of tectonic uplift in areas of high erosion and potential soil production rates leads to a positive feedback in which erosion rates and factors conducive to soil production (e.g., high bedrock damage values and severe, frequent wildfires) correlate and coevolve with potential soil production rates.
documented similar power-law relationships between bedrock fracture density and local fault density in the SGM specifically.I define the bedrock damage Earth Surf.Dynam.Discuss., doi:10.5194/esurf-2016-37,2016 Manuscript under review for journal Earth Surf.Dynam.Published: 16 August 2016 c Author(s) 2016.CC-BY 3.0 License.

Figure 4A .
Figure 4A.The presence of two relatively large P 0,meas values at low elevations in Figure 4A is a consequence of the influence of bedrock damage on P 0 , since these locations are close to range-bounding faults and hence have large D values.Mean canopy height, constrained from the Existing Vegetation Height layer of the U.S.G.S. LANDFIRE database (U.S. Earth Surf.Dynam.Discuss., doi:10.5194/esurf-2016-37,2016   Manuscript under review for journal Earth Surf.Dynam.Published: 16 August 2016 c Author(s) 2016.CC-BY 3.0 License.

Figure 2 .Figure 3 .
Figure 2. Color maps illustrating spatial variations of the damage index (D), potential soil production rate (P 0 ), predicted and observed values of slope gradient, S, soil thickness, h, and erosion rate, E. (A) Color map of damage index D (eqn.(3)) with fault traces superimposed.(B) Color map of P 0 values estimated as described in Section 2.1.(C) Color map of S values predicted by equations (7)&(8), smoothed by a moving average filter with a 1-km length scale to emphasize patterns at the landscape scale.(D)

Figure 4 .
Figure 4. (A) Plot of P 0,meas versus elevation, z.The dashed curve identifies the maximum values or "envelope" of the data.(B) Plot of mean canopy height versus elevation using the U.S. Geological Survey LANDFIRE database.(C) Plot of measured versus predicted values for the soil production rate, P. The predicted value is from equation (2) with c 1 = 3.5 m/Myr.(D) Plot of soil thickness, h, versus slope gradient, S. Results of the linear regression of the logarithms of h and S also shown.5 but relatively uncommon in granitic terrain such as the SGM.