Discussion of SOC prediction model performance and significant variables

Predictor variables for depth and soil reaction (pH) were included in modeling datasets as an attempt to account, for modeling purposes, for site-specific variabilities that exist within soil sample datasets. While depth was selected as a highly significant predictor variable for all MLR models, also playing an influential role in PCA models’ “Depth component”, the pH variable was only found to be significant in certain alluvial MLR models. Although models supplied by the PCA technique all (except loess Zr-normalized models) utilized a “pH-dependent component for SOC predictions, the lack of this predictor in Louisiana loess soils’ MLR models is

surprising, due to the greater extent of chemical weathering that has occurred in these soils (Almond and Tonkin, 1999), compared to weathering trends in Louisiana alluvial soils.

The use of Ti and Zr concentrations for stable element stabilization were employed to account for elemental translocations resulting from chemical and physical weathering. In the more highly weathered loess soils, MLR prediction models fail to select pH as a significant predictor variable, however the satisfactory performance of the stable-element models suggest

that certain elemental predictor ratios are indicative of the processes of weathering, and so remove the need for a separate predictor variable accounting for soil acidity. The predictor variables selected for by Ti- and Zr-stable models would logically provide correlations associated with the translocation of organic carbon-associated elements in response to weathering.

Several significant factors explaining models’ satisfactory or diminished performances between wet and dry applications can be identified upon close examination of the effects of moisture on PXRF elemental readings. Comparison of average elemental values for wet and dry datasets show that PXRF detections of Pb and Cu, for loess samples, and Mn, Fe, Co, Rb, Pb, Cu, and Zr, for alluvial samples, all demonstrate reductions in mean PXRF readings > 15% (of dry values) in wet PXRF datasets. Differences in PXRF elemental readings (between wet and dry datasets) were correlated with moisture contents to determine whether increases in soil moisture are related to larger discrepancies between wet and dry PXRF elemental detections. Results showed that in alluvial soil samples having moisture contents > 20%, PXRF readings for K, Ca, Ti, Mn, and Ba demonstrated significant differences when compared to dry PXRF soil sample readings. Soil samples having < 20% moisture showed greatly reduced effects on PXRF

elemental readings, with only loess readings for Pb experiencing significant decreases, compared to dry PXRF concentrations.

Previous research has shown that Pb and Cu are found in both stable and acid-soluble fractions of organic matter (Egli et al., 2009). This would suggest that the PXRF-detectable concentrations of these elements reflect differences between dry and moist datasets, with their inclusion in field-moist prediction models being reflective of the soluble, rather than total, organic fraction. The significant differences between PXRF detections of Pb in wet and dry

datasets exhibiting moisture contents of < 20% can be explained by a reduced ability of this instrument to detect Pb signatures emanating from the soluble organic matter fraction.

Alluvial soil samples were found to experience differences in PXRF elemental detections of Fe and Co (between wet and dry datasets) that increase as moisture content (> 20%) increases. This corresponds to previous findings that acknowledge that high Fe concentrations (such as the concentrations observed in alluvial datasets) can produce elevated PXRF readings for Co, due to the effects of k orbital spectral interferences associated with alterations in secondary

fluorescence detections when moisture is present in scanned samples (Hettipathirana 2004; Innov-X Systems, 2003). This effect is not seen in Fe and Co readings obtained from PXRF analysis of loess soil samples; however, the PXRF detections of Ca and Cr concentrations demonstrate a similar trend in this parent material dataset. As these elements do not exhibit the same electron orbital configurations assumed by Fe and Co, a different mechanism is responsible for the field-moist PXRF concentrations of Ca and Cr observed in loess datasets.

Previous research has identified Ca as a major component of the humic acid fraction of soil organic matter, which is less vulnerable to solubilization in the dissolved organic matter fraction under acidic soil conditions (Nael et al., 2009; Donisa et al., 2002). Field-moist PXRF readings in loess soils having a low pH would be more subject to variability in the detection of fulvic acid-associated elements (Zn, Pb, and Cu) in the soil moisture component of samples, due to its greater potential for solubilization under low pH conditions. While Ca constitutes a

significant predictor variable in all loessal MLR prediction models, insoluble and soluble fractions both experience a high degree of correlation between Ca and organic carbon.

Additionally, Ca concentrations have been shown to be strongly linked with pH in acting as a control over dissolved organic carbon contents. As Ca concentrations increase, dissolved organic

carbon becomes more incorporated in the Ca-associated insoluble organic fraction (Romkens et al., 1996), with this relationship being stronger as soil acidity approaches neutrality. With many of the loessal soil samples exhibiting low pH values, it would appear that the PXRF readings of Ca in the soluble organic fraction would add a level of uncertainty to models utilizing this element as an independent predictor in MLR modeling.

Another way of looking at differences between predictor variable usage in the MLR models is to evaluate their relative weights, and observe how depth differences may influence the way in which additional variables contribute to predicted SOC values. Weights are calculated by determining average predictor variable values for each dataset, which are multiplied by model regression coefficients. The product of each predictor variable is divided by the total of all average values multiplied by their respective coefficients. This provides the percent contribution of individual predictor variables to predicted SOC values.

Depth constitutes the largest percent contributor in all wet MLR models. Other variables used for SOC prediction modeling can be seen in Figures 4.5.1.1 and 4.5.1.2. These figures provide relative model weights at 5 and 50cm depths, illustrating how predictor variable weights change as depth increases through the profile.

For application of dry models to wet validation sub-datasets, certain elements experience a decrease in average concentration in wet PXRF datasets, compared to concentrations obtained from dry soil PXRF analysis. Those elements acting as positive predictor variables cause underestimation of SOC when dry modeling parameters are applied to wet validation sub-

datasets. The reduced detection of predictor elements in the wet dataset causes wet MLR models to apply a greater coefficient to predictor variables than those use dry MLR models. Application of the wet models to dry datasets therefore results in an overestimate of predicted SOC values.

Table 4.5.1 Relative predictor variable weights are provided for 5 and 50cm depths of Raw MLR prediction models as applied to validation sub-datasets.

variable average 5cm 50cm variable average 5cm 50cm variable average 5cm 50cm variable average 5cm 50cm

Depth 72 32 82 Depth 40 11 55 Depth 75 16 84 Depth 62 23 75

Mn 5 12 3 Ca 7 10 5 K 13 16 8 K 13 27 9 Zn 4 11 3 Ti 16 24 12 Ca 3 4 2 Ca 3 7 2 Sr 9 21 5 Co 4 7 3 Zn 2 2 1 Ti 14 28 9 Ba 5 13 3 Zn 1 2 1 Rb 5 6 3 Sr 2 5 2 Pb 5 11 3 Rb 16 24 12 Pb 2 2 1 Zr 5 11 4 Ba 21 31 15 Pb 1 1 0 Zr 5 7 4 pH 5 8 4

Raw MLR model parameters

dry wet

alluvium

weight

dry wet

loess

Table 4.5.2 Relative predictor variable weights are provided for 5 and 50cm depths of stable-element MLR prediction models, as applied to validation sub-datasets.

variable average 5cm 50cm variable average 5cm 50cm variable average 5cm 50cm variable average 5cm 50cm

Depth 66 26 78 Depth 51 16 65 Depth 81 50 91 Depth 75 35 84

K 3 6 2 Ca 1 1 1 K 2 6 1 K 4 9 2 Mn 1 3 1 Co 3 4 2 Ca 1 3 0 Ca 2 4 1 Fe 9 20 6 Rb 23 39 16 Sr 2 8 1 Fe 2 6 1 Co 5 12 3 Sr 4 7 3 Ba 5 16 3 Co 7 17 4 Ba 4 9 3 Ba 8 14 6 Pb 5 18 3 Zn 7 19 5 Pb 9 19 6 Pb 2 4 2 Sr 4 11 3 pH 3 6 2 pH 9 15 6

Ti-stable MLR model parameters

weight weight dry loess wet weight weight dry wet alluvium

variable average 5cm 50cm variable average 5cm 50cm variable average 5cm 50cm variable average 5cm 50cm

Depth 89 59 94 Depth 67 27 79 Depth 87 54 92 Depth 78 40 87

Mn 0 1 0 Ca 4 9 3 K 6 22 4 K 8 21 5 Zn 3 10 2 Ti 8 19 5 Ca 0 1 0 Ca 0 0 0 Sr 2 7 1 Co 0 0 0 Sr 1 4 1 Ti 5 13 3 Pb 6 23 4 Zn 1 2 1 Ba 2 6 1 Fe 4 12 3 Rb 9 21 6 Pb 4 13 2 Co 1 4 1 Ba 0 1 0 Zn 2 4 1 Pb 1 3 1 Cu 2 5 1 pH 9 20 6 weight Zr-stable MLR model parameters

dry wet dry wet

alluvium loess

weight weight

Predictor variables experiencing a significant decrease in wet, as compared to dry, PXRF datasets, average values include K, Ca, Ti, Mn, and Ba in alluvial samples, and Pb is the loessal dataset. These elements are associated with very low (less than or equal to 5% weights)

influence, by weight, on dry alluvial models (especially the Zr-stable model) and loessal (especially the Raw) prediction models. Models experiencing a greater degree of dependence (<5% weight) upon these variables include all wet alluvial models. No wet loessal models contain Pb, preventing diminished model performances upon their application to dry validation data.

While successful prediction models exert a lesser dependence upon predictors whose concentrations are significantly reduced under wet conditions, several models’ predicted SOC contents exhibit non-linear relationships tp laboratory-measured SOC values. Models that produce predicted SOC values that correlate to measured SOC for both wet and dry applications include the Zr-stable, wet model for alluvium and the Ti-stable, wet model for loess.

The non-linear prediction results seen in other models is likely due to the way that predictor variable weights change as depth increases through the profile. As models rely heavily upon depth for generating SOC predictions (especially those constructed from wet datasets), the influence of other predictor variables may be more pronounced in surface depths, compared to their relative weights at lower depths, where depth is typically the dominant predictor.

Tables 4.5.1.1 and 4.5.1.2 list the relative weights of model predictor variables at 5 and 50cm depths. Average weight values were provided earlier, and can be seen in Tables 4.2.1.4, 4.2.2.1, and 4.2.2.2. Both alluvial and loessal prediction models weigh Ca, Rb, and Sr more heavily at surface depths (5cm), while Pb is more influential at lower depths (50cm).

Figure 4.5.1 Relative predictor variable weights are provided for 5 and 50cm depths of MLR prediction model applications to alluvial validation sub-datasets.

Figure 4.5.2 Relative predictor variable weights are provided for 5 and 50cm depths of MLR prediction model applications to loessal validation sub-datasets.

Loess models also exhibit greater influence of Fe, Ti, and Zn at the surface, while increasing depths cause alluvial models to utilize Ti more heavily for SOC predictions.

The non-linearity of predicted vs. laboratory-measured SOC contents of dry models applied to dry validation datasets, and vice versa, is thus far unexplained by the effects of

moisture. Field-mist loessal models experience nearly linear relationships to laboratory SOC data when applied to wet validation sub-datasets, whereas alluvial models demonstrate consistent under-predictions of SOC. The complexity of alluvial PXRF datasets collected from wet soil samples prevents a consistently accurate MLR prediction from being generated, as several elemental species experience significant reductions in PXRF elemental concentrations. Because wet alluvial models place significant influence on several elements that experience these

reductions, SOC predictions are subject to underestimate SOC contents, as positive predictors (such as K, Ca, and Mn) are represented imprecisely, especially in samples having moisture contents greater than 20%. As MLR models are unable to account for differential elemental detections that occur at different depths, pH, and SOC levels, PCA models instead provide a modeling strategy that is able to account for differently weighted factors (i.e. depth, pH, and nutrient components, respectively.) This allows for a sort of calibration of models to the local physicochemical conditions that may influence PXRF elemental detections under field settings. Further research into PXRF detection of elements found in the soluble organic matter fraction would be beneficial in understanding how models can be calibrated further to mitigate the effects of differential elemental solubility on modeling.

The PCA method provided the best overall alluvial model for wet SOC determinations. Alluvial PCA models utilized four components for the prediction of SOC contents. These four components were designated: fine-fraction, pH-dependent, depth-dependent, and nutrient-

components. Applications of PCA factors in multiple linear regression analysis showed that for the Ti-stable, wet alluvial model, depth was the most influential factor for SOC predictions, followed by fine-fraction, pH-dependent, and nutrient-associated components. It seems that the Ti-stable model’s improved performance can be attributed to the minimal use of certain elements within its four PCA components. The elements K, Ca, Ti, Mn, and Cu showed significant

differences between wet and dry alluvial datasets, when moisture contents were > 20%. The minimal influence of these elements as significant factors make SOC predictions from this model more robust for both dry and wet dataset applications.

The best SOC prediction model examined in this study for Louisiana loess soils proved to be the field-moist, Ti-stable model determined through the use of multiple linear regression analysis. All wet models, lacking Pb as significant predictor variable, demonstrated enhanced SOC determination capabilities, compared to results from dry MLR model applications. Oven- dry loess models selected Pb as a significant predictor variable; however, due to the significant differences observed between wet and dry PXRF readings for this element, application of dry models to wet datasets experienced significant reductions in SOC prediction accuracy.

The Ti-stable model exhibited improved performances over other wet MLR models, due to its selection of certain predictor variables. This model benefited from its use of Sr, rather than Ti and Cu, which were included in the wet Zr-stable model. The interrelations observed by multicollinearity testing of wet and dry datasets indicate the presence of significant correlations existing between Ti and Pb, and between Cu and Pb, not observed in dry loess datasets. This observation suggests a higher potential for variability between loessal wet and dry modeling datasets, which resulted in the reduced SOC prediction performance of the moist Zr-stable

Previous research has suggested that Zr may provide a better stable-element index for soils experiencing high chemical weathering rates, as Ti shows greater susceptibility to the effects of physical weathering (Smeck and Wilding, 1980). However, Zr-stable Cu ratios, selected for via MLR modeling, fail to provide a consistent predictor variable for SOC determination of both field-moist and oven-dry datasets. Additionally, research by Hodson (2001) shows that Ti/Zr ratios can experience a high degree of variability (up to 57%),

suggesting that these elements reflect very different modes of translocation and stability within soil profiles. Ti-normalization, reported to provide a more accurate stable-element index in soils having high silt and clay-sized fractions (Stiles et al., 2003), produces a dataset whose predictor variables are more able to accurately reflect their association with organic carbon, in both wet and dry states.

4.6 Comparison of PXRF elemental models with other SOC determination methods Previous work by Weindorf et al. (2012) demonstrated the successful use of Zr-

normalized PXRF data for SOC determination in soil samples collected from Idaho and Alaska, USA. Multiple linear regression analysis generated models using PXRF elemental data and laboratory-measured SOC contents, with results achieving R2 values of 0.93, 0.95, and 0.99, for combined ID & AK, AK, and ID model applications respectively. Predictor variables for Mn, Zn, and Sr were shown to be significant in all three models, with K, Ca, Fe, Co, Rb, Ba, Pb, and Cu also chosen for selection by various models. Idaho models, with samples exhibiting lesser amounts of volcanic ash in predominantly loamy/sandy upper profile materials, utilized K, Ca, Co, and Pb, in addition to Mn, Zn, and Sr. Alaska pedons demonstrated greater overall variability with volcanic ash contents of <15 – 85%, by volume. The use of Ca, Cr, Fe, and Rb (in addition to Mn, Zn, and Sr), explained 95% of the variability observed in SOC contents. Combined AK &

ID models made use of Fe, Cu, Ba, and Pb to model SOC contents over a variable range of volcanic and glacial outwash soils. Similar elemental predictor variables were identified by MLR analysis of Louisiana alluvial and loess soils, however comparisons between model elemental selections are difficult due to the heavy weight allocated to depth variables in models generated for this study. The influence of moisture on the predictive performance of previous models is unknown; however, the results of this study suggest that the Idaho model, having several loamy soils within its dataset, would experience somewhat reduced performance levels upon application to field-moist datasets, due to its use of 4/7 predictor variables (Ca, Co, Pb, and Sr) which exhibit low-to-moderate PXRF moisture-sensitivities in Louisiana silt loam loess soils. Alaska and combined models both utilized 3/7 moisture-sensitive elements in MLR modeling, possibly allowing for improved prediction capabilities upon application to field-moist datasets.

Visible near-infrared diffuse reflectance spectroscopy (VisNIR-DRS) is another

spectroscopic method that has been evaluated for its ability to accurately determine soil organic carbon contents from in situ data analysis. Results from various studies provide prediction values that satisfactorily agree with laboratory-measured SOC contents, with R2 values ranging from 0.84 – 0.90 from model applications to dry soil samples. Results from the current study suggest that the use of PXRF elemental data allows for enhanced SOC prediction capabilities for localized soil samples, with moisture effects shown to minimally affect prediction accuracies when field-moist data is used for model construction.

Root mean square error (RMSE) values were calculated for PXRF models exhibiting best overall performances for dry and wet applications. For alluvium, the Ti-stable, wet MLR model exhibited RMSE values of 3.37 and 1.03 for model performances upon dry and wet validation datasets, respectively. The PCA model for wet, Ti-stable alluvial SOC predictions resulted in

RMSEs of 1.16 and 2.06, and the loessal MLR model using Ti-stable, wet PXRF demonstrated RMSE values of 0.19 and 0.34, for dry and wet applications, respectively.

For dry soil SOC determination using VisNIR data, Viscarra-Rossell and Behrens (2010) report RMSE values ranging from 0.75 – 1.49, using a variety of modeling strategies. Vohland et al. (2011) calculated values of 0.15 – 0.28. Cozzolino and Moron (2006) examined soil organic carbon in different particle size fractions, with silt+clay combined fraction predictions

demonstrating RMSE values ranging from 0.4 – 2.1. These results describe applications of VisNIR prediction models to dry soil sample data.

Studies examining the performance of models upon application to data obtained from analysis of wet soil samples show that increases in RMSE values are associated with VisNIR determinations of SOC contents. Reported results include RMSE values of 5.4 g kg-1 (Morgan et al., 2009) and 7.2 – 29.4 (Sankey et al., 2001). The results reported here for PXRF analysis are for models constructed from field-moist PXRF elemental data, as applied to both wet and dry validation sub-datasets. Model performances on wet datasets, with RMSE values ranging from 0.34 – 2.06 are lower than those reported for VisNIR model performances on wet data. This indicates that PXRF elemental data provides modeling datasets that are better able to determine SOC contents under field condition, when compared to results obtained through the use of VisNIR spectroscopy for SOC determination.

The VisNIR technique relies on a direct spectral signature of organic carbon, identified by the identification of specific wavelengths in the detection spectrum, to predict SOC contents. The PXRF method presented here relies instead upon indirect measurements of soil elements to infer SOC contents on the basis of organic matter complexation with PXRF-detectable elements.