CHARACTERIZING THE SPATIAL PATTERN OF SOIL CARBON ANDNITROGEN POOLS IN THE TURKEY LAKES WATERSHED:
A COMPARISON OF REGRESSION TECHNIQUES
I. F. CREED1,2∗, C. G. TRICK2, L. E. BAND3 and I. K. MORRISON4
1 Department of Geography, University of Western Ontario, London, ON, Canada; 2 Department ofPlant Sciences, University of Western Ontario, London, ON, Canada; 3 Department of Geography,University of North Carolina, Chapel Hill, NC, U.S.A.; 4 Canadian Forest Service, Sault Ste. Marie,
ON, Canada(∗ author for correspondence, e-mail: [email protected], fax: 519 661 3935)
(Received 2 April 2001; accepted 20 December 2001)
Abstract. There is considerable spatial heterogeneity in organic carbon (C), total nitrogen (N),and potentially mineralizable nitrogen (PMN) pools in the soils of the Turkey Lakes Watershed.We hypothesized that topography regulates the spatial pattern of these pools through a combinationof static factors (slope, aspect and elevation), which influence radiation, temperature and moistureconditions, and dynamic factors (catenary position, profile and planar curvature), which influencethe transport of materials downslope. We used multiple linear regression (MLR) and tree regression(TR) models as exploratory techniques to determine if there was a topographic basis for the spatialpattern of the C, N and PMN pools. The MLR and TR models predicted similar integrated totals(i.e., within 5% of each other) but dissimilar spatial patterns of the pools. For the combined litter,fibric and hemic layer, the MLR models explained a significant portion of the variance (R2 = 0.38,0.23 and 0.28 for C, N and PMN, respectively), however, the residuals were large and biased (thesmallest contents were over-predicted and the largest contents were under-predicted). The TR models(9-branch), in contrast, explained a greater portion of the variance (R2 = 0.75, 0.67 and 0.62 for C, Nand PMN, respectively) and the residuals were smaller and unbiased. Based on our sampling strategy,the models suggested that static factors were most important in predicting the spatial pattern of thenutrient pools. However, a nested sampling strategy that included scales where both static (amonghillslopes) and dynamic (within hillslope) factors result in a systematic variation in soil nutrient poolsmay have improved the predictive ability of the models.
Keywords: carbon, forest, model, multiple linear regression, nitrogen, potentially mineralizablenitrogen, soil, topography, tree regression
1. Introduction
Predicting organic carbon (C) and total nitrogen (N) pools within forest soils isessential to understanding the nutrient budgets of catchments. Spatial heterogeneityin the net rates of accumulation, mineralization and transport of nutrients may res-ult in a catchment that is not uniform in the distribution of either C or N pools. Thus,some areas within a catchment may serve as sites of C or N accumulation. Whileit is ultimately important to understand the fluxes of C and N within a catchment,an understanding of the processes regulating the formation of the pools of C and N
is essential for modeling C and N biogeochemistry within the catchment (Lexer etal., 1999; Gessler et al., 2000).
Topography has been hypothesized to be an important regulator of the formationof C and N pools in soils. The theoretical basis for this hypothesis is provided bythe catena concept (Milne, 1936). Few soils develop in response to 1-dimensionalprocesses operating on flat, featureless land surfaces. Rather, most soils developin response to 3-dimensional processes related to a catena, with soils from eachcatenary position connected by the continuous flow of water and the particulate anddissolved materials carried in the water. The catena represents interplay betweenstatic and dynamic factors resulting in soils of different properties (Young, 1972,1976). Static factors are controlled by the elevation, slope and aspect and influencethe radiation, temperature and moisture at the site. Dynamic factors are controlledby the relative position of the site within the catena and influence the transportof particulate and dissolved materials downslope. Soils formed in a single mater-ial differ because of water transport processes that result in differential drainageconditions, differential transport and deposition of suspended materials, and/ordifferential leaching, translocation and redeposition of soluble materials (Hall andOlson, 1991). Differences in soil production and transport processes that result inmass movement may also cause soil differentiation (Dietrich et al., 1995). Catenaryprocesses may result in predictable heterogeneity of both the physical and chemicalproperties of the soil, including the precursors and products of the transformationof biologically important nutrients, such as C and N.
Previous efforts to characterize topographic regulation of the distribution ofsoil C or N pools that are based on some derivative of the catena concept spanover 50 years. These efforts encompass both the distribution of nutrient pools(Aandahl, 1948) and rates of nutrient transformation, including mineralization,nitrification (Zak et al., 1986) and denitrification (Bowden, 1986; Groffman andTiedje, 1989a, b). Topography was found to influence the distribution of nutrientsin the soil in landscapes ranging from gentle, moderate to steep relief in tundra,temperate and tropical biomes (e.g., Gosz and White, 1986; Huntington et al.,1988; Zak et al., 1989; Hairston and Grigal, 1991; Raghubanshii, 1992; Gartenet al., 1994).
The use of regression models to capture the topographic regulation of soil C andN pools has grown in recent years (e.g., Furley, 1968; Crosson and Protz, 1973;Moore et al., 1993; Garten et al., 1994; Chang, 1995; Arrouays et al., 1998; Lexeret al., 1999; McKenzie and Ryan, 1999; Bell et al., 2000; Chen and Chiu, 2000;Gessler et al., 2000; Johnson et al,. 2000; Chaplot et al., 2001). Different regressiontechniques have been used for the prediction of soil properties, including multiplelinear regression (Moore et al., 1993) and tree regression (McKenzie and Ryan,1999). Tree regression models have the advantage of permitting non-monotonic,non-linear, and non-parametric relationships among variables and of allowing fornesting of the variables that predict the C and N pools.
TOPOGRAPHIC CONTROL OF SOIL NUTRIENT POOLS 83
The objectives of this article were to characterize the concentration and massof C, N and potentially mineralized nitrogen (PMN) and to compare the multiplelinear regression and tree regression techniques for modeling topographic controlson the spatial heterogeneity of these soil nutrient pools within the Turkey LakesWatershed (TLW), in central Ontario, Canada.
2. Methods
2.1. STUDY AREA
The TLW is a 10.5 km2 experimental forest centered at 47◦03′00′′N and 84◦25′00′′Wabout 60 km north of Sault Ste. Marie in the Algoma Highlands of central Ontario(Figure 1). The climate is continental, with a strong influence from Lake Superior.The topography is controlled by the bedrock, with 400 m of relief from its outlet (at244 m a.s.l.) to the summit of Batchawana Mountain (at 644 m a.s.l.). The bedrockis overlain by a thin and discontinuous moraine of silty to sandy till with variabledepth (Jeffries and Semkin, 1982). The soils that have developed in the tills areclassified as Orthic Ferro-Humic and Humo-Ferric podzols, however in many loc-ations the soils had poorly-differentiated soil horizons. Dispersed pockets of highlyhumified organic deposits (Ferric Humisols) are found at all elevations in bedrock-controlled depressions and adjacent to lakes and streams (Canada Soil SurveyCommittee, 1978). The uneven-aged, mature forest is composed of 90% sugarmaple, 8% yellow birch and 1–2% of scattered stems of minor species (Wickwareand Cowell, 1983, 1985).
2.2. PREDICTOR VARIABLES
For the TLW, a digital elevation model (DEM, 25 × 25 m grid size) was generatedfrom 1:12 000, 3.2 m (10 ft) digital contours using the procedure of Hutchin-son (1989). From the DEM, terrain attributes (slope, aspect, planar and profilecurvature, and catenary index) were calculated. Planar curvature is a measure oftopographic convergence and divergence and provides an indication of the potentialfor water to converge as it flows down a hillslope. Profile curvature is a measure ofthe rate of change of the potential gradient and provides an indication of changes inwater velocity and sediment transport processes. The catenary index (ln [a/tanβ],where a is the specific contributing area in m2 and β is the local slope in degrees;Beven and Kirkby, 1979) is a measure of the position of a particular site within thecatena and provides an indication of the relative water and sediment movement atthe site. The formulae for calculating these terrain attributes are described in Mooreet al. (1991). Forest attributes were generated from plot estimates of biomass (totalof root, stem and foliar biomass), derived from allometric equations generated fromdata collected in 1981 from 216 sites on a 250 × 250 m grid covering the watershed,that were interpolated using the procedure of Hutchinson (1989).
84 I. F. CREED ET AL.
Figure 1. Map of the soil sampling sites within the Turkey Lakes Watershed (TLW) centered at47◦03′00′′N and 84◦25′00′′W.
TOPOGRAPHIC CONTROL OF SOIL NUTRIENT POOLS 85
2.3. RESPONSE VARIABLES
A provisional model of catenary controls on the distribution of C, N and PMNpools in the soil was used to allow the development of a sampling plan.
2.3.1. Sampling StrategyFor an effective sampling strategy, the criteria include the following: (1) predict-ive variables must be sampled evenly in attribute space; (2) predictive variablesmust be sampled randomly to ensure an unbiased sample; (3) inefficiencies dueto spatial dependence in soil properties must be minimized; and (4) inefficienciesdue to errors in location between the digital terrain model and the real world mustbe minimized (Gessler et al., 1995). In designing the sampling strategy, we com-puted frequency distributions for the terrain attributes representing both the staticand dynamic factors of catena development and divided them into five percentileclasses (i.e. 0–20, 20–40, 40–60, 60–80, 80–100%). From each of the five per-centile classes, about 15 sampling sites were randomly selected (Criteria 1 and2). To minimize inefficiencies due to the spatial dependence in soil properties, thesampling sites had to be chosen using information about the spatial dependencestructure of the soil nutrients. Since a priori information of the spatial dependencestructure of the soil nutrients was not available, this structure was inferred fromthe spatial dependence structure of one of the terrain attributes. A variogram of thecatenary index indicated a nugget = 0.3, a sill = 1.0, and a range = 250 m (Websterand Oliver, 1990). Based on the variogram, sampling sites were randomly spaced atdistances greater than the range (≥250 m) (Criterion 3). To minimize inefficienciesdue to errors in location, sampling sites were placed only in homogeneous patches(≥0.1 ha), with sampling site coordinates estimated using a Global Position Systemreceiver (GPS) and refined using field notes on site conditions (Criterion 4).
2.3.2. Sample Collection and AnalysisSample collection occurred in the late summer of 1994. At each sampling site, thedepth and bulk density of the soil were determined. Depth (surface to bedrock)was the average of 10 measurements distributed within the 10 × 10 m2 samplingsite and was determined by penetrating a 150 cm steel rod into the soil until it hitbedrock. Bulk density was determined for the organic layer as the average of three10 × 10 cm2 litter (L) or fibric-hemic (FH) samples and for the mineral layer as theaverage of three soil core samples for each sampling depth interval. Each samplewas dried at 105 ◦C and weighed. The soil profiles were generally poorly differen-tiated. Thus, at each sampling site, a minimum of 10 soil cores was collected andcomposited at regular interval depths (L, FH, 0–5, 5–10, 10–15, 15–20, 20–30 and>30 cm) rather than at horizons to arrive at a representative soil profile for the site.Each soil sample was dried (<60 ◦C), passed through a 2 mm sieve and stored inplastic vials until analyzed. The concentration of organic matter (% or g/102 g, dryweight) was determined using a modified chromic acid oxidation method (Walkley
86 I. F. CREED ET AL.
and Black, 1934) and transformed to C (g/102 g) using the Van Bemmelen factor(i.e. C = organic matter/0.58; Kalra and Maynard, 1991). The concentration ofN (% or g/102 g, dry weight) was determined using the procedure of Kjeldahl(1883). The concentration of the PMN (g/106 g, dry weight) was determined usingthe procedure of Stanford and Demar (1969) as modified by Smith and Stanford(1971) and Stanford and Smith (1976) but simplified for routine analysis (Keeney,1982).
2.4. MODEL DEVELOPMENT
A combination of multiple linear regression (SIGMASTAT 2.03 1997) and tree re-gression (S-PLUS 4.0 1997) models was used to explore the possibility of signific-ant relationships existing between catchment characteristics and the concentrationand mass of C, N and PMN in the soils. Once the regression models were generated,cross-validation was conducted. Cross-validation requires application of the modelto a new set of observations that was not used to estimate the parameters of themodel. Given the relatively small number of samples (maximum n = 81), a globalcross-validation was used in which an average prediction error was computed byiteratively removing one observation from the data set, re-fitting the model, andthen generating the prediction error for the removed samples. Comparisons of thepredictive ability of the MLR and TR models were based on the R2, residuals andcross-validations analyses.
3. Results and Discussion
The TLW soils were shallow. While the depth of individual soil cores may haveexceeded 20 cm, the total mass of sample collected below 20 cm was much smaller,sufficient for only one analysis (C or N) or for none. For this reason, we focused onthe physical and chemical characteristics of the organic and the 0–20 cm minerallayers.
The nutrient pools in the TLW soils were highly heterogeneous. For the sampledsites, the average and standard deviation for each depth increment of the soil pro-files for C, N and PMN are presented in Table I. The average soil profile indicatedthat the largest concentrations of C, N and PMN occurred in the litter (L) and fibric+ hemic (FH) layers and decreased with depth while the largest masses occurredin the 0–5 cm depth increment and decreased with depth. There was substantialvariation in the nutrient pools at each depth increment of the soil profile. For thesampled profiles, the coefficient of variation (CV) for the concentration of nutrientswas smaller for the organic layer (i.e. L and FH) than the mineral layer (i.e. the 5 cmdepth increments, from the surface [0–5 cm] to the deepest sampling depth). TheCV ranged from 5–96, 6–70 and 13–51% for C, N and PMN, respectively. TheCV for the mass of nutrients was more consistent between the organic and mineral
TOPOGRAPHIC CONTROL OF SOIL NUTRIENT POOLS 87
TABLE I
Concentration (g g−1 dry weight±standard deviation), mass (g m−2±standarddeviation), and coefficients of variation (CV, %) of organic carbon (C), totalnitrogen (N) and potentially mineralizable nitrogen (PMN) within the soilprofiles
C (g C 102 g−1) CV (%) C (g C m−2) CV (%)
L 49.7±2.68 5 287±71.5 25
FH 46.2±6.13 13 1320±468.9 36
0–5 cm 13.9±9.69 70 4000±1929.1 48
5–10 cm 7.3±6.07 83 2383±858.5 36
10–15 cm 7.2±6.02 84 2349±817.1 35
15–20 cm 7.0±6.70 96 2233±872.9 39
N (g N 102 g−1) CV (%) N (g N m−2) CV (%)
L 1.9±0.12 6 11±2.3 21
FH 2.0±0.13 7 56±18.9 34
0–5 cm 0.8±0.32 40 241±77.3 32
5–10 cm 0.5±0.30 60 159±77.1 48
10–15 cm 0.4±0.28 70 135±46.9 35
15–20 cm 0.4±0.28 70 127±45.3 36
PMN (g N 106 g−1) CV (%) PMN (g N m−2) CV (%)
L 1111±146.8 13 0.64±0.16 25
FH 1340±167.8 13 3.78±1.18 31
0–5 cm 621±200.0 32 19.70±7.31 37
5–10 cm 354±180.4 51 12.48±6.03 48
10–15 cm NA NA NA NA
15–20 cm NA NA NA NA
layers and ranged from 25–48, 21–48 and 25–48% for C, N and PMN, respectively(Table I).
The degree of heterogeneity that exists within soils places limits on the ability topredict the distribution of soil properties. As a measure of judging the explanatorypower of our statistical models, we compared the predictive power of our statisticalmodels to those of general-purpose soil surveys (Gessler et al., 1995). In suchsurveys, <50% of the variance in measured physical properties and <10% of thevariance in chemical properties could be explained (Webster, 1977). Hence statist-ical models with a R2 > 10% would be an improvement from the general-purposesoil surveys).
Multiple linear regression (MLR) models were used to establish if there was
88 I. F. CREED ET AL.
a topographic influence on the spatial distribution of soil nutrient pools. Priorto conducting the analyses, the predictor variables were evaluated to see if theymet the data assumption of regression models (i.e. test for normality, constantvariance, and independence of residuals). In some cases, none of the standarddata transformations were successful in transforming the data to meet the assump-tions of regression models, and thus, only the results of the MLR models fornon-transformed data are presented (Table II).
The MLR models explained from <10 to about 40% of the variance in the meas-ured C, N and PMN, depending on whether the values were a concentration or massand depending on the depth of the soil profile being evaluated (Table II). The largestexplanation of variance was in the combined LFH (litter + fibric + hemic) layer,with R2 = 0.38, 0.23 and 0.28 for C, N and PMN, respectively (Table II). For thecombined LFH layer, the MLR models predicted a total of 1559, 65 and 4 kg ha−1
for C, N and PMN, respectively. Slope, a static factor in catenary development,was the main terrain attribute controlling the variance in C, N and PMN pools,with aspect and elevation also important contributing factors (Table III). Within theTLW region, larger soil nutrient pools occurred in the relatively deep soils on gentleslopes with southerly aspects typical at lower elevations. There was a reduction inthe soil nutrient pools at sites where the soils became shallower on steeper slopeswith more northerly aspects typical at higher elevations. These observations areconsistent with those reported by Arrouays et al. (1998), who reported slope as themain factor controlling heterogeneity in C (g m−2) in the upper 0 to 30 cm of soilsunder a mature pine (Pinus pinaster Ait.) forest within a similar regional area (i.e.60 km2).
Tree regression (TR) models provide an alternative technique for exploratorydata analyses. Compared to MLR, TR models have the advantage of permittingnon-monotonic, non-linear, and non-parametric relationships among variables andallowing for nesting of the variables that predict the C and N pools. TR modelsare designed to iteratively divide the samples into a binary tree of subsamplesthat separate a response variable based on one or more predictor variables. Theselection of the splitting predictor variable is designed to maximize the sum ofsquares reduction within the resulting subsamples. Therefore, different predictorvariables may be used to partition the samples in different branches of the tree,creating a flexible, explicitly nested operation that searches for the most uniquesubsamples at each branch. The splitting process is recursively applied to eachsubsample until a preset stopping criterion is met or all subsamples are too smallto separate statistically, at which point the subsample is assigned a constant value.One of the dangers of TR models is that the analyses could overfit the data andthus the tree could not be applied to other situations. To avoid an elaborate tree thatoverfits the data, trees are pruned back to a desired number of branches, based onheuristic criteria or on an efficiency optimization in terms of the residual varianceand the number of branches (Breiman et al., 1984; Efron and Tibshirani, 1991).
TOPOGRAPHIC CONTROL OF SOIL NUTRIENT POOLS 89
TABLE II
Summary of multiple linear regression (MLR) analyses. Data were tested for normality(A), constant variance (B) and independence of residuals (C), with � indicating thetest passed and × indicating the test failed. Bolded regression analyses were selectedto become the focus of the comparison of MLR and Tree Regression models
n A B C R2 F p Power
(α = 0.05)
C (%) L 69 � � � 0.148 1.516 0.179 0.909
FH 69 × × � 0.209 2.304 0.038 0.980
5 68 × × � 0.130 1.276 0.278 0.860
10 68 × × � 0.065 0.593 0.759 0.544
15 69 × � � 0.065 0.610 0.746 0.565
20 69 × � � 0.054 0.502 0.830 0.488
C (g m−2) L 69 � � � 0.121 1.202 0.316 0.839
FH 69 � � � 0.389 5.538 <0.001 1.000
5 65 × � � 0.077 0.681 0.688 0.613
10 66 × � � 0.067 0.592 0.759 0.555
15 67 � � � 0.125 1.205 0.314 0.841
20 65 × � � 0.139 1.312 0.261 0.869
LFH 69 � � � 0.375 5.231 <0.001 1.000
LFH5 65 � × � 0.115 1.062 0.399 0.795
LFH10 65 � � � 0.067 0.583 0.767 0.548
LFH15 65 � � � 0.054 0.463 0.857 0.460
LFH20 65 � � � 0.075 0.633 0.727 0.583
N (%) L 81 � � � 0.106 1.240 0.292 0.848
FH 81 � � � 0.103 1.200 0.313 0.837
5 81 × × � 0.104 1.216 0.305 0.841
10 81 × × � 0.080 0.905 0.508 0.728
15 81 × � � 0.099 1.143 0.035 0.819
20 81 × � � 0.082 0.930 0.489 0.739
N (g m−2) L 81 � � � 0.112 1.309 0.258 0.866
FH 81 � � � 0.228 3.083 0.007 0.996
5 78 � � � 0.082 0.890 0.519 0.721
10 79 × � � 0.119 1.376 0.229 0.881
15 79 × � � 0.156 1.878 0.086 0.954
20 77 � � � 0.165 1.941 0.076 0.959
LFH 81 × � � 0.229 3.091 0.007 0.996
LFH5 78 � � � 0.074 0.802 0.589 0.677
LFH10 78 � � � 0.073 0.782 0.604 0.667
LFH15 78 × � � 0.079 0.861 0.542 0.707
LFH20 76 × � � 0.123 1.367 0.234 0.880
90 I. F. CREED ET AL.
Figure 2. Tree regression models (9-branches) for the LFH layer: (a) C (g m−2); (b) N (g m−2); (c)PMN (g m−2).
TOPOGRAPHIC CONTROL OF SOIL NUTRIENT POOLS 91
TABLE II
(continued)
n A B C R2 F p Power
(α = 0.05)
PMN (g g−1) L 69 � � � 0.272 3.263 0.005 0.997
FH 69 � � � 0.247 2.861 0.012 0.993
5 69 × � � 0.068 0.637 0.723 0.584
10 69 × × � 0.139 1.411 0.217 0.890
PMN (g m−2) L 69 � � � 0.101 0.982 0.453 0.764
FH 69 � � � 0.302 3.767 0.002 0.999
5 66 � � � 0.078 0.704 0.668 0.627
10 67 × � � 0.142 1.397 0.224 0.887
LFH 69 � � � 0.283 3.442 0.004 0.998
LFH5 66 � � � 0.051 0.445 0.869 0.446
LFH10 66 � � � 0.085 0.772 0.613 0.665
TABLE III
Parameters for the multiple linear regression models for organic carbon (C), total nitrogen (N) andpotentially mineralizable nitrogen (PMN) in the litter + fibric + hemic (LFH) layer of the soil profile
C (g m−2) in LFH N (g m−2) in LFH PMN (g m−2) in LFH
a Aspect was transformed to a linear variable by taking the absolute value of (180 – aspect (degrees)).
To facilitate comparison, we calculated TR models for C, N and PMN (g m−2)in the LFH layer, the soil layer that produced the best MLR models (Figure 2).Examining the R2, residuals and cross-validation results of the models comparedthe effectiveness of the MLR and TR models in explaining the variance in themeasured C, N and PMN pools.
92 I. F. CREED ET AL.
Figure 2c. (Continued).
The R2 suggested that the predictive ability of the TR models was better thanthe MLR models. For C, the R2 of the TR models were 0.75, 0.61 and 0.41 for the9-, 6-, and 3- branch models, respectively, compared to a R2 of 0.38 for the MLR.For N, the R2 of the TR models were 0.67, 0.65 and 0.36 for the 9-, 6-, and 3-branch models, respectively, compared to a R2 of 0.23 for the MLR. For PMN, theR2 of the TR models were 0.62, 0.52 and 0.35 for the 9-, 6- and 3-branch models,respectively, compared to a R2 of 0.28 for the MLR (Table IV). For TR models,fewer branches create a more conservative model. Even the most conservative trees(the 3-branch models) explained more of the variance in the samples than the MLRmodels (Table IV). Based on the R2, the TR models were better than the MLRmodels; however, it should be noted that the R2 are computed differently, and thus,they are not fully comparable statistics.
A residual analysis of the regression models suggested that the predictive abilityof the TR models was better than the MLR models. The residuals of the MLRmodels indicated that the these regression models systematically overestimated thesize of the nutrient pools at sites containing smaller masses of nutrients and sys-
TOPOGRAPHIC CONTROL OF SOIL NUTRIENT POOLS 93
Fig
ure
3.R
esid
uals
ofre
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mod
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for
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94 I. F. CREED ET AL.
Fig
ure
3.(C
onti
nued
).
TOPOGRAPHIC CONTROL OF SOIL NUTRIENT POOLS 95
TABLE IV
Comparison of the predictive ability of the multiple linear regression (MLR) and tree regres-sion (TR) models for organic carbon (C), total nitrogen (N) and potentially mineralizablenitrogen (PMN) in the litter + fibric + hemic (LFH) layer of the soil profile
MLR TR-3 branch TR-6 branch TR-9 branch
C in LFH (g m−2)
R2, predicted vs. observed (n) 0.38 0.41 0.61 0.75
R2, predicted vs. observed (n-1) 0.20 0.18 0.27 0.29
N in LFH (g m−2)
R2, predicted vs. observed (n) 0.23 0.36 0.65 0.67
R2, predicted vs. observed (n-1) 0.09 0.27 0.20 0.22
PMN in LFH (g m−2)
R2, predicted vs. observed (n) 0.28 0.35 0.52 0.62
R2, predicted vs. observed (n-1) 0.10 0.07 0.04 0.04
tematically underestimated at sites containing larger masses of nutrients (Figure 3),resulting in a narrower range in the predicted C, N and PMN pools (Figures 4 to6, MLR models). In contrast, the residuals of the TR models are more balanced,without a systematic bias in the predicted nutrient pools. When we evaluated treespruned back to 6 or 3 branches, the size and pattern of the residuals were not sub-stantially different (data not shown). Without the systematic bias in the residuals,the TR models expressed the full range of the measured nutrient pools, and thus,analyses using TR models provide a distribution over the landscape that is moreconsistent with the analyzed soil profiles (Figures 4 to 6, TR models), leading usto conclude that the non-monotonic and non-linear relationships observed betweenthe controlling terrain attributes and the C and N pools may be true characteristicsof the system.
A global cross-validation analysis of the regression models was conducted toevaluate the stability of the models. Iteratively removing a single sample from thedata set, generating the model, and then generating the prediction error for theremoved sample performed the global cross-validation analysis. For each of theMLR and TR models, the R2 (n-1) was substantially lower than the R2 for theentire data set (n) (Table IV). The prediction error statistics, including the meanabsolute error and the bias in the error, were similar for the MLR and TR models.These results suggest some instability in the models. A larger number of samplesshould improve the stability and the predictive ability of the models.
The TR models appeared to perform better than MLR models in predictingnutrient pools in the comparatively complex topography of the TLW. The MLR
96 I. F. CREED ET AL.
Fig
ure
4.P
redi
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C(g
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onfo
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.
TOPOGRAPHIC CONTROL OF SOIL NUTRIENT POOLS 97
Fig
ure
5.P
redi
cted
N(g
m−2
)di
stri
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laye
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LR
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98 I. F. CREED ET AL.
Fig
ure
6.P
redi
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PM
N(g
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-an
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.
TOPOGRAPHIC CONTROL OF SOIL NUTRIENT POOLS 99
and TR models predicted similar watershed inventories of C, N and PMN pools.The MLR models predicted a total of 1559, 65 and 4 kg ha−1 for C, N and PMN,respectively. In contrast, the TR models predicted a total of 1486, 1460 and 1508 kgha−1 of C, 59.13, 59.08 and 59.06 kg ha−1 of N and 4.22, 4.16 and 4.08 kg ha−1
of PMN, for the 9-, 6- and 3- branch models, respectively. While the MLR and TRmodels predicted similar watershed inventories of the pools (i.e., the inventorieswere generally within 5% of each other), the spatial patterns of the pools weredifferent; the MLR models, with their continuous distribution of predicted data,created more heterogeneous distributions than the TR models.
The TR models, like the MLR models, indicated that slope was the main terrainattribute for explaining the variance among the samples in the initial branch of thetrees (Figure 2). Other terrain attributes that represented static and dynamic factorsof catena development were important in the branches further down the trees. Theimportance of this hierarchy of topographic controls on the spatial pattern of nutri-ent pools results in a clear dichotomy in the distribution of C, N and PMN in theLFH below and above elevations around 400 m (Figure 2). For C (g m−2), there isabout a 50% increase and for N (g m−2) about a 100% increase in the respectivesoil nutrient pools in the gentle slopes at elevations below 403 m. The branchesfurther down the tree indicate that while static factors explain a large degree of thevariance in the distribution of the C and N pools within the TLW, other dynamicfactors are also important. For PMN (g m−2), the effect of elevation is subtler, asindicated by its occurrence at a branch near the bottom of the tree.
While better than the general-purpose soil surveys described by Webster (1977),the results of both the MLR and TR models indicated that the majority of thevariance in C, N and PMN pools remained unexplained. These results suggest thatthere are limits to the explanation of variance that may be a function of the samplingstrategy. At the scale of the TLW region (10 km2), the soil nutrient pools were dom-inated by terrain attributes that regulate the static factors of soil development. Incomplementary studies at finer scales (<10 km2), which cover a single hillslope or aseries of contiguous hillslopes, soil properties were controlled by terrain attributesthat regulate the more dynamic factors of soil development. Moore et al. (1993)were able to explain from 41 to 64% of the variance and Gessler et al. (1995) wereable to explain 63 to 68% of the variance in measured soil properties by consideringtopography. Both of these studies were based in agricultural systems. Garten etal. (1994) were able to explain from 50 to 70% of the variance in measured soilproperties in a oak-hickory forest, values approaching the maximum predicted ex-planation of variance (70%) using terrain analysis techniques (Moore et al., 1993).In all of these studies, the catenary index and/or planar and profile curvature wereimportant predictor variables in these systems. Our sampling strategy may not havebeen designed to effectively capture these more dynamic factors of soil develop-ment. Based on the MLR and the more conservative 3-branch TR, up to 40% of thevariance in the nutrient pools in the LFH layer could be topographically explainedby our ‘coarse’ sampling strategy. A larger amount of the variance may have been
100 I. F. CREED ET AL.
explained if we had adopted a nested sampling strategy, including both coarse andfiner sampling scales.
The results of the TR models suggest that it was important to permit nestingof the variables that predict the C and N pools. To develop more robust modelswe should have included a nesting sampling strategy that incorporated the mul-tiple scales that factors influence soil development (Bellehumeur and Legendre,1998; McKenzie and Ryan, 1999; Ryan et al., 2000). At the regional scale, thedominant topographic factors are those that affect the static factors of soil develop-ment that influence external inputs to the system, including radiation, temperature,moisture and nutrient loadings (slope, aspect, elevation). At the local scale ofindividual hillslopes or catchments, the dominant topographic factors are thosethat affect the dynamic factors of soil development, including drainage conditions,transport and deposition of suspended materials and/or leaching, translocation andredeposition of soluble materials (catenary index, planar or profile curvature). Asampling strategy based on a nesting of topographic features (e.g. from hillslopes,to catchments, to the watershed) should be chosen to capture these different scalesof heterogeneity. In this study, we captured one scale of influence (regional) butnot the other scales of influence (hillslope or catchment). To confirm this scale-dependent heterogeneity, future research will be based on a sampling design basedon a nesting of the scales of soil development processes.
Acknowledgements
NSERC and Tri-Council Eco-Research Doctoral Fellowships to IFC and NSERCoperating grants to CGT and LEB supported this research. We acknowledge PeterBilawski, Tracy Clarke, Todd Dunne and Joel Mostoway for assistance in the col-lection of the soil samples. We acknowledge Trevor Robak for assistance in thestatistical analyses. We also wish to thank P. Gessler and an anonymous reviewerfor their constructive comments on a previous version of this article.
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