Pergamon Phys. Chem. Earth (B). Vol. 26. No. 1, pp. 41-45, 2001

© 2000 Elsevier Science Ltd All rights reserved

1464-1909/00/$ - see front matter PII: S 1464-1909(00)00214-8

Soil-Landscape Modelling to Quantify Spatial Variability of Soil Texture

A. Gobin, P. Campling and J. Feyen

Katholieke Universiteit Leuven, Institute for Land and Water Management, V. Decosterstraat 102, B-3000 Leuven, Belgium

Received 2 August 1999; accepted 8 August 2000

Abstract. Soil-landscape models were developed to predict the spatial distribution of soil texture at the surface horizon across a catchment in southeastern Nigeria. A discretised thin-plate spline technique, in conjunction with a connected drainage-enforcement algorithm supplemented with the incorporation of ridge and stream-line data, was used to ensure proper hydrogeomorphic properties of the output Digital Elevation Model (DEM). Terrain attributes were derived from the resulting DEM. Stepwise multiple-linear regression was performed on the normalised terrain attributes and on the principal components constructed from the normalised terrain attributes to avoid multi-collinearity. The derived soil-landscape models were used to predict clay, silt, sand, ironstone and thickness of the surface horizon from the o[,iginal terrain attributes for the entire study area (R2=0.41 to 0.75). The models were further validated using statistical criteria. Only for the soil variable clay did the soil-landscape model improve after stratification according to geological formation (R 2 increased from 0.47 to 0.76). Cell-based algorithms were used to map the soil-landscape models spatially. The resulting spatial patterns correctly showed a significant relationship with the terrain attributes. This relationship is useful when studying patterns of sediment movement. © 2000 Elsevier Science Ltd. All rights reserved.

1 Introduction

Conventional soil surveys often rely on qualitative analysis of the landscape, where it is assumed that properties of modal profiles apply to the entire mapping unit (Dent and Young, 1981). Such surveys are not detailed enough for studying sediment movement in a landscape. Geostatistical methods of spatial interpolation fulfil the increasing need for quantitative soil information, but require intensively sampled areas to establish spatial autocorrelation and are of limited use in situations of complex terrain with discontinuities (Webster and Olliver,

Correspondence to: Anne Gobin

1990). Moreover, they express soil variation only in spatial terms and exclude knowledge of the relationship between soil properties and landscape.

In many landscapes, soil development processes are a response to subsurface and overland water flow. The understanding that soil patterns and topography are closely linked enables the prediction of soil attributes from landscape position (Moore et al., 1993). Quantitative soil surveys, together with terrain modelling, may therefore provide a suitable paradigm for the spatial prediction of single soil characteristics such as soil texture, and may give insight into the terrain attributes influencing the movement of sediments from hillslope to channel.

The objectives in this paper are to establish soil-landscape models based on landscape features and to spatially predict soil texture at the surface horizon across a catchment in southeastern Nigeria.

2 Regional setting

The 589 km 2 study area includes a part of the Nsukka Cuesta, and a section of the Cross River Plains located in southeastern Nigeria (Fig. 1). The region was part of the Anambra Syncline and has a complex sedimentary history. In general, argillaceous rocks underlie the plains, while the cuesta is formed in sandstone.

The Nsukka Cuesta consists of a steep east-facing escarpment and a plateau with a gentle dip-slope towards the west (Pritchard, 1979). Flat-topped hills or ridges with surface ironstone separate wide flat-bottomed dry valleys on the plateau. Gully erosion is severe in the friable sandstone formations of the escarpment (Gobin et al., 1999), and provides a heavy sediment load, which is transported by meandering river systems and deposited on the mudstone and shale formation of the plains. The interfluve east of the escarpment is undulating to rolling due to various stages of denudation (Gobin et al., 1998). At local heights in the landscape, concretionary ironstone occurs at the surface or at shallow depth. Elsewhere, the clay-enriched subsoil sometimes displays iron mottles

41

42 A. Gobin et al.: Soil-Landscape Modelling

within 2 m depth. Towards the catchment outlet the interfluve becomes flat to undulating with many seasonally inundated areas, where plinthite occurs in the subsoil.

Scarp N ~ ~ . _ L~e • Sample Locations ~'~ , ~ ~ i ~ ! i : : ~ : ~ Escarn. A/Rivers

~ ~ ~ ~ : ~ , ' ~ m e ~ n ~ = Contour Lines

Fig. 1 Regional setting and sample locations.

3. Materials and methods

Soil samples were collected from the surface horizon of 72 soil profile pits (Fig. 1). The sample locations were geo- referenced using a Global Positioning System - Trimble Pathfinder Basic. The thickness of the surface horizon was measured, and an averaged sample of about 2 kg was collected from the freshly exposed face of the horizon. The samples were air-dried, pulverised and passed through a 2 nun sieve. The percentage of ironstone was weighed, and the particle-size distribution was determined using the pipette method on the fraction smaller than 2 ram.

ANUDEM (Hutchinson, 1989) was used to create a hydrologically correct Digital Elevation Model (DEM) on the basis of contours, river and stream lines, and spot heights from a 1:50,000 topographic map. The knowledge that water is the primary erosive force determining the general shape of most landscapes was applied by imposing a connected drainage structure and correct representation of ridges and streams. A discretised thin-plate spline technique forced the fitted DEM to follow abrupt changes in terrain, such as streams and ridges. The resolution of the DEM was set at 50 m. Land surface characteristics were quantified on a cell-by-cell basis. A fourth-order polynomial was fitted to a surface of a 3-by-3 square grid window (Zevenbergen and Thorne, 1987):

h = A f ' g 2 + B f ' g + Cfg 2 + D f 2 + Eg z + Ffg + G f + Hg + I

(1)

where f and g are spatial coordinates, h is elevation and the coefficients A, B, C, D, E, F, G, H and I can be calculated from the cell heights of the 3-by-3 window. The primary terrain attributes (slope gradient, curvature, aspect and contributing area) were directly derived from the DEM,

while the secondary attributes (compound topographic index, stream power index and slope aspect index) were derived from the primary terrain attributes (Table 1) (Moore et al., 1991).

Table 1: Calculation method and transformation to normality for terrain attributes. Terrain attribute Symbol Formula Transfor-

mation Elevation h From DEM In Slope

Aspect q~ 180- arc~Hl+90 ~

Plan curvature ~b - 2 DG2 + EH2 - FGH G2 + H 2

2 DH~ + E G 2 - F G H Profile curvature m G 2 + H 2 Curvature ~ 2E+2D

l n Contributing Area Aj _ ~at e) In(In)

b t=l

Topographic Index CT1 I

Stream Power Index SP1 Aj.tanp Slope Aspect Index SA1 qJ.tanp

A, B, C, D, E, F, G and H were derived according to Eq.(l). ¢*) where a, represents an upslope grid cell at point i draining into point j, n is the number of cells draining into j, and b is the contour width approximated by the grid resolution (Speight, 1980).

Both CTI and SPI are widely used in environmental modelling, and consist of Aj to indicate the upslope area that flows into each cell. CTI, also referred to as the wetness index, is often used to predict zones of surface saturation in catchments (Beven and Kirkby, 1979). SPI provides a measure of the erosive power of overland flow (Moore and Nieber, 1989).

Exploratory data analysis on all variables included descriptive statistics and a check for normality by a Shapiro and Wilk test (SAS, 1990). Transformations were applied to the terrain and soil texture variables to normalise them. Most terrain variables were transformed to normal distribution using a natural logarithm or square root (Table 1). Soil texture was transformed according to Eq. (2); the amount of ironstone was transformed according to Eq. (3) (Webster and Olliver, 1990).

- lnF (u + 0 _ 1 ) . ] tiu- L(loo-(.+o.1))J

(2)

(3)

where t is sand, silt or clay fraction expressed as percentage of fine earth, and u is the percentage of ironstone gravel.

A data matrix, X, was constructed containing the normalised terrain variables for 72 surface horizon observations. Principal components (SAS, 1990) were extracted from the correlation matrix, Rx, using the equation Z--XV, where Z is the matrix of unstandardised

A. Gobin et al.: Soil-Landscape Modelling 43

principal components and V the matrix of eigenvectors (Jobson, 1992). The solution is an eigenvalue problem according to [R x -A}V = 0, where A is a diagonal matrix

of eigenvalues of Rx and V is orthogonal to Rx. As the principal components were standardised, the values of the standardised components for n observations were

determined using X = ZV, where X is the standardised

data matrix, Z = Z A -1/2 and V = A I / 2 v . A second data matrix, Y, was constructed to include the normalised soil variables for the surface horizon. Y contained sand, silt and clay fractions, ironstone content and surface horizon thickness. Stepwise multiple linear regression was carried out to predict soil texture, ironstone content and horizon thicknessaccording to:

Y = a + [ ~ X + e (4)

V =,~ +[~ ~ +e (5)

where Y are the normalised soil variables, a and 13 are parameter estimates and ~ are the error terms with 0 mean and constant variance. The terrain variables (X) and

standardised principal components ( Z ) were entered at a 0.15 significance level of the F value and removed from the model at a 0.05 significance level. The two sets of regression equations were statistically validated according to the model R 2, mean error (ME), and root mean square error (RMSE).

M E : I ~ ( y , - ~ , ) (6) n i=1

1 ~ )2] 0.5 RMSE = In ~ (Y i - Y i (7)

The principal components were rotated to the original terrain variables, and cell-based algorithms were utilised to map the soil-landscape models spatially in ARCINFO (ESRI, 1996).

The data matrices were split along the two major geological formations, sandstone and shale, and the effect of stratification was compared for principal component regression (Eq. (5)) using the statistical criteria R ~, ME and /~4SE.

4. Results

In general, the soils of the study area were strongly related to parent material, which was reflected in the texture and ironstone content of the surface horizon (Table 2). The highest amounts of sand were observed in the sandstone- derived soils of the escarpment (,~ = 89.1%) and plateau

(.~= 79.8%), followed by the riverbanks ( ~ = 71.6%). At

the residual hills, more than half of the topsoil consisted of ironstone (.~ = 55.7%). The clay content was highest in the

surface horizon of the residual hills and hills and ridges of

the interfluve. Percentages silt were highest in the waterlogged areas (~ = 38.7%).

Table 2: Variation in soil texture within the surface horizon of each landform class. Landform Sand Silt Clay Ironstone

(y + SE) (>501am) (50-2 ~tm) (<2~tm) (>2ram)

Plateau 79.8±2.7 3.9±0.5 16.3±2.3 0.8±0.5 Escarpment 89.1±2.4 3.3±1.3 7.6±1.6 0.1±0.0 Resi~alHills 45.7±4.2 21.7±2.2 32.6±3.9 55.7±6.1 Inte~uve: Hills#ides 46.4±4.9 26.1±2.9 27.6±2.5 18.6±1.2 Middle-~werslopes 49.7±2.9 35.0±2.7 15.4±1.1 2.7±0.7 Wa~rlog~d* 36.6±4.5 38.7±3.0 24.8±2.8 1.3±0.7

Rive~k 71.6±5.9 14.8±3.4 13.6±2.6 0.8±0.4 OVERALL 59.6±2.6 20.2±1.9 20.2±1.4 11.8±2.6 * The waterlogged interfluve includes the floodplain, y is mean, SE is standard error. The sum of sand, silt and clay is 100%.

Primary and secondary terrain attributes were calculated from the digital elevation model. Shaded class intervals of some primary and secondary terrain attributes were compared for a sample area in the middle of the study area, featuring a hill, streams and a river (Fig.2).

1. Contours/rivers 2. Sqrt(tanl3)

3. In[In(A1)] 4. ln[Aj.(tanl3)"

s. AAtanl3) 6. q~.(tanl3)

Fig. 2 Spatial distribution patterns of transformed terain attributes for a sample area (I): slope gradient (2), contributing area (3), compound topographic index (4), stream power index (5) and slope aspect index (6).

The terrain attributes were normalised and in a form that was used to establish the soil-landscape models (Fig. 2). The slope gradient, compound topographic index and slope aspect index were successful in representing the hill. The

44 A. Gobin et al.: Soil-Landscape Modelling

contributing area, compound topographic index and stream power index picked out the streams and rivers. An interesting feature was that the terrain modelling allowed for additional drainage to be detected ffig. 2, 3-6). The three curvature variables m, dp and X, could not be transformed to meaningful attributes that represented terrain characteristics and were therefore excluded from further analyses.

The derived soil-landscape models predicted the soil variables from the transformed terrain attributes (Table 3). Listed on the top line are the transformed soil attributes to be predicted. Each column represents one soil-landscape model with values for the intercept and coefficients for the transformed terrain attributes. The models explained 41% to 75% of the variability of the measured soil attributes. Considering the coarse resolution of the digital terrain model (50 m) and the high variability in soil properties, the predictive power is good.

Table 3: Soil-landscape models using stepwise multiple linear regression according to Eq.(4).

Clay Silt Sand Stone Thick Intercept 0.672 2.132 -1.428 6.372 -6.389 Lnh -0.069 -0.316 0.304 9.575 Taul3 -6.014 q~ 0.003 -0.011 Aj 0.337 -4.848 CTI 0.013 -1,648 SAI SPI /~ 0.414 0.748 0 .548 0.582 0.497 Prob>F 0.005 0.000 0.006 0.000 0.082 ME 0.000 0.000 0.000 0.000 0.000 RMSE 0.108 0.143 0 .249 2 .192 8.194

Transformations of variables are according to Table 1, Eq.(2) arid Eq.(3).

Overall, a better fit was obtained with stepwise multiple regression after constructing principal components through the transformed terrain attributes (Table 4). This second set of soil-landscape models explained 47% to 75% of the variability of the measured soil attributes. The R M S E

improved slightly as compared to the first set of soil- landscape models.

Table 4: Soil-landscape models using stepwise multiple principal component regression according to Eq.(5).

Clay Clay e> Silt Sand Stone Thick (Plains)

Intercept 0 .405 0.438 0.392 0.837 -4.235 29.181 Lnh -0.041 -0.069 -0.159 0.135 -0.022 3.843 Taul3 -0.033 -0.062 -0.095 0.053 0.436 0.222 q~ -0.004 0.038 -0.019 0.016 -0.963 2.588 Aj 0.007 0.029 0.019 0.077 -1.181 -0.228 CTI 0.031 0.058 0.085 0.001 -0.971 -1.000 SAI -0.033 -0.054 -0.101 0.072 -0.223 2.158 SPI -0.015 -0.031 -0.045 0.099 -0.625 0.431 R 2 0.467 0.755 0.749 0.575 0.645 0.501 Prob>F 0.000 0.000 0.000 0.000 0.000 0.000 ME 0.000 0.000 0.000 0.000 0.000 0.000 RMSE 0.095 0.058 0.143 0.244 2.058 8.171

Transformations of variables are according to Table 1, Eq.(2) and Eq.(3). Note that the terrain variables are standardised, which allows for comparison between estimated parameters per soil-landscape model. ~*) Soil-laudscape model for predicting clay in the surface horizon of soils developed in shale.

The dominance of aspect (q)), elevation (lnh) and the slope aspect index (SAI) in the model predicting thickness (Table 4) reflected the fact that the surface horizon was deepest on the plateau, followed by the escarpment and plains. The thinnest surface horizons occurred on the hills and ridges. Soils dominated by ironstone were found on the ridges and hills, which were characterised by very low values for the contributing area (Aj) and compound topographic index (CTI). Both Aj and CTI had the highest parameter estimates in the soil-landscape model for predicting ironstone (Table 4). Low values for the contributing area (Aj) and stream power index (SPI) were generally associated with soils dominated by larger particles such as sand and ironstone, whereas high values for the compound topographic index (CTI) and low slope gradients (tanl3) were typical for soils with high clay and silt contents. The relationships between soil characteristics and terrain attributes were reflected in parameter estimates of the different soil-landscape models (Table 4).

Principal component regression was used to develop separate soil-landscape models for soils developed in sandstone and for soils developed in shale. Stratification according to the two major geological formations improved the predictive power of the soil-landscape model only for surface clay content of soils developed in shale. These soils are located on the Plains, east of the Nsukka Plateau (Fig.l). The model R 2 increased from 0.47 to 0.76, and the R M S E decreased from 0.095 to 0.058 (Table 4). The predicted against observed clay content, transformed to original fractal percentage, showed a good fit (Fig.3). Compared with soil-auger observations in the area, the spatial distribution of surface clay content in the Plains was generally well predicted (Fig. 4). An overprediction occurred only on the floodplain of rivers that transport and subsequently deposit sand from the rapidly eroding Nsukka Escarpment. +45t

30

[ ~ " R 2 = 0 .755

O - I I I

0 15 30 45

Observed Clay (%)

Fig. 3: Goodness of fit for the soil-landscape model predicting clay content of the soils located on the Plains, east of the Nsukka Plateau (Fig. 1) (n=35).

A. Gobin et al.: Soil-Landscape Modelling 45

Fig. 4: Predicted clay content (%) of surface horizon in the Plains.

5. Conclusion

Significant correlations between soil characteristics and terrain attributes can be expressed as soil-landscape models, which al low for studying sedimentation patterns in terms o f landscape features. The compound topographic index and slope gradient correlate well with smaller particle sizes (clay and silt), whereas larger particle fractions correlate better with the contributing area and stream power index. The development o f soil- landscape models is less data consuming as compared to univariate geostatistical methods and follows the underlying catena-based model used to collect soil data during conventional soil surveys. This enables the use o f previous surveys to be included in the sampling strategy. In case o f clay, the soil-landscape model improved after stratification by geology.

Future work will include validation with an extensive soil-auger survey carried out in the region and prediction o f subsoil attributes. Subsoil attributes may show an even greater response to terrain attributes, as soil and land management does not influence them. The impact o f DEM resolution and non-l inear effects will also be investigated.

Acknowledgements. Funding for this research was provided by the Belgian Agency for Development Cooperation (BADC) through the Inter- University Project on 'Water Resources Development for domestic use and small scale irrigation in the rural areas of south eastern Nigeria'. The authors wish to thank the Belgian Soil Service for analysing the soil samples. Reviews by Dr. A.J. Gerrard and Dr. R.J. Huggett improved the manuscript.

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