Journal of Arid Environments (1998) 39: 441–455 Article No. ae970365
Using remote sensing and geostatistics to map 137 Cs-derived net soil flux in south-west Niger
A. Chappell*† School of Environmental Science, Nene–University College Northampton, Park Campus, Northampton NN2 7AL, U.K. (Received 1 October 1997, accepted 26 November 1997) A small (760 m 3 740 m) study area in south-west Niger was sparsely sampled for 137Cs which was modelled to provide measurements of net soil flux. A variogram of net soil flux was computed and a model fitted using weighted least squares. The parameters of the variogram were used to solve kriging equations to provide net soil flux estimates and estimation variances over 20 m 3 20 m blocks throughout the study area. At the sample locations net soil flux was substituted for the block-averaged net soil flux estimates in order to compute additional auto- and cross-variograms of intensively sampled SPOT satellite data (20 m 3 20 m). These variograms were modelled as before and the parameters used to solve co-kriging equations to provide net soil flux estimates and estimation variances. The co-kriging estimation variances were considerably smaller than those for ordinary kriging, suggesting that problems of accurately mapping net soil flux can be overcome by making use of the additional sampling intensity of the spatially interdependent data in SPOT band XS3. This methodology has considerable potential for accurate and cheap net soil flux mapping over very large areas with limited 137Cs ground measurements. ©1998 Academic Press Limited Keywords: soil erosion; wind erosion; caesium-137 (137Cs); remote sensing; SPOT data; geostatistics; co-kriging; Niger
Introduction In semi-arid regions, particularly those dominated by aeolian processes, there is great difficulty in quantifying the soil redistribution (erosion and deposition) rates (Lal, 1993). This is because the effect of wind erosion is insidious until large amounts of soil have either been removed from or deposited on the land. Wind erosion is spatially and temporally very variable rendering only the longest and spatially intensive monitoring campaigns representative. Few studies meet these criteria because of the large costs involved. *E-mail:
[email protected] †Present address: Department of Geography, University College London, 26 Bedford Way, London WC1H 0AP, U.K. E-mail:
[email protected] 0140–1963/98/030441 + 15 $25.00/0
© 1998 Academic Press Limited
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The use of the 137Cs technique for measuring soil redistribution has received considerable attention in semi-arid regions (Kulander & Stromquist, ¨ 1989; Loughran et al., 1993; Walling & Quine, 1993; Chappell et al., 1996a) because it offers the potential to quantify the net soil flux rate for the last 30 years with a single field visit (Ritchie & McHenry, 1990; Sutherland & de Jong, 1990; Walling & Quine, 1991). However, few studies have conducted spatially intensive investigations over large areas because measurement of 137Cs in the laboratory is time-consuming and because many samples are needed to describe its spatial variation and thus soil redistribution (Sutherland, 1994). Those few studies that have accurately mapped net soil flux have used innovative sampling designs and/or geostatistical procedures to reduce the number of 137Cs samples (de Roo, 1991; Chappell et al., 1996b). Geostatistics provides a framework for estimation of expensive-to-measure properties such as 137Cs at unsampled locations. It requires information about the spatial variation of a property and is dependent on sampling intensity. The variogram is commonly used to construct a model of spatial property variation. The parameters of this model are used for kriging, a local weighted average, for estimation at unsampled locations. Unfortunately, the variogram can be unreliable when there are few samples (Webster & Oliver, 1992), causing estimation variances to increase in areas where there are few samples. One solution is to utilize the spatial interdependence between a sparsely sampled property and a more intensively sampled property to improve the estimation procedure of the property of interest. This geostatistical technique is called co-kriging and is the logical extension of kriging. It has been used in many applications to improve the mapping accuracy of expensive-to-measure properties using one or more cheaperto-measure properties (McBratney & Webster, 1983; Leenaers, 1990; Zhang et al., 1992). The benefits of this technique are maximized when the amount of secondary data is considerably larger than the primary data. Remotely sensed data provide cheap, intensively sampled spatial information for use with this technique (e.g. Atkinson et al., 1994). The aim here is to combine digital, multispectral SPOT satellite data with groundbased measurements of 137Cs (converted to net soil flux) by co-kriging to improve the net soil flux map estimates of ordinary kriging. There exists no direct quantitative relationship between these data but there is an a priori model: soil redistribution processes (erosion or deposition) at the soil surface affect the total 137Cs inventory (net soil flux) and change the composition of the material and structure of the soil surface which affects the remotely sensed radiance (Dn) values. Results from this small study area will be used to test the ability of this a priori model to provide a methodology for large area mapping of net soil flux. Methods Field and laboratory procedures In a study area (760 m 3 740 m) of south-west Niger (Fig. 1), 74 samples of 137Cs were available on a nested grid with intersections at 5 m, 20 m and 100 m (Fig. 2(a)). The purpose of the nested grid was to cover a range of sampling intervals to ensure that the main sources of variation were identified as part of a larger study of the spatial variation of net soil flux (Chappell, 1995). Each soil sample was obtained from an area of 6·25 cm2 and bulked over a given depth in the profile. Sampling took place between July and October 1992. The 137Cs activity was measured by γ-ray energy spectrometry on a horizontallyorientated, 20% relative efficiency, hyper-pure germanium γ-ray detector (Chappell, 1995). Validity of the 137Cs technique for measuring soil redistribution has been established for this region(Chappell et al., 1998). The model developed by Zhang et al.
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(1990) for rangeland areas was used here to estimate surface lowering at sites where erosion was occurring. The model for erosion is not applicable to sites where there has been deposition. For these sites a proportional model (Sutherland & de Jong, 1990), modified for preferential accumulation of 137Cs-enriched dust, was used (Chappell, 1995; Chappell et al., 1998). These models were used to convert 137Cs (Bq m–2) to net soil flux (t ha–1 year–1). The high resolution visible (HRV) sensors of SPOT are capable of operating in the multispectral mode and are sensitive in the three bands XS1 (green, 0·50–0·59 µm), XS2 (red, 0·61–0·68 µm) and XS3 (near infrared, 0·79–0·89 µm). The instantaneous field of view (IFOV) at nadir is 20 m 3 20 m. The scene used here was acquired for 20 August 1992 to coincide with soil sampling and prior to seasonal rainfall and increased vegetation cover which would obscure the soil surface reflectance. This image was already preprocessed to include radiometric adjustments and geometric corrections of systematic distortions due to the earth’s rotation and panoramic effects. Figure 3(a–c) shows data in the three bands (XS1, XS2 and XS3) for a subscene coincident with the study area. The brighter area in the south-western region of the image is associated with the upper part of the valley in the study area which is dominated by sparsely vegetated aeolian quartz sand deposits with hematite clay coatings and very little organic matter content at the soil surface. Distinct lineations are visible here and are associated with the largest vegetation-lined gullies. The same pixel shade is evident in clusters throughout the darker north-eastern corner of the image. These clusters are vegetation islands (brousse tigr´ee) within which the soil comprises a humus-rich gravelly loam of kaolinitic clay. The islands are surrounded by bare areas of a humuspoor gravelly loam of ferricrete cobbles. Geostatistical procedures ‘Geostatistics’ is the term applied to a suite of statistical techniques for describing the correlation of spatially distributed random variables and their estimation at unsampled
Figure 1. Orthographic projection (UTM coordinates in metres) of elevation in the study area relative to mean sea level.
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Figure 2. Isarithmic map (UTM coordinates in metres, north towards the top) for the study area of net soil flux (t ha–1 year–1) using (a) inverse distance squared interpolation and showing soil sample locations, (b) ordinary block kriging and (c) ordinary block co-kriging.
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Figure 3. SPOT subscene of the study area (with north towards the top), sensed in the HRV bands (a) XS1 (0·50–0·59 µm), XS2 (0·61–0·68 µm) and (c) XS3 (0.79–0·89 µm).
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locations. These techniques are based on Regionalized Variable Theory (Matheron, 1971). The central tool is the semi-variogram (or more commonly known as the variogram) which measures the degree of spatial dependence or autocorrelation in data arising from the underlying spatial structure in the variation (Oliver & Webster, 1987). The variogram can be used with the sample data for estimation by kriging at unsampled locations (Oliver et al., 1989). Essentially, kriging is a method of local weighted averaging where the weights are derived from the variogram (Webster & Oliver, 1990). Hence, the estimates are based on the spatial variation of the property. Kriging has been found to be one of the most reliable two-dimensional spatial estimators (Laslett et al., 1987). Furthermore, Laslett (1994) has shown that kriging estimates benefit from the use of multi-stage sampling designs intended to give reliable estimation of the variogram. Co-kriging is the logical extension of kriging to situations where two or more variables are spatially interdependent and the one of immediate interest is undersampled (McBratney & Webster, 1983). Using traditional ordinary co-kriging (Deutsch & Journel, 1992) the estimate is a weighted average of the available data with weights chosen so that the estimate is unbiased and has minimum variance and in practice only near observations carry enough weight to have effect (McBratney & Webster, 1983). This is because the sum of the weights applied to the primary variable is set to one, and the sum of the weights applied to any other variable is set to zero. Other non-bias conditions are possible with different types of co-kriging (Deutsch & Journel, 1992). This second condition tends to limit severely the influence of the secondary variable. Since K2 covariance functions are required when K different variables are considered, the reduction in estimation variance is not worth the additional modelling effort unless the primary variable is underestimated relative to the secondary variable(s) (Deutsch & Journel, 1992). The linear model of co-regionalization provides a framework for modelling the autoand cross-variograms of two or more variables so that the variance of any possible linear combination of these variables is always positive (Journel & Huijbregts, 1978). Each variable is characterized by its own sample auto-variogram and each pair of variables by their own sample cross-variogram. The model for each of these sample variograms may consist of one or more conditional negative semi-definite (or authorized) models. However, the same basic model (with the same range values) must appear in each auto- and cross-variogram (Isaaks & Srivastava, 1989). Experimental variograms were computed using the computer software VARIOWIN (Pannatier, 1997). Theoretical models were fitted to the experimental variograms with the GEOPACK software (Yates & Yates, 1989) using weighted least-squares approximation and checked with cross-validation. The best fit model parameters (Table 1) of the net soil flux variogram were used to solve block kriging equations to estimate net soil flux over 20 m blocks with the GEOPACK software. However, the best fit models were modified to meet the constraints of the linear model for co-regionalization. A combination of power and spherical models were fitted to each Table 1. Parameters of the ‘best’ models fitted to the variograms
Model parameters
Net soil flux (sample)
Net soil flux (20 m block)
SPOT band XS3
Net soil flux (20 m) –SPOT XS3
Model Range/Power Sill/Slope Nugget
Spherical 199·10 1481·40 227·10
Spherical 253·06 864·00 0·00
Power 0·855 0·378 0·000
Power 1·00 0·24 0·00
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variogram and the parameters (Table 2) were used to solve block co-kriging equations to estimate net soil flux over 20 m blocks using the GSLIB software (Deutsch & Journel, 1992). Maps of the net soil flux estimates and estimation variances were produced using SURFER (Golden Software Inc., 1990). Results and discussion The variogram models The experimental variograms for data in SPOT bands XS1, XS2 and XS3 are shown in Fig. 4. The steepness of the initial slope of the variogram indicates the rate of change in a property with distance and the rate of decrease in spatial dependence. Where the extent and intensity of sampling enables the scale of spatial dependence to be determined, the variogram will reach a maximum, called the sill variance, where it Table 2. Parameters of models used for co-regionalization
Model parameters Power model Power Slope Nugget Spherical model Range Sill Nugget
Net soil flux (20 m block)
SPOT band XS3
Net soil flux (20 m) –SPOT XS3
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1·060 0·091 2·750
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Figure 4. Isotropic variograms of SPOT bands XS1 ( + ), XS2 (*) and XS3 (h) for the study area, and model data ( — ).
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flattens. The lag at which the sill is reached is the range, or limit of spatial dependence. The variogram often has a positive intercept on the ordinate called the nugget variance which arises partly from measurement error, purely random variation, but also from the spatially dependent variation that occurs over distances much smaller than the sampling design. Notably, all variograms have very little nugget variance suggesting that most of the spatial dependence at this scale has been encompassed by the intensive coverage. The SPOT bands XS1 and XS2 (Fig. 4) exhibit a bounded structure. Band XS3 appears to be unbounded and was fitted best with a convex upwards power model (Fig. 4; Table 1). However, variograms computed for the valley and plateau regions separately (not shown) suggest that it is bounded. It is unlikely that the unbounded structure of the variogram for data in band XS3 is evidence of non-stationary behaviour (trend). A more plausible explanation of the unbounded structure is due to the inclusion of data from two distinctly different regions (Chappell, 1995; Chappell et al., 1996b). Ideally, the study area should have been separated between the plateau and valley regions and the variograms computed separately for each region. Unfortunately, the sparsity of net soil flux samples precluded this because it would have made regional variograms unreliable. The variogram of data in band XS3 is more variable than data in the other bands and the range appears to be greater than that of bands XS1 and XS2 which are very similar despite considerable difference in the variance. There are no statistically significant correlations between any single band (or any combination of these bands) and the sample net soil flux (Table 3). The product moment correlation is a poor summary statistic when non-linear relationships are present in the data. However, the rank-order correlation, which is not affected by the magnitude of the values, did not reveal any significant relationships. The product moment correlation coefficient for XS3 was an order of magnitude larger than the coefficients for net soil flux and the other bands. For this reason data in SPOT band XS3 were selected for co-kriging with net soil flux. The experimental variogram for point sampled net soil flux is shown in Fig. 5. It is fitted best, in the least-squared sense, by a spherical model. The first lag of the variogram had very few comparisons at small lags and when included in preliminary analyses it increased the nugget variance and decreased the fit of the spherical model. Consequently it was omitted from the final model fitting stage. The parameters of the model are shown in Table 1 and were used to solve kriging equations to estimate net soil flux over 20 m blocks. The nugget variance of the sampled net soil flux is approximately 15% of the sill variance and this is largely due to the sparsity of samples. The structure of the variogram may also be due to the effect of the nested sampling design. For example, the average separation distance between the four sampling clusters is approximately 180 m which is very close to the range (199 m) of the net soil flux variogram. However, the net soil flux range is similar to the range (202 m) of the variogram for percentage vegetation cover (Chappell & Oliver, 1997) which was found to be one of the main controls on sediment redistribution in this region (Chappell, 1995; Chappell et al., 1996b). Table 3. Different correlations and their coefficients for sampled net soil flux against SPOT band(s)
Correlation coefficients XS1 XS2 XS3
Product moment correlation
Rank-order correlation
0·001 0·002 0·020
–0·110 –0·145 0·034
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Since the size (support) of net soil flux samples is considerably smaller than the support of the remotely sensed pixels it is necessary for compatibility to estimate average net soil flux over equivalent sized blocks. This was achieved by substituting the block-averaged estimates of net soil flux for the sampled net soil flux at each sample location for subsequent auto- and cross-variograms of net soil flux. The experimental variograms for sampled net soil flux and 20 m block-averaged net soil flux are shown with fitted models in Fig. 5. The nugget and sill variance of the model fitted to the block-averaged net soil flux variogram (Table 1) have been reduced considerably by comparison with the parameters of the net soil flux sample variogram (Table 1). This is due to the smoothing effect of estimating net soil flux over 20 m blocks and to the minimization of variance. Furthermore, regularization is a technique which enables the computation of a block-averaged variogram model from the point sample variogram. Although this technique was not used here, the theoretical basis (Journel & Huijbregts, 1978, p. 78) was used to check the validity of the variogram for block-averaged net soil flux (Fig. 5). Experimental variograms for 20 m block-averaged net soil flux, the SPOT band XS3, and the cross-variogram of net soil flux and XS3 are shown in Fig. 6. The models fitted to the variograms were constrained by the linear model of co-regionalization. The parameters of these models are listed in Table 2. A positive cross-variogram between SPOT band XS3 and net soil flux exists (Fig. 6) suggesting a positive spatial interdependence and validates the a priori model between these variables. A poor correlation between these variables (as found in the data; Table 3) would give a crossvariogram of zero: that the value is not zero provides additional support for the existence of correlation at different spatial scales. Anisotropy effects Directional variograms are typically calculated in at least four directions to identify anisotropy. Unfortunately, with so few 137Cs-derived net soil flux samples directional variograms were highly erratic and unreliable. Mineral magnetic properties (χLf, χFd), which are related to soil redistribution and were available at over 400 locations throughout the study area, were assessed for directional variation as part of a larger
Figure 5. Isotropic variograms of sampled net soil flux ( + ) and 20 m block-averaged net soil flux (G) with best fit spherical models ( — ) and a validation model (····).
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study (Chappell, 1995): the results did not show any evidence of anisotropy. Since variation was isotropic for these properties it was assumed that it was representative of net soil flux and isotropic variograms were used for block kriging and block co-kriging. Comparison of estimation procedures The model parameters (Table 2) fitted to experimental variograms (Fig. 6) were used to solve ordinary block kriging equations and ordinary block co-kriging equations for net soil flux and maps of the estimates are shown using the same contour intervals in Fig. 2(b) and (c), respectively. Summary statistics are listed in Table 4. The improvement of block kriging estimates over a simple inverse distance squared interpolation is evident by comparing Fig. 2(a) and (c). The concentric structure in the
Figure 6. Isotropic variograms of 20 m block-averaged net soil flux (G), SPOT band XS3 (h) and the isotropic cross-variogram ( 3 ) all fitted with power-spherical models ( — ) constrained by the linear model of co-regionalization.
Table 4. Summary statistics for the original samples and geostatistical estimates
Estimates Net soil flux statistics N Average S.D. CV Min. Max. MAE MSE
Estimation variances
Original samples
kriging
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74 –32·56 38·49 –1·18 –135·95 10·54 30·25 1461·44
1406 –33·67 27·41 –0·81 –125·24 10·64 0·31 3·61
1406 –33·14 25·90 –0·78 –121·66 9·08 0·24 1·57
1406 966·19 672·03 0·70 58·39 3073·30 55·05 80799·69
1406 418·64 289·09 0·69 55·58 1703·06 24·45 16642·02
MAE=mean absolute error; MSE=mean squared error.
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former map is an artefact of the technique which is avoided in the latter by using the variogram to provide information on the spatial dependence. The standard deviation and error measures (Table 4), mean absolute error (MAE) and mean squared error (MSE), show a reduction between the net soil flux samples and the block kriging estimates suggesting a reduction in spread and bias of the error distribution. There appears to be very little difference in the general pattern exhibited by the kriging and co-kriging estimation maps (Fig. 2(b) and (c)). However, the summary statistics show that the co-kriging estimates have a slightly smaller standard deviation and smaller absolute and squared estimation errors than the kriging estimates. On closer inspection of the maps the plateau region (north-east corner) shows considerably more small-scale variation in the co-kriging estimates than in the kriging estimates. There are few net soil flux samples in this region suggesting that the variation in the SPOT band XS3 (Fig. 3(c)) is responsible for the net soil flux variation. Perspective diagrams of the kriging and co-kriging estimation variances are shown using the same scale in Fig. 7(a) and (b), respectively. In general, these diagrams show that kriging estimation variances (Fig. 7(a)) are larger than those for co-kriging (Fig. 7(b)). This is supported by the summary statistics for the estimation variances (Table 4). The distribution of the estimation variances generally coincide with the sample locations. Hence, the larger estimation variances occur in the corners of the diagrams rather than in the centre. It is in the areas where net soil flux samples are sparse that the greatest improvement in estimation variance has been made (more than 50%) by the co-kriging technique (Fig. 8). It is also apparent from Fig. 8 that co-kriging has reduced the estimation variance at almost all estimation locations throughout the study area. Conclusions The significance of the spherical model best fit for net soil flux is that the sources of variation controlling the redistribution of net soil flux in the study area have been encompassed by the nested sampling strategy. The range of the net soil flux variogram for the entire study area is consistent with the range of other property variograms for the valley region (Chappell, 1995; Chappell & Oliver, 1997) that were associated with bare areas exposed to wind and water erosion. In this region it is thought that soil redistribution is dominated by aeolian processes controlled by seasonal easterly squalls (Chappell et al., 1996b). The net soil flux for the entire study area was calculated using the kriging and co-kriging estimates by using an arithmetic average of the negative estimates which was added to the average of the positive estimates. Little difference was evident between the average net soil flux for the kriging technique (–36·1 t ha–1 year–1) and that of the co-kriging technique (–35·7 t ha–1 year–1). Despite this small difference, more confidence can be placed in the co-kriging average or in any single co-kriging estimate because its estimation variances are considerably smaller than those for ordinary kriging. Correlation between the SPOT bands and net soil flux was so poor that linear regression could not be undertaken. However, there was sufficient spatial interdependence between data from SPOT band XS3 and net soil flux to undertake co-kriging and to improve the estimates and estimation variances of ordinary kriging. The results provide support for the a priori model suggesting that changes in the soil surface conditions due to aeolian processes (in this study) are represented by alterations in the 137 Cs inventory and the radiance values of the SPOT band XS3. This methodology provides a strong basis for further investigations into the combination of expensive, sparsely-sampled ground measurements of 137Cs with cheap, intensively-sampled remotely sensed data to map net soil flux over very large areas.
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Figure 8. Difference in net soil flux estimation variance (t ha–1 year–1)2 between block kriging (Fig. 7(a)) and block co-kriging (Fig. 7(b)), showing soil sample locations. Fieldwork was conducted whilst the author was in receipt of a NERC framework award. The author is grateful to P. Kabat and the HAPEX-Sahel committee for enabling this research to be conducted under their auspices and for provision of the SPOT satellite data. Assistance with γ-ray measurements by M. Charlton, the geostatistical support from M. Oliver and the helpful advice from M. Barnsley are greatly appreciated. The author is also grateful for comments provided by G. McTainsh and G. Hudson which did much to improve the manuscript during the reviewing process.
References Atkinson, P.M., Webster, R. & Curran, P.J. (1994). Cokriging with airborne MSS imagery. Remote Sensing Environment, 50: 335–345. Chappell, A. (1995). Geostatistical mapping and ordination analyses of 137Cs-derived net soil flux in south-west Niger. Unpublished doctoral thesis, University of London. Chappell, A. & Oliver, M.A. (1997). Geostatistical analysis of soil redistribution in SW Niger, West Africa. In: Baafi, E.Y. & Schofield, N.A. (Eds), Quantitative Geology and Geostatistics, Vol. 8/2, pp. 961–972. London: Kluwer. Chappell, A., Warren, A. & Oliver, M.A. (1996a). Net soil flux derived from multivariate soil property classification, SW Niger: a quantified approach based on 137Cs. In: Buerkert, B., Allison, B.E. & von Oppen, M. (Eds), Wind Erosion in West Africa: the problem and its control, pp. 69–85 Welkersheim, Germany: Margraf Verlag. Chappell, A., Oliver, M.A., Warren, A., Agnew, C. & Charlton, M.A. (1996b). Examining the factors controlling the spatial scale of variation in soil redistribution processes from south-
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