Alfred Stein

Constrained optimisation of soil sampling for minimisation of the kriging variance

This paper introduces the extended Spatial Simulated Annealing (SSA) method to optimise spatial sampling schemes for obtaining the minimal kriging variance. Sampling schemes are optimised at the point level. Boundaries and previous observations can be taken into account. This procedure extends ordinary SSA which focuses entirely on variogram estimation and even distribution of observations over the area. We applied it to texture and phosphate content on a river terrace in Thailand. First, sampling was conducted for estimation of the variogram using ordinary SSA. The variograms thus obtained were used in extended SSA, yielding a reduction of the mean kriging variance of the sand percentage from 28.2 to 23.7(%)2. The variograms were used subsequently in a geomorphologically similar area. Optimised sampling schemes for anisotropic variables differed considerably from those for isotropic ones. The schemes were especially efficient in reducing high values of the kriging variance near boundaries of the area.

Spatial statistics for remote sensing

Preface. Contributors and editors. Introduction. I. 1. Description of the data B. Gorte. 2. Some basic elements of statistics A. Stein. 3. Physical principles of optical R.S. F. van der Meer. 4. Remote Sensing and GIS S. de Bruin, M. Molenaar. II. 5. Spatial Statistics P.M. Atkinson. 6. Spatial prediction by linear kriging A. Papritz, A. Stein. 7. Issues of scale and optimal pixel size P.J. Curran, P. M. Atkinson. 8. Conditional Simulation J.L. Dungan. 9. Supervised image classification B. Gorte. 10. Unsupervised class detection C.H.M. van Kemenade, et al. 11. Spectral unmixing F. van der Meer. III. 12. Accuracy assessment A.K. Skidmore. 13. Spatial sampling schemes J. de Gruijter. 14. Decision support systems A. Sharifi. Bibliography.

Soil-landscape modelling using fuzzy c-means clustering of attribute data derived from a Digital Elevation Model (DEM).

Abstract This study explores the use of fuzzy c -means clustering of attribute data derived from a digital elevation model to represent transition zones in the soil-landscape. The conventional geographic model used for soil-landscape description is not able to properly deal with these. Fuzzy c -means clustering was applied to a hillslope within a small drainage basin in southern Spain. Cluster validity evaluation was based on the coefficient of determination of regressing topsoil clay data on membership grades. The resulting clusters occupied spatially contiguous areas. We found a high degree of association with measured topsoil clay data ( r a 2 =0.68) for three clusters and a weighting exponent of 2.1. Location of the clusters coincided with observable terrain characteristics. Therefore we concluded that the coefficient of determination of regressing soil sample data on membership grades efficiently supports deciding upon the optimum fuzzy c -partition. The study confirms that fuzzy c -means clustering of terrain attribute data enhances conventional soil-landscape modelling, as it allows representation of fuzziness inherent to soil-landscape units.

Quantification of the Effects of Land-Cover-Class Spectral Separability on the Accuracy of Markov-Random-Field-Based Superresolution Mapping

This paper explores the effects of class separability in Markov-random-field-based superresolution mapping (SRM). We propose to account for class separability by means of controlling the balance tuned by a smoothness parameter between the prior and the likelihood terms in the posterior energy function. A generally applicable procedure estimates the optimal smoothness parameter, based on local energy balance analysis. The study shows how the optimal value of the smoothness parameter depends quantitatively and monotonically upon the class separability and the scale factor. Effects are studied on an image synthesized from an agricultural scene with field boundary subpixels. We varied systematically the class separability, the scale factor, and the smoothness parameter values. The accuracy of the resulting land-cover-map image is assessed by means of the kappa statistic at the fine-resolution scale and the class area proportion at the coarse-resolution scale. Performance is compared with a hard and a soft classification of the coarse-resolution image. We demonstrate that an optimal value of the smoothness parameter exists for each combination of scale factor and class separability. This allows us to reach a high classification accuracy (kappa = 0.85) even for poorly separable classes, i.e., with a transformed divergence equal to 0.5 and a scale factor equal to 10. The developed procedure agrees with the empirical data for the optimal smoothness parameter. The study shows that SRM is now applicable to a larger set of images with class separability ranging from poor to excellent.

Modelling, interpolation and stochastic simulation in space and time of global solar radiation.

Global solar radiation data used as daily inputs for most cropping systems and water budget models are frequently available from only a few weather stations and over short periods of time. To overcome this limitation, the Campbell–Donatelli model relates daily maximum and minimum air temperatures to solar radiation. In this study, calibrated values of model site specific parameters and efficiencies of radiation estimates are reported for 29 stations in northern Italy. Their average root mean squared error equals 2.9 MJ m−2 per day. Model inputs and model output show a clear spatial and temporal structure. For large scale model application, atmospheric transmissivity is calculated with ‘calculate first, interpolate later’ (CI) procedures and ‘interpolate the inputs, calculate later’ (IC) procedures. The mean squared error for CI equals 0.0359, whereas that for IC equals 0.0636. Comparison of ‘calculate first, simulate later’ (CS) procedures with ‘simulate the inputs, calculate later’ (SC) procedures shows a higher spatial sensitivity of SC procedures. The study shows how the model can be best applied to estimate global solar radiation, both at visited and unvisited locations, over a large and productive agricultural area in Italy, and hence, to better use water budget/crop productivity models. In addition, CS procedures show the associated error.

Spatial variability of soil properties at different scales within three terraces of the Henares River (Spain)

Abstract This paper applies statistical and geostatistical procedures to a soil chronosequence on the terraces of the Henares River (NE Madrid) to analyse the spatial distribution of several soil properties and use the contribution of geostatistics to establishing a landscape evolution model of the area. Particle-size distribution, pH, calcium carbonate and organic carbon were analysed. Statistical procedures focus on analysing differences between terraces. Geostatistical procedures identify short- and medium-range variations within individual terraces at different scales. Standard transitive variogram models describe the properties of the younger terrace, whereas the linear intransitive model fits the majority of variograms of the older terrace. The analysis confirms and quantifies the decrease in variability of soil properties from young to old deposits, showing thus an increment of soil homogenisation with time. Ageing of the terraces causes the variables to show nontransitive variogram models with unbounded variances within the observation range.

Integrating spatial statistics and remote sensing

This paper presents an integrated approach towards spatial statistics for remote sensing. Using the layer concept in Geographical Information Systems we treat successively elements of spatial statistics, scale, classification, sampling and decision support. The layer concept allows to combine continuous spatial properties with classified map units. The paper is illustrated with five case studies: one on heavy metals in groundwater at different scales, one on soil variability within seemingly homogeneous units, one on fuzzy classification for a soillandscape model, one on classification with geostatistical procedures and one on thermal images. The integrated approach offers a better understanding and quantification of uncertainties in remote sensing studies.

Bayesian classification and class area estimation of satellite images using stratification

The paper describes an iterative extension to maximum a posteriori (MAP) supervised classification methods. A posteriori probabilities per class are used for classification as well as to obtain class area estimates. From these, an updated set of prior probabilities is calculated and used in the next iteration. The process converges to statistically correct area estimates. The iterative process can be combined effectively with a stratification of the image, which is made on the basis of additional map data. Moreover, it relies on the sample sets being representative. Therefore, the method is shown to be well applicable in combination with an existing GIS. The paper gives a description of the procedure and provides a mathematical foundation. An example is presented to distinguish residential, industrial, and greenhouse classes. A significant improvement of the classification was obtained.

Parameters for describing soil macroporosity derived from staining patterns

Abstract Macroporosity influences the dynamics of water and dissolved solutes in the soil. Size, shape and continuity of macropores is affected by soil management. In this study, dye staining technique, followed by digital image processing, are used to quantify macroporosity under field conditions in a short time at low cost. We compared 17 macroporosity parameters, in 55 staining patterns from three fields with different soil management types at five depths, within one soil type. Factor analysis indicates that five factors explain 95% of the variation. The first factor equals the ‘pore extent’, and was similar for the three fields, but showed significantly lower values with increasing depths. The second factor is the ‘individual pore size’, and the third factor the ‘shape’ of the pores. Both were influenced by soil management. Factors four and five were equal to the range and the nugget of the indicator variogram, respectively. We concluded that the most appropriate parameters to quantify staining patterns in an explanatory analysis are the number of pores, the average area per pore and the pore-shape, whereas the best parameter to quantify staining patterns with only one characteristic is the fractal dimension Ds.

Yield Loss in Apple Caused by Monilinia fructigena (Aderh. & Ruhl.) Honey, and Spatio-temporal Dynamics of Disease Development

Monilinia fructigena (Aderh. & Ruhl.) Honey causes considerable yield losses in pome fruit culture. During a field study in the Netherlands in 1997 and 1998, the increase in disease incidence in time was assessed and final pre- and post-harvest losses were recorded in the susceptible apple cultivars James Grieve and Coxs Orange Pippin. Each individual tree was considered as a unique quadrat, and the spatial distribution of diseased fruits among fruit trees at every assessment date was characterised by a dispersion index, Lloyds index of patchiness (LIP). Spatial autocorrelation was applied to detect potential clustering of trees with diseased fruits within rows. In cv. James Grieve, the rate of increase of disease incidence was constant up to harvest time, whereas in cv. Coxs Orange Pippin disease incidence increased markedly 3 weeks before harvest time, which coincided with the harvest of cv. James Grieve in neighbouring rows. Pre-harvest disease incidence was 4.2–4.3% in cv. James Grieve in both years, in cv. Coxs Orange Pippin this was 4.4% in 1997 and 2.7% in 1998. Post-harvest yield losses amounted on average 1.5–2.0% for both cultivars, no significant differences were found between the cultivars (t-test, P=0.05). Both in 1997 and 1998, clustering of diseased fruits among fruit trees was detected; LIP values were significantly higher than 1 (P=0.05 in 1997, P=0.01 in 1998). Clustering of trees with diseased fruits was detected in 1998, when significant (P=0.05) positive correlation coefficients occurred for 2nd, 3rd and 4th lag-order distances in cv. James Grieve, and a significant (P=0.05) positive first-order correlation in cv. Coxs Orange Pippin. Wounding agents, such as insects and birds, may play an important role in the underlying disease dynamics, and crop losses may be minimised by control of these agents.