Interpolation algorithm ranking using cross-validation and the role of smoothing effect. A coal zone example

For a property measured at several locations, interpolation algorithms provide a unique and smooth function yielding a locally realistic estimation at any point within the sampled region. Previous studies searching for optimal interpolation strategies by measuring cross-validation error have not found consistent rankings; this fact was traditionally explained by differences in the distribution, spatial variability and sampling patterns of the datasets. This article demonstrates that ranking differences are also related to interpolation smoothing, an important factor controlling cross-validation errors that was not considered previously. Indeed, smoothing in average-based interpolation algorithms depends on the number of neighbouring data points used to obtain each interpolated value, among other algorithm parameters. A 3D dataset of calorific value measurements from a coal zone is used to demonstrate that different algorithm rankings can be obtained solely by varying the number of neighbouring points considered (i.e. whilst maintaining the distribution, spatial variability and sampling pattern of the dataset). These results suggest that cross-validation error cannot be used as a unique criterion to compare the performance of interpolation algorithms, as has been done in the past, and indicate that smoothing should be also 26 coupled to search for optimum and geologically realistic interpolation algorithms

Comparing Deterministic and Stochastic Methods in Geospatial Analysis of Groundwater Fluoride Concentration

Dental and skeletal fluorosis caused by consuming high-fluoride groundwater has been reported over several decades globally. Prediction maps to estimate the fluoride contaminated area rely on interpolation methods. This study presents a comparison of the accuracy of nine spatial interpolation methods in predicting the fluoride in groundwater. Leave-one-out cross-validation (LOOCV), hold-out validation and validation with an independent dataset were used to assess the precision of the interpolation methods. This is the first study on fluoride with a large dataset (N = 13,585) applied at the regional level in India. Our findings showed that the inverse distance weighted (IDW) algorithm outperformed other methods in terms of less discrepancy between measured and predicted fluoride. IDW and local polynomial interpolation (LPI) were the only methods to predict contaminated areas (fluoride > 1.5 mg/L). However, the area estimated by the typical assessment of the percentage of unsuitable samples was much higher (6.1%) compared to that estimated by IDW (0.2%) and LPI (0.2%). LOOCV provided viable results than the other two validation methods. Interpolation methods are accompanied with uncertainty which are regulated by the sample size, sample density, sample distribution, minimum and maximum measured concentrations, smoothing and border effects. Drawing a comparison among variegated interpolation methods capturing a wide range of prediction uncertainty is suggested rather than relying on one method exclusively. The high-fluoride areas identified in this study can be used by the Government in planning remediation actions

Comparison of spatial interpolators for variability analysis of soil chemical properties in Cuamba (Mozambique)

Costa, A. C., & Bofana, J. D. R. (2017). Comparison of spatial interpolators for variability analysis of soil chemical properties in Cuamba (Mozambique). African Journal of Agricultural Research, 12(25), 2153-2162. https://doi.org/10.5897/AJAR2016.12415The knowledge of spatial distribution of soil attributes, particularly chemical ones, which is very relevant for agricultural planning. Several studies have focused on spatial interpolation of soil properties, but only a few of them have been undertaken in sub-Saharan Africa. This study aims to analyse the spatial variability of hydrogen potential (pH) and electric conductivity (EC) within an agricultural region in Cuamba district of Mozambique. Efficiency of a deterministic and a stochastic interpolator were compared, namely Inverse Distance Weighting (IDW) and Ordinary kriging, respectively. Soil samples were collected at random locations scattered through the study region, and were later analyzed in water and soil laboratory. These point data were then used to produce interpolated surfaces of soil chemical properties. Efficiency of spatial interpolation methods was assessed based on prediction errors’ statistics derived from cross-validation. Results show that ordinary kriging was less biased and more accurate than IDW at samples’ locations. Hence, maps produced using the former method are a valuable contribution for the spatial characterization of soil quality, according to its chemical properties. Considering the spatial patterns of pH, southeast area is characterized by clayey soils, which has a high fertility potential for food crops.publishersversionpublishe

Geostatistical evaluation of the eastern ore field one (EF1) orebody, Rosh Pinah zinc mine, Namibia

A Dissertation submitted in fulfilment of the requirements for the degree of Master of Science in Engineering to the Faculty of Engineering and the Built Environment, School of Mining Engineering, University of the Witwatersrand, Johannesburg, 2018The geometry, size and quality of a deposit are key parameters required for decision-making regarding mining methods, capital investments or divestments, economic viability and processing methods. The dissertation uses a quantitative approach to assess three geological modelling methods for orebody geometry. It applies Principal Components Analysis (PCA) in order to understand the variability and correlation in the data. The dissertation aims to determine the significance of increasing the composite size to 3 m for grade estimation and to estimate the tonnes and grades of the Eastern Ore Field 1 in-situ resource as on 31 December 2016. A MineSight, a Leapfrog and a hybrid of MineSight and Leapfrog modelling method were assessed, aiming to reduce the modelling time. The Minesight and Leapfrog hybrid model is recommended for modelling complex sedimentary exhalative deposits. The PCA was carried out using Matlab. Based on the correlation of 0.998, the first principal component increases with increasing Ag, Zn and Pb and it correlates most strongly with Ag. The second principal component increases with Zn, with a correlation of 0.985. With a correlation of 0.927, the third component increases with Mg. A 3 m composite size is recommended for estimating EF1 because the generated block-model estimates have lower means, standard deviations, variances and numbers of extreme outliers. The 3 m composite size is closer to the SMU at Rosh Pinah, and produces a better block estimate than 1.5 m composites, the later gives more tonnes and higher grade due to the volume-variance effect, which ultimately leads to overestimation of the mineral deposit. The total in-situ EF1 resource estimated using the Ordinary Kriging interpolation method as on 31 December 2016 was 814,100 tonnes at 8.58% Zn, 3.19% Pb and 79.22 ppm Ag.MT201

Development of a hybrid model to interpolate monthly precipitation maps incorporating the orographic influence

[EN] This paper proposes an interpolation model for monthly rainfall in large areas of complex orography. It has been implemented in the Iberian Peninsula (continental territories of Spain and Portugal), Balearic and Canary Islands covering a territory of almost 600.000km(2). To do this a data set that comprises a total number of 11,822 monthly precipitation series has been created (11,042 provided by the Spanish Meteorological Agency and 780 provided by the National Water Resources Information System of the Portuguese Water Institute). The data set covers the period from October 1940 until September 2005. The interpolation model has been based on the assumption of two different components on monthly precipitation. The first component reflects local and seasonal characteristics and 24 different mean monthly precipitation maps (12) and SDs maps (12) compose it. It considers the varying influence of physiographic variables such as altitude and orientation. The second precipitation component reflects the synoptic pattern that dominated each month of the series and it is composed by series of anomalies of monthly precipitation (780). Anomalies have been interpolated by means of ordinary kriging once local spatial continuity was assumed. Gridded maps of each variable have been developed at 200m resolution following a hybrid methodology that implements two different interpolation techniques. The first technique applies a regression analysis to derive maps depending on altitude and orientation; the second one is a weighting technique to consider the non-linearity of the precipitation/altitude dependence. Cross validation has been applied to estimate the goodness of both techniques. Results show an average annual precipitation of 655mm/year. Although this figure is only 4% less than the estimate of MAGRAMA (2004), regional and local differences are highlighted when the spatial distribution is considered. The model constitutes a comprehensive implementation considering the availability of historical records and the need of avoiding slow calculations in large territories.Ministry of Economy, Industry and Competitiveness, Grant/Award Number: CGL2014-52571-RÁlvarez-Rodríguez, J.; Llasat, M.; Estrela Monreal, T. (2019). Development of a hybrid model to interpolate monthly precipitation maps incorporating the orographic influence. International Journal of Climatology. 39(10):3962-3975. https://doi.org/10.1002/joc.6051S396239753910AEMET.2011Atlas Climático Ibérico. (Iberian Climate Atlas) VV.AA. Agencia Estatal de Meteorología. Ministerio de Medio Ambiente. ISBN: 978‐84‐7837‐079‐5. Available at:http://www.aemet.es/documentos/es/conocermas/publicaciones/Atlas-climatologico/Atlas.pdf[Accessed 14th February 2018]Álvarez‐Rodríguez J.2011.Estimación de la distribución espacial de la precipitación en zonas montañosas mediante métodos geoestadísticos (Analysis of spatial distribution of precipitation in mountainous areas by means of geostatistical analysis). PhD Thesis. Polytechnic University of Madrid Higher Technical School of Civil EngineeringÁlvarez-Rodríguez, J., Llasat, M. C., & Estrela, T. (2017). Analysis of geographic and orographic influence in Spanish monthly precipitation. International Journal of Climatology, 37, 350-362. doi:10.1002/joc.5007Barros, A. P., Kim, G., Williams, E., & Nesbitt, S. W. (2004). Probing orographic controls in the Himalayas during the monsoon using satellite imagery. Natural Hazards and Earth System Sciences, 4(1), 29-51. doi:10.5194/nhess-4-29-2004Barstad, I., Grabowski, W. W., & Smolarkiewicz, P. K. (2007). Characteristics of large-scale orographic precipitation: Evaluation of linear model in idealized problems. Journal of Hydrology, 340(1-2), 78-90. doi:10.1016/j.jhydrol.2007.04.005Creutin, J. D., & Obled, C. (1982). Objective analyses and mapping techniques for rainfall fields: An objective comparison. Water Resources Research, 18(2), 413-431. doi:10.1029/wr018i002p00413Daly, C., Neilson, R. P., & Phillips, D. L. (1994). A Statistical-Topographic Model for Mapping Climatological Precipitation over Mountainous Terrain. Journal of Applied Meteorology, 33(2), 140-158. doi:10.1175/1520-0450(1994)0332.0.co;2Daly, C., Halbleib, M., Smith, J. I., Gibson, W. P., Doggett, M. K., Taylor, G. H., … Pasteris, P. P. (2008). Physiographically sensitive mapping of climatological temperature and precipitation across the conterminous United States. International Journal of Climatology, 28(15), 2031-2064. doi:10.1002/joc.1688Daly, C., Slater, M. E., Roberti, J. A., Laseter, S. H., & Swift, L. W. (2017). High-resolution precipitation mapping in a mountainous watershed: ground truth for evaluating uncertainty in a national precipitation dataset. International Journal of Climatology, 37, 124-137. doi:10.1002/joc.4986Dhar, O. N., & Nandargi, S. (2004). Rainfall distribution over the Arunachal Pradesh Himalayas. Weather, 59(6), 155-157. doi:10.1256/wea.87.03Falivene, O., Cabrera, L., Tolosana-Delgado, R., & Sáez, A. (2010). Interpolation algorithm ranking using cross-validation and the role of smoothing effect. A coal zone example. Computers & Geosciences, 36(4), 512-519. doi:10.1016/j.cageo.2009.09.015Fiering, B., & Jackson, B. (1971). Synthetic Streamflows. Water Resources Monograph. doi:10.1029/wm001Gambolati, G., & Volpi, G. (1979). A conceptual deterministic analysis of the kriging technique in hydrology. Water Resources Research, 15(3), 625-629. doi:10.1029/wr015i003p00625Gómez-Hernández, J. J., Cassiraga, E. F., Guardiola-Albert, C., & Rodríguez, J. Á. (2001). Incorporating Information from a Digital Elevation Model for Improving the Areal Estimation of Rainfall. geoENV III — Geostatistics for Environmental Applications, 67-78. doi:10.1007/978-94-010-0810-5_6Goovaerts, P. (2000). Geostatistical approaches for incorporating elevation into the spatial interpolation of rainfall. Journal of Hydrology, 228(1-2), 113-129. doi:10.1016/s0022-1694(00)00144-xHanson, C. L. (1982). DISTRIBUTION AND STOCHASTIC GENERATION OF ANNUAL AND MONTHLY PRECIPITATION ON A MOUNTAINOUS WATERSHED IN SOUTHWEST IDAHO. Journal of the American Water Resources Association, 18(5), 875-883. doi:10.1111/j.1752-1688.1982.tb00085.xLloyd, C. D. (2005). Assessing the effect of integrating elevation data into the estimation of monthly precipitation in Great Britain. Journal of Hydrology, 308(1-4), 128-150. doi:10.1016/j.jhydrol.2004.10.026Marquı́nez, J., Lastra, J., & Garcı́a, P. (2003). Estimation models for precipitation in mountainous regions: the use of GIS and multivariate analysis. Journal of Hydrology, 270(1-2), 1-11. doi:10.1016/s0022-1694(02)00110-5Martínez-Cob, A. (1996). Multivariate geostatistical analysis of evapotranspiration and precipitation in mountainous terrain. Journal of Hydrology, 174(1-2), 19-35. doi:10.1016/0022-1694(95)02755-6Mitáš, L., & Mitášová, H. (1988). General variational approach to the interpolation problem. Computers & Mathematics with Applications, 16(12), 983-992. doi:10.1016/0898-1221(88)90255-6Naoum, S., & Tsanis, I. K. (2004). Orographic Precipitation Modeling with Multiple Linear Regression. Journal of Hydrologic Engineering, 9(2), 79-102. doi:10.1061/(asce)1084-0699(2004)9:2(79)Ninyerola, M., Pons, X., & Roure, J. M. (2006). Monthly precipitation mapping of the Iberian Peninsula using spatial interpolation tools implemented in a Geographic Information System. Theoretical and Applied Climatology, 89(3-4), 195-209. doi:10.1007/s00704-006-0264-2Pebesma, E. J. (2004). Multivariable geostatistics in S: the gstat package. Computers & Geosciences, 30(7), 683-691. doi:10.1016/j.cageo.2004.03.012Rotunno, R., & Ferretti, R. (2001). Mechanisms of Intense Alpine Rainfall. Journal of the Atmospheric Sciences, 58(13), 1732-1749. doi:10.1175/1520-0469(2001)0582.0.co;2Singh, P., Ramasastri, K. S., & Kumar, N. (1995). Topographical Influence on Precipitation Distribution in Different Ranges of Western Himalayas. Hydrology Research, 26(4-5), 259-284. doi:10.2166/nh.1995.0015Tabios, G. Q., & Salas, J. D. (1985). A COMPARATIVE ANALYSIS OF TECHNIQUES FOR SPATIAL INTERPOLATION OF PRECIPITATION. Journal of the American Water Resources Association, 21(3), 365-380. doi:10.1111/j.1752-1688.1985.tb00147.xTHIESSEN, A. H. (1911). PRECIPITATION AVERAGES FOR LARGE AREAS. Monthly Weather Review, 39(7), 1082-1089. doi:10.1175/1520-0493(1911)392.0.co;2Tobin, C., Nicotina, L., Parlange, M. B., Berne, A., & Rinaldo, A. (2011). Improved interpolation of meteorological forcings for hydrologic applications in a Swiss Alpine region. Journal of Hydrology, 401(1-2), 77-89. doi:10.1016/j.jhydrol.2011.02.010Weber, D., & Englund, E. (1992). Evaluation and comparison of spatial interpolators. Mathematical Geology, 24(4), 381-391. doi:10.1007/bf00891270Weber, D. D., & Englund, E. J. (1994). Evaluation and comparison of spatial interpolators II. Mathematical Geology, 26(5), 589-603. doi:10.1007/bf02089243World Climate Programme.1985. World Meteorological Organization. Review of Requirements for Area‐Averaged Precipitation Data Surface‐Based and Space‐Based Estimation Techniques Space and Time Sampling Accurancy and Error; Data Exchange. Boulder Colorado EE.UU. 17–1

Hydrology of the upper Hunter catchment

One of the ten objectives of the 2004 Australian National Water Initiative is to manage surface and groundwater as a single resource. In order to do that it is necessary to understand the interactions between surface and groundwater, as well as the impacts of water abstraction, land use change and climate variability. In Australia, not just the quantity of water, but also its quality and particularly its salinity are critically important. Some of the difficulties facing agencies in managing surface and groundwater as a single resource are the extreme variability of climate in Australia, the lack of long-term streamflow and groundwater level data sets and the very limited temporal records on water quality. This thesis presents a study of surface and groundwater interaction and salinity in a selected catchment in the Hunter Valley in mid New South Wales, eastern Australia, where data records are limited and incomplete. The hypotheses tested in this work are that (1) salinity discharge in the Hunter is largely determined by mineral weathering and deep groundwater inflows and (2) a simple parameter-efficient coupled surface and groundwater model can accurately predict groundwater and streamflow behaviour over monthly time scale and is useful in determining surface-groundwater interactions.<....

Development of techniques to classify marine benthic habitats using hyperspectral imagery in oligotrophic, temperate waters

There is an increasing need for more detailed knowledge about the spatial distribution and structure of shallow water benthic habitats for marine conservation and planning. This, linked with improvements in hyperspectral image sensors provides an increased opportunity to develop new techniques to better utilise these data in marine mapping projects. The oligotrophic, optically-shallow waters surrounding Rottnest Island, Western Australia, provide a unique opportunity to develop and apply these new mapping techniques. The three flight lines of HyMap hyperspectral data flown for the Rottnest Island Reserve (RIR) in April 2004 were corrected for atmospheric effects, sunglint and the influence of the water column using the Modular Inversion and Processing System. A digital bathymetry model was created for the RIR using existing soundings data and used to create a range of topographic variables (e.g. slope) and other spatially relevant environmental variables (e.g. exposure to waves) that could be used to improve the ecological description of the benthic habitats identified in the hyperspectral imagery. A hierarchical habitat classification scheme was developed for Rottnest Island based on the dominant habitat components, such as Ecklonia radiata or Posidonia sinuosa. A library of 296 spectral signatures at HyMap spectral resolution (~15 nm) was created from >6000 in situ measurements of the dominant habitat components and subjected to spectral separation analysis at all levels of the habitat classification scheme. A separation analysis technique was developed using a multivariate statistical optimisation approach that utilised a genetic algorithm in concert with a range of spectral metrics to determine the optimum set of image bands to achieve maximum separation at each classification level using the entire spectral library. These results determined that many of the dominant habitat components could be separated spectrally as pure spectra, although there were almost always some overlapping samples from most classes at each split in the scheme. This led to the development of a classification algorithm that accounted for these overlaps. This algorithm was tested using mixture analysis, which attempted to identify 10 000 synthetically mixed signatures, with a known dominant component, on each run. The algorithm was applied directly to the water-corrected bottom reflectance data to classify the benthic habitats. At the broadest scale, bio-substrate regions were separated from bare substrates in the image with an overall accuracy of 95% and, at the finest scale, bare substrates, Posidonia, Amphibolis, Ecklonia radiata, Sargassum species, algal turf and coral were separated with an accuracy of 70%. The application of these habitat maps to a number of marine planning and management scenarios, such as marine conservation and the placement of boat moorings at dive sites was demonstrated. Committee Informatio

Advances in Computational Intelligence Applications in the Mining Industry

This book captures advancements in the applications of computational intelligence (artificial intelligence, machine learning, etc.) to problems in the mineral and mining industries. The papers present the state of the art in four broad categories: mine operations, mine planning, mine safety, and advances in the sciences, primarily in image processing applications. Authors in the book include both researchers and industry practitioners