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BME prediction of continuous geographical properties using auxiliary variables

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Abstract

Using auxiliary information to improve the prediction accuracy of soil properties in a physically meaningful and technically efficient manner has been widely recognized in pedometrics. In this paper, we explored a novel technique to effectively integrate sampling data and auxiliary environmental information, including continuous and categorical variables, within the framework of the Bayesian maximum entropy (BME) theory. Soil samples and observed auxiliary variables were combined to generate probability distributions of the predicted soil variable at unsampled points. These probability distributions served as soft data of the BME theory at the unsampled locations, and, together with the hard data (sample points) were used in spatial BME prediction. To gain practical insight, the proposed approach was implemented in a real-world case study involving a dataset of soil total nitrogen (TN) contents in the Shayang County of the Hubei Province (China). Five terrain indices, soil types, and soil texture were used as auxiliary variables to generate soft data. Spatial distribution of soil total nitrogen was predicted by BME, regression kriging (RK) with auxiliary variables, and ordinary kriging (OK). The results of the prediction techniques were compared in terms of the Pearson correlation coefficient (r), mean error (ME), and root mean squared error (RMSE). These results showed that the BME predictions were less biased and more accurate than those of the kriging techniques. In sum, the present work extended the BME approach to implement certain kinds of auxiliary information in a rigorous and efficient manner. Our findings showed that the BME prediction technique involving the transformation of variables into soft data can improve prediction accuracy considerably, compared to other techniques currently in use, like RK and OK.

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References

  • Akita Y, Carter G, Serre ML (2007) Spatiotemporal non-attainment assessment of surface water tetrachloroethene in New Jersey. J Environ Qual 36:508–520

    Article  CAS  Google Scholar 

  • Angulo JM, Yu H-L, Langousis A, Kolovos A, Wang J-F, Madrid D, Christakos G (2013) Spatiotemporal infectious disease modeling: a BME-SIR approach. PLoS-One 8(9):e72168. doi:10.1371/journal.pone.0072168

    Article  CAS  Google Scholar 

  • Baxter SJ, Oliver MA (2005) The spatial prediction of soil mineral N and potentially available N using elevation. Geoderma 128:325–339

    Article  CAS  Google Scholar 

  • Beven KJ, Kirkby MJ (1979) A physically based variable contributing area model of basin hydrology. Hydrol Sci J 24:46–58

    Google Scholar 

  • Bogaert P (2002) Spatial prediction of categorical variables: the BME approach. Stoch Environ Res Risk Assess 16:425–448

    Article  Google Scholar 

  • Bogaert P (2004) Predicting and simulating categorical random fields: the BME approach. In: Proceeding of the 1st international conference for advances in mineral resources management & environmental geotechnology (AMIREG 2004), 119–126, Chania, 7–9 June 2004

  • Bogaert P, D’Or D (2002) Estimating soil properties from thematic soil maps: the Bayesian maximum entropy approach. Soil Sci Soc Am J 66:1492–1500

    Article  CAS  Google Scholar 

  • Bogaert P, Fasbender D (2007) Bayesian data fusion in a spatial prediction context: a general formulation. Stoch Environ Res Risk Assess 21:695–709

    Article  Google Scholar 

  • Bogaert P, Wibrin MA (2004) Combining categorical and continuous information within the BME paradigm. In: Proceedings of the geoenv v-geostatistics for environmental applications, Neuchatel, 13–15 Oct 2004

  • Bremner JM (1960) Determination of nitrogen in soil by the Kjeldahl method. J Agric Sci 55:11–33

    Article  CAS  Google Scholar 

  • Brus DJ, Heuvelink GBM (2007) Towards a soil information system with quantified accuracy; three approaches for stochastic simulation of soil maps. Statutory research tasks unit for nature and the environment. WOt-Rapport 58, Wageningen

  • Brus DJ, de Gruijter JJ, Marsman BA, Visschers R, Bregt AK, Breeuwsma A, Bouma J (1996) The performance of spatial interpolation methods and choropleth maps to estimate properties at points: a soil survey case study. Environmetrics 7:1–6

    Article  Google Scholar 

  • Brus DJ, Bogaert P, Heuvelink GBM (2008) Bayesian maximum entropy prediction of soil categories using a traditional soil map as soft information. Eur J Soil Sci 59:166–177

    Article  Google Scholar 

  • Choi KM, Serre ML, Christakos G (2003) Efficient mapping of California mortality fields at different spatial scales. J Expo Anal Environ Epidemiol 13:120–133

    Article  Google Scholar 

  • Choi KM, Yu HL, Wilson ML (2008) Spatiotemporal statistical analysis of influenza mortality risk in the State of California during the period 1997–2001. Stoch Environ Res Risk Assess 22:15–25

    Article  Google Scholar 

  • Christakos G (1985) Modern statistical analysis and optimal estimation of geotechnical data. Eng Geol 22(2):175–200

    Article  Google Scholar 

  • Christakos G (1987) A stochastic approach in modelling and estimating geotechnical data. Int J Numer Anal Methods Geomech 11(1):79–102

    Article  Google Scholar 

  • Christakos G (1990) A Bayesian/maximum-entropy view to the spatial estimation problem. Math Geol 22:763–777

    Article  Google Scholar 

  • Christakos G (1992) Random field models in earth sciences. Academic Press, San Diego, CA

    Google Scholar 

  • Christakos G (1998) Spatiotemporal information systems in soil and environmental sciences. Geoderma 85(2–3):141–179

    Article  Google Scholar 

  • Christakos G (2000) Modern spatiotemporal geostatistics. Oxford University Press, New York, NY

    Google Scholar 

  • Christakos G (2008) Spatiotemporal statistics and geostatistics. In: Mateu J, Porcu E (eds) Positive definite functions: from Schoenberg to space-time challenges-chapter 5. UJI Publ, Castello de la Plana, pp 117–153

    Google Scholar 

  • Christakos G, Li X (1998) Bayesian maximum entropy analysis and mapping: a farewell to kriging estimators? Math Geol 30:435–462

    Article  Google Scholar 

  • Christakos G, Serre ML (2000) BME analysis of spatiotemporal particulate matter distributions in North Carolina. Atmos Environ 34:3393–3406

    Article  CAS  Google Scholar 

  • Christakos G, Bogaert P, Serre ML (2002) Temporal GIS. Springer-Verlag, New York

    Google Scholar 

  • Coulliette AD, Money ES, Serre ML, Noble RT (2009) Space/time analysis of fecal pollution and rainfall in an eastern North Carolina estuary. Environ Sci Technol 43:3728–3735

    Article  CAS  Google Scholar 

  • D’Or D, Bogaert P (2003) Continuous valued map reconstruction with the Bayesian maximum entropy. Geoderma 112:169–178

    Article  Google Scholar 

  • D’Or D, Bogaert P, Christakos G (2001) Application of the BME approach to soil texture mapping. Stoch Environ Res Risk Assess 15:87–100

    Article  Google Scholar 

  • De Nazelle A, Arunachalam S, Serre ML (2010) Bayesian maximum entropy integration of ozone observations and model predictions: an application for attainment demonstration in North Carolina. Environ Sci Technol 44:5707–5713

    Article  CAS  Google Scholar 

  • Douaik A, van Meirvenne M, Toth T, Serre ML (2004) Space-time mapping of soil salinity using probabilistic BME. Stoch Environ Res Risk Assess 18:219–227

    Article  Google Scholar 

  • Douaik A, Meirvenne M, Toth T (2005) Soil salinity mapping using spatio-temporal Kriging and Bayesian maximum entropy with interval soft data. Geoderma 128:234–248

    Article  Google Scholar 

  • Gao SG, Zhu ZL, Liu SM, Jin R, Yang GC, Tan L (2014) Estimating the spatial distribution of soil moisture based on Bayesian maximum entropy method with auxiliary data from remote sensing. Int J Appl Earth Observ Geoinform 32:54–66

    Article  Google Scholar 

  • Gesink Law DC, Bernstein K, Serre M, Schumacher CM, Leone PA, Zenilman JM, Miller WC, Rompalo AM (2006) Modeling a syphilis outbreak through space and time using the Bayesian maximum entropy approach. Ann Epidemiol 16:797–804

    Article  Google Scholar 

  • Goovaerts P (1997) Geostatistics for natural resources evaluation. Oxford University Press, New York

    Google Scholar 

  • Gummer B (2009) The scourging angel—the black death in the British Isles. The Bodley Head, London

    Google Scholar 

  • Herbst M, Diekkruger B, Vereecken H (2006) Geostatistical co-regionalization of soil hydraulic properties in a micro-scale catchment using terrain attributes. Geoderma 132:206–221

    Article  Google Scholar 

  • Heywood BG, Brierley AS, Gull SF (2006) A quantified Bayesian maximum entropy estimate of Antarctic krill abundance across the Scotia Sea and in small-scale management units from the CCAMLR-2000 survey. CCAMLR Sci 13:97–116

    Google Scholar 

  • Huang CY (1999) Soil science. China Agriculture Press, Beijing (In Chinese)

    Google Scholar 

  • Huang B, Sun WX, Zhao YC, Zhu J, Yang RQ, Zou Z, Ding F, Su JP (2007) Temporal and spatial variability of soil organic matter and total nitrogen in an agricultural ecosystem as affect by faming practies. Geoderma 139:336–345

    Article  CAS  Google Scholar 

  • Jiang YF, Woodbury AD (2006) A full-Bayesian approach to the inverse problem for steady-state groundwater flow and heat transport. Geophys J Int 167:1501–1512

    Article  Google Scholar 

  • Kolovos A, Christakos G, Serre ML, Miller CT (2002) Computational BME solution of a stochastic advection–reaction equation in the light of site-specific information. Water Resour Res 38:1318–1334

    Article  Google Scholar 

  • Kolovos A, Skupin A, Christakos G, Jerrett M (2010) Multi-perspective analysis and spatiotemporal mapping of air pollution sensor data. Environ Sci Technol 44:6738–6744

    Article  CAS  Google Scholar 

  • Lamsal S, Grunwald S, Bruland GL, Bliss CM, Comerford NB (2006) Regional hybrid geospatial modeling of soil nitrate-nitrogen in the Santa Fe River watershed. Geoderma 135:233–247

    Article  CAS  Google Scholar 

  • Lee CJ, Lee KJ (2006) Application of Bayesian network to the probabilistic risk assessment of nuclear waste disposal. Reliab Eng Syst Saf 91:515–532

    Article  Google Scholar 

  • Lee SJ, Balling R, Gober P (2008a) Bayesian maximum entropy mapping and the soft data problem in urban climate research. Ann Assoc Am Geogr 98:309–322

    Article  Google Scholar 

  • Lee SJ, Wentz EA, Gober P (2008b) Applying Bayesian maximum entropy to extrapolating local water consumption in Maricopa County, Arizona. Water Resour Res. doi:10.1029/2007WR006101

    Google Scholar 

  • Lee SJ, Wentz EA, Gober P (2009) Space–time forecasting using soft geostatistics: a case study in forecasting municipal water demand for Phoenix, Arizona. Stoch Environ Res Risk Assess 24:283–295

    Article  Google Scholar 

  • Li Y (2010) Can the spatial prediction of soil organic matter contents at various sampling scales be improved by using regression kriging with auxiliary information? Geoderma 159:63–75

    Article  CAS  Google Scholar 

  • Lian G, Guo XD, Fu BJ, Hu CX (2009) Prediction of the spatial distribution of soil properties based on environmental correlation and geostatistics. Trans Chin Soc Agric Eng 25:237–242 (in Chinese)

    Google Scholar 

  • LoBuglio JN, Characklis GW, Serre ML (2007) Cost-effective water quality assessment through the integration of monitoring data and modeling results. Water Resour Res 43:W03435. doi:10.1029/2006WR005020

    Article  Google Scholar 

  • McBratney AB, Mendonca ML, Minasny B (2003) On digital soil mapping. Geoderma 117:3–52

    Article  Google Scholar 

  • Messier KP, Akita Y, Serre ML (2012) Integrating address geocoding, land use regression, and spatiotemporal geostatistical estimation for groundwater tetrachloroethylene. Environ Sci Technol 46:2772–2780

    Article  CAS  Google Scholar 

  • Moore ID, Gessler PE, Nielsen GA, Peterson GA (1993) Soil attributes prediction using terrain analysis. Soil Sci Soc Am J 57:443–452

    Article  Google Scholar 

  • Nurnata I, Soares JV, Roberts DA, Leonidas FC, Chadwick OA, Batista GT (2003) Relationships among soil fertility dynamics and remotely sensed measures across pasture chronosequences in Rondonia, Brazil. Remote Sens Environ 87:446–455

    Article  Google Scholar 

  • Odeh IOA, McBratney AB, Chittleborough DJ (1994) Spatial prediction of soil properties from landform attributes derived from a digital elevation model. Geoderma 63:197–214

    Article  Google Scholar 

  • Odeh IOA, McBratney AB, Chittleborough DJ (1996) Further results on prediction of soil properties from terrain attributes: heterotopic cokriging and regression-kriging. Geoderma 67:215–226

    Article  Google Scholar 

  • Orton TG, Lark RM (2007a) Accounting for the uncertainty in the local mean in spatial prediction by BME. Stoch Environ Res Risk Assess 21:773–784

    Article  Google Scholar 

  • Orton TG, Lark RM (2007b) Estimating the local mean for Bayesian maximum entropy by generalized least squares and maximum likelihood, and an application to the spatial analysis of a censored soil variable. J Soil Sci 58:60–73

    Article  Google Scholar 

  • Papantonopoulos G, Modis K (2006) A BME solution of the stochastic three-dimensional Laplace equation representing a geothermal field subject to site-specific information. J Stoch Environ Res Risk Assess 20:23–32

    Article  Google Scholar 

  • Parkin R, Savelieva E, Serre ML (2005) Soft geostatistical analysis of radioactive soil contamination. In: Renard Ph (ed) GeoENV V-Geostatistics for environmental applications. Kluwer Academic, Dordrecht

    Google Scholar 

  • Pei T, Qin CZ, Zhu AX, Yang L, Luo M, Li BL, Zhou CH (2010) Mapping soil organic matter using the topographic wetness index: a comparative study based on different flow-direction algorithms and kriging methods. Ecol Indic 10:610–619

    Article  CAS  Google Scholar 

  • Puangthongthub S, Wangwongwatana S, Kamens RM, Serre ML (2007) Modeling the space/time distribution of particulate matter in Thailand and optimizing its monitoring network. Atmos Environ 41:7788–7805

    Article  CAS  Google Scholar 

  • Querido A, Yost R, Traore S, Doumbia MD, Kablan R, Konare H, Ballo A (2007) Spatiotemporal mapping of total carbon stock in agroforestry systems of Sub-Saharan Africa. In: Proceedings of ASA-CSSA-SSSA international annual meetings, New Orleans, Louisiana, 4–8 Nov 2007

  • Savelieva E, Demyanov V, Kanevski M, Serre ML, Christakos G (2005) BME-based uncertainty assessment of the Chernobyl fallout. Geoderma 128:312–324

    Article  CAS  Google Scholar 

  • Serre ML, Christakos G (1999) Modern geostatistics: computational BME in the light of uncertain physical knowledge—the Equus beds study. Stoch Environ Res Risk Assess 13:1–26

    Article  Google Scholar 

  • Serre ML, Christakos G, Li H, Miller CT (2003a) A BME solution to the inverse problem for saturated groundwater flow. Stoch Environ Res Risk Assess 17:354–369

    Article  Google Scholar 

  • Serre ML, Kolovos A, Christakos G, Modis K (2003b) An application of the holistochastic human exposure methodology to naturally occurring Arsenic in Bangladesh drinking water. Risk Anal 23:515–528

    Article  CAS  Google Scholar 

  • Stacey KF, Lark RM, Whitmore AP, Milne AE (2006) Using a process model and regression kriging to improve predictions of nitrious oxide emissions from soils. Geoderma 135:107–117

    Article  CAS  Google Scholar 

  • Sturges HA (1926) The choice of a class interval. J Am Stat Assoc 21:65-66

  • Sumfleth K, Duttmann R (2008) Prediction of soil property distribution in paddy soil landscapes using terrain data and satellite information as indicators. Ecol Ind 8:485–501

    Article  Google Scholar 

  • Tuia D, Fasbender D, Kanevski M, Bogaert P (2007) Spatial resolution enhancement of ASTER images using Bayesian Data Fusion. J Photogramm Eng Remote Sens (Special issue on Data Fusion)

  • Vyas VM, Tong SN, Uchrin C, Georgopoulos PG, Carter GP (2004) Geostatistical estimation of horizontal hydraulic conductivity for the Kirkwood-Cohansey aquifer. J Am Water Resour Assoc 40:187–195

    Article  Google Scholar 

  • Wibrin MA, Bogaert P, Fasbender D (2006) Combining categorical and continuous spatial information within the Bayesian maximum entropy paradigm. Stoch Environ Res Risk Assess 20:423–433

    Article  Google Scholar 

  • Yu HL, Wang CH (2010) Retrospective prediction of intraurban spatiotemporal distribution of PM2.5 in Taipei. Atmos Environ 44:3053–3065

    Article  CAS  Google Scholar 

  • Yu HL, Wang CH (2013) Quantile-Based Bayesian maximum entropy approach for spatiotemporal modeling of ambient air quality levels. Environ Sci Technol 47:1416–1424

    CAS  Google Scholar 

  • Yu HL, Chen JC, Christakos G, Jerrett M (2007a) Estimating residential level ambient PM10 and ozone exposures at multiple time-scales in the Carolinas with the BME method. Environ Health Perspect 117:537–544

    Article  CAS  Google Scholar 

  • Yu HL, Christakos G, Modis K, Papantonopoulos G (2007b) A composite solution method for physical equations and its application in the Nea Kessani geothermal field (Greece). J Geophys Res Solid Earth 112:B06104. doi:10.1029/2006JB004900

    Article  Google Scholar 

  • Yu HL, Kolovos A, Christakos G, Chen J-C, Warmerdam S, Dev B (2007c) Interactive spatiotemporal modelling of health systems: the SEKS-GUI framework. J Stoch Environ Res Risk Assess 21(5):555–572

    Article  Google Scholar 

  • Yu HL, Chiang CT, Lin ST, Chang TK (2010) Spatiotemporal analysis and mapping of oral cancer risk in Changhua county (Taiwan): an application of generalized Bayesian Maximum Entropy method. Ann Epidemiol 20:99–107

    Article  Google Scholar 

  • Yu HL, Wang CH, Liu MC, Kuo YM (2011) Estimation of fine particulate matter in Taipei using landuse regression and Bayesina maximum entropy methods. Int J Environ Res Public Health 8:2153–2169

    Article  Google Scholar 

  • Yu HL, Ku SJ, Kolovos A (2012) Advanced space-time predictive analysis with STAR-BME. In: Proceedings of the 20th international conference on advances in geographic information systems. ACM, Redondo Beach, California, pp 593–596

  • Zhang H, Zhang GL, Gong ZT (2004) The progress of quantitative soil-landscape modeling: a review. Chin J Soil Sci 35:339–346 (in Chinese)

    Google Scholar 

  • Zhang SW, Huang YF, Shen CY, Ye HC, Du YC (2012) Spatial prediction of soil organic matter using terrain indices and categorical variables as auxiliary information. Geoderma 171–172:35–43

    Article  CAS  Google Scholar 

  • Zhu AX, Qi F, Moore A, Burt JE (2010) Prediction of soil properties using fuzzy membership. Geoderma 158:199–206

    Article  Google Scholar 

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Acknowledgments

The research was supported by National Natural Science Foundation of China (Grant No. 41101193). Opinions in the paper do not constitute an endorsement or approval by the funding agencies and only reflect the personal views of the authors.

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Authors and Affiliations

  1. Department of Resource and Environmental Information, College of Resources and Environment, Huazhong Agricultural University, Wuhan, 430070, China

    Yong Yang, ChuTian Zhang & Ruoxi Zhang

  2. Key Laboratory of Arable Land Conservation (Middle and Lower Reaches of Yangtse River), Ministry of Agriculture, Wuhan, China

    Yong Yang, ChuTian Zhang & Ruoxi Zhang

  3. Department of Geography, San Diego State University, San Diego, CA, 92182-4493, USA

    Yong Yang

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  1. Yong Yang
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  2. ChuTian Zhang
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Correspondence to Yong Yang.

Appendix I

Appendix I

Probability distribution patterns of TN categories according to different interval

See Appendix Table 11.

Table 11 Probability distribution patterns of TN categories according to different interval
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Yang, Y., Zhang, C. & Zhang, R. BME prediction of continuous geographical properties using auxiliary variables. Stoch Environ Res Risk Assess 30, 9–26 (2016). https://doi.org/10.1007/s00477-014-1005-1

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