Estimating the spatial distribution of soil moisture based on Bayesian maximum entropy method with auxiliary data from remote sensing

Abstract Soil moisture (SM) plays a fundamental role in the land–atmosphere exchange process. Spatial estimation based on multi in situ (network) data is a critical way to understand the spatial structure and variation of land surface soil moisture. Theoretically, integrating densely sampled auxiliary data spatially correlated with soil moisture into the procedure of spatial estimation can improve its accuracy. In this study, we present a novel approach to estimate the spatial pattern of soil moisture by using the BME method based on wireless sensor network data and auxiliary information from ASTER (Terra) land surface temperature measurements. For comparison, three traditional geostatistic methods were also applied: ordinary kriging (OK), which used the wireless sensor network data only, regression kriging (RK) and ordinary co-kriging (Co-OK) which both integrated the ASTER land surface temperature as a covariate. In Co-OK, LST was linearly contained in the estimator, in RK, estimator is expressed as the sum of the regression estimate and the kriged estimate of the spatially correlated residual, but in BME, the ASTER land surface temperature was first retrieved as soil moisture based on the linear regression, then, the t-distributed prediction interval (PI) of soil moisture was estimated and used as soft data in probability form. The results indicate that all three methods provide reasonable estimations. Co-OK, RK and BME can provide a more accurate spatial estimation by integrating the auxiliary information Compared to OK. RK and BME shows more obvious improvement compared to Co-OK, and even BME can perform slightly better than RK. The inherent issue of spatial estimation (overestimation in the range of low values and underestimation in the range of high values) can also be further improved in both RK and BME. We can conclude that integrating auxiliary data into spatial estimation can indeed improve the accuracy, BME and RK take better advantage of the auxiliary information compared to Co-OK, and BME outperforms RK by integrating the auxiliary data in a probability form.

[1]  Thomas J. Jackson,et al.  In Situ Validation of the Soil Moisture Active Passive (SMAP) Satellite Mission , 2011 .

[2]  George Christakos,et al.  BME representation of particulate matter distributions in the state of California on the basis of uncertain measurements , 2001 .

[3]  Qing Xiao,et al.  Heihe Watershed Allied Telemetry Experimental Research (HiWATER): Scientific Objectives and Experimental Design , 2013 .

[4]  I. Rodríguez‐Iturbe,et al.  Models of soil moisture dynamics in ecohydrology: A comparative study , 2002 .

[5]  Yanchen Bo,et al.  Blending multi-resolution satellite sea surface temperature (SST) products using Bayesian maximum entropy method , 2013 .

[6]  C. Ottlé,et al.  Effect of atmospheric absorption and surface emissivity on the determination of land surface temperature from infrared satellite data , 1993 .

[7]  Pierre Goovaerts,et al.  Using elevation to aid the geostatistical mapping of rainfall erosivity , 1999 .

[8]  W. V. Dooremolen,et al.  Cokriging Point Data on Moisture Deficit , 1988 .

[9]  Saravanan Arunachalam,et al.  Bayesian maximum entropy integration of ozone observations and model predictions: an application for attainment demonstration in North Carolina. , 2010, Environmental science & technology.

[10]  Patrick Bogaert,et al.  Estimating soil properties from thematic soil maps: the Bayesian maximum entropy approach , 2002 .

[11]  G. Christakos.  A Bayesian/maximum-entropy view to the spatial estimation problem , 1990 .

[12]  P. Goovaerts.  Ordinary Cokriging Revisited , 1998 .

[13]  Yanchen Bo,et al.  Bayesian maximum entropy data fusion of field-observed leaf area index (LAI) and Landsat Enhanced Thematic Mapper Plus-derived LAI , 2013 .

[14]  Marc Van Meirvenne,et al.  Soil salinity mapping using spatio-temporal kriging and Bayesian maximum entropy with interval soft data , 2005 .

[15]  H. Vereecken,et al.  Potential of Wireless Sensor Networks for Measuring Soil Water Content Variability , 2010 .

[16]  Dimitri D'Or.  Spatial prediction of soil properties : the Bayesian Maximum Entropy approach , 2003 .

[17]  Venkat Lakshmi,et al.  Observations of land surface temperature and its relationship to soil moisture during SGP99 , 2000, IGARSS 2000. IEEE 2000 International Geoscience and Remote Sensing Symposium. Taking the Pulse of the Planet: The Role of Remote Sensing in Managing the Environment. Proceedings (Cat. No.00CH37120).

[18]  J. Vrugt,et al.  On the value of soil moisture measurements in vadose zone hydrology: A review , 2008 .

[19]  Jiancheng Shi,et al.  The Soil Moisture Active Passive (SMAP) Mission , 2010, Proceedings of the IEEE.

[20]  D. Brus,et al.  A comparison of kriging, co-kriging and kriging combined with regression for spatial interpolation of horizon depth with censored observations , 1995 .

[21]  Z. Niu,et al.  Watershed Allied Telemetry Experimental Research , 2009 .

[22]  Alexandra N. Kravchenko,et al.  Stochastic Simulations of Spatial Variability Based on Multifractal Characteristics , 2008 .

[23]  James E. Bartlett,et al.  Organizational research: Determining appropriate sample size in survey research , 2001 .

[24]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[25]  D. D'Or,et al.  Application of the BME approach to soil texture mapping , 2001 .

[26]  Carol A. Gotway,et al.  Statistical Methods for Spatial Data Analysis , 2004 .

[27]  Yann Kerr,et al.  The SMOS Mission: New Tool for Monitoring Key Elements ofthe Global Water Cycle , 2010, Proceedings of the IEEE.

[28]  N. Cressie.  The origins of kriging , 1990 .

[29]  George Christakos,et al.  Modern Spatiotemporal Geostatistics , 2000 .

[30]  George Christakos,et al.  Comparative spatiotemporal analysis of fine particulate matter pollution , 2009 .

[31]  A. Warrick,et al.  Estimating Soil Water Content Using Cokriging1 , 1987 .

[32]  Gerard B. M. Heuvelink,et al.  About regression-kriging: From equations to case studies , 2007, Comput. Geosci..

[33]  R. Webster,et al.  Optimal interpolation and isarithmic mapping of soil properties. II. Block kriging. , 1980 .

[34]  J. Qu,et al.  Satellite remote sensing applications for surface soil moisture monitoring: A review , 2009 .

[35]  Ian F. Akyildiz,et al.  Wireless sensor networks: a survey , 2002, Comput. Networks.

[36]  John Triantafilis,et al.  Five Geostatistical Models to Predict Soil Salinity from Electromagnetic Induction Data Across Irrigated Cotton , 2001 .

[37]  S. Yates,et al.  Use of pseudo-crossvariograms and cokriging to improve estimates of soil solute concentrations , 1997 .

[38]  Charles R. Hart,et al.  At Chapel Hill , 1947 .

[39]  A. Douaik,et al.  Space-time mapping of soil salinity using probabilistic bayesian maximum entropy , 2004 .

[40]  George Christakos,et al.  Some Applications of the Bayesian, Maximum-Entropy Concept in Geostatistics , 1991 .

[41]  Juan Manuel Dupuy,et al.  Combining geostatistical models and remotely sensed data to improve tropical tree richness mapping , 2011 .

[42]  David G. Hopkins,et al.  Improved Prediction and Mapping of Soil Copper by Kriging with Auxiliary Data for Cation-Exchange Capacity , 2003 .

[43]  Alexander Kolovos,et al.  Total ozone mapping by integrating databases from remote sensing instruments and empirical models , 2004, IEEE Transactions on Geoscience and Remote Sensing.

[44]  George Christakos,et al.  BME Estimation of Residential Exposure to Ambient PM10 and Ozone at Multiple Time Scales , 2008, Environmental health perspectives.

[45]  A. Stein,et al.  Universal kriging and cokriging as a regression procedure. , 1991 .

[46]  Patrick Bogaert,et al.  Spatiotemporal modelling of ozone distribution in the State of California , 2009 .

[47]  Robert J. Wright,et al.  Soil spatial variability relationships in a steeply sloping acid soil environment , 1996 .

[48]  Seung-Jae Lee,et al.  A Bayesian Maximum Entropy approach to address the change of support problem in the spatial analysis of childhood asthma prevalence across North Carolina. , 2009, Spatial and spatio-temporal epidemiology.

[49]  F. Moral.  Comparison of different geostatistical approaches to map climate variables: application to precipitation , 2010 .

[50]  George Christakos,et al.  Bayesian Maximum Entropy Analysis and Mapping: A Farewell to Kriging Estimators? , 1998 .

[51]  D. Myers.  Matrix formulation of co-kriging , 1982 .

[52]  George Christakos,et al.  BME analysis of spatiotemporal particulate matter distributions in North Carolina , 2000 .

[53]  Sabine Grunwald,et al.  Incorporation of spectral data into multivariate geostatistical models to map soil phosphorus variability in a Florida wetland , 2007 .

[54]  Mary Sue Younger,et al.  A First Course in Linear Regression , 1985 .

[55]  Xavier Emery,et al.  Cokriging random fields with means related by known linear combinations , 2012, Comput. Geosci..

[56]  Marc L. Serre,et al.  Modern geostatistics: computational BME analysis in the light of uncertain physical knowledge – the Equus Beds study , 1999 .

[57]  David M. Le Vine,et al.  Aquarius and Remote Sensing of Sea Surface Salinity from Space , 2010, Proceedings of the IEEE.

[58]  Rachel T. Pinker,et al.  Case study of soil moisture effect on land surface temperature retrieval , 2004, IEEE Geoscience and Remote Sensing Letters.

[59]  S. DeGloria,et al.  Spatial Prediction of Soil Organic Matter Content Using Cokriging with Remotely Sensed Data , 2009 .

[60]  Pilar Barreiro,et al.  A Review of Wireless Sensor Technologies and Applications in Agriculture and Food Industry: State of the Art and Current Trends , 2009, Sensors.

[61]  Shen Zhi-bao,et al.  SOME ACHIEVEMENTS IN SCIENTIFIC RESEARCH DURING HEIFE , 1994 .

[62]  Ji Zhou,et al.  Intercomparison of methods for estimating land surface temperature from a Landsat-5 TM image in an arid region with low water vapour in the atmosphere , 2012 .

[63]  Donald E. Myers,et al.  Estimation of the Spatial Distribution of Soil Chemicals Using Pseudo-Cross-Variograms , 1992 .

[64]  Thomas J. Jackson,et al.  Validation of AMSR-E Soil Moisture Products Using In Situ Observations , 2009 .

[65]  Denis Marcotte,et al.  Comparison of approaches to spatial estimation in a bivariate context , 1995 .