Due to its complexities in both mathematicM formulations and applications, universal co-kriging （UCK） has not been sufficiently discussed in literature. An extended and simpler matrix formulation UCK with incorporat...Due to its complexities in both mathematicM formulations and applications, universal co-kriging （UCK） has not been sufficiently discussed in literature. An extended and simpler matrix formulation UCK with incorporation of a polynomial variable trend is proposed in this paper. Estimators of the value and expectation of a regionMized vector taken in a point are obtained on the basis of cross-covaxiance and cross-vaxiogram, respectively. The complex expressions of co-kriging with trend are greatly simplified by introducing special matrix operations, such as Kronecker product, into the formulations. This simplification offers a feasible and easier approach for computer coding of the UCK, and helps the practitioners to use the UCK technique conveniently in real cases.展开更多
Background:Aboveground biomass(AGB)is a fundamental indicator of forest ecosystem productivity and health and hence plays an essential role in evaluating forest carbon reserves and supporting the development of target...Background:Aboveground biomass(AGB)is a fundamental indicator of forest ecosystem productivity and health and hence plays an essential role in evaluating forest carbon reserves and supporting the development of targeted forest management plans.Methods:Here,we proposed a random forest/co-kriging framework that integrates the strengths of machine learning and geostatistical approaches to improve the mapping accuracies of AGB in northern Guangdong Province of China.We used Landsat time-series observations,Advanced Land Observing Satellite(ALOS)Phased Array L-band Synthetic Aperture Radar(PALSAR)data,and National Forest Inventory(NFI)plot measurements,to generate the forest AGB maps at three time points(1992,2002 and 2010)showing the spatio-temporal dynamics of AGB in the subtropical forests in Guangdong,China.Results:The proposed model was capable of mapping forest AGB using spectral,textural,topographical variables and the radar backscatter coefficients in an effective and reliable manner.The root mean square error of the plotlevel AGB validation was between 15.62 and 53.78 t∙ha^(−1),the mean absolute error ranged from 6.54 to 32.32 t∙ha^(−1),the bias ranged from−2.14 to 1.07 t∙ha^(−1),and the relative improvement over the random forest algorithm was between 3.8%and 17.7%.The largest coefficient of determination(0.81)and the smallest mean absolute error(6.54 t∙ha^(−1)were observed in the 1992 AGB map.The spectral saturation effect was minimized by adding the PALSAR data to the modeling variable set in 2010.By adding elevation as a covariable,the co-kriging outperformed the ordinary kriging method for the prediction of the AGB residuals,because co-kriging resulted in better interpolation results in the valleys and plains of the study area.Conclusions:Validation of the three AGB maps with an independent dataset indicated that the random forest/cokriging performed best for AGB prediction,followed by random forest coupled with ordinary kriging(random forest/ordinary kriging),and the random forest model.The proposed random forest/co-kriging framework provides an accurate and reliable method for AGB mapping in subtropical forest regions with complex topography.The resulting AGB maps are suitable for the targeted development of forest management actions to promote carbon sequestration and sustainable forest management in the context of climate change.展开更多
GA （geostatistical analyst） is an indispensable tool to analyze various and plenty of data in GIS （geographic information system）. Spatial distribution is the most effective factor for predicting of meteorological...GA （geostatistical analyst） is an indispensable tool to analyze various and plenty of data in GIS （geographic information system）. Spatial distribution is the most effective factor for predicting of meteorological maps at the point of performance or reliability of the model. Generally, classical interpolation methods may not be sufficient to produce accurate maps. GA is more considerable in this state. Secondary variables affect the precious of prediction models especially meteorological data mapping. In this study 245 meteorological data stations have been evaluated to produce precipitation model maps in Turkey. Long term （25 years） mean annual and monthly precipitation data from Turkish State Meteorological Service and elevation, slope and aspect values from DEM （Digital Elevation Model） were registered. OK （Ordinary Kriging）, OCK （Ordinary Co-Kriging） and GWR （Geographically Weighted Regression） have been used as a method to compare the models. With the study if there are effects of secondary variables to precipitation models have been illustrated on the prediction maps. Besides comparing statistical values, regional effects of secondary variables have been determined and illustrated on the maps numerically. As a result to define precipitation distribution spatially R2 values between measured and predicted values have been calculated 0.55 for Kriging, 0.67 for OCK and 0.86 for GWR. Cross validation indicated that GWR interpolation yields the smallest prediction error with elevation, slope and aspect. Spatial distribution of meteorological stations is also other important factor for similar studies.展开更多
Constructing high approximation accuracy surrogate model with lower computational cost has great engineering significance. In this paper, using co-Kriging method, an efficient multi-fidelity surrogate model is constru...Constructing high approximation accuracy surrogate model with lower computational cost has great engineering significance. In this paper, using co-Kriging method, an efficient multi-fidelity surrogate model is constructed based on two independent high and low fidelity samples. Co-Kriging method can use a greater quantity of low-fidelity information to enhance the accuracy of a surrogate of the high-fidelity model by modeling the correlation between high and low fidelity model, thus computational cost of building surrogate model can be greatly reduced. A wing-body problem is taken as an example to compare characteristics of co-Kriging multi-fidelity （CKMF） model with traditional Kriging based multi-fidelity （KMF） model. A sampling convergence of the CKMF model and the KMF model is conducted, and an appropriate sampling design is selected through the sampling convergence analysis. The results indicate that CKMF model has higher approximation accuracy with the same high-fidelity samples, and converges at less high-fidelity samples. A wing-body drag reduction optimization design using genetic algorithm is implemented. Satisfying design results are obtained, which validate the feasibility of CKMF model in engineering design.展开更多
There are various occasions where simple, ordinary, and universal kriging techniques may find themselves incapable of performing spatial prediction directly or efficiently. One type of application concerns quantificat...There are various occasions where simple, ordinary, and universal kriging techniques may find themselves incapable of performing spatial prediction directly or efficiently. One type of application concerns quantification of cumulative distribution function (CDF) or probability of occurrences of categorical variables over space. The other is related to optimal use of co-variation inherent to multiple regionalized variables as well as spatial correlation in spatial prediction. This paper extends geostatistics from the realm of kriging with uni-variate and continuous regionalized variables to the territory of indicator and multivariate kriging, where it is of ultimate importance to perform non-parametric estimation of probability distributions and spatial prediction based on co-regionalization and multiple data sources, respectively.展开更多
Climate data of mean monthly temperature and total monthly precipitation compiled from different sources in northern Patagonia were interpolated to 20-km resolution grids over the period 1997-2010. This northern Patag...Climate data of mean monthly temperature and total monthly precipitation compiled from different sources in northern Patagonia were interpolated to 20-km resolution grids over the period 1997-2010. This northern Patagonian climate grid （NPCG） improves upon previous gridded products in terms of its spatial resolution and number of contributing stations, since it incorporates 218 and 114 precipitation and temper- ature records, respectively. A geostatistical method using surface elevation from a Digital Elevation Model （DEM） as the ancillary variable was used to interpolate station data into even spaced points. The maps provided by NPCG are consistent with the broad spatial and temporal patterns of the northern Patagonian climate, showing a comprehensive representation of the latitudinal and altitudinal gradients in temperature and precipitation, as well as their related patterns of seasonality and continentality. We compared the per- formance of NPCG and various other datasets available to the climate community for northern Patagonia. The grids used for the comparison included those of the Global Precipitation Climatology Project, ERA- Interim, Climate Research Unit （University of East Anglia）, and University of Delaware. Based on three statistics that quantitatively assess the spatial coherence of gridded data against available observations （bias, MAE, and RMSE）, NPCG outperforms other global grids. NPCG represents a useful tool for understand- ing climate variability in northern Patagonia and a valuable input for regional models of hydrological and ecological processes. Its resolution is optimal for validating data from the general circulation models and working with raster data derived from remote sensing, such as vegetation indices.展开更多
The Bayesian Multi-Fidelity Surrogate(MFS)proposed by Kennedy and O’Hagan(KOH model)has been widely employed in engineering design,which builds the approximation by decomposing the high-fidelity function into a scale...The Bayesian Multi-Fidelity Surrogate(MFS)proposed by Kennedy and O’Hagan(KOH model)has been widely employed in engineering design,which builds the approximation by decomposing the high-fidelity function into a scaled low-fidelity model plus a discrepancy function.The scale factor before the low-fidelity function,ρ,plays a crucial role in the KOH model.This scale factor is always tuned by the Maximum Likelihood Estimation(MLE).However,recent studies reported that the MLE may sometimes result in MFS of bad accuracy.In this paper,we first present a detailed analysis of why MLE sometimes can lead to MFS of bad accuracy.This is because,the MLE overly emphasizes the variation of discrepancy function but ignores the function waviness when selectingρ.To address the above issue,we propose an alternative approach that choosesρby minimizing the posterior variance of the discrepancy function.Through tests on a one-dimensional function,two high-dimensional functions,and a turbine blade design problem,the proposed approach shows better accuracy than or comparable accuracy to MLE,and the proposed approach is more robust than MLE.Additionally,through a comparative test on the design optimization of a turbine endwall cooling layout,the advantage of the proposed approach is further validated.展开更多
文摘Due to its complexities in both mathematicM formulations and applications, universal co-kriging （UCK） has not been sufficiently discussed in literature. An extended and simpler matrix formulation UCK with incorporation of a polynomial variable trend is proposed in this paper. Estimators of the value and expectation of a regionMized vector taken in a point are obtained on the basis of cross-covaxiance and cross-vaxiogram, respectively. The complex expressions of co-kriging with trend are greatly simplified by introducing special matrix operations, such as Kronecker product, into the formulations. This simplification offers a feasible and easier approach for computer coding of the UCK, and helps the practitioners to use the UCK technique conveniently in real cases.
基金the Natural Science Foundation of China(Nos.31670552,31971577)China Postdoctoral Science Foundation(No.2019 M651842)the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD).
文摘Background:Aboveground biomass(AGB)is a fundamental indicator of forest ecosystem productivity and health and hence plays an essential role in evaluating forest carbon reserves and supporting the development of targeted forest management plans.Methods:Here,we proposed a random forest/co-kriging framework that integrates the strengths of machine learning and geostatistical approaches to improve the mapping accuracies of AGB in northern Guangdong Province of China.We used Landsat time-series observations,Advanced Land Observing Satellite(ALOS)Phased Array L-band Synthetic Aperture Radar(PALSAR)data,and National Forest Inventory(NFI)plot measurements,to generate the forest AGB maps at three time points(1992,2002 and 2010)showing the spatio-temporal dynamics of AGB in the subtropical forests in Guangdong,China.Results:The proposed model was capable of mapping forest AGB using spectral,textural,topographical variables and the radar backscatter coefficients in an effective and reliable manner.The root mean square error of the plotlevel AGB validation was between 15.62 and 53.78 t∙ha^(−1),the mean absolute error ranged from 6.54 to 32.32 t∙ha^(−1),the bias ranged from−2.14 to 1.07 t∙ha^(−1),and the relative improvement over the random forest algorithm was between 3.8%and 17.7%.The largest coefficient of determination(0.81)and the smallest mean absolute error(6.54 t∙ha^(−1)were observed in the 1992 AGB map.The spectral saturation effect was minimized by adding the PALSAR data to the modeling variable set in 2010.By adding elevation as a covariable,the co-kriging outperformed the ordinary kriging method for the prediction of the AGB residuals,because co-kriging resulted in better interpolation results in the valleys and plains of the study area.Conclusions:Validation of the three AGB maps with an independent dataset indicated that the random forest/cokriging performed best for AGB prediction,followed by random forest coupled with ordinary kriging(random forest/ordinary kriging),and the random forest model.The proposed random forest/co-kriging framework provides an accurate and reliable method for AGB mapping in subtropical forest regions with complex topography.The resulting AGB maps are suitable for the targeted development of forest management actions to promote carbon sequestration and sustainable forest management in the context of climate change.
文摘GA （geostatistical analyst） is an indispensable tool to analyze various and plenty of data in GIS （geographic information system）. Spatial distribution is the most effective factor for predicting of meteorological maps at the point of performance or reliability of the model. Generally, classical interpolation methods may not be sufficient to produce accurate maps. GA is more considerable in this state. Secondary variables affect the precious of prediction models especially meteorological data mapping. In this study 245 meteorological data stations have been evaluated to produce precipitation model maps in Turkey. Long term （25 years） mean annual and monthly precipitation data from Turkish State Meteorological Service and elevation, slope and aspect values from DEM （Digital Elevation Model） were registered. OK （Ordinary Kriging）, OCK （Ordinary Co-Kriging） and GWR （Geographically Weighted Regression） have been used as a method to compare the models. With the study if there are effects of secondary variables to precipitation models have been illustrated on the prediction maps. Besides comparing statistical values, regional effects of secondary variables have been determined and illustrated on the maps numerically. As a result to define precipitation distribution spatially R2 values between measured and predicted values have been calculated 0.55 for Kriging, 0.67 for OCK and 0.86 for GWR. Cross validation indicated that GWR interpolation yields the smallest prediction error with elevation, slope and aspect. Spatial distribution of meteorological stations is also other important factor for similar studies.
基金supported by the Seventh Framework Programme of China-EU Collaborative Projects
文摘Constructing high approximation accuracy surrogate model with lower computational cost has great engineering significance. In this paper, using co-Kriging method, an efficient multi-fidelity surrogate model is constructed based on two independent high and low fidelity samples. Co-Kriging method can use a greater quantity of low-fidelity information to enhance the accuracy of a surrogate of the high-fidelity model by modeling the correlation between high and low fidelity model, thus computational cost of building surrogate model can be greatly reduced. A wing-body problem is taken as an example to compare characteristics of co-Kriging multi-fidelity （CKMF） model with traditional Kriging based multi-fidelity （KMF） model. A sampling convergence of the CKMF model and the KMF model is conducted, and an appropriate sampling design is selected through the sampling convergence analysis. The results indicate that CKMF model has higher approximation accuracy with the same high-fidelity samples, and converges at less high-fidelity samples. A wing-body drag reduction optimization design using genetic algorithm is implemented. Satisfying design results are obtained, which validate the feasibility of CKMF model in engineering design.
基金Supported by the National 973 Program of China (No. 2007CB714402-5)
文摘There are various occasions where simple, ordinary, and universal kriging techniques may find themselves incapable of performing spatial prediction directly or efficiently. One type of application concerns quantification of cumulative distribution function (CDF) or probability of occurrences of categorical variables over space. The other is related to optimal use of co-variation inherent to multiple regionalized variables as well as spatial correlation in spatial prediction. This paper extends geostatistics from the realm of kriging with uni-variate and continuous regionalized variables to the territory of indicator and multivariate kriging, where it is of ultimate importance to perform non-parametric estimation of probability distributions and spatial prediction based on co-regionalization and multiple data sources, respectively.
基金Supported by the Instituto Nacional de Tecnología Agropecuaria,Consejo Nacional de Investigaciones Científicas y TcnicasAustralian Research Council(ARC DP120104320)+1 种基金Inter-American Institute for Global Change Research(IAICRN02-47)
文摘Climate data of mean monthly temperature and total monthly precipitation compiled from different sources in northern Patagonia were interpolated to 20-km resolution grids over the period 1997-2010. This northern Patagonian climate grid （NPCG） improves upon previous gridded products in terms of its spatial resolution and number of contributing stations, since it incorporates 218 and 114 precipitation and temper- ature records, respectively. A geostatistical method using surface elevation from a Digital Elevation Model （DEM） as the ancillary variable was used to interpolate station data into even spaced points. The maps provided by NPCG are consistent with the broad spatial and temporal patterns of the northern Patagonian climate, showing a comprehensive representation of the latitudinal and altitudinal gradients in temperature and precipitation, as well as their related patterns of seasonality and continentality. We compared the per- formance of NPCG and various other datasets available to the climate community for northern Patagonia. The grids used for the comparison included those of the Global Precipitation Climatology Project, ERA- Interim, Climate Research Unit （University of East Anglia）, and University of Delaware. Based on three statistics that quantitatively assess the spatial coherence of gridded data against available observations （bias, MAE, and RMSE）, NPCG outperforms other global grids. NPCG represents a useful tool for understand- ing climate variability in northern Patagonia and a valuable input for regional models of hydrological and ecological processes. Its resolution is optimal for validating data from the general circulation models and working with raster data derived from remote sensing, such as vegetation indices.
基金the financial support from the National Science and Technology Major Project,China(No.2019-Ⅱ-0008-0028)Key Program of National Natural Science Foundation of China(No.51936008)。
文摘The Bayesian Multi-Fidelity Surrogate(MFS)proposed by Kennedy and O’Hagan(KOH model)has been widely employed in engineering design,which builds the approximation by decomposing the high-fidelity function into a scaled low-fidelity model plus a discrepancy function.The scale factor before the low-fidelity function,ρ,plays a crucial role in the KOH model.This scale factor is always tuned by the Maximum Likelihood Estimation(MLE).However,recent studies reported that the MLE may sometimes result in MFS of bad accuracy.In this paper,we first present a detailed analysis of why MLE sometimes can lead to MFS of bad accuracy.This is because,the MLE overly emphasizes the variation of discrepancy function but ignores the function waviness when selectingρ.To address the above issue,we propose an alternative approach that choosesρby minimizing the posterior variance of the discrepancy function.Through tests on a one-dimensional function,two high-dimensional functions,and a turbine blade design problem,the proposed approach shows better accuracy than or comparable accuracy to MLE,and the proposed approach is more robust than MLE.Additionally,through a comparative test on the design optimization of a turbine endwall cooling layout,the advantage of the proposed approach is further validated.
