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Space-time dataUniversal kriging model for spatio-temporal data (Heuvelink Grith, 2010): T (s, t) = m(s, t) + ε(s, t) (1)where m(s, t) is the deterministic part of the variation (i.e. a linearfunction of the auxiliary variables), ε(s, t) is the residual for every(s, t). R workshop, Mar 21th 2011
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Space-time semivariance γ(si , ti ; sj , tj ) = 0.5 · E ( (si , ti ) − (sj , tj ))2 (2) R workshop, Mar 21th 2011
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ResidualsResiduals ( ) consist of three stationary and independentcomponents (Heuvelink Grith, 2010): (s, t) = s (s) + t (t) + s,t (s, t) (3)where s (s) is a purely spatial process (with constant realizationsover time), t (t) is a purely temporal process, and s,t (s, t) is aspace-time process for which distance in space is made comparableto distance in time by introducing a space-time anisotropy ratio. R workshop, Mar 21th 2011
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Zonal anisotropiesThe covariance structure can be represented by (Snepvangers et al.,2003): C(h, u) = Cs (h) + Ct (u) + Cs,t ( h2 + (α + u)2 ) (4)where C(h, u) is the covariance at distance h in space, andtime-distance u, Cs (h) + Ct (u) allow the presence of zonalanisotropies (dierent variogram sills in dierent directions), andCs,t ( h2 + (α + u)2 ) allows the presence of geometric anisotropyrepresented with the ratio α. R workshop, Mar 21th 2011
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Some experiences By adding the time component we are better o. R workshop, Mar 21th 2011
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Some experiences By adding the time component we are better o. Automation of space-time regression-kriging (overlay, regression modeling, variogram tting, predictions, visualization in Google Earth) is anticipated. R workshop, Mar 21th 2011
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Some experiences By adding the time component we are better o. Automation of space-time regression-kriging (overlay, regression modeling, variogram tting, predictions, visualization in Google Earth) is anticipated. Fitting and visualization of space-time variograms is a bottle-neck! R workshop, Mar 21th 2011
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Some experiences By adding the time component we are better o. Automation of space-time regression-kriging (overlay, regression modeling, variogram tting, predictions, visualization in Google Earth) is anticipated. Fitting and visualization of space-time variograms is a bottle-neck! Predictions need to be visualized as animations. R workshop, Mar 21th 2011
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Some experiences By adding the time component we are better o. Automation of space-time regression-kriging (overlay, regression modeling, variogram tting, predictions, visualization in Google Earth) is anticipated. Fitting and visualization of space-time variograms is a bottle-neck! Predictions need to be visualized as animations. We have ignored the one-way auto-correlation (time works only one way)? R workshop, Mar 21th 2011
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Universal space-time referenceEach observation should have by default: Longitude and latitude (WGS84) (or projected X, Y coordinates + proj4 string); Begin / end of the time interval in UTC (GMT) system; Support size (in square meters); Uncertainty or measurement error; R workshop, Mar 21th 2011
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Space-time algebra re-visited Should we (re)dene and (re)implement space-time (4D) algebra? R workshop, Mar 21th 2011
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What does this mean? Distances always on a sphere (sphere geometry); R workshop, Mar 21th 2011
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What does this mean? Distances always on a sphere (sphere geometry); Always use information about uncertainty (weighted regression); R workshop, Mar 21th 2011
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What does this mean? Distances always on a sphere (sphere geometry); Always use information about uncertainty (weighted regression); Always use information about the support size (nugget estimation, cross-validation); R workshop, Mar 21th 2011
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What does this mean? Distances always on a sphere (sphere geometry); Always use information about uncertainty (weighted regression); Always use information about the support size (nugget estimation, cross-validation); Re-implement also any raster processing (geomorphometry, resampling, ltering etc); R workshop, Mar 21th 2011
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What does this mean? Distances always on a sphere (sphere geometry); Always use information about uncertainty (weighted regression); Always use information about the support size (nugget estimation, cross-validation); Re-implement also any raster processing (geomorphometry, resampling, ltering etc); Use Google Earth to visualize any type of geographic data; R workshop, Mar 21th 2011
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