This document discusses space-time regression-kriging using time series of images. It presents a universal kriging model for spatio-temporal data that treats observations as having both spatial and temporal components. Variograms are fitted separately for the spatial and temporal dimensions as well as for their combined zonal anisotropy. The data set examined consists of daily soil moisture observations over multiple years at various locations. Automation of the full space-time regression-kriging process and improved visualization of predictions over time are areas for future work.
Uma mistura de traços clássicos e modernos são os pontos chaves da Linha Málaga. Estes produtos foram pensados para famílias modernas, com filhos e muitos amigos, que gostem de se reunir em jantares e festas. Por isso os móveis são espaçosos e funcionais. Balcão Málaga com 2 portas de correr , compartimente interno dividido por prateleira com amplo espaço. Conta ainda com 3 gavetas na parte superior, para uso de utensílios menores do dia a dia .A combinação de vidro e madeira e as curvas suaves da linha trazem o ar contemporâneo aos móveis.Produto fabricado em Pinus. Para mais informações, clique aqui
Crime Risk Forecasting and Predictive Analytics - Esri UCAzavea
Presentation at the 2011 Esri User Conference that included an overview of HunchLab features related to forecasting, specifically near repeat forecasts and load forecasts.
Uma mistura de traços clássicos e modernos são os pontos chaves da Linha Málaga. Estes produtos foram pensados para famílias modernas, com filhos e muitos amigos, que gostem de se reunir em jantares e festas. Por isso os móveis são espaçosos e funcionais. Balcão Málaga com 2 portas de correr , compartimente interno dividido por prateleira com amplo espaço. Conta ainda com 3 gavetas na parte superior, para uso de utensílios menores do dia a dia .A combinação de vidro e madeira e as curvas suaves da linha trazem o ar contemporâneo aos móveis.Produto fabricado em Pinus. Para mais informações, clique aqui
Crime Risk Forecasting and Predictive Analytics - Esri UCAzavea
Presentation at the 2011 Esri User Conference that included an overview of HunchLab features related to forecasting, specifically near repeat forecasts and load forecasts.
Certificate of Recognition
This certificate is awarded to <speaker> in recognition and commendation for his valuable
contribution and exemplary performance as Resource Speaker during the “Intra IIT LATEX workshop” jointly
organized by the Student Academic Board and Research Scholar Forum, Department of Mathematics, IIT
Guwahati, Guwahati, on 18th February, 2017.
Certificate of Recognition
This certificate is awarded to <speaker> in recognition and commendation for his valuable
contribution and exemplary performance as Resource Speaker during the “Intra IIT LATEX workshop” jointly
organized by the Student Academic Board and Research Scholar Forum, Department of Mathematics, IIT
Guwahati, Guwahati, on 18th February, 2017.
3. Space-time data
Universal 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 linear
function of the auxiliary variables), ε(s, t) is the residual for every
(s, t).
R workshop, Mar 21th 2011
5. Space-time semivariance
γ(si , ti ; sj , tj ) = 0.5 · E ( (si , ti ) − (sj , tj ))2 (2)
R workshop, Mar 21th 2011
6. Residuals
Residuals ( ) consist of three stationary and independent
components (Heuvelink Grith, 2010):
(s, t) = s (s) + t (t) + s,t (s, t) (3)
where s (s) is a purely spatial process (with constant realizations
over time), t (t) is a purely temporal process, and s,t (s, t) is a
space-time process for which distance in space is made comparable
to distance in time by introducing a space-time anisotropy ratio.
R workshop, Mar 21th 2011
7. Zonal anisotropies
The 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, and
time-distance u, Cs (h) + Ct (u) allow the presence of zonal
anisotropies (dierent variogram sills in dierent directions), and
Cs,t ( h2 + (α + u)2 ) allows the presence of geometric anisotropy
represented with the ratio α.
R workshop, Mar 21th 2011
13. Some experiences
By adding the time component we are better o.
R workshop, Mar 21th 2011
14. 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
15. 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
16. 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
17. 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
18. Universal space-time reference
Each 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
19. Space-time algebra re-visited
Should we (re)dene and (re)implement
space-time (4D) algebra?
R workshop, Mar 21th 2011
20. What does this mean?
Distances always on a sphere (sphere geometry);
R workshop, Mar 21th 2011
21. What does this mean?
Distances always on a sphere (sphere geometry);
Always use information about uncertainty (weighted
regression);
R workshop, Mar 21th 2011
22. 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
23. 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
24. 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