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Offsets between tide gauges in South America estimated from
the filtered satellite-only mean dynamic topography
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
R. Čunderlík
cunderli@svf.stuba.sk
Faculty of Civil Engineering Slovak University of Technology
Bratislava Slovakia
Department of Mathematics and Descriptive Geometry
Outline
•Motivation
- geodetic approach to model the satellite-only MDT
• Nonlinear diffusion filtering on closed surfaces
- regularized surface Perona-Malik model
• Nonlinear filtering of the satellite-only MDT
- combination of DTU13_MSS and GO_CONS_GCF_2_DIR_R5 - special treatment to prolong information towards continents
• Interpolated values along coastlines or at tide gauges
- in South America - detail in area of Caribbean Sea
• Conclusions
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
Combination of altimetry and gravity field
DTU13_MSS GO_CONS_GCF_2_DIR_R5 (SH up to d/o 300)
Satellite altimetry: Satellite-only geopotential models:
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
Satellite-only MDT in South America
GGMMSSMDT Nhh −=
DTU13_MSS
Satellite-only MDT
GO_CONS_GCF_2_DIR_R5
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
Satellite-only MDT
satellite-only MDT DTU13_MSS - GOCE_DIR5
(SH up to 300)
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
Nonlinear diffusion filtering on a closed surface
∆S - the Laplace-Beltrami operator
Linear heat equation on a (closed) surface:
Regularized surface PM model
∇S - surface gradient Edge detector
- nonlinear parabolic PDE
21
1)(σ
νuH
gS∇+
= More details: Čunderlík R, Mikula K, Tunega M (2013) Nonlinear diffusion filtering of data on the Earth’s surface. Journal of Geodesy, Vol. 87(2), pp. 143–160
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
Satellite-only MDT
Initial data DTU13_MSS - GOCE_DIR5
(SH up to 300)
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
Satellite-only MDT
2 iterations
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
Satellite-only MDT
4 iterations
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
Satellite-only MDT
6 iterations
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
Satellite-only MDT
8 iterations
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
Satellite-only MDT
10 iterations
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
Satellite-only MDT
12 iterations
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
Stripping noise due to omission errors
Statistics TOTAL Pacific
Mean [m2s-2] 0.019 -0.004
STD [m2s-2] 2.687 1.201
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
How to prolong MDT towards to lands?
Satellite-only MDT DTU13_MSS - GOCE_DIR5
(SH up to 300)
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
How to prolong MDT towards to lands?
Nearest neighbor (NN) (using GS Surfer ®)
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
How to prolong MDT towards to lands?
Local mean values
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
How to prolong MDT towards to lands?
Local mean values + NN
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
(using GS Surfer ®)
1st pre-filtering
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
+
2nd pre-filtering
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
+
3rd (final) filtering
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
+
Final filtering
Initial data
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
Final filtering
2 iterations
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
Final filtering
4 iterations
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
Final filtering
6 iterations
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
Final filtering
8 iterations
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
Final filtering
10 iterations
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
Filtered satellite-only MDT
8 iterations
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
MDT along coastlines in South America
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
West coast
MDT along coastlines in South America
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
East coast
West coast
Interpolated values at tide gauges
East coast
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
Estimated offsets between tide gauges
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
Source: (SIRGAS-2014: Sánchez )
Estimated offsets between tide gauges
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
Source: (SIRGAS-2014: Sánchez )
Bias: -0.25 m
Detail in Caribbean Sea
DTU13_MSS
GO_CONS_GCF_2_DIR_R5
(SH up to d/o 300)
Satellite altimetry:
Satellite-only geopotential models:
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
Detail in Caribbean Sea
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
GGMMSSMDT Nhh −=
Satellite-only MDT
Filtered MDT
(after nonlinear diffusion filtering)
Offsets estimates at tide gauges
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
Filtered satellite-only MDT
Pacific coast
Atlantic coast
Cuba
Hispaniola
Tide gauges:
Conclusions
⇒ nonlinear diffusion filtering of the satellite-only MDT can efficiently reduce the stripping noise ⇒ appropriate way how to prolong information from the satellite-only MDT from oceans towards lands is essential in the process of detecting reliable values at tide gauges (or along coastlines ) ⇒ the filtered satellite-only MDT can be useful for a unifications of local vertical datums as well as for an establishment of the World Height System
Muchas gracias por la atención
SIRGAS-2015 18 – 20 November 2015, Santo Domingo, Dominican Rep.
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