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Virtual Tide Gauges

A virtual tide gauge (VTG) is a mathematical device which mimics the function of a physical tide gauge (PTG). The VTG indicates sea level changes caused by astronomic and atmospheric forcing fields. Advantages of a VTG are numerous. Where maintaining a PTG in a remote area or harsh environment can be costly or infeasible, a VTG is a good substitute. A VTG is also a good backup for a PTG in case of instrument failure. A VTG can also predict future water levels whereas a PTG cannot.

Behind the VTG is a core technique called the All-Source Green's Function (ASGF; Xu, 2007, 2011). The ASGF is derived from a global numerical model and is a pre-calculated matrix. Each column of the matrix is a Green's function that corresponds to a source point, and all source points of the world ocean are included (hence the name of the function). Water levels at a POI are determined by convolutional effects of global forcing fields. The ASGF is used as a convolution kernel to quickly compute water levels on a POI in response to any kind of external forcing field, which can be isolated and impulsive (e.g., a submarine earth quake) or spatially continuous and long lasting (e.g., a moving hurricane in the air). The ASGF has been used to predict tsunami arrivals (Xu and Song 2013; Mosher et al, 2010) and to simulate storm surges (Xu 2015a,b; Xu et al 2015).

The VTG is a new application of the ASGF, which converts global astronomic and atmospheric forcing fields into water response at a POI. The global astronomic forcing field for tide-generation is computed with NASA/JPL solar system ephemerids, and the global atmospheric forcing field for storm surge generation is computed with GEM4 model outputs for air pressures and winds issued daily by environment Canada. A VTG can be implemented anywhere. This talk will show a demonstrative VTG implemented at Sept-Iles Quebec.

A network of VTGs is being implemented in collaboration with the Canadian Hydrographic Service (CHS) for the national Ocean Protection Plan. The VTG network not only backs up the existing CHS's network of PTGs, but also the VTG network makes it possible to predict water levels in a place where there are no permanent PTGs. The VTGs can be also used to provide the barotropic components of the open boundary conditions needed by regional ocean models.


1) Xu Z. (2015a). The all-source Green's function (ASGF) and its applications to storm surge modeling, part I: from the governing equations to the ASGF convolution. Ocean Dynamics. Volume 65, Issue 12, pp 1743-1760. doi:10.1007/s10236-015-0893-z (link)

2) Xu Z. (2015b). The all-source Green's function (ASGF) and its applications to storm surge modeling, part II: from the ASGF Convolution to Forcing Data Compression and A Regression Model. Ocean Dynamics. Volume 65, Issue 12, pp 1761-1778. doi:10.1007/s10236-015-0894-y (link)

3) Xu Z., J-P Savard and D Lefaivre (2015). Data assimilative hindcast and climate forecast of storm surges with an ASGF Regression Model. Atmosphere and Ocean. Volume 53, Issue 5, pp 464-475. doi:10.1080/07055900.2015.1079774 (link)

4) Xu Z., & Song, Y. T. 2013. Combining the All-Source Green's Functions and the GPS-Derived Source Functions for Fast Tsunami Predictions -- Illustrated by the March 2011 Japan Tsunami. Journal of Atmospheric and Oceanic Technology, 30(7), 1542-1554. (link)

5) Xu Z. 2011. The All-Source Green's Function of Linear Shallow Water Dynamic System: Its Numerical Constructions and Applications to Tsunami Problems. In: Tsunami, Research and Technologies, Nils-Axel Mörner (Ed.), page numbers (509-540), ISBN: 978-953-307-552-5. (link)

6) Mosher, D. C., Xu, Z., & Shimeld, J. (2010). The Pliocene Shelburne mass-movement and consequent tsunami, western Scotian Slope. In Submarine Mass Movements and Their Consequences (pp. 765-775). Springer Netherlands. (link)

7) Xu Z. 2007. The all-source Green's function and its applications to tsunami problems. Science of Tsunami Hazards, Vol. 26, No. 1, pages 59-69 (2007). (link)