Proveedor de Servicios de Administración y funciones de la Sociedad Gestora. 137

SPOTL (Some Programs for Ocean Tidal Loading) package [Agnew, 2013] is, as its name indicates, a set of programs related to Ocean Tide Loading computation. It uses an integration mesh consisting of concentric rings around the point considered, with width and number of subdivisions depending on the distance from the site. In particular, given an ocean tidal model, SPOTL can compute in any location the effects produced by the load tides, i.e., gravity, induced potential, displacement, tilt and strain load tides. SPOTL is also able to predict tides from harmonic constituents.

SPOTL is used in this Thesis to obtain the vertical displacement that a given GPS site would undergo, depending on the water mass load in its surroundings. In particular, SPOTL is used to estimate the vertical subsidence a GPS station would experience if a tsunami of fixed characteristics was approaching to it. In Chapter 7, the subsidence computed by SPOTL from selected models that predict real water conditions are compared to GPS estimated vertical motion to validate the latter. Later, in Chapter 8, some tsunami models are processed by SPOTL to compute the expected vertical subsidence.

4.3.1 Input Preparation and Subprograms Used

NLOADF [Agnew, 1997] is a subprogram from SPOTL that calculates ocean loadings at a site. It needs the coor- dinates of the site to be considered (latitude, longitude, height), the ocean tide model selected and a specification of the distribution of land and sea in the area that the model covers. It also needs the loading functions for the deformation of the Earth’s surface, called Green Functions [Farrell, 1972]. NLOADF uses a polar grid centered on the site with grid dimensions increasing with distance from the center. It outputs gravity, induced potential, displacement, tilt and strain load tides.

The models to be fed to SPOTL must be reshaped into SPOTL format conventions and then converted to binary format and stored in the corresponding folder. The conventions for the format can be found in the SPOTL manual [Agnew, 2013]. In order to compute a certain area of vertical subsidence, a custom script is run calling NLOADF for all the points in a grid.

The SPOTL land-sea mask has a 1/64 degree resolution, approximately 1.7 km at the equator. NLOADF uses Green functions to estimate the load. The Green functions chosen in this case for the Earth model are the "Gutenberg-Bullen Model A average Earth", computed and tabulated by Farrell [1972]. For these Green func- tions, NLOADF calculates the load only on points marked as sea in the land-sea mask. However, it can be forced to calculate the load also in points that correspond to land. This way, NLOADF can estimate the subsidence related to a particular flooding if water height data is available.

The selected Green functions have a resolution depending on the radial distance to the point where the load is to be computed. From the point to a radius of 0.02 degrees, 95 subintervals are considered, spaced by 0.0002 degrees. From 0.02 deg to 0.05, there are 30 subintervals spaced 0.001 degrees. From 0.5 to 1 degree far from the point, the 95 subintervals are spaced 0.01 degrees. From 1 to 10 degrees, 90 subintervals are defined, spaced 0.1 degrees. From 10 to 90 degrees away from the point, the spacing of the 160 subintervals is of 0.5 degrees. And

from 90 to 180 degrees away from the point, the 90 subintervals are spaced 1 degree. Each subinterval is divided into sections, defined by the following adaptative equation:

max(150, 360 · sinψ) (4.2)

whereψ is the spherical distance in radians.

This is, the closer the subinterval to the point where the load is to be computed, the smaller the sections it is divided into. The minimum of divisions is 150, and the maximum corresponds to the last subinterval, which is divided into 360 sections.

4.3.2 Used Models

SPOTL pre-defines several ocean tide models, both local and global, like the global FES2004 model [Lyard et al., 2006]. FES2004 is also used by Bernese to correct GPS time series, and OTL from FES2004 will be used in Chapter 6. Also, different ocean model can be introduced to SPOTL. In this Thesis, the used water height models depend on the aim of each test case.

In Chapter 7, three surge models are used. First, two model simulations of water heights are considered. The first is the ocean model BSHcmod (hereafter called DWD/BSH), the regional operational numerical circulation model of the German Federal Maritime and Hydrographic Agency (BSH) [Dick et al., 2001]. It is driven by the meteorological models GME and COSMO-EU of the German weather service (DWD). Its output is the predicted sea level. The surge is computed by subtracting from the model output the tide predicted by BSH. Wind speed data from COSMO-EU/DWD and wave height data from the Local Wave Model (LSM, hereafter DWD/BSH) are used, the latter also driven by the DWD winds [Behrens and Schrader, 1994]. The second model (hereafter ECMWF/JRC) is the JRC Storm Surge Calculation System, called Hyflux2 [Probst and Franchello, 2012]. It uses meteorological forecasts produced by the European Centre for Medium-Range Weather Forecasts (ECMWF) to estimate with a 3-day lead-time potential storm surges due to cyclones or general storm events. Wind speed data from ECMWF, six-hourly surface pressure and wind speed data from the NOAA/NCEP Global Forecast System (GFS) model and from the ECMWF Interim Reanalysis model (ERA Interim), and sea wave height data from ERA Interim, are used as well. The third surge model is obtained by a simulation using the DWD COSMO-EU wind field as forcing for the JRC code HyFlux2 (hereafter DWD/JRC).

The three models show the surge of the seawater during a storm generated by Cyclone Xaver in December 2013 in northern Germany, and are available with a 15 minutes (DWD/BSH) and 60 minutes (DWD/JRC, ECMWF/JRC) sampling. DWD/JRC and ECMWF/JRC models have a spatial resolution of 0.033 degrees (3.7 km). They cover an area from 48.5166 to 62.983 degrees Latitude and from -12.8833 to 24.9833 degrees Longitude. For DWD/BSH model, the spacing is of 0.05 deg in Latitude and 0.08 deg in Longitude, corresponding to 5.56 and 9.26 km, respectively. This model covers an area from 48.575 to 65.875 degrees Latitude and -4.0417 to 30.375 degrees Longitude. The three models were reshaped to cover a region from 49 to 62 degrees Latitude and from -3 to 15 degrees Longitude.

In Chapter 8 several tsunami models are used:

A worst- and best-case scenarios representative of the SW Iberian coast were kindly handed over by M.Sc. Ricardo Tavares da Costa [personal communication]. They include the Gulf of Cádiz and the West of the Strait of Gibraltar, with models adopted from the Joint Research Centre of the European Commission [Annunziato, 2007]. The mesh resolution goes from 60 arc-seconds in the open ocean (0.017o, about 1.8 Km) to 15 arc-seconds close to the coast (0.004o, about 0.46 Km). For each scenario, a tsunami surge model is given for every two minutes in the 3 hours after the earthquake origin. The best-case scenario corresponds to a quake generated in the MPF with epicenter in [36.895, -10.067] and a Mw8.5 magnitude, as computed by Lima et al. [2010]. The worst-case scenario is

a multi-fault scenario, including two epicenters in two different faults, HSF and MPB, as computed by Matias et al.[2013]. The epicenter coordinates are [35.796, -9.913] and [36.574, -9.890] respectively, and both have the

same magnitude, Mw8.6. These models cover the area between 39 and 33 degrees latitude and between -6 and

12 degrees longitude. The unstructured grid was transformed into a mesh with 1201x1201 points, this is, 0.005o spacing (about 0.55 Km).

Also, several tsunami models for the maximum credible earthquake, or worst-case scenario, comprising only the city of Cádiz and surroundings were handed over by Prof. Mauricio González and Prof. Luis Otero, from the University of Cantabria [personal communication]. Such models were created for the TRANSFER project [UCA and IGN, 2009] in order to study the effect of a possible tsunami in the Western part of Andalucía in terms of personal and economic losses, and is focused on the risk related to flooding. The models show the state of the sea at the point where the highest values are found near the city of Cádiz and surroundings. Each model corresponds to the different tsunami source zones: GBF (Gorringe Bank Fault, Mw8.2), HSF (Horseshoe Fault, Mw8.3), MPF

(Marqués de Pombal Fault, Mw8.1), PBF (Portimao Bank Fault, Mw8.0) and CWF (Cádiz Wedge Fault, Mw8.6)

(see Section 3.1.3.1). The models only comprise a small area, 36.37355 to 36.64105 deg Latitude and -6.40696 to -6.11946 deg Longitude (536x576 points). Opposite to the best- and worst- case models introduced in the previous paragraph, these models include the astronomical tide corresponding to the mean equinoctial high tide. It is of 3.55 meters in the harbor of Cádiz [Moreno, S. personal communication], and this value is subtracted from the models thus only the surge is considered for further studies.