A new ocean tide loading model in the Canary Islands region

Journal of Geodynamics 41 (2006) 100 111 A new ocean tide loading model in the Canary Islands region J. Arnoso a,, M. Benavent a, B. Ducarme b, F.G. Montesinos a a Instituto de Astronomía y Geodesia (CSIC-UCM), Facultad de Matemáticas, Plaza de Ciencias, 3. 28040 Madrid, Spain b Chercheur Qualifié au FNRS, Royal Observatory of Belgium, Av. Circulaire, 3. 1180 Brussels, Belgium Accepted 30 August 2005 Abstract A new high-resolution (1/12 l/12 ) regional ocean tide model for Canary Islands region (Spain), by assimilating TOPEX/Poseidon altimetry data and tide gauge measurements into a hydrodynamic model, is presented. This regional ocean tide model is also refined along all the coastlines in the Canary region, using automatic grid discretization and bilinear interpolation. The new ocean model obtained reveals differences in some areas when we compare it with global models. The results confirm that data assimilation for high resolution models improves the ocean tide estimation in complex areas as the Canarian Archipelago. Gravity tide measurements, which are available in two islands of the Canarian Archipelago, have been used to test the ocean tide model. In addition, a comparison of nine global ocean tide models, supplemented with the regional model, is done for the M2 and O1 tidal constituents. The tidal gravity residues reveal that, for the M2 wave, there exists a dependence of the global ocean tide model considered. In general, the agreement of the nine ocean models is rather similar, although TPXO.2 and SCHW displays the most discrepant results. Among the ocean tide models, which are in close agreement at both places for M2 and O1 tidal waves, no one of them give better results than other. 2005 Elsevier Ltd. All rights reserved. Keywords: Ocean tidal loading; Canary Islands region; TOPEX/Poseidon altimetry data; Tide gauge measurements; Hydrodynamic model 1. Introduction The largest source of uncertainty in the ocean loading computation is due to errors in the ocean tide models. The relatively coarse grid of global ocean tide models (even the most recent with 0.25 0.25 resolution) are not enough to describe accurately the geometry of coastal areas and small islands. Combination of dynamical modelling and data assimilation allows us to develop a more accurate tide model. On the one hand, hydrodynamic models can be designed with a resolution as high as desired compensating the limited resolution of the empirical models. On the other hand, the inaccuracies of hydrodynamic models (from bathymetry data and unknown friction and viscosity parameters) can be recovered by observational data (Matsumoto et al., 2000). The assimilation of data into dynamical models for ocean tides has been studied for long time. Schwiderski (1980) was the first author to assimilate coastal and island tide gauge data into a dynamical model. More recently, with the advance of satellite altimetry, several global ocean tide models that assimilate altimeter data have been developed, e.g., NAO99.2 (Matsumoto et al., 2000), CSR4.0 (Eanes and Bettadpur, 1995), GOT00.2 (Ray, 1999), TPXO6.2 (Egbert and Corresponding author. Tel.: +34 913944589; fax: +34 913944615. E-mail address: jose arnoso@mat.ucm.es (J. Arnoso). 0264-3707/$ see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jog.2005.08.034

J. Arnoso et al. / Journal of Geodynamics 41 (2006) 100 111 101 Erofeeva, 2002). An interesting review of data assimilation techniques can be found in Egbert and Bennet (1996). The general data assimilation approaches have in common the inclusion of the dynamical information and the observational data into a single tidal solution. However, how the dynamical information is incorporated varies considerably. Some approaches make only indirect use of the dynamics (e.g., fitting tidal data with Proudman functions) as the statistical interpolation approach proposed by Jourdin et al. (1991). Others, as the generalized inverse approaches, directly incorporate the dynamics by minimizing an explicit defined penalty function. Zahel (1991) used conjugate gradients to minimize the penalty function iteratively and Egbert et al. (1994) stated the minimizer of the penalty function in terms of the representers of data functionals. More recently, Egbert and Erofeeva (2002) showed a variant of the representer approach based on the efficient calculation of the representers. In our study a new high-resolution (1/12 1/12 ) regional ocean tide model for the area of the Canarian Archipelago is developed, which we call the Canary Island Data Assimilated Tide Model, version 1 (CIAM1). The model has been calculated by assimilating TOPEX/Poseidon data together with several tide gauge measurements into a hydrodynamical model. The ocean tide model obtained is also refined along all the coastlines in the Canary region (1.3 km of resolution around the islands, excepting for El Hierro Island, which has 0.2 km), using a new software, which subdivide recursively the grid cells until the required resolution is reached, having into account the land/sea distribution from different sources and tide values interpolated from the CIAM1 model. In this work we also examine diverse global oceanic models through the evaluation of their tidal loading effects in Canary Islands, which are rather large due to its proximity to the Atlantic Ocean. In particular, we have compared the tidal gravity observations, made with LaCoste and Romberg spring gravimeters at two stations located in Lanzarote and Tenerife islands (Fig. 2), with the oceanic loading computations using nine global ocean tide models (see Table 4). The tidal analysis of the gravity observations was performed with the VAV program (Venedikov et al., 2003) and the tidal gravity loading was computed using the Farrell (1972) formalism. 2. Ocean tide model for the region of Canary Islands 2.1. Model domain, bathymetry and grid We have considered here a model domain with limits 341 347.5 in longitude and 26.5 30 in latitude. The grid spacing is l/12 l/12, which gives some 9 km resolution. The bathymetry in the region has been obtained by averaging the 2 minutes resolution bathymetry ETOPO2 (Smith and Sandwell, 1997) in our grid (Fig. 1). 2.2. Data assimilation into a hydrodynamical model To obtain the regional model CIAM1 we have followed the efficient data assimilation scheme and we used the Oregon State University Tidal Inversion Software, OTIS (Egbert and Erofeeva, 2002). There are numerous studies that describe this data assimilation technique (Egbert et al., 1994; Egbert, 1997; Egbert and Erofeeva, 2002). Therefore, in this section, we briefly outline the methodology used, the assimilated data set and the main characteristics of the model obtained. Fig. 1. Model domain and bathymetry used for the regional model of the Canaries.

102 J. Arnoso et al. / Journal of Geodynamics 41 (2006) 100 111 2.2.1. Hydrodynamical model Several authors have studied the semidiurnal and diurnal tidal currents for the area that surrounds the Canary Islands. From the tidal time series analysis they found that the tidal currents in this area are dominated by the barotropic mode (i.e., depth-independent) (Martínez et al., 1999). Therefore, the basic equations of the hydrodynamic model used are the two-dimensional depth-integrated barotropic shallow water equations (SWE). The governing equations for mass conservation and momentum are given by Eqs. (1) and (2), respectively: ( ζ u t = x + v ) (1) y u t v t = fv gh ζ ( 2 x F + A u H x 2 + 2 u y 2 = fu gh ζ y F + A H ( 2 v x 2 + 2 v y 2 ) ( + F u gh ζ SAL x ), ) ( + F v gh ζ SAL y where ζ is the elevation of the water above the mean level and U is the horizontal velocity with components (u, v). In the momentum equation f is the Coriolis parameter, H (x, y) the depth of the water and g is the gravitational acceleration. F is the bottom friction parameterized as follows: F = C D ( u0 H ) U with a dimensionless drag coefficient set to C D =3 10 3 and water speed u 0, estimated as function of the position in the model domain. We have considered a horizontal viscosity coefficient A H = 200 m 2 s 1 that is similar to those used in other numerical models for the area (e.g., Álvarez et al., 1997). The last term in the brackets for each momentum equation contains the tide generating force, determined from the astronomical potentials given by Cartwright (1977) with corrections for solid Earth tide, and tidal loading and ocean self-attraction accounted for the term ζ SAL.Wehave used the load tides computed from the global tide model TPXO6.2. The dynamic model for eight principal tidal constituents (M2, S2, N2, K2, O1, K1, P1 and Q1) has been obtained by direct matrix factorization of the linearized SWE, where open boundary conditions are used along the edge of the domain with the specified elevations interpolated from the GOT00.2 model. We have selected this global model from the comparison between several ocean tide models carried out in the Canaries. We compared the observed and computed loading tides by means of several ocean tide models at two distant locations of the Canaries. The results provided for GOT00.2 model allow us to select it for our area of study. In any case, we have extended the model domain to include T/P crossover data points in the nearby of the open boundaries (Fig. 2). Due to this fact, these observed data are used to optimize the boundary conditions set along the open boundaries. 2.2.2. Assimilated data Assimilated data consist of elevations from satellite altimetry and tide gauge data. The altimeter data used comprise 364 cycles of TOPEX/Poseidon (T/P), from 1992 to 2004, from a modified version of the PATHFINDER database (Koblinsky et al., 1999) with no tidal corrections applied. We have used the altimeter data for 276 points, including 5 crossover points in the model domain (Fig. 2). The altimeter data along track have been used with original spacing of 7 km, which are comparable to the spatial resolution for the dynamical model. Additionally to the T/P data, the regional model has been assimilated with data from seven tide gauges in several islands of the Canaries. Fig. 2 shows the tide gauge stations and the corresponding coordinates are given in Table 1. The amplitude and phase values at each tide gauge location (Table 2) were provided by the Tide Gauge Network of Spanish State Ports (REDMAR, 2003) and IEO (Álvarez et al., 1997). 2.2.3. Assimilated model The next step is to set the errors in dynamics and data. The dynamical error covariance provides prior information about the magnitude and spatial characteristic of the errors in the hydrodynamic model and the boundary conditions. We have assumed dynamical errors spatially correlated (Egbert et al., 1994), with a constant decorrelation length scale of 50 km ( 9 grid cells in each direction). Finally, to obtain the assimilated model CIAM1 (final solution) we ) (2) (3)

J. Arnoso et al. / Journal of Geodynamics 41 (2006) 100 111 103 Table 1 Location of the tide gauges and length of the data series (in days) used to obtain the harmonic constants Station Latitude Longitude Record length Provided by 1. Pto. S.C. Palma 28 40 58.8 342 27 00.0 366 IEO 2 La Estaca 27 48 00.0 342 06 06.0 128 REDMAR 3 Granadilla 28 05 00.0 343 29 06.0 272 REDMAR 4 Pto. S.C. Tenerife 28 28 42.0 343 45 35.0 364 REDMAR 5 Pto. Las Palmas 28 08 53.0 344 35 37.0 335 REDMAR 6 Arinaga 27 51 00.0 344 36 00.0 282 REDMAR 7 Arrecife 28 57 00.0 346 25 58.8 366 IEO have computed the minimum of the quadratic penalty functional, which is a sum of the dynamical model and a linear combination of the representers. These representers have been computed at a selected subset of data locations that comprises tide gauge data locations, all T/P crossover points and ten along track sites between crossovers (see Fig. 2). 2.3. Model results In this section, we show the model obtained and we compare it with a global model in the area. Fig. 2. (Top) location of the REDMAR and IEO tide gauges (black stars). The open circles indicate T/P along track data points, in which black circles mean representers. T/P crossover are pointed with black squares. Triangles show the location of the stations Cueva de los Verdes (CV), Teide-Parador (TP) and Balneario Pozo de la Salud (BA) in Lanzarote, Tenerife and El Hierro islands, respectively. (Bottom right) zoom of the grid over Lanzarote, which shows the center of the polygons of the local/regional model. (Bottom left) zoom over El Hierro, which shows the spatial distribution of the grid cells. The cells size decrease from 9 km (crosses) resolution to 1.3 km (diamonds) and 0.2 km (small dots) around the island.

104 J. Arnoso et al. / Journal of Geodynamics 41 (2006) 100 111 Table 2 Amplitudes (in cm) and Greenwich phases (in ) of the tide gauges used for data assimilation Station M2 S2 N2 K2 Amplitude Phase Amplitude Phase Amplitude Phase Amplitude Phase Pto. S.C. Palma 63.20 28.70 23.40 54.90 11.90 18.40 5.90 41.00 La Estaca 58.81 22.73 21.05 42.43 12.66 3.02 Granadilla 60.83 25.25 24.33 45.82 12.31 12.07 6.71 42.81 Pto. S.C. Tenerife 72.83 29.28 27.90 52.42 14.79 16.09 7.83 48.97 Pto. Las Palmas 76.11 28.61 29.21 52.77 15.60 14.94 8.24 49.83 Arinaga 68.16 28.69 26.46 50.60 13.87 14.82 7.49 48.93 Arrecife 79.0 41.5 28.9 63.1 14.4 28.1 9.1 69.0 O1 P1 K1 Q1 Amplitude Phase Amplitude Phase Amplitude Phase Amplitude Phase Pto. S.C. Palma 4.30 294.20 2.70 41.20 6.10 41.30 La Estaca 4.23 291.91 6.71 28.42 1.56 228.75 Granadilla 4.63 290.51 1.52 28.85 6.24 37.40 1.55 230.28 Pto. S.C. Tenerife 4.58 291.83 2.28 28.56 6.67 41.74 1.47 229.86 Pto. Las Palmas 4.85 294.19 2.12 42.84 5.85 39.22 1.59 235.63 Arinaga 4.66 292.32 1.90 23.83 6.23 37.02 1.59 233.59 Arrecife 5.10 300.50 2.10 36.40 6.70 50.70 An empty field indicates data unavailable. 2.3.1. Cotidal and cophase charts for the main constituents M2 and O1 Fig. 3 illustrates the tidal amplitudes and phases of the regional model CIAM1 for M2 and O1 waves. For M2, the amplitudes increase towards the Northeast and the phases propagate from South to North of our domain. Results Fig. 3. (Top) cotidal chart (left) and cophase lines (right), drawn with an interval of 2, of M2 wave. (Bottom) cotidal chart (left) and cophase lines (right), drawn with an interval of 1, of O1 wave. The phases, in degrees, are given with respect to Greenwich.

J. Arnoso et al. / Journal of Geodynamics 41 (2006) 100 111 105 agree with the general patterns (from global ocean tide models) associated with the propagation of this tidal wave in this region. Fig. 3 (top) exhibits the strong spatial variability of the tides around the biggest islands, as pointed out Álvarez et al. (1997). Measurements show an amplitude of 66 cm at the South of Tenerife far from the 80 cm at the North of Gran Canaria. The distance between these two points in our model corresponds to 20 grid cells, while for a global model of typically 0.5 grid resolution corresponds to only 3 grid cells. This fact evidences the importance of a high-resolution model for this area. The tides are dominated by the semidiurnal constituents (Martínez et al., 1999) and, therefore, the cotidal chart for the O1 wave (Fig. 3) shows smaller variations than M2. The phases for the diurnal constituent O1 are propagated from South to North and the tidal amplitudes increase towards the African shoreline, according to the global tidal charts for the area. 2.3.2. Tide height comparison between models We have compared our regional model with the global model GOT00.2 in the area. The amplitude and phase differences between the two models for M2 and O1 are shown in Fig. 4. For M2, the largest difference in amplitude appears in the straits between Tenerife and Gran Canaria islands where the tides varies strongly, as shown in previous section. Gran Canaria island is characterized by a narrow shelf that rises sharply from 2000 to 3000 m depth. Martínez et al. (1999) showed that the island shelf and, therefore, the effect of the shallower waters are responsible for the amplitude variation around this island. The maximum difference between the models (10 12 cm) found at the South of Gran Canaria reveals that the fine resolution of CIAM1 is better to represent this tide variation in contrast with the global ocean tide model. The shallow waters also produce important tidal differences for M2, both in amplitude and phase, between the two models at the South of Fuerteventura and at the Amanay Seamount (see Fig. 1). For O1, the magnitude and the tidal variations around the main islands of the Canarian Archipelago are smaller than M2. Therefore, we obtain minor differences (a maximum value of 0.2 0.3 cm in amplitude) between GOT00.2 and CIAM1 models for this wave. Finally, in the Cape Yubi region, located in the African coast (see Fig. 1), the difference between the two models is also significant, for both M2 and O1 waves. Probably, the complex coastal structure of the African coastline from North (out of our domain) down to Cape Yubi could be responsible for this discrepancy. Fig. 4. (Top) difference between CIAM1 and GOT00.2 models for M2 wave. (Bottom) difference between CIAM1 and GOT00.2 models for O1 wave. The amplitudes (left) are in centimetres and the phases (right), in degrees, are given with respect to Greenwich.

106 J. Arnoso et al. / Journal of Geodynamics 41 (2006) 100 111 2.3.3. Refining the regional ocean tide model To get a more thorough modelling of the ocean tide loading effects we have refined along all the coastlines the ocean tide model obtained for the Canary Islands region. This refined model, named CIAM1 HI, has been designed with a new software developed, GDTI (Grid Discretization and Tide Interpolation) written in Fortran language, which discretizes automatically the ocean grid uniformly and progressively towards the coastline. The grid obtained is composed of 18,488 polygons with three different cell sizes varying from 300 300 over the deep ocean down to 42.9 42.9 along all the coastlines in the Canary region, excepting for El Hierro island that has 8.6 8.6 (Fig. 2). The code allows to input different sources to determine the land/sea distribution. In our model, the land/sea distribution was taken from the digital terrain model of 1:25,000 scale for El Hierro (provided by the National Geographic Institute of Spain) and the High-Resolution Shoreline Database (Wessel and Smith, 1996) for the remaining islands of the Canaries. Appropriate amplitude and phase values for tides are obtained automatically by bilinear interpolation from our model CIAM1. 2.3.4. Comparison to gravity tide loading In order to test the CIAM HI ocean tide model we have used the gravity tide measurements available in Canary Islands up to now, that is, in Lanzarote and Tenerife. Also, the gravity measurements allowed us to improve the CIAM1 HI model by minimising the gravity tide residuals in the surrounding waters (e.g., following Jentzsch et al., 2000; Francis and Mazzega, 1991; Baker, 1980). In Lanzarote island, the station is situated at the Geodynamics Laboratory of Lanzarote (Vieira et al., 1991), which is located inside the lava tunnel of La Corona volcano to the Northeast of the island. In Tenerife island, the station is placed in the basement of the Parador Nacional, inside the National Park of Las Cañadas del Teide (see Fig. 2). The gravity tide measurements were carried out with LaCoste and Romberg (LCR) G 434 gravimeter at Cueva de los Verdes (CV) station in Lanzarote, for a period of 10 years (from May 1987 to March 1997) (Arnoso et al., 2001a,b). In Tenerife island, at Teide-Parador (TP) station, the LCR G 665 gravimeter was used for a period of 7 months (from December 1998 to June 1999) (Arnoso et al., 2000). In both cases the gravimeters were equipped with an electrostatic feedback system and the calibrations have been done by means of the gravimeter screw. Both of them have been normalized on the Brussels tidal factors by taking the LCR-665 gravimeter to Brussels and by comparing Brussels gravimeters (LCR-336 and LCR-003) in Lanzarote. An average value of calibration has been selected in this study for each gravity meter. The instrumental levelling was controlled periodically and no noticeable change in the sensitivity was detected during the period of observation. The tidal analysis of the data series were evaluated by the least squares harmonic analysis method with the program VAV (Venedikov et al., 2003, 2005). The tidal potential used is Tamura (1987) and the Earth response is computed according to the DDW elastic model (Dehant et al., 1999) for body tides. The results of tidal harmonic analysis from the two stations are shown in Table 3 for M2 and O1 tidal waves, respectively. The residual tidal vectors given in this table show the strong loading effect at both stations. For M2 the tidal analysis yields a difference of 1.6% in the amplitude factor and 2.1 in the phase lead between both stations. For O1 the amplitude factors differ in some 0.5%, whereas the difference in the phase lead is 0.2. The mean square errors listed in the table are computed with program VAV taking Table 3 Observed gravimetric factors (δ), phases (α) and the tidal residual vector (B, β) for the constituents M2 and O1 at stations CV (latitude: 29.1601 N, longitude: 13.4411 W, elevation: 37 m, distance to the sea: 1.6 km) and TP (latitude: 28.2167 N, longitude: 16.6167 W, elevation: 2150 m, distance to the sea: 18 km) δ α B β LANZAROTE-CV M2 1.0176 ± 0.0004 2.267 ± 0.022 8.53 ± 0.07 164.3 ± 0.02 O1 1.1571 ± 0.0007 1.603 ± 0.036 0.86 ± 0.04 83.1 ± 0.04 TENERIFE-TP M2 1.0019 ± 0.0011 0.128 ± 0.065 9.23 ± 0.07 179.2 ± 0.07 O1 1.1624 ± 0.0034 1.795 ± 0.166 0.97 ± 0.13 76.0 ± 0.17 The mean square errors are given for δ and α and the error bars of the residual vectors are obtained from the analysis through the error in the observed amplitude vectors. Amplitudes are given in microgal (1 microgal = l 10 8 ms 2 ) and phases, in degree, with respect to the local theoretical gravity tide.

J. Arnoso et al. / Journal of Geodynamics 41 (2006) 100 111 107 Table 4 Main characteristics of the nine ocean tide models considered in this study (T/P: TOPEX/POSEIDON satellite; ERS1, ERS2: European remote sensing satellites) Model Resolution Coverage Modeling Data Reference SCHW 1 1 90 N 78 S Hydrodynamic Assimilation from tide gauge Schwiderski (1980) FES95.2 0.5 0.5 90 N 85 S Hydrodynamic Assimilation from Le Provost et al. (1998) TOPEX/POSEIDON TPXO.2 0.5 0.5 70 N 78 S Empirical TOPEX/POSEIDON Egbert et al. (1994) TPXO.6 0.25 0.25 90.125 N 90.125 S Empirical TOPEX/POSEIDON Egbert and Erofeeva (2002) CSR3.0 0.5 0.5 90 N 78 S Empirical TOPEX/POSEIDON Eanes and Bettadpur (1995) CSR4.0 0.5 0.5 90 N 90 S Empirical TOPEX/POSEIDON Eanes and Bettadpur (1995) NA0.99b 0.5 0.5 89.75 N 89.75 S Hydrodynamic Assimilation from tide gauge and Matsumoto et al. (2000) TOPEX/POSEIDON GOT99.2b 0.5 0.5 90 N 90 S Empirical TOPEX/POSEIDON Ray (1999) GOT00.2 0.5 0.5 90 N 90 S Empirical TOPEX/POSEIDON-ERS1- ERS2 Ray (1999) into account the colored character of the noise. These errors correspond to the internal precision of the observed data series, which is fairly lower than the real precision due, for instance, to errors in the gravimeter calibration. To calculate the ocean loading and attraction effects we have used the code ATC (Arnoso, 1996). The code computes the loading effect through the convolution integral between the ocean tide distribution and the gravity Green s functions, given by Farrell (1972) for the Gutenberg Bullen s Earth model with an oceanic model. For comparison, we have used nine global ocean models to compute the loads (see Table 4), supplemented with CIAM1 HI model for the Canary region. Table 5 lists the numerical values of the calculation for M2 and O1 tidal waves, as well as the tidal amplitude factors and phases corrected from ocean loading and attraction at Lanzarote-CV and Tenerife-TP stations for those ocean models. The table shows also the loading effect due to the model CIAM1 HI in order to see its loading contribution. Depending on the crustal and upper mantle structure we should expect some changes in the results obtained for the loading calculations according to the value of the Green s functions adopted. If we take into account this possibility and compute the ocean loading also for the PREM model, the maximum difference obtained for all ocean tide models is of some 0.1 microgal and 0.1 for M2. There are not differences in amplitude for O1 and the phases differ in 0.1 maximum. At station CV the corrected gravimetric factors for M2 are in the range of 1.15542 (CSR4.0) 1.13037 (TPXO.2), which lead to a discrepancy of 0.4 to 2.7% with the DDW model, respectively. Excluding the results obtained for SCHW and TPXO.2, the corrected phases of the models give differences of less than tenth of degree. For O1, the corrected gravimetric factors are in the range of 1.15740 (FES95.2) 1.16135 (TPXO.2) and their respective discrepancies with the DDW model are +0.4 to +0.7%. The corrected phases differ by less than 0.2 between the different ocean models, excepted TPXO.2. At TP station the results for M2 give corrected gravimetric factors in the range of 1.16457 (SCHW) 1.14087 (TPXO.2) that lead a discrepancy of +0.4 to 1.7% with the DDW gravimetric factor. Similar to CV, the models SCHW and TPXO.2 present the largest difference in the corrected phases with respect to the other ocean tide models, which differ in 0.1 maximum. In the case of O1, the corrected gravimetric factors are in the range of 1.15936 (FES95.2) to 1.16507 (TPXO.2) and the discrepancy is +0.6 to +1.1% with respect to the DDW. As in station CV, the corrected phases differ by less than 0.2 for all the models, excepting for TPXO.2 model. It should be noted that the disagreement between global ocean tide models can produce discrepancies up to 2% on the corrected tidal gravimetric factor for M2, but that these discrepancies reduce to 1% if SCHW and TPXO.2 models are eliminated. These models give also anomalous phases (Table 5). A similar inadequacy of SCHW and TPXO.2 models for semi-diurnal waves had been already shown in Western Europe by Ducarme et al. (2002) in a study of the tidal gravimetric observations obtained with superconducting gravimeters. For O1 the discrepancies are lower than 0.5%. However, TPXO.2 is offset by 0.3 in phase with respect to all the other models. Keeping these facts in mind, we computed mean corrected tidal factors (Table 5) and associated standard deviations (STD). The relative error in amplitude is better than 0.4% for M2 and close to 0.1% for O1. The STD on the phases is always lower than 0.1. We found that the mean phase is practically zero for M2 but has a systematic lag of 0.3 for O1. Concerning

Table 5 Amplitudes and phases of the ocean loading vector (L,λ), computed based on the nine global ocean tide models supplemented with the CIAM1 HI model, for the waves M2 and O1, at CV and TP stations LANZAROTE-CV TENERIFE-TP M2 O1 M2 O1 DDW 1.16034 1.15276 1.16033 1.15276 Model δ c α c L λ δ c α c L λ δ c α c L λ δ c α c L λ SCHW 1.15417 0.41 8.07 166.9 1.15950 0.43 0.63 96.8 1.16457 0.52 9.49 177.1 1.16195 0.33 0.77 90.2 CSR3.0 1.15533 0.01 8.26 163.7 1.15926 0.32 0.69 95.7 1.15924 0.06 9.17 179.6 1.16110 0.20 0.84 88.7 CSR4.0 1.15542 0.12 8.30 162.9 1.15904 0.33 0.68 95.3 1.15922 0.04 9.17 178.9 1.16073 0.23 0.82 88.0 TPXO.2 1.13037 0.66 6.68 166.5 1.16135 0.73 0.48 104.7 1.14087 0.26 8.10 178.8 1.16507 0.60 0.63 97.5 TPX0.6 1.14740 0.00 7.82 162.9 1.15907 0.50 0.59 96.1 1.15391 0.01 8.86 179.2 1.16125 0.37 0.75 88.8 FES95.2 1.15030 0.06 7.96 163.7 1.15740 0.39 0.65 91.7 1.15598 0.07 8.98 179.7 1.15936 0.28 0.80 85.4 NA0.99b 1.14322 0.07 7.57 162.9 1.15894 0.48 0.60 95.7 1.15031 0.01 8.65 179.2 1.16104 0.37 0.75 88.4 GOT99.2b 1.15017 0.05 7.99 162.8 1.15908 0.39 0.65 95.6 1.15613 0.02 8.99 179.0 1.16097 0.25 0.81 88.4 GOT00.2 1.15062 0.01 8.00 163.2 1.15868 0.37 0.66 94.6 1.15649 0.02 9.01 179.3 1.16053 0.25 0.81 87.6 MEAN 1.15035 a 0.01 b 1.15887 a 0.40 a 1.15590 b 0.02 b 1.1609 a 0.29 a STD 0.00428 0.07 0.00064 0.07 0.00310 0.05 0.00074 0.08 CIAM1 HI 3.15 174.2 0.21 101.2 5.13 173.8 0.35 97.3 δ c and α c are the observed amplitude factors and phases after ocean loading correction. Mean corrected tidal gravity factors (MEAN) and standard deviation (STD) are computed excluding the anomalous results. The DDW elastic model is given for comparison with δ c values. The gravity ocean loading contribution of CIAM1 HI model is indicated at the bottom. Amplitudes are in microgal and phases, in degrees, are given with respect to the local theoretical gravity tide. a TPXO.2 excluded. b SCHW and TPXO.2 excluded. 108 J. Arnoso et al. / Journal of Geodynamics 41 (2006) 100 111

J. Arnoso et al. / Journal of Geodynamics 41 (2006) 100 111 109 the mean corrected amplitude factor, the offset is 0.86% (CV) and 0.38% (TP) for M2. The larger discrepancy at CV is probably due to the complicated local situation with lava tunnels filled by water, going very close to the station. For O1 we have an opposite situation with +0.53% (CV) and +0.71% (TP). It should be pointed out that a calibration error cannot explain the fact that the corrected tidal amplitude factors are too low compared to the DDW tidal gravimetric factor for M2 and too large for O1 in both stations. An instrumental time lag should produce a phase lag double on M2 than on O1. Instrumental errors cannot explain the observed discrepancies between observations and modelling. We computed also the tidal gravity residue X(X,χ) for M2 and O1 tidal waves, after removing the solid Earth tide and the ocean loading, following the notation used by Melchior and De Becker (1983), through: X = B L (4) where B = (B, β) is the observed residual and L = (L, λ) is the computed oceanic effect. The X cosχ (in phase) and X sinχ (out of phase) components for CV and TP are shown in Fig. 5. For the harmonic M2, the ocean models SCHW and TPXO.2 give clearly the most anomalous results, while the rest of the models shows a good agreement at both stations. In the case of O1 wave, the TPXO.2 model presents the most anomalous value at both stations. It is interesting to note the good agreement of SCHW model for this harmonic, taking into account that this model is not based on modern techniques. Fig. 5. Phasor plots showing the final residue vector at CV (top) and TP (bottom) stations, for M2 and O1 waves, based on nine global ocean models supplemented with the model CIAM1 HI. Error bars are shown on the side of each plot.

110 J. Arnoso et al. / Journal of Geodynamics 41 (2006) 100 111 Besides, except for SCHW and TPXO.2 models at both stations, the out of phase component for M2 is comprised between some ±0.1 microgal. For O1 wave, excepting TPXO.2 model, this component is similar at both stations and ranges between 0.10 and 0.25 microgal. The magnitudes of the out of phase components are equivalent to less than the calibration errors of the gravimeters at both stations (accepting a calibration accuracy of 1% this gives a calibration error of the gravimeters 0.58 and 0.30 microgal for M2 and O1, respectively), although this component is actually affected by errors in determining the phase lags caused by feedback, filters and data acquisitions systems (Baker and Bos, 2003). Except for SCHW and TPXO.2, the in phase component for M2 displays a good agreement for the rest of the models. Nevertheless, its magnitude is slightly different at both stations, reaching the largest value for the NAO.99b model (some 1.0 and 0.6 microgal at CV and TP, respectively), i.e. larger than 1%, and the smallest value for the CSR models (some 0.3 and 0.1 microgal at CV and TP, respectively), i.e. less than 0.5%. For O1, this component shows also a good agreement for all the models (except TPXO2) and takes the value of some +0.2 microgal, i.e. less than 0.7%. Therefore, the results for M2 exhibit a dependence of the global ocean tide model considered whereas for O1, which is less turbulent wave, all models agree. Finally, excluding again the anomalous values for SCHW and TPXO.2 models, the in phase component for M2 at both locations is negative. For O1 wave the in phase component is always positive for all ocean models. It cannot be explained by calibration errors. These facts could be related with differences in the local characteristics of the crust or lithosphere in these islands (Arnoso et al., 2001a). 3. Conclusions We have developed a high-resolution model of the ocean tides around Canary Islands, CIAM1, by assimilating 12 years of TOPEX/Poseidon altimeter data as well as tide gauge measurements into a hydrodynamical model. Although the tidal maps obtained for the M2 and O1 waves show similar patterns in comparison with the global ocean tide model GOT00.2, these maps reveal differences in some areas. Certainly, the 0.5 0.5 resolution of GOT00.2 is too coarse to describe properly the complicated tides as, for example, in the strait between Tenerife and Gran Canaria or in the shallow waters at South of Fuerteventura. The island s tide gauges assimilated in our high resolution model help us to improve the ocean tide estimation in these areas. We have also refined the ocean tide model CIAM1 for all the coastlines in the region by bilinear interpolation. This refined version, named CIAM1 HI, has a resolution varying from 9 to 1.3 km along the coastlines in the Canaries and reach to 0.2 km in the coastline of El Hierro island. To test the CIAM1 HI model we have compared the ocean tide loading computations, using nine global ocean tide models supplemented with this new one, with tidal gravity measurements made in two islands of the Canarian Archipelago. The results allow us to quantify some differences between ocean models in the region, in terms of the gravimetric loading tides. Thus, the agreement of the nine ocean tide models considered in this study is, in general, rather similar. Nevertheless, the TPXO.2 model displays the most discrepant results, as much for M2 as for O1, at the stations CV and TP in Lanzarote and Tenerife islands, respectively. For the M2 wave, the model SCHW shows serious discrepancies with the other models at both locations. Also, NAO.99b model exhibits somewhat disagreement for M2 wave at both stations. In the case of O1, the TPXO.2 is the one that gives more discrepancies in these two islands. In summary, we found that TPXO.2 model presents the most anomalous results at the two stations, both for M2 and O1 waves. For M2 wave, the SCHW model evidence important discrepancies at both places. However, we want to point out that, among the ocean tide models which present a better agreement at both stations (GOT00.2, GOT99.2b, TPXO.6, CSR3.0, CSR4.0 and FES95.2), for M2 and O1 tidal waves no one of them gives better results than the other when we compare them with the tidal gravity measurements made at these two gravity stations in the Canarian Archipelago, except CSR models which fit much better the observations for M2. As a conclusion, we can recommend for further tidal gravity studies CSR models for M2 and any model, except TPXO.2 for O1. On the other hand, the gravity tide measurements available in the Canaries allowed us to improve substantially the CIAM1 HI model by minimising the gravity tide residuals. Further measurements, as we will carry on in El Hierro island, would provide more constraints for the ocean model developed. Acknowledgements This study was funded by the Spanish Project REN2002-00544/RIES. J. Arnoso is supported by the program I3P of the European Social Fund. Part of the work of M. Benavent was carried out at the Royal Observatory of Belgium

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