Strain tides observed by two geodetic laser strainmeters at Canfranc (Spain): clues on nonlinear and minor ocean tides in the Bay of Biscay.

Global ocean tidal models are very accurate in deep ocean, but errors still arise in coastal areas. While tide gauge and bottom pressure data have strictly local spatial sensitivity and satellite altimetry may suffer temporal aliasing, continuous geodetic measurements of tidal loading (e. g. strain, tilt, and gravity) can provide useful benchmarks to validate ocean tidal models at regional scale without temporal aliasing. Strain and tilt are spatially more discriminative than gravity, because the decrease of strain and tilt with distance to the source is more rapid than the decrease of gravity. Thus, strainmeters and tiltmeters provide an intermediate spatial resolution between tidal gauges and gravimeters. Despite the potential utility of geodetic observations of nonlinear tides, few studies (mainly focused on M4) have been published so far, using data from superconducting gravimeters, tiltmeters, and continuous GPS. To our best knowledge, strain data have never been used to investigate nonlinear and minor ocean tides and validate ocean tidal models. We present and analyze about 2.5 years of strain data recorded by two near-orthogonally-oriented 70-m-long high-resolution geodetic laser strainmeters (interferometers), which have been installed in the Canfranc underground laboratory under the Central Pyrenees (Spain) and can provide precise measurements of the Earth crustal deformation. Strain spectra show clear tidal peaks whose frequencies range from the diurnal band to at least 8 cycles per day. Most tidal peaks at frequencies higher than 2 cpd are ascribable to ocean loading by nonlinear shallow-water constituents, mainly from the Bay of Biscay (more than 120 km from the measurement site); strain amplitudes (relative change in length for each strainmeter) range from few picostrains (e. g. 2MK6) to tens of nanostrains (M4). First, we use diurnal and semidiurnal strain tides to (i) estimate local strain distortions, (ii) check the goodness of the computed coupling coefficients between remote and local strain, and (iii) validate FES2012 minor semidiurnal tides.The reliability of observations and corrections for local distortions are testified by the excellent agreement between measurements and computations for all the diurnal and semi-diurnal tides included in TPXO8-atlas and/or FES2012 ocean models, except maybe L2, regardless of the relative size of load and body tides. Observed higher-frequency strain tides are quantitatively compared with computations using TPXO8-atlas (MN4, M4, and MS4) and FES2012 (M3, N4, MN4, M4, MS4, and M6). Computations fully agree with M4 observations for one strainmeter, overestimate M4 by about 30% for the other strainmeter and M6 by about a factor of two, and underestimate the other tides. These results are supported by tidal gauge data. This work shows that data from high-sensitivity strainmeters installed in high-quality sites may provide useful peculiar information for studying the nonlinear tidal dynamics and energetics of coastal waters and minor ocean tides, at spatial resolutions of tens to thousands square kilometers, depending on the strainmeter location with respect to the coastline.