Measuring water waves in the field from bottom mounted pressure sensors
Authors: Touboul Julien , Bertin Xavier , Pelinovsky Efim 
Published: March 2021

&lt;p&gt;For various experimental reasons, the measurement of water waves propagating in shallow water environments such as surf zones or coastal areas is a difficult task. Deploying surface measuring instruments can be inconvenient, dangerous, or simply expensive. Thus, such measurements are often performed using bottom mounted pressure sensors. Unfortunately, the problem of reconstructing surface elevation based on a single point pressure sensor is an ill-posed problem.&lt;/p&gt;&lt;p&gt;Indeed, the pressure data collected should be inverted to provide the related water elevation. However, the transfer function traditionally used to perform this inversion is subject to question. When considering very long waves, like tides and tsunamis, the pressure is hydrostatic as long as dispersive effects can be neglected and recovering surface elevation from the bottom pressure does not imply any particular difficulty. Yet, for steeper waves propagating in such depth conditions, nonlinearity might play a significant role (Didenkulova et al., 2021).&lt;/p&gt;&lt;p&gt;In coastal areas, the propagation of water waves is more complex, and often involves dispersion or nonlinearity. In such areas, one may find wind waves, which are strongly dispersive, even in the coastal zone. Using linear theory might be helpful, in such cases, but is also subject to questions (Touboul &amp; Pelinovsky, 2018). Besides, other corrections related to their dispersive behaviour might play a significant role. Various phenomena, such as partially standing waves (Touboul &amp; Pelinovsky, 2014), or the superimposition of current, might also play a significant role.&lt;/p&gt;&lt;p&gt;In this work, we investigate the performance of classical reconstruction techniques, but also more recent approaches (Oliveras et al., 2012, Clamond &amp; Constantin, 2013, Bonneton et al., 2018), by confronting their prediction to field data collected in the central part of the Bay of Biscay using current meters mounted with pressure and acoustic surface tracking sensors . These data are obtained in various depth conditions, often in extreme conditions and provide pressure records, current velocity, and direct measurement of the water elevation. Thus, the use of methods presenting various degrees of sophistication allows us to analyze in details the respective roles played by the current, the dispersion, and the nonlinearity.&lt;/p&gt;&lt;p&gt;The joint French-Russian grant No. 19-55-15005 is acknowledged.&lt;/p&gt;&lt;p&gt;[1] E. Didenkulova, E. Pelinovsky &amp; J. Touboul, Long-wave approximations in the description of bottom pressure, Wave Motion, vol. 100, No. 1, 102668 (2021)&lt;/p&gt;&lt;p&gt;[2] J. Touboul &amp; E. Pelinovsky, &quot;On the use of linear theory for measuring surface waves using bottom pressure distribution&quot;, Eur. J. Mech. B: Fluids, 67, 97&amp;#8211;103, (2018).&lt;/p&gt;&lt;p&gt;[3] J. Touboul &amp; E. Pelinovsky, &quot;Bottom pressure distribution under a solitonic wave reflecting on a vertical wall&quot;, Eur. J. Mech., B. Fluids, 48, p. 13-18, (2014).&lt;/p&gt;&lt;p&gt;[4] K.L. Oliveras, V. Vasan, B. Deconinck, D. Henderson, Recovering the water wave profile from pressure measurement, SIAM J. Appl. Math. 72 (3) 897&amp;#8211;918 (2012).&lt;/p&gt;&lt;p&gt;[5] P. Bonneton, D. Lannes, K. Martins., H. Michallet, A nonlinear weakly dispersive method for recovering the elevation of irrotational surface waves from pressure measurements, Coastal Engineering 138, 1&amp;#8211;8 (2018).&lt;/p&gt;&lt;p&gt;[6] D. Clamond, A. Constantin, Recovery of steady periodic wave profiles from pressure measurements at the bed, J. Fluid Mech. 714, 463&amp;#8211;475 (2013).&lt;/p&gt;