paper.md

title	tags	authors	affiliations	date	bibliography
CalValWaves: A Python package for wave reanalysis calibration with satellite altimeter data	Python wave reanalysis calibration satellite data buoy validation	name orcid affiliation Javuer Tausia Hoyal^[Custom footnotes for e.g. denoting who the corresponding author is can be included like this.] 0000-0002-2299-2915 1 name affiliation Fernando J. Méndez Incera 1, 2	name index University of Cantabria 1 name index Geocean group, ETSICCP 2	7 October 2020	paper.bib

Summary

Numerical wave reanalysis are very useful as they have information of different variables for a very long and constant period of time. In this case, this data will be used after been calibrated to propagate waves from the point where the node of the reanalysis is located to shallow waters, and it is very important to have constant data along a very large period of time, so the propagations can be representative. The problem now is that these hindcasts are not perfect, and this is why we must calibrate them first with satellite data and validate them after all with a nerby buoy to see if data correlates. For this purpose, the calibration will be related with the direction of the incident waves and their shape (local wind generated waves or ground swells).

Statement of need

CalValWaves is a Python package for wave reanalysis calibration. Python is a very high level language that allows the code to be easily understood and changed if required. All the operations have been performed using commonly known python libraries such us scipy, numpy and pandas. These friendly features make the usage of the package available to the all oceanography researchers that are not familiar with the python language, although use all the potential of it.

CalValWaves was designed to be used by both oceanography researchers and by students in courses on oceanography and related studies. It was used in a master's thesis, which results can be seen in the main repository, as the package allows the creation of very useful plots for the data analtsis. The combination of speed, and design in CalValWaves enables exciting scientific explorations of wave reanalysis data all over the world by students and experts alike.

Mathematics

A simple linear regression is performed that takes into account the existent different types of waves that appear at the same moment in the wave reanalysis, using all of them, which do a total of 32 coefficients (16 directions · 2 types of waves), to estimate the bulk significant wave height of the waves, measured by the satellite radars. This linear regression equation can be summarized as follows:

$$ H^{Sat2} = \sum_{i=0}^{15}a_i^2 H_i^{Sea2} + \sum_{i=0}^{15}b_i^2 H_i^{Swell2} + \epsilon^2 $$

where the linear regression is applied over the squares of the significant wave heights, as the energy is what can be compared in summations, but not just the height. With this simple linear regression, 32 coefficients are obtained that give an idea about what waves are over and underestimate by the numerical wave reanalysis.

Figures

Some figures can be obtained using this tool, but the most important ones are the calibration of the hindcast and the validation with the buoy, all shown below:

References