FES2014c new equilibrium waves
##############################

In FES2014c, some long period waves that used to be neglected have been added to the spectrum.
They are all obtained by equilibrium. They are : M0 MSf Mf_1 Mf_2 Mm_1 Mm_2 Sa_1 Sta .
All but MSf have a new name.
After the `general principles`_ behind theses new names, the new `M0`_, `Mf_1 and Mf_2`_, `Mm_1 and Mm_2`_, `Sa_1`_ and `Sta`_ waves will be presented.

General principles
------------------

As shown in the SiROcCo Tools sources, in tides.h_ and tides.def_,
our wave names are inspired by the Darwin convention as detailed by `Schureman (1940)`_, in particular its Table 2 pp.164-167.

.. _tides.def: https://hg.legos.obs-mip.fr/tools/file/tip/src/tides.def
.. _tides.h: https://hg.legos.obs-mip.fr/tools/file/tip/src/tides.h
.. _Schureman (1940): http://www.archive.org/details/manualofharmonic00schu

Below is the table giving :
  
  1. the (eventually new) names
  2. the ``Ref. No.``, given in the first column of `Schureman (1940)`_'s Tab.2
  3. the Doodson number

==== ======== =======
name Ref. No. Doodson
==== ======== =======
M0    A1      0555555
Sa_1  B2      0565545
Sta   B7      0585545
Mm_2  A64     0655556
Mm_1  A8      0656553
MSf   A5      0735555
Mf_1  A3      0753555
Mf_2  A65     0754556
==== ======== =======

M0
--

It is only there because its nodal correction gives Omega1.
Its name comes from the facts that it is : 
  
  - lunar, like Mm, Mf, M1, M2 and many others
  - and permanent, like Z0 .

Sa_1
----

Its frequency at 0.041066678 deg/h is extremely close to
that of Sa at 0.041068639 deg/h,
and it would indeed take a bit more that 20940 years to seperate them.

Sta
---

Following the conventions used for Ssa and Mtm, its name comes from the facts that:
  
  - it is solar
  - and it takes the third of a year .

Mm_1 and Mm_2
-------------

Their frequencies of 0.553658367 deg/h and 0.549016532 deg/h respectively are
very close to that of Mm at 0.544374697 deg/h,
and it would indeed take around 4.4 and 8.8 years respectively to seperate them from Mm.
Please note that Mm_2 is of order 3.

Mf_1 and Mf_2
-------------

Their frequencies of 1.088749395 deg/h and 1.093391230 deg/h respectively are
very close to that of Mf at 1.098033064 deg/h,
and it would indeed take around 4.4 and 8.8 years respectively to seperate them from Mf.
Please note that Mf_2 is of order 3.