Add MESMER_M Changelog entries (MESMER-group#463)

* add MESMER_M Changelog entries
---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Mathias Hauser <mathias.hauser@env.ethz.ch>
Co-authored-by: Mathias Hauser <mathause@users.noreply.github.com>

CHANGELOG.rst

@@ -6,6 +6,7 @@ v0.11.0 - unreleased
 
 New Features
 ^^^^^^^^^^^^
+- Integrated MESMER-M into the code base, see `Integration of MESMER-M`_.
 - Added number of observations to the output of the AR process (`#395 <https://github.com/MESMER-group/mesmer/pull/395>`_).
   By `Victoria Bauer`_.
 
@@ -45,6 +46,65 @@ Internal Changes
 - Unshallow the mesmer git repository on rtd (`#456 <https://github.com/MESMER-group/mesmer/pull/456>`_).
   By `Victoria Bauer`_.
 
+Integration of MESMER-M
+^^^^^^^^^^^^^^^^^^^^^^^
+
+This release integrates MESMER-M into the existing MESMER infrastructure. This includes
+some refactoring, bugfixes and enhancements of the MESMER-M functionality. Note
+that this led to some numerical changes compared to the MESMER-M publication
+(`Nath et al. 2022 <https://doi.org/10.5194/esd-13-851-2022>`_).
+
+- move MESMER-M scripts into mesmer (
+  `#419 <https://github.com/MESMER-group/mesmer/pull/419>`_, and
+  `#421 <https://github.com/MESMER-group/mesmer/pull/421>`_).
+
+**Yeo-Johnson power transformer**
+
+-  Ensure the power transformer yields the correct normalization for more cases (
+   `#440 <https://github.com/MESMER-group/mesmer/issues/440>`_):
+
+   -  expand the upper bound of the first coefficient from :math:`1` to :math:`\infty`,
+      i.e. to all positive numbers  (
+      `#446 <https://github.com/MESMER-group/mesmer/pull/446>`_)
+   -  remove jacobian ``rosen_der`` from fit (
+      `#447 <https://github.com/MESMER-group/mesmer/pull/447>`_)
+   -  change opimization method from *SLSQP* to *Nelder-Mead* (
+      `#455 <https://github.com/MESMER-group/mesmer/pull/455>`_)
+-  adjust the first guess to assume the data is normally distributed (
+   `#429 <https://github.com/MESMER-group/mesmer/pull/429>`_)
+-  rewrite power transformer to work with xarray, and refactor from a class structure to functions (
+   `#442 <https://github.com/MESMER-group/mesmer/pull/442>`_, and
+   `#474 <https://github.com/MESMER-group/mesmer/pull/474>`_)
+-  fix small code issues and clean the docstrings (
+   `#436 <https://github.com/MESMER-group/mesmer/pull/436>`_,
+   `#444 <https://github.com/MESMER-group/mesmer/pull/444>`_,
+   `#439 <https://github.com/MESMER-group/mesmer/pull/439>`_,
+   `#475 <https://github.com/MESMER-group/mesmer/pull/475>`_, and
+   `#425 <https://github.com/MESMER-group/mesmer/pull/425>`_)
+- add tests (`#430 <https://github.com/MESMER-group/mesmer/pull/430>`_)
+
+
+**Harmonic model**
+
+-  Performance and other optimizations:
+
+   - only fit orders up to local minimum and use coeffs from precious order as first guess (`#443 <https://github.com/MESMER-group/mesmer/pull/443>`_)
+   - infer the harmonic model order from the coefficients (`#434 <https://github.com/MESMER-group/mesmer/pull/434>`_)
+-  return residuals instead of the loss for the optimization (`#460 <https://github.com/MESMER-group/mesmer/pull/460>`_)
+-  add helper function to upsample yearly data to monthly resolution (
+   `#418 <https://github.com/MESMER-group/mesmer/pull/418>`_, and
+   `#435 <https://github.com/MESMER-group/mesmer/pull/435>`_)
+- de-duplicate the expression of months in their harmonic form (`#415 <https://github.com/MESMER-group/mesmer/pull/415>`_)
+- fix indexing of harmonic model coefficients (`#415 <https://github.com/MESMER-group/mesmer/pull/415>`_)
+-  Refactor variable names, small code improvements, fixes and clean docstring (
+   `#415 <https://github.com/MESMER-group/mesmer/pull/415>`_,
+   `#424 <https://github.com/MESMER-group/mesmer/pull/424>`_, and
+   `#433 <https://github.com/MESMER-group/mesmer/pull/433>`_)
+- add tests (
+  `#431 <https://github.com/MESMER-group/mesmer/pull/431>`_, and
+  `#458 <https://github.com/MESMER-group/mesmer/pull/458>`_)
+
+By `Victoria Bauer`_ and `Mathias Hauser`_.
 
 v0.10.0 - 2024.01.04
 --------------------