From 2267c24457b39ac9053f209b7a891953c2f12795 Mon Sep 17 00:00:00 2001
From: David Huard <huard.david@ouranos.ca>
Date: Fri, 8 Sep 2023 15:51:16 -0400
Subject: [PATCH] update bibtex. Debug math equations

---
 docs/references.bib          | 27 ++++++++++++++++++++++++
 xclim/indices/_conversion.py | 40 +++++++++++++++++++++++-------------
 2 files changed, 53 insertions(+), 14 deletions(-)

diff --git a/docs/references.bib b/docs/references.bib
index e269a50ff..1ccf861a5 100644
--- a/docs/references.bib
+++ b/docs/references.bib
@@ -2046,3 +2046,30 @@ @misc{usda_2012
 	author = {{USDA Agricultural Research Service}},
 	year = {2012},
 }
+
+@article{chen_2020,
+title = {Impacts of climate change on wind resources over North America based on NA-CORDEX},
+journal = {Renewable Energy},
+volume = {153},
+pages = {1428-1438},
+year = {2020},
+issn = {0960-1481},
+doi = {https://doi.org/10.1016/j.renene.2020.02.090},
+url = {https://www.sciencedirect.com/science/article/pii/S0960148120302858},
+author = {Liang Chen},
+keywords = {Climate change, Wind energy, NA-CORDEX, North America}
+}
+
+@article{tobin_2018,
+doi = {10.1088/1748-9326/aab211},
+url = {https://dx.doi.org/10.1088/1748-9326/aab211},
+year = {2018},
+month = {apr},
+publisher = {IOP Publishing},
+volume = {13},
+number = {4},
+pages = {044024},
+author = {I Tobin and W Greuell and S Jerez and F Ludwig and R Vautard and M T H van Vliet and F-M Bréon},
+title = {Vulnerabilities and resilience of European power generation to 1.5°C, 2°C and 3°C warming},
+journal = {Environmental Research Letters}
+}
diff --git a/xclim/indices/_conversion.py b/xclim/indices/_conversion.py
index d5ca712c5..bcb76123c 100644
--- a/xclim/indices/_conversion.py
+++ b/xclim/indices/_conversion.py
@@ -2031,11 +2031,7 @@ def wind_profile(
 ):
     r"""Wind speed at a given height estimated from the wind speed at a reference height.
 
-    Estimate the wind speed based on a power law profile relating wind speed to height above the surface:
-
-    .. math::
-
-        v = v_h \\left( \frac{h}{h_r} \right)^{\alpha}
+    Estimate the wind speed based on a power law profile relating wind speed to height above the surface.
 
     Parameters
     ----------
@@ -2050,6 +2046,18 @@ def wind_profile(
     kwds : dict
         Additional keyword arguments to pass to the method. For `power_law`, this is `alpha`, which takes a default
         value of 1/7.
+
+    Notes
+    -----
+    The power law profile is given by
+
+    .. math::
+
+        v = v_r \left( \frac{h}{h_r} \right)^{\alpha},
+
+    where :math:`v_r` is the wind speed at the reference height, :math:`h` is the height at which the wind speed is
+    desired, and :math:`h_r` is the reference height.
+
     """
     # Convert units to meters
     h = convert_units_to(h, "m")
@@ -2114,23 +2122,27 @@ def wind_power_potential(
     by the cut-in wind speed (:math:`u_i`), the rated speed (:math:`u_r`) and the cut-out speed (:math:`u_o`).
     Power production is zero for wind speeds below the cut-in speed, increases cubically between the cut-in
     and rated speed, is constant between the rated and cut-out speed, and is zero for wind speeds above the cut-out
-    speed to avoid damage to the turbine (10.1088/1748-9326/aab211):
+    speed to avoid damage to the turbine :cite:p:`tobin_2018`:
 
     .. math::
 
         \begin{cases}
         0,  &  v < u_i \\
-        (v - u_i)^3 / (u_r - u_i)^3,  & u_i <= v < u_r \\
-        1, & u_r <= v < u_o \\
-        0, v >= u_o
-        \\end{cases}
+        (v - u_i)^3 / (u_r - u_i)^3,  & u_i ≤ v < u_r \\
+        1, & u_r ≤ v < u_o \\
+        0, & v ≥ u_o
+        \end{cases}
 
-    For non-standard air density, the wind speed is scaled using
-    :math:`v_n = v \\left( \frac{\rho}{\rho_0} \right)^{1/3}`.
+    For non-standard air density (:math:`\rho`), the wind speed is scaled using
+    :math:`v_n = v \left( \frac{\rho}{\rho_0} \right)^{1/3}`.
 
     Note that the temporal resolution of the wind speed time series has a significant influence on the results,
-    but percent changes in the wind power potential projections are similar across resolutions.
-    https://doi.org/10.1016/j.renene.2020.02.090
+    but percent changes in the wind power potential projections are similar across resolutions :cite:p:`chen_2020`.
+
+    References
+    ----------
+    :cite:cts:`chen_2020,tobin_2018`.
+
     """
     # Convert units
     cut_in = convert_units_to(cut_in, wind_speed)