diff --git a/docs/sphinx/source/whatsnew/v0.11.1.rst b/docs/sphinx/source/whatsnew/v0.11.1.rst
index 7c8f01743e..781a68f32f 100644
--- a/docs/sphinx/source/whatsnew/v0.11.1.rst
+++ b/docs/sphinx/source/whatsnew/v0.11.1.rst
@@ -30,6 +30,10 @@ Enhancements
 * Added function for calculating wind speed at different heights,
   :py:func:`pvlib.atmosphere.windspeed_powerlaw`.
   (:issue:`2118`, :pull:`2124`)
+* Implemented closed-form solution for alpha in detect_clearsky, obviating
+  the call to scipy.optimize that was prone to runtime errors and minimizing
+  computation, :py:func:`pvlib.clearsky.detect_clearsky`. Resolves :issue:`2712`.
+
 
 Bug fixes
 ~~~~~~~~~
@@ -74,3 +78,4 @@ Contributors
 * Marcos R. Escudero (:ghuser:`marc-resc`)
 * Bernat Nicolau (:ghuser:`BernatNicolau`)
 * Eduardo Sarquis (:ghuser:`EduardoSarquis`)
+* Andrew B Godbehere (:ghuser:`agodbehere`)
\ No newline at end of file
diff --git a/pvlib/clearsky.py b/pvlib/clearsky.py
index 62d83bc1f4..3b36262dda 100644
--- a/pvlib/clearsky.py
+++ b/pvlib/clearsky.py
@@ -3,15 +3,14 @@
 to calculate clear sky GHI, DNI, and DHI.
 """
 
+import calendar
 import os
 from collections import OrderedDict
-import calendar
 
+import h5py
 import numpy as np
 import pandas as pd
-from scipy.optimize import minimize_scalar
 from scipy.linalg import hankel
-import h5py
 
 from pvlib import atmosphere, tools
 from pvlib.tools import _degrees_to_index
@@ -874,24 +873,11 @@ def detect_clearsky(measured, clearsky, times=None, infer_limits=False,
         clear_meas = meas[clear_samples]
         clear_clear = clear[clear_samples]
 
-        def rmse(alpha):
-            return np.sqrt(np.mean((clear_meas - alpha*clear_clear)**2))
-
-        optimize_result = minimize_scalar(rmse)
-        if not optimize_result.success:
-            try:
-                message = "Optimizer exited unsuccessfully: " \
-                           + optimize_result.message
-            except AttributeError:
-                message = "Optimizer exited unsuccessfully: \
-                           No message explaining the failure was returned. \
-                           If you would like to see this message, please \
-                           update your scipy version (try version 1.8.0 \
-                           or beyond)."
-            raise RuntimeError(message)
-
-        else:
-            alpha = optimize_result.x
+        # Compute arg min of MSE between model and observations
+        C = (clear_clear**2).sum()
+        if not (pd.isna(C) or C == 0):  # safety check
+            # only update alpha if C is strictly positive
+            alpha = (clear_meas * clear_clear).sum() / C
 
         if round(alpha*10000) == round(previous_alpha*10000):
             break
diff --git a/pvlib/tests/test_clearsky.py b/pvlib/tests/test_clearsky.py
index 4e353e997c..79502db01c 100644
--- a/pvlib/tests/test_clearsky.py
+++ b/pvlib/tests/test_clearsky.py
@@ -1,22 +1,17 @@
 from collections import OrderedDict
 
 import numpy as np
-from numpy import nan
 import pandas as pd
-import pytz
-from scipy.linalg import hankel
-
 import pytest
+import pytz
+from numpy import nan
 from numpy.testing import assert_allclose
-from .conftest import assert_frame_equal, assert_series_equal
+from scipy.linalg import hankel
 
+from pvlib import atmosphere, clearsky, irradiance, solarposition
 from pvlib.location import Location
-from pvlib import clearsky
-from pvlib import solarposition
-from pvlib import atmosphere
-from pvlib import irradiance
 
-from .conftest import DATA_DIR
+from .conftest import DATA_DIR, assert_frame_equal, assert_series_equal
 
 
 def test_ineichen_series():
@@ -677,12 +672,16 @@ def test_detect_clearsky_not_enough_data(detect_clearsky_data):
     with pytest.raises(ValueError, match='have at least'):
        clearsky.detect_clearsky(expected['GHI'], cs['ghi'], window_length=60)
 
-
-def test_detect_clearsky_optimizer_failed(detect_clearsky_data):
+@pytest.mark.parametrize("window_length", [5, 10, 15, 20, 25])
+def test_detect_clearsky_optimizer_not_failed(
+        detect_clearsky_data, 
+        window_length
+    ):
     expected, cs = detect_clearsky_data
-    with pytest.raises(RuntimeError, match='Optimizer exited unsuccessfully'):
-        clearsky.detect_clearsky(expected['GHI'], cs['ghi'], window_length=15)
-
+    clear_samples = clearsky.detect_clearsky(
+        expected["GHI"], cs["ghi"], window_length=window_length
+    )
+    assert isinstance(clear_samples, pd.Series)
 
 @pytest.fixture
 def detect_clearsky_helper_data():