Merge pull request #1363 from eliteuser26/master

Calculation of Lifted Index

docs/_templates/overrides/metpy.calc.rst

@@ -73,6 +73,7 @@ Soundings
       el
       lcl
       lfc
+      lifted_index
       mixed_layer
       mixed_layer_cape_cin
       mixed_parcel

docs/references.rst

@@ -48,6 +48,11 @@ References
            *Mon. Wea. Rev.*, **137**, 3137-3148,
            doi: `10.1175/2009mwr2774.1 <https://doi.org/10.1175/2009MWR2774.1>`_.
 
+.. [Doswell-Schultz2006] Doswell, C. A., and Schultz, D. M., 2006: On the Use of Indices and
+           Parameters in Forecasting Severe Storms. *Electronic Journal of Severe Storms
+           Meteorology*,
+           `EJSSM <https://ejssm.org/ojs/index.php/ejssm/issue/view/3>`_.
+
 .. [Esterheld2008] Esterheld, J., and Giuliano, D., 2008: Discriminating between Tornadic and
            Non-Tornadic Supercells: A New Hodograph Technique. *E-Journal Of Severe Storms
            Meteorology*, **3(2)**, Retrieved May 10, 2018.
@@ -79,6 +84,11 @@ References
            Services and Supporting Research, 2003.
            `FCM-R19-2003 <_static/FCM-R19-2003-WindchillReport.pdf>`_, 75 pp.
 
+.. [Galway1956] Galway, J. G., 1956: The Lifted Index as a Predictor of Latent Instability.
+           *American Meteorology Society*,
+           doi:`10.1175/1520-0477-37.10.528
+           <https://doi.org/10.1175/1520-0477-37.10.528>`_.
+
 .. [Garratt1994] Garratt, J.R., 1994: *The Atmospheric Boundary Layer*. Cambridge
            University Press, 316 pp.
 

src/metpy/calc/thermo.py

@@ -2574,3 +2574,46 @@ def specific_humidity_from_dewpoint(pressure, dewpoint):
     """
     mixing_ratio = saturation_mixing_ratio(pressure, dewpoint)
     return specific_humidity_from_mixing_ratio(mixing_ratio)
+
+
+@exporter.export
+@preprocess_xarray
+@check_units('[pressure]', '[temperature]', '[temperature]')
+def lifted_index(pressure, temperature, parcel_profile):
+    """Calculate Lifted Index from the pressure temperature and parcel profile.
+
+    Lifted index formula derived from [Galway1956]_ and referenced by [Doswell-Schultz2006]_:
+    LI = T500 - Tp500
+    where:
+    T500 is the measured temperature at 500 hPa.
+    Tp500 is the temperature of the lifted parcel at 500 hPa.
+
+    Calculation of the lifted index is defined as the temperature difference between the
+    observed 500 hPa temperature and the temperature of a parcel lifted from the
+    surface to 500 hPa.
+
+    Parameters
+    ----------
+    pressure : `pint.Quantity`
+        The atmospheric pressure level(s) of interest, in order from highest to
+        lowest pressure.
+    temperature : `pint.Quantity`
+        The atmospheric temperature corresponding to pressure.
+    parcel_profile : `pint.Quantity`
+        The temperature profile of the parcel.
+
+    Returns
+    -------
+    `pint.Quantity`
+        Lifted Index.
+
+    """
+    # find the index for the 500 hPa pressure level.
+    idx = np.where(pressure == 500 * units.hPa)
+    # find the measured temperature at 500 hPa.
+    T500 = temperature[idx]
+    # find the parcel profile temperature at 500 hPa.
+    Tp500 = parcel_profile[idx]
+    # calculate the lifted index.
+    lifted_index = T500 - Tp500.to(units.degC)
+    return lifted_index

tests/calc/test_thermo.py

@@ -11,8 +11,8 @@
                         brunt_vaisala_period, cape_cin, density, dewpoint,
                         dewpoint_from_relative_humidity, dewpoint_from_specific_humidity,
                         dry_lapse, dry_static_energy, el, equivalent_potential_temperature,
-                        exner_function, isentropic_interpolation, lcl, lfc, mixed_layer,
-                        mixed_layer_cape_cin, mixed_parcel, mixing_ratio,
+                        exner_function, isentropic_interpolation, lcl, lfc, lifted_index,
+                        mixed_layer, mixed_layer_cape_cin, mixed_parcel, mixing_ratio,
                         mixing_ratio_from_relative_humidity,
                         mixing_ratio_from_specific_humidity, moist_lapse,
                         moist_static_energy, most_unstable_cape_cin, most_unstable_parcel,
@@ -1557,3 +1557,28 @@ def test_lcl_grid_surface_LCLs():
     temp_truth = np.array([15, 9.10391763, 13]) * units.degC
     assert_array_almost_equal(lcl_pressure, pres_truth, 4)
     assert_array_almost_equal(lcl_temperature, temp_truth, 4)
+
+
+def test_lifted_index():
+    """Test the Lifted Index calculation."""
+    pressure = np.array([1014., 1000., 997., 981.2, 947.4, 925., 914.9, 911.,
+                         902., 883., 850., 822.3, 816., 807., 793.2, 770.,
+                         765.1, 753., 737.5, 737., 713., 700., 688., 685.,
+                         680., 666., 659.8, 653., 643., 634., 615., 611.8,
+                         566.2, 516., 500., 487., 484.2, 481., 475., 460.,
+                         400.]) * units.hPa
+    temperature = np.array([24.2, 24.2, 24., 23.1, 21., 19.6, 18.7, 18.4,
+                            19.2, 19.4, 17.2, 15.3, 14.8, 14.4, 13.4, 11.6,
+                            11.1, 10., 8.8, 8.8, 8.2, 7., 5.6, 5.6,
+                            5.6, 4.4, 3.8, 3.2, 3., 3.2, 1.8, 1.5,
+                            -3.4, -9.3, -11.3, -13.1, -13.1, -13.1, -13.7, -15.1,
+                            -23.5]) * units.degC
+    dewpoint = np.array([23.2, 23.1, 22.8, 22., 20.2, 19., 17.6, 17.,
+                         16.8, 15.5, 14., 11.7, 11.2, 8.4, 7., 4.6,
+                         5., 6., 4.2, 4.1, -1.8, -2., -1.4, -0.4,
+                         -3.4, -5.6, -4.3, -2.8, -7., -25.8, -31.2, -31.4,
+                         -34.1, -37.3, -32.3, -34.1, -37.3, -41.1, -37.7, -58.1,
+                         -57.5]) * units.degC
+    parcel_prof = parcel_profile(pressure, temperature[0], dewpoint[0])
+    LI = lifted_index(pressure, temperature, parcel_prof)
+    assert_almost_equal(LI, -7.9176350 * units.delta_degree_Celsius, 2)