Issue with CAPE Calculation

[Stone-Shaw]

I am encountering a problem where the calculated CAPE value is very large, but the TlnP plot shows it is actually quite small.
Version: 1.6.3
What I have tried:

1. Checked the MetPy source code and found different results when running step-by-step versus calling the function directly.
2. Removed the data above 100 hPa found different results again, but it is still different from step-by-step result.

I am unsure what the issue might be.

from metpy.units import units
from metpy.calc import parcel_profile 
from metpy.calc import lfc,el
from metpy.calc.thermo import _find_append_zero_crossings
from metpy.calc import dewpoint_from_relative_humidity
from metpy.calc import cape_cin
from metpy.calc.tools import _less_or_close, _greater_or_close
from metpy import constants as mpconsts
import numpy as np

P = [1000.,  975.,  950.,  925.,  900.,  875.,  850.,  825.,  800.,
        775.,  750.,  700.,  650.,  600.,  550.,  500.,  450.,  400.,
        350.,  300.,  250.,  225.,  200.,  175.,  150.,  125.,  100.,
         70.,   50.,   30.,   20.,   10.,    7.,    5.,    3.,    2.,
          1.] 
T = [ 26.601715 ,  25.321442 ,  23.64029  ,  22.3544   ,  21.61026  ,
        20.53189  ,  19.3378   ,  18.081207 ,  16.891754 ,  15.679352 ,
        14.605133 ,  11.797516 ,   8.922485 ,   4.584381 ,   0.8770447,
        -2.8042297,  -7.650421 , -13.071838 , -19.521637 , -27.249115 ,
       -36.776184 , -41.891373 , -47.43611  , -55.09149  , -63.31491  ,
       -70.46591  , -74.436005 , -73.86389  , -62.693848 , -52.720825 ,
       -47.223602 , -41.97264  , -34.355484 , -29.62732  , -15.841644 ,
        -4.863159 , -11.00827  ]

R = [8.7531734e-01, 8.7178373e-01, 9.2426902e-01, 9.7321486e-01,
       9.7158509e-01, 9.6182829e-01, 9.7018987e-01, 9.7185606e-01,
       9.5916349e-01, 9.4788438e-01, 9.2271966e-01, 9.3404025e-01,
       8.3645624e-01, 8.2847106e-01, 8.3991808e-01, 8.0008334e-01,
       7.7837539e-01, 7.8936952e-01, 8.8870806e-01, 8.9821351e-01,
       9.3429244e-01, 1.0480621e+00, 9.7989351e-01, 9.9125290e-01,
       1.0505068e+00, 9.9932271e-01, 6.5298730e-01, 2.0224983e-01,
       2.8747728e-02, 4.7798837e-03, 1.6737868e-03, 4.7243937e-04,
       1.4527883e-04, 6.6689492e-05, 1.0917375e-05, 2.7924066e-06,
       2.4962396e-06]

P_value_unit = P * units.hPa
T_value_unit = T * units.degC
R_value_unit = R * units.dimensionless
Td_value_unit = dewpoint_from_relative_humidity(T_value_unit, R_value_unit)

def cape_cin_steps(pressure,temperature,dewpoint, parcel_profile):
	lfc_pressure, _ = lfc(P_value_unit, T_value_unit, Td_value_unit,
						parcel_temperature_profile=parcel_profile, which='bottom')

	# If there is no LFC, no need to proceed.
	if np.isnan(lfc_pressure):
		print("LFC_p is None")
		cape = units.Quantity(0, 'J/kg')
		cin  = units.Quantity(0, 'J/kg')
	else:
		el_pressure, _ = el(pressure, temperature, dewpoint,
						parcel_temperature_profile=parcel_profile, which='top')

		if np.isnan(el_pressure):
				el_pressure = pressure[-1]
		else:
				el_pressure = el_pressure

		y = (parcel_profile - temperature).to(units.degK)
		x, y = _find_append_zero_crossings(np.copy(pressure), y)

		# CAPE
		# Only use data between the LFC and EL for calculation
		p_mask = _less_or_close(x, lfc_pressure) & _greater_or_close(x, el_pressure)
		x_clipped = x[p_mask].magnitude
		y_clipped = y[p_mask].magnitude
		cape = (mpconsts.Rd
				* units.Quantity(np.trapz(y_clipped, np.log(x_clipped)), 'K')).to(units('J/kg'))
		# CIN
		# Only use data between the surface and LFC for calculation
		p_mask = _greater_or_close(x, lfc_pressure)
		x_clipped = x[p_mask].magnitude
		y_clipped = y[p_mask].magnitude
		cin = (mpconsts.Rd
			* units.Quantity(np.trapz(y_clipped, np.log(x_clipped)), 'K')).to(units('J/kg'))
		if cin > units.Quantity(0, 'J/kg'):
			cin = units.Quantity(0, 'J/kg')
	return(cape,cin)

parcel_profile_value_unit = parcel_profile(P_value_unit, T_value_unit[0], Td_value_unit[0]).to('degC')
cape,cin = cape_cin_steps(P_value_unit, T_value_unit, Td_value_unit, parcel_profile_value_unit)
print(f"My CAPE:{cape:.2f}	MY CIN:{cin:.2f}")

#* metpy CAPE
CAPE,CIN = cape_cin(P_value_unit, T_value_unit, Td_value_unit, parcel_profile_value_unit)
print(f"Metpy CAPE:{CAPE:.2f}	 CIN:{CIN:.2f}")

output:

My CAPE:864.72 joule / kilogram	MY CIN:-12.96 joule / kilogram
Metpy CAPE:-114565.61 joule / kilogram	 CIN:-8.88 joule / kilogram

when I Removed the data above 100 hPa:

index = -10
P = P[:index]
T = T[:index]
R = R[:index]

output:

My CAPE:864.72 joule / kilogram	MY CIN:-12.96 joule / kilogram
Metpy CAPE:913.12 joule / kilogram	 CIN:-8.88 joule / kilogram

[denivt]

I also have similar issue! I think at some point they fixed it but it resurfaced. Here are 2 examples:
Try_radiosonde2.txt
Try_radiosonde.txt

So using the following code:

'#Calculating the indecies of instability
p = df["hPa"].values * units.hPa
T = df["temp"].values * units.degC
Td = df["dew_point"].values * units.degC
h = df['m'].values * units.m
wind_spd = df["wind_spd"].values * units("m/s")
wind_dir = df["wind_dir"].values * units("deg")

# compture parcel temperature
prof = parcel_profile(p, T[0], Td[0]).to('degC')
cape_cin1 = cape_cin(p, T, Td, prof)
cape_cin2 = surface_based_cape_cin(p, T, Td)

print(cape_cin1, cape_cin2)'

I get: (<Quantity(9229.5619, 'joule / kilogram')>, <Quantity(-15018.6255, 'joule / kilogram')>) (<Quantity(9229.5619, 'joule / kilogram')>, <Quantity(-15013.9171, 'joule / kilogram')>)
This is the Skew-T logP plot for the first sounding:

So I think the issue is with the detection of the LFC and EL. I hope they fix it soon!

[leaver2000]

The difference you are seeing in your calculation and the MetPy implementation is a result of MetPys usage of the virtual_temperature

    # Convert the temperature/parcel profile to virtual temperature
    temperature = virtual_temperature_from_dewpoint(pressure, temperature, dewpoint)
    parcel_profile = virtual_temperature(parcel_profile, parcel_mixing_ratio)

https://github.com/Unidata/MetPy/blob/main/src/metpy/calc/thermo.py#L2692

[denivt]

I don't get why I get such low (By definition I think incorrect) values for CAPE. Also in this case I think if virtual temperature is used the LFC will be the lowest available level, so the negative CAPE values still baffle me

[leaver2000]

This results you are seeing from MetPy start at the parcel_mixing_ratio where likely due to the extreme low pressure values at the top of your profile you are getting some negative and undesirable results.

parcel_mixing_ratio = np.where(
    below_lcl, saturation_mixing_ratio(pressure, dewpoint), saturation_mixing_ratio(pressure, temperature)
)
[..., 0.9166021107486749 -1.171439514221464 -0.9994846347383932] dimensionless

Which then causses more poor values in the upper portion of the parcel_profile ... -58771.?

parcel_profile = virtual_temperature(parcel_profile, parcel_mixing_ratio)
[..., -185.40719644051342 38.854250815237435 -58771.36246072502] degree_Celsius

and because you are taking the top EL you end up with a EL at the top of the atmosphere.

el_pressure, _ = el(pressure, temperature, dewpoint, parcel_profile, which="top")
1.998969650438882 hectopascal

Then there is some masking that happens, to insure the data used is below the EL which pretty much all of it is because your EL is so high, before being called into np.trapz. Below is a simplified version of that, as you can see there is a shift that occurs in the temperature delta y[1:] + y[:-1].

def trapezoid(
    y,  # parcel_profile - temperature
    log_p,  # log(pressure)
):
    d = np.diff(log_p)
    x = d * (y[1:] + y[:-1]) / 2.0
    # return x.sum() # typical trapezoid
    return x  # not taking the sum

Here is the upper portion of that profile prior to the sum reduction.

mpconsts.Rd * (trapezoid(y_clipped, np.log(x_clipped)) * units.degK)[::-1][-3:]
[..., -15310.98768360323 -25967.3543268382 -23106.97890795206] joule/kilogram

and because the top of your parcel_profile is -58771.36246072502 the sum ends up weird.

mpconsts.Rd * (trapezoid(y_clipped, np.log(x_clipped)) * units.degK).sum()
-114565.49636964439 joule / kilogram

I don't think that the parcel_mixing_ratio is supposed to be < 0 so maybe taking the abs?

    parcel_mixing_ratio = np.where(
        below_lcl, saturation_mixing_ratio(pressure, dewpoint), np.abs(saturation_mixing_ratio(pressure, temperature))
    )

I think another decent solution would be to omit any data above 3 hPa

m = P > 3 * units.hPa
cape_cin(P[m], T[m], Td[m], T_profile[m])
(<Quantity(913.204771, 'joule / kilogram')>,
 <Quantity(-8.88430648, 'joule / kilogram')>)

[denivt]

Sorry for the late response!

I think you were answering all the time to the previous question. If that is the case, I am sorry. I don't know why in my case i get such values since the el and lfc seem normal.