# 47r3 new parameters: CAPE and CIN

In ECMWF Technical Memorandum 852 plans for introducing several new CAPE and CIN parameters as outputs from the Integrated Forecasting System (IFS) were announced. With the IFS model cycle 47r3 these new CAPE and CIN parameters will become operational, and more details about them are provided below.

Currently, in the IFS, the Convective Available Potential Energy (CAPE) is provided as a model output for diagnostic purposes. It is computed assuming a pseudo-adiabatic parcel ascent (all condensate is removed as soon as it forms). For computational efficiency CAPE in the IFS is approximated to:

${\rm CAPE}_{\theta_e} \approx \int_{\rm LFC}^{\rm EL} \quad g \left( \frac{\theta_{ep} - \bar{\theta}_{esat}}{\bar{\theta}_{esat}} \right) dz$

using environmental saturated equivalent potential temperature  $$\bar\theta_{esat}$$  and equivalent potential temperature of the parcel $$\theta_{ep}$$ :

$\theta_{ep} = T_k \left( \frac{p_0}{p_k} \right)^{\frac{R}{c_p}} \exp \left( \frac{Lq_k}{c_p\ T_k} \right)$

where Tk, pk and qk are the temperature, pressure and specific humidity respectively of the parcel lifted from a model level k,  p0 = 1000 hPa is the reference pressure,  cp is the specific heat capacity of dry air at constant pressure, R is the gas constant of dry air and L is the latent heat of vaporization.   $$\theta_{ep}$$ is conserved during a pseudo-adiabatic parcel ascent. The integral is computed from the Level of Free Convection (LFC) to the Equilibrium Level (EL).   $${\rm CAPE}_{\theta_e}$$ is computed for parcels departing from each model level up to the 350 hPa pressure surface. For parcels ascending from the lowest 60 hPa, mixed-layer values are used, for layers that are 30 hPa deep. Hence, a surface parcel (a parcel departing from “just” the lowest model level) is not considered. The maximum CAPE from all the parcels is retained. Entrainment and detrainment are not considered in the $${\rm CAPE}_{\theta_e}$$ computation.

With the IFS model cycle 47r3 a new most unstable CAPE (hereafter MUCAPE) is implemented. The only difference from the $${\rm CAPE}_{\theta_e}$$ described above is that MUCAPE is computed using virtual potential temperature of the parcel   $$\theta_{vp}$$ which replaces the equivalent potential temperature $$\theta_{ep}$$ , and virtual potential temperature of the environment $$\bar{\theta}_{v}$$ which replaces $$\bar{\theta}_{esat}$$ . This change provides an estimate (of CAPE for the most unstable parcel) which is more in line with parcel theory, and with what forecasters should diagnose from vertical profiles of the atmosphere (Figure 1). Figure 1. Skew-T-log-p diagram illustrating a number of key parameters for forecasting (severe) convective storms including CAPE and CIN. Thick red curve represents the environmental temperature whilst the thin red line represents the virtual temperature. Note that virtual temperature is always higher than the actual temperature when there is water vapour in the air.

The new MUCAPE has overall higher values than   $${\rm CAPE}_{\theta_e}$$ (Figure 2).

Convective inhibition (CIN) of the most unstable parcel (MUCIN) which corresponds to MUCAPE is not changing as it already uses the virtual temperature correction (see Changes in CIN to concur with forecasting practice for details). For the time being as CIN and MUCIN parameters in the IFS are identical, one should still use CIN (parameterID=228001) to retrieve the data from MARS. Figure 2. MUCAPE – $${\rm CAPE}_{\theta_e}$$ difference.

CAPE values represented in box-and-whisker form on ECMWF’s vertical profile product (on ECMWF’s Open Charts and ecCharts platforms) will change to now denote MUCAPE. For the time being, for the computation of maximum CAPE and maximum CAPE-shear in the last 6 hours, ECMWF will continue to use $${\rm CAPE}_{\theta_e}$$ , not MUCAPE. Likewise, the EFI and SOT for CAPE and CAPE-shear will also be based on $${\rm CAPE}_{\theta_e}$$ , not MUCAPE. A switch from $${\rm CAPE}_{\theta_e}$$ to MUCAPE in the computation of those will take place at a later date, with IFS cycle 48r1.

In addition to MUCAPE, a new mixed-layer CAPE (MLCAPE) is implemented as well for two different depths of the mixed layer – the lowest 50 and the lowest 100 hPa of the atmosphere – together with two corresponding mixed-layer CIN (MLCIN) fields. In accordance with the theory, MLCAPE for the 50 hPa mixed layer ordinarily has higher values than MLCAPE for the 100 hPa layer. An example of all three new CAPE parameters, and $${\rm CAPE}_{\theta_e}$$ (the only one output with cycle 47r2) is shown in Figure 3, for a 47r3 forecast valid at 15 UTC on 24 June 2021, a few hours before a devastating F4 tornado hit the southeast of the Czech Republic. In Figure 4 the corresponding CIN parameters are also shown.

To facilitate the use of MUCAPE and MUCIN, the Departure Level of the most unstable parcel (MUDLP) expressed in Pascal (Pa) is also implemented. In the case that MUCAPE is zero, MUDLP depicts the pressure of the second closest model level to the ground, which is currently model level 136 for both HRES and ENS. An example of MUDLP for the same forecast as Figure 3 is also provided (Figure 5a) along with a version of that field masked where MUCAPE < 100 J/kg (Figure 5b).

Note that for all CIN parameters, values are encoded as missing if they exceed 1000 J/kg as such magnitudes denote that deep moist convection is basically impossible. This means that one can notice that at some gridpoints CIN is missing but CAPE > 0. For plotting purposes in ecCharts missing CIN values are automatically set to 1000 J/kg. Figure 3. All CAPE parameters available with IFS cycle 47r3: a) $${\rm CAPE}_{\theta_e}$$ ; b) MUCAPE c) MLCAPE for the lowest 50 hPa and d) MLCAPE for the lowest 100 hPa. The black triangle denotes the F4 tornado which developed over the south-east of the Czech Republic on 24 June 2021, at around 17:30 UTC. Figure 4. All CIN parameters available with IFS cycle 47r3: a) MUCIN; b) MLCIN for the lowest 50 hPa and c) MLCIN for the lowest 100 hPa. The black triangle denotes the F4 tornado which developed over south-east of the Czech Republic on 24 June 2021, at around 17:30 UTC. Figure 5. Most unstable departure level in hPa: a) full field; b) masked where CAPE < 100 J/kg.

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