Input parameters

Surface Temperature (T)

Air temperature at ground level.

-3050

Temperature at which the air becomes saturated.

-4050

Eq. relative humidity: ~53.8%

Environmental Lapse Rate (Γenv)

Rate of cooling of the surrounding atmosphere with altitude. Typical values: 5–7 °C/km (standard atmosphere ≈ 6.5).

°C/km

212

Model atmospheric constants

Γd = 9.8 °C/km (dry adiabatic)Γdp ≈ 1.8 °C/km (dew point)

Results

LCL Altitude

1250

≈ 4101 ft

Base T.: 12.75 °C

CCL Altitude

2128

≈ 6981 ft

Base T.: 11.17 °C

Dew Point Depression

°C

Convective Temperature

32.02

°C

The CCL computed with a fixed environmental lapse rate is a theoretical approximation. In the real atmosphere, Γenv varies with altitude and time of day. Operational forecasts use radiosonde data and Skew-T Log-P diagrams.

Atmospheric Profile

Fundamentals & Explanation

What is the Condensation Level?

The Condensation Level is the altitude at which a rising parcel of air reaches saturation (Relative Humidity = 100%) and water vapor begins to condense, forming the base of clouds. In thermodynamic meteorology, there are two primary mechanisms that determine this altitude:

LCL (Lifting Condensation Level) — Achieved when an air parcel is mechanically forcedto rise (e.g., by mountains or weather fronts). The parcel cools at the dry adiabatic lapse rate (Γ_d), while its dew point decreases more slowly (Γ_dp). The altitude where both temperatures converge is the LCL.
CCL (Convective Condensation Level) — Achieved when solar heating of the ground generates free convection. In this scenario, the parcel rises through the surrounding air mass, meaning the environmental temperature profile (Γ_env) determines the intersection with the constant mixing ratio line (dew point).

Linear Model Equations

Under the linear thermal lapse rate model, cloud base altitudes are obtained through the mathematical intersection of the cooling rates:

LCL — Forced ascent

Z_{LCL} = \frac{T - T_d}{\Gamma_d - \Gamma_{dp}}

CCL — Thermal convection

Z_{CCL} = \frac{T - T_d}{\Gamma_{env} - \Gamma_{dp}}

Where T is the surface temperature and T_d is the dew point. Note that the fundamental difference lies in the denominator: the LCL depends exclusively on the adiabatic physics of the parcel (Γ_d), while the CCL requires knowing the atmospheric environmental sounding (Γ_env).

Once the convective cloud base altitude (Z_CCL) and its temperature (T_CCL) are found, we can descend virtually back to the surface along the dry adiabatic curve to find the Convective Temperature (T_c). This represents the surface temperature required to trigger spontaneous storm activity:

Convective Temperature

T_c = T_{CCL} + \Gamma_d \cdot Z_{CCL}

Magnus-Tetens Approximation

To provide input parameter flexibility, this module incorporates the Magnus-Tetens equation (modified by Alduchov and Eskridge, 1996), which allows for precise bidirectional conversion between Relative Humidity (RH) and Dew Point (T_d) based on saturation vapor pressure.

Relative Humidity (%)

RH = 100 \cdot \exp\left( \frac{17.67 \cdot T_d}{243.5 + T_d} - \frac{17.67 \cdot T}{243.5 + T} \right)

Conversely, to find the dew point from a reported relative humidity, an intermediate coefficient $\alpha$ is defined to solve for $T_d$:

Coefficient α

\alpha = \ln\left(\frac{RH}{100}\right) + \frac{17.67 \cdot T}{243.5 + T}

Dew Point (T_d)

T_d = \frac{243.5 \cdot \alpha}{17.67 - \alpha}

Thermodynamic Constants

Γd ≈ 9.8 °C/km

Dry Adiabatic Lapse Rate. Derived directly from gravitational acceleration (g) and the specific heat of dry air at constant pressure (Cp). Expressed theoretically as Γd = g / Cp.

Γdp ≈ 1.8 °C/km

Dew Point Lapse Rate. An average empirical value describing how a parcel's dew point temperature drops as it expands adiabatically during ascent.

Limitations and Assumptions

Physical Limits: The dew point (T_d) can never exceed the air temperature (T). When T ≈ T_d, surface condensation (fog) occurs.
Unstable Atmosphere: If Γ_env > Γ_d (superadiabatic), the system will warn of severe conditions, and the CCL will be calculated lower than the LCL.
Stable Atmosphere: If Γ_env ≤ Γ_dp, the environmental lapse rate line will never intersect the dew point line, rendering the CCL mathematically invalid.
Constant Lapse Rates: The model assumes perfect linear variations in the troposphere. In real forecasting, radiosondes reveal complex non-linear curves on Skew-T diagrams.

Academic References

[1] Alduchov, O. A., & Eskridge, R. E. (1996). Improved Magnus Form Approximation of Saturation Vapor Pressure. Journal of Applied Meteorology, 35(4), 601–609. doi.org/10.1175/1520-0450(1996)035<0601:IMFAOS>2.0.CO;2
[2] Bolton, D. (1980). The Computation of Equivalent Potential Temperature. Monthly Weather Review, 108(7), 1046–1053. doi.org/10.1175/1520-0493(1980)108<1046:TCOEPT>2.0.CO;2
[3] Tetens, O. (1930). Über einige meteorologische Begriffe. Zeitschrift für Geophysik, 6, 297–309.
[4] Wallace, J. M., & Hobbs, P. V. (2006). Atmospheric Science: An Introductory Survey (2nd ed.). Academic Press.

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Condensation Level LCL / CCL

Input parameters

Results

Atmospheric Profile

Fundamentals & Explanation

What is the Condensation Level?

Linear Model Equations

Magnus-Tetens Approximation

Thermodynamic Constants

Limitations and Assumptions

Academic References

What is the Condensation Level?

Linear Model Equations

Magnus-Tetens Approximation

Thermodynamic Constants

Limitations and Assumptions

Academic References