# Lifted condensation level

The lifted condensation level or lifting condensation level (LCL) is formally defined as the height at which the relative humidity (RH) of an air parcel will reach 100% when it is cooled by dry adiabatic lifting. The RH of air increases when it is cooled, since the amount of water vapor in the air (i.e., its specific humidity) remains constant, while the saturation vapor pressure decreases almost exponentially with decreasing temperature. If the air parcel is lifting further beyond the LCL, water vapor in the air parcel will begin condensing, forming cloud droplets. (In the real atmosphere, it is usually necessary for air to be slightly supersaturated, normally by around 0.5%, before condensation occurs; this translates into about 10 meters or so of additional lifting above the LCL.) The LCL is a good approximation of the height of the cloud base which will be observed on days when air is lifted mechanically from the surface to the cloud base (e.g., due to convergence of airmasses).

Schematic of the LCL in relation to the temperature and dew point and their vertical profiles; the moist adiabatic temperature curve above the LCL is also sketched for reference.

## Determining the LCL

The LCL can be either computed numerically, approximated by various formulas, or determined graphically using standard thermodynamic diagrams such as the Skew-T log-P diagram or the Tephigram. Nearly all of these formulations make use of the relationship between the LCL and the dew point, which is the temperature to which an air parcel needs to be cooled isobarically until its RH just reaches 100%. The LCL and dew point are similar, with one key difference: to find the LCL, an air parcel's pressure is decreased while it is lifted, causing it to expand, which in turn causes it to cool. To determine the dew point, in contrast, the pressure is kept constant, and the air parcel is cooled by bringing it into contact with a colder body (this is like the condensation you see on the outside of a glass full of a cold drink). Below the LCL, the dew point temperature is less than the actual ("dry bulb") temperature. As an air parcel is lifted, its pressure and temperature decrease. Its dew point temperature also decreases when the pressure is decreased, but not as quickly as its temperature decreases, so that if the pressure is decreased far enough, eventually the air parcel's temperature will be equal to the dew point temperature at that pressure. This point is the LCL; this is graphically depicted in the diagram.

Using this background, the LCL can be found on a standard thermodynamic diagram as follows:

1. Start at the initial temperature (T) and pressure of the air parcel and follow the dry adiabatic lapse rate line upward (provided that the RH in the air parcel is less than 100%, otherwise it is already at or above LCL).
2. From the initial dew point temperature (Td) of the parcel at its starting pressure, follow the line for the constant equilibrium mixing ratio (or "saturation mixing ratio") upward.
3. The intersection of these two lines is the LCL.

Interestingly, there is actually no exact analytical formula for the LCL, since it is defined by an implicit equation without an exact solution. Normally an iterative procedure is used to determine a highly accurate solution for the LCL (i.e., an altitude is guessed, and the RH for a parcel lifted to that altitude is computed; if it is below 100%, then a higher altitude is taken as the next step in the iteration, or if it is above 100%, then a lower altitude is taken; this is repeated until the desired accuracy for the computed LCL is reached).

There are also many different ways to approximate the LCL, to various degrees of accuracy. The most well known and widely used among these is Espy's equation, which Espy formulated already in the early 19th century. His equation makes use of the relationship between the LCL and dew point temperature discussed above. In the Earth's atmosphere near the surface, the lapse rate for dry adiabatic lifting is about 9.8 K/km, and the lapse rate of the dew point is about 1.8 K/km (it varies from about 1.6-1.9 K/km). This gives the slopes of the curves shown in the diagram. The altitude where they intersect can be computed as the ratio between the difference in the initial temperature and initial dew point temperature (T-Td) to the difference in the slopes of the two curves. Since the slopes are the two lapse rates, their difference is about 8 K/km. Inverting this gives 0.125 km/K, or 125 m/K. Recognizing this, Espy pointed out that the LCL can be approximated as:

$h_{LCL} = \frac{T - T_d}{\Gamma_d - \Gamma_{dew}} = 125 (T - T_d)$

where h is height of the LCL (in meters), T is temperature in degrees Celsius (or kelvins), and Td is dew point temperature (likewise in degrees Celsius or kelvins, whichever is used for T). This formula is accurate to within about 1% for the LCL height under normal atmospheric conditions, but requires knowing the dew point temperature.

Another simple approximation for determining the LCL for moist air makes use of a rule-of-thumb relationship between the dew point depression (the temperature difference T-Td) and the RH, which is that the RH decreases by 5% for every degree (Celsius) increase in the dew point depression, starting at RH=100% when T − Td = 0 (for more information, see dew point). Applying this directly in Espy's formula, however, results in a substantial overestimate of the LCL at lower temperatures. A correction for this is provided by Lawrence's formula:[1]

$h_{LCL} = (20 + \frac{T}{5}) (100 - RH)$

where T is the temperature at the ground level in degrees Celsius, and RH is the ground level relative humidity in percent. This formula is very simple to use (so that you only need to know T and RH to estimate the LCL, even without a calculator), yet accurate to within about 10% for the LCL height under normal atmospheric conditions, provided RH>50% (it becomes inaccurate for drier air).

In addition to these simple approximations, several much more complex and more accurate approximations have been proposed in the scientific literature, for instance by Bolton (1980) and Inman (1969).

## Relation with CCL

The convective condensation level (CCL) results when strong surface heating causes buoyant lifting of surface air and subsequent mixing of the planetary boundary layer, so that the layer near the surface ends up with a dry adiabatic lapse rate. As the mixing becomes deeper, it will get to the point where the LCL of an air parcel starting at the surface is at the top of the mixed region. When this occurs, then any further solar heating of the surface will cause a cloud to form topping the well-mixed boundary layer, and the level at which this occurs is called the CCL. If the boundary layer starts off with a stable temperature profile (that is, with a lapse rate less than the dry adiabatic lapse rate), then the CCL will be higher than the LCL. In nature, the actual cloud base is often initially somewhere between the LCL and the CCL. If a thunderstorm forms, then as it grows and matures, processes such as increased saturation at lower levels from precipitation and lower surface pressure usually lead to a lowering of the cloud base.

Finally, the LCL can also be considered in relation to the level of free convection (LFC). A smaller difference between the LCL and LFC (LCL-LFC) is conducive to the rapid formation of thunderstorms. One reason for this is that a parcel requires less work and time to pass through the layer of convective inhibition (CIN) to reach its level of free convection (LFC), after which deep, moist convection ensues and air parcels buoyantly rise in the positive area of a sounding, accumulating convective available potential energy (CAPE) until reaching the equilibrium level (EL).