Observations in subtropical regions show that stratiform low cloud cover is well correlated with the lower-troposphere stability (LTS), defined as the difference in potential temperature θ between the 700-hPa level and the surface.

！https://www.researchgate.net/publication/315672693_Effects_of_Environment_Forcing_on_Marine_Boundary_Layer_Cloud-Drizzle_Processes/figures?lo=1

Figure 7. Lower tropospheric stability (LTS) every 3 h on 27 July 2010 (type I) calculated from MERRA-2 reanalysis data.

https://www.researchgate.net/publication/216836936_Low-Cloud_Fraction_Lower-Tropospheric_Stability_and_Large-Scale_Divergence
MLM成功地再现了低云分数和低对流层稳定性之间的正相关性

On the relationship between low cloud variability and lower tropospheric stability in the Southeast Pacific

在这项研究中，我们研究了东南太平洋的海洋低云量变化及其与时间尺度范围内的低对流层稳定性（LTS）的关系。在每日和每年的时间尺度上，LTS和低云量在南方夏季（DJF）非常相关。同时在冬季（JJA），当环境LTS增加时，LTS低云关系显着减弱。多年来DJF LTS低云关系也因环境LTS值异常大而减弱。这些通常是强烈的厄尔尼诺年，其中DJF LTS值与JJA中常见的相当。因此，LTS-低云关系受季节周期和ENSO现象的强烈调制。我们还研究了与南半球夏季低云变化密切相关的LTS异常的起源。我们发现海洋和大气独立地参与了LTS的异常，从而导致了东南太平洋低云层的变化。这突出了气候系统的物理（而不是化学）组成部分在低云量中产生内部变化的重要性。它还说明了该地区气候系统的耦合性质，并提出了与LTS相关的云反馈的可能性。最后，我们通过解决东南太平洋LTS低云关系对人为气候变化的低云反馈的影响得出结论。这突出了气候系统的物理（而不是化学）组成部分在低云量中产生内部变化的重要性。它还说明了该地区气候系统的耦合性质，并提出了与LTS相关的云反馈的可能性。最后，我们通过解决东南太平洋LTS低云关系对人为气候变化的低云反馈的影响得出结论。这突出了气候系统的物理（而不是化学）组成部分在低云量中产生内部变化的重要性。它还说明了该地区气候系统的耦合性质，并提出了与LTS相关的云反馈的可能性。最后，我们通过解决东南太平洋LTS低云关系对人为气候变化的低云反馈的影响得出结论。

On the Relationship between Stratiform Low Cloud Cover and Lower-Tropospheric Stability

Observations show that on daily to interannual time scales, stratiform low cloud fraction (CF) is strongly correlated with the lower-tropospheric stability (LTS), defined as the difference between the potential temperature θ of the free troposphere (700 hPa) and the surface, LTS = θ₇₀₀ − θ₀ (Slingo 1987; Klein and Hartmann 1993; Klein 1997; Wood and Hartmann 2006).

在每日到年际时间尺度上，层状低云分数（CF）与对流层低层稳定性（LTS）密切相关，定义为自由对流层（700 hPa）的潜在温度θ与地表之间的差异。，LTS = *θ *₇₀₀ - *θ *₀（的Slingo 1987 ; Klein和1993哈特曼 ; 1997年克莱因 ; 木材和2006哈特曼）

FIG 1 Idealized profile (thick solid line) of lower-tropospheric structure during periods of undisturbed flow. Moist adiabats are shown as light dotted lines.

https://climlab.readthedocs.io/en/latest/_modules/climlab/utils/thermo.html#estimated_inversion_strength

def potential_temperature(T,p):
    """Compute potential temperature for an air parcel.

    Input:  T is temperature in Kelvin
            p is pressure in mb or hPa
    Output: potential temperature in Kelvin.

    """
    theta = T*(ps/p)**kappa
    return theta

# Lower Tropospheric Stability (theta700 - theta0)

def estimated_inversion_strength(T0,T700):
    '''Compute the Estimated Inversion Strength or EIS,
    following Wood and Bretherton (2006, J. Climate)

    Inputs: T0 is surface temp in Kelvin
           T700 is air temperature at 700 hPa in Kelvin

    Output: EIS in Kelvin

    EIS is a normalized measure of lower tropospheric stability acccounting for
    temperature-dependence of the moist adiabat.
    '''
    # Interpolate to 850 hPa
    T850 = (T0+T700)/2.;
    # Assume 80% relative humidity to compute LCL, appropriate for marine boundary layer
    LCL = lifting_condensation_level(T0, 0.8)
    # Lower Tropospheric Stability (theta700 - theta0)
    LTS = potential_temperature(T700, 700) - T0
    #  Gammam  = -dtheta/dz is the rate of potential temperature decrease along the moist adiabat
    #  in K / m
    Gammam = (g/cp*(1.0 - (1.0 + Lhvap*qsat(T850,850) / Rd / T850) /
             (1.0 + Lhvap**2 * qsat(T850,850)/ cp/Rv/T850**2)))
    #  Assume exponential decrease of pressure with scale height given by surface temperature
    z700 = (Rd*T0/g)*log(1000./700.)
    return LTS - Gammam*(z700 - LCL)

cp = 1004. # specific heat at constant pressure for dry air (J / kg / K)
Rd = 287. # gas constant for dry air (J / kg / K)
kappa = Rd / cp
ps = 1000. # approximate surface pressure (mb or hPa)