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Relative Humidity Tendency

Uses vertical profiles (e.g. atmospheric soundings) of a clear-sky convective boundary layer to quantify the contributions of dry air entrainment, boundary layer growth, boundary layer heating, and surface fluxes to changes in top of the boundary layer relative humidity. This is done using an analytical approach that assumes a well-mixed boundary layer.

Enables the separation of factors contributing to changes in relative humidity at the top of the boundary layer, and therefore the factors relating to cumulus formation. Specifically, non-evaporative terms (dry entrainment, boundary layer growth, and boundary layer heating) can be separated from the evaporative fraction contribution to cloud formation. See Figure 10 in Ek and Holtslag (2004).

The physical pathway leading to increasing relative humidity at the top of the convective boundary layer can also be better understood by looking at the time evolution of each contributing factor during hours prior to cumulus formation. See Table 1 from Ek and Holtslag (2004).

Sensitivity tests that vary soil moisture content can be performed to explore whether drier or wetter soils tend to favor cumulus formation. See Table 2 from Ek and Holtslag (2004).

Can also be calculated from observations where atmospheric soundings and surface fluxes are available at sub-daily timescales. Westra et al. (2012)

Required Input Data:

Needs vertical profiles of


specific humidity



surface latent heat flux

surface sensible heat flux

boundary layer height

Best suited for well-mixed convective boundary layers.

The primary assumption is a well-mixed boundary layer. If this assumption is not entirely met than strange estimates of relative humidity changes can result. Furthermore, estimates of the heat entrainment ratio needs to be estimated; however, this quantity is difficult to retrieve from observations and models. Currently the entrainment ratio is calculated in the CoMeT code using the mixing diagram approach.

Prototype Subroutine Call

subroutine rh_tend_calc ( nlev , ntim , &
tmp_in , qhum_in, hgt_in, press_in, &
pbl_h , shf , lhf_in, dt , &
ef , ne , &
pbl_heating, pbl_growth, dry_entrain, dRH_estimate, &
missing )

Required Input


How to Calculate

Relevant Citations

Method Description 

M. Ek and L. Mahrt, 1994: Daytime Evolution of Relative Humidity at the Boundary Layer Top. Mon. Wea. Rev., 122, 2709–2721. doi: 10.1175/1520-0493

M. B. Ek and A. A. M. Holtslag, 2004: Influence of Soil Moisture on Boundary Layer Cloud Development. J. Hydrometeor, 5, 86–99. doi: 10.1175/1525-7541

  Detailed Evaluation 

D. Westra, G. J. Steeneveld, and A. A. M. Holtslag, 2012: Some Observational Evidence for Dry Soils Supporting Enhanced Relative Humidity at the Convective Boundary Layer Top. J. Hydrometeor, 13, 1347–1358. doi: 10.1175/JHM-D-11-0136.1