Research papersEstimation of grass reference evaporation and sensible heat flux using surface renewal and Monin-Obukhov similarity theory: A simple implementation of an iterative method

- Non-linear hydrometeorological processes require iterative procedures.
- Examples include grass reference evaporation which requires surface temperature.
- Others include surface renewal and Monin-Obukov similarity theory sensible heat H.
- There were differences in ETo by iteration compared when not applied for dry climates.
- H using iterative methods compared favourably with Bowen ratio and eddy covariance.

An iterative method was applied to daily crop reference evaporation ETo. The method correctly evaluated the slope of the saturation water vapour pressure vs temperature relationship between surface temperature and air temperature. Using daily meterological data spanning several decades from four selected locations in Australia, South Africa and USA, differences in ETo estimates were noted with and without the iteration method applied. The largest difference, which occurred under high water vapour pressure deficit conditions, ranged from 1.65 mm/day for Griffith, Australia to 0.51 mm/day for Pretoria, South Africa. The aerodynamic component of the ETo equation was more affected by not applying the spreadsheet iterative procedure compared to the radiative component. Other spreadsheet examples of the iterative method employed included obtaining the roots of a depressed cubic polynomial in the air temperature surface renewal (SR) ramp. This value was used for the measurement of sensible heat flux using surface renewal. An iterative method, together with Monin-Obukhov similarity theory (MOST) and surface-layer scintillometer (SLS) measurements in a mesic grassland, was also used to calculate the sensible heat flux. The simple iterative method is quick, accurate and convenient, easy to repeat following changes to equations or data, allows easy manipulation and allows convenient visual inspection of data and graphics. Sub-hourly measurements of sensible heat flux for the mesic grassland using SR and SLS MOST iterative methods compared favourably with Bowen ratio and eddy covariance measurements.