A graphical derivation and statistical evaluation of simplified polynomials to determine vapour pressure deficit for use in ultra-low power microcontroller applications

Abstract

The aim of this work has been to derive and statistically evaluate the accuracy of second-order and third-order polynomials to determine vapour pressure deficit (VPD). These polynomials take air temperature and relative humidity measurements to determine VPD without the use of an exponential function, as proposed by F W Murray in 1967. Replacing the exponential function with a 2nd or 3rd order polynomial may be beneficial in ultra-low power microcontroller-based measurement applications where; code size, memory usage and power requirements are critical design drivers. However, oversimplification may impact precision. This work presents alternative 2nd order and 3rd order equations that have been derived from a Murray equation dataset where VPD isothermal datasets were plotted against relative humidity. These linear relationships allow y = mx + c analysis where, (i) 'c' can be set to zero with a offset in the relative humidity data, and, (ii) 'm' can be derived from a 2nd or 3rd order polynomial where 'm' = f(