# Corrections to the August-Roche-Magnus equation in pwsFWI

Now that version 0.9.0 of my Fire Weather Index for personal weather stations (pwsFWI) has been released in the context of CumulusUtils (I may separate it later into an independent program), it is time to look at formula corrections.

For the calculation of the pwsFWI, I make use of the VPD, the Vapour Pressure Deficit. In my blog describing the theory, I indicate a correction for altitude must be made and I give a pressure drop per 100m (which must then still be converted to the partial water pressure). However, after thinking this over, at the moment I believe no correction has te be made: the VPD is available through direct measurement and no corrections are necessary. No doubt I will think this over again and I may come back on this.

The saturation pressure for water is a calculation dependent on temperature and I make use of the August-Roche-Magnus equation (the Clausius–Clapeyron equation for water vapour under typical atmospheric conditions (near standard temperature and pressure)) :

$\dpi{120}&space;\fn_jvn&space;\LARGE&space;\fn_cm&space;\large&space;P_{sat}&space;=&space;A&space;\times&space;e^{\frac{B\times&space;T}{(T+C)}}$

Where A = 6.1094, B= 17.625 and C= 243.04 are the coefficients of the August-Roche-Magnus equation as found here. Psat in hPa and T in °C

The constants were found on the Wikipedia but recently I turned to the Guide to Meteorological Instruments and Methods of Observation (WMO-No. 8, CIMO Guide). In Chapter 4. Measurement Of Humidity, Annex 4.B. Formulae For The Computation Of Measures Of Humidity you will find the formulas needed.

I will add the following corrections:

1. I will add the Saturation Pressure for water over ice, so for sub-zero temperatures;
2. I will use the constants as shown in the CIMO-guide (slightly different from the ones I use now;
3. I will abandon the idea of altitude correction unless I am convinced otherwise.

So for above zero temperatures the constants for the Agust-Roche-Magnus equation become: A = 6.112, B=17.62 and C=243.12; for sub zero temperatures these constants become: A = 6.112, B=22.46 and C=272.62.

No other corrections in the pwsFWI equation will be implemented at this moment.

These will be available from 0.91 onwards.