The i.evapo.mh module incorrectly converts net radiation from W/m²/day to MJ/m²/day using the formula:

ra = ra * (24.0 * 60.0 * 60.0 / 1000.0); /* convert W -> MJ/d */ (Line 16 in mh_original.c)

This multiplies by 86.4, which actually converts W/m²/day to kJ/m²/day, not MJ/m²/day.

However, the module then applies the constant 0.408, which assumes radiation is in MJ/m²/day (Line 17 in mh_original.c). This inconsistency results in a ~1000× overestimation of evapotranspiration (ET), violating the physical energy balance. The comment in the code is also misleading, stating it converts to MJ/d when it does not.

To reproduce

Run the following commands:
r.mapcalc "netrad = 100"
r.mapcalc "avg_temp = 20"
r.mapcalc "min_temp = 10"
r.mapcalc "max_temp = 30"

i.evapo.mh -h \ netradiation_diurnal=netrad \ average_temperature=avg_temp \ minimum_temperature=min_temp \ maximum_temperature=max_temp \ output=i_evapo_mh_output

r.univar -g map=i_evapo_mh_output

Observed Output:
mean=1370.593094

Expected behavior

With:
Ra = 100 W/m²/day
Ra in MJ = 100 × 0.0864 = 8.64 MJ/m²/day
ET = 1.370593 (0.0023 * 0.408 * 8.64 * ((10+30/2)+ 17.8) * pow((30-10), 0.5)))

Screenshots

System description

• Operating System: Windows Subsystem for Linux (WSL)

• GRASS GIS version: 8.4

• details about further software components

  • version=8.5.0dev
  • python version=3.10.12

Additional context

I wrote a test to compare output ET from i.evapo.mh to a theoretical radiation-limited maximum using the formula in the cited paper. The module regularly exceeds this threshold by thousands of mm/day. Upon reviewing the C code, the unit mismatch became evident. I found the same error in the modified formula of Hargreaves approach in mh_samani.c file.

I would be happy to help prepare a patch.