To whom it may concern,

We developed a 3D model simulating 4 dry infiltration wells. The model is 20x20 m in x and y by 35 m in z. Initial conditions are equilibrium pressure heads with a water table ~5 m deep; horizontal boundaries are constant head with the same equilibrium conditions; and upper and lower boundaries are no-flow. Each well is simulated using nodal recharge with a constant rate of 9.08 m3/d at one node for each well, totaling 36.3 m3/d. The model is run for 1 day.

The question concerns how nodal recharge is accounted for the mass balance output. Below is the Balance.out at t = 1 day:

Volume [L3] 0.13095E+05 0.13095E+05

VolumeW [L3] 0.41564E+04 0.41627E+04

InFlow [L3/T] 0.20482E+00 0.20482E+00

hMean [L] 0.11690E+02 11.690

WatBalT [L3] 0.35730E+02

WatBalR [%] 57.587

The model runs well, giving values of pressure-head and water-content that would be expected. However, a large absolute error of 35.7 m3 is reported, and this error increases linearly for every 0.05-day increment reported.

It appears that cumulative fluxes do not include nodal recharge. When the constant head boundaries are simulated as time independent, Cum_Q.out reports CumQ1 = 32.1 m3 at t = 1 day. However, when the constant head boundaries are simulated as time dependent (even though head is held constant, identical to the time-independent simulation), Cum_Q.out reports CumQ1 = 0 for all times and CumQ7 = 32.1 m3 at t = 1 day. The time series of time-independent CumQ1 and time-dependent CumQ7 are identical. It seems like CumQ1 should include the nodal recharge values, but it does not. All other fluxes in Cum_Q.out are zero, as expected.

Additionally, it appears that when HYDRUS computes absolute error using eq. 5.26 of the Technical Manual, nodal fluxes are left out of the fourth term of this equation. Thus, Balance.out reports a mass balance error of 35.7 m3. The linear increase in error is consistent with the constant nodal fluxes. If you subtract total nodal recharge of 36.3, however, that gives an error of only 0.6 m3, which is only 1.6% of total nodal recharge.

Finally, we ran the same model with a finer mesh and smaller water-content tolerance (reduced from 1e-4 to 1e-5; pressure-head tolerance remained at 1 cm) and got essentially identical mass balance results.

Any feedback on this problem would be greatly appreciated.

Thanks,

Won

## Nodal recharge accounting in water balance

### Re: Nodal recharge accounting in water balance

I have quickly done two runs (on a smaller scale) with either head or flux nodal source, and they both have a small mass balance error (indicating that the mass balance calculations are carried out correctly). J.