Question on the formulation to calculate the groundwater reservoir flux

[RY4GIT]

I have a question on the formulation to calculate the groundwater reservoir flux.

Current behavior

The README document says the groundwater module is identical to the NWM formulation. However, there is a little difference in the formulation. Essentially, the NWM uses exp(z), and the CFE uses exp(z)-1 to calculate outflux from the groundwater reservoir. Then, in CFE, the parameter expon is less important and the parameter Coeff (a.k.a. Kgw) is more important in determining groundwater flux than NWM.

I wonder if:

1. there is a reason for the change
2. if there is anyone calculated parameter range suited for the exp(z)-1 formulation

In my view, both formulations make sense: the CFE exp(x)-1 formulation will result in 0 flux from the groundwater reservoir when groundwater storage is zero. On the other hand, since flux becomes equal to the groundwater reservoir is small, exp(x)-1 is not necessary, and the exp(x) NWM model also makes sense.

the NWM formulation (according to WRF-Hydro technical description)

the CFE formulation

[fred-ogden]

The source code for wrf_hydro when CFE was developed used this line for calculating the outflow from the conceptual groundwater reservoir:

qout_gwsubbas(bas) = C(bas)*(EXP(ex(bas)*z_gwsubbas(bas)/(z_mx(bas)/1000.))-1) !Exp.model. q_out (m^3/s)

From file: module_GW_baseflow.F

[andywood]

I wonder if it may be worth introducing a different formulation as an option. There's a variation that is similar but does not force the assumption of exponential (vs generic power law) baseflow form, and also has parameters that can be estimated from recession analysis of observed flows.

Qout = k * (S/Smax) ^ expon

There's a paper discussing this, written by (no surprise) Martyn Clark. This formulation is in SUMMA and also (in a slightly different way) in CLM/CTSM.

The paper is here, btw: https://onlinelibrary-wiley-com.cuucar.idm.oclc.org/doi/epdf/10.1002/hyp.7154. (I can share a copy if it's not accessible).

[RY4GIT]

@fred-ogden Thank you for digging into the source code! I understood that the CFE and WRF-Hydro use the same equation.
@andywood Thank you for the paper suggestion, this is exactly what I need now to figure out groundwater parameters. I've got the paper and will read it.

[andywood]

:) I think Fred wrote the source code!

[RY4GIT]

Oh no! I am sorry for not understanding the context 😟

[andywood]

No worries ;) just trying to add a shout out for Fred's contribution.