likely bug in the (new) thermal conductivity parameterization

[har917]

It would appear that there is a bug in the code in routine cbl_conductivity!

The orginal paper (tracked down to Johansen(1975) and Peters-Lidard (1998)) gives the formula for Ksat as kappas^(1-n) kappai^(n-xu) kappaw^xu (eqn 9).

Our code has

Ksat(j,k) =  Ktmp * &
                  (2.2 ** (soil%ssat_vec(j,k)*(1.0-liq_frac(j,k) ) ) )*&
                  (0.57**(liq_frac(j,k)))

where kappas^(1-n) = Ktmp, kappai^(n-xu) = kappai^n(1-xu/n) = (2.2 ** (soil%ssat_vec(j,k)*(1.0-liq_frac(j,k) ) ) ) correctly since xu/n = liq_frac, but kappaw^xu = kappw^n xu/n = (0.57**(liq_frac(j,k))) which is incorrect.

The code should be

Ksat(j,k) =  Ktmp * &
                  (2.2 ** (soil%ssat_vec(j,k)*(1.0-liq_frac(j,k) ) ) )*&
                  (0.57**(soil%ssat_vec(j,k)*liq_frac(j,k)))

In practice this error reduces the thermal conductivity of saturated soils by up to 30% - nevertheless the current parameterization (with error) is much better than the previous representation that is active in ACCESS-ESM1.5.

Thee is also a second difference from the source literature in that the Kersten number variation with soil moisture does not include the different behaviour with soil texture. - this is likely intentional but is not well documented.

@rml599gh @JhanSrbinovsky - I do not propose to fix this for ESM1.6 but will need to think through how to write this up.

[JhanSrbinovsky]

ok @har917 - further investigation in CABLE repo, possibly in an AM3 environment (i.e. post library implementation) ?

[har917]

It looks like this was an error in the original implementation by Mark Dekker - I need to go through the source reference in more detail to make sure I haven't made an error (but on dimensional grounds I can't see how)