Opened 4 years ago

Closed 4 years ago

# Definition of Kersten number for soil thermal conductivity

Reported by: Owned by: aducharne somebody major IPSLCM6.v1 Physical processes trunc

### Description

1) Based on an analysis by Anne Verhoef (ISMC-GEWEX-SOILWat Soil hydraulic and thermal PTFs exercise), the thermal conductivity in ORCHIDEE does not monotically increase with soil moisture, and shows a "peak" at low relative saturation (Sr).

After discussion with Fuxing, it comes from a misinterpretation of the equations proposed by Peters-Lidard et al 1998 for the Kersten number Ke (Eq 11), which is used to weight the thermal conductivities for dry and saturated soils.

Eq 11 gives two different functions for Ke depending if the soil is coarse or fine. There is also a condition on Sr being larger than a value that si different for fine and coarse soils.

Fuxing interpreted this as a single rule for all soils, with two formulatiosn depending on the range of Sr. This is what's creates the peak.

The proposed solution is to go back to Eq 11, but we need to define which soils are fine and coarse.

In Peters-Lidard et al 1998 (p1212), it is found that "Particle size. A soil with more than 5% of material having grain size less than 2 m m is considered ‘‘fine’’ (Farouki 1986). Thermal conductivity calculations assuming both fine and coarse soils at average values of other parameters indicated that the difference in predicted values versus grain size was not significant. In light of the lack of availability of grain size data, we consider all soils to be fine in subsequent analyses.

If we stick to this choice, it is very easy, since Eq 11 becomes unique :
Ke = log(Sr) + 1 if Sr > 0.1 else it is zero.

2) Peters-Lidard et al 1998 also define Ke=Sr for frozen soil. This was implemented by Fuxing in thermosoil_cond as following:

```!! 2. Kerston Number (ake)
DO jg = 1,ngrnd
IF ( (sh2o(ji,jg) + 0.0005) <  smc(ji,jg) ) THEN
! Frozen
ake(ji,jg) = satratio(ji,jg)
ELSE
! Unfrozen
IF ( satratio(ji,jg) >  0.1 ) THEN
ake(ji,jg) = LOG10 (satratio(ji,jg)) + 1.0
ELSEIF ( satratio(ji,jg) >  0.05 .AND. satratio(ji,jg) <=  0.1 ) THEN
ake(ji,jg) = 0.7 * LOG10 (satratio(ji,jg)) + 1.0
ELSE
ake(ji,jg) = 0.0  ! use k = kdry
END IF
END IF
END DO ! DO jg = 1,ngrnd
```

Note that sh2o is the unfrozen moisture content, such that the frozen content = smc-sh2o.

Thus, (sh2o(ji,jg) + 0.0005) < smc(ji,jg) means that the frozen content is greater than epsilon (0.0005).

Since the soil freezing has been introduced in the trunk later on, is Fuxing solution still adapted?

### comment:2 Changed 4 years ago by fwang

For point (1):

I agree with Agnès.
I re-checked the thermal conductivity implemented in NOAH LSM which also takes equations from Peters-Lidard et al., 1998. They use the 'fine' soil equation (eq. 11 in Peters-Lidard et al., 1998) for both Sr > 0.1 and 0 for Sr<1.
Website, https://ral.ucar.edu/solutions/products/noah-multiparameterization-land-surface-model-noah-mp-lsm
Files are in tar.gz format. e.g., the version implemented in WRFv3.6 HRLDAS-v3.6.tar.gz

For point (2):

under the frozen situation, I think we can keep the current solution.
If I understand correctly, the frozen modifies the thermal conductivity only at here (thermosoil_cond).
The frozen modifies the heat capacity, but not conductivity (in thermosoil_getdiff for example).
Maybe Catherine can confirm.

Fuxing

### comment:3 Changed 4 years ago by cottle

I have checked the code for the frozen case. The parametrization follows correctly the one proposed by Peters-Lidard.
I agree also with the interpretation of the Kersten number parameterisation according to particle size and I think that we should use the coarse parameterization for the first 3 sand classes of USDA and the "sand" class of FAO. I dont see any reason for not implementing completely and correctly the Peters-Lidard model, so I suggest to implement the two cases "coarse and fine" for the calculation of the Kersten number.
I suggest also to take advantage of correcting the code and to change all the "Kerston" in KERSTEN in the comments.
Catherine

### Changed 4 years ago by fwang

Test of conductivity using different kersten number in offline model

### Changed 4 years ago by fwang

Test of conductivity using different kersten number in offline model

### Changed 4 years ago by fwang

Test of conductivity using different kersten number in offline model

### comment:4 Changed 4 years ago by fwang

A test of using different kersten number in conductivity was done in ORCHIDEE offline model.
-- detailes of the experiment and the impacts on surface T and sensible heat flux are under:
https://forge.ipsl.jussieu.fr/orchidee/attachment/ticket/406/conductivity_using_different_kersten_number.pdf
-- the impacts of the (2) method is larger than the (3) method. the (3) method almost does not affects the resutls.
-- The influences of (2) method on soil moisture/latent heat flux are quite small.

Fuxing

### comment:5 Changed 4 years ago by aducharne

Email de Frédérique Chéruy le 24/10/2017:

J ai un petit soucis avec le graphe ci-dessus.

Si je comprends bien " utiliser les équations maintenant en Orchidee " réfère à la version " bugée" avec une evolution non monotone de la conductivité en fonction de l humidité relative et une sur-restimation ponctuelle pour les faibles valeur de la saturation relative.

Les deux autres expériences doivent permettre une évolution monotone et plutôt une diminution de la conductivité thermique (pour gommer la bosse, non?) et de suite de l inertie thermique. Dans ce cas, les travaux que nous avons faits avec Sonia et Jean-Louis indiquent que de telles modifications devraient conduirent à un refroidissement (en tout cas en couplé ) alors que les graphes montrent un réchauffement.

Du coup, soit les modifs faites n aboutissent pas à une réduction de l inertie thermique superficielle.

soit le fait de travailler en forcé modifie les résultats (?) (quelles sont les conventions pour le flux sensible?)
soit nos travaux sont faux (!), ce qui m ennuirait beaucoup.
soit les figures sont inversées.

Avez vous des suggestions?

### comment:6 Changed 4 years ago by aducharne

Réponse à Frédérique:

Oui, Eq1 sur les graphes de Fuxing renvoie au trunk actuel, buggé.
Eq2 renvoie à la correction proposée, qui doit effectivement diminuer la conductivité aux valeurs faibles de l'humidité relative, en supprimant la "bosse".
Par contre, pour la texture "coarse", la correction conduit à utiliser une autre fonction.
Et le cas Eq3 correspond à utiliser la fonction "fine" dans tous les cas.

Eq3 change très peu les températures de surface par rapport à Eq1, alors que Eq2 augmente pas mal ces températures dans les zones de texture coarse. C'est sans doute lié au fait que la fonction "coarse" donne des conductivités plus fortes que la fonction "fine".

Cf fichier xls attaché ci-dessous créé par Fuxing (avec les params hydrodynamiques de la classe sand de l'USDA) https://forge.ipsl.jussieu.fr/orchidee/attachment/ticket/406/ORCHIDEE_conductivity.xlsx

• courbe bleue correspond à Eq1 (version actuelle buggée avec bosse)
• courbe jaune correspond à Eq2 : plus de bosse, mais on augmente la conductivité qqsoit l'humidité relative car on utilise la fonction "coarse"
• courbe verte équivalente à Eq3: plus de bosse et valeurs correspondant à la fonction "fine" (qui est actuellement utilisée pour toutes les textures sauf aux faibles humidité relatives).
Last edited 4 years ago by aducharne (previous) (diff)

### comment:7 Changed 4 years ago by cottle

je confirme, la prise en compte de la texture coarse, affecte les sols sableux (zones désertiques essentiellement) et conduit à une augmentation de la conductivité thermique, et donc à des températures plus chaudes. C'est bien cohérent avec vos précédents résultats.
Catherine

### Changed 4 years ago by fwang

conductivity test results with diurnal cycles

### comment:8 Changed 4 years ago by fwang

The test results with diurnal cyles are under:
http://forge.ipsl.jussieu.fr/orchidee/attachment/ticket/406/conductivity.2.pdf

by Fuxing W. on 8/11/2017:
-The reference value of Qg is negative in north hemisphere in JJA (absorbing heat), and positive in south hemisphere in JJA (releasing heat).
-Qg is positive in north hemisphere in JJA (releasing heat), and nagative in south hemisphere in DJF (absorbing heat).
-The increase of thermal conductivity leads to an increase of Ground heat transfer in both summer and winter.
-It means negative values become more negative (blue in figure, more heat absorbed), and positive values become more positive (red in figure, more heat released).
-The latent heat flux changes much smaller than sensible heat flux (< +/- 1 W/m2).

Catherine O. on 14/11/2017:
The sensible heat flux varies well in line with the surface temperature as expected.

Fuxing

### comment:9 Changed 4 years ago by jgipsl

Done in the trunk rev [4767]

### comment:10 Changed 4 years ago by jgipsl

• Resolution set to fixed
• Status changed from new to closed

### comment:11 Changed 4 years ago by fcheruy

Message envoyé le 14/11/"017 oar Frédérique

j ai effectué les simulations en mode guidé avec LMDZ -CM6.11 (branche
IPSL6-CM11) , ORCHIDEE trunk, rev. 4751 + modif thermosoil de fuxing

• Orchidee de reference (LMSMIPbis) (condflag=1,capaflag=1)
• Orchidee ou seulement la conductivité thermique a été corrigée par

Fuxing. (LMSMIPcond) (condflag=2,capaflag=1)

• Orchidée ou la capacité thermique et la conductivité thermique on été

corrigée (LMSMIPcondcap). (condflag=2,capaflag=2)

Les atlas sont disponibles a l adresse:

Les differences sont vraiment minimes. Comme on s y attendait c est sur
les zones seches qu elles apparaissent. On distingue des differences sur
le Sahara et sur le désert de Kalahari par exemple.

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