Thermo-hydrologic modelling of permafrost with OpenFOAM®: perspectives of applications to the study of weathering in boreal areas

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Thermo-hydrologic modelling of permafrost with OpenFOAM®: perspectives of applications to the study

of weathering in boreal areas

L. Orgogozo, Oleg S. Pokrovsky, Y. Godderis, Christophe Grenier, J. Viers, D.

Labat, S. Audry, Anatoly S. Prokushkin

To cite this version:

L. Orgogozo, Oleg S. Pokrovsky, Y. Godderis, Christophe Grenier, J. Viers, et al.. Thermo-hydrologic modelling of permafrost with OpenFOAM®: perspectives of applications to the study of weathering in boreal areas. EGU General Assembly 2015, Apr 2015, Vienne, Austria. �hal-01882547�

Thermo-hydrologic modelling of permafrost with OpenFOAM®: perspectives of applications to the study of weathering in boreal areas

Thermo-hydrologic modelling of permafrost with OpenFOAM®: perspectives of applications to the study of weathering in boreal areas

Context : study of the element fluxes in permafrost catchments of central Siberia in the frame work of the GDRI CAR WET SIB.

Conclusion : permaFOAM allows to give relevant thermo-hydrologic input data for weathering modelling in permafrost dominated areas.

Next step : application to a field data set of the Kulingdakan watershed (e.g.: Prokushkin et al., 2007). Slope space scale, annual time scale, layered medium, use of massively parallel computing. (Orgogozo et al., in prep.)

L. Orgogozo ^1* , O.S. Pokrovsky ¹ , Y. Goddéris ¹ , C. Grenier ² , J. Viers ¹ , D. Labat ¹ , S. Audry ¹ , A.S. Prokushkin ³

1 GET, UMR 5563 CNRS-IRD-UPS, 14 avenue Edouard Belin, 31400 Toulouse, France (*corresponding author: laurent.orgogozo@get.obs-mip.fr)

2 LSCE, UMR 8212 CNRS-CEA-UVSQ, Orme des merisiers, 91191 Gif-sur-Yvette Cedex, France.

3 V.N. Sukachev Institute of Forest, SB RAS, Krasnoyarsk, Russia

Hydro-thermal conditionning of weathering modelisations : computing water and thermal fluxes in a river bank of a permafrost affected watershed (illustrative example)

Problematic:

Climate change and weathering in boreal areas with a continuos permafrost

Studied area:

Central SIberia, watersheds of the Nizhnaya Tungunska, homogeneous vegetation cover and lithology ; main spatial variability : south

aspected / north aspected slopes

N S

S tr ea m v al le y

Goals :

(i) Influence of seasonnal freeze/thaw of the active layer on the geochemical fluxes related to weathering

(ii) Impact of the interannual variations of these cycles du to anthropogenic climate change

Methodological approach :

Mechanistic modeling of thermal and

hydrological transfers from the plot scale to the experimental watershed scale

→ Time scales : annual to multidecennal Space scales : 1 m

²

to 10's of km

²

Other potential context of application: thermokarstic areas in Western Siberia

LITTER ACTIVE

LAYER

PERMA- FROST

(i) Coupled transfers within soils of water and energy with phase

change : e.g.: Kennedy and Lielmezs, 1973, Harlan 1973, Guymon and Luthin 1974, Jame and Norum 1980, Seregina 1989, Boike et al. 2003, Hansson et al. 2004, McKenzie et al. 2007, Painter 2011, Frampton et al. 2011, Grenier et al. 2012, Rivière 2012, Kurylyk et al. 2014, ...

(ii) Large computation times may be encountered : use of parallel computation is expected to be necessary (Painter et al. 2013).

=> Our approach : developing a devoted solver with OpenFOAM® :

permaFOAM

See Orgogozo et al., 2014, in « Permafrost disribution, composition and impacts on infrastructure and ecosystems », ed. O.S. Pokrovsky.

(ii) Steef problems, non-linearities, couplings, few references solutions :

INTERFROST Benchmark, C. Grenier (LSCE, Continental Hydrology) 1D analytical validation cases, 2D intercomparison cases

https://wiki.lsce.ipsl.fr/interfrost/doku.php?id=home

See talk of C. Grenier, Session CR1.1/SSS0.20, 15/04 14H room B13

OpenFOAM® : an open source CFD tool box - Developed in C++

- Finite volumes

- Allow multiphysics modelling

- Enable to implement home-made solvers - Designed for massively parallel computing

- OF for geosciences, e.g.: Orgogozo et al., CPC 2014 RichardsFOAM

Parallel performances of RichardsFOAM:

3 km

²

, 10 m thick loam slope 36 millions mesh cells

10 days of infiltration

Accuracy of the numerical modeling : example of the mesh refinement and of the constitutive laws

2D test case: the frozen inclusion Interfrost benchmark* TH2

A sand box of 3m*1m, initially at 5°C, with a frozen inclusion (-5°C).

The medium is submitted to an hydraulic gradient of 0.15

Exponential constitutive laws for the frozen soil (freezing curve and

frozen permeability).

*https://wiki.lsce.ipsl.fr/interfrost/doku.php

Linear constitutive laws of the freezing curve and of the frozen permeability ?

0 7200 14400 21600 28800 36000 43200 50400 57600 64800 72000 79200 86400 -5

-4 -3 -2 -1 0 1 2 3 4 5

Temperature at the coldest point

150*50 300*100 600*200 1200*400

Time (s)

T ( °C )

0 7200 14400 21600 28800 36000 43200 50400 57600 64800 72000 79200 86400 -5

-4 -3 -2 -1 0 1 2 3 4

5 Temperature at the coldest point

Linear parametrisations

Exponential parametrisations

Time (s)

T ( °C )

Results may be

sensitive to the chosen parametrisation of the constutive laws of the medium. A carefull

attention must then be paid to the choice of these laws (see Kurylyk and Watanabe AWR

2014 for a discussion on this topic)

On the right :convergence study regarding mesh

refinement in the case of a linear parametrisation.

It shows that relevant results are obtained with a mesh with 0.5cm cell length (600*200

cells). It is less than in the

exponential case (see above).

Thus the parametrisation may also impacts strongly the

needed computation times.

0 7200 14400 21600 28800 36000 43200 50400 57600 64800 72000 79200 86400 -5

-4 -3 -2 -1 0 1 2 3 4 5

Temperature at the coldest point

150*50 300*100 600*200 1200*400 2400*800

Time (s)

T ( °C )

0 7200 14400 21600 28800 36000 43200 50400 57600 64800 72000 79200 86400 0.3

0.31 0.32 0.33 0.34 0.35 0.36 0.37

Average liquid water content

150*50 300*100 600*200 1200*400 2400*800

Time (s)

V o lu m et ri c li q u id w at er c o n te n t (% )

Convergence study regarding the refinement of the mesh: for an average quantity (mean liquid water content) above and for a ponctual quantity (T at the center of the frozen inclusion) below. The convergence is obtained for a coaser mesh for the mean value (1cm length cells, 300*100) than for ponctual value (0.25cm, 1200*400). The

relevant mesh refinement depends on the kind of results that are needed.

0 300 600 900 1200 1500 1800 2100 2400

-2 -1 0 1 2 3 4

Computation times for various mesh refinements

real computation time

CPU time (time*number of cores)

Number of cells along x axis

L o g (t im e) , w it h t im e in h o u rs

The mesh refinement has a strong impact on the computation times, and thus on the scales of applicability of the modelling tool.

Results with exponential constitutive laws

T (K), 6H T (K), 3H

T (K), 0H Liquid water content, 0H

Liquid water content, 3H

Liquid water content, 6H

All computations done with

permaFOAM on the CALMIP cluster (http://www.calmip.

univ-toulouse.fr)

0 10 20 30 40 50 60 70 80 90

-2 -1 0 1 2 3

Time (d) A v e ra g e d s o il te m p e ra tu re ( °C )

0 10 20 30 40 50 60 70 80 90

0 0.1 0.2 0.3 0.4

Time (d) A v e ra g e d l iq u id w a te r c o n te n t (% )

2D illustrative case: freezing of a river bank initially at 5°C submitted to a freezing event:

top boundary at -1.75°C and downslope boundary (contact with the river) at 0.5°C

T=-1.75°C

T=0.5°C Thermal

insulation Loamy bank

Length: 4m Thickness: 1m Slope = 25 % Duration of the freezing event : 90d

No flux

Unsaturated: no flux

Saturated: atm. pressure

Hydrostat.

pressure (river)

Hydro BC+Total water content field (~cst) Thermal BC + Initial temperature field

t=0j

t=40j

t=90j

t=0j t=0j

t=40j t=40j

t=90j t=90j

Temperature field (°C) Liquid water content field ( %) Icy water content field ( %)

Time evolution of averaged temperature and water content

fields in the soil : typical thermo-hydrologic input data for

weathering modellisations (e.g.: Goddéris et al. 2006, 2012)