Water and energy transfer modeling in a permafrost-dominated, forested catchment of Central Siberia: The key role of rooting depth

HAL Id: hal-02014619

https://hal.archives-ouvertes.fr/hal-02014619

Submitted on 11 Feb 2019

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Siberia: The key role of rooting depth

Laurent Orgogozo, Anatoly Prokushkin, Oleg Pokrovsky, Christophe Grenier, Michel Quintard, Jérome Viers, Stephane Audry

To cite this version:

Laurent Orgogozo, Anatoly Prokushkin, Oleg Pokrovsky, Christophe Grenier, Michel Quintard, et al..

Water and energy transfer modeling in a permafrost-dominated, forested catchment of Central Siberia:

The key role of rooting depth. Permafrost and Periglacial Processes, Wiley, In press. �hal-02014619�

For Peer Review

Water and energy transfer modeling in a permafrost- dominated, forested catchment of Central Siberia: the key

role of rooting depth.

Journal: Permafrost and Periglacial Processes Manuscript ID PPP-18-0020.R2

Wiley - Manuscript type: Research Article Date Submitted by the

Author: n/a

Complete List of Authors: Orgogozo, Laurent; Universite Toulouse III Paul Sabatier, Geosciences Environment Toulouse

Prokushkin, Anatoly; V.N. Sukachev Institute of Forest Pokrovsky, Oleg; CNRS, Geosciences Environment Toulouse Grenier, Christophe; LSCE/CEA,

Quintard, Michel; CNRS, IMFT

Viers, Jérôme; Universite Toulouse III Paul Sabatier, Geosciences Environment Toulouse

Audry, Stéphane; Observatoire Midi-Pyrenees, Geosciences Environment Toulouse

Keywords: Permafrost, cryohydrogeology modeling, massively parallel computation, OpenFOAM®, evapotranspiration, active layer dynamics

Note: The following files were submitted by the author for peer review, but cannot be converted to PDF.

You must view these files (e.g. movies) online.

Data_S2_permaFoam_package.zip

For Peer Review

1 Water and energy transfer modelling in a permafrost-dominated, forested catchment of

2 Central Siberia: the key role of rooting depth

3 L. Orgogozo ¹ , A.S. Prokushkin ² , O.S. Pokrovsky ^1,3 , C. Grenier ⁴ , M. Quintard ^5,6 , J. Viers ¹ , S.

4 Audry ¹

5

6

GET (Géosciences Environnement Toulouse), UMR 5563 CNRS / UR 234 IRD / UPS, Observatoire Midi- 7 Pyrénées, Université de Toulouse, 14 avenue Édouard Belin, 31400 Toulouse, France

8

V.N. Sukachev Institute of Forest, Siberian Branch, Russian Academy of Sciences, Akademgorodok 50/28, 9 Krasnoyarsk, Russia.

10

BIO-GEO-CLIM laboratory, Tomsk State University, Lenina 35, Tomsk, Russia

11

Laboratoire des Sciences du Climat et de l’Environnement, Université Paris-Saclay, IPSL / LSCE, UMR 8212 12 CNRS-CEA-UVSQ, Orme des Merisiers, 91191 Gif-sur-Yvette Cedex, France

13 Orme des Merisiers, 91191 Gif-sur-Yvette Cedex, France

14

Université de Toulouse, INPT, UPS, IMFT (Institut de Mécanique des Fluides de Toulouse), Allée Camille 15 Soula, F-31400 Toulouse, France

16

CNRS, IMFT: F-31400 Toulouse, France 17

18 Abstract

19 In order to quantify the impact of evapotranspiration phenomena on active layer dynamics in a

20 permafrost-dominated forested watershed in Central Siberia, we performed a numerical

21 cryohydrological study of water and energy transfer using a new open source cryohydrogeology

22 simulator, with two innovative features: the spatially distributed, mechanistic handling of

23 evapotranspiration and the inclusion of the developed numerical tool in the high performance

24 computing tool box for numerical simulation of fluid dynamics OpenFOAM ^® . In this region, the

25 heterogeneity of solar exposure leads to strong contrasts in vegetation cover, which constitute the

26 main source of variability of hydrological conditions at the landscape scale.

27 The uncalibrated numerical results reasonably reproduce the measured soil temperature profiles and

28 the dynamics of infiltrated waters revealed by previous biogeochemical studies. The impacts of the

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

For Peer Review

29 thermo-hydrological processes on the water fluxes from the soils to the stream are discussed

30 through comparison between numerical results and field data. The impact of evapotranspiration on

31 water fluxes is studied numerically, which highlights a strong sensitivity to the variability of rooting

32 depth and corresponding evapotranspiration at the slopes of different aspects in the catchment.

33

34 Keywords

35 Permafrost, cryohydrogeology modelling, massively parallel computation, OpenFOAM ^® ,

36 evapotranspiration, active layer dynamics.

37 38

39 1. Introduction

40 Climate change is strongly pronounced in high latitudes, and it produces important changes

41 of the permafrost distribution, ¹ which extends on roughly a quarter of emerged land of the northern

42 hemisphere. Due to the multiple interactions among water transfers, thermal transfers and

43 permafrost dynamics, these changes are likely to trigger modifications in the hydrology of these

44 regions. ^2,3,4 Since water fluxes constitute the vectors of dissolved and suspended matter (including

45 carbon) transfers along the land-to-ocean continuum, these fluxes should in turn experience major

46 changes as well. For quantifying this, accurate and quantitative modelling of the coupled thermo-

47 hydrological behaviour of permafrost catchments is needed.

48 Weathering of rocks is among the most important processes involved in dissolved and

49 suspended transfers in continental surfaces. Weathering modelling in permafrost affected areas is

50 thus a key point in the prediction of future global carbon dynamics. ⁵ In order to develop predictive

51 modelling of weathering in boreal areas, relevant thermo-hydrological input data describing with

52 enough accuracy the seasonal dynamics of infiltrated waters such as drainage, temperature, water

53 content and water state along the soil profiles, water residence time within the slopes are necessary,

54 because infiltrated waters are both the agent of chemical weathering and the vector of riverine

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

For Peer Review

55 fluxes. ⁶ Another important point for the interaction between permafrost dynamics and the carbon

56 cycle is the fate of the soil organic carbon during permafrost thawing ^7,8 and thermokarst genesis.

57 ^9,10,11 Modelling efforts of some of the involved phenomena has already been undertaken at the

58 continental scale, ¹² but the high sensitivity of the produced results to the hydrological regime ¹³

59 illustrates the need of careful assessments of the thermo-hydrological processes involved. For this,

60 mechanistic modelling studies at the scale of individual catchments are required.

61 For the study of biogeochemical dynamics of boreal areas, cryohydrogeological modelling,

62 which deals with coupled hydrological and thermal transfers within variably saturated porous media

63 (e.g.: soils or geological bodies) with freeze-thaw of the pore water, is essential. The numerical

64 resolutions of the associated systems of governing equations are difficult problems, due to

65 numerous and strong non-linearities and strong couplings. Thus many studies have been carried out

66 on this subject, from early seventies ¹⁴ until present days ^15,16 . It is now recognized as a hot topic in

67 permafrost studies. ⁴ As emphasized above, cryohydrogeological modelling is highly needed for

68 biogeochemical studies of boreal areas, but there are many other potential fields of applications of

69 cryohydrogeological models, such as geotechnics ¹⁷ , nuclear waste long term storage, ^18,19,20 cold

70 regions water resources, ^21,22 thermal transfers around pipe-lines in cold regions, ^23,24 infrastructures

71 stability ^25,26,27 and geothermics in cold regions. ²⁸

72 One of the major difficulties in cryohydrogeological modelling lies in the fine temporal and

73 spatial discretisations needed to numerically solve the involved equations. ²⁹ Such high resolution

74 simulations require large and high performance computational resources, ³⁰ as it is now

75 acknowledged for the whole field of hydrological modelling. ³¹ For these reasons, massively parallel

76 simulation tools have been developed in the last years. ^32,33 Indeed, in the biogeochemical

77 applications evocated above, large temporal and spatial scales may be encountered (typically tens of

78 years and of square kilometres in the case of the study of climate at the watershed scale), which

79 requires high performance computing techniques.

80 In this work, we developed a dedicated cryohydrogeology numerical simulator in the

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

For Peer Review

81 framework of OpenFOAM ^® (www.openfoam.com), an open source tool box for computational

82 fluid dynamics widely used in various industrial and scientific applications. One of the main

83 strengths of OpenFOAM ^® is its capability to use massively parallel computing techniques

84 efficiently. The parallel performances of OpenFOAM ^® are for instance assessed in some

85 geosciences applications. ^34,35 As discussed in Orgogozo et al. (2014a), ³⁵ working in an open source

86 generalist framework such as OpenFOAM ^® allows benefiting from community driven

87 developments by large groups of users and developers. In this way, many state of the art pre-

88 processing, solving and post-processing tools that are continuously developed within the

89 OpenFOAM ^® community could be applied for various specific problems. ^36,37 These two aspects,

90 namely the good parallel performances and the integration in an open source generalist framework,

91 motivated our choice of developing permaFoam, an OpenFOAM ^® solver for cryohydrogeology.

92 The permaFoam numerical approach was successfully validated recently from two bidimensional

93 and fully saturated test cases within a benchmark of 13 codes. ³⁸

94 In this paper we will focus on the modelling of water and energy transfer in an experimental

95 watershed of Central Siberia, located within the siberian basaltic trap province and covered by larch

96 forests. The remoteness, the vast extension (~1.5 million km ² ) and the lithological and landscape

97 homogeneity of this area make it an ideal region for studying chemical weathering processes and

98 river export fluxes in permafrost terrain. 39,40,41,42 The main spatial variability in these landscapes is

99 related to the south or north aspects of the slopes. The Kulingdakan watershed is a small (~40 km ² )

100 catchment in this region, and it has been monitored for more than a decade in order to characterize

101 its biogeochemical dynamics. ^43,44 The cryohydrogeological modelling of this catchment is thus of

102 great interest, because it can both benefit from the already acquired biogeochemical knowledge and

103 help to further interpret the available data.

104 The heterogeneity in amount of solar radiation slopes received at different aspect leads to

105 highly contrasted thermo-hydrological conditions in the considered catchment, as it has also been

106 observed in other permafrost-dominated environments. ^45,46 In the Kulingdakan catchment, the

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

For Peer Review

107 evapotranspiration variability in relation with solar exposure has been identified as a key control on

108 active layer dynamics. ⁴⁷ In this work we investigated this variability through mechanistic numerical

109 modelling of the active layer dynamics of the slopes of this watershed, using a distributed,

110 processes-based estimator of the evapotranspiration flux which is an adaptation of Orgogozo

111 (2015) ⁴⁸ to permafrost environments. For this we compared numerical results of a coupled thermo-

112 hydrological mechanistic modelling with field measurements of temperature profiles in both south

113 aspected slopes (SAS) and north aspected slopes (NAS). The quantitative estimations of the water

114 fluxes obtained from numerical results allow us to discuss the different terms of the hydrological

115 budget based on the field knowledge acquired on the water and heat transfer in the Kulingdakan

116 watershed, with a focus on seasonal dynamics of infiltrated waters. Further, the sensitivity of

117 evapotranspiration fluxes to the spatial variability of tree morphology (rooting depth) inherited from

118 the spatial variability of the solar exposure were investigated by means of numerical experiments

119 that compute evapotranspiration fluxes for various rooting depths. Results of this study will be

120 useful for prediction of water fluxes and pathways responsible to the change of environmental

121 conditions such as active layer thickness and vegetation dynamics.

122 123

124 2. Material and Methods

125

126 In this part we present the numerical tool permaFoam, the studied site and the associated

127 data set, and finally, the set up of the proposed modelling.

128

129 2.1 The permaFoam simulator

130

131 2.1.1 Considered governing equations

132 The cryohydrogeological numerical model permaFoam deals with coupled water and

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

For Peer Review

133 thermal transfers within 3D heterogeneous variably saturated porous media, with freeze-thaw of the

134 pore water. The considered media may be four-phase media with a solid phase, a liquid water

135 phase, an ice phase and an air phase. Our goal was to find a trade-off between the accuracy of the

136 description of physical phenomena and the ability to deal with large spatial and temporal scales,

137 which implies fast and robust computations. First, the variations of water density with respect to its

138 state (liquid/frozen) and temperature have been neglected, and the solid matrix is non-deformable.

139 Thus soil mechanics and cryoturbations ⁴⁹ are not taken into account, as well as water natural

140 convection due to density driven flow and cryosuction. Cryosuction, which is responsible for liquid

141 water fluxes toward the freezing fronts, ^50,51 is closely related to cryo-mechanical processes, jointly

142 with the ice volumetric expansion. ⁵² The freezing point depression effect has also not been taken in

143 consideration, and since salt concentrations in soil pore waters of studied sites are low, the

144 maximum temperature at which the ice can exist is considered as a constant. We assumed the

145 existence of local thermal equilibrium, which is classical in this field. ⁴ At last, we consider a

146 Richards formulation for describing the flow of water, and we do not take into account advective

147 transport of heat and water vapor by air ⁵³ . These simplifying assumptions lead to a system of

148 equations of classical form ^15,16 with two coupled equations.

149 First, a modified Richards equation with a source term accounting for actual

150 evapotranspiration governs the total mass balance for water and ice (see Appendix S1 in electronic

151 supporting information for the fully detailed equation system with complete nomenclature):

152 (1)

153 The left hand side of equation (1) is the mass storage term, whereas the first term on the right is the

154 divergence of the Darcy flux and the second term is a sink term for evapotranspiration. From this

155 first equation the filtration velocity field is computed on the basis of the field of pressure head (the

156 primary variable of equation (1)), by a generalised Darcy's law:

157 (2)

158 Second, a macro-scale heat transfer equation for the porous medium with a term of latent

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

For Peer Review

159 heat exchange governs the thermal transfers:

160 (3)

161 In the left hand side of equation (3), the first term is the heat storage term (which includes the heat

162 stored in latent form) and the second term is the advective flux term, in which appears the filtration

163 velocity computed in equation (2). The right hand side of the equation (3) is the term that represents

164 the conductive flux. The apparent hydraulic conductivity in a variably saturated and variably frozen

165 porous medium is here given by:

166 (4)

167 The liquid water / ice equilibrium in the soil is described through an empirical Soil Freezing

168 Characteristic (SFC) function ²⁰ as:

169 (5)

170 and the ice volume fraction is calculated from the total water volume fraction as:

171 (6)

172 The physical meanings and the units of the symbols used in the equations are listed in Table 1.

173 Classical parameterizations are considered for the coefficients of these equations, described

174 in details in electronic supporting information (Appendix S1). We use a Mualem-van Genuchten

175 approach ⁵⁴ for the retention curve, the capillary capacity and the relative hydraulic conductivity

176 with respect to saturation and an empirical power law parameterization for the relative

177 hydraulic conductivity with respect to the freezing of the porous medium . ^19,55 One

178 should note that the primary variable of the considered generalised Richards equation (Eq. (1)) is a

179 pressure head defined for the total water phase (liquid + ice). A similar approach is used for

180 example in Guymon and Luthin (1974) ¹⁴ and Weismüller et al. (2011) ⁵⁶ . The obstruction of the

181 porous medium by freezing is taken into account through a heuristic approach by the multiplication

182 of the classical apparent unfrozen hydraulic conductivity by (Eq. (4)). The

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

For Peer Review

183 used estimator of the actual evapotranspiration is based on the potential evapotranspiration

184 and on the geometry of the evapotranspiration zone ⁴⁸ . The adopted approach consists in allowing

185 actual evapotranspiration whenever and wherever there is enough water in the soil of the

186 evapotranspiration zone in order to satisfy potential evapotranspiration. The only modification done

187 in permaFoam compared to the implementation of Orgogozo (2015) ⁴⁸ is the use of the volumetric

188 liquid water content instead of the volumetric total water content in the computation of the actual

189 evapotranspiration sink term, in order to take into account the freezing of the water phase in the soil

190 pore space of the root zone. Concerning the evaluation of the apparent thermal conductivity of the

191 variably saturated and variably frozen porous medium , we adopt a simple mixture model. ⁵⁷

192 We neglect the thermal dispersion in soils, which is generally small compared to thermal

193 diffusion ¹⁵ . The apparent heat capacity of the variably saturated and variably frozen porous medium

194 is classically evaluated with an arithmetic mean of the heat capacity of each phase. ⁵⁸ One

195 should note here that the air phase is taken into account in the computation of the effective thermal

196 properties of the considered four-phase medium, although Richards assumptions lead to a

197 formulation of water transfers in variably saturated porous media in which the air phase does not

198 appear explicitly. The latent heat exchanges are handled with a simple apparent specific heat

199 method. ^19,59

200

201 2.1.2 Numerical methods

202 We use two Picard loops to deal with non-linearities, one for Richards equation (1) and one for the

203 thermal equation (3), and a sequential operator splitting approach to deal with the couplings

204 between these two equations. Thus at each time step, the water balance (Eq. (1)) is solved first, with

205 a Picard loop to deal with its non linearities, and then the thermal equation (Eq. (3)) is solved with

206 updated effective properties of the porous medium and water fluxes, and also with its own Picard

207 Loop. Since permaFoam is based on OpenFOAM ^® (www.openfoam.com), ⁶⁰ the partial differential

208 equations are solved in 3D by a finite volume method. An empirically based automatic adaptive

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

For Peer Review

209 time step strategy has been implemented, based on the convergences of both of the Picard loops. ⁶¹

210 Additional numerical details (including validations) regarding the resolution of Richards equation

211 (Eq. (1)) with OpenFOAM ^® may be found in Orgogozo et al. (2014a) ³⁵ , and the approaches

212 adopted here to deal with the thermal equation (Eq. (3)) are very similar. The OpenFOAM ^® solver

213 permaFoam implemented in the way described above has been successfully validated in saturated

214 conditions by comparison with 1D benchmark test cases available in the literature, ^55,62 and with 2D

215 test cases in the framework of the international benchmark InterFrost. ³⁸ Further validation and

216 details of permaFoam are given in electronic supporting information (Data S1 and Data S2,

217 respectively).

218 219

220 2.2 Studied site, field data set and estimations of thermo-hydrological forcings

221

222 In this section we describe the thermo-hydrological setting of the Kulingdakan watershed

223 and how we used the acquired data to estimate the fluxes of water and heat to the soil of the

224 catchment slopes.

225

226 2.2.1 The experimental watershed of Kulingdakan

227 The Kulingdakan watershed is situated at 64°17′N, 100°11′E, about 5 km North East of the Tura

228 town, in a continuous permafrost area. It has a roughly rectangular shape (~8 km E-W, ~5 km N-S),

229 and the stream is oriented from East to West, thus it may be divided in two areas of about equal

230 surfaces differentiated solely by their aspects, one north aspected and the other south aspected. The

231 average incline of the watershed slopes is 20%, and the altitude difference between the outlet and

232 the highest point is about 500 m. ⁴⁷ No taliks are known to exist in the Kulingdakan watershed, ⁴²

233 thus one can make the hydrological balance of the watershed on the basis of the meteorological

234 water input only. It is a propitious situation to make a simplified representation of the watershed by

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

For Peer Review

235 two 2D transects (Figure 1), each of them representing a side of the watershed, either for north

236 aspected slopes (NAS) or for south aspected slopes (SAS).

237 The structural differences between the soils of each side exhibit important controls on their thermo-

238 hydrological regimes, ⁶³ and a pedological survey of the Kulingdakan watershed allows to assess this

239 structural variability. ⁶⁴ The soils of this watershed are constituted of two horizons: a mineral

240 horizon (mainly rocky/gravely loam) resulting from the weathering of underlying basalts and,

241 overlaying, an organic horizon composed of the larch, moss and dwarf shrubs litter. These soils are

242 topped by a thick insulating layer constituted of mosses and of lichens. The thicknesses of these

243 layers vary from NAS to SAS. For example, organic soils in SAS have an averaged thickness of 8

244 cm, while in NAS this averaged thickness is 12 cm. The averaged thickness of the moss and lichen

245 layer ranges from 6.5 cm in SAS to 13 cm in NAS. The vegetation cover strongly varies between

246 SAS and NAS, both in terms of aerial biomass (SAS: 3.02 kgC/m ² ; NAS : 1.53 kgC/m ² ) and in

247 terms of Leaf Area Index (SAS: 0.69 m ² /m ² ; NAS: 0.2 m ² /m ² ). The rooting depth also strongly

248 differs between slopes (depth into the mineral horizon: 60 cm in SAS, 10 cm in NAS), although the

249 root biomass is not very contrasted (SAS: 0.44 kgC/m ² ; NAS: 0.55 kgC/m ² ). This high

250 morphological variability of the tree stands between slopes stems from the fact that better insolation

251 in SAS leads to fewer but higher, larger and healthier trees than in NAS (see Figure 1). One can

252 refer to Prokushkin et al. (2018) ⁶⁵ for more details on the vegetation cover of this region.

253

254 2.2.2 Monitoring of soil thermal state and of meteorological conditions

255 In order to characterize the dynamics of the active layers of this watersheds, time series of

256 temperature profiles have been acquired at daily time resolution using TR-52 sensors (T&D Corp.,

257 Japan) both on SAS and NAS (Figure 1) at different depths (top of the moss layer, top of the

258 organic layer, top of the mineral horizon and 10cm and 20cm depth within it) and at an altitude of

259 about 100m above the outlet of the watershed. These time series of soil temperature profiles, along

260 with the meteorological data acquired at Tura (daily measurements), were processed to produce a

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

For Peer Review

261 multi-annual average data set (time window: from 2003 to 2012) of monthly soil temperatures and

262 monthly climatic forcing data (liquid rain water input and potential evapotranspiration) in order to

263 study thermo-hydrological dynamics that are representative of current conditions. We consider

264 monthly averaged data because we are interested in transfers within the soils, which have smooth

265 variations compared to surface transfers. Thus all the results in this work will be presented at a

266 monthly temporal resolution, and all the analysis will be done at this resolution. Note that modelling

267 the transfer in the watershed with a higher temporal resolution would require considering 1)

268 complete surface runoff processes, 2) transfers within the highly conductive moss layer and 3)

269 snowpack dynamics. These issues were beyond the scope of this paper. This data set of multi-

270 annual averages of monthly values is presented in Figure 2, which shows the forcings used as input

271 data for the modelling (i.e.: the data used in order to build boundary conditions and potential

272 evapotranspiration fields).

273 Figure 2A presents for both NAS and SAS the temperatures at the top of the organic layer rather

274 than the surface temperatures (i.e., the temperatures at the top of the moss layer), in order to have

275 thermal input data that characterize the soils itself, encompassing the effects of different radiation

276 dynamics and thermal transfers within the snow packs and the moss layers in each slopes. In Figure

277 2B, the liquid water flux at the top of the organic layer is estimated as the monthly total of the liquid

278 rain (i.e., interception losses are neglected) when the monthly mean temperature at the top of the

279 moss layer (data not shown) is above 0°C. This liquid water flux at the top of the soils is not total

280 rain nor the infiltration flux, but only the part of the rain that falls in liquid state when the frozen

281 ground starts to thaw, and which thus may infiltrate into soils, depending on the hydric status of the

282 considered soil. The part of this top water flux that actually infiltrates is computed depending on the

283 saturation status of each mesh cell of the top boundary at each time step. When the snow pack melts

284 during spring flood, we assume that the entire flux of snowmelt goes directly to the river through

285 surface runoff or flows within the moss layer. This assumption seems reasonable since the spring

286 flood is a fast phenomenon (about two weeks in the end of May – beginning of June) which occurs

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

For Peer Review

287 when the organic (top) layer of the soils is still frozen. Indeed, frozen organic layer hydraulic

288 conductivity is very low while the saturated moss hydraulic conductivity is on the contrary very

289 high, ^66,67 thus the lateral drainage of snowmelt waters through the thick moss layer is likely to be

290 fast compared to the infiltration rate within the still frozen organic layer. However, the snowpack

291 distribution and its rate of melting are controlled by complex phenomena that depend for example

292 on land cover, insolation, and snow depths ^68,69 , which are all variable between NAS and SAS.

293 Moreover, there are field observations of snowmelt waters that infiltrate in the soil of some

294 permafrost affected areas at the very beginning of the spring flood, due for example to frost

295 cracks ⁷⁰ . Although these points were beyond the scope of this study, they merit further investigation

296 to take into account the impact of the spring flood phenomena on the active layer dynamics.

297

298 2.2.3 Estimation of potential evapotranspiration

299 Here, potential evapotranspiration (Figure 2B) has been computed using the Hamon formula, ^71,72

300 which has already been used in studies of forested boreal areas (spruce/moss boreal forest). ⁷³

301 (7)

302 In equation (7), PET d is the daily potential evapotranspiration [mm.d ^-1 ], L d is the daytime length

303 which is the time from the sunrise to the sunset in multiples of 12 hours [12h ^-1 ] (which depends

304 mainly on latitude - data not shown), and T air is the daily mean air temperature [°C] (data not

305 shown).

306 This formula takes into account the temporal but not spatial variations of solar insolation, nor the

307 variations of the land cover. Thus these two effects are taken into account only in the computation

308 of the actual evapotranspiration, through the differences of thermal and hydrological status in each

309 slope, and through the prescribed geometry of the evapotranspiration zone. It means that the

310 considered potential evapotranspirations is the same in NAS and in SAS (although the actual

311 evapotranspirations in NAS and in SAS are different, see section 2.3.3).

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

For Peer Review

313

314 2.3 Modelling set up

315

316 2.3.1 Geometry and properties of the computational domains

317 Each slopes of the watershed, both NAS and SAS, are represented by a 2D transect of 2.5

318 km of length and 20% incline, corresponding to the average sloping in the watershed. This means

319 that we neglect the morphological variability of the watershed along the stream and the lateral

320 fluxes along the direction of the stream axis, and that the small tributaries of the main stream are not

321 considered. The thickness of these transects (from the top of the soil to the bottom of the modelling

322 domain) is fixed to 10m, because it is a common depth of a year-round stable temperature in boreal

323 environments. ⁷⁴ We model only the soil horizons (organic and mineral), without considering the

324 water and energy balances at the surface of the moss layer or the transfers within it. This is justified

325 by the availability of temperature data at the interface between the moss layer and the organic layer

326 and by fast water transfers within the moss layer. Thus we have a simple heterogeneous medium

327 with two layers: the upper organic layer and the underlying mineral horizon, in which we do not

328 differentiate between the secondary clays, weathered basalt and fresh bedrock. The hydrodynamic

329 and thermal properties of these two components of the Kulingdakan slopes have been taken from

330 the literature ^14,75,76 , without any calibration and fitting, and are presented in details in electronic

331 supporting information (Appendix S2).

332

333 2.3.2 Boundary conditions

334 The considered boundary conditions, as well as the geometrical features of the considered

335 modelling domains, are summarized in Figure 3.

336 For the thermal equation (Eq. (2)), we considered a monthly fixed temperature at the top of

337 the domain, equal to the measured value of temperature at the top of the organic layer (see Figure

338 2A). In this way, the thermal top boundary conditions for our simulations already encompass the

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

For Peer Review

339 effects of radiation dynamics and thermal transfers within the snow pack and the moss layer, and as

340 a consequence we do not need to model these complex processes. The bottom boundary condition is

341 a fixed flux boundary condition, with a flux equal to the geothermal flux in the region of the

342 Putorana plateau (0.038 W.m ^-2 ). ⁷⁷ The upslope and the down slope vertical boundary conditions are

343 no thermal gradient boundary conditions.

344 From the point of view of hydrology, we impose a boundary condition of fixed monthly flux

345 equal to the liquid water flux at the top of the organic layer (see Figure 2B) if the upper boundary is

346 unsaturated. In the case of a saturated upper boundary, the infiltration of water is impossible, and

347 then we switch to an atmospheric pressure head boundary condition, so that we can model

348 exfiltration (i.e.: flux of water that comes out of the soil due to subsurface flow). As such, there is

349 no direct and complete modelling of surface runoff, because we are mainly interested in the

350 infiltration of water into the soil necessary for future weathering modelling. A fully coupled surface

351 flow - subsurface flow approach would be needed in order to quantify the total stream flow, but this

352 complex problem ^78,33 is beyond the scope of this study. The bottom boundary condition is a zero

353 water flux, since the rock is completely frozen all year round at 10 m depth (and even much

354 shallower) and since there is no taliks in the watershed. The downslope boundary condition is a

355 hydrostatic boundary condition, taking into account the presence of the stream. Finally, the upslope

356 hydrological boundary condition is a no water flux (i.e. symmetry) boundary condition.

357

358 2.3.3 The efficiency of potential evapotranspiration: field of actual evapotranspiration

359 Since we have a forested and cold environment, we assume that the evapotranspiration flux

360 is due mainly to transpiration by vegetation, and we neglect physical evaporation phenomenon. As a

361 consequence, we identify the evapotranspiration zone and the root zone, whose thickness is

362 different between NAS and SAS. Evapotranspiration water uptake is then assumed to occur only in

363 the root layer, which is developed up to 60 cm depth within the mineral horizon in SAS and up to

364 10 cm depth within the mineral horizon in the NAS. ⁷⁹ The root layer thickness is then the only

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

For Peer Review

365 parameter that is considered here in order to take into account the variability of vegetation

366 morphology between SAS and NAS in the computation of evapotranspiration fluxes. Actual

367 evapotranspiration water uptake is computed for both slopes in each point of this layer and at each

368 time step on the basis (i) of the potential evapotranspiration and (ii) of the thermo-hydrological

369 status of the soil, considering that the evapotranspiration uptake of soil water can occur only in the

370 parts of the root layer in which there is available liquid water (i.e. where pressure head is greater

371 than the wilting point ⁴⁸ and where temperature is above 0°C). The differences in actual

372 evapotranspiration fluxes between NAS and SAS stems from different thermal forcings at the top of

373 the soil (see Figure 2A) as well as different tree covers (and thus different rooting depths).

374

375 2.3.4 Simulated point evolutions

376 In order to sample the inner fields along the computations, observation nodes that record the

377 temperature and water content at each time step of the computations have been implemented at

378 10cm depth and 20cm depth within the mineral horizon at five points regularly disposed along the

379 slopes (see Figure 3A). The second points from the bottom of the slopes (reported in italic green in

380 Figure 3A) are at a position close to the one of the measurement sites in the field, and thus they are

381 used for the comparison between the numerical results and the observations. Besides, having the

382 points regularly disposed along the slopes allowed us to investigate the variability of the thermo-

383 hydrological regime along the slope.

384

385 2.3.5 Initial conditions and spin up

386 The initial conditions have been estimated in the following way. First, an estimate of the

387 spatially averaged mean annual temperature in each slopes have been obtained by a steady state

388 computation of purely diffusive thermal flux in water-saturated slopes. Then these spatially

389 averaged mean annual temperatures have been used as the values of uniform initial temperature

390 fields for a first year of transient modelling of the coupled thermo-hydrological behaviour of the

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

For Peer Review

391 total domains. The initial water pressure head field was fixed to a hydrostatic field in the mineral

392 soil (i.e. fully saturated mineral horizon) and to the field capacity pressure head within the organic

393 layer. Then the values of the temperature and the pressure head fields at the end of the first year of

394 transient modelling have been used as the initial conditions for a second year of transient modelling,

395 and so on until a dynamic equilibrium is reached. We stop the cycling process when we reach a

396 stabilisation of the temperature field (difference between year n and year n+1 at the same dates at

397 the points of sampling lower than 0.1°C), of the total water content field (difference between year n

398 and year n+1 at the same dates at the points of sampling lower than 0.01%) and of the water fluxes

399 across the upper boundary (relative difference between year n and at year n+1 at the same dates

400 lower than 5%). The results of the last year of cycling were considered as steady-state thermo-

401 hydrological dynamic regime in each slope under current climatic conditions, and these results that

402 are presented below.

403

404 2.3.6 Numerical discretisations and precisions of computations

405 The 2D domains are discretised by vertically graded meshes of about 2.5 million cells (cells

406 of thicknesses ranging from 5.10 ^-3 m at the top of the domain to 0.2m at the bottom; constant width

407 of 0.2m; 200 cells over vertical axis; about 12500 cells over horizontal axis). The requested

408 precisions of the linear solvers and of the linearization loops varied along the considered month and

409 the considered slope, because thermo-hydrological regimes were strongly different. They have been

410 established through a careful convergence study, for which we have compared the actual results

411 with those obtained with refined computations with 10 millions mesh cells, 100 times higher

412 resolutions for linear solvers, 10 times higher resolutions for linearization loops, and 10 times

413 smaller maximum time step values. The differences between the actual computations and the

414 refined ones for the temperature and the total water content fields were evaluated at all the

415 numerical probes, and were lower than 0.05°C for the temperature field and lower than 0.001 for

416 the total water content field. The convergence is less satisfactory for the water fluxes across the

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

For Peer Review

417 upper boundary, with an upper bound of 33% in relative difference between actual computations

418 and refined computations.

419

420 2.3.7 Used computational resources

421 The computations have been done by requests of 20 cores to 500 cores (processors: Intel(r)

422 IVYBRIDGE 2,8 Ghz 10-cores) on the CALMIP cluster EOS (www.calmip.univ-toulouse.fr). The

423 provided good parallel capabilities of permaFoam were necessary to achieve computations with

424 such unprecedented spatio-temporal resolutions. A brief assessment of the parallel performances

425 experienced with permaFoam on the EOS cluster is given in electronic supporting information

426 (Appendix S3).

427

428 3. Results

429

430 3.1 Temperature and water contents within the active layer

431

432 A comparison between numerical results and field measurements for the temperature in the mineral

433 soils of both SAS and NAS of Kulingdakan watershed demonstrated a reasonable agreement

434 (Figure 4). These values (either computed or measured) are values at the points of sampling (Figure

435 3). Only comparisons between monthly averaged numerical results and monthly averaged field

436 observations could be done, because the intrinsic simplifications of the modelled domains and

437 phenomena would not allow making relevant analysis at a finer time scale. Besides, a monthly time

438 scale analysis is coherent with our main objective, the study of seasonal dynamics of infiltrated

439 waters.

440 One can see that, as expected, SAS are generally warmer than NAS. The soil temperatures exceed

441 0°C about a month earlier in SAS than in NAS. One can also see the effect of depth on these

442 temperatures, with smaller amplitudes of seasonal variations when depth increases. These features

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

For Peer Review

443 are well reproduced by the numerical modelling. The mean absolute differences are below 1°C for

444 both slopes, with RMSE between measured and computed values of 0.74 °C in NAS and of 1.07 °C

445 in SAS. The variations of thermal regimes observed in north and south aspected slopes are closely

446 related to the variation of hydric states between them.

447 The computed seasonal variations of total water, liquid water and ice contents at the sampling

448 points in both slopes (Figure 5) demonstrated that, as expected, the SAS are dryer and thaw earlier

449 than the NAS. These hydric patterns correlate well with the thermal dynamics observed above.

450 Although the comparison between numerical results and field measurements has only been done on

451 point values, bi-dimensional variability has been detected from the simulations. Thus, temperature

452 profiles along the slope at 20cm depth in the mineral soil in both SAS and NAS are dependent on

453 the distance to the stream (Figure 6).

454 There are strong differences between the top temperature and the near stream temperature both in

455 SAS (3.5°C) and NAS (4.7°C). Nevertheless, an area of low variability may be observed far from

456 the boundaries. The difference of temperature at the bottom of the slopes between NAS and SAS is

457 mainly a numerical artefact due to the separate modelling of each slope. A more realistic

458 geometrical description such as a V-shaped section that represent both slopes at the same time

459 would have enforce temperature continuity at the bottom of the slopes. But one should note that a

460 flat riparian area up to 100m wide exists around the stream at the bottom of the slopes, which gives

461 some consistency to the separate slopes approach adopted here.

462

463 3.2 Water fluxes from south and north aspected slopes

464

465 3.2.1 Evapotranspiration

466 The major water flux outward the soils of the slopes is the evapotranspiration flux. Since the

467 Kulingdakan watershed is almost completely forested and the climate is cold (mean annual air

468 temperature: -8°C), the main component of evapotranspiration is transpiration by trees.

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

For Peer Review

469 Consequently, the actual evapotranspiration should be strongly impacted by tree morphology, for

470 instance by rooting depth, which is highly variable between NAS and SAS. ⁷⁹ In order to analyse the

471 impact of the rooting depth on water fluxes, numerical experiments were performed for different

472 thicknesses of the root layers. The actual results presented in Figure 4, 5 and 6 were obtained by

473 considering in the computations the measured rooting depth in NAS (10cm within mineral horizon)

474 and SAS (60cm within mineral horizon, about the mean value observed in boreal forests ⁸⁰ ). This set

475 of computations and results will be called the Actual Conditions case (AC case) in the subsequent

476 discussion. An additional set of computations has then been done which is completely similar to

477 this previous one, except that a constant 1m rooting depth (equal to the global mean value ⁸⁰ ) has

478 been considered in both NAS and SAS. This second set of computations and results will be

479 designated the Artificially Deeper Roots case (ADR case) below. The comparative analysis of

480 these two sets of computations allows investigating the impact of the rooting depth on water fluxes

481 in boreal forested environments. One can see in Figure 7 the computed actual evapotranspiration for

482 both slopes, for the two sets of numerical computations: actual results with the observed rooting

483 depths (AC case), and the results of the numerical experiment with a constant 1m thick root zone

484 (ADR case).

485 Strongly contrasted behaviours occur in the two sets of computations. The AC case exhibits large

486 differences of actual evapotranspiration between SAS and NAS, due to a faster and stronger

487 increase of active layer thickness in SAS than in NAS. The computed maximum (end of July) active

488 layer thickness is 1.41 m in SAS and 0.62 m in NAS. It should be noted that these numerical results

489 are in good agreement with the field data, which report a 1.22 m maximum active layer thickness in

490 SAS and a 0.58 m maximum active layer thickness in NAS. ⁶⁴ In the ADR case, the maximum active

491 layer thicknesses are almost equal (1.1 m in SAS and 0.9 m in NAS), which drives to smaller

492 differences of actual evapotranspiration between slopes than in the AC case. The resulting

493 differences of hydric regimes between the two set of numerical computations are particularly strong

494 in NAS, which are year round water saturated in the AC case while they experience a drying period

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

For Peer Review

495 (i.e.: time with actual evapotranspiration higher than rain) in summer in the ADR case. This

496 indicates that the rooting depth exerts strong controls on the evapotranspiration fluxes in such

497 forested, permafrost-dominated areas, with important impacts on the thermal and hydrological

498 states in the uppermost layers of the soil. One should note that the field observations of

499 hydromorphism in NAS are in good agreement with the AC case results.

500

501 3.2.2 Exfiltration

502 The other water flux from the soils of the slopes is exfiltration, i.e. the flux of sub-surface

503 water coming out of the soil due to sub-surface flow. Our computations show that the exfiltration

504 flux represents less than 1% of the evapotranspiration flux. The explanation of this huge difference

505 between evapotranspiration and exfiltration fluxes may be that most of infiltrated waters are

506 evapotranspirated before reaching the permafrost table, above which they should flow to feed the

507 exfiltration flux that comes out of the soil through the top surface of the active layer at the bottom

508 of the slopes. Nevertheless the exfiltration is an important flux when considering weathering

509 processes, because the exfiltration exports the matter directly from the soil to the stream. Note that

510 in this analysis we do not take into account snow pack melt and runoff due to rainfalls that exceed

511 infiltration capacity of the soil (hortonian runoff), because in these cases the water comes to the

512 stream as surface flow without getting into the soil. The computed seasonal evolutions of

513 exfiltration flux in SAS and in NAS for both AC case and ADR case are shown in Figure 8.

514 The computed exfiltration rates exhibit in both cases strong differences between NAS and SAS, in

515 terms of both maximum values and seasonal dynamics. The behaviours are also extremely

516 contrasted between AC and ADR cases, both in spatial and temporal location of the maximum

517 fluxes. This shows again the importance of rooting for hydrological processes in the considered

518 environments. In the AC case, a continuous but small exfiltration flux is coming out of SAS all

519 along the active period, while in NAS, the exfiltration flux starts only in June, at the beginning of

520 the active layer thaw, and it experiences a strong increase in August so that the exfiltration flux in

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60