Abstract
In the Lake Chad basin, the quaternary phreatic aquifer (named hereafter QPA) presents large piezometric anomalies referred to as domes and depressions whose depths are ~15 and ~60 m, respectively. A previous study (Leblanc et al. in Geophys Res Lett, 2003, doi:10.1029/2003GL018094) noticed that brightness temperatures from METEOSAT infrared images of the Lake Chad basin are correlated with the QPA piezometry. Indeed, at the same latitude, domes are ~4–5 K warmer than the depressions. Leblanc et al. (Geophys Res Lett, 2003, doi:10.1029/2003GL018094) suggested that such a thermal behaviour results from an evapotranspiration excess above the piezometric depressions, an interpretation implicitly assuming that the QPA is separated from the other aquifers by the clay-rich Pliocene formation. Based on satellite visible images, here we find evidence of giant polygons, an observation that suggests instead a local vertical connectivity between the different aquifers. We developed a numerical water convective model giving an alternative explanation for the development of QPA depressions and domes. Beneath the depressions, a cold descending water convective current sucks down the overlying QPA, while, beneath the dome, a warm ascending current produces overpressure. Such a basin-wide circulation is consistent with the water geochemistry. We further propose that the thermal diurnal and evaporation/condensation cycles specific to the water ascending current explain why domes are warmer. We finally discuss the possible influence of the inferred convective circulation on the transient variations of the QPA reported from observations of piezometric levels and GRACE-based water mass change over the region.
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References
Antoine R, Baratoux D, Rabinowicz M, Fontaine FJ, Bachèlery P, Staudacher T, Saracco G, Finizola A (2009) Thermal infrared images analysis of a quiescent cone on Piton de La Fournaise volcano: evidence for a convective air flow within an unconsolidated soil. J Volcanol Geotherm Res. doi:10.1016/j.jvolgeores.2008.12.003
Arad A, Kafri U (1974) Geochemistry of groundwaters in the Chad basin. J Hydrol 25:105–127
Archambault J (1960) L’alimentation des nappes en Afrique Occidentale. Cpt. R. de l’Hydro., Soc. Hydro. France, 383
Aranyossy J-F, Ndiaye B (1993) Formation of piezometric depressions in the Sahelian zone: study and modelling. J Water Sci. doi:10.7202/705167ar
ASME (1968) The1967 ASME steam tables. Nav Eng J. doi:10.1111/j.1559-3584.1968.tb04564.x
Avbovbo AA, Ayoola EO, Osahon GA (1986) Depositional and structural styles in Chad basin of Northeastern Nigeria. Am Assoc Petrol Geol Bull 70(12):1787–1798
Bader J-C, Lemoalle J, Leblanc M (2011) Modèle Hydrologique du Lac Tchad. Hydrol Sci J. doi:10.1080/02626667.2011.560853
Balmino G, Vales N, Bonvalot S, Briais A (2011) Spherical harmonic modeling to ultra-high degree of Bouguer and isostatic anomalies. J Geod. doi:10.1007/s00190-011-0533-4
Bruinsma S, Lemoine J-M, Biancale R, Valès N (2010) CNES/GRGS 10-day gravity field models (Release 2) and their evaluation. Adv Space Res. doi:10.1016/j.asr.2009.10.012
Byrne GF, Begg JE, Fleming PM, Dunin FX (1979) Remotely sensed land cover temperature and soil water status—a brief review. Remote Sens Environ. doi:10.1016/0034-4257(79)90029-4
Carroll D (1959) Ion exchange in clays and others minerals. Bull Geol Soc Am. doi:10.1130/0016-7606(1959)70[749:IEICAO]2.0.CO;2
Cartwright JA, Dewhurst DN (1998) Layer-bound compaction faults in fine-grained sediments. Bull Geol Soc Am. doi:10.1130/0016-7606(1998)110<1242:LBCFIF>2.3.CO;2
Chapelle FH (2000) The significance of microbial processes in hydrogeology and geochemistry. Hydrogeol J. doi:10.1007/PL00010973
Clauser C, Huenges E (1995) Thermal conductivity of rocks and minerals. In: Ahrens TJ (ed) Rock physics and phase relations: a handbook of physical constants. American Geophysical Union, Washington. doi:10.1029/RF003p0105
Cretaux J-F, Birkett C (2006) Lake studies from satellite radar altimetry. C R Geosci. doi:10.1016/j.crte.2006.08.002
Descloitres M, Chalikakis K, Legchenko A, Moussa AM, Genthon P, Favreau G, Le Coz M, Bouchera M, Oï M (2013) Investigation of groundwater resources in the Komadugu Yobe Valley (Lake Chad basin, Niger) using MRS and TDEM methods. J Afr Earth Sci 87:71–85
Dieng B, Ledoux E, de Marsily G (1990) Paleohydrogeology of the Senegal sedimentary basin: a tentative explanation of the piezometric depressions. J Hydrol 118:357–371
Eberschweiler C (1993) Monitoring and management of groundwater resources in the Lake Chad basin: mapping of aquifers water resource management—final report. R35985, CBLT-BRGM, France
Eldursi K, Branquet Y, Guillou-Frottier L, Marcoux E (2009) Numerical investigation of transient hydrothermal processes around intrusions: heat-transfer and controlled mineralization patterns. Earth Planet Sci Lett. doi:10.1016/j.epsl.2009.09.009
Fontaine FJ, Rabinowicz M, Boulègue J, Jouniaux L (2002) Constraints on hydrothermal processes on basaltic edifices: inferences on the conditions leading to hydrovolcanic eruptions at Piton de la Fournaise, Réunion Island, Indian Ocean. Earth Planet Sci Lett. doi:10.1016/S0012-821X(02)00599-X
Garven G (1995) Continental-scale groundwater flow and geologic processes. Annu Rev Earth Planet Sci 23:89–117
Garven G, Freeze A (1984a) Theoretical analysis of the role of groundwater flow in the genesis of stratabound ore deposits. 1. Mathematical and numerical model. Am J Sci 284:1085–1124
Garven G, Freeze A (1984b) Theoretical analysis of the role of groundwater flow in the genesis of stratabound ore deposits. 2. Quantitative results. Am J Sci 284:1125–1174
Gaston A (1996) The pastoral vegetation of the Lake Chad basin. In: CIRAD (ed) Livestock Atlas of the Lake Chad basin. Centre Technique de Cooperation Agricole et Rurale, Wageningen, pp 39–56
Gay A, Lopez M, Cochonat P, Sermondadaz G (2004) Polygonal faults-furrows system related to early stages of compaction—upper Miocene to recent sediments of the Lower Congo basin. Basin Res. doi:10.1111/j.1365-2117.2003.00224.x
Genik GJ (1993) Regional framework, structural and petroleum aspects of rift basins in Niger, Chad and the Central African Republic (C.A.R.). Tectonophysics. doi:10.1016/0040-1951(92)90257-7
Genthon P, Rabinowicz M, Foucher J-P, Sibuet J-C (1990) Hydrothermal circulation in an anisotropic sedimentary basin: application to the Okinawa Back Arc basin. J Geophys Res. doi:10.1029/JB095iB12p19175
Greigert J (1979) Atlas des Eaux Souterraines du Niger—Tome 1, fascicule VII: La Nappe Pliocène et le système phréatique du Manga, BGRM
Griffin DL (2006) The late Neogene Sahabi rivers of the Sahara and their climatic and environmental implications for the Chad basin. J Geol Soc. doi:10.1144/0016-76492005-049
Guideal R, Bala AE, Ikpokonte AE (2011) Preliminary estimates of the hydraulic properties of the Quaternary aquifer in N’Djaména area, Chad republic. J Appl Sci. doi:10.3923/jas.2011
Guillou-Frottier L, Carre C, Bourgine B, Bouchot V, Genter A (2013) Structure of hydrothermal convection in the Upper Rhine Graben as inferred from corrected temperature data and basin-scale numerical models. J Volcanol Geotherm Res. doi:10.1016/j.jvolgeores.2013.02.008
Gvirtzman H, Garven G, Gvirtzman G (1997) Thermal anomalies associated with forced and free ground-water convection in the Dead Sea rift valley. Geol Soc Am Bull. doi:10.1130/0016-7606(1997)109<1167:TAAWFA>2.3.CO;2
Holzbecher E (2004) Free convection in open-top enclosures filled with a porous medium heated from below. Numer Heat Transf Part A Appl. doi:10.1080/10407780490474726
Idso SB, Schmugge TJ, Jackson RD, Reginato RJ (1975) The utility of surface temperature measurements for the remote sensing of surface soil waters status. J Geophys Res. doi:10.1029/JC080i021p03044
Irvine TF, Duignan MR (1985) Isobaric thermal expansion coefficients for water over large temperature and pressure ranges. Int Commun Heat Mass. doi:10.1016/0735-1933(85)90040-5
Isiorho SA, Matisoff G, When KS (1996) Seepage relationships between Lake Chad and the Chad aquifers. Ground Water. doi:10.1111/j.1745-6584.1996.tb02076.x
Kestin J, Sokolov M, Wakeham WA (1978) Viscosity of liquid water in the range −8 °C to 150 °C. J Phys Chem. doi:10.1063/1.555581
Kilty K, Chapman DS (1980) Convective heat transfer in selected geologic situations. Ground Water. doi:10.1111/j.1745-6584.1980.tb03413.x
Kopf AJ (2002) Significance of mud volcanism. Rev Geophys. doi:10.1029/2000RG000093
Leblanc M, Razack M, Dagorne D, Mofor L, Jones C (2003) Application of Meteosat thermal data to map soil infiltrability in the central part of the Lake Chad basin, Africa. Geophys Res Lett. doi:10.1029/2003GL018094
Leblanc M, Favreau G, Maley J, Nazoumou Y, Leduc C, Stagnitti F, van Oevelen PJ, Delclaux F, Lemoalle J (2006) Reconstruction of Megalake Chad using shuttle radar topographic mission data. Palaeogeogr Palaeoclimatol. doi:10.1016/j.palaeo.2006.01.003
Leduc C (1991) Les ressources en eau du département de Diffa, Projet PNUD-DCTCDNER/86/001/. Direction Départementale de l’Hydraulique de Diffa, Diffa
Leduc C, Loireau M (1997) Fluctuations piézométriques et évolution du couvert végétal en zone sahélienne (sud-ouest du Niger). Sustainability of Water Resources under Increasing Uncertainty. In: Proceedings of the Rabat Symposium S1, IAHS, 240
Luo X, Vasseur G (2002) Natural hydraulic craking: numerical model and sensitivity study. Earth Planet Sci Lett. doi:10.1016/S0012-821X(02)00711-2
Maduabuchi C, Faye S, Maloszewski P (2006) Isotope evidence of palaeorecharge and palaeoclimate in the deep confined aquifers of the Chad basin, NE Nigeria. Sci Total Environ 370:467–479
Mahe G, Leduc C, Amani A, Paturel J-E, Girard S, Servat E, Dezetter A (2003) Augmentation récente du ruissellement de surface en region soudano-sahélienne et impact sur les ressources en eau. Hydrology of the Mediterranean and Semiarid Regions, Proceedings of an international symposium, IAHS, 278
Mainsant G, Jongmans D, Chambon G, Larose E, Baillet L (2012) Shear-wave velocity as an indicator for rheological changes in clay materials: lessons from laboratory experiments. Geophys Res Lett. doi:10.1029/2012GL053159
McKenzie DP, Roberts JM, Weiss NO (1974) Convection in the earth’s mantle: towards a numerical simulation. J Fluid Mech. doi:10.1017/S0022112074000784
Neal JT, Langer AM, Kerr PF (1968) Giant desiccation polygons of Great Basin playas. Bull Geol Soc Am. doi:10.1130/0016-7606(1968)79[69:GDPOGB]2.0.CO;2
Norton DL (1984) Theory of hydrothermal systems. Annu Rev Earth Planet Sci 12:155–177
Nwankwo CN, Ekine AS (2010) Geothermal gradients in the Chad basin, Nigeria, from bottom hole temperature logs. Sci Afr 9(1):37–45
Olivry JC, Chouret A, Vuillaume G, Lemoalle J, Briquet JP (1996) Hydrologie du lac Tchad. Monogr Hydrol 12:266
Olugbemiro OR, Ligouis B (1999) Thermal maturity and hydrocarbon potential of the Cretaceous (Cenomanian-Santonian) sediments in the Bornu (Chad) basin, NE Nigeria. Bull Soc Géol France 170(5):759–772
OSS-UNESCO (2001) Les ressources en eau des pays de l’Observatoire du Sahara et du Sahel: évaluation, utilisation et gestion. Rapport UNESCO, p 88
Pouclet A, Durand A (1983) Structures cassantes Cénozoïques d’après les phénomènes volcaniques et néotectoniques au nord-ouest du lac Tcahd (Niger Oriental). Ann Soc Géol Nord CIII (France), pp 143–154
Pribnow D, Schellschmidt R (2000) Thermal tracking of upper crustal fluid flow in the Rhine Graben. Geophys Res Lett. doi:10.1029/2000GL008494
Quintard M, Bernard D (1986) Free convection in sediments. In: Burrus J (ed) Thermal modeling in sedimentary basins. Editions Technip, Paris, pp 271–286
Rabinowicz M, Boulègue J, Genthon P (1998a) Two- and three-dimensional modeling of hydrothermal convection in the sedimented Middle Valley segment, Juan de Fuca Ridge. J Geophys Res. doi:10.1029/98JB01484
Rabinowicz M, Sempéré J-C, Genthon P (1998b) Thermal convection in a vertical permeable slot: Implications for hydrothermal circulation along mid-ocean ridges. J Geophys Res. doi:10.1029/1999JB900259
Ramillien G, Biancale R, Gratton S, Vasseur X, Bourgogne S (2011) GRACE-derived surface mass anomalies by energy integral approach. Application to continental hydrology. J Geod. doi:10.1007/s00190-010-0438-7
Ramillien G, Seoane L, Frappart F, Biancale R, Gratton S, Vasseur X, Bourgogne S (2012) Constrained regional recovery of continental water mass time-variations from GRACE-based geopotential anomalies over South America. Surv Geophys. doi:10.1007/s10712-012-9177-z
Ramillien G, Frappart F, Seoane L (2014) Application of the regional water mass variations from GRACE satellite gravimetry to large-scale water management in Africa. Remote Sens. doi:10.3390/rs6087379
Roche MA (1980) Traçage naturel isotopique et salin des eaux du système hydrologique du Lac Tchad, Paris
Sabins LF (1999) Remote sensing: principles and interpretation. W. H. Freeman, San Francisco
Schneider JL (1969) Carte hydrogéologique de la République du Tchad, B.R.G.M
Schneider JL, Wolff JP (1992) Carte Géologique et Hydrogéologique à 1/1 500 000 de la république du Tchad. Mémoire explicatif, B.R.G.M
Schroeter P, Gear D (1973) Etude des ressources en eau du bassin du Lac Tchad en vue d’un programme de développement. FAO-PNUD-CBLT, Rome
Schuster M, Roquin C, Duringer P, Brunet M, Cagny M, Fontugne M, Mackaye HT, Vignaud P, Ghienne J-F (2005) Holocene Lake Mega-Chad palaeoshorelines from space. Quat Sci Rev. doi:10.1016/j.quascirev.2005.02.001
Schwinka V, Moertel H (1999) Physicochemical properties of illite suspensions after cycles of freezing and thawing. Clays Clay Miner 47:718–725
Sclater JG, Christie PAF (1980) Continental stretching: an explanation of the post-mid-Cretaceous subsidence of the central North Sea basin. J Geophys Res. doi:10.1029/JB085iB07p03711
Serafeimidis K, Anagnostou G (2015) The solubilities and thermodynamic equilibrium of anhydrite and gypsum. Rock Mech Rock Eng. doi:10.1007/s00603-014-0557-1
Sylvia DM (2004) Principles and applications of soil microbiology, 2nd edn. Pearson Prentice Hall, New Jersey
Turcotte DL, Schubert G (2002) Geodynamics, 2nd edn. Cambridge University Press, Cambridge
Zairi R (2008) Etude géochimique et hydrodynamique de la nappe libre du Bassin du Lac Tchad dans les regions de Diffa (Niger oriental) et du Bornou (nord-est du Nigeria). Ph.D. thesis
Acknowledgments
This research has benefited from the support by the French Space Agency CNES and TOSCA (Terre, Océan, Surfaces continentales, Atmosphère) support. It has also benefited from the support of Commissariat Général au Développement Durable (CGDD) from the French Ministry of Environment, as part of the CEREMA internal research project HYDROGEO. Thanks are due to the “Bureau Gravimétrique International (BGI)/International Association of Geodesy” for providing the EGM model. We thank G. de Marsily and G. Vasseur for their constructive criticisms, and the Editor in Chief for editorial suggestions, which significantly improved the paper. This paper arises from the ISSI Workshop on Remote Sensing and Water Resources.
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Appendices
Appendix 1: Governing Equations, Parameters and Equations of State
The mass conservation equation for a fluid of variable density within a fluid-saturated porous medium (rock matrix) without an internal fluid source is:
where ε is the porosity, ρ f the fluid density (kg m−3), t the time and \(\vec{u}\) the Darcy velocity vector (m s−1). We write \(\vec{u} = (U,V)\), U and V being the fluid velocity component parallel to the x and z directions, respectively. The fluid is incompressible with a constant chemical composition, and its density is temperature dependent.
Darcy’s law is used to describe the fluid velocity field \(\vec{u}\):
where K is the permeability, µ is the viscosity of the fluid, \(\vec{g}\) is the gravity vector and p is the fluid pressure. The fluid density varies linearly with temperature T in °C:
where α is the thermal expansion coefficient and ρ 0 is the fluid density at T 0 = 20 °C, the surface temperature of the model.
Heat transport is achieved by both conduction and advection and is described for an incompressible single-phase fluid by:
where C L is the volumetric heat capacity defined by C L = ρ f C P, C P is the specific heat capacity, C eq and λ eq are the weighted average volumetric heat capacity and equivalent thermal conductivity, respectively, as defined in saturated porous media of porosity ϕ:
where f and s are subscripts for the fluid and the porous matrix, respectively. We assume that C L remains approximately constant, a reasonable assumption since the decrease in density with temperature roughly balances the increase in the specific heat capacity with temperature. The equivalent thermal conductivity is written as:
where λ f and λ s are the thermal conductivities of the fluid and the porous matrix, respectively.
The vertical Rayleigh number Ra characterises the vigour of the convection within the stratified porous medium and is defined as follows:
where K z represents the vertical permeability, g is the acceleration due to gravity, h is the height of the layer and γ is the vertical temperature gradient.
Appendix 2: Parameter values
In our calculations, the parameter describing the temperature dependence, α, follows from the results obtained by Irvine and Duignan (1985). The viscosity of the fluid μ (given in units of Pa s) also varies with temperature, based on the following analytical expression (ASME 1968; Kestin et al. 1978; Rabinowicz et al. 1998a, b):
The pressure dependence of viscosity is not included, because it is small in the range of depth considered here (Norton 1984). Equation (8) shows that the fluid viscosity decreases from 17.5 × 10−5 to 13.5 × 10−5 Pa s in the 2–200 °C temperature interval. Above 200 °C, the viscosity remains approximately constant. In our model, the thermal conductivity λ eq varies with temperature for each type of formation (crystalline rock, sandstone, shale). We used the experimental data provided by Clauser and Huenges (1995) for the thermal conductivities of sandstone, shale and quartz-rich crystalline rock between 0 and 300 °C. Finally, the other parameters such as the porosity ϕ, the heat capacity C of each phase (rock and fluid) and the density of each phase at 20 °C assigned to each geological formation are listed in Table 1.
Appendix 3: Method and Boundary Conditions
The simulations are performed using the Comsol Multiphysics™ finite-element code, which has already been tested and successfully implemented for convective process simulations in various configurations (Holzbecher 2004; Eldursi et al. 2009; Guillou-Frottier et al. 2013). A two-dimensional grid constituted of square elements of size d = 200 m was considered. Thus, given the dimensions of the basin, the grid is composed of 40 elements in the z direction and 1500 elements in the x direction. The ratio 0.8d/V max, where V max represents the maximal amplitude of the Darcy velocity, determines the optimal time step at which the time evolution of the convective process can be realistically simulated.
The top of the model represents the surface topography of the Lake Chad basin, which is impermeable (the vertical velocity at the interface is zero) and maintained at a constant temperature of 20 °C. The bottom of the model consists of a quartz-rich substratum. It is maintained at a constant temperature of 247 °C and has a permeability low enough to be considered as impermeable (~10−18 m2). The flow and temperature along the lateral boundaries of the model are symmetric. All these chosen boundary conditions are the usual ones, except the flow condition along the top interface. Indeed, a real free condition would be mathematically more elegant. The latter condition is needed to adjust the depth of the piezometer (i.e. of the saturated zone) at each iteration, in order to obtain a zero pressure along that interface. That method is particularly costly and difficult to handle, because it does not necessarily ensure the incompressibility of the fluid. Besides, it is not necessarily justified as the depth of variation of the piezometer is small (~60 m) compared to the depth of the basin. Therefore, the pressure perturbation due to convection and surface topography is small in comparison with the lithostatic pressure variations in the basin. Accordingly, in our model, the coincidence of the surface topography with the piezometer results to be an acceptable first-order approximation (McKenzie et al. 1974). Besides, it is extremely cost-effective as it does not require internal iterations between two time steps of the temperature equation. As the program retrieves the pressure after each time step, we can a posteriori compute the height of the piezometer with first-order precision. Because the topography along the borders of the basin is not flat, local flows are generated and eventually combine with those developed by convection. Actually, they have a notable impact on the circulation recovered in the model over the Kadzell and Kanem area (Sect. 2).
Appendix 4: Evaluation of the Hydrological and Thermal Characteristics of Our Model
The maps of the fluid viscosity of the thermal expansion and of the effective thermal conductivity of the basin of our convective model are displayed in Fig. 16a–d. From these maps, we deduce that, within the Bima horizon, at the location of the P1 profile: γ = 57 °C km−1, K = 2 × 10−13 m2, h = 400 m, α = 2.9 × 10−4 °C−1, λ eq = 2.3 W °C−1 m−1, μ = 5 × 10−4 Pa s, and thus, the Rayleigh number is equal to 21 (Eq. 1). Alternatively, around P2: γ = 62 °C km−1, h = 900 m, α = 3.8 × 10−4 °C−1, and μ = 3 × 10−4 Pa s, and the Rayleigh number is equal to 230. Finally, to evaluate the vertical Rayleigh number of the whole basin above faults 5 and 6, we chose the following numbers: γ = 43 °C km−1, K = 10−14 m2, h = 4000 m, α = 2.6 × 10−4 °C−1, k = 2 W °C−1 m−1, μ = 10−3 Pa s, and thus, the Rayleigh number is equal to 31. These numbers indicate that (a) convection likely develops in the Bima horizon outside the block separated by faults 1 and 2, and (b) the basin-wide cell is not split into smaller ones in the graben delimited by faults 5 and 6. Below Kanem, the evaluation of the effective Rayleigh number for the entire depth of the basin is more problematic, due to the permeability variations along the trajectory of the warm current. First, at the eastern border of the basin, the permeability of the contiguous Bima blocks is 2 × 10−13 m2 in a channel extending from 4 km to ~700 m depth. In that channel, the vertical Rayleigh number is ~380 (i.e. much greater than 4π 2) and the mean vertical velocity is 10 cm year−1.
Actually, in a real 3D geometry, hydrothermal convective currents parallel to the walls of the basin may develop (Rabinowicz et al. 1998a, b). Despite the ~150-m-thick Fika formation (located eastward of fault 8, Fig. 3a), the warm current reaches the QPA through the zone of the Fika formation shift induced by throws of faults 7 and 8 (ellipses A and B in Fig. 3a). In the last ~700-m-thick upper sediments, the intensity of the flow remains strong as the mean vertical velocity is ~4 cm year−1. The strength of this warm current explains the intensity of the backflow of the basin-wide convection, which reaches a horizontal velocity of 39 cm year−1 over the Kanem, and down to ~7 cm year−1 at Kadzell. The resulting top pressure drop from Kanem to Kadzell explains the piezometric level topography.
Finally, let us suppose that the ascending and descending convective velocities along the lateral border of the basin-wide cell are constant and have an intensity equal to V. Then, an analytical 1D solution for the steady temperature (Eq. 4) shows that:
and
where Pe represents the Péclet number, which is written as:
In Eqs. (9) and (10), z represents the height in the column of total thickness h, where the flow is ascending or descending, respectively. Over Kanem, +V ~ 4 cm year−1, h ~ 700 m and λ eq ~ 2 W °C−1 m−1 and thus Pe ~ 1.9. If we assume that Pe ≫ 1, we see that:
Alternatively, below Kadzel, where V ~ −4 mm year−1, h ~ 1000 m and λ eq ~ 2 W °C−1 m−1, Pe ~ 0.3. Therefore, assuming that Pe ≪ 1, we see that:
For Kadzell, close to the top of P1 profile, where the axis of the descending current associated with the basin-wide cell is approximatively located, the observed conductive heat flow is ~110 mW m−2 and the convective heat flow is ~70 mW m−2. These values show that the approximation deduced from Eq. (13) is valid. Over the Kanem, close to the top of the P3 profile, the conductive heat flow is ~100 mW m−2 and the convective one is ~200 mW m−2. The approximation given by Eq. (12), which is specifically valid for a fast ascending flow, leads to a good match with this last pair of heat flow values.
In Sect. 2, we emphasise that the mean heat flows at the top of our models are not significantly different when fluids circulate by convection and when the transport of heat at the surface is purely conductive: here 110 mW m−2, instead of 90 mW m−2. Actually, this result can be rationalised as follows. Along the interface of the sediment and the basement, inside the Bima formation, the mean horizontal velocity V of the L ~ 240 km basin-wide cell is ~10 cm year−1. Besides, the temperature contrast ΔT between the descending current along P1 and the basement is ~30 °C (Fig. 10). For a boundary layer approximation of the mean heat flow ϕ along a cooling plate (Turcotte and Schubert 2002):
This expression correctly accounts for the difference of heat flows between the convective and conductive models.
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Lopez, T., Antoine, R., Kerr, Y. et al. Subsurface Hydrology of the Lake Chad Basin from Convection Modelling and Observations. Surv Geophys 37, 471–502 (2016). https://doi.org/10.1007/s10712-016-9363-5
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DOI: https://doi.org/10.1007/s10712-016-9363-5