li 452 A.F.G. Jucrd~.~,A. VerIiocj7Joitr11alof H~clrolog~188-189 (1997)433-452 Boast. C.W. and Robertson. T.M.. 1982. A "micro-lysimeter" method for determining evaporation from bare Journal soil: description and laboratory evaluation. Soil Sci. Soc. Am. J., 46: 689-696. of Choudhuny. B.J. and Monleith. J.L.. 1988. A four-layer model for the heat budget of homogeneous land surface. Q.J.R. Met. Soc., 112: 373-398. Hydrology Garatt. J.R., 1992. The Atmospheric Boundary Layer. Cambridge Atmospheric and Space Sci. Series. 316 pp. ELSEVI ER Journal of Hydrology 188-189 (1997) 453-465 Gates. D.M., 1980. Biophysical Ecology. Springer-Verlag, New York. 61 I pp. Goutorhe, J.-P.. Lebel.. T.. Tinga. A., Bessemoulin. P.. Brouwer. J., Dolman. A.J., Engman. E.T.. Gash. J.H.C., . S., Hoepffner, M., Kabat. P.. Kerr, Y.H.. Monteny. E., Prince. Said, F.. Sellers. P. and Wallace. J.S.. 1991. HAPEX-Sahel: a large scale study of land atmosphere inlemotions in the semi-arid tropics. Ann. Geophys.. 12: 53-64. Hrathcote. A., 1933. The Arid Lands. Longman, London. The correction of soil heat flux measurements to derive an Heusinkveld, B.G.. de Bruin. H.A.R., Verhoef. A.. Anlonysen. F. and Hillc.11. W.C.A.M., 1994. Procedures for reliable eddy covariance mcasurenients of atmospheric heat and C02-fluxes. In: WMO, Instruments and accurate surface energy balance by the Bowen ratio method observing methods. TECEMO. Repon NO. 57. Jacobs. A.F.G.. Van Boxel. J.H. and El-Kilani. R.M.M.. 1991. Nighttime free convection chnracteristics within a Alain Passerat de Silansa'*, Bruno A. ontenyh, Jean Pau Lhommeb plant canopy. Bound.-Layer Mereorol.. 62: 375-387. J 'Cmrro dc Tec11do~qi11-LIFP6. 58050 Joüo Pfwoa.Br(i:il Jakob. M.. 1950. Heat Transfer. John Wiley and Sons. New York. 758 pp. hC~~ttri*ORSTOM (If, h?'t111t/11*/1k/',B.P.P h1Offt/JC/I¡t~~,FrlttIW Kreith. F. and Bohn. hl.S.. 1986. Principles of Hrat Trxisfer. Harper agit1 Row Publishers. New York, 700 pp. 5035. Lebe1.T.. Sauvagcot, H.. Hoepffner, M.. Desbois. M.. Guillo!. B. and Huhcrt. P.. 1097. Rainlilll estilnation in tile Sahel: EPSAT-NICER experiment. J. Hydrol. Sci., 37: 201-215. the J., Lloyd. C.R.. Bessemoulin. P., de Bruin. H.. Cropley. F.. Culf. A.D., Dolm:ln. A.J., Elhers. Moncrieff. J.. Monteny. B. and Verhoef, A.. 1996. A comp;irison of surfice llus II1e:IstIrellletlts during HAPEX-Sahel. A 1)s t r:ict J. Hydrol.. this issue. Massman. W.J.. 1992. A surfine energy bdancr method for p:lrtirioniltg e\~npotrilnspiriIliond;it;l into plilnl illld A method is presented for ca1cul;iting conductive heat nilx ;it the soil surface (G,l)from measured soil coinpoileilts for :I SiIrfilCe with p~tr1i:l~cnn~ipy cilver. Wilter Ilcsc>llrces1:~s.. 2R: 1723- 1731. soil he;lt Ilus (G) sonic centimetres hcnenth the ground surfilce. The niethod does not require Montcith. J.L.. 198 I. Ev;ipor;ltioll ;ind ihc etivirotinietIt. Symp. SOC.13xp. 13it>i.. ICJ: 11i5-23~. cxtilil:liioli of tlicrmill properties ;mtl is valid ror inhonlogeneous soils with regard to their therni;il R:ltlpach. M.R.. 1'192. Dcig :ind drag pmition on rougll surklces. 13o~111cl.-I.;1ycrbletcorol.. 60: 375-395. Shuttleworth. W.J. :ml W:illiice.J.S., IYS.5. Eviipocilion from sparse crop - ;LI1 energy colllhillntiolrtheory. Q.J.R. properties. D:ita froin the ccntriil suh-site ol' the Eastern Super Site cil' the HAPEX-Sahel experimet11 Met. SOC..I I I: X39-855. ilre LIS~LIto illustrntc the nieihod. Finally. the inlluence oc using corrected values of surhice soil hcnt Vrrhorl; A.. Van den Hiirk. D.J.M.. J:wohs. A.F.C. und Ilcusinkvcld. l1.G.. 1095. ~l'l1crt11;tl soil pnipcrtics firr Ilux GI,,r;itlicr t11;tn tiie;isurcd villues (if G. in the energy budget with the Rowen ratio is evnlu:itcd. vineyard (EFEDA-Il :ind (I l.-lPEX-S~hcl)sites. Agric. l;c>r. ~Ictc~irl~l..subinitled. -Flic corrcctiolls liir G ;ire biii;iII ill c;ixe the highly tlifl'usivc hoil lhe Sahel. Errors in J.S.. s;iv;iiiii:1 the of ol' Wallace. Lloyd. C.R. and Siv:ktlln;lr. M.V.K.. 1993. Me;isurcn)eni of soil. ~I;IIII;tot1 toi;ll ev:lpor:ttion from csti111:1til1g I:Itetlt heilt llux with G instcad of GII;ire ncgligihle. I-lowever, c;ilcul;itions show th;lt millet in Niger. Agric. For. Meleorol.. 63: 119-169. [hest err<irSco~ild he nillcll morc important for other soils with lower soil thermal ciiffllsivity.@ 11N7 Henderson-Sellers. A. iind Gornitz. V.. 1l)S.L PossihLe climate imp . l;lll[~ rr;lllsf[)rmarions, Elsevier Science B.V. o11 rropic;il tlelbres~:ition.Clim. Change. 6 23 1-2.is. I.Introduction The I3owcn ratio nicthocl is corninonly u.sctl lo cstitn;tlc scnsihk and iatent hear Iluxcs nt thc Earth's surl':ìcc. 'The method is hnscd on the energy hutlgct equation. Ibt which .soil hc:it Ilux ;ìt the surflice lia\ to hc known. Cotntnon methods for estinialing soil heat llux at the surflice, Glr. include the null-alignriicnt (Kiniholl and Jnck.sot1. 1975). the 1i:trnionic (I-lorton ;uncl Wicrcnga, 1983) nnd the finik difference nv3hod (Balabanis, 1987; Sharratl et al., I992), which arc ;III briscd on soil tempcriiturt mcasurcnientb. The comhinntion method (Fuchs. Massman, 1992) combines - -._ 1986: tcmpcrnturc with heat flux nicasurcments. Soil heat flux nleasurements cannot he mnde directly at the surface because ol' exposure of the sensor to radiation; nor cm they he made very close to the soil surface, because of the nlodification induced by the sensor in moisture tnovetnent. When heat fl ' COI Ic\pl"ldlllg :111t1101. 1997- 00/7-1h~~1/97/Y17.00O El\e\ier Science B.V. AI PII SO022-I694(06)03 187-3 i A. 454 Passerat de Silans al./Jow" of Hydrolog. (1997) A. er 188-189 153-465 Passerar dc Silaits er al./Joenml of tIydro1og.v 185-189 (1997) 453-465 45s beneath the soil surface, the combination method provides a correction yielding estimates Using the following transformations (Nerpin and Chudnovskii (1984). given by Massman of the soil heat flux at the surface. A large number of works conceming sensible and latent (1993)): heat fluxes at the soil surface computed by the Bowen ratio method do not make this correction. They assume that soil heat flux measured a few centimetres into the soil is a (3) good approximation of the actual value at the surface. Although this might be realistic when temperature gradients at the soil surface are small, such as beneath a dense canopy, it win not be for the case of a sparse canopy. this latter being a Kirschoff type transformation, where CL is soil thermal diffusivity, Eq. (2) Temperature-based methods for determining soil heat flux at the surface require becomes knowledge of the volumetric heat capacity as well as of the thermal conductivity of ' the soil. For the combination method, knowledge of the volumetric heat capacity only (4) is needed. Thermal properties of soils are difficult to measure or to estimate. However, in the case of the HAPEX-Sahel experiment, soil thermal diffusivity has been esti- mated for the whole period of intensive observations (TOP) at a subsite of the Eastern I with Central Super Site, by Passerat de Silans et al.. (1996). Their work shows vertical inhomogeneity in soil thermal properties in the 0-0.25 m layer, and therefore com- mon methods for surface soil heat flux estimation are not applicable. Inhomogeneity of the thermal properties is caused by variation in bulk dry soil density and soil Mere, single and double primes indicate respectively the first and second derivative with moisture. In that study, no attempt was made to relate soil thermal diffusivity to 'respect to depth. The product AC is the so-called thermal admittance. Subscript zero in soil moisture because water content profiles are unknown in the upper soil layer (0- Eq. (4) indicates properties for the soil surface level. 0.025 m). I Assuining = O, Eq. (4) is transformed in the transient heat conduction equation for The purpose of this paper is to propose an analytical method for estimating the soil constant thcrninl properties with dopth, taking its values at the soil surface: heat flux at the surface, Go. when soil heat flux is measured at a depth :, and to examine the consequences of correcting the soil hcnt flux on the latent heat fluxes. The proposed method is applicable in inhomogcncous soil, i.c. when thernial propor- ties vary with depth, and does not require the knowledge of thcrnlol properties. Variation of the thermal properties in the uppcr soil laycr is very difficult to estirnate bccausc of the link between thcrmnl propertics and soil water content. f+r t11~pro- posed method, only tenipcrnture mcasuremcn~sat the sanie depth :where the heat flux plate is placed and at the soil surface arc neccssary. Datu collected during thc that HAPEX-Sahel IOP at a grass layer in the snvannll site arc ttsed ror the purposc. 2. Tlieoretical background The transient heat conduction equation is whore T' is dcfincd hy .I X where C is the volumelric heat capacity (J ni-' K-'), and the thermal conductivity and x (W III-' KI). Considering that both these paramcters are depth dependent, Eq. (1) gives C' x' C'2 X'C' c"c-c,2 yx-x" Wd3= (c+J -4 (c'+=) +4 ( c' + The invcrted ratio of thermal admittance in dation to the expression of variable r *ì--- 4 eoi 451 4 456 A.