INVERSE ESTIMATE OF SOIL PARAMETERS AND SURFACE ENERGY BUDGET FROM IN SITU MEASUREMENTS

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1 INVERSE ESTIMATE OF SOIL PARAMETERS AND SURFACE ENERGY BUDGET FROM IN SITU MEASUREMENTS KUN YANG, TOSHIO KOIKE Departent of Civil Engineering, Univerity of Toyo, Hongo 7-3-, Bunyo-u, Toyo , Japan BAISHENG YE Cold and Arid Region Environental& Engineering Reearch Intitute, Chinee Acadey of Science, Lanzhou, China Baed on eaily eaurable variable in field experient, thi tudy develop a yte to inverely etiate oil paraeter and urface energy partition. The yte conit of a forward odel to iulate land urface and uburface procee, an invere odel to decribe the dicrepancy between eaured and odel-predicted value of oil oiture and teperature, and an optiization chee to find the global iniu of the dicrepancy. The optiized paraeter include oil layer diviion, oil hydraulic and theral paraeter, and the oil urface evaporation reitance. Application of thi yte with ynthetic data and field-collected data indicate that the optiized value of odel paraeter i not very enitive to odel error, and i able to etiate the theral conductivity and the oil evaporation reitance. But the optiized hydraulic paraeter ight diagree with experiental reult, becaue the forer repreent the ean propertie of the oil layer while the latter repreent the propertie of a all oil aple. In addition, the ethod can produce reaonable urface energy budget by ean of yntheizing variou obervation. INTRODUCTION In recent year, any field project were ipleented to addre hydrological cycle and land-atopheric interaction. Thee experient uually eaured turbulent heat and water vapor fluxe by the eddy-correlation technique, which are often unatifactory due to low energy cloure ratio, a entioned in any tudie [e.g. Nie et al., 99]. In contrat to turbulent quantitie, ean variable can be eaily eaured with high accuracy. Since the turbulent heat fluxe are trongly controlled by oil condition, the proble to reproduce the eaured value of oil variable by a odel ight be the ae a that to reproduce the turbulent fluxe. Thi peculation otivate u to develop a yte that can well reproduce the eaured oil oiture and teperature, and equentially generate reliable turbulent fluxe. However, it i rather difficult to fully calibrate a land urface odel, becaue there are any odel paraeter affecting oil variable and oe paraeter lie oil hydraulic propertie have a quite large variability fro ite to ite. Many early tudie inverely etiate the oil hydraulic paraeter baed on eaured oil water potential and oiture [Kool and Parer, 988; Tooran

2 and Wierenga, 99; Parin et al., 995], while few tudie inverely etiate oil theral paraeter [Nir et al., 99; Hopan, et al., ]. We propoe an invere yte to iultaneouly etiate oil hydraulic paraeter, theral paraeter, and other odel paraeter fro field-collected data. The invere yte conit of a forward odel (land urface odel) to predict oil oiture and teperature profile, an invere odel to expre the dicrepancy between oberved and odel-predicted value of oil oiture and teperature. The yte will be applied to idealized cae and to two ite on the Tibetan Plateau. FORWARD MODEL: A SINGLE-SOURCE LAND SURFACE MODEL A ingle-ource odel doe not ditinguih the contribution of turbulent fluxe fro the vegetation and the one fro the ground. Yang et al. [4] indicate that thi concept hold if the urface i covered with pare and hort vegetation. Baed on thi concept, we propoe a land urface odel a follow. Surface flux paraeterization The turbulent fluxe are calculated by: H E = Θ Θ g a = ρ c p () ra q ( T ) rh q g a ρ () ra + r rh = exp( ψ g / R T ) (3) g w g where ra ( - ) i the heat tranfer reitance, and r ( - ) i the urface reitance for evaporation. rh i the equilibriu relative huidity near the urface of the oil. All other quantitie have their coon eaning. The aerodynaic reitance r a i calculated fro flux-profile relationhip that follow Monin-Obuhov iilarity theory [Yang et al. ]. The oil reitance r i a function of the oil type, which ut increae with drying of the urface oil layer. [ c c θ θ ) /( θ θ )] r = exp ( (4) fc r r where c and c are two coefficient depending on the oil type. θ fc ( 3-3 ) i the urface oil water content, θ ( 3-3 ) i the aturated water content, and θ r ( 3-3 ) i the reidual water content correponding to oil water potential. Soil water flow Soil oiture iulation follow Richard Law: θ ψ ( θ ) K( θ = K ( θ ) ) t z z z (5)

3 3 b+ 3 K ( θ ) = K ( θ / θ ) (6) b ψ ( θ ) = ψ ( θ / θ ) (7) where t () i the tie, z () i the oil depth, K (θ ) ( - ) i the oil hydraulic conductivity, ψ (θ ) () i the water preure head. K and ψ are hydraulic paraeter. Soil theral flow The teperature profile i governed by the theral diffuion equation: ρ c T t T = λ z z (8) where T (K) i the oil teperature, ρ (g -3 ) i the oil bul denity, the pecific heat capacity, λ (W - K - ) i the theral conductivity. The oil heat capacity i calculated by c (Jg - K - ) i ρ c = ρd cd + ρ wcwθ (9) ρ w c w = 4.95 J K () ρ ( / ) J K () d c d = d w where ρ d (g -3 ) i the bul denity of a dry oil, cd (Jg - K - ) i the pecific heat capacity of the dry oil, and ρ w (g -3 ) i the denity of water. The theral conductivity follow the following forula: λ = λd + ( λ λd )exp[ T ( θ / θ )] () λ =.35ρ ) /(7.947ρ ) (3) d ( d d where λ d (W - K - ) and λ (W - K - ) are the iniu and axiu oil theral conductivity, repectively. T i a coefficient and ha a value of.36 for noral oil, but ay be different for a oil with high content of organic atter. INVERSE MODEL In general, an invere proble can be decribed a finding a et of paraeter to iniize a cot function. In thi tudy, the function i defined a F = F + T (4) F T = t n F θ n T t n W n T = i = T [ T i p ( t, z ) T i ( t, z )] (5)

4 4 F θ = t n nθ tn W θ n θ = i = [ θ ( t, z i p ) θ ( t, z )] i (6) where t n i the nuber of eaureent over tie, n θ and n T are the nuber of oil oiture and teperature eaureent over pace, repectively. i the enor index, z i it correponding poition. θ ( t, z) and T ( t, z) are the eaured oil oiture p p and teperature at tie t, repectively, and θ ( t, z) and θ ( t, z) are the one predicted by the forward odel. F θ and FT denote the dicrepancy between oberved and odelpredicted value of oil oiture and teperature, repectively. WT and W T θ are weight nuber uch that the dicrepancy of the oil oiture and that of the oil teperature contribute equally to the cot function F. Epirically, we give z / z W T = nt 4 and W θ = 5. Thi tudy adopt the Shuffled Coplex Evolution ethod developed at The Univerity of Arizona (SCE-UA) [Duan et al., 99] to find the global iniu of the cot function. Table. Optiized odel paraeter Hydraulic paraeter K K f ( and ), f ( and )] Theral paraeter Soil urface reitance * [ K in K ax * [ fψ ( andin), fψ ( andax * [ fb( clayin ), fb( clay) ax ψ ψ )] b b ] λ λ [ fλ (), fλ ()] T * T [.,.] c c [6, ] c c [,] * The four function with ateri follow Coby [984] and Johanen [975]: and f ( and) = K f ( and ) =. ψ.88.3and f b ( clay) = clay f λ ( q c ) =.5 θ (7.7 qc. ) qc θ where, and q denote and, clay and quartz content in the dry oil, repectively. and clay c A hown in above ection, there are any paraeter in the forward odel. In order to reduce coputational cot, we identify the paraeter in Table for the optiization. The input data of the yte include in itu eaured eteorological condition, oil oiture and teperature profile. The eteorological data are routinely eaured at autoatic weather tation (AWS); and oil oiture and teperature are eaured by a oil oiture and teperature eauring yte (SMTMS). The SMTMS conit of

5 5 high accuracy teperature enor (~.K) and TDR (tie doain reflectoetry) oiture enor (~.3), and ha ulti-level eaureent and a high apling frequency. CASE STUDIES WITH SYNTHETIC DATA.E-5.E-6 (a) h ydrau lic conductivity.5 (b) retention curve H ydraulic conductivity( - ).E-7.E-8.E-9.E-.E- fo rw ard, to p.e- invere,to p.e-3 fo rw ard, bo tto.e-4 invere,bo tto.e W ater content( 3-3 ) forw ard,to p invere,to p forw ard,botto invere,botto.. W ater content( 3-3 ) P re u re h e ad ( ). (c ) ther alconductivity 3 (d)urface evaporation reitance Theralconductivity(W - K - ).5. forw ard,to p.5 invere,to p forw ard,botto invere,botto oilre itan c e ( - ) fo rw ard invere W ater content( 3-3 ) W ater content( 3-3 ) Figure. Coparion in oil hydraulic and theral propertie between the true value and the optiized value in idealized Cae 5 (a) Senible heat flux (b) Latent heat flux 4 5 Accurate (W - ) 3 Accurate (W - ) Optiized (W - ) 5 5 Optiized (W - ) Figure. Coparion in the enible heat flux and latent heat flux between the true value and the optiized value in idealized Cae In thi ection, tudie with ynthetic data are ued to how the applicability of the invere ethod. We aue that a.5 deep tan contain oil with three layer; the topoil i a typical and and the botto oil i a typical clay loa, between which i a

6 tranitional layer; the botto of the tan i ipereable and adiabatic. The oil i ubject to a wetting proce in the firt day and a drying proce in the following nine day. The forward odel generate oil oiture and oil teperature profile, and their value are eaured at ix level (.5,.,.,.3,.4, and.5) every in. Thee data are ued a the input of the invere odel. To tet the robutne of the invere ethod, we deign two cae tudie that have different eaureent error. Cae i applied to howing the enitivity of optiized value to the odel reolution. The forward odel ue a fine reolution with 4 grid and tie tep to generate eaured data, while the invere odel ue a coare reolution with grid and tie tep to optiize paraeter. Cae i ued to how the enitivity of optiized value to the choice of the hydraulic odel. The invere odel till ue Eq. (6-7) that were propoed by Clapp and Hornberger [978], while the forward odel ue the Muale-Genuchten relationhip [98]. Fig. how the coparion in the paraeter value between the truth and the optiization in Cae. The optiized value of oil hydraulic conductivity, water retention and theral conductivity are quite cloe to the true one. The optiized urface evaporation reitance i le than the true one for θ <., but the difference doen t caue ignificant difference in evaporative flux becaue thi flux becoe quite all in thi ituation. Siilar concluion can be drawn fro Cae (not hown). Fig. how the coparion in the enible heat and latent heat between the optiization and the truth in Cae. It indicate that urface energy partition i not everely changed by the all paraeter inconitence. In Cae, the accuracy of the iulated energy budget i even better than that in Cae (not how). CASE STUDIES WITH IN SITU DATA The data were collected at two ite in the central Tibetan Plateau: Anduo (Lat. 3.4ºN, Lon ºE, Elev. 47), and Naqu (Lat ºN, Lon. 9.9ºE, elev. 458). Intenive obervation were carried out at Anduo during May-Sepeteber 998 and at Naqu ite fro Septeber to Augut. The optiized paraeter are evaluated below. Soil hydraulic propertie Fig. 3 how the experiental and optiized retention curve and the iulated water content at Anduo. The retention curve for the top layer i far deviated fro the experient while that for the deep layer i agreeable with the experient (Fig. 3a). The water content iulated with the optiized paraeter alway agree with the obervation, even during the 3 day beyond the optiizing period, while the water content iulated with the experiental paraeter i uch lower than the oberved one near the urface (Fig. 3b). Thee reult indicate that the optiized paraeter characterize the uburface water flow better than the experiental paraeter do. The reaon i that the optiized paraeter repreent the ean propertie of the oil layer, 6

7 while the experiental paraeter are deducted baed on all oil aple and thu their repreentativene ight be quetionable if the oil layer i not hoogeneou. Soil theral propertie Fig. 4 how the conitency between the oberved and optiized oil teperature at Anduo ite during Augut -, a tie beyond the optiization duration, indicating that the theral conductivity i indeed retrieved by thi ethod. Surface energy budget Fig. 5a and 5b how that the optiized heat flux i agreeable with the direct eaureent, and the optiized latent heat flux i alo cloe to that derived fro the Bowen ratio ethod at Anduo ite. Thi coparion in urface energy budget ugget that the invere ethod indeed provide a reaonable etiate to the turbulent fluxe and the urface oil heat flux. Siilar concluion can be drawn fro the reult at Naqu ite. 7 Water content(3-3, %) (a) retention curve 5c exp. 5c exp. c exp. c exp. 6c exp. top opt. botto opt... Preure head () Water content ( 3-3 ) (b) water content at 4c depth 4c ob 4c exp+i 4c opt+i Tie(day) Figure 3. Coparion in retention curve and water content between the field obervation, the laboratory experient, and the optiization at Anduo ite 95 9 (a) oil teperature at Anduo ite 5c ob c ob c ob 5c opt c opt c opt T (K) Day of Augut, 998 Figure 4. Coparion in oil teperature between the eaureent and the iulation at Anduo ite

8 8 4 (a) Senible heat flux 5 (b) Latent heat flux 3 4 Optiized (W - ) Optiized (W - ) Obervated (W - ) Bowen ratio-derived (W - ) Figure 5. Coparion at Anduo ite (a) enible heat between optiization and eaureent, and (b) latent heat between optiization and profile-paraeterized one CONCLUSIONS Thi wor develop an invere yte to tudy the urface and uburface procee. The yte ha three ditinct feature copared with early tudie. Firt, it conider the interaction between oil theral proce and hydraulic proce. Second, it can be applied to field experient that ay contain variou uncertaintie. Third, thi yte can not only retrieve the odel paraeter but alo yield reaonable urface energy budget. REFERENCES [] Clapp R.B. and Hornberger G.M., Epirical equation for oe hydraulic propertie, Water Reour. Re., 4 (978), [] Duan Q., Soroohian S. and Gupta V. K., Effective and efficient global optiization for conceptual rainfall-runoff odel, Water Reour. Re. 8 (99), 5-3. [3] Hopan J. W., Siune J. and Britow K. L., Indirect etiation of oil theral propertie and water flux uing heat pule probe eaureent: Geoetry and diperion effect, Water Reour. Re., 38 (), U77-U9. [4] Johanen O., Theral conductivity of oil, Ph.D. thei, Trondhei, Norway, (CRREL Draft tranlation 637, 977), 975. [5] Kool J. B. and Parer J. C., Analyi of the invere proble for tranient unaturated flow, Water Reour. Re., 4 (988), [6] Mihra S. and Parer J. C., Paraeter etiation for coupled unaturated flow and tranport, Water Reour. Re., 5 (989), [7] Nie D., Kaneau E. T., Fritchen L. J., Weaver H. L., Sith E. A., Vera S. B., Field R. T., Kuta W. P. and Stewart J. B., An intercoparion of urface-energy flux eaureent yte ued during FIFE 987, J. Geophy. Re., 97 (D7) (99), 8,75-8,74. [8] Nir A., Doughty C. and Tang CF, Validation of deign procedure and perforance odeling of a heat and fluid tranport field experient in the unaturated zone, Adv. Water Reour., 5 (99),

9 [9] Parin G. W., Kachanoi R. G., Elric D. E. and Gibon R. G., Unaturated hydraulic conductivity eaured by tie doain reflectoetry under a rainfall iulator, Water Reour. Re., 3 (995), [] Siune J. and van Genuchten M. T., Etiating unaturated oil hydraulic propertie fro tenion dic infilitroeter data by nuerical inverion, Water Reour. Re., 3 (996), [] Tooran A. F., Wierenga P. J. and Hill R. G., Paraeter etiation of hydraulic propertie fro one-tep outflow data, Water Reour. Re., 8 (99), [] van Genuchten M. T., A cloed-for equation for predicting the hydraulic conductivity of unaturated oil, Soil Sci. Soc. A. J., 44 (98), [3] Yang, K., T. Koie, H. Fujii, K. Taagawa, and N. Hiroe, Iproveent of urface flux with a turbulence-related length, Q. J. R. Meteor. Soc, 8(), [4] Yang K., Koie T., Ihiawa H. and Ma Y., Analyi of the Surface Energy Budget at a ite of GAME/Tibet uing a Single-Source Model, J. Meteorol. Soc. Jpn., 8() (4). 9