The Impact of Soil Freezing/Thawing Processes on Water and Energy Balances

ADVANCES IN ATMOSPHERIC SCIENCES, VOL.28, NO.1, 2011, 169-177The Impact of Soil Freezing/Thawing Processeson Water and Energy BalancesZHANG Xia*1 (张霞) and SUN Shufen2 (孙菽芬)1 Key Laboratory of Regional Climate Environment Research for Temperate East Asia,Institute of Atmospheric Physics, Chinese Academy of Science, Beijing 100029'Siate Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics,Institute of Almospheric Physics, Chinese Academy of Science, Bejing 100029(Received 25 November 2009; revised 6 April 2010)ABSTRACTA frozen soil parameterization coupling of thermal and hydrological processes is used to investigate howfrozen soil processes afect water and energy balances in seasonal frozen soil. Simulation results of soil liquidwater content and temperature using soil model with and without the inclusion of freezing and thawingprocesses are evaluated against observations at the Rosemount field station. By comparing the simulatedwater and heat fluxes of the two cases, the role of phase change processes in the water and energy balances isanalyzed. Soil feeing induces upward water flow towards the freeaing front and increases soil water contentin the upper soil layer. In particular. soil ice obviously prevents and delays the infiltration during rain atRosemount. In addition, soil freeing/thawing processes alter the partitioning of surface energy fuxes andlead the soil to release more sensible heat into the atmosphere during freezing periods.Key words: frozen soil, water and energy balances, freexing/thawing processes, surface fuxCitation: Zhang, X., and S. F. Sun. 2011: The impact of soil freezing/thawing processes on water andenergy balances. Adv. Atmos. Sci, 28(1), 169 -177, doi: 10.1007/s00376-010-9206-0.1. Introductionergy balance and the partitioning of sensible and la-tent heat fuxes. which affect atmospheric boundaryThe area of frozen soil including permafrost andprocesses, regional circulation (Gao et al., 2005), andseasonal frost accounts for about 20% of Earth's landregional climate (Poutou et al.. 2004). Romanovskyarea (Peixoto and Oort. 1992). First, soil freezing pro-and Osterkamp (2000) showed that unfrozen water incesses efficiently dampen large temperature variationsthe freezing and frozen active layer and near-surfacefrom the surface down to the deep soil layer due to permafrost also protects the ground from rapid coolinglatent heat of phase change (Luo et al.. 2003); on theand creates a strong thermal gradient at the groundother hand, since the thermal conductivity of ice is foursurface that increases the heat fAux out of the ground.times larger than that of water and the heat capacity Boone et al. (2000) included the freezing in a Soil-of ice is one half that of water. frozen soil with high iceVegetation-Atmosphere transfer scheme and found ancontent will transport heat quickly due to the higher improvement in surface termperature and soil temper-thermal conduetivity compared to soil with an equiva-ature and the overall surface fAux prediction. There-lent liquid water content and lower soil thermal storagefore, it is significant to investigate the impacts of freez-capacity, which means the soil temperature will change ing/thawing processes on water and energy balances ingreatly. By decreasing soil hydraulic conductivity, thiscold regions, for weather forecastine and regional cli-will also block the liquid water flow in frozen soil andmate s中国煤化Ivestigations havechange soil water content (Cherkauer et al.. 1999).whollyhe present studyHSoil temperature and moisture infuence surface en-provide. CNM H G quaifatco oft*Corresponding author: ZHANG Xia, zhangx@tea.ac.cn回China National Committee for International Association of Meteorology and Atmospheric Sciences (IAMAS), Institute of AtmosphericPhysics (IAP) and Science Press and Springer-Verlag Berlin Heidelberg 2010.170IMPACT OF SOIL FREEZING/THAWING PROCESSESVOL. 28how freezing/thawing processes afect the energy and (Harlan, 1973):water balance in cold regions.In this paper, we use a one-dimensional (1-D)品(C.T)=2(眾)+LP.Ot ,(2)frozen soil parameterization which couples the ther-mal and hydrological proceses (Zhang et al, 2007) to where C。is efective volumetrie heat capacity of theexamine the effect of frozen soil processes parameter-soil (J m-3。C-1), Li is the latent heat of fusionization on simulated soil water and energy balances.(J kg-1), and入is the thermal conductivity (WSimulation results using a soil model with and with-;_180paramneterized using the modified methodout the inclusion of freezing and thawing processes areof Johanson (1975) (Farouki, 1981, 1986; Peters et al.,evaluated by using observational data from the Univer- 1998).sity of Minnesota Rosemount Agriculture ExperimentNeglecting soil water osmotic potential, the rela-Station in seasonally frozen soil region. We then focustionship of soil matric potential and temperature inon dscussing the diferenre in simulated water and en- frozen soil, rferred to as the fezing point depressionergy balance components between these two cases toequation, can be written as (illams, 1967):quantify the infuence.ψ=LqT(3)2. MethodologygTowhere g is the gravitation (m s~ 2), T is soil temper-2.1 Brief model descriptionature (°C), and To is the freezing point of free waterA 1-D frozen soil model with numerical stability, (273.16 K).mass- and energy-conservation, and coupling of ther-The constitutive relationship between matric po-mal and hydrological processes has been developed tential and liquid moisture content in unfrozen soilby Zhang et al. (2007). The model is based on the (Clapp and Hornberger, 1978) is used in frozen soilmixed-form Richards' equation and Fourier equation, in this paperand a new modified Picard iteration scheme is ex-tended to solve the implicit difference scheme of theψ=咖o(4)Richards' equation with phase change. The mixed-where 4o is saturated matric potential (m), Osat is theform Richards' equation used to describe the verticalsaturated water content (m3 m-3), and b is the Clapp-profile of soil moisture in a frozen or unfrozen soil zoneHornberger constant.is accomplisbed by combining Darcy's Law and theIn this frozen soil parameterization, the Clapp-conservation of mass, and is given as (Flerchinger andHornberger relation for unsaturated hydraulic conduc-Saxton, 1989; Hansson et al., 2004):tivity K in unfrozen soil is modified following Jameand Norum (1980) by considering the impedance of06__ ρ00;_ 8 (-K型+K)the ice to liquid moisture fow in frozen soil:otρot 0zD心\K= 10-E0Ksae( )(5)10 (Drv0)+ Dov，(1)ρzVz)Here, Ksgat is the saturated hydraulic conductivity ofunfrozen soil (ms~ ) and E; is an dimensionless empir-where A and 0; are volumetric liquid water content ical constant for the impedance from jice and is givenand ice content (m3 m-3), t is the time (s), p1 and piby an empirical equation (Shoop and Bigl, 1997):are the densities of liquid water and ice, respectively(kg m-3), Z is the soil depth (m), K is soil bydraulicE= (K(Ksat-3)2 +6，(6)conductivity (ms- "), T is soil temnperature (°C), ψ iswhere Ksat is in centimeters per hour.soil matric potential (m), Drv is thermal vapor difur-sivity (kg m-2 s~1) due to temperature gradient, andThe upper boundary condition for Eq. (1) on aDvv is the vapor difusivity (kg m-1。C-1 s-1) duebare soil surface is given by the vertical moisture fAuxto soil matric potential gradient. The three terms on 90 (ms5+ and isdefind阳中国煤化工the right hand side of Eq. (1) are phase change rate,(7)liquid water fux, and net vapor fux into a soil layer,YHCNMHGrespectively.where E IS evaporation rate (m s-'), Up is rainfall rateThe heat balance equation with water phase (m s-1) on the soil surface, and Rs is surface runoffchange in soil used in this model can be written as fux (m s-1).NO. 1ZHANG AND SUN171The upper boundary condition for Eq. (2) on aTwo basic simulations were performed with andbare soil surface is given by the ground heat fux G without frozen soil parameterization using observa-(W m-2) and is defined astions from the University of Minnesota RosemountG= ρCTp(Up- R)+R-H.-pLvE，(8)Agriculture Experiment Station (Zhang et al, 2007),to show the difference in soil water and energy bal-where C1 is volumetric heat capacity of liquid water (J ances due to soil freezing/thawing processes. For sim-m-3°C-1), Tp is the temperature of rain (°C), Rn is plicity in presentation, we relfer to the soil model runsnet radiation Aux (W m~), H。is sensible heat fux (W with and without feezing-thawing proceses as the FTm-), and pLIvE is latent heat fAux from evaporation model and NOFT model.(Wm-2). The term pCTp(Up- R)inEq. (8)rep- 2.3 Station descriptionresents the heat fux due to rain infltration (W m- 2).The sensible and latent heat fuxes are calculated im-The Rosemount Station is located approximatelyplicitly in each time step using Monin-Obukhov theory30 km south of St. Paul, Minnesota (44°43°N,and are expressed as93°05°W, 290-m elevation). All measurements weremade at the center of a relatively fAat, 17-hm2 farmH。=paCpT.-T. ,(9) field. Available meteorological data for this site in-Taclude air temperature and relative humidity, windPa. 9。-9a .speed, incoming and outgoing short-wave and long-ρ1raw +rswave radiation fuxes, net radiation fAux, and precipita-where Pa is the density of air (kg m' -3), Cp is specifiction at 30-min time increments. Observational groundheat of air (J kg-1 °C-1), T, and T。are temperaturessurface temperature, soil temperature, and volumetricof the top soil layer and of air at the reference height,liquid water content (5-, 10-, 16-, 20-, 31-. 48-, 65-, andrespectively (°C), 9s and 9a are specifc humidities of100-cm depths) are available at same times. Unfortu-air at the soil surface layer and at the reference height,nately, sensible and latent heat fuxes and ground heatrespectively, r'ah and raw are aerodynamic resistancesfux were not measured. The soil is silt loam and thefor heat fux and evaporation, respectively (s m-),soil parameters used in this simulation are the sameand rs is soil resistance (s m-1). The soil resistance isas in Zbang et al. (2007).calculated using the empirical formula from Sellrs et3. Results and discussional. (1992):rs = exp (8.2 - 4.2250/0sat) .(11) 3.1 Soil temperature and water content 8imu-lationFor the lower boundary conditions, the gradientsof temperature and matric potential are both equal toSince this frozen soil model does not include a snowzero. However, the gravitational flow still exists for component, in this section, we only evaluate the sim-water Aux at the lower boundary.ulation before 21 November 1996, when there was noThe discretisation of the above equation and thesnowfall occurring and precipitation was taken to beapproaches to its numerical solutions are described in rain, as the air temperature was above 2.2C (Yangetdetail in Zhang et al. (2007).al, 1997). Figure 1 shows observed air temperatureand precipitation during the simulation period from 92.2Model setup and experimental designOctober to 9 December. During the evaluation periodThe frozen soil model is compcsed of 10 layers. with (ie., before 21 November), two frost events ocurredthe topsoil layer thickness of 1 cm. In the simulation Figure 2 displays half-hourly observed and simulatedstudy, we set up the layers so as to align the midpointssoil temperature and volumetric liquid water contentof the layers with the observation depths for easy com-at various depths with and without frozen soil param-parison. The botton boundary position is placed at a eterization. Simulated soil temperatures using the FTdepth of 6 m. Initial soil water content and tempera model are in good agreenent with observed values.ture profiles were estimated by interpolation from the Simulated diurnal variation of temperatures in the topmeasured values. Simulations were run with a time soil layers using the NOFT model are higher thanstep of 30 min.those using the FT model during the nighttime freez-Because of errors in simulated snow thermal con-ingan中国煤化工In the FT model .ductivity and snow depth, the evaluation and compar- simulaYH: change makes soilison of simulation results is limited to snow-free condi-tempeCNMHGthsof10cmandtions in this study, with no consideration of the efet 16 cm in the two frost events relative to soil tempera-of snow cover.ture in the NOFT model.172IMPACT OF SOIL FREEZING/THAWING PROCESSESVOL. 28巴20{之-101wwwn10T 160CT 210CT 260CT INOV 6NOV 1INOV 16NOV 21NOV 26NOV 1DEC 6DEC199620-5|10CT 160CT 210CT 260CT INOV 6NOV 1INOV 16NOV 21INOV 26NOV 1DEC 6DECFig.1. Observed air temperature and precipitation rate at Rosemount from9 October to 9 December 1996Surfaco soil layerSNOV SNOV 7NOV 9NOV 11NOV 13NOV 15NOV 17NCV 19NOVb3NOV SNOV 7NOV 9NOV 11NOV 13NOV 1SNOV 17NOV 19NOV16em3NOV SNOV 7NOV 9NOV 11NOV 13NOV 15NOV 17NOV 19NOV”5cm0.4-0.3-0.13NOV 5NOV 7NOV 9NOV 11NOV 13NOV 15NOV 17NOV ↑ 9NOV10cm5 0.3.SNOV 5NOV 7NOW 9NOV 11NOV 13NOV 15NOV 17NOV 19NOV16cm0.40.3.0TNOV SNOV 5NOV 7NOV 9NOV 11NOV 13NOV 15NOV_ 17NOV 19NOV中国煤化工Fig. 2. Observed (solid lines) and simulatedMHCNMHGvolumetric liquid water content (m3 m-3) (d,e,11 wiu cuc r 1 lucI (uaooulines) and NOFT model (dotted lines) soil frost processes at the indicateddepth at Rosemount from 9 October to 21 November 1996.NO.1ZHANG AND SUN173During the two frost periods, simulated soil liquid shown in Fig. 4. A downward vertical water fux ap-water content using the FT model matches the ob- pears in the upper soil layer at night and penetratesserved values very well, except at 16 cm depth duringinto the deeper soil layer to 60 cm depth after noon15- -21 November (Figs. 2d, e, f). It seems that a slight under the NOFT model. Whereas, there is almost nounderestimation of simulated soil temperatures by less downward water vertical fux with the FT model atthan 1°C at a depth of 16 cm leads to a slower increase night. Only when simulated soil temperature in thein volumetric liquid water content, resulting in later FT model begins to rise after noon, from the surfacethawing than observed after 17 November. Figure 2 to the deep soil, does soil thawing occur. Infiltrationshows that simulated volumetric liquid water contentis enhanced, as shown at 1800 LST on 17 Novemberby the frozen soil model increases later and is lower in Fig. 4. Then, simulated volumetric liquid waterthan simulated by the NOFT model due to impedancecontent increases rapidly (Fig. 2), which is consistentof ice against infiltration when rain occurs on 17-18 with observations above a depth of 16 cm. This exper-November.iment demonstrates that the presence of ice in frozensoil could drastically reduce and delay soil infiltration3.2 Soil water fluxc 8imulationat this site.Figure 3 shows simulated soil water vertical fuxes3.3 Surface energy and water balances simu-at four times on November 14 from these two models.lationThere is an upward soil water fux in the layers between about 10- and 30-cm depth, where the freezingSimulated net radiation fuxes using the FT andfront passes, as shown in Fig. 1. When drastic freez- NOFT models are in good agreement with the ob-ing occurs at night, the largest upward water fAux is at served values, as shown in Fig. 5. The mean absolute20 cm depth. This upward water movement towards errors (MAEs) and the root-mean-square errors (RM-the freezing front results from the gradient in matric SEs) of 6.38 and 9.22 W m- 2 for net radiation fuxpotential induced by soil freezing. It could be inter- with FT are all less than those of9.14 and11.8 W m* 2,preted by Eq. (3) as connecting soil temperature withrespectively, with the NOFT model. It can be seenmatric potential when the freezing occurs and latent that inclusion of the freezing/ thawing processes leadsheat is released. Freezing induced water movement, a to an improvement in the simulation of net radiationsignificant phenomenon in frozen soil physics and en- fux. Even though there are no observed ground heatgineering, causes deep soil water to transfer into the fuxes or sensible and latent heat fuxes for evaluation,upper soil and freeze near the frost front. The aver-it is reasonable to conclude that simulation results forage soil volumetric moisture content (including liquid surface energy fuxes with the FT model are basicallywater and ice) of 0.38 above a depth of 20 cm as simu- better than those with the NOFT model, based onlated by FT is larger than the value of 0.32 simulatedthe better simulation in ground surface temperature,by NOFT model on November 14. If the freezing pro- soil temperature, and volumetric liquid water contentcesses continue in winter, the total water content will (Zhang et al, 2007).increase in the upper soil layer and decrease in theDifferences in four components of the surface en-deep soil layer. When thawing occurs only in the up- ergy balance between the two models in the frostper soil layer in spring, the high liquid water contentevents are ilustrated in Fig. 6. Diferences in thewill produce more water fux to the atmosphere.ground heat fux term are most significant, and theseIn the top soil layer, water Aux simulated by the diferences seem to partition primarily into the sen-frozen soil model is effectively shut off due to the muchsible heat fux. Differences in net radiation are verylower hydraulic conductivity in the presence of high ice small between the two models (less than 25 W m~ 2).content. Whereas, the NOFT model simulates the up-The latent heat fuxes with the FT model are smallerward water fux, which is higher during the day thanat than those with the NOFT model, with the typicalnighttime, indicating that surface evaporation clearly maximum difference at midday being approximatelyoccurs. This disparity in water vertical fux distri-27 W m-2. Simulated sensible heat fuxes using FTbution between the two soil models suggest that soil are lower than those from NOFT during the day andfreezing in winter would eficiently limit evaporation higher at nighttime when freezing and thawing occur,due to the decrease of liquid water content producingdue to the frozen soil model producing smaller diurnallarge soil surface resistance. Molders et al. (2003) have variati中国煤化工surface layer thanalso shown that soil frost affects the water supply to the Nd:es in ground heatthe atmosphere through this mechanism.fux a.gYHCN M H G in sensible heatSimulated vertical soil water fuxes at four times fux but opposite in sign (downward ground heat fuxon 17 November during periods of precipitation are is positive and upward sensible heat fux is positive).174IMPACT OF SOIL FREEZING/THAWING PROCESSESVOL.2819961114 00:0019961114 06:00营an0021.219961114 12:0019961114 18:00aa2go.12Soil Water Flux (1.0E-8m/a)Soil Water Flux (1.0E- -8m/a)Fig.3. Soil water vertical fuxes simulated in the FT model (solid lines) andNOFT model (dotted lines) at four times (LST) on 14 November 1996 atRosemount.19961117 00:0019961117 06:00goae19961117 12:0019961117 18:0080Soil Water Flux (1.0E-8m/s)Fig. 4. Soil water vertical fuxes simulated in the FT model (solid lines) andNOFT model (dotted lines) at four times (LST) on 17 November 1996 atThe maximum absolute diference in sensible heat fux periodare listed in Table 1, which shows that soilis approximately 108 W m-2 due to the maximum freezing/ thawing processes infuence the partitioningdifference in soil surface layer temperature of nearly of surface energy fluxes and change ground and sen-69C, which occurs during the freezing period, while sible.中国煤化工net radiation andthe maximum difference in ground heat Aux is approx- latent: period.imately 146 W m-2.Tol|YCNMHGsofphasechange,The mean absolute differences in four components we show tne autterences In tour components of theof the surface energy balance during the simulation daily mean surface energy balance between the twoNO.1ZHANG AND SUN17540300200; 100&0-1001INOV3NOV SNOV 7NOV 9NOV 11NOV 13NOV 15NOV~ 17NOV 19NOV1996Fig. 5. Observed (solid lines) and simulated net radiation fux from the FTmodel (dashed lines) and NOFT model (dotted lines) at Rosemount from1 to21 November 1996.100050-50? -100; -150-3NOV SNOV 7NOV 9NOV 1INOV 13NOV 15NOV 17NOV 19NOV150-100， scTNO3NOW SNOW 7NOV 9NOV 11NOV 13NOV 15NOV 17NOV 19NOV，50-50.3NOW5NOV 7NOW 9NOV 1NON 13NOV 15NOV 17NOW 19NOVs， 50_of合-10NOV 3NOV SNOV 7NOV 9NOV 11NOV 13NOV 1ISNOV 17NOV 19NOVFig. 6. Difference between with the FT model (F) and NOFT mode! (N) innet radiation fux (Rn) (a), latent heat fux (LE) (b), sensible heat fAux (H、)(c), and ground heat fAux (G) (d) at the soil surface simulated at Rosemountfrom 1 to 21 November 1996.models as well as daily mean latent heat from freez-file results in the soil releasing/absorbing more grounding and thawing simulated by the frozen soil model heat fux into/from the atmosphere. The ground heatin Fig. 7. Please note that this figure covers the peAux differences appear to primarily partition into theriod after the soil began freezing on 1 November and sensibl煤化弋during the freeextends through 9 December to show that the govern- ing pe中国煤ned into all threeing mechanisms discussed are quite robust, even overof sensJYHCNMHGradiationduringa relatively longer period. Figure 7 ilustrates that thawing perods. Note tnat tne release/absorption ofthe freezing/thawing processes in the whole soil pro- latent heat from the phase change in the whole soil176IMPACT OF SOIL FREEZING/THAWING PROCESSESVOL. 28Table 1. Mean absolute differences in the surface energyshould be genrally applicable for bare soil in winter.balance between simulations with and without frost pro-Figure 8 ilustrates that differences (FT minuscesses (W m-2).NOFT) in daily mean ground surface temperatureRnEHaGwith maximum differences of 2.1°C are mostly smallerin magnitude than the differences in daily mean 101Novto21Nov4.214.9213.516.79cm soil temperature, with maximum differences 021Novto9Dec3.503.8112.0914.493.3°C during the freezing and thawing periods. Notethat there are mostly larger upward and downwardprofle provides/consurnes most of the ground heat fux temperature gradients in near-surface frozen soil dur-when feezing/thawing occurse As shown in Table ing feexing and thawing periods, which could explain1, the changes in energy partitioning due to frozen how fezing/thawing leads soil to release/absorb moresoil processes are quite consistent before and ater 21 ground heat fAux.November. This also suggests that the impacts cfreezing/thawing processes on surface energy balances4. ConclusionA 1-D frozen soil model coupling the thermal and40hydrological processes has been used to simulate frozensoil processes in frozen soil at the Rosemount station.Inclusion of frozen soil parameterization in the soil皇220model has improved the simulation of net radiationfux, soil temperature, and liquid water content com-∈pared against the observations. Moreover, due to thisprogress, the frozen soil model should produce sub-stantially better simulation results for ground heat fAuxand sensible and latent heat fuxes. Freezing/thawinggprocesses have been shown to have significant impacts吉on vertical water fux and the surface energy balances.40-In particular, diferences in simulated vertical waterfux between runs with and without inclusion of the1996NOV 11NOV 16NOV 21NOW 26NOV 1DEC 6DECfrozen soil parameterization also indicate that freez-ing/thawing processes strongly infuence the hydrolog-ical processes by altering the matric potential and hy-draulic conductivity at the Rosemount field site, whichFig. 7. Daily mean sensible (H) and latent (LE) heatsuggests the obvious coupling of the thermal and hy-fuxes, net radiation fAux (Rn), and ground heat fux (G)drological processes in freezing soil. With respect tosimulated using the FT model, and the difference besurface energy balances, differences of up to 146 Wtween with FT the model and NOFT model at Rose-m-2 in ground heat fux, 108 W m-2 in sensible heatmount. Right y-axis denotes the simulated mean dailyAux, and 27 W m-2 in latent heat fux are found berelease/ absorption rate of latent heat of phase change (Wm-3) in the whole soil profile.tween simulations with and without inclusion of frozensoil processes. In addition, the maximum differencesin surface soil layer temperature and 10 cm soil tem-?3perature of 6°C and 5°C are found between these twocases.1Freezing/thawing processes change ground andsensible heat fuxes more greatly than net radiationfuxes and latent heat fiuxes during early winter. Release of latent heat from phase change produces largertemperature gradients in near-surface frozen soil, re1INOV 6NOV 11NOV 16NOV 21NOV 26NOV 1DEC 6DECsulting in more ground heat fAux relative to the soilwithol; processes. Thepartiti中国煤化工设het fux dueFig. 8. Differences in simulated daily mean soil surfacelayer temperature (solid line) and 10 cm soil temperature ing rHCNMHGntwiththatdur-(dashed line) between with the FT model (F) and NOFTing thawing periods. About 80% of the ground heat(N) model at Rosermount.fux differences are primarily partitioned into the sen-NO. 1ZHANG AND SUN177sible heat during the freezing periods, and during theheat transport in frozen soil: Numerical solution andthawing periods these differences are comparably par-freeze/thaw applications. Vadose Zone Jouma, 3,titioned into the sensible heat fux and also latent heat693- 704.fux and net radiation fux.Harlan, R. L., 1973: Analysis of coupled heat-fuid trans-port in partially frozen soil. Water Resource Re-During the relatively short term of the 40 days insearch, 9, 1314-1323.the study period, freezing and thawing occurred inJame, Y. W., and D. I. Norum. 1980: Heat and masstwo frost events and the soil freezing front penetratedtransfer in a freezing unsaturated porous medium.to the depth of 16 cm into the soil layer in the lat-Water Resource Research, 117, 811-819.ter event, making for good test cases for the models.Thermal conductivity of soils. PhThe observed impacts of freezing/ thawing processesD. dissertation, University of Trondheim, 236pp.on the partitioning of surface energy fuxes at Rose- Luo, L. F, and Coauthors, 2003: Effects of frozen soilmount should be helpful for identifying similar pro-on soil temperature, spring infltration, and runof:cesses occurring in seasonal frozen soil over the longResults from the PILPS 2 (d) experiment at Valdai,term elsewhere.Russia. J. Hydrometeor, 4, 334-351.Molders, N., U. Haferkorn, J. Doring; and G. Kramm,Acknowledgements. This work is supported by the2003: Long-term numerical investigations on thewater budget quantities predicted by the hydro-National Basic Research Program of China under Grantthermodynamic soil vegetation scheme (HTSVS)-No. 2006CB400504 and National Natural Science Founda-Part I: Description of the model and impact of long-tion of China under Grant Nos. 40605027 and 40775050.wave radiation, roots, snow, and soil frost. Meteorol.The authors would like to thank John M. Baker from theAtmos. Phys, 84, 115-135.University of Minnesota for providing the data from Rose-Peixoto. J.. and A. H. Oort. 1992: Physics of Climate.mount Agricultural Experiment Station.American Institute of Pbysics, 200pp.Peters-Lidard. C. D., E. Blackburn. X. Liang, and E. F.REFERENCESWood, 1998: The efect of soil thermal conductivityParameterization on surface energy fuxes and tem-Boone, A., V. Masson, T. Meyers, and J. Noilhan, 2000:perature. J. Atmos. 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