A simultaneous heat and water transfer model in frozen and thawed soil

Transcription

1 A simultaneous heat and water transer model in roen and thawed soil Zhenghui Xie Liye Song Aiwen Wang ICCES/LASG Institute o Atmospheric Physics Chinese Academy o Sciences (xie@lasg.iap.ac.cn) Xiaobing Feng (University o ennessee at Knoxville) LMWG and BGCWG Meetings NCAR Mesa Lab 8-0 February 00

2 Outline Introduction A moving boundary problem A heat and water transer model Model validation Summary and discussion

3 Solar radiation Sun cloud H O N O CO O 3 Land-Atmos. interaction Ice snowatmosphere Snow Glacier roen soil atmo. Desert-Oasis-air CH 4 CO N O Ice cover-snow roen soil Soil reee/thaw processes including change o rost/thaw depths signiicantly inluence energy and water exchanges between land surace and subsurace as well as vegetation growth and organic matter decomposition through thermal and hydrological processes ecosystemm Soil reee/thaw Processes land surace

4 Froen soil distribution in the North Hemisphere Froen by sea Permarost Seasonal Froen soil:all inds o ice-containing roen soil at 0 or below 0 Permarost and seasonally roen soil account or 4% and 30% o the land area in the north Hemisphere respectively; Russia and Canada are the countries where the roen soil are most widely distributed.

5 Distribution o roen soil types in China

6 Earth System Responses and Feedbacs o Soil Freee/haw Processes Soil Freee/haw Processes Cold Land/Atmosphere Energy Exchanges Boundary Layer urbulence and Stability Eects o Clouds on Radiation Energy Fluxes Precipitation Characteristics Liquid Water Movement through Soil Water Vapor Movement hrough Soil Energy Sin F E E D B A C K S Process-Oriented State Variables Soil Froen/haw Depths Froen Soil Internal Energy (relative to melting point) Soil Moisture Soil emperature Liquid Water Content

7 Introduction he soil reeing-thawing processes including change o rost/thaw depth signiicantly inluence energy and water exchanges between land surace and sub-surace; Accurate representation o rost and thaw depths and their climate eedbac is signiicant or improving simulations o the hydrological and greenhouse gas exchange processes in cold regions; Current land surace models used or climate studies do not represent suitably the dynamics o rost/thaw depths and their eedbac to the climate system which give delayed or rapid reeing/thaw due to the roen soil parameteriation in the models.

8 he purpose o this wor A heat and water transer model with representation o the dynamics o rost/thaw depths and their eedbac to the climate system was developed; It treats the soil rost/thaw depths as moving interaces governed by some Stean-type moving boundary conditions and describes the liquid water and solid ice states as well as the positions o the rost/thaw depths; An adaptive mesh method or the moving boundary problem is adopted to solve the relevant equations and to determine rost/thaw depths water content and temperature distribution.

9 Outline Introduction A moving boundary problem A heat and water transer model Model validation Summary and discussion

10 wo moving boundaries: Phase-transition interaces Frost and thaw depths 0 A thawed one rom ground surace to the irst phasetransition interace (namely thawed one haw thaw depth); A roen one rom the irst phase-transition interace to the second phase-transition interace (namely rost depth); thaw depth roen one rost depth ξ ζ Froen An unroen one rom rost depth to the bottom o the unroen one Unroen calculation depth. L

11 Control equations Energy balance equations thawed one thaw depth ξ 0 haw roen one rost depth unroen one ζ Froen Unroen Mass balance equation

12 ( ) ( ) 0 0 L S q K D t t c L t c v u u ζ ξ θ θ ζ ξ ζ ξ A moving boundary problem or heat and water transer processes. dt d Q dt d Q u u ζ ξ ζ ζ ξ ξ ζ ζ ξ ξ Moving boundary conditions Initial and boundary conditions ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) > > > t t L L t g G L g t t t t t t r g L θ θ θ θ Xie Song Feng Science in China(A) 008

13 Outline Introduction A moving boundary problem A heat and water transer model Model validation Summary and discussion

14 Land surace 0 Z Δ haw Froen Z i ξ i ξ ζ i ζ Unroen L Z n Δ n

15 ( ) ( ) ( ) ( ) ( ) 0 0 b u u b u u u b v v v v c c b b b h h c D h h q q h h q q S K K D D h D D h D ω ω ω ω ω ω θ θ ω θ θ ω θ ( ) ( ) 0 b b b h h c D ω ω. ω the bacward Euler scheme ω0 the explicit Euler scheme Finite dierence scheme or the control equations

16 Algorithm Step. Choose the initial datum unctions; Step. Compute soil temperature and soil moisture and Soil roen/thaw depths by the Finite dierence scheme; Step 3. Chec whether the stopping criterion is met. I the relative error o two iterates is less than a prescribed tolerance stop the iteration and set : ; go bac to Step ; Otherwise let the iteration run until the maximum number o iterations is reached then either stop or set : and go bac to Step. Step 4 Continue the time integration until t tnal.

17 Outline Introduction A moving boundary problem A heat and water transer model Model validation Summary and discussion

18 Numerical Experiment Purpose: o test the eects o the surace temperature on the simulated rost and thaw depths; With the simulated surace temperature ( ) ( ) t 0 Gtt A0 sin ωt 0 : mean annual ground surace temperature (GS) G t : the rising rate o GS A 0 :annual amplitude o GS A 0 3 C ; ω π 8760

19 he ground surace temperature and the simulated rost/thaw depths (a) Soil surace temperature; (b) rost and thaw depths or G t 0; (c) those or G t 0.0; (d) those or G t -0.0.

20 Numerical Experiment With the observed surace temperature and soil moisture as the upper boundary conditions D66 D0

21 he Simulated rost and thaw depths at D66 station rom to 998.8

22 he Simulated soil moisture and temperature at D66 station rom to 998.8

23 he Simulated rost and thaw depths at D0 station rom to Finish a reee-thaw cycle in July Begin to reee in late September Begin to melt in Early April

24 Outline Introduction A moving boundary problem A heat and water transer model Model validation Summary and discussion

25 Summary A new simultaneous heat and water transer model or simulating the active layer and rost/thaw depths is developed; he new model explicitly tracs the reeing-thawing interace and rost/thaw depths ; An adaptive mesh method or the moving boundary problem is adopted to solve the relevant equations and to determine rost/thaw depths water content and temperature distribution.

26 Future wors and discussion he dynamical representation o rost/thaw depth was coupled to CLM 3.0 coupling with updated version o the CLM Models and its validation should be done ; Soil temperature was calculated by using rost and thaw depths as mesh points then soil liquid and ice content were adusted by the variety o phase change; Land surace models with dynamical representation o rost/thaw depth can improve the ability to model the soil moisture and temperature.

27 hans or your Attentions! Reerence Zhenghui Xie Liye Song Xiaobing Feng A moving boundary problem derived rom heat and water transer processes in roen and thawed soils and its numerical simulation Science in China(A) 5(8) 50-5 doi:0.007/s x 008.