Modeling of thermal properties of peat soil Dyukarev E.A. Institute of monitoring of climatic and ecological systems SB RAS, Tomsk

n Peat deposit is a complex organic-mineral system with specific properties. Peat layers has high porosity, and contains large amount of weakly decomposed water saturated organic matter. Thermal regimes of peat deposit and mineral soil are essentially differs. Temperature of peat influences on course and rate of physical, chemical, and microbiological processes in the peat deposit. Studying of temperature regime allows to reveal features of heat, water and gas regimes of peatland ecosystems. 2

Study area Bakcharskoe bog Tomsk 3

Pine-shrub-sphagnum community (Low ryam) 4

Observation data 2 5 10 15 25 Water table Soil temperature at - 20 cm 2,5,10,15,25,40,60,80 cm 40 from 28 june 2005 60 to 7 september 2010 Time step: 80 15 min (summer) 60 min (winter) 5 Peat depth – 2 m

Daily air temperature (Ta), soil temperature at 2 – 80 cm (T2, T5, T10, T15, T25, T40, T60, T80), snow depth (SDP, cm), soil freeze depth (FD, cm), water table level (WTL, см ) and daily precipitation (PRC, mm). S D P P R C 6 4 0 S D P P R C 3 0 0 0 F D 2 0 W T L W T L F D , ¡ 2 0 4 0 T a 6 0 0 T a -‑2 0 1 0 T 2 T 2 1 0 0 T 5 T 5 0 1 0 T 10 1 0 T 10 T 15 0 T 15 0 5 T 25 T 25 5 0 T 40 T 40 0 5 T 60 T 60 5 0 T 80 T 80 0 01/05/05 01/09/05 01/01/06 01/05/06 01/09/06 01/01/07 01/05/07 01/09/07 01/01/08 01/05/08 01/09/08 01/01/09 01/05/09 01/09/09 6

Data examples 7

Annual course of soil temperature 25 ⎯ 2 tempertaure, о С ⎯ ⎯ 5 ⎯ ⎯ 10 20 ⎯ ⎯ 15 ⎯ ⎯ 25 ⎯ 15 ⎯ 40 ⎯ ⎯ 60 ⎯ ⎯ 80 ⎯ 10 5 0 7.3315 7.332 7.3325 7.333 7.3335 7.334 7.3345 7.335 time 5 x 10 8

Diurnal temperature variations ⎯ 2 ⎯ ⎯ 5 ⎯ 26 ⎯ 10 ⎯ ⎯ 15 ⎯ temperature, о С 24 ⎯ 25 ⎯ ⎯ 40 22 ⎯ ⎯ 60 ⎯ 20 ⎯ 80 ⎯ 18 16 14 12 10 8 7.3323 7.3324 7.3324 7.3324 7.3324 7.3324 7.3324 time 5 x 10 9

Peat warming at water infiltration 24 temperature, о С 22 20 18 16 ⎯ 2 ⎯ ⎯ 5 14 ⎯ ⎯ 10 ⎯ 12 ⎯ 15 ⎯ ⎯ 25 ⎯ 10 ⎯ 40 ⎯ ⎯ 60 8 ⎯ ⎯ 80 ⎯ 6 7.3252 7.3252 7.3252 7.3252 7.3253 7.3253 7.3253 7.3253 7.3253 time 5 10 x 10

Data pre-processing 11

In-situ data calibration using “zero curtain” 4.5 ⎯ 2 ⎯ 4 ⎯ 5 ⎯ ⎯ 10 ⎯ 3.5 ⎯ 15 ⎯ ⎯ 25 3 ⎯ ⎯ 40 ⎯ 2.5 ⎯ 60 ⎯ ⎯ 80 ⎯ 2 1.5 1 0.5 0 -0.5 7.3388 7.3388 7.3388 7.3388 7.3388 7.3388 7.3388 7.3388 7.3388 7.3389 5 12 x 10

Removing data quantification – observation temperature, о С 6.25 – smoothing 6.24 6.23 6.22 dT = 0.01 о С 6.21 6.2 6.19 T (80 cm) 6.18 1.2175 1.218 1.2185 1.219 1.2195 1.22 1.2205 13 5 x 10

Soil thermal properties a - apparent heat diffusivity T T ∂ ∂ ∂ ⎛ ⎞ ( ) a z = ⎜ ⎟ t z z ∂ ∂ ∂ ⎝ ⎠ 14

Methods of determination of soil thermal properties n Experimental methods – Field – Laboratory n Computation using soil mechanical properties and composition n Computation using temperature data – Amplitude method – Phase method – Direct numerical method – Inverse problem

Amplitude method of apparent heat diffusivity calculation 2 T T ∂ ∂ a = 2 t z ∂ ∂ ( ) T ( 0 , t ) T A sin t = + ω 0 0 ⎛− ⎞ ⎛ ⎞ ω ω T ( z , t ) T A exp z sin t z ⎜ ⎟ ⎜ ⎟ = + ω − 0 0 ⎜ ⎟ ⎜ ⎟ 2 a 2 a ⎝ ⎠ ⎝ ⎠ 2 z z ⎛ ⎞ ω − a 1 2 ⎜ ⎟ = ⎜ ⎟ ( ) 2 ln A / A ⎝ ⎠ 1 2

Monthly soil temperature. 2005-2010 averaged. temperature, о С Т почвы , о С 17

Heat diffusivity, cm 2 /day. Amplitude method. Annual oscillation. 10000 1000 100 1893 505 259 128 122 112 10 20 1 2-5 5-10 10-15 15-25 25-40 40-60 60-80 18 layer

Monthly amplitudes of diurnal temperature, 2005-2010 averaged. Temperatude amplitude, о С 19

Heat diffusivity, cm 2 /day. Amplitude method. Daily oscillation. 300 250 200 a, ¡ см2/сут 150 205 100 165 144 50 0 2-‑5 5-‑10 10-‑15 20 layer

Heat diffusivity, cm 2 /day. Annual and daily oscillations. 10000 Суточная амплитуда 1000 Годовая амплитуда 100 205 165 144 10 1893 128 112 122 259 505 20 1 2-5 5-10 10-15 15-25 25-40 40-60 60-80 21 слой

Numerical methods 22

Numerical soluton of heat equation T T ∂ ∂ ∂ ⎛ ⎞ ( ) a z = ⎜ ⎟ t z z ∂ ∂ ∂ ⎝ ⎠ t+ τ n Semi-explicit scheme n Boundary condition of 1 type n 8 layers a (i) a (i+1) t z-h z z+h 23

Model data - regular oscillations. Direct solution. a = const = 200 cm 2 /day T0 = 15 + 7,5 sin (2 π t) temperature, о С 22 20 18 16 14 12 10 8 6 1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000 time 24

Inverse problem n Initial condition - а 0(z) n Model spin-up - 3 days n Minimization of function M N 1 1 1 − ( ) 2 0 J ( a ) T T ∑∑ = − ij ij N 2 M m − − j m i 2 = = n Iterations for accurate definition a(z)

Inverse problem (a=200) Temperature Heat 22 diffusivity 20 18 16 error 14 12 10 8 6 -‑0,15 -‑0,1 -‑0,05 0 0,05 1300 1350 1400 1450 1500 0 -6 1E-6 10 x 10 Depth, cm 8 6 20 4 0,02 2 30 0 -2 -4 40 -6 1300 1350 1400 1450 1500 50 Error of temperature 60 -0,11 dT = T(modeled) – T(measured) 70 80 26

300 Two layers: а 1 = 300, а 2 =100) 100 Heat Temperature diffusivity 20 error 15 10 400 420 440 460 480 500 520 540 560 580 600 1E-5 Depth, cm -5 x 10 0,35 3 2 1 0 -1,37 -1 400 420 440 460 480 500 520 540 560 580 600 Error of temperature 27 dT = T(modeled) – T(measured)

Real data – soil temperature august 2009 Heat Temperature diffusivity 22 error 20 18 16 0 100 200 300 400 500 14 0 12 207 10 8 10 6 4 Depth, cm 2 20 0 100 200 300 400 500 600 1,0 30 397 1 40 0.5 50 0 -0.5 60 -1 70 70 -1.5 0 100 200 300 400 500 600 Error of temperature 28 80 dT = T(modeled) – T(measured)

Heat diffusivity, cm 2 /day. Methods comparison. 600 Суточная амплитуда 500 Годовая амплитуда Численное решение 400 300 397 200 341 261 207 205 100 165 144 1893 94 128 112 122 259 505 70 70 20 0 2-5 5-10 10-15 15-25 25-40 40-60 60-80 layer

Tasks n Winter period n Evaporation, freezing, melting n Heat conduction at water infiltration 30

Спасибо за внимание ! Foto: S.V. Smirnov 31

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