Modeling of thermal properties of peat soil Dyukarev E.A. - - PowerPoint PPT Presentation

Modeling of thermal properties

• f 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

• f heat, water and gas regimes of peatland ecosystems.

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Study area

Bakcharskoe bog Tomsk

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Pine-shrub-sphagnum community (Low ryam)

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Peat depth – 2 m

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2 5 10 15 25 40 60 80

Soil temperature at 2,5,10,15,25,40,60,80 cm from 28 june 2005 to 7 september 2010 Time step: 15 min (summer) 60 min (winter)

Water table

• 20 cm

Observation data

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).

5 T 80 5 T 60 5 T 40 5 T 25 1 0 T 15 1 0 T 10 1 0 T 5 1 0 T 2 6 0 4 0 2 0 F D , ¡ W T L

• ­‑2 0

2 0 T a 4 0 S D P 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 3 6 P R C T a T 80 T 60 T 40 T 25 T 15 T 10 T 5 T 2 S D P F D W T L P R C

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Data examples

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Annual course of soil temperature

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7.3315 7.332 7.3325 7.333 7.3335 7.334 7.3345 7.335 x 10

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5 10 15 20 25

⎯ ⎯ 2 ⎯ ⎯ 5 ⎯ ⎯ 10 ⎯ ⎯ 15 ⎯ ⎯ 25 ⎯ ⎯ 40 ⎯ ⎯ 60 ⎯ ⎯ 80

time tempertaure, оС

Diurnal temperature variations

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7.3323 7.3324 7.3324 7.3324 7.3324 7.3324 7.3324 x 10

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8 10 12 14 16 18 20 22 24 26

⎯ ⎯ 2 ⎯ ⎯ 5 ⎯ ⎯ 10 ⎯ ⎯ 15 ⎯ ⎯ 25 ⎯ ⎯ 40 ⎯ ⎯ 60 ⎯ ⎯ 80

time temperature, оС

Peat warming at water infiltration

10 7.3252 7.3252 7.3252 7.3252 7.3253 7.3253 7.3253 7.3253 7.3253 x 10

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6 8 10 12 14 16 18 20 22 24

⎯ ⎯ 2 ⎯ ⎯ 5 ⎯ ⎯ 10 ⎯ ⎯ 15 ⎯ ⎯ 25 ⎯ ⎯ 40 ⎯ ⎯ 60 ⎯ ⎯ 80

time temperature, оС

Data pre-processing

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In-situ data calibration using “zero curtain”

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7.3388 7.3388 7.3388 7.3388 7.3388 7.3388 7.3388 7.3388 7.3388 7.3389 x 10

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• 0.5

0.5 1 1.5 2 2.5 3 3.5 4 4.5

⎯ ⎯ 2 ⎯ ⎯ 5 ⎯ ⎯ 10 ⎯ ⎯ 15 ⎯ ⎯ 25 ⎯ ⎯ 40 ⎯ ⎯ 60 ⎯ ⎯ 80

Removing data quantification

13 1.2175 1.218 1.2185 1.219 1.2195 1.22 1.2205 x 10

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6.18 6.19 6.2 6.21 6.22 6.23 6.24 6.25

– observation – smoothing

T (80 cm)

temperature, оС dT = 0.01 оС

Soil thermal properties

a - apparent heat diffusivity

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( )

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ ∂ ∂ ∂ = ∂ ∂ z T z a z t T

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 2 1 2 1 2 2

/ ln 2 2 sin 2 exp ) , ( sin ) , ( ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛− + = + = ∂ ∂ = ∂ ∂ A A z z a a z t a z A T t z T t A T t T z T a t T ω ω ω ω ω

Monthly soil temperature. 2005-2010 averaged.

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Т почвы, оС

temperature, оС

Heat diffusivity, cm2/day. Amplitude method. Annual oscillation.

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20 128 112 122 259 505 1893 1 10 100 1000 10000 2-5 5-10 10-15 15-25 25-40 40-60 60-80

layer

Monthly amplitudes of diurnal temperature, 2005-2010 averaged.

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Temperatude amplitude, оС

Heat diffusivity, cm2/day. Amplitude method. Daily oscillation.

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144 205 165

50 100 150 200 250 300 2-­‑5 5-­‑10 10-­‑15 a, ¡см2/сут

layer

Heat diffusivity, cm2/day. Annual and daily oscillations.

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144 205 165 20 128 112 122 259 505 1893 1 10 100 1000 10000

2-5 5-10 10-15 15-25 25-40 40-60 60-80

Суточная амплитуда Годовая амплитуда

слой

Numerical methods

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Numerical soluton of heat equation

n Semi-explicit scheme n Boundary condition of 1 type n 8 layers

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t t+τ z-h z z+h a (i)

( )

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ ∂ ∂ ∂ = ∂ ∂ z T z a z t T

a (i+1)

Model data

• regular oscillations.

Direct solution.

a = const = 200 cm2/day T0 = 15 + 7,5 sin (2π t)

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time temperature, оС

Inverse problem

n Initial condition - а0(z) n Model spin-up - 3 days n Minimization of function n Iterations for accurate definition a(z)

( )

∑∑

= − =

− − − =

M m j N i ij ij

T T m M N a J

1 2 2

1 2 1 ) (

10 20 30 40 50 60 70 80

• ­‑0,15
• ­‑0,1
• ­‑0,05

0,05

Inverse problem (a=200)

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• 6
• 4
• 2

• 6 1E-6

0,02

• 0,11

Temperature Error of temperature dT = T(modeled) – T(measured) Heat diffusivity error

Depth, cm

Two layers: а1= 300, а2 =100)

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400 420 440 460 480 500 520 540 560 580 600 10 15 20 400 420 440 460 480 500 520 540 560 580 600

• 1

1 2 3 x 10

• 5

300 100

1E-5

0,35

• 1,37

Temperature Error of temperature dT = T(modeled) – T(measured) Heat diffusivity error

Depth, cm

10 20 30 40 50 60 70 80 100 200 300 400 500

Real data – soil temperature august 2009

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• 1.5
• 1
• 0.5

1,0

207 397 70

Temperature Error of temperature dT = T(modeled) – T(measured) Heat diffusivity error

Depth, cm

Heat diffusivity, cm2/day. Methods comparison.

144 205 165 20 128 112 122 259 505 1893 207 261 341 397 94 70 70 100 200 300 400 500 600 2-5 5-10 10-15 15-25 25-40 40-60 60-80

Суточная амплитуда Годовая амплитуда Численное решение

layer

Tasks

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

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Спасибо за внимание!

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Foto: S.V. Smirnov