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Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź, Poland Brian Offerle Göteborg University, Göteborg, Sweden; Indiana University, Bloomington, USA Sue Grimmond Indiana University, Bloomington, USA
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Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź,

Mar 28, 2015

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Page 1: Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź,

Slab surface energy balance scheme and its application to parameterisation of the

energy fluxes on urban areas

Krzysztof Fortuniak University of Łódź, Poland

Brian OfferleGöteborg University, Göteborg, Sweden;

Indiana University, Bloomington, USA

Sue Grimmond Indiana University, Bloomington, USA

Page 2: Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź,

Outline

1) Urban atmosphere and urban models

2) Motivation3) Slab surface energy balance

model4) Energy balance measurements

in Lodz5) Modeled and measured urban

energy balance components6) Model applications7) Conclusions

Page 3: Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź,

urban boundary layer

urban canopy layer

1. Very complex models: vegetation, windows, indoor processes, etc.

2. More generalized models: simplified geometry, uniformed surfaces

3. Slab models: town is treated as a single entity with specified physical parameters

Boundary layer models: different models from 3D to 1D with different turbulence parameterizations

Surface energy balance models:

3. Slab models: town is treated as a single entity with specified physical parameters

1D model with first order turbulence closure

presented model

Urban Atmosphere and Urban Models

Page 4: Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź,

Motivation

Why slab approach ?• Simple – low time consuming

• Easy to link with mesoscale and GSM models

• Good for studies on the role of individual parameter

Questions:• Is a slab model able to capture

singularities of the urban energy balance components?

• Which parameters are crucial for modification of the local climate by urbanization?

Page 5: Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź,

The model

Page 6: Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź,

Radiation budget: Q* = (1-α) Itoth + εL↓ – εσTs4

Itoth - short-wave radiation on the horizontal surface after Davis at al. (1975):

3 6 9 12 15 18 210

100200300400500600700

W m

-2

18 III 1999

h

3 6 9 12 15 18 210

100200300400500600700

W m

-2

21 I 1999

h

3 6 9 12 15 18 210

100200300400500600700800900

1000

W m

-2 10 V II 1999

h

Validation of the Itoth model again Lodz data (selected sunny days)

Itoth = S0sinhs·τwa·τda(1 + τws·τds·τrs)/2

S0 - solar constant, hs - solar height, and τ - transmissions due to water vapor absorption, aerosol absorption, water vapor scattering, aerosol

scattering, and Raleyigh scattering L↓ -incoming longwave radiation: taken constan or calculated with empirical formula (e.g. Idso & Jackson, 1969)

L↓= [1 – 0.261·exp{-7.77·10-4 · (273-T)2}] σT4

The surface energy balance model: Radiation budget: Q*+QG+QH+QLE=0

Page 7: Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź,

Heat flux to the ground (QG) and temperature profile is found by numerical solution of the one-dimensional heat diffusion equation:

2

2

g zT

νtT

νg - thermal diffusivity

T-temperature at depth z

Numerical scheme: Crank-Nicholson

Number of levels: 10 levels

Lower boundary conditions:constant temperature

Upper boundary conditions: temporal evolution of the surface temperature

The surface energy balance model: Heat flux to the ground: Q*+QG+QH+QLE=0

Q*+QG+QH+QLE+QS=0

QS

QG

QG

Q*+QG+QH+QLE=0

0. 5cm3cm7. 5cm

1. 5cm5cm10. 5cm

15. 5cm25. 5cm

45. 5cm

95. 5cm

Page 8: Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź,

Validation of ground temperature calculations – comparison with temperature (5cm above ground) evolution at Lodz-Lublinek meteorological station in calm, cloudless nights (QH,QLE=0)

0 2 4 6 8 10 12t [h]

6

8

10

12

14

16

18

20

22

T [

0C

]

8/9.09.1999 C =1.3 10 -6J m -3K -1

k=0.3 W m -1K -1

L =315 W m -2

T o=21.5 oC , T G=24.4 oC T o=12 oC

0 2 4 6 8t [h]

0

2

4

6

8

10

12

T [

0 C]

23/24.05.1999 C =1.3 10 -6J m -3K -1

k=0.2 W m -1K -1

L =290 W m -2

T o=10.5 oC , T G=18.6 oC T o=8 oC

0 2 4 6 8t [h]

6

8

10

12

14

T [

0 C]

9/10.06.1999 C =1.3 10 -6J m -3K -1

k=0.4 W m -1K -1

L =315 W m -2

T o=13.5 oC , T G=18.8 oC T o=6 oC

0 2 4 6 8 10t [h]

4

6

8

10

12

14

16

18

T [

0 C]

16/17.08.1997 C =1.2 10 -6J m -3K -1

k=0.2 W m -1K -1

L =305 W m -2

T o=16.4 oC , T G=20.8 oC T o=12 oC

0 2 4 6 8 10 12 14t [h]

-14

-12

-10

-8

-6

-4

-2

T [

0 C]

25/26.01.1998 C =1.3 10 -6J m -3K -1

k=0.3 W m -1K -1

L =228 W m -2

T o=-3 .5 oC , T G=3.4 oC T o=8 oC

0 2 4 6 8 10 12t [h ]

- 2

0

2

4

6

8

1 0

1 2

1 4

T [

0 C]

30/31.03.1999 C =1.7 10 -6J m -3K -1

k=0.7 W m -1K -1

L =250 W m -2

T o=12.5 oC , T G=10.5 oC T o=10 oC

Surface cooling in calm cloudless nights Energy balance: Q*+QG+QH+QLE=0

Page 9: Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź,

Parametrisation of turbulent heat fluxes (QH and QLE) bases on Monin-Obukhov similarity theory with Businger’s functions for the flux-profile relationships. Method proposed by Louis (1979) with Mascar at al. (1995) modification is used.

Fuxes: and

are found from profile relationships:

Lz

Lz

zz

lnku

)z(u m0mm

m0

2'' uuw u''w

Lz

Lz

zz

lnk

R h0hh

h0

stability parameter z/L is found by iterative solution of:

Lz

Lz

zz

ln

Lz

Lz

zz

ln

RRi

Lz

h0hh

h0

2

m0mm

m0b2b u

gzRi

where Rib is the bulk

Richardson number :

In calculations of the turbulent moisture flux additional surface resistance is considered acording to Best (1998) method.

The surface energy balance model: Turbulent heat fluxes : Q*+QG+QH+QLE=0

Page 10: Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź,

One dimensional first order model

– 28 levels form 2m to 5000m

– constant upper boundary condition

– different local turbulence closure schemes tested ( K–l ):

o Louis (1979)o Mellor and Yamada (1982)o Gambo (1978)o Sievers and Zdunkowski (1986)

- advection estimated by simultaneous calculation for rural and urban points

The boundary layer model

Page 11: Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź,

5 10 15 200

500

1000

1500

2000

Modeled (dashed) versus measured (solid) temperature and humidity profiles in day 33 Wangara experiment (9.00h, 12.00h, 15.00h)

5 10 15 200

500

1000

1500

2000

5 10 15 200

500

1000

1500

2000

5 10 15 200

500

1000

1500

2000

0 0.002 0.004q[kg/kg]

0

500

1000

1500

2000

0 0.002 0.004q[kg/kg]

0

500

1000

1500

2000

0 0.002 0.004q[kg/kg]

0

500

1000

1500

2000

0 0.002 0.004q[kg/kg]

0

500

1000

1500

2000

Louis Mellor-Yamada

Gambo Sievers & Zdunkowski

temperature [C] temperature [C] temperature [C] temperature [C]

The boundary layer model – model validation

Page 12: Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź,

Modeled temperature and wind speed profiles over urban and rural sites in the night

1 0 1 2 1 4 1 6 1 8 2 0temperature [C]

0

100

200

300

400

high

t [m

]

urbanrural

0 1 2 3 4 5 6 7wind speed [ms- 1]

0

100

200

300

400

high

t [m

]

urbanrural

Model testing – vertical profiles

Page 13: Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź,

Energy balance

measurements in

Lodz

Page 14: Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź,

#Y#Y

#Y

1 0 1 2 3 4 5 Kilometers

N

EW

S

old town

blocks of flats

industrial Energy balance measurement point

Lodz-Lublinek

meteorologicalstation

Measurements in Lodz

Page 15: Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź,

Energy balance measurement point

Page 16: Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź,

Energy balance measurement point

Page 17: Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź,

Energy balance measurement point

Page 18: Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź,

Measured and

modeled energy

balance components

Page 19: Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź,

The energy balance components for the center of Lodz. Comparison of the results of measurement (thin lines) and simulation (thick lines)

Measured and modeled urban energy balance components in Lodz (March 7th, 2001)

0 3 6 9 12 15 18 21 24t [h]

-200

0

200

400

[Wm

-2]

Q*

Q

Q

Q

H

E

7.03.2001

0 3 6 9 12 15 18 21 24t [h]

-200

0

200

400

[Wm

-2]

Q*

Q

Q

Q

H

E

7.03.2001

Parameters used in simulation: ground heat capacity: Cg = 2.0 106 J m

-3 K-1; ground thermal conductivity: kg = 1.5 Wm-

1K-1; roughness length for momentum: z0m= 0.6 m; roughness length for heat: z0h = 0.00001 m;

incoming longwave radiation: 230 Wm-1 albedo: α = 0.08; emissivity: ε = 0.9;soil moisture content: SMC = 35%

Page 20: Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź,

The energy balance components for the center of Lodz. Comparison of the results of measurement (thin lines) and simulation (thick lines)

Measured and modeled urban energy balance components in Lodz (March 28th, 2001)

Parameters used in simulation: ground heat capacity: Cg = 2.0 106 J m

-3 K-1; ground thermal conductivity: kg = 1.5 Wm-

1K-1; roughness length for momentum: z0m= 0.6 m; roughness length for heat: z0h = 0.00001 m;

incoming longwave radiation: 220 Wm-1 albedo: α = 0.13; (snow)emissivity: ε = 0.85;soil moisture content: SMC = 15%

0 3 6 9 12 15 18 21 24t [h]

-200

0

200

400

600[W

m-2

]Q*

Q

Q

Q

H

E

28.03.2001

0 3 6 9 12 15 18 21 24t [h]

-200

0

200

400

600[W

m-2

]Q*

Q

Q

Q

H

E

28.03.2001

Page 21: Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź,

The energy balance components for the center of Lodz. Comparison of the results of measurement (thin lines) and simulation (thick lines)

Measured and modeled urban energy balance components in Lodz (April 30th – May 3rd, 2001)

Parameters used in simulation: ground heat capacity: Cg = 2.0 106 J m

-3 K-1; ground thermal conductivity: kg = 1.5 Wm-

1K-1; roughness length for momentum: z0m= 0.6 m; roughness length for heat: z0h = 0.00001 m;

incoming longwave radiation: 310 Wm-1 albedo: α = 0.08; emissivity: ε = 0.9;soil moisture content: SMC = 3%

0 3 6 9 12 15 18 21 24t [h]

-200

0

200

400

600

800

[Wm

-2]

Q*

Q

Q

Q

H

E

30.04-3.05.2001

0 3 6 9 12 15 18 21 24t [h]

-200

0

200

400

600

800

[Wm

-2]

Q*

Q

Q

Q

H

E

30.04-3.05.2001

Page 22: Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź,

The energy balance components for the center of Lodz. Comparison of the results of measurement (thin lines) and simulation (thick lines)

Measured and modeled urban energy balance components in Lodz (July 7th, 2001)

Parameters used in simulation: ground heat capacity: Cg = 2.0 106 J m

-3 K-1; ground thermal conductivity: kg = 1.5 Wm-

1K-1; roughness length for momentum: z0m= 0.6 m; roughness length for heat: z0h = 0.00001 m;

incoming longwave radiation: 370 Wm-1 albedo: α = 0.08; emissivity: ε = 0.9;soil moisture content: SMC = 8%

0 3 6 9 12 15 18 21 24t [h]

-200

0

200

400

600

800

[Wm

-2]

Q*

Q

Q

Q

H

E

7.07.2001

0 3 6 9 12 15 18 21 24t [h]

-200

0

200

400

600

800

[Wm

-2]

Q*

Q

Q

Q

H

E

7.07.2001

Page 23: Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź,

The energy balance components for the center of Lodz. Comparison of the results of measurement (thin lines) and simulation (thick lines)

Measured and modeled urban energy balance components in Lodz (August 19th, 2001)

Parameters used in simulation: ground heat capacity: Cg = 2.0 106 J m

-3 K-1; ground thermal conductivity: kg = 1.5 Wm-

1K-1; roughness length for momentum: z0m= 0.6 m; roughness length for heat: z0h = 0.00001 m;

incoming longwave radiation: 370 Wm-1 albedo: α = 0.08; emissivity: ε = 0.9;soil moisture content: SMC = 7%

0 3 6 9 12 15 18 21 24t [h]

-200

0

200

400

600[W

m-2

]

Q*

Q

Q

Q

H

E

19.08.2001

0 3 6 9 12 15 18 21 24t [h]

-200

0

200

400

600[W

m-2

]

Q*

Q

Q

Q

H

E

19.08.2001

Page 24: Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź,

The energy balance components for the center of Lodz. Comparison of the results of measurement (thin lines) and simulation (thick lines)

Measured and modeled urban energy balance components in Lodz (October 10th, 2001)

Parameters used in simulation: ground heat capacity: Cg = 2.0 106 J m

-3 K-1; ground thermal conductivity: kg = 1.5 Wm-

1K-1; roughness length for momentum: z0m= 0.6 m; roughness length for heat: z0h = 0.00001 m;

incoming longwave radiation: 340 Wm-1 albedo: α = 0.08; emissivity: ε = 0.9;soil moisture content: SMC = 4%

0 3 6 9 12 15 18 21 24t [h]

-200

0

200

400

[Wm

-2]

Q*

Q

Q

Q

H

E

3.10.2001

0 3 6 9 12 15 18 21 24t [h]

-200

0

200

400

[Wm

-2]

Q*

Q

Q

Q

H

E

3.10.2001

Page 25: Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź,

The energy balance components for the center of Lodz. Comparison of the results of measurement (thin lines) and simulation (thick lines)

Measured and modeled urban energy balance components in Lodz (December 12th, 2001)

Parameters used in simulation: ground heat capacity: Cg = 2.0 106 J m

-3 K-1; ground thermal conductivity: kg = 1.0 Wm-

1K-1; roughness length for momentum: z0m= 0.6 m; roughness length for heat: z0h = 0.00001 m;

incoming longwave radiation: 200 Wm-1 albedo: α = 0.23; (snow)emissivity: ε = 0.85;soil moisture content: SMC = 35%

0 3 6 9 12 15 18 21 24t [h]

-200

0

200

400

[Wm

-2]

Q*

Q

Q

Q

H

E

8.12.2001

0 3 6 9 12 15 18 21 24t [h]

-200

0

200

400

[Wm

-2]

Q*

Q

Q

Q

H

E

8.12.2001

Page 26: Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź,

The energy balance components for the center of Łódź (left) and nightly temperatures courses at a rural and urban station (right). Comparison of the

results of measurement (thin lines) and simulation (thick lines)

Modeled and measured temperature evolution

0 3 6 9 12 15 18 21 24t [h]

-200

0

200

400

600

800

[Wm

-2]

Q *

Q H

Q E

Q

12 15 18 21 0 3 6 9 12t [h]

10

15

20

25

30

T [

oC

]

Tu

Tr

28 July 2001 27/28 July 2001

0 3 6 9 12 15 18 21 24t [h]

-200

0

200

400

600

800

[Wm

-2]

Q *

Q H

Q E

Q

12 15 18 21 0 3 6 9 12t [h]

10

15

20

25

30

T [

oC

]

Tu

Tr

28 July 2001 27/28 July 2001

0 3 6 9 12 15 18 21 24t [h]

-200

-100

0

100

200

[Wm

-2]

12 15 18 21 0 3 6 9 12t [h]

-15

-10

-5

0

T [

oC

]

Tu

Tr

8 December 2001 7/8 December 2001

0 3 6 9 12 15 18 21 24t [h]

-200

-100

0

100

200

[Wm

-2]

12 15 18 21 0 3 6 9 12t [h]

-15

-10

-5

0

T [

oC

]

Tu

Tr

8 December 2001 7/8 December 2001

Page 27: Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź,

Model applications

Page 28: Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź,

Dependence of the urban-rural temperature differences on the distance from a city border. Curves show a logarithmic fit to

the data

Model application – UHI and population

0 5000 10000 15000 20000 25000 30000D [m ]

0

1

2

3

4

5

Tm

x [o

C]

Ug[ms-1] L [Wm-2] SMCR 3 320 0.05 5 320 0.05 3 I&J 0.05 5 I&J 0.05 3 320 0.20 5 320 0.20

∆Tmx ~  log (D )

P ~  D2

∆Tmx ~  log (P )

Page 29: Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź,

0 2 4 6 8 10 12 14 16U g [m s -1]

0

1

2

3

4

5

6

7

Tm

x [o

C]

0.40 0.01

0.20 0.05

0.05 0.05

0.30 0.30

SMCR SMC U

L =320 Wm -2

0 2 4 6 8 10 12 14 16U g [m s -1]

0

1

2

3

4

5

6

7

Tm

x [o

C]

0.40 0.01

0.20 0.05

0.05 0.05

0.30 0.30

SMCR SMC U

L - I&J

Modeled dependence of the UHI intensity (T) on the wind speed

Model application – UHI and wind speed

3) power

2) exp.

Function types:

1) classical va(N)

T

vb(N)ea(N)T

dc)(va(N)

T

0 2 4 6 8 10 12 14 16U g [m s -1]

0

1

2

3

4

5

6

7

Tm

x [o

C]

0.40 0.01

0.20 0.05

0.05 0.05

0.30 0.30

SMCR SMC U

L - I&J

0 2 4 6 8 10 12 14 16U g [m s -1]

0

1

2

3

4

5

6

7

Tm

x [o

C]

0.40 0.01

0.20 0.05

0.05 0.05

0.30 0.30

SMCR SMC U

L =320 Wm -2

0 2 4 6 8 10 12 14 16U g [m s -1]

0

1

2

3

4

5

6

7

Tm

x [o

C]

0.40 0.01

0.20 0.05

0.05 0.05

0.30 0.30

SMCR SMC U

L - I&J

0 2 4 6 8 10 12 14 16U g [m s -1]

0

1

2

3

4

5

6

7

Tm

x [o

C]

0.40 0.01

0.20 0.05

0.05 0.05

0.30 0.30

SMCR SMC U

L =320 Wm -2

Page 30: Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź,

Isotherms of the UHI intensity (ΔTmx) as a function of wind and cloudiness

Model application – UHI and wind speed

V [m/s]

N

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8 9 10

1

2

34

A

V [m/s]

N

0

1

2

3

4

5

6

7

8

1 2 3 4 5 6 7 8 9 10

1

2

34

B

V [m/s]

N

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8 9 10

1

2

34

C

V [m/s]

N

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8 9 10

1

2

34

D

A – spline functions fitted to the data from Łódź (1997-1999)

B – classical fit ∆Tmx = (3.43 -0.033N

2)∙v −0.5 Explains 58.7% of T variance

C – power fit ΔTmx = (14.9 -0.14·N

2)· ·(2.28 + v)–1.22

Explains 61.0% of T variance

D – exponential fit ΔTmx = (5.51 – 0.50·N)·

·e –(0.41–0.067·N+0.005·N·N) ·v

Explains 61.2% of T variance

Page 31: Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź,

Modeled nighttime temperature courses for sites which differ roughness length only. On the left plot sites with different roughness length of temperature z0h

(the same z0m=0.2); on the right plot sites with different roughness length of momentum z0m (the same z0h=0.01);

- 1 2 - 9 - 6 - 3 0 3 6 9 1 2

1 6

2 0

2 4

2 8 z 0h [m]1e- 11e- 21e- 31e- 41e- 51e- 6

- 1 2 - 9 - 6 - 3 0 3 6 9 1 2

1 6

2 0

2 4

2 8 z 0m [m]0. 010. 10. 51. 02. 04. 0

Model application – the role of roughness lengths

Page 32: Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź,

SUEB and UHI– the role the thermal admittance

Modeled variation of the surface temperature following sunset for materials with different thermal admittances (μ) of the ground:

1) μ=600, 2) μ=1000, 3) μ=1400, 4) μ=1800, and 5) μ=2200 J m‑2 s‑1/2 K‑1.

Different combinations of initial surface temperature (To) and temperature of deep soil (TG) selected. In all cases L↓=260 Wm‑1

0 2 4 6 8 10t [h]-8

-6

-4

-2

0

2

4

6

8

T [o C

]

1

2

3

45

0 2 4 6 8 10t [h]-8

-6

-4

-2

0

2

4

6

8

T [o C

]

1

2

3

4

5

Tsurf=7oC, Tdeep=0oC

Tsurf=7oC, Tdeep=7oC Tsurf=7oC, Tdeep=14oC

Page 33: Slab surface energy balance scheme and its application to parameterisation of the energy fluxes on urban areas Krzysztof Fortuniak University of Łódź,

Slab models with properly chosen parameters can satisfactorily reproduce many singularities of the urban climate and can be use as a tool for investigation of the modification of a local climate by the urbanization.

Conclusions: