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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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Outline 1)Urban atmosphere and urban models 2)Motivation 3)Slab surface energy balance model 4)Energy balance measurements in Lodz 5)Modeled and measured urban energy balance components 6)Model applications 7)Conclusions

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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

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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?

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The model

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Radiation budget: Q * = (1-α) I toth + εL – εσT s 4 I toth - short-wave radiation on the horizontal surface after Davis at al. (1975): Validation of the I toth model again Lodz data (selected sunny days) I toth = S 0 sinh s ·τ wa ·τ da (1 + τ ws ·τ ds ·τ rs )/2 S 0 - solar constant, h s - 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 }] σT 4 The surface energy balance model: Radiation budget: Q*+Q G +Q H +Q LE =0

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Heat flux to the ground (Q G ) and temperature profile is found by numerical solution of the one-dimensional heat diffusion equation: ν g - 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*+Q G +Q H +Q LE =0 Q*+Q G +Q H +Q LE + D Q S =0 DQSDQS QGQG QGQG Q*+Q G +Q H +Q LE =0

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Validation of ground temperature calculations – comparison with temperature (5cm above ground) evolution at Lodz-Lublinek meteorological station in calm, cloudless nights (Q H,Q LE =0) Surface cooling in calm cloudless nights Energy balance: Q*+Q G +Q H +Q LE =0

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Parametrisation of turbulent heat fluxes (Q H and Q LE ) bases on Monin-Obukhov similarity theory with Busingers 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: stability parameter z/L is found by iterative solution of: where Ri b 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*+Q G +Q H +Q LE =0

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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

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Modeled (dashed) versus measured (solid) temperature and humidity profiles in day 33 Wangara experiment (9.00h, 12.00h, 15.00h) LouisMellor-YamadaGambo Sievers & Zdunkowski temperature [C] The boundary layer model – model validation

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Modeled temperature and wind speed profiles over urban and rural sites in the night Model testing – vertical profiles

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Energy balance measurements in Lodz

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old town blocks of flats industrial Energy balance measurement point Lodz-Lublinek meteorological station Measurements in Lodz

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Energy balance measurement point

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Measured and modeled energy balance components

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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 7 th, 2001) Parameters used in simulation: ground heat capacity: C g = 2.0 10 6 J m -3 K -1 ; ground thermal conductivity: k g = 1.5 Wm -1 K -1 ; roughness length for momentum: z 0m = 0.6 m; roughness length for heat: z 0h = 0.00001 m; incoming longwave radiation: 230 Wm -1 albedo: α = 0.08; emissivity: ε = 0.9; soil moisture content: SMC = 35%

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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 28 th, 2001) Parameters used in simulation: ground heat capacity: C g = 2.0 10 6 J m -3 K -1 ; ground thermal conductivity: k g = 1.5 Wm -1 K -1 ; roughness length for momentum: z 0m = 0.6 m; roughness length for heat: z 0h = 0.00001 m; incoming longwave radiation: 220 Wm -1 albedo: α = 0.13; (snow) emissivity: ε = 0.85; soil moisture content: SMC = 15%

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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 30 th – May 3 rd, 2001) Parameters used in simulation: ground heat capacity: C g = 2.0 10 6 J m -3 K -1 ; ground thermal conductivity: k g = 1.5 Wm -1 K -1 ; roughness length for momentum: z 0m = 0.6 m; roughness length for heat: z 0h = 0.00001 m; incoming longwave radiation: 310 Wm -1 albedo: α = 0.08; emissivity: ε = 0.9; soil moisture content: SMC = 3%

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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 7 th, 2001) Parameters used in simulation: ground heat capacity: C g = 2.0 10 6 J m -3 K -1 ; ground thermal conductivity: k g = 1.5 Wm -1 K -1 ; roughness length for momentum: z 0m = 0.6 m; roughness length for heat: z 0h = 0.00001 m; incoming longwave radiation: 370 Wm -1 albedo: α = 0.08; emissivity: ε = 0.9; soil moisture content: SMC = 8%

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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 19 th, 2001) Parameters used in simulation: ground heat capacity: C g = 2.0 10 6 J m -3 K -1 ; ground thermal conductivity: k g = 1.5 Wm -1 K -1 ; roughness length for momentum: z 0m = 0.6 m; roughness length for heat: z 0h = 0.00001 m; incoming longwave radiation: 370 Wm -1 albedo: α = 0.08; emissivity: ε = 0.9; soil moisture content: SMC = 7%

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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 10 th, 2001) Parameters used in simulation: ground heat capacity: C g = 2.0 10 6 J m -3 K -1 ; ground thermal conductivity: k g = 1.5 Wm -1 K -1 ; roughness length for momentum: z 0m = 0.6 m; roughness length for heat: z 0h = 0.00001 m; incoming longwave radiation: 340 Wm -1 albedo: α = 0.08; emissivity: ε = 0.9; soil moisture content: SMC = 4%

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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 24 th, 2001) Parameters used in simulation: ground heat capacity: C g = 2.0 10 6 J m -3 K -1 ; ground thermal conductivity: k g = 1.0 Wm -1 K -1 ; roughness length for momentum: z 0m = 0.6 m; roughness length for heat: z 0h = 0.00001 m; incoming longwave radiation: 220 Wm -1 albedo: α = 0.10; emissivity: ε = 0.9; soil moisture content: SMC = 4%

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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 12 th, 2001) Parameters used in simulation: ground heat capacity: C g = 2.0 10 6 J m -3 K -1 ; ground thermal conductivity: k g = 1.0 Wm -1 K -1 ; roughness length for momentum: z 0m = 0.6 m; roughness length for heat: z 0h = 0.00001 m; incoming longwave radiation: 200 Wm -1 albedo: α = 0.23; (snow) emissivity: ε = 0.85; soil moisture content: SMC = 35%

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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

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Model applications

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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 T mx ~ log (D ) P ~ D 2 T mx ~ log (P )

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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

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Isotherms of the UHI intensity (ΔT mx ) as a function of wind and cloudiness Model application – UHI and wind speed A – spline functions fitted to the data from Łódź (1997-1999) B – classical fit T mx = (3.43 -0.033N 2 )v 0.5 Explains 58.7% of T variance C – power fit ΔT mx = (14.9 -0.14·N 2 )· ·(2.28 + v) –1.22 Explains 61.0% of T variance D – exponential fit ΔT mx = (5.51 – 0.50·N)· ·e –(0.41–0.067·N+0.005·N·N) ·v Explains 61.2% of T variance

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Model application – typical course of UHI L =320 Wm -2 L =[1–0,261·exp{–7,77·10 –4 ·(273–T) 2 }]σT 4 L =([1–0,261·exp{–7,77·10 –4 ·(273–T) 2 }]σT 4 + 320)/2 Modeled nocturnal course of the urban-rural temperature contrasts for different courses of L

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Modeled nighttime temperature courses for sites which differ roughness length only. On the left plot sites with different roughness length of temperature z 0h (the same z 0m =0.2); on the right plot sites with different roughness length of momentum z 0m (the same z 0h =0.01); Model application – the role of roughness lengths

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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 (T o ) and temperature of deep soil (T G ) selected. In all cases L =260 Wm 1 T surf =7 o C, T deep =0 o CT surf =7 o C, T deep =7 o CT surf =7 o C, T deep =14 o C

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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:

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Fifth International Conference on Urban Climate 1-5 September 2003 Lodz, Poland http://www.geo.uni.lodz.pl/~icuc5/

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