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Krzysztof Fortuniak University of Łódź, Poland Brian Offerle

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

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Krzysztof Fortuniak University of Łódź, Poland Brian Offerle

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  1. 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

  2. Outline Urban atmosphere and urban models Motivation Slab surface energy balance model Energy balance measurements in Lodz Modeled and measured urban energy balance components Model applications Conclusions

  3. Urban Atmosphere and Urban Models Boundary layer models: different models from 3D to 1D with different turbulence parameterizations 1D model with first order turbulence closure urban boundary layer presented model urban canopy layer Surface energy balance models: 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 3. Slab models: town is treated as a single entity with specified physical parameters

  4. 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?

  5. The model

  6. The surface energy balance model: Radiation budget: Q*+QG+QH+QLE=0 Radiation budget: Q* = (1-α) Itoth + εL↓ – εσTs4 Itoth - short-wave radiation on the horizontal surface after Davis at al. (1975): 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 Validation of the Itoth model again Lodz data (selected sunny days)

  7. The surface energy balance model:Heat flux to the ground:Q*+QG+QH+QLE=0 Heat flux to the ground(QG) and temperature profile is found by numerical solution of the one-dimensional heat diffusion equation: 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 Q*+QG+QH+QLE=0 Q*+QG+QH+QLE+DQS=0 DQS QG QG

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

  9. The surface energy balance model:Turbulent heat fluxes :Q*+QG+QH+QLE=0 Parametrisation ofturbulent 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: stability parameter z/L isfoundby iterative solution of: where Rib is the bulk Richardson number: In calculations of the turbulent moisture flux additional surface resistance is considered acording to Best (1998) method.

  10. The boundary layer model One dimensional first order model • 28 levels form 2m to 5000m • constant upper boundary condition • different local turbulence closure schemes tested ( K–l ): Louis (1979) Mellor and Yamada (1982) Gambo (1978) Sievers and Zdunkowski (1986) - advection estimated by simultaneous calculation for rural and urban points

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

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

  13. Energy balance measurements in Lodz

  14. Measurements in Lodz Lodz-Lublinek meteorologicalstation old town blocks of flats Energy balance measurement point industrial

  15. Energy balancemeasurement point

  16. Energy balancemeasurement point

  17. Energy balancemeasurement point

  18. Measured and modeled energy balance components

  19. Measured and modeled urban energy balance components in Lodz (March 7th, 2001) The energy balance components for the center of Lodz. Comparison of the results of measurement (thin lines) and simulation (thick lines) Parameters used in simulation: ground heat capacity: Cg = 2.0 106 Jm-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-1albedo: α = 0.08; emissivity: ε = 0.9; soil moisture content: SMC = 35%

  20. Measured and modeled urban energy balance components in Lodz (March 28th, 2001) The energy balance components for the center of Lodz. Comparison of the results of measurement (thin lines) and simulation (thick lines) Parameters used in simulation: ground heat capacity: Cg = 2.0 106 Jm-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-1albedo: α = 0.13; (snow) emissivity: ε = 0.85; soil moisture content: SMC = 15%

  21. Measured and modeled urban energy balance components in Lodz (April 30th – May 3rd, 2001) The energy balance components for the center of Lodz. Comparison of the results of measurement (thin lines) and simulation (thick lines) Parameters used in simulation: ground heat capacity: Cg = 2.0 106 Jm-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-1albedo: α = 0.08; emissivity: ε = 0.9; soil moisture content: SMC = 3%

  22. Measured and modeled urban energy balance components in Lodz (July 7th, 2001) The energy balance components for the center of Lodz. Comparison of the results of measurement (thin lines) and simulation (thick lines) Parameters used in simulation: ground heat capacity: Cg = 2.0 106 Jm-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-1albedo: α = 0.08; emissivity: ε = 0.9; soil moisture content: SMC = 8%

  23. Measured and modeled urban energy balance components in Lodz (August 19th, 2001) The energy balance components for the center of Lodz. Comparison of the results of measurement (thin lines) and simulation (thick lines) Parameters used in simulation: ground heat capacity: Cg = 2.0 106 Jm-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-1albedo: α = 0.08; emissivity: ε = 0.9; soil moisture content: SMC = 7%

  24. Measured and modeled urban energy balance components in Lodz (October 10th, 2001) The energy balance components for the center of Lodz. Comparison of the results of measurement (thin lines) and simulation (thick lines) Parameters used in simulation: ground heat capacity: Cg = 2.0 106 Jm-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-1albedo: α = 0.08; emissivity: ε = 0.9; soil moisture content: SMC = 4%

  25. Measured and modeled urban energy balance components in Lodz (December 12th, 2001) The energy balance components for the center of Lodz. Comparison of the results of measurement (thin lines) and simulation (thick lines) Parameters used in simulation: ground heat capacity: Cg = 2.0 106 Jm-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-1albedo: α = 0.23; (snow) emissivity: ε = 0.85; soil moisture content: SMC = 35%

  26. Modeled and measured temperature evolution 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)

  27. Model applications

  28. Model application – UHI and population Dependence of the urban-rural temperature differences on the distance from a city border. Curves show a logarithmic fit to the data ∆Tmx ~  log(D) P ~  D2 ∆Tmx ~  log(P)

  29. Model application – UHI and wind speed Modeled dependence of the UHI intensity (DT) on the wind speed Function types: 1) classical 2) exp. 3) power

  30. Model application – UHI and wind speed Isotherms of the UHI intensity (ΔTmx) as a function of wind and cloudiness A – spline functions fitted to the data from Łódź (1997-1999) B – classical fit ∆Tmx= (3.43 -0.033N2)∙v−0.5 Explains 58.7% of DT variance C – power fit ΔTmx = (14.9 -0.14·N2)··(2.28 + v)–1.22 Explains 61.0% of DT 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 DT variance

  31. Model application– the role of roughness lengths 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);

  32. 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 Tsurf=7oC, Tdeep=0oC Tsurf=7oC, Tdeep=7oC Tsurf=7oC, Tdeep=14oC

  33. Conclusions: 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.

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