# Flexible Treatment of Radiative Transfer in Complex Urban Canopies for Use in Weather and Climate Models

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## Abstract

We describe a new approach for modelling the interaction of solar and thermal-infrared radiation with complex multi-layer urban canopies. It uses the discrete-ordinate method for describing the behaviour of the radiation field in terms of a set of coupled ordinary differential equations that are solved exactly. The rate at which radiation intercepts building walls and is exchanged laterally between clear-air and vegetated parts of the urban canopy is described statistically. Key features include the ability to represent realistic urban geometry (both horizontal and vertical), atmospheric effects (absorption, emission, and scattering), and spectral coupling to an atmospheric radiation scheme. In the simple case of a single urban layer in a vacuum, the new scheme matches the established matrix-inversion method very closely when eight or more streams are used, but with the four-stream configuration being of adequate accuracy in an operational context. Explicitly representing gaseous absorption and emission in the urban canopy is found to have a significant effect on net fluxes in the thermal infrared. Indeed, we calculate that for the mid-latitude summer standard atmosphere at mean sea level, 37% of thermal-infrared energy is associated with a mean free path of less than 50 m, which is the typical mean line-of-sight distance between walls in an urban area. The interaction of solar radiation with trees has been validated by comparison to Monte Carlo benchmark calculations for an open forest canopy over both bare soil and snow.

## Keywords

Discrete ordinate method Three-dimensional radiative transfer Urban form Urban vegetation## Notes

### Acknowledgements

Sue Grimmond is thanked for valuable comments on the manuscript and Valéry Masson, Robert Schoetter, William Morrison, and Meg Stretton are thanked for useful discussions. Jean-Luc Widlowski provided the Monte Carlo simulations shown in Fig. 5. The building geometry for London used in Fig. 1 was obtained from Emu Analytics, whose data combine building outlines from Ordnance Survey Open Map with building height from lidar data collected in 2014 and 2015. The tree locations and sizes used in the same figure were released by the London Borough of Camden under the Open Government License v3.0.

## References

- Baklanov A, Grimmond CSB, Carlson D, Terblanche D, Tang X, Bouchet V, Lee B, Langendijk G, Kolli RK, Hovsepyan A (2018) From urban meteorology, climate and environment research to integrated city services. Urban Clim 23:330–341CrossRefGoogle Scholar
- Flatau PJ, Stephens GL (1998) On the fundamental solution of the radiative transfer equation. J Geophys Res 93:11037–11050CrossRefGoogle Scholar
- Gastellu-Etchegorry JP (2008) 3D modeling of satellite spectral images, radiation budget and energy budget of urban landscapes. Meteorol Atmos Phys 102:187–207CrossRefGoogle Scholar
- Grimmond CS, Oke TR (1999) Aerodynamic properties of urban areas derived from analysis of surface form. J Appl Meteorol 38:1262–1292CrossRefGoogle Scholar
- Grimmond CS, Blackett M, Best MJ, Barlow J, Baik J, Belcher SE, Bohnenstengel SI, Calmet I, Chen F, Dandou A, Fortuniak K, Gouvea ML, Hamdi R, Hendry M, Kawai T, Kawamoto Y, Kondo H, Krayenhoff ES, Lee S, Loridan T, Martilli A, Masson V, Miao S, Oleson K, Pigeon G, Porson A, Ryu Y, Salamanca F, Shashua-Bar L, Steeneveld G, Tombrou M, Voogt J, Young D, Zhang N (2010) The international urban energy balance models comparison project: first results from phase 1. J Appl Meteorol Climatol 49:1268–1292CrossRefGoogle Scholar
- Harman IN, Best MJ, Belcher SE (2004) Radiative exchange in an urban street canyon. Boundary-Layer Meteorol 110:301–316CrossRefGoogle Scholar
- Hogan RJ (2019) An exponential model of urban geometry for use in radiative transfer applications. Boundary-Layer Meteorol 170:357–372CrossRefGoogle Scholar
- Hogan RJ, Bozzo A (2018) A flexible and efficient radiation scheme for the ECMWF model. J Adv Model Earth Syst 10:1990–2008CrossRefGoogle Scholar
- Hogan RJ, Schäfer SAK, Klinger C, Chiu J-C, Mayer B (2016) Representing 3D cloud-radiation effects in two-stream schemes: 2. Matrix formulation and broadband evaluation. J Geophys Res 121:8583–8599Google Scholar
- Hogan RJ, Quaife T, Braghiere R (2018) Fast matrix treatment of 3-D radiative transfer in vegetation canopies: SPARTACUS-Vegetation 1.1. Geosci Model Dev 11:339–350CrossRefGoogle Scholar
- Krayenhoff ES, Voogt JA (2016) Daytime thermal anisotropy of urban neighbourhoods: morphological causation. Remote Sens 8:108CrossRefGoogle Scholar
- Krayenhoff ES, Christen A, Martilli A, Oke TR (2014) A multi-layer radiation model for urban neighbourhoods with trees. Boundary-Layer Meteorol 151:139–178CrossRefGoogle Scholar
- Lindberg F, Holmer B, Thorsson S (2008) SOLWEIG 1.0: modelling spatial variations of 3D radiant fluxes and mean radiant temperature in complex urban settings. Int J Biometeorol 52:697–713CrossRefGoogle Scholar
- Lindberg F, Grimmond CSB, Martilli A (2015) Sunlit fractions on urban facets: impact of spatial resolution and approach. Urban Clim 12:65–84CrossRefGoogle Scholar
- Masson V (2000) A physically-based scheme for the urban energy budget in atmospheric models. Boundary-Layer Meteorol 94:357–397CrossRefGoogle Scholar
- McClatchey RA, Fenn RW, Selby JEA, Volz FE, Garing JS (1972) Optical properties of the atmosphere, 3rd edn. Air Force Cambridge Research Laboratories, Report no. AFCRL72-0497, L. G. Hanscom FieldGoogle Scholar
- Meador WE, Weaver WR (1980) Two-stream approximations to radiative transefer in planetary atmospheres: a unified description of existing methods and a new improvement. J Atmos Sci 37:630–643CrossRefGoogle Scholar
- Meier F, Scherer D, Richters J, Christen A (2011) Atmospheric correction of thermal-infrared imagery of the 3-D urban environment acquired in oblique viewing geometry. Atm Meas Tech 4:909–922CrossRefGoogle Scholar
- Mlawer EJ, Taubman SJ, Brown PD, Iacono MJ, Clough SA (1997) Radiative transfer for inhomogeneous atmospheres: RRTM, a validated correlated-k model for the longwave. J Geophys Res Atmos 102:16 663–16 682CrossRefGoogle Scholar
- Morrison W, Kotthaus S, Grimmond CSB, Inagaki A, Tin T, Gastellu-Etchegorry J-P, Kanda M, Merchant CJ (2018) A novel method to obtain three-dimensional urban surface temperature from ground-based thermography. Rem Sens Environ 215:268–283CrossRefGoogle Scholar
- Oleson KW, Bonan GB, Feddema J, Vertenstein M, Grimmond CS (2008) An urban parameterization for a global climate model: 1. Formulation and evaluation for two cities. J Appl Meteor Climatol 47:1038–1060CrossRefGoogle Scholar
- Redon EC, Lemonsu A, Masson V, Morille B, Musy M (2017) Implementation of street trees within the solar radiative exchange parameterization of TEB in SURFEX v8.0. Geosci Model Dev 10:385–411CrossRefGoogle Scholar
- Schubert S, Grossman-Clarke S, Martilli A (2012) A double-canyon radiation scheme for multi-layer urban canopy models. Boundary-Layer Meteorol 145:439–468CrossRefGoogle Scholar
- Stamnes K, Tsay SC, Wiscombe W, Jayaweera K (1988) Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media. Appl Opt 27:2502–2509CrossRefGoogle Scholar
- Sykes J (1951) Approximate integration of the equation of transfer. Mon Not R Astron Soc 11:377–386CrossRefGoogle Scholar
- Thomas GE, Stamnes K (1999) Radiative transfer in the atmosphere and ocean. Cambridge, 517 ppGoogle Scholar
- Widlowski J-L, Pinty B, Clerici M, Dai Y, De Kauwe M, de Ridder K, Kallel A, Kobayashi H, Lavergne T, Ni-Meister W, Olchev A, Quaife T, Wang S, Yang W, Yang Y, Yuan H (2011) RAMI4PILPS: an intercomparison of formulations for the partitioning of solar radiation in land surface models. J Geophys Res Biogeosci 116:G02019. https://doi.org/10.1029/2010JG001511 CrossRefGoogle Scholar
- Yang X, Li Y (2015) The impact of building density and building height heterogeneity on average urban albedo and street surface temperature. Build Environ 90:146–156CrossRefGoogle Scholar