Urban Climate Model MUKLIMO 3 and the Cuboid Method

1 Appendix A

2 Urban climate model MUKLIMO_3 and the cuboid method

3 The urban climate model MUKLIMO_3 (in German: 3D Mikroskaliges Urbanes 4 KLImaMOdell) is a non-hydrostatic micro-scale model with z-coordinates, which solves 5 Reynolds-averaged Navier–Stokes equations to simulate atmospheric flow fields in presence 6 of buildings (Sievers and Zdunkowski 1985; Sievers 1990; Sievers 1995). The thermo- 7 dynamical version of the model includes prognostic equations for air temperature and 8 humidity, the parameterization of unresolved buildings, short-wave and long-wave radiation, 9 balanced heat and moisture budgets in the soil (Sievers et al. 1983) and a vegetation model 10 based on Siebert et al. (1992). The numerical approach for the calculation of short-wave 11 irradiances at the ground level, the walls and the roof of buildings in an environment with 12 unresolved built-up is described by Sievers and Früh (2012). The MUKLIMO_3 model uses a 13 simple formulation for turbulent mixing with the first-order closure of the turbulence scheme 14 based on the Monin-Obukhov similarity theory (MOST) and the Prandtl mixing length 15 approach (Sievers, 1987; 2012). Above the lowest atmospheric level, the model uses the

16 Blackadar’s mixing length (l∞=30 m for neutral and stable conditions) which is adapted 17 according to the stability criteria. The height of the convective layer calculated within the 18 time-varying 1D model (see below) is used to estimate the mixing length for unstable 19 conditions. In addition, the mixing length is modified in presence of buildings and trees. The 20 model takes into account the effects of cloud cover on radiation. However, it does not include 21 cloud processes, precipitation, horizontal runoff or anthropogenic heat.

22 The flow between buildings is parameterized through a porous media approach for 23 unresolved buildings (Gross, 1989). Maximum of 99 different land use classes can be 24 defined including specific land surface characteristics listed in a lookup table. In general, the 25 values are derived from geographical (GIS) data, which are provided by local and federal 26 authorities. Some of the data can be derived from airborne and satellite remote sensing. For 27 example, the identification of buildings and their heights can be provided with an overall 28 accuracy of more than 90% (Wurm and Taubenböck, 2010). Land use types are divided into 29 four main categories: built-up areas, traffic, vegetation and water. For each land use class, a 30 set of parameters is defined to describe land use properties and urban structures: fraction of

31 built area (γb), mean building height (hb), wall area index (wb), fraction of pavement of the

32 non-built area (v), fraction of tree cover (σt) and fraction of low vegetation of the remaining

33 surface (σc), height (hc) and leaf area index (LAIc) of the canopy layer as well as mean height

34 (ht) and leaf area index (LAIt) of the trees with separated values for the tree trunk and the tree 35 crown area. The vegetation is described in vertical layers: tree crown, tree trunk and low 36 vegetation. Grid cells with buildings do not include a tree fraction, but low vegetation is 37 assumed.

38 To initialize and drive the 3D simulation a 1D model version of MUKLIMO_3 is used. The 1D 39 simulation is initialized by atmospheric profiles of air temperature, humidity and wind, as well 40 as estimated values for soil temperature and moisture. At the beginning, soil temperature 41 and moisture are set constant throughout the soil column. After running the 1D model for 24 42 hours, the values for air temperature, relative humidity and wind are used to initialize the 3D 43 model run taking into account terrain height and soil type. The first hour of the 3D model 44 simulation, where the applied initial vertical profiles from the 1D model are adjusted for the 45 urban area, is excluded from the analysis. The 1D model continues to provide upper 46 boundary conditions for the entire duration of the 3D model run. The top layer of the 3D 47 model is constrained by hourly values for wind, air temperature and relative humidity 48 provided by the 1D model, which is generally higher than the 3D model. The lateral sides of 49 the 3D model have free boundary conditions with horizontal advection terms being zero at 50 the upstream domain boundaries.

51 In order to calculate climate indices for a 30-year period (e.g. mean annual number of SU), 52 the dynamical modelling approach is combined with the so-called “cuboid method” (Früh et 53 al. 2011; Zuvela-Aloise et al. 2014). The cuboid method refers to a tri-linear interpolation of 54 meteorological fields derived by single-day simulations from the urban climate model 55 MUKLIMO_3. Eight 3D simulations with duration of 24 hours for two prevailing wind 56 directions are calculated representing the cuboid corners. Calculation of mean annual SU for

57 the 30-year period is based on interpolated Tmax fields from the eight single-day simulations 58 using daily time series of the mean air temperature (T), relative humidity (rh) and wind speed 59 (v), including hourly wind direction from a reference station as input.

60 The cuboid corners are defined based on the observational data for summer heat conditions.

61 In case of Vienna, the cuboid range is: Tcmin = 15°C, Tcmax = 25°C; rhcmin = 42 %, rhcmax = 80 %

62 and vcmin = 0.7 m/s, vcmax = 4 m/s. The climatological data show that when the regional daily

63 mean air temperature is below Tcmin=15°C, the Tmax in the city centre will hardly exceed 25°C. 64 Therefore, these situations can be excluded from the calculation of summer days. The 1D 65 model runs which drive the 3D simulation are calculated for the rural station as they are

66 intended to represent the regional weather conditions with the mean daily values of (Tc, rhc,

67 vc) corresponding to the cuboid corners. It is important to note that these are idealized 68 simulations that do not necessarily represent typical summer day conditions. They 69 characterise rather a range of weather situations where a summer day can occur. Therefore, 70 the simulations are initialized with different stability conditions, cloudiness (from 0 to 0.875), 71 soil moisture, soil temperature (16°C, 23°C) and indoor temperature (20°C, 25°C) and the

72 initial 1D profiles are fitted to result in the given range of values for (Tc, rhc, vc).

73 All simulations are started on July 15 with 1 day spin up for the 1D boundary model. 74 Climatological records support that most summer days occur between June to August and 75 July 15 is chosen as a representative day since this day has an average sun height and day 76 length for the conditions in June to August. The 3D simulations are started on July 16 at 9 77 am CEST (Central European Summer Time) and ended on July 17 at 9 am CEST. Only the 78 time period between 10 am CEST on July 16 until 9 am CEST on July 17 is evaluated.

79 a) b)

81 Figure A1: Fraction of buildings (a), pavement (b), trees (c) and low vegetation (d) calculated on the 82 100 m horizontal resolution model grid. Source: Austrian Institute of Technology. Original data: Stadt 83 Wien - ViennaGIS. 84 85 References 86 Gross G (1989) Numerical simulation of the nocturnal flow systems in the Freiburg area for 87 different topographies. Beiträge zur Phys. Atmos. 62, 57–72

88 Siebert J, Sievers U, Zdunkowski W (1992) A one-dimensional simulation of the interaction 89 between land surface processes and the atmosphere. Bound.-Layer Meteor. 59, 1–34.

90 Sievers U, Forkel R, Zdunkowski W (1983) Transport equations for heat and moisture in the 91 soil and their application to boundary layer problems. Beiträge Physik der Atmosphäre 56, 92 58-83

93 Sievers U, Zdunskowski W (1985) A numerical simulation scheme for the albedo of city 94 street canyons. Boundary-Layer Meteorology 33, 245-257

95 Sievers U, Mayer I and Zdunkowski WG (1987) Numerische Simulation des urbanen Klimas 96 mit einem zweidimensionalen Modell, Meteorol. Rundschau 40(1 and 3), 40–52 and 65– 97 83

98 Sievers, U (1990) Dreidimensionale Simulationen in Stadtgebieten. Umwelt-meteorologie, 99 Schriftenreihe Band 15: Sitzung des Hauptausschusses II am 7. und 8. Juni in Lahnstein. 100 Kommission Reinhaltung der Luft im VDI und DIN, Düsseldorf. S. 92–105.

101 Sievers U (1995) Verallgemeinerung der Stromfunktionsmethode auf drei Dimensionen. Met. 102 Zeit. 4, 3-15

103 Sievers U, Früh B (2012) A practical approach to compute short-wave irradiance interacting 104 with subgrid-scale buildings. Met. Zeit. 21, 349-364

105 Sievers U (2012) Das kleinskalige Strömungsmodell MUKLIMO_3 Teil 1: Theoretische 106 Grundlagen, PC-Basisversion und Validierung. Berichte des Deutschen Wetterdienstes; 107 240, 142 pp., ISBN 978-3-88148-465-7

108 Wurm and Taubenböck (2010) Die lokale Ebene: Raumbezogene Analysen auf 109 Gebäudelevel. – In: Taubenböck, H. and S. Dech (Ed.): Fernerkundung im urbanen 110 Raum. Erdbeobachtung auf dem Weg zur Planungspraxis. – Wissenschaftliche 111 Buchgesellschaft, Darmstadt, 66 – 75.