This discussion paper is/has been under review for the journal Geoscientific Model Development (GMD) Please refer to the corresponding final paper in GMD if available Discussion Paper Geosci Model Dev Discuss., 7, 4463–4525, 2014 www.geosci-model-dev-discuss.net/7/4463/2014/ doi:10.5194/gmdd-7-4463-2014 © Author(s) 2014 CC Attribution 3.0 License | Introduction Conclusions References Tables Figures Published by Copernicus Publications on behalf of the European Geosciences Union Back Close Discussion Paper Correspondence to: M Jähn (jaehn@tropos.de) M Jähn et al Abstract Leibniz Institute for Tropospheric Research, Permoserstrasse 15, 04318 Leipzig, Germany Received: 16 June 2014 – Accepted: 27 June 2014 – Published: 18 July 2014 ASAM v2.7 | M Jähn, O Knoth, M König, and U Vogelsberg 7, 4463–4525, 2014 Discussion Paper ASAM v2.7: a compressible atmospheric model with a Cartesian cut cell approach GMDD Title Page Full Screen / Esc | Printer-friendly Version Discussion Paper | 4463 Interactive Discussion Introduction Conclusions References Tables Figures Back Close Title Page Full Screen / Esc Printer-friendly Version Discussion Paper | 4464 M Jähn et al | 25 ASAM v2.7 Abstract Discussion Paper 20 In this paper we present the numerical solver ASAM (All Scale Atmospheric Model) that has been developed at the Leibniz Institute for Tropospheric Research (TROPOS), Leipzig ASAM was initially designed for CFD (Computational Fluid Dynamics) simulations around buildings where obstacles are included within a Cartesian grid by a cut cell method This approach is also used to include real orographic data in the model domain With this attempt one remains within the Cartesian grid and no artificial forces in the vicinity of an obstacle or topographic structure occur in comparison to other coordinate systems like terrain-following coordinates (Lock et al., 2012) Several techniques have been developed to overcome these non-physical errors, especially when spatial scales of three-dimensional models become finer Tripoli and Smith (2014a) introduced a Variable-Step Topography (VST) surface coordinate system within a nonhydrostatic host model Unlike the traditional discrete-step approach, the depth of a grid box intersecting with a topographical structure is adjusted to its height, which leads to straight 7, 4463–4525, 2014 | 15 Introduction GMDD Discussion Paper | 10 In this work, the fully compressible, nonhydrostatic atmospheric model ASAM is presented A cut cell approach is used to include obstacles and orography into the Cartesian grid Discretization is realized by a mixture of finite differences and finite volumes and a state limiting is applied An implicit time integration scheme ensures numerical stability around small cells To make the model applicable for atmospheric problems, physical parameterizations like a Smagorinsky subgrid scale model, a two-moment bulk microphysics scheme, precipitation and vertical surface fluxes by a constant flux layer or a more complex soil model are implemented Results for three benchmark test cases from the literature are shown A sensitivity study regarding the development of a convective boundary layer together with island effects at Barbados is carried out to show the capability to perform real case simulations with ASAM Discussion Paper Abstract Interactive Discussion 4465 | ASAM v2.7 M Jähn et al Abstract Introduction Conclusions References Tables Figures Back Close Discussion Paper Title Page Full Screen / Esc | Printer-friendly Version Discussion Paper 25 7, 4463–4525, 2014 | 20 GMDD Discussion Paper 15 | 10 Discussion Paper cut cells Numerical tests show that this technique produce better results than the conventional approaches for different topography (severe and smooth) types (Tripoli and Smith, 2014b) In their cases, also the computational costs with the VST approach are reduced because there is no need of extra functional transform calculations due to metric terms Steppeler et al (2002) derived approximations for z coordinate nonhydrostatic atmospheric models by using the shaved-element finite-volume method There, the dynamics are computed in the cut cell system, whereas the physics computation remains in the terrain-following system The cut cell method is also used in the Ocean– Land–Atmosphere Model (OLAM) (Walko and Avissar, 2008a), which extends the Regional Atmospheric Modeling System (RAMS) to a global model domain In OLAM, the shaved-cell method is applied to an icosahedral mesh (Walko and Avissar, 2008b) When using cut cells, no matter what particular scheme, low-volume cells will always be generated To avoid instability problems around these small cells, the time integration scheme has to be adapted For this, linear-implicit Rosenbrock time integration schemes are used in ASAM The here presented model is a developing research code and has a lot of different options to choose like different numerical methods (e.g split-explicit Runge–Kutta schemes), number of prognostic variables, physical parameterizations or the change to spherical grid types ASAM is a fully parallelized software using the Message Passing Interface (MPI) and the domain decomposition method The code is easily portable between different platforms like Linux, IBM or Mac OS With these features, large eddy simulations (LES) with spatial resolutions of O(100 m) can be performed with respect to a sufficiently resolved terrain structure The model was recently used for a study of dynamic flow structures in a turbulent urban environment of a building-resolving resolution (König, 2013) A separately developed LES model at TROPOS is called ASAMgpu (Horn, 2012) It includes some basic features of the ASAM code and runs on graphics processing units (GPUs), which enables very time-efficient computations and post-processing However, Interactive Discussion M Jähn et al Introduction Conclusions References Tables Figures Back Close Title Page Full Screen / Esc | Description of the All Scale Atmospheric Model ASAM v2.7 Abstract Discussion Paper 7, 4463–4525, 2014 | 20 GMDD Discussion Paper 15 | 10 Discussion Paper this model is not as adjustable as the original ASAM code and the inclusion of threedimensional orographical structures is not implemented so far This paper is structured as follows The next section deals with a general description of the model It includes the basic equations that are solved numerically and the used energy variable Also, the cut cell approach and spatial discretization as well as the used time integration scheme are described In Sect 3, mandatory physical parameterizations for LES like subgrid scale model, microphysics etc are presented Results of three two-dimensional benchmark test cases are shown in Sect The first one is a cold bubble that sinks down and creates a density current as described in Straka et al (1993) A moist rising bubble case in a supersaturated environment by Bryan and Fritsch (2002) has been chosen to show the effects of latent heat release and the condensation process To demonstrate the capability of the cut cell method, the results of a third case with simulated flow around an idealized row of mountains and a subsequent generation of gravity waves are presented (Schaer et al., 2002) Some more complex simulations are performed in Sect There, a 3-D LES sensitivity study dealing with island effects at the Caribbean island Barbados (13◦ 06 N, 59◦ 37 W) is done The island shape and topography are directly included in the grid An analysis of the terrain effect and changes in wind speed and moisture load is carried out Section describes how to get access to the model code and which visualization software is used followed by concluding remarks in the final section Printer-friendly Version Governing equations The flux-form compressible Euler equations for the atmosphere are ∂ρ + ∇ · (ρv ) = ∂t (1) | 4466 Discussion Paper 2.1 Interactive Discussion (2) (3) T Rv − − qc Rd (4) p = ρRd θρ 15 p p0 κm (5) κm Introduction Conclusions References Tables Figures Back Close Title Page Full Screen / Esc Printer-friendly Version Discussion Paper | 4467 M Jähn et al | 20 In the above two equations θ = T (p0 /p) is the potential temperature, qv = ρv /ρ is the mass ratio of water vapor in the air (specific humidity), qc = ρc /ρ is the mass ratio of cloud water in the air, p0 a reference pressure and κm = (qd Rd +qv Rv )/(qd cpd +qv cpv + qc cpl ) the Poisson constant for the air mixture (dry air, water vapor, cloud water) with qd = ρd /ρ Rd and Rv are the gas constants for dry air and water vapor, respectively The number of additional equations like Eq (3) depends on the complexity of the used microphysical scheme Furthermore, tracer variables can also be included The values of all relevant physical constants are listed in Table ASAM v2.7 Abstract Discussion Paper where the equation of state can be expressed as follows: 7, 4463–4525, 2014 | θ ρ = θ + qv GMDD Discussion Paper 10 | where ρ is the total air density, v = (u, v, w) the three-dimensional velocity vector, p the air pressure, g the gravitational acceleration, Ω the angular velocity vector of the earth, φ a scalar quantity and Sφ the sum of its corresponding source terms The energy equation in the form of Eq (3) is represented by the (dry) potential temperature θ In the presence of water vapor and cloud water, this quantity is replaced by the density potential temperature θρ (Emanuel, 1994) as a more generalized form of the virtual potential temperature θv : Discussion Paper ∂(ρv ) + ∇ · (ρv v ) = −∇p − ρg − 2Ω × (ρv ) ∂t ∂(ρφ) + ∇ · (ρv φ) = Sφ ∂t Interactive Discussion M Jähn et al Introduction Conclusions References Tables Figures Back Close Title Page Full Screen / Esc | Printer-friendly Version Discussion Paper | 4468 ASAM v2.7 Abstract Discussion Paper 25 7, 4463–4525, 2014 | 20 GMDD Discussion Paper 15 The spatial discretization is done on a Cartesian grid with grid intervals of lengths ∆xi , ∆yj , ∆zk and can easily be extended to any logically orthogonal rectangular grid like spherical or cylindrical coordinates First, it is described for the Cartesian case Generalizations are discussed afterwards Orography and other obstacles like buildings are presented by cut cells, which are the result of the intersection of the obstacle with the underlying Cartesian grid In Fig different possible configurations are shown for the three-dimensional case For each Cartesian cell, the free face area of the six faces and the free volume area of the cell are stored This is the part that is outside of the obstacle These values are denoted for the grid cell i , j , k by FUi −1/2,j ,k , FUi +1/2,j ,k , FVi ,j −1/2,k , FVi ,j +1/2,k , FWi ,j ,k−1/2 , FWi ,j ,k+1/2 , Vi ,j ,k respectively In the following, the relative notations FUL and FUR are used, e.g as shown in Fig The spatial discretization is formulated in terms of the grid interval length and the face and volume areas The variables are arranged on a staggered grid with momentum at the cell faces and all other variables at the cell center The discretization is a mixture of finite volumes and finite differences In the finite volume context the main task is the reconstruction of values and gradients at cell faces from cell centered values The discretization of the advection operator is performed for a generic cell centered scalar variable φ In the context of a finite volume discretization point values of the scalar value φ are needed at the faces of this grid cell Knowing these face values, the advection operator in U direction is discretized by (FUR UFR φR − FUL UFL φL )/VC To approximate these values at the faces, a biased upwind third-order procedure with additional limiting is used (Van Leer, 1994) Assuming a positive flow in the x direction, the third order approximation at xi +1/2 is obtained by quadratic interpolation from the three values as shown in Fig The interpolation condition is that the three cell-averaged values are fitted: | 10 Cut cells and spatial discretization Discussion Paper 2.2 Interactive Discussion hC (hL + hC ) (φR − φC ) + (hC + hR )(hL + hC + hR ) = φC + α1 (φR − φC ) + α2 (φC − φL ) hC hR (hL + hC )(hL + hC + hR ) (φC − φL ) (6) To achieve positivity in Eq (6), we apply state limiting For this task (Eq 6) is rewritten in slope-ratio formulation Discussion Paper φFR = φC + | where K = α1 10 φR − φC φC − φL + α2 (8) Then K is replaced by the limiter 15 , min(δ, K ) , δ=2 (9) hL = VL /FL (10) hC = 0.5VC /(FL + FR ) (11) References Tables Figures Back Close Full Screen / Esc Printer-friendly Version | 4469 Conclusions Discussion Paper as proposed by Sweby (1984) This limiter has the property that the unlimited higher order scheme (Eq 6) is used as much as possible and it is utilized only then when it is needed In the case of φ = 0, the scheme degenerates to the simple first-order upwind scheme The coefficients α1 and α2 can be computed in advance to minimize the overhead for a non-uniform grid In the case of a uniform grid the coefficients are constant, i.e they are equal to 1/3 and 1/6 For a detailed discussion of the benefits of this approach and numerical experiments also see Hundsdorfer et al (1995) This procedure is applied in all three grid directions, where the virtual grid sizes h are defined by Introduction Title Page | 20 φC − φL M Jähn et al Abstract Discussion Paper φ = max 0, φR − φC ASAM v2.7 | (7) 7, 4463–4525, 2014 Discussion Paper φFR = φC + K (φC − φL ) GMDD Interactive Discussion (13) The tendency interpolation from cells (TULC , TURC ) to a face (TUF ) is obtained by the arithmetic mean of the two tendencies of the two shifted cell components originated from the same face For a cut face the interpolation takes the form TUF = VR TULC FUR + FUC + VL TURC FUL + FUC FUC (14) 2.3 Time integration After spatial discretization an ordinary differential equation y(t) = F (y(t)) (15) Introduction Conclusions References Tables Figures Back Close Title Page Full Screen / Esc Printer-friendly Version | 4470 M Jähn et al Abstract Discussion Paper The pressure gradient and the Buoyancy term are computed for all faces with standard difference and interpolation formulas with the grid sizes taken from the underlying Cartesian grid ASAM v2.7 | 20 if FUL ≥ FUR else Discussion Paper 15 UFL UFL FUL + UFR (FUR − FUL )UFR 7, 4463–4525, 2014 | ULC = GMDD Discussion Paper To solve the momentum equation, the non-linear advection term is needed on the face This is achieved by a shifting technique introduced by Hicken et al (2005) for the incompressible Navier–Stokes-Equation For each cell two cell-centered values of each of the three components of the cartesian velocity vector are computed and transported with the above advection scheme for a cell-centered scalar value The obtained tendencies are then interpolated back to the faces For a normal cell the shifted values are obtained from the six momentum face values, whereas for a cut cell the shift operation takes into account the weights of the faces of the two opposite sides | 10 (12) Discussion Paper hR = VR /FR Interactive Discussion i −1 (I − τγJ) ki = τF (yn + i −1 αi j uj ) + i = 1, , s (16) j =1 | j =1 βi j kj , 10 Sk1 = τF (yn ) , 15 (18) (19) M Jähn et al Introduction Conclusions References Tables Figures Back Close Title Page Full Screen / Esc | Sk2 = τF yn + k1 − k1 , 3 yn+1 = yn + k1 + k2 , 4 S = I − γτJ, J ≈ F (yn ) Printer-friendly Version | 4471 Discussion Paper (20) √ with γ = + or in matrix form in Table A second method was constructed from a low storage three stage second-order Runge–Kutta method, which is used in split-explicit time integration methods in the Weather Research and Forecasting (WRF) Model (Skamarock et al., 2008) or in the 20 (17) ASAM v2.7 Abstract Discussion Paper where yn is a given approximation at y(t) at time tn and subsequently yn+1 at time tn+1 = tn + τ In addition J is an approximation to the Jacobian matrix ∂F/∂y A Rosenbrock method is therefore fully described by the two matrices A = (αi j ), Γ = (γi j ) and the parameter γ Among the available methods are a second order two stage method after Lanser et al (2001) 7, 4463–4525, 2014 | αs+1j kj , j =1 GMDD Discussion Paper s yn+1 = yn + Discussion Paper is obtained that has to be integrated in time (method of lines) To tackle the small time step problem connected with tiny cut cells, linear implicit Rosenbrock-W-methods are used (Jebens et al., 2011) A Rosenbrock method has the form Interactive Discussion A zero block indicates that this block is not included in the Jacobian or is absent The derivative with respect to ρ is only taken for the buoyancy term in the vertical momentum equation Note that this type of approximation is the standard approach in the derivation of the Boussinesq approximation starting form the compressible Euler equations The matrix J can be decomposed as ∂F ρ ∂F ρ 0 0 ∂ρ ∂V ∂F ∂FV ∂FV + 0 V (22) J = JT + JP = ∂V 0 ∂FΘ ∂Θ 20 J = JT + JP = 0 ∂FV ∂V 0 ∂F + ∂ρV ∂FΘ ∂Θ Conclusions References Tables Figures Back Close ∂FΘ ∂V Full Screen / Esc Printer-friendly Version ∂F ρ ∂V ∂FΘ ∂V ∂FV ∂Θ (23) | 4472 Discussion Paper ∂ρ Introduction Title Page ∂Θ or ∂F ρ M Jähn et al | ∂ρ ASAM v2.7 Abstract Discussion Paper 15 ∂Θ ∂FΘ ∂Θ 7, 4463–4525, 2014 | 10 ∂V ∂FΘ ∂V GMDD Discussion Paper | ∂ρ Discussion Paper Consortium for Small-scale Modeling (COSMO) model (Doms et al., 2011) Its coeffcients are given in Table The above described Rosenbrock-W-methods allows a simplified solution of the linear systems without loosing the order When J = JA + JB the matrix S can be replaced by S = (I−γτJA )(I−γτJB ) Further simplification can be reached by omitting some parts of the Jacobian or by replacing of the derivatives by the same derivatives of a simplified operator F˜ (w n ) For instance higher-order interpolation formula are replaced by the first-order upwind method The structure of the Jacobian is ∂F ρ ∂F ρ ∂ρ ∂V ∂F ∂FV ∂FV V J= (21) Interactive Discussion Discussion Paper | 1111111111 0000000000 0000000000 1111111111 0000000000 1111111111 0000000000 1111111111 0000000000 1111111111 1111 0000 0000 1111 0000 1111 markers 111111 000000 000000 111111 000000 111111 000000 111111 000000 111111 000000 111111 000000 111111 markers markers 111 000 000 111 000 111 000 111 111 000 000 111 000 111 markers Fig Possible Possible configurations for cut cell intersection Thecell last two cases are excluded The last two cases are excluded Figure configurations for cut intersection F WR V F UL F F UR C F C UR U UL φR UR > ✲ 240 hL hC where yn is a given approximation at y(t) at time tn and subsequently yn+1 at time tn+1 = tn + τ In addition J is an approximation to the Jacobian matrix ∂F/∂y A Rosenbrock method is therefore fully described by the two matrices A = (αij ), Γ = (γij ) and the parameter γ Among the available methods are a second order two stage method after Lanser et al (2001) 4512Sk1 =τ F (yn ) , (17) 245 Tables Figures Back Close | Fig Stencil for third-order approximation hR References Discussion Paper Fig Cut cell with face and volume area information (left) and arrangement of face and cell centered momentum (right) φC Conclusions Sk =τ F y + k − k , Full Screen / Esc Printer-friendly Version F WL φL Introduction Title Page | C C M Jähn et al Abstract Discussion Paper markers 11111111 00000000 00000000 11111111 00000000 11111111 00000000 11111111 00000000 11111111 00000000 11111111 00000000 11111111 ASAM v2.7 | M Jăahn: ASAM v2.7 7, 4463–4525, 2014 Discussion Paper GMDD (18) Interactive Discussion 1111 0000 0000 1111 0000 1111 markers markers 111111 000000 000000 111111 000000 111111 000000 111111 000000 111111 000000 111111 000000 111111 markers markers 111 000 000 111 000 111 000 111 markers Discussion Paper 1111111111 0000000000 0000000000 1111111111 0000000000 1111111111 0000000000 1111111111 0000000000 1111111111 11111111 00000000 00000000 11111111 00000000 11111111 00000000 11111111 00000000 11111111 00000000 11111111 00000000 11111111 111 000 000 111 000 111 7, 4463–4525, 2014 ASAM v2.7 | F UL F F UR UR U UL F WL Cut cellFigure with face area information (left) area and arrangement face and centered momentum (right) 2.and Cutvolume cell with face and volume informationof(left) andcell arrangement of face and cell centered momentum (right) φL φC UR > φR hC hR References Tables Figures Back Close where yn is a given approximation at y(t) at time tn and Full Screen / Esc subsequently yn+1 at time tn+1 = tn + τ In addition J is an approximation to the Jacobian matrix ∂F/∂y A RosenbrockPrinter-friendly Version method is therefore fully described by the two matrices A = Interactive Discussion (αij ), Γ = (γij ) and the parameter γ Among the available methods are a second order two stage method after Lanser et al (2001) Sk1 =τ F (yn ) , Stencil for third-order approximation 245 4513 Sk2 =τ F yn + k1 − k1 , 3 | Time integration Conclusions Discussion Paper 240 hL Introduction Title Page | ✲ Abstract Discussion Paper C VC C F C | F WR M Jähn et al Discussion Paper Possible configurations for cut cell intersection The last two cases are excluded GMDD (17) (18) F UL F F UR C F 7, 4463–4525, 2014 Discussion Paper C VC F WL UR U GMDD UL ASAM v2.7 | M Jähn et al φL φC Discussion Paper Fig Cut cell with face and volume area information (left) and arrangement of face and cell centered φR UR > ✲ Title Page | Introduction where yAbstract appro n is a given subsequently at time Conclusions yn+1 References approximation toFigures the Jacob Tables method is therefore fully d (αij ), Γ = (γij ) and the pa Among the available me Back Closeet al ( method after Lanser hL hC hR Figure Stencil for third-order approximation | Time integration After spatial discretization an ordinary differential equation | 4514 Printer-friendly Version Sk2 =τInteractive F ynDiscussion + k1 − yn+1 =yn + k1 + k2 , 4 S =I − γτ J, J ≈ F Discussion Paper 245 y(t) = F (y(t)) Full Screen / Esc Sk1 =τ F (yn ) , Fig Stencil for third-order approximation 2.3 Discussion Paper 240 (15) 1√ Discussion Paper GMDD 7, 4463–4525, 2014 ASAM v2.7 | -1 Wf (m s ) -4 -5 Tables Figures -7 1e-07 1e-06 0.001 0.01 Asurf = 520 Discussion Paper Interactive Discussion In order to account for th mosphere and the high di ical variables in the surfa plemented into ASAM In model, the computation o | Sv is the source term of water vapor in units of [kg m−3 s−1 ] 4515 Considering Eq (A33), adding the sensible heat flux and ne- Close L Σ|A AR Full Screen / Esc j − j | Printer-friendly 3.5 Soil modelVersion Figure Terminal fall velocity of raindrops after Eq (52) Fig Terminal fall velocity of raindrops after Eq (52) Back | 1e-05 0.0001 -3 r (kg m ) where the superscripts L right neighbor cell, respe puted by Discussion Paper 515 -6 490 References ∂ Page ∂(ρθρ ) Title R + (ρθ u )= ρ R ∂t Abstract ∂xj Introductionj -3 -8 1e-08 Conclusions | -2 M Jähn et al Discussion Paper -1 t=0s Discussion Paper which a nsidering nd Fritsch around an simulated the flow | t = 300 s M Jähn et al Abstract Introduction Conclusions References Tables Figures Back Close Discussion Paper t = 900 s ASAM v2.7 | t = 600 s 7, 4463–4525, 2014 Discussion Paper nt simulacase, the m in hordirection The total e is a dry viscosity ly homotion (cold GMDD Title Page Full Screen / Esc | (78) Printer-friendly Version 10 12 14 16 18 Distance (km) Figure Perturbation potential temperature isolines (contour interval K) at different times Since the result is symmetric, only the right part of the model domain is shown Fig Perturbation potential temperature isolines (contour interval 4516 K) at different times Since the result is symmetric, only the right | (79) Discussion Paper Interactive Discussion Discussion Paper Table LES model configura GMDD study 10 7, 4463–4525, 2014 ASAM v2.7 | Discussion Paper Domain M Jähn et al Grid cells Lateral boundary conditions Title Page Start time (LT) Introduction Abstract Integration time Conclusions References Topography data Tables Turbulence schemeFigures Cloud microphysics Surface fluxes | Discussion Paper Back Close | Full Screen / Esc Application for real case sitivityPrinter-friendly study Version -4 -2 Distance (km) Discussion Paper Interactive Discussion | For the following sensitivity performed on a 110 × Figure Perturbation equivalent potential temperature isolines (contour interval 0.5 K) at t = 720 256 × 256 × 38 grid points an 1000 s Fig Perturbation equivalent potential temperature isolines (conary conditions The vertical s tour interval 0.5 K) at t = 1000 4517 s to better represent the orogra Discussion Paper performed on a 110 × 720 256 × 256 × 38 grid points an Fig Perturbation equivalent potential temperature isolines (conary conditions The vertical GMDD tour interval 0.5 K) at t = 1000 s to better represent the orogra 7, 4463–4525, 2014 boundary layer dynamics mo data with a ASAM 100 mv2.7 resolution 10 725 tium for Spatial Information ( M Jähn et al pography Mission (SRTM) da The Coriolis parameter f = Title a latitude value ofPage φ = 13.18◦ Abstract Introduction for all simulations, starting a 730 the LESConclusions model configuration References Idealized initial Figures profiles Tables drostatic equilibrium with po Nd = 11 × 10−3 s−1 , ground θ0 = 298.15 K and air pressu 735 an inversion relativ Backlayer, the Close -20 -10 10 20 creasing upFulltoScreen a height of / Esc Distance (km) strong decrease down to hal −1 Printer-friendly Version Figure Steady state solution of the vertical velocity field (contour interval 0.05 m s , negative is slowly increasing again A contours dashed) at t = 7200 s Interactive Discussion zL = 300 m is applied to take Fig Steady state solution of the vertical velocity field (contour −1 interval 0.05 m s , negative contours dashed) at t = 7200 s 740 Above this level, there is a un | Discussion Paper | Discussion Paper | Discussion Paper | 19.5 km vertically with grid4518 spacings of ∆x = 500 m and ∆z = 300 m The structure of the mountain ridge is repre- u(z) = log(z/z0 ) u0 log(z L /z0 ) if z u0 if z Discussion Paper 12 | -2 Discussion Paper 500 Q s (W m ) 7, 4463–4525, 2014 Table Overview of the p dos sensitivity ASAMstudy v2.7 600 400 300 200 | Discussion Paper 100 -100 GMDD 12 15 Time of day (h) 18 21 24 Fig Model parameterization for the sensible surface heat flux over Barbados after Eq (84) 790 | Barbados as it is parameterized 4519 in the model The underlying cosine function takes to following form: Discussion Paper Figure Model parameterization for the sensible surface heat flux over Barbados after Eq (84) Label Topograph Title Page Abstract REF FLAT Tables U05 RH80 Introduction yes no Figures yes yes Conclusions References Back Close Full Screen / Esc together with potential te Printer-friendly Version above sea level at 14:00 Discussion patternInteractive over the island is in Fig 10 The L-shaped north-eastern part of Ba are mainly descent flows field at 400 m height is m | 785 M Jähn et al M Jăahn: ASAM v2.7 Discussion Paper GMDD 7, 4463–4525, 2014 ASAM v2.7 | M Jähn et al Introduction Conclusions References | Tables Figures Back Close Discussion Paper Discussion Paper Abstract Title Page Full Screen / Esc | Printer-friendly Version Interactive Discussion Fig 11 Same as Fig 9, but | Fig Snapshot at 14:00 LT for the vertical velocity field and density potential temperature isolines (lowest value 302.5 K in light grey, darker lines for higher values, contour interval 0.5 K) at 400 m 4520 height asl for the REF case simulation Discussion Paper Figure Snapshot at 14:00 LT for the vertical velocity field and density potential temperature isolines (lowest value 302.5 K in light grey, darker lines for higher values, contour interval 0.5 K) at 400 m height asl for the REF case simulation | Cloud cover Discussion Paper grey, darker lines for higher values, contour interval 0.5 K) at 400 m height asl for the REF case simulation GMDD RH80 0.0025 U05 7, 4463–4525, 2014 0.002 ASAM v2.7 0.0015 M Jähn et al Discussion Paper 0.001 Title Page Abstract 0.0005 Introduction Conclusions References | Tables Figures Discussion Paper Back series Close Fig 12 Time of total c cases Full Screen / Esc | Printer-friendly Version Fig 10 Topographic map of Barbados (SRTM output) 840 Shallow cumulus clouds are most likely located along the Discussion streets areInteractive frequently observ noon hours if there is no larg The performed simulation ble to resolve boundary lay as well as island-induced sh eration Considering numeri | 4521 Discussion Paper Figure 10 Topographic map of Barbados (SRTM output) Discussion Paper | GMDD 7, 4463–4525, 2014 ASAM v2.7 M Jähn et al Abstract Introduction Conclusions References | Tables Figures Back Close Discussion Paper Discussion Paper Title Page Full Screen / Esc | Printer-friendly Version Figure 11 Same as Fig 9, but for the FLAT case simulation Fig 11 Same as Fig 9, but for the FLAT case simulation | 4522 Discussion Paper nht m 13 Interactive Discussion Fig 11 Same as Fig 9, but for the FLAT case simulation Discussion Paper | RH80 U05 0.0025 0.001 0 14 16 18 M Jähn et al Introduction Conclusions References Tables Figures Back Close Title Page Full Screen / Esc | 10 12 Time of day (h) ASAM v2.7 Abstract Discussion Paper 0.0005 7, 4463–4525, 2014 | 0.0015 GMDD Discussion Paper 0.002 Cloud cover enght 0m Printer-friendly Version Fig 12 Time series of total cloud cover for the RH80 and U05 cases streets are frequently observed every 2-3 days during after- | 4523 Discussion Paper Figure 12 Time series of total cloud cover for the RH80 and U05 cases Interactive Discussion Discussion Paper 0.16 CWP RWP LWP 0.12 0.1 870 0.08 | 0.06 0.02 875 10 16 18 | 12 14 Time of day (h) Discussion Paper 0.04 Discussion Paper 0.14 | Cloud/rain/liquid water path (g m-2) 14 Fig 13 Time series of domain averaged cloud, rain and liquid water path for the RH80 case 7, 4463–4525, 2014 Code availability a ASAM v2.7 M Jähn etcode al The ASAM is m sion control and source Title to Pagethe sourc get access Abstract Introduction a and postprocessing, ing Conclusions website References https://gito tionalTables information Figures can //asam.tropos.de) As visualization too VisIt (https://wci.llnl.g Back Close over 120 scientific file Full Screen / Esc clude own scripts, if ne dowsPrinter-friendly and MacVersion worksta Interactive Discussion Conclusions and f | 4524 Discussion Paper Figure 13 Time series of domain averaged cloud, rain and liquid water path for the RH80 case GMDD 880 A detailed description Discussion Paper Fig 13 Time series of domain averaged cloud, rain and liquid water path for the RH80 case Conclusions and future w GMDD | 4463–4525, 2014 A detailed7,description of the f static All Scale Atmospheric M ASAM v2.7 Since the cut cell method is M.the Jähnspatial et al discr the concept of Rosenbrock time integration sc 885 cobian were outlined Title Page Sophist tions (Smagorinsky subgrid sc Abstract Introduction microphysics scheme, multilay Conclusions References plication in different existing Tables Figures ASAM A special technique t 890 fluxes with respect to the irreg described The model produce benchmark test cases from the Back Close it is possible to perform three-d Full Screen / Esc tions for an island-ocean system 895 LT The convective boundary Figure 14 RH80 case: cloud field visualization for the island surrounded area at 14:40 Printer-friendly Version layer −1 Isosurfaces of specific cloud water content of qc = 0.1 g kg as well as cut cells around theis well resolved and also the de Interactive Discussion island orography the lowest-level temperature field are shown Fig 14 and RH80 case: cloud field visualization for the island surcloud streets can be simulated rounded area at 14:40 LT Isosurfaces of specific cloud water conwith observations Model resul tent of qc = 0.1 g kg−1 as well as cut cells around the island orogupcoming measurements from raphy and the lowest-level temperature field are shown 900 The focus on future model 4525 apsects Firstly, for the descrip namic) Smagorinsky models (e 880 Discussion Paper | Discussion Paper | Discussion Paper | Copyright of Geoscientific Model Development Discussions is the property of Copernicus Gesellschaft mbH and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission However, users may print, download, or email articles for individual use ... 111 7, 4463–4525, 2014 ASAM v2. 7 | F UL F F UR UR U UL F WL Cut cellFigure with face area information (left) area and arrangement face and centered momentum (right) 2.and Cutvolume cell with face... Furthermore, tracer variables can also be included The values of all relevant physical constants are listed in Table ASAM v2. 7 Abstract Discussion Paper where the equation of state can be expressed as follows:... Dynamics) simulations around buildings where obstacles are included within a Cartesian grid by a cut cell method This approach is also used to include real orographic data in the model domain With