Test Cases
From ASAMWiki
Contents 
Mountain waves
2D hydrostatic and nonhydrostatic mountain waves
 Examples after Gallus and Klemp (2000) .
 Orography , , variable.
 Stratification , .
a  Δx  Δz 

1 km  200 m  100 m 
10 km  2 km  100 m 
100 km  20 km  100 m 
Schaer test case
 Examples after Schaer (1990) .
 Orography , , ,.
 Stratification , .
 Example was defined to promote a new type of boundary following coordinates.
Density Current
The density current test case is documented in Straka et al. (1993) .
 Geometry:
 Computational domain extends in horizontal direction from 25.6 to 25.6 km
and in vertical direction from 0 to 6.4 km.
 Integration time: t=1800s
 Profile:
 A fixed physical viscosity is used with .
 A horizontally homogeneous environment with is used.
 Perturbation:
 The perturbation (cold bubble) is defined by
where
and , , and .
 For the translating current the position is shifted to the left.
Density current at the beginning and after 300 s, 600 s and 900 s, starting from rest

Translating density current at the beginning and after 300 s, 600 s and 900 s, horizontal wind 20 m/s

Examples of the sphere
 Examples taken from Tomita and Satoh (2004)
 Geometry:
 Model height = 10km
 Twenty equidistant vertical layers
 In longitudelatitude 128 × 64 grid points are used
 integration time: Maximal time step is 1800s
Acoustic waves
 Profile:
 ,
 Basic state is isothermal
 , amplitude of the pressure perturbation

 Without diffusion and rotation of the earth
 Perturbation:
 A perturbation is superimposed on the basic pressure
 is the amplitude of the pressure perturbation
 is a constant distance
 stands for the vertical mode
 is the distance along a great circle from to with
 and are horizontal and vertical distribution functions
 Pressure perturbation horizontally propagates as a concentric circle with the acoustic wave speed (theoretical value of acoustic wave speed in this case is
 Perturbation field has a structure similar to the Lamb wave; its amplitude exponentially decays in the upward direction
Gravity waves
 Profile:
 Basic state is isothermal

 Basic state for the thermodynamic variables is a stratified state with a constant Brunt Väisälä frequency
 Three test cases:
 Case 1: ,
 Case 1: ,
 Case 1: ,
 Perturbation:
 A perturbation is superimposed on the basic potential temperature
 is the amplitude of the potential temperature perturbation
 Gravity waves propagate as a concentric circle similar to the acoustic wave experiment
 Theoretically: phase speed of the gravity wave with vertical mode in the stratified layer with the constant
 is estimated on the hydrostatic approximation as
 ( is the top of the model domain, which is constant in the entire globe)
Mountain waves
 Orography:
 Previous: gravity waves generated by the initial potential temperature perturbation
 Now: gravity waves generated by the orography
 Terrain following coordinates
 Shape of mountain is given as an ideal bell shape:
with as the height at the center of the mountain, as the halfwidth of the mountain, and as the distance from the center
 Profile:
 Center of the mountain is placed at the equator at and halfwidth is set to 1250 km
 To avoid the reflection of gravity waves at the top boundary, the Rayleigh damping for the velocity and the Newtonian cooling to the basic state for the temperature are imposed.
Linear anelastic equations for atmospheric vortices
 Examples after Hodyss and Nolan
 Construction of a test example
 A wind, density and temperature field is constructed fitting in the hydrostatic and gradient wind balance including a wind domain which rotates around the centre.
 First step: Construction of a radial wind field
 The radial profile of the azimuthal windfield is computed from the radial integration of a Gaussian vorticity profile:
with and .
 The vertical components of vorticity is defined by:
with and
 The windfield is extended into the vertical with:
where indicates the depth of the barotropic part of the vortex, and is the vertical decay rate of the wind in the baroclinic region.
 Second step: Evaluation of the thermodynamic variables: density, pressure, temperature
 This has to fit the hydrostatic
and gradient wind balance as well as the equation of states.
 The potential temperature profile outside of the vortex is given by the buoyancy frequency which represents boundary conditions for
a sufficient large radius. This potential temperature is used to calculate
the density and pressure profile. These profiles may be computed by integration in r and zdirection for every
grid cell from the edge of the grid to the centre.
 Profile of potential temperature for the total grid:
 A more realistic profile:
height / m  density / kg m^{ − 3}  pressure / Pa 

23867  0.05  3000 
22047  0.07  4000 
20658  0.08  5000 
19546  0.1  6000 
17826  0.14  8000 
16535  0.18  10000 
15227  0.22  12500 
14137  0.25  15000 
13193  0.29  17500 
12353  0.32  20000 
10894  0.38  25000 
9647  0.44  30000 
8553  0.49  35000 
7573  0.55  40000 
6682  0.6  45000 
5870  0.66  50000 
5123  0.71  55000 
4427  0.76  60000 
3779  0.81  65000 
3171  0.87  70000 
2599  0.92  75000 
2058  0.97  80000 
1545  1.02  85000 
1057  1.07  90000 
590  1.12  95000 
141  1.16  100000 
0  1.18  101630 
 Following
radial geometry may be transfered into a Cartesian coordinate system by interpolation.
1.)
2.)
 Next step is to add a potential perturbation to the potential temperature as followed:
where , , , , and .
 Configuration of model domain:
 horizontal grid points with spacing
 , spacing of
 necessity of periodic outer boundary conditions in both directions
 necessity of constant timestep of
 Profile:

 Vertical gravity wave reflection from the top of the domain is supressed by a Rayleigh damping layer.
 advective time step:
 internal diffusivity for momentum: , and for temperature:
 Simulation with ASAM:
 Horizontal cross section of vertical velocity , ,
 Horizontal cross section of vertical velocity with/without potential perturbation at , ,
Valley wind systems
 Examples after Schmidli (2008)
 part of the Terraininduced Rotor Experiment
 Grid:
 across valley (xdirection): 120 km with spacing of 1 km
 along valley (ydirection): 400 km with spacing of 1 km
 vertical direction: 6.2 km with spacing of 20 m near the ground up to 200 m above 2 km
 lateral boundary conditions are periodic
 as top boundary conditions a Rayleigh sponge was specified
 Coriolis force is turned off for all simulations
 models were integrated for 12 hours from sunrise (0600 local time (LT)) to sunset (1800 LT)
 Valley:
z = h(x,y) = h_{p}h_{x}(x)h_{y}(y)
where
and
with
 valley depth
 valley floor half width
 sloping sidewall width
 plateau half width in crossvalley direction
 plateau half width in alongvalley direction

 X_{2} = V_{x} + S_{x}
 X_{3} = V_{x} + S_{x} + P_{x}
 X_{4} = V_{x} + 2S_{x} + P_{x}
 Y_{2} = P_{y} + S_{y}
 Profile:
 all simulations are started from an atmosphere in rest
 potential temperature:
 with , , ,
 suface pressure:
 constant relative humidity of 40 %
 constant stratification of
 sensible heat flux for the uncoupled simulations: Q(t) = Q_{0}sin(ωt) with , and the time t donates hours since sunrise
Valley wind systems II
 Examples after Schmidli (2008)
 Construction of a testexample for the uncoupled simulations
 First step: construction of the testvalley after Schmidli (2008)
 Grid:
 across valley (xdirection): 120 km with spacing of 1 km
 along valley (ydirection): 400 km with spacing of 1 km
 vertical direction: 10 km with spacing of 100 m
 Second step: construction of the startprofiles after Schmidli (2008)
 Profile:
 all simulations are started from an atmosphere in rest
 potential temperature:
 with , , ,
 constant relative humidity of 40 %
 testcase like the uncoupled simulations, but only with heating process
 Results:
 maximum of the alongvalley wind speed: v = 5.77m/s
 vertical wind speeds across the valley: w = 0.5m/s upward and w = 0.15m/s downward