Michael Böttinger Introduction to Vector Field Visualization · 2013. 11. 11. · Avizo:...

Deutsches Klimarechenzentrum German Climate Computing Centre

Michael Böttinger

Introduction to Vector Field Visualization

Michael Böttinger: Vector Field Visualization

3D Vector fields in Earth System Modeling:

◦ Wind

◦ Ocean Currents

“Flow Fields”: Time dependent, discreet time steps

◦ Exception: Temporal means of circulation data ->

“Steady Flow”

Data


Methods intended for steady data

◦ Arrows

◦ (Illuminated) Streamlines

◦ Line Integral Convolution (LIC)

Methods for time dependent data

◦ Particle Pathlines (Trajectories)

◦ Methods for steady flow

Methods (available in Avizo)


Methods: Vector Arrows


Arrows visualize the local direction and magnitude (length) of the vector field

Methods: Streamlines


Streamlines: Curves, which are everywhere tangent to the corresponding velocity vectors of a flow field - at one point in time.

Methods: Streamlines


Streamlines: Curves, which are everywhere tangent to the corresponding velocity vectors of a flow field - at one point in time. 2D streamlines: sources and sinks, although the 3D flow field is a zero divergence field!

Avizo: 3D Illuminated Streamlines (DisplayISL)


Methods: Line Integral Convolution (LIC)


Image based method: 1.) Computation of streamlines

2.) For each pixel, a noise texture is convolved along the respective stream line

Cabral and Leedom, 1993

Hege and Stalling, 1997


LIC: from sparse streamlines to a continous image based representation of the flow field.

Advances: LIC shows more detailed the critical points or regions in the flow field.



LIC: The use of colours can add information and emphasize specific structures. Example: Magnitude of the velocity Sqrt(U*U+V*V+W*W)


Multivariate Visualization: LIC + Color (Magnitude) Overlays: BumpSlice (VILW) and Isolines (SLP)


Time Dependent Flow: Arrows + Color (Magnitude)



Time Dependent Flow: LIC + Color (Magnitude)

Particle Advection / Trajectories


Particle Advection (in Avizo: ParticlePathlines) Weightless particles are “released” in the 3D vector field Suppose initial position - seed point – is (x0, y0, z0) How does the path ( x(t), y(t), z(t) ) develop over time?

Motion of a particle is given by: dx/dt = vx; dy/dt = vy; dz/dt = vz Three ordinary differential equations with initial conditions at

time zero: x(0) = x0; y(0) = y0; z(0) = z0

Time Dependent Flow: Particle Advection


In 2D, we have:

(x0,y0)

Velocity at initial position: (vx,vy)

Simple solution: Euler’s method dp/dt = ( p(t+∆t) - p(t)) / ∆t = v(p(t)) with p= (x, y, z), v=(vx, vy, vz) hence the position for the next time step is

p(t+∆t) = p(t) + ∆t v(p(t))

Velocity values (vxn, vyn, vzn) need to be interpolated for each new position (xn,yn,zn) – e.g. by trilinear interpolation.


In 2D, we have: Velocity at initial position: (vx0,vy0)

∆t.vx,∆t.vy

Velocity at new position: (vx1,vy1)

p(t +∆t)

p(t)



• Problem: if the time step ∆t is large, dx/dt can be >> grid spacing and the velocity varies along the path

• Euler’s method is inaccurate, unless dx/dt is small compared to the grid spacing!

• Look at velocity maxima and grid spacing in order to estimate the appropriate maximal time step - dx/dt should be less than the grid spacing!

dx/dt for large ∆t

xi

xi+1



• Better: Runge-Kutta (Here: 2nd order) • Estimate new particle position x*(t+1) with Euler • Estimate velocity vector v*at new position x* • For advection, use the mean of the velocity vectors v and v*

x* = x(t) + ∆t vx(p(t)) (Euler)

x (t+∆t) = x(t) + ∆t { vx(p(t)) + vx(p*)}/2

• Method allows for moderately larger integration steps

vx(p*)

vx(p(t))

vx(p(t)) vx(p*)


Vector Field Visualization – Methods: Particles (Trajectories)


Hybrid (Sigma) Coordinates ◦ Terrain following near the surface ◦ Pressure levels at the top of the atmosphere ◦ Interpolated in between

Vertical Coordinates of Atmospheric Models


Avizo supports Height levels Pressure levels cdo ml2hl,hlevels

cdo ml2pl,plevels

The input files should contain (beside the desired quantity)

log. surface pressure or the surface pressure.

Orography (surface geopotential)


Vertical Coordinates of Atmospheric Models

Coordinates of Vector Components in Climate Models


Atmosphere: k points upwards Ocean: k points downwards

Avizo needs all vector components on one common

grid

Interpolation onto the scalar grid:

Horizontal Interpolation of U and V onto Scalar Grid Points

cdo remapbil,

Vertical Interpolation of W onto Scalar Grid Points

cdo intlevel,

Grids and Coordinates


Rotation of Vector Components


Rotation: Needed for Rotated Regional Grids (REMO, CLM)

Rotation of Vector Components


Rotation: Needed for Curvilinear Grids (MPI-OM)

MPI-OM: Interpolation and Rotation of horizontal Vector Components


cdo mrotuvb

Vertical Velocity in Atmosphere Models


code description 130 temperature [K] 133 specific humidity [kg/kg] 134 Surface pressure [Pa] 135 Vertical velocity [Pa/s]

Vertical Velocity (code 135) is mostly given in [Pa/s].

Avizo needs [m/s] in all 3 Dimensions! Conversion: New cdo command – not yet mentioned in the documentation: cdo vertwind

Quantities needed for vertwind


Thank you for your attention!

[email protected] http://www.dkrz.de

Convert MPI-OM GRIB data to NetCDF

cdo -f nc -t mpiom1 -r copy gr15-1.2.3-core-010_500.grb gr15_test.nc

Vertical interpolation from W-point levels to levels of scalar points

cdo_intlevel,6,17,27,37,47,57,69,83,100,123,150,183,220,263,310,363,420,485,560,645,7

40,845,960,1085,1220,1365,1525,1700,1885,2080,2290,2525,2785,3070,3395,3770,4195,4

670,5170,5720 GR15_WO.nc GR15_WO_s.nc

Horizontal Interpolation of U and V onto Scalar grid and Rotation of

Velocity Vectors

cdo_-r mrotuvb -setgrid,/pool/data/MPIOM/GR15/GR15u.nc -selvar,UKO gr15_test.nc -

setgrid,/pool/data/MPIOM/GR15/GR15v.nc -selvar,VKE gr15_test.nc ukovke_nswe.nc cdo

setgrid,/pool/data/MPIOM/GR15/GRID_-180_180/GR15s.nc uko_vke_nswe.nc

uko_vke_nsweG.nc

Set Grid Description to Scalar Grid

cdo setgrid,/pool/data/MPIOM/GR15/GRID_-180_180/GR15s.nc ukovke_nswe.nc

ukovke_nsweG.nc

Processing Workflow for MPI-OM (1)


Combine U,V,W

cdo –r merge ukovke_nsweG.nc gr15_WO_s.nc gr15_UVW.nc

Get or Create Mask

…

Reassign Special Values to U,V,W

cdo ifthen



Remapping onto regular grid

Compute interpolation weights (OpenMP parallel)

cdo -P 4 genbil,r4096x2048 vel75_0031-07-01_0031-12-31_s.nc

remap_weights_TP06_vel_r4096x2048.nc

Do remapping

cdo remap,r4096x2048,remap_weights_TP06_vel_r4096x2048.nc vel75_0031-

07-01_0031-12-31m.nc vel75_0031-07-01_0031-12-31_reg_temp.nc

Re-order longitudes

> cdo selindexbox,2049,2048,1,2048 vel75_0031-07-01_0031-12-

31_reg_temp.nc vel75_0031-07-01_0031-12-31_reg.nc

> \rm vel75_0031-07-01_0031-12-31_reg_temp.nc



�Michael Böttinger�Introduction to Vector Field Visualization�DataMethods (available in Avizo)Methods: Vector ArrowsMethods: StreamlinesMethods: StreamlinesAvizo: �3D Illuminated Streamlines (DisplayISL)Avizo: �3D Illuminated Streamlines (DisplayISL)Methods: Line Integral Convolution (LIC)Methods: Line Integral Convolution (LIC)Methods: Line Integral Convolution (LIC)Multivariate Visualization: LIC + Color (Magnitude)�Overlays: BumpSlice (VILW) and Isolines (SLP)Time Dependent Flow: Arrows + Color (Magnitude)Time Dependent Flow: LIC + Color (Magnitude)Particle Advection / TrajectoriesTime Dependent Flow: Particle AdvectionTime Dependent Flow: Particle AdvectionTime Dependent Flow: Particle AdvectionTime Dependent Flow: Particle AdvectionVector Field Visualization �– Methods: Particles (Trajectories)Vertical Coordinates of Atmospheric ModelsVertical Coordinates of Atmospheric ModelsCoordinates of Vector �Components in Climate ModelsGrids and CoordinatesRotation of Vector ComponentsRotation of Vector ComponentsMPI-OM: Interpolation and �Rotation of horizontal Vector ComponentsVertical Velocity in Atmosphere ModelsFoliennummer 30Processing Workflow for MPI-OM (1)Processing Workflow for MPI-OM (2)Processing Workflow for MPI-OM (3)

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