GrADS Script Calculate Velocity Potential
Build GrADS diagnostics for velocity potential, divergence, grid setup, levels, units, plotting, and reusable scripts with export-ready results today.
fish_chi(u,v)Calculator and script settings
Optional point diagnostic
Use local finite differences for a quick divergence check. This does not replace the full GrADS field solution.
Generated GrADS script
* GrADS velocity potential template * Generated by this calculator 'reinit' * 'open your_data.ctl' 'set lon 0 360' 'set lat -90 90' 'set lev 200' 'set t 1' * Example variables: u and v 'define chi = fish_chi(u,v)' 'define div = hdivg(u,v)' 'set gxout shaded' 'd chi' 'cbarn'
Formula used
Velocity potential: ∇²χ = ∇·V
Horizontal divergence: ∇·V = ∂u/∂x + ∂v/∂y
Divergent wind: Vχ = ∇χ
For spherical data, metric factors and solver assumptions matter. Use a GrADS-compatible spherical function when available.
How to use this calculator
- Enter the GrADS names for U and V components.
- Select a velocity-potential solver and grid type.
- Set longitude, latitude, pressure level, and time.
- Add dataset information when you want an open command.
- Use the point derivatives for a divergence check.
- Generate the script and review any validation messages.
- Copy or download the script for your GrADS session.
- Export settings and results with CSV or PDF.
Example table
| Case | U | V | ∂u/∂x | ∂v/∂y | Divergence | Interpretation |
|---|---|---|---|---|---|---|
| Tropical example | 12 | -5 | 1.0×10⁻⁵ | -4.0×10⁻⁶ | 6.0×10⁻⁶ | Net divergence |
| Balanced example | 8 | 3 | 5.0×10⁻⁶ | -5.0×10⁻⁶ | 0 | Locally neutral |
| Convergent example | -6 | 4 | -8.0×10⁻⁶ | 2.0×10⁻⁶ | -6.0×10⁻⁶ | Net convergence |
Understanding velocity potential in GrADS
Velocity potential describes the divergent part of a vector field. It is useful when winds contain both rotational and divergent motion. The scalar potential is commonly written with the symbol χ. Its horizontal gradient gives the divergent wind component. A Poisson equation links χ with horizontal divergence. This relationship makes velocity potential a diagnostic field.
GrADS workflows often begin with gridded U and V components. The script sets the spatial domain first. It can also select a pressure level and time. A compatible function then solves for velocity potential. Different GrADS installations may offer different extension functions. The generated script therefore keeps solver choices visible. Users should confirm installed functions before operational use.
Grid and solver considerations
Global latitude-longitude data needs spherical treatment for best consistency. Cartesian approximations can work for limited domains. Grid spacing should match the underlying dataset. Missing values must also be handled carefully. Invalid coverage can produce unstable or incomplete diagnostics. A global solver may also require complete longitude coverage.
The calculator validates basic geographic limits and spacing values. It also builds common GrADS setup commands. These commands include longitude, latitude, level, and time selections. Optional dataset input adds an open command. Plot settings create a quick diagnostic display. Users can then modify the generated script as needed.
Interpreting the results
Positive divergence means flow spreads outward locally. Negative divergence indicates local convergence. Velocity potential itself depends on the entire field solution. Its absolute value is less intuitive than its gradients. Comparing χ patterns across times can reveal changing divergent circulation. Pairing velocity potential with streamfunction can separate divergent and rotational structures.
The point diagnostic only checks local derivative inputs. It does not solve the full Poisson equation. Use it as a quick validation aid. Final analysis should use complete gridded data inside GrADS. Exported CSV files preserve settings for documentation. PDF reports provide a compact summary for sharing. The generated script keeps the workflow reproducible and easier to audit.
FAQ
What is velocity potential?
Velocity potential is a scalar field whose gradient represents divergent flow.
What equation is solved?
The main equation is ∇²χ = ∇·V.
What does fish_chi do?
It is commonly used as a Poisson-style velocity-potential solver in supported GrADS environments.
When should I use sh_chi?
Use it when spherical-harmonic support exists and matches your global-grid workflow.
Why can a function be undefined?
Your GrADS build may lack the required extension or library.
Can I use regional grids?
Yes, but solver assumptions and boundary conditions need careful review.
Does this calculator solve a whole field?
No. It generates scripts and provides a local divergence diagnostic.
Can I export my setup?
Yes. Use the CSV, PDF, or GrADS script download buttons.
Review solver availability before running production diagnostics in GrADS.