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Code Supplement for Grid Convergence Study
Manuscript: "Stationary Solutions and Oscillatory Dynamics in a Mathematical 
Model of a Saturated Moist Atmosphere"
Author: Dalila Remaoun Bourega
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This archive contains the Python scripts required to reproduce the grid 
convergence check (Delta z = 10m, 5m, 1m) and generate the nu(Sigma) 
dependence curves discussed in the Interactive Public Peer Review.

--- HOW TO RUN ---
MAIN SCRIPT:
> python plotnusigma1.py
(Note: You can change the spatial step size 'hz' directly in this file 
to verify the grid convergence). 

This is the main executable script. It will run the numerical integration, 
find the intersection points for the stationary solutions (Humid and Dry 
cases), display the values of Alpha, and generate the output figure (.eps).

--- HELPER SCRIPTS (Called automatically) ---
You do not need to run these scripts manually. They must simply remain in 
the same folder as the main script:

1. getHydrostaticProfiles2.py 
   Computes the target q0 values based on hydrostatic atmospheric profiles.

2. getrhoTatz1.py 
   Acts as the objective function. It computes the error between the simulated 
   flux and the target flux, and calculates the physical parameters Sigma and 
   Alpha based on the spatial integral.

3. solveSpatialProfileshelper2.py 
   The core numerical integrator solving the coupled ODE system for the 
   vertical structure (density and temperature) using the explicit Euler 
   scheme, and evaluating the cumulative integral using the trapezoidal rule.

--- REQUIREMENTS ---
- Python 3.x
- NumPy
- Matplotlib
- SciPy 
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