Seasonal Water State Transition Model 🌊 This repository contains a Markov Chain-based simulation for modeling the seasonal transition of water states (Vapor, Liquid, and Ice) across different climates: Summer, Winter, and Spring. The model computes stationary distributions for each season and uses a Dirichlet distribution to simulate variations in water state proportions.
📌 Features
✅ Markov Chain Simulation: Defines seasonal transition matrices to model state changes in water.
✅ Stationary Distribution Calculation: Uses eigenvalues and eigenvectors to compute equilibrium states.
✅ Dirichlet Distribution Modeling: Introduces realistic probabilistic variation in seasonal water compositions.
✅ Visualization: Generates bar plots showing the average proportions of Vapor, Liquid, and Ice in different seasons.
📂 Files in this Repository • seasonal_water_model.py – Main Python script for running the simulation. • README.md – Explanation of the model and how to use it. • plots/ – Example output images from the model.
📊 How It Works
1️⃣ Define transition matrices for Summer, Winter, and Spring.
2️⃣ Compute stationary distributions to determine equilibrium state proportions.
3️⃣ Use Dirichlet distribution to simulate realistic seasonal variations.
4️⃣ Plot results showing seasonal water compositions.
🚀 How to Run the Code
Install Dependencies
Ensure you have Python installed, then install required libraries:
pip install numpy scipy matplotlib
Run the script:
python seasonal_water_model.py
result:
The script will generate bar plots showing water composition in different seasons.
🔬 Scientific Relevance
This model can be applied to: ✔ Environmental Science – Understanding seasonal water cycle dynamics.
✔ Climate Modeling – Predicting shifts in atmospheric water phases under different climate conditions.
✔ Probabilistic Simulations – Using Markov Chains and Dirichlet distributions to model real-world transitions.
🛠 Future Improvements
🔹 Add more seasonal states (e.g., Fall).
🔹 Introduce climate change effects on transition probabilities.
🔹 Extend the model to geographical variations.
📜 License
This project is open-source under the MIT License. Feel free to use and modify!