GPS-Radio-Occultation-Atmospheric-Temperature-Retrieval

Project Overview

This project implements an end-to-end Remote Sensing Retrieval Pipeline for GPS Radio Occultation (GPS-RO) data. It simulates the physics of the COSMIC-2 satellite mission to retrieve atmospheric temperature profiles from space.

The pipeline performs two key functions:

1. Forward Modeling: Simulates satellite "Bending Angle" telemetry based on a Standard Atmosphere model (including realistic sensor noise).
2. Inverse Retrieval: Solves the Inverse Abel Transform and integrates the Hydrostatic Equation to recover the temperature profile from the noisy telemetry.

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Results (Validation)

The algorithm successfully retrieves the temperature profile (Blue), matching the "True" input atmosphere (Red) within <1% error in the core region (10km–40km). It correctly identifies the Tropopause at ~11km.

(Note: This plot is generated automatically by running the pipeline)

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This project solves the classic Inverse Problem of Radio Occultation.

1. The Abel Inversion

The core challenge is converting the satellite's raw measurement (Bending Angle, $\alpha$) into Atmospheric Refractivity ($n$). This requires solving a Volterra integral equation of the second kind numerically:

$$ n(a) = \exp\left( \frac{1}{\pi} \int_{a}^{\infty} \frac{\alpha(x)}{\sqrt{x^2 - a^2}} , dx \right) $$

• Implementation: Discretized using the Trapezoidal rule with singularity handling at the lower bound ($x=a$).

2. Hydrostatic Integration

Once Refractivity ($N$) is known, density is derived. Pressure ($P$) is calculated by integrating the air column from the Top of Atmosphere (TOA) downwards:

$$ P(z) = \int_{z}^{z_{top}} \rho(h) \cdot g(h) , dh $$

Temperature ($T$) is then retrieved via the Ideal Gas Law relation for Refractivity:

$$ T(z) = 77.6 \cdot \frac{P(z)}{N(z)} $$

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