PRAVAH

The problem

Air-quality measurements are sparse in space and time. PRAVAH investigates how a physical transport model can connect those observations to source estimates and choices about where to measure next.

The mathematical idea

The modeling starting point is an advection–diffusion–removal equation:

Here $c$ is pollutant concentration, $\mathbf{u}$ is wind velocity, $D$ describes diffusion, $\lambda$ is a removal rate, and $s$ represents sources. Boundary conditions and discretization are part of the model, not incidental details.

Computational approach

The toolkit connects PDE simulations, inverse source estimation, and sensor-placement experiments. Synthetic observations let the inference procedure be studied against a known simulated source before interpreting real measurements.

Limits of the model

Synthetic experiments do not establish real-world deployment performance. Wind uncertainty, boundary assumptions, sensor errors, and unmodeled processes can all affect source estimates. This overview makes no claim of a validated operational forecasting or monitoring system.

Next questions

How sensitive are inferred sources to imperfect transport assumptions? Which sensor locations provide complementary information rather than simply more measurements of the same signal?