TY  - JOUR
AU  - Reddy, Cherlacola Srinivas
AU  - Vaishnavi, CH.
AU  - Anuhya, D.
AU  - Kavya, K. N.
AU  - Vaishnavi, N.
AU  - Sindhuja, V.
AU  - Shruthi, P.
PY  - 2026
DA  - 2026/08/13
TI  - Mathematical Modelling of PM2.5 Dynamics in Hyderabad: A First-Order ODE Approach with Wind-Driven Removal
JO  - ICCK Journal of Applied Mathematics
T2  - ICCK Journal of Applied Mathematics
JF  - ICCK Journal of Applied Mathematics
VL  - 2
IS  - 3
SP  - 221
EP  - 232
DO  - 10.62762/JAM.2026.575197
UR  - https://www.icck.org/article/abs/JAM.2026.575197
KW  - air quality modelling
KW  - PM2.5
KW  - Ordinary differential equation
KW  - Differential Evolution
KW  - Runge--Kutta method
KW  - Hyderabad
AB  - Daily mean PM\(_{2.5}\) concentrations in Hyderabad routinely exceed both the 24-hour (\(60\,\mu\text{g/m}^3\)) and the annual (\(40\,\mu\text{g/m}^3\)) National Ambient Air Quality Standards, motivating the development of transparent and inexpensive descriptive models of their seasonal behaviour. To this end, we develop and calibrate a parsimonious first-order linear ordinary differential equation (ODE) that describes the daily evolution of ambient PM\(_{2.5}\) as the balance between a seasonally varying emission source \(E(t)=E_{0}+A\cos(2\pi(t-\varphi)/365)\) and a wind-driven first-order removal \(\lambda(t)=\alpha v(t)+\lambda_{0}\). The five parameters are estimated by Differential Evolution against a year (2024) of measured daily PM\(_{2.5}\) and wind data from three monitoring stations in Hyderabad---Zoo Park (urban), Bollaram (industrial), and the University of Hyderabad (peri-urban). The model is integrated by the forward Euler and classical fourth-order Runge--Kutta schemes and verified against the analytical integrating-factor solution. The calibrated model successfully reproduces the winter peak and the monsoon minimum, explaining between 63% and 83% of the weekly variability in PM\(_{2.5}\), with weekly root-mean-square errors in the range \(8.7\)--\(15.4\,\mu\text{g/m}^3\). It also yields physically plausible station-dependent removal coefficients (\(\alpha_{\mathrm{HCU}}>\alpha_{\mathrm{ZP}}>\alpha_{\mathrm{B}}\)) consistent with each station's exposure to ventilation, while a cross-year test quantifies the loss of skill under inter-annual variability. Overall, this demonstrates that a minimal five-parameter ODE, coupled with a robust global optimiser and a high-order integrator, serves as an effective descriptive tool for seasonal PM\(_{2.5}\) analysis in data-sparse urban environments and verifies the classical convergence theory of the two numerical schemes on real environmental data.
SN  - 3068-5656
PB  - Institute of Central Computation and Knowledge
LA  - English
ER  - 

@article{Reddy2026Mathematic,
  author = {Cherlacola Srinivas Reddy and CH. Vaishnavi and D. Anuhya and K. N. Kavya and N. Vaishnavi and V. Sindhuja and P. Shruthi},
  title = {Mathematical Modelling of PM2.5 Dynamics in Hyderabad: A First-Order ODE Approach with Wind-Driven Removal},
  journal = {ICCK Journal of Applied Mathematics},
  year = {2026},
  volume = {2},
  number = {3},
  pages = {221-232},
  doi = {10.62762/JAM.2026.575197},
  url = {https://www.icck.org/article/abs/JAM.2026.575197},
  abstract = {Daily mean PM\(\_{2.5}\) concentrations in Hyderabad routinely exceed both the 24-hour (\(60\,\mu\text{g/m}^3\)) and the annual (\(40\,\mu\text{g/m}^3\)) National Ambient Air Quality Standards, motivating the development of transparent and inexpensive descriptive models of their seasonal behaviour. To this end, we develop and calibrate a parsimonious first-order linear ordinary differential equation (ODE) that describes the daily evolution of ambient PM\(\_{2.5}\) as the balance between a seasonally varying emission source \(E(t)=E\_{0}+A\cos(2\pi(t-\varphi)/365)\) and a wind-driven first-order removal \(\lambda(t)=\alpha v(t)+\lambda\_{0}\). The five parameters are estimated by Differential Evolution against a year (2024) of measured daily PM\(\_{2.5}\) and wind data from three monitoring stations in Hyderabad---Zoo Park (urban), Bollaram (industrial), and the University of Hyderabad (peri-urban). The model is integrated by the forward Euler and classical fourth-order Runge--Kutta schemes and verified against the analytical integrating-factor solution. The calibrated model successfully reproduces the winter peak and the monsoon minimum, explaining between 63\% and 83\% of the weekly variability in PM\(\_{2.5}\), with weekly root-mean-square errors in the range \(8.7\)--\(15.4\,\mu\text{g/m}^3\). It also yields physically plausible station-dependent removal coefficients (\(\alpha\_{\mathrm{HCU}}>\alpha\_{\mathrm{ZP}}>\alpha\_{\mathrm{B}}\)) consistent with each station's exposure to ventilation, while a cross-year test quantifies the loss of skill under inter-annual variability. Overall, this demonstrates that a minimal five-parameter ODE, coupled with a robust global optimiser and a high-order integrator, serves as an effective descriptive tool for seasonal PM\(\_{2.5}\) analysis in data-sparse urban environments and verifies the classical convergence theory of the two numerical schemes on real environmental data.},
  keywords = {air quality modelling, PM2.5, Ordinary differential equation, Differential Evolution, Runge--Kutta method, Hyderabad},
  issn = {3068-5656},
  publisher = {Institute of Central Computation and Knowledge}
}