Extreme weather hazards happens more often these days due to climate changes and increased human industrial activities, and one of most notorious of them is haze. State-of-the-art haze removal methods generally work well with light haze conditions, however when haze gets heavier, the physical model tend to produce over-shadowed, noisy, and color distorted restorations. A new physical model has been proposed in this paper for heavy haze weathers. An airlight vector map has been proposed to address the problem caused by uneven aerosol distribution w.r.t. altitude variation. A Random Decision Forest model has been adopted to deal with the additional light attenuation and transmission map underestimation problem caused by heavy haze. Experiment shows the proposed model produces much better visual restoration for heavy haze weathers compared to state-of-the-art methods in terms of colour fidelity, noise reduction, and overall contrast.