Modelling the lifted minimum phenomenon in the atmospheric

Abstract

The Ramdas Paradox, also known as the lifted minimum phenomenon, has been a longstanding micrometeorological puzzle. It concerns the vertical distribution of air temperature which, near the ground during nights, generally shows an increase with height up to some distance above the ground before it starts falling.

In 1932, Ramdas and Atmanathan reported that on calm, clear nights in Pune and other places in India they observed the minimum temperature not at the ground but at a height of about 20 cm above it. These observations are intriguing because the ground (with infrared emissivity close to one) is a good radiator compared to air (emissivity less than 0.3) and hence may be expected to cool to a temperature below that of the air above it. However, Ramdas and Atmanathan found that the layer of air at 20 cm remained cooler than the ground for well over three hours.

Although these results were initially treated with suspicion, they have since been amply confirmed by many other investigators in different parts of the world, leading to what has become known as the lifted minimum phenomenon or Ramdas paradox.

The present thesis attempts to explain the phenomenon by formulating and solving the appropriate energy transport equation under the conditions necessary to cause the lifted minimum. The resulting initial/boundary value problem is then solved by the method of lines.

In the first instance, heat transfer due to radiation alone is considered, and the resulting equation is integrated up to two hours. It is shown that these temperature profiles are characterized by discontinuities at the ground and strongly depend on the emissivity and cooling rate of the ground.

It is then demonstrated that the lifted minimum is formed by smoothing of the discontinuity by molecular diffusion, and inclusion of turbulent thermal diffusivity tends to destroy the lifted minimum structure.

The effects of ground emissivity, ground cooling rate, humidity content near the ground, surface Boltzmann number (ratio of convective energy flux to radiative energy flux), and other associated nondimensional numbers on the lifted minimum are studied, leading to maps which should be useful in predicting the phenomenon.

Finally, the phenomenon is also explained in the framework of the Rayleigh–Bénard problem.