A simple model of convection with memory

There are at least three distinct timescales that are relevant for the evolution of atmospheric convection. These are the timescale of the forcing mechanism, the timescale governing the response to a steady forcing and the timescale of the response to variations in the forcing. The last of these, tmem, is associated with convective lifecycles, which provide an element of memory in the system. A highly simplified model of convection is introduced, which allows for investigation of the character of convection as a function of the three timescales. For short tmem, the convective response is strongly tied to the forcing as in conventional equilibrium parameterisation. For long tmem, the convection responds only to the slowly-evolving component of forcing and any fluctuations in the forcing are essentially suppressed. At intermediate tmem, convection becomes less predictable: conventional equilibrium closure breaks down and current levels of convection modify the subsequent response.