Applications of the transilient matrix to atmospheric transport

A method is introduced for diagnosing a transilient matrix for steady-state convection. This transilient matrix quantifies the nonlocal transport of air by convective eddies: for every height z, it gives the distribution of starting heights z' for the eddies that arrive at z. In recent work, the transilient matrix demonstrated that the first 100 meters of the sub-cloud layer is the source for the majority of sub-cloud-layer air in cumulus and cumulonimbus. With some modifications, the transilient matrix can also be used to quantify convective momentum transport and the vertical redistribution of aerosols. This flexibility makes the transilient matrix an attractive framework for subgrid models of vertical mixing.