The Fourth Workshop on Fluids and PDE was held at the National Institute of Pure and Applied Mathematics (IMPA) in Rio de Janeiro, Brazil, from Monday 26 May to Friday 30 May 2014. This workshop is held every two to three years in Brazil. The fourth edition of the workshop was the closing event of a Thematic Program on Incompressible Fluids Dynamics, to be held at IMPA next Spring. Hence, the focus of the workshop will be incompressible fluid mechanics .

A novel sampling scheme for the state of a system of partial differential equations, the Influence Sampling - Monte Carlo scheme, is presented for systems with fast-determining variables. The concept of fast-determining variables is an extension of the concept of determining variables on the attractor. The scheme uses a formula for the compatibility between fast-determining and trailing values to settle the most appropriate model for taking over the control run of an ongoing prediction among those models in use the sampling scheme. Predictability tests are conducted on unstable solutions of a moist convective rotating shallow water system of equations with time-varying coefficients using the constant coefficient version of this model in the sampling scheme .