Clouds are chaotic, difficult to predict, but above all, magnificent natural phenomena. There are different types of clouds: stratus, a layer of clouds that may produce drizzle, cirrus, clouds in the higher parts of the atmosphere, and cumulus, clouds that arise in convective updrafts. Thermals, rising air that is often used by birds and gliders to gain height, are an example of atmospheric convection. When the sun heats Earth’s surface layer, warm and moist air rises in thermals to higher parts of the atmosphere. In this way, convection transports heat and moisture vertically in the atmosphere. This often leads to the formation of clouds and heavy rainfall. A major part of the rainfall on Earth, especially in the tropics, is produced by cumulus clouds. Furthermore, convection and cloud formation affect the large-scale planetary circulation. In the atmosphere, these processes are of major importance for Earth’s weather and climate. Convection and clouds also play a major role in numerical simulations of weather and climate. With general circulation models, the large-scale wind circulation and variables such as temperature and humidity are calculated on a three-dimensional global grid. The model grid resolution is low, and therefore, smaller-scale processes such as convection and cloud formation can not be calculated explicitly. The impact of these small-scale processes has to be determined in another way. They are represented by parameterizations that give an estimate of the effect of the smallscale processes on the large-scale model variables. For models with relatively large columns, the presence of a large number of realizations of the same small-scale process justifies the expression of their effect on the large-scale variables in terms of statistical properties. For example, the effect of a large number of clouds can be represented statistically. A problem arises from the fact that the resolution of operational weather and climate models tends to increase. Generally speaking, with higher model resolutions the atmosphere can be simulated more accurately. However, if resolutions keep increasing, the expression of the small-scale effects in terms of statistical properties can no longer be justified. In a small model column, there is for example only space for a small number of clouds. The chaotic behavior of convective clouds becomes an important factor and deterministic parameterizations no longer give accurate estimates. The increase of fluctuations and randomness is a motivation for using stochastic convection parameterizations. The central research theme in this dissertation is stochastic convection parameterization. Stochastic processes are used in the representation of convective clouds. Traditional deterministic parameterizations only give an estimate of the expected value of the effect of small-scale variables. Stochastic parameterizations can deviate from this expected value and can produce a range of convective responses. Especially in models with a relatively high resolution, it is important that parameterizations can represent fluctuations around the expected value. There are several ways of introducing stochastics. In this dissertation, Markov chains are examined, stochastic processes that are named after the famous Russian mathematician Andrei Markov (1856-1922). Markov chains have a finite number of states of which the transition probabilities can be estimated from data. By inferring transition probabilities from high-resolution data of convection, Markov chains mimic convective behavior.
A Large-Eddy Simulation model is used to construct a data set. Large-Eddy Simulation models are able to resolve clouds and convection in detail. After inference of the Markov chains, they are able to mimic clouds and convection as observed in a field-experiment near Barbados. The same method has also been applied for convective clouds in Brazil. These Markov chains only work for a very specific range of atmospheric circumstances. Therefore, another Markov chain model is constructed from a large observational data set from a rain radar in Darwin, Australia. A larger range of atmospheric circumstances is covered, and the Markov chains can be applied more generally. The Darwin Markov chains are implemented in a climate model to stochastically parameterize convection. This improves the variability related to convection as well as the distribution of the simulated tropical precipitation. The Markov-chain model is not perfect yet; however, a large step has been made in the development of this stochastic method for usage in state-of-the-art weather and climate models.