Machine learning is becoming an increasingly important tool for climate scientists, but hampered by lacking uncertainty quantification. Here, a machine learning approach for detecting patterns indicating a changing climate is combined with probabilistic modelling to retrieve uncertainty values. We train neural networks on climate model simulations of temperature and precipitation under historical and future scenarios. We find that the resulting so-called Bayesian neural network (BNN) has similar predictive strength to an Artificial neural network (ANN), with a post-year 2000 mean absolute error of 9.00 years for temperature, but over-fits less. The BNN is able to recognise temperature change starting in 1994, which is 14 years later than the ANN. Our analysis shows that uncertainties in found climate patterns are much higher than the patterns themselves, reducing their value for further use. This work demonstrates that BNNs are a suitable tool for quantifying uncertainties of patterns indicating a changing climate.

Long-term sea level change and its spatial and temporal variability measured with tide gauge stations along the Dutch coast have been studied. This study investigates how time series length and modeling choices influence the adoption of a quadratic over a linear sea level model. We apply linear and quadratic models to corrected tide gauges, for differing model start years. Longer models show more consistent results between stations, with less inter-station variability and smaller uncertainties. This improvement of consistency diminishes when using time series longer than 40 years. We find indications of a break-point in trends in the period 1978-1998. Quadratic models result in minor but relevant acceleration for longer time series, but do not perform sufficiently for time series shorter than 20 years. Comparing model quality between linear and quadratic models generally indicate better performance of quadratic models, but results are not conclusive to justify model adoption. A station mean is less conclusive for quadratic models than for linear models and sensitive to choice of stations and model length. Keywords: mean sea level variability, sea level change, sea level acceleration, tide gauge records, Dutch coast