The skewness of a time series is commonly used to quantify the extent to which positive (negative) deviations from the mean are larger than negative (positive) ones. However, in some cases, traditional skewness may not provide reliable information about time series skewness, motivating the development of a waveform skewness index in this paper. The waveform skewness index is used to show that changes in the relationship strength between climate time series could arise from changes in skewness.

Present climate models discuss climate change but show no sign of bifurcation in the future. Is this because there is none or because they are in essence too simplified to be able to capture them? To get elements of an answer, we ran a laboratory experiment and discovered that the answer is not so simple.

In this study, a recent algorithmic framework called Direct Bayesian Model Reduction (DBMR) is applied which provides a scalable probability-preserving identification of reduced models directly from data. The stochastic method is tested in a meteorological application towards a model reduction to latent states of smaller scale convective activity conditioned on large-scale atmospheric flow.

Glacial isostatic adjustment is the delayed reaction of the Earth's lithosphere and mantle to changing mass loads of ice sheets or water. The deformation behaviour of the Earth's surface depends on the ability of the Earth's mantle to flow, i.e. its viscosity. It can be estimated from sea level observations, and in our study, we estimate mantle viscosity using sea level observations from the past. This knowledge is essential for understanding current sea level changes due to melting ice.

The outputs from Earth system models are optimally combined with satellite observations to produce accurate forecasts through a process called data assimilation. Many existing data assimilation methodologies have some assumptions regarding the shape of the probability distributions of model output and observations, which results in forecast inaccuracies. In this paper, we test the effectiveness of a newly proposed methodology that relaxes such assumptions about high-dimensional models.

The difference between the energy that the Earth receives from the Sun and the energy it emits as black-body radiation is stored in a scaling hierarchy of structures in the ocean, soil and hydrosphere. The simplest scaling storage model leads to the fractional energy balance equation (FEBE). We examine the statistical properties of FEBE when it is driven by random fluctuations. In this paper, we explore the statistical properties of this mathematically simple yet neglected equation.

We find a new kind of non-stationarity. This new kind of non-stationarity is caused by the intrinsic randomness. Results show that the new kind of non-stationarity is widespread in small-scale variations of CO₂ turbulent fluxes. This finding reminds us that we need to handle the short-term averaged turbulent fluxes carefully, and we also need to re-screen the existing non-stationarity diagnosis methods because they could make a wrong diagnosis due to this new kind of non-stationarity.

The weather is chaotic and hard to predict, but the chaos implies an effective control where a small control signal grows rapidly to make a big difference. This study proposes a control simulation experiment where we apply a small signal to control nature in a computational simulation. Idealized experiments with a low-order chaotic system show successful results by small control signals of only 3 % of the observation error. This is the first step toward realistic weather simulations.