The transformed-stationary approach: a generic and simplified methodology for non-stationary extreme value analysis

Statistical approaches to study extreme events require, by definition, long time series of data. In many scientific disciplines, these series are often subject to variations at different temporal scales that affect the frequency and intensity of their extremes. Therefore, the assumption of stationarity is violated and alternative methods to conventional stationary extreme value analysis (EVA) must be adopted. Using the example of environmental variables subject to climate change, in this study we introduce the transformed-stationary (TS) methodology for non-stationary EVA. This approach consists of (i) transforming a non-stationary time series into a stationary one, to which the stationary EVA theory can be applied, and (ii) reverse transforming the result into a non-stationary extreme value distribution. As a transformation, we propose and discuss a simple time-varying normalization of the signal and show that it enables a comprehensive formulation of non-stationary generalized extreme value (GEV) and generalized Pareto distribution (GPD) models with a constant shape parameter. A validation of the methodology is carried out on time series of significant wave height, residual water level, and river discharge, which show varying degrees of long-term and seasonal variability. The results from the proposed approach are comparable with the results from (a) a stationary EVA on quasi-stationary slices of non-stationary series and (b) the established method for non-stationary EVA. However, the proposed technique comes with advantages in both cases. For example, in contrast to (a), the proposed technique uses the whole time horizon of the series for the estimation of the extremes, allowing for a more accurate estimation of large return levels. Furthermore, with respect to (b), it decouples the detection of non-stationary patterns from the fitting of the extreme value distribution. As a result, the steps of the analysis are simplified and intermediate diagnostics are possible. In particular, the transformation can be carried out by means of simple statistical techniques such as low-pass filters based on the running mean and the standard deviation, and the fitting procedure is a stationary one with a few degrees of freedom and is easy to implement and control. An open-source MAT-LAB toolbox has been developed to cover this methodology, which is available at https://github.com/menta78/tsEva/(Mentaschi et al., 2016).

Influence of the sea state on Mediterranean heavy precipitation: a case-study from HyMeX SOP1

Sea state can influence the turbulent air–sea exchanges, especially the momentum flux, by modifying the sea-surface roughness. The high-resolution non-hydrostatic convection-permitting model MESO-NH is used here to investigate the impact of a more realistic representation of the waves on heavy precipitation during the Intense Observation Period (IOP) 16a of the first HyMeX Special Observation Period (SOP1). Several quasi-stationary mesoscale convective systems developed over the western Mediterranean region, two of them over the sea, and resulted in heavy precipitation on the French and Italian coasts on 26 October 2012. Three different bulk parametrizations are tested in this study: a reference case (NOWAV) without any wave effect, a parametrization taking into account theoretical wave effects (WAV) and a last one with realistic wave characteristics from the MFWAM analyses (WAM). Using a realistic wave representation in WAM significantly increases the roughness length and the friction velocity with respect to NOWAV and WAV. The three MESO-NH sensitivity experiments of the IOP16a show that this surface-roughness increase in WAM generates higher momentum fluxes and directly impacts the low-level dynamics of the atmosphere, with a slowdown of the 10 m wind, when and where the wind speed exceeds 10 m s−1 and the sea state differs from the idealized one. The turbulent heat fluxes are not significantly influenced by the waves, these fluxes being controlled by the moisture content rather than by the wind speed in the simulations. Although the convective activity is globally well reproduced by all the simulations, the difference in the low-level dynamics of the atmosphere influences the localization of the simulated heavy precipitation. Objective evaluation of the daily rainfall amount and of the 10 m wind speed against the observations confirms the positive impact of the realistic wave representation on this simulation of heavy precipitation.

The interaction between two oppositely travelling, horizontally offset, antisymmetric quasi-geostrophic hetons

We investigate numerically the nonlinear interactions between hetons. Hetons are baroclinic structures consisting of two vortices of opposite sign lying at different depths. Hetons are long-lived. They most often translate (they can sometimes rotate) and therefore they can noticeably contribute to the transport of scalar properties in the oceans. Heton interactions can interrupt this translation and thus this transport, by inducing a reconfiguration of interacting hetons into more complex baroclinic multipoles. More specifically, we study here the general case of two hetons, which collide with an offset between their translation axes. For this purpose, we use the point vortex theory, the ellipsoidal vortex model and direct simulations in the three-dimensional quasi-geostrophic contour surgery model. More specifically, this paper shows that there are in general three regimes for the interaction. For small horizontal offsets between the hetons, their vortices recombine as same-depth dipoles which escape at an angle. The angle depends in particular on the horizontal offset. It is a right angle for no offset, and the angle is shallower for small but finite offsets. The second limiting regime is for large horizontal offsets where the two hetons remain the same hetonic structures but are deflected by the weaker mutual interaction. Finally, the intermediate regime is for moderate offsets. This is the regime where the formation of a metastable quadrupole is possible. The formation of this quadrupole greatly restrains transport. Indeed, it constrains the vortices to reside in a closed area. It is shown that the formation of such structures is enhanced by the quasi-periodic deformation of the vortices. Indeed, these structures are nearly unobtainable for singular vortices (point vortices) but may be obtained using deformable, finite-core vortices.