Physical measures and tipping points in a changing climate

<p>For an autonomous dynamical system, an invariant measure is called <em>physical</em> or <em>natural</em> if it describes the statistics of a typically chosen trajectory that started an arbitrarily long time ago in the past, i.e. without transients. In order to apply such a concept to systems where there is time-varying forcing, we need to develop an analogous notion for such nonautonomous dynamical systems, where the measure is not fixed but evolves in time under the action of the nonautonomous system. The importance of such measures, and the pullback attractors on which they are supported, for interpreting climate statistics have been highlighted by Chekroun, Simmonet and Ghil (2011) <em>Physica D </em><strong>240</strong>:1685. We seek to gain a deeper understanding of these measures and implications for tipping points. We present some results for two classes of nonautonomous systems: autonomous random dynamical systems driven by stationary memoryless noise, and deterministic nonautonomous systems that are asymptotically autonomous in the negative-time limit. In both cases we show existence of a physical measure under suitable assumptions. We  highlight further questions about defining rates of mixing in such a setting, as well as implications for prediction of tipping points.</p><p><em>This work has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 820970 (TiPES).</em></p>

Extreme fluctuations of wind speed for a coastal/offshore climate: statistics and impact on wind turbine loads

For measurements taken over a decade at the coastal Danish site Høvsøre, we find the variance associated with wind speed events from the offshore direction to exceed the prescribed extreme turbulence model of the IEC 61400-1 Ed.3 standard for wind turbine safety. The variance of wind velocity fluctuations manifested during these events is not due to extreme turbulence; rather, it is primarily caused by ramp-like increases in wind speed associated with larger-scale meteorological processes. The measurements are both linearly detrended and high-pass filtered in order to investigate how these events – and such commonly-used filtering – affect the estimated 50-year return period of turbulence levels. The impact of the observed events on a wind turbine are investigated using aeroelastic simulations, that are driven by constrained turbulence simulation fields. Relevant wind turbine component loads from the simulations are compared with the extreme turbulence load case prescribed by the IEC standard. The loads from the event simulations are generally lower for all considered load components, with one exception: ramp-like events where the wind speed rises to exceed rated wind speed can lead to extreme tower base fore-aft loads that exceed DLC 1.3 of the IEC standard.

A Postprocessing Method for Seasonal Forecasts Using Temporally and Spatially Smoothed Statistics

A statistical postprocessing method for seasonal forecasts based on temporally and spatially smoothed climate statistics is introduced. The method uses information available from seasonal hindcasts initialized at the beginning of 12 calendar months. The performance of the method is tested within both deterministic and probabilistic frameworks using output from the ensemble of seasonal hindcasts produced by the Canadian Seasonal to Interannual Prediction System for the 30-yr period 1981–2010. Forecast skill improvements are found to be greater when forecast adjustment parameters estimated for individual seasons and at individual grid points are temporally and spatially smoothed. The greatest skill improvements are typically achieved for seasonally invariant parameters while skill improvements due to additional spatial smoothing are modest.

Non–stationarity in annual maxima rainfall across Australia – implications for Intensity–Frequency–Duration (IFD) relationships

Rainfall Intensity–Frequency–Duration (IFD) relationships are commonly required for the design and planning of water supply and management systems around the world. Currently IFD information is based on the "stationary climate assumption" – that weather at any point in time will vary randomly and that the underlying climate statistics (including both averages and extremes) will remain constant irrespective of the period of record. However, the validity of this assumption has been questioned over the last 15 years, particularly in Australia, following an improved understanding of the significant impact of climate variability and change occurring on interannual to multidecadal timescales. This paper provides evidence of non-stationarity in annual maxima rainfall timeseries using 96 daily rainfall stations and 66 sub-daily rainfall stations across Australia. Further, the effect of non-stationarity on the resulting IFD estimates are explored for three long-term sub-daily rainfall records (Brisbane, Sydney and Melbourne) utilising insights into multidecadal climate variability. It is demonstrated that IFD relationships may under- or over-estimate the design rainfall depending on the length and time period spanned by the rainfall data used to develop the IFD information. It is recommended that non-stationarity in annual maxima rainfall be explicitly considered and appropriately treated in the ongoing revisions of Engineers Australia's guide to estimating and utilising IFD information, "Australian Rainfall and Runoff", and that clear guidance needs to be provided on how to deal with the issue of non-stationarity of extreme events (irrespective of whether that non-stationarity is due to natural or anthropogenic climate change). The findings of our study also have important implications for other regions of the world that exhibit considerable hydroclimatic variability and where IFD information is based on relatively short data sets.