# Temporal Coherence: A Model for Non-stationarity in Natural and Simulated Wind Records

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## Abstract

We present a novel methodology for characterizing and simulating non-stationary stochastic wind records. In this new method, non-stationarity is characterized and modelled via temporal coherence, which is quantified in the discrete frequency domain by probability distributions of the differences in phase between adjacent Fourier components. Temporal coherence can also be used to quantify non-stationary characteristics in wind data. Three case studies are presented that analyze the non-stationarity of turbulent wind data obtained at the National Wind Technology Center near Boulder, Colorado, USA. The first study compares the temporal and spectral characteristics of a stationary wind record and a non-stationary wind record in order to highlight their differences in temporal coherence. The second study examines the distribution of one of the proposed temporal coherence parameters and uses it to quantify the prevalence of nonstationarity in the dataset. The third study examines how temporal coherence varies with a range of atmospheric parameters to determine what conditions produce more non-stationarity.

## Keywords

Non-stationarity Phase difference distributions Stochastic wind simulation Temporal coherence Turbulence## Notes

### Acknowledgments

The authors would like to gratefully acknowledge the multiple funding sources for this work. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. 1106401. The work was also supported by the U.S. Department of Energy, Office of Science, Office of Workforce Development for Teachers and Scientists, Office of Science Graduate Student Research (SCGSR) program. The SCGSR program is administered by the Oak Ridge Institute for Science and Education for the U.S. Department of Energy under contract number DE-AC05-06OR23100. This work was also supported by the U.S. Department of Energy under Contract No. DE-AC36-08GO28308 with the National Renewable Energy Laboratory. Funding for the work was provided by the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, Wind and Water Power Technologies Office. The authors thank the anonymous reviewers for their thoughtful and constructive comments.

## Supplementary material

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