EWEC 2009 - European Wind Energy Conference & Exhibition

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Monday, 16 March 2009
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Poster Session / Session consacrée aux posters
Poster Session Track / Session Code: PO
Tuesday, 17 March 2009, 14:00 - 15:30

PROFILING WIND DIRECTION IN ORDINARY KRIGING OF PERIODIC IN-SITU SENSOR DATA
Zlatko Zlatev, IT Innovation, United Kingdom
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Co-author(s):

Stuart Middleton, United Kingdom (1)
(1) IT Innovation

Summary

We examine the issues presented by wind direction in spatial interpolation using an ordinary kriging algorithm applied to in-situ sensor data. We propose a simple but effective solution, based on vector rotation and stochastic simulation, to the problem of estimating periodic variables. In cases where for the region of interest all wind direction vectors span 180 degrees, we rotate them so they lie between 90 and 270 degrees and apply kriging directly to the geodesic angle. Else, we transform the geodesic angle to Cartesian coordinates, apply kriging and use simulation to transform the kriging estimates back to geodesic angle.

Full description

In our ordinary kriging implementation for wind direction spatial interpolation we tackle the problem of estimating a periodic real valued random variable with a simple but effective solution based on vector rotation and stochastic simulation. Ordinary kriging, like most statistical estimation techniques, is not fit for estimating periodic variables. Estimates at unobserved locations are obtained from measurements at observed locations and a variogram, which models spatial dependences. Numerically close measurements reveal high dependence. Wind direction vectors? geodesic angles at the period beginning and end are close in terms of direction, but are distant numerically. This disagreement makes the direct application of kriging inappropriate. A tempting approach is to transform angles to Cartesian coordinates, apply kriging using the transformed data and perform backward transformation to angle estimates. The angle estimate is the arctangent of the ratio of the Cartesian estimates, which are assumed to be Gaussians. The Gaussian ratio distribution has no simple analytical solution [Hinkley, 1969] let alone taking an arctangent.

Our in-situ sensor dataset contains observations for 17 locations, over an area of 200x125 km, for 5 years with sensor sampling periods between 30 minutes and 3 hours. We perform spatial interpolation in half-hourly time slices. Within a time slice we check the wind direction vectors? span. If the span is 180 degrees or less, which is in about 80% of the cases, we rotate the wind direction vectors to lie between 90 and 270 degrees. This eradicates the periodicity problem as the numerical distance between the angle values corresponds to the distance between the direction vectors and enables kriging. The kriging estimates are rotated backwards to obtain the final results. Otherwise, for spans over 180 degrees, we transform the geodesic angle to Cartesian coordinates and perform kriging on the transformed data. For the backward transformation, from Cartesian estimates to geodesic angle, we use stochastic simulations and calculate the most likely value and the 95% confidence interval from the simulated sample. This simulation approach was tested on 50 by 50 grid using commodity hardware. Backward transformation with sample size allowing results to approach direct angle kriging results takes on average about 5 minutes.

For a medium size (~200x125 km) area the majority (~80%) of cases will need vector rotation. In the other cases simulations? time-accuracy-trade-off is a drawback but on high performance hardware and with parallelisation these simple simulations can be easily accelerated.