**By Jack Kline, Consulting Meteorologist**

**RAM Associates**

One year of wind resource data collection is typically considered the minimum duration from which a reasonable estimate of long-term wind speed can be calculated at a potential new wind energy site. However, one year of data is rarely sufficient to produce an accurate estimate of long-term wind speed. It is simply too short of a time period for reliable data and subject to uncertainty.

What’s more: as data accumulates, long-term estimates continue to change with successive analyses and almost never stabilize or converge on a constant value.

Examination of long-term wind speed estimates shows uncertainty and a strong likelihood that results are subjected to high or low-bias, regardless of the technique or methodology employed in its production. Fortunately, this bias can be corrected, producing long-term wind speed estimates that are more accurate and stable over time — and with reduced uncertainty.

The types of variability and bias were illustrated in a case study conducted at a meteorological mast site in the northern Great Plains. Hourly wind speed data, pre-screened with quality assurance, at the 60 m level of three met masts were provided by the project developer. The duration of the data is 4.7 years (56 months) at the site (known as Site 1).

In this analysis, data from a nearby MERRA2 node was used as the long-term reference. MERRA2 is the second generation of MERRA — Modern-Era Retrospective analysis for Research and Applications — reanalysis data (learn more here). Missing data at the met mast was estimated using the MERRA2 data by a matrix method and provided data sets with 100% data recovery. The wind speed data from the MERRA2 node and the met masts were reduced to daily averages and the correlation R^{2} between the reference and the met mast is 0.81.

For simplicity’s sake, the long-term wind speed at the reference site is held constant throughout the analysis.

**Estimating wind data
**In this study, the researchers tested two commonly used techniques for long-term wind speed estimation.

**1. Orthogonal regression**, which is similar to a standard least-squares regression analysis, producing the equation for the “best-fit” line through two sets of data.

**2. A simple wind-speed ratio method** in which the “target” site’s wind speed is adjusted by the ratio of the reference site’s long-term wind speed to its observed average wind speed.

The orthogonal regression was used in separate annual (12-month) periods, which shows the range of long-term estimates that were obtained using only one year of data at a time. Then, both methods were used with durations of cumulative data from one year and up.

Successive estimates of long-term wind speed at Site 1 were calculated using one year (ANN REG) of data at a time in one-month time steps, which illustrates the high level of variability in long-term wind speed estimates produced from a single year of data. These estimates are compared to those obtained by using cumulative data sets applying either orthogonal regression (CUM. REG) or wind speed ratios (CUM. RATIO).

Given N months of data at the met mast, a total of N-11 long-term wind speed estimates would be calculated by stepping through the data in one-month increments, starting with one full year. Site 1 had 56 months of data, so there were 45 estimates of long-term wind speed. All three series are shown in the graph *Moving annual and cumulative long-term wind speed estimates*.

The long-term wind speed estimates using annual data periods have quite a large range, from a low of 7.05 m/s to a high of 7.32 m/s — all based on the long-term mean wind speed at the MERRA2 node of 6.59 m/s. The estimates using cumulative data sets have a much lower dynamic range and track each other closely, producing long-term estimates from as low as 7.12 m/s up to 7.20 m/s. However, after including as much as three or four years of cumulative data, the long-term estimates have failed to converge.

What’s more, the estimates show a propensity of bias. This is revealed by plotting the individual long-term estimates (cumulative regression and ratio) with respect to their concurrent average wind speeds at the MERRA2 node in *Cumulative long-term wind site estimates at Site1 vs MERRA*.

This graph shows a distinct tendency to produce higher estimates of long-term wind speed at Site 1 when the average wind speed at the MERRA node is lower, and lower estimates when the wind speed at MERRA is higher. The slopes of the trend lines indicate that the ratio estimates have a stronger tendency to be biased than the orthogonal regression estimates.

This bias is typical and depicts what are referred to as negative bias. The opposite of this, positive bias is also observed at some project sites but seems to be less prevalent than negative bias.

So, why is there negative bias and how does one correct for it?

**Understanding bias**

Negative bias occurs because the wind speeds observed at Site 1 are less sensitive to the meteorological phenomena that produce wind than the wind speeds represented by the MERRA2 data.

A sensitivity analysis of the concurrent average wind speeds at Site 1 versus MERRA shows that on average, the sensitivity of Site 1 wind speed to MERRA = 0.78. This means that on average, with a 1.00% change in wind speed at MERRA, there is only a 0.78% change in observed wind speed at Site 1. For example, during a time period when the long-term average at the MERRA node is, say, 2.0% above its average wind speed during the data period, the ratio method will apply a 2.0% upward adjustment to the concurrent average wind speed at Site 1.

However, given the observed sensitivity, the adjustment should only be 1.56%, which leads to an over-adjustment and negative bias. Of course, the converse also applies, when the average wind speed at the MERRA node is above its long-term average. The orthogonal regression estimates have similar tendencies, although not as extreme, which produces the lower magnitude of the slope of its trend line in the *Site 1 vs MERRA* graph.

In general:

- When the met mast’s wind speed sensitivity with respect to the reference is < 1.00 there will tend to be negative bias in long-term wind speed estimates
- When the sensitivity is > 1.00 there will tend to be positive bias

De-biasing the estimates is quite simple. One need only apply the equations for the trend lines in the *Site 1 vs MERRA* graph to de-bias both estimates by inserting the long-term average wind speed at the MERRA2 node as the “x” value, producing a long-term estimate of 7.16 m/s.

**Reliable estimates
**De-biasing the estimates will produce long-term wind speed estimates that are more stable as more data is added, and with lower uncertainty. To illustrate this, the researchers used the same long-term wind speed estimates based on orthogonal regression of cumulative data sets (as shown in the first graph).

The initial estimate is produced using 12 months of data, the second uses 13 months of data, and so on. After 15 months of data were collected (the fourth iteration), the process of de-biasing began. The researchers calculated the linear fit of the long-term wind speed estimates to the concurrent average wind speeds at the MERRA node and inserted the long-term average speed at the MERRA node into the resulting equation.

The final graph, *Cumulative long-term wind site estimates*, shows both the time-series of long-term wind speed estimates by orthogonal regression of cumulative data and the de-biased estimates. The first de-biased estimate appears in iteration four. By iteration seven (18 months of data), the de-biased estimate of long-term wind speed is 7.16 m/s. As subsequent iterations are added the de-biased wind speed estimate varies only slightly thereafter, whereas the regression estimates show significantly higher variability.

The de-biased estimate represents the most likely wind speed at Site 1 when the MERRA speed is equal to its long-term average.

**Final thoughts**

Long-term wind speed estimation at a meteorological mast site is a key component of a reliable wind-resource assessment. Such estimates are typically biased because of unequal levels of sensitivity of the wind speeds at the met mast with respect to the long-term reference. Applying the de-biasing technique described here produces long-term wind speed estimates that are more accurate, and with less variability and with lower uncertainty, using as little as two years of continuous data.

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