a. Data collection and experiment design

Two WSR-88D sites known to experience WTC are Dodge City, Kansas (KDDC), and Great Falls, Montana (KTFX), and were chosen as the locations for two intensive experimental campaigns. The wind farm near KDDC comprises 170 individual turbines located approximately 40 km southwest of the radar while the wind farm near KTFX includes 6 turbines located 6 km northwest of the radar. The goal of the experiments was to collect unfiltered time series data in a variety of formats for processing and further examination.

The experiment at Dodge City was performed on a WSR-88D with a Sigmet RVP8 digital receiver. Time series data were collected in spotlight mode (continuous data collection with a stationary antenna), range–height indicator (RHI) scan mode, and normal volume coverage pattern (VCP) scanning modes. Spotlight mode data collection was performed to examine the detailed temporal evolution of the WTC Doppler spectrum. RHI scan mode was implemented to ascertain the extent to which the WTC is detected by the antenna sidelobes. VCP scans were performed to provide cases with which to test the mitigation algorithms that were to be developed for operational usage. The highest PRF was used for the spotlight and RHI collections to maximize the Nyquist velocity and reduce the aliasing effect on the WTC Doppler spectrum. A PRF of 1282 Hz was used, resulting in a Nyquist velocity of 33.1733 m s⁻¹ (wavelength of 10.35 cm). Range oversampling was implemented to obtain 25-m range gate spacing and increase the likelihood of gathering single-turbine spectra. Having multiple turbines present complicates the analysis and is discussed further in the next section. The scanning modes were left to the discretion of the operator, but several hours of data were collected using VCP 21. This VCP is generally used in convective situations and the operator has the option to adjust the PRF for the Doppler cuts (Office of the Federal Coordinator for Meteorological Services and Supporting Research 2006). In this case, the operator chose the highest PRF available.

The experiment in Great Falls was also performed with a WSR-88D using a Sigmet RVP8 digital receiver. Due to the proximity of the radar to the turbines, in addition to documenting normal WTC patterns, it was expected that observations of WTC multipath scattering effects could be obtained. The same scanning strategies used for KDDC were also used to obtain the time series data for this experiment. Data were collected in spotlight and RHI mode using a PRF of 1310 Hz (33.8983 m s ⁻¹ aliasing velocity) and 25-m gate spacing. Again, several hours of VCP 21 scanning data were collected.

b. Experimental results and interpretation

Examples of the evolution of a WTC Doppler spectrum obtained in spotlight mode for a 4-s time period for each radar site are shown in Fig. 2. To calculate the spectra 64 samples were used and a Blackman–Harris window has been applied. Careful consideration was given to the spotlight scan azimuth selection to ensure that the spectra were produced by a single turbine. While clutter signals from multiple turbines are also useful for documentation, it is beneficial to observe the effects of a single turbine for better understanding. The impacts of multiple turbines within a single gate can be observed as a repeated single-turbine pattern, shifted in time. A strong return [>60 dB signal-to-noise ratio (SNR)] is present at the zero Doppler velocity throughout the duration of the scan and is attributed to the wind turbine tower as it is a stationary structure. The aliased periodic rise in power level as the spectrum evolves is attributed to the echo returns from the wind turbine blades as they pass a vertical position (either straight up or down). For a three-blade wind turbine, such as the type near KDDC and KTFX, this would occur 6 times per rotation. The 23.5-m wind turbine blades for the wind farm near KDDC rotate at a fixed rate of 28.5 rpm. With this rotation rate and given the duration of the data, the turbine should have rotated approximately twice over the 3.88-s time sample. The hypothesis holds as there are 11 flashes visible in Fig. 2a, denoted by the arrows. In addition, it is known that the wind direction during the time of the scan was west-northwesterly at 300° and the maximum tip velocity for this particular turbine is 70 m s⁻¹. The blade face would be 41° off radial, thus making the radial component of the maximum tip velocity approximately 53 m s⁻¹. Aliased flashes in Fig. 2a confirm this calculation. The wind turbines near KTFX have a variable rotation rate that is determined by the wind speed, thus making it difficult for a similar analysis to be conducted. However, the wind direction is known and thus the blade face orientation could be calculated. While the radial component of the maximum tip speed is not known, the Doppler spectra did exhibit distinct periodic behavior due to the limited number of turbines that make up the wind farm. As such, an estimate can be calculated from the turbine blade length, 38.5 m, and examining the number of rotations visible in Fig. 2b. One rotation occurs over 3.32 s, producing a rotation rate of approximately 18 rpm and a maximum tip velocity of 73 m s⁻¹. Notice that the periodic signal recorded at KTFX, instead of the well-defined flashes from KDDC, appears as a detailed sinusoid. One possible reason for this is due to high radar sensitivity at this proximity, which may allow for the detection of additional portions of the blade that might not appear at greater distances. In addition, the turbine blade rotation rate is much slower than the turbines near KDDC and the radar is able to capture smaller portions of the blade rotation in each time frame.

Examples of spectra evolution for elevation angles between 0.5° and 2.9° obtained from the RHI scans are shown in Fig. 3. The first null and sidelobe of the WSR-88D antenna are at 2.1° and 2.6°, respectively (Sirmans 1993). As the elevation angle approaches 2.1°, the impact of the blades and the tower on the Doppler spectrum is reduced. Then, as the beam approaches 2.6°, the power level increases as expected. Thus, the WSR-88D antenna sidelobes will detect both aspects of WTC contamination (tower and blades) and cannot be completely ignored. In some instances, however, it is possible that the power of the weather signals would significantly exceed that of the blade signal. A significant contribution from the tower would still remain due to its radar cross section as compared to the blades and, for such cases, the remaining tower contamination could be handled by standard clutter-filtering methods to reduce the majority of the WTC effects.

As predicted, the proximity of KTFX to the wind farm allows for the measurement of WTC multipath scattering effects. These effects will cause a region of elevated power in range gates behind the wind farm. An image illustrating this effect is shown in Fig. 4. The wind farm is visible at approximately 6 km from the radar at 315° azimuth and is circled in black. The false-echo region of higher power that extends behind the wind farm is likely due to multipath scattering effects and is circled in red. It is possible that a pulse transmitted by a radar could be reflected between multiple turbines, or between a turbine and other ground targets, and could eventually settle on a trajectory leading back to the radar. Only a small percentage of the transmitted power is reflected at each stage, so the proximity to the radar is an important factor in observing this effect.

In further exploration of multipath scattering, the spectra of gates down range from the known turbine locations were examined with the expectation that the typical WTC Doppler spectra would be present but at a much lower power. As seen in Fig. 5, this is indeed the case. Typical WTC Doppler signatures can be identified at distances surpassing 13 km despite the significant decrease in power.

a. Creation of a dataset for objective examination

The data collected during the experiments described in section 2 do not contain any mixed weather and WTC signals. Data collection was not possible during times where severe weather was a possibility since spotlight and RHI scans require the operator to relinquish control of the radar. To test the effectiveness of the mitigation algorithm on cases other than clear air, a test set of data was created by combining separate weather signals with WTC through a simple direct sum of the time series of the in-phase and quadrature (I–Q) voltage values. This could be achieved by the fact that the data were recorded in time series format. Conventional processing techniques could still be used to calculate the three spectral moments of interest: reflectivity, radial velocity, and spectrum width (Doviak and Zrnić 1993). Only scans with similar PRFs were combined to ensure minimal artifacts that might result from the dataset creation. Also, precisely the same range gates were used from each scan to preserve sampling volumes. Using this scheme, any interaction between the weather and wind turbine echoes is absent but such effects are thought to be insignificant. The separate and combined signals allowed for objective measurements to be made regarding the efficiency of the mitigation algorithm without the use of synthetic data.

b. Multiquadric interpolation and spatial data

Multiquadric interpolation was first proposed by Hardy (1971) as a means of creating a regularly spaced grid from irregularly spaced topographical data. Franke (1982) explores several global interpolation techniques and ranks the multiquadric method among the highest. Nuss and Titley (1994) make use of multiquadric interpolation with meteorological data and find it outperforms both the Cressman and Barnes techniques, although the extent of their claims of better performance versus the Barnes method were later challenged by Barnes (1995). While Nuss and Titley (1994) perform their comparison on smooth fields such as temperature and pressure, the original intent of Hardy (1971) was for multiquadric interpolation to be used on highly variable topographic data, a natural spatial phenomenon. With the exception of velocity aliasing, it is believed that the multiquadric method is applicable to the highly variable products of weather radar. Multiquadric interpolation is a global interpolation technique that uses radial basis functions to approximate missing data, reflectivity in this case, through the following equation:

View Expanded

and Q(X − X_i) is a radial basis function defined as

View Expanded

where X − X_i is the distance from any point X_i to a central point X and b is a user-defined constant (typically around 0.391 for this case). Rippa (1999) discusses several methods for selecting the constant b. Much care must be given to the selection of this parameter as large values of b can lead to system instability. The α_is are found by simply solving the set of linear Eqs. (1) resulting from a group of N known observations. The unknown value is then determined using the calculated weights. While reflectivity is used in Eq. (1), any spatially varying field can be interpolated (Nuss and Titley 1994) provided that a new set of α_is is generated for each.

c. Interpolation schemes and nowcasting

One of the most important tasks prior to the application of any interpolation scheme is simply identifying which data points to use. In this application of multiquadric interpolation, field values of gates corrupted with WTC are to be replaced with data fitted to a surface comprising uncontaminated field values. Both contaminated and uncontaminated data points are established a priori and stored in a static file. WTC-corrupted points were identified by examining several clear-air scans and applying a simple thresholding technique. Latitudes and longitudes of individual turbines were also used to verify the identification scheme. An interpolation window extends from the borders of the corrupt region with a range approximately matching the width–depth of said region. Studies examining the necessary interpolation window size for WTC scenarios are incomplete at this time; however, larger windows may stray from the assumption of spatial continuity necessary for global interpolation schemes.

The aforementioned multiquadric interpolation can be applied to the spectral moments in both two and three dimensions. The third dimension is included by utilizing the higher-elevation cuts from the same VCP scan that do not contain interference from the WTC. Additionally, the multiquadric method can be used to interpolate each spectral component by treating each spectral bin as a separate data field and will herein be referred to as spectral interpolation. It is expected that the spectral interpolation will preserve the fine features of the Doppler spectrum and increase the accuracy of the estimated moments. The three-dimensional interpolation is also expected to provide a more accurate representation of the storm structure and again increase the accuracy of the algorithm provided the storm occupies multiple elevations.

Nowcasting is a short-term forecast that attempts to incorporate the temporal continuity of weather into traditional forecasting and is explored here as an enhancement to the effectiveness of the interpolation algorithms discussed before. Many techniques exist that identify storm cells or particular features of storms and track the motion over several temporal frames. The Storm Cell Identification and Tracking (SCIT; Johnson et al. 1998) algorithm and the Machine Intelligent Gust Front Algorithm (MIGFA; Delanoy and Troxel 1993) are two such techniques and are extremely effective in their designed tasks, but are overly complicated for the WTC scenario, at least at this early stage of development. For WTC mitigation, temporal evolution is incorporated by employing a simple nowcasting technique that was adapted from an early method developed by Rinehart and Garvey (1978). A two-dimensional cross correlation is calculated between a designated sector of the current and previous PPI reflectivity images. Due to the inherent difficulties of advecting a three-dimensional field, when only one dimension (radial) is sampled, radial velocity was not considered. The sizes of the sectors were determined by estimated maximum storm velocities and the revisit times of the WSR-88D (Office of the Federal Coordinator for Meteorological Services and Supporting Research 2006). The first moment is calculated for the two-dimensional cross correlation giving the spatial shift between the PPI images. The previous scan data are then translated in the determined direction. The next step is to combine the translated and interpolated data in an optimum way, which is accomplished via a least mean squares scheme. First, a set of test gates are selected outside of the contaminated region where the interpolated, nowcasted, and true values are all either calculated or known. Next, a least mean squares criterion is used to calculate weights that minimize the mean square error between the linear combination of the interpolated and nowcasted values and the true values. Finally, the weights are used in the contaminated region to optimally combine the interpolation and nowcasting data and will herein be referred to as the hybrid technique. This procedure is summarized below for clarity and the optimization process is further described in mathematical terms.

1. Calculate the two-dimensional cross correlation over a specified window with current and previous scans as input;

2. calculate the first moment of the cross correlation to reveal the motion vector;

3. translate the previous scan according to the motion vector;

4. compute the optimized weights by completing a least squares analysis on the translated, interpolated, and known values for a set of test gates; and

5. combine the interpolated and advected data using the optimized weights.

The following equation describes how the interpolated power estimates (P_il, … ,P_ik) are combined with the nowcasting power estimates (P_nl, … ,P_nk) to form a single estimate vector P_c:

View Expanded

where w is the [2 × 1] weighting vector determined by minimizing the cost function,

View Expanded

and P_t is the test-gate vector with E[·] representing the expected value. The minimization of J with respect to w results in the following solution:

View Expanded

The selection of the test area, represented by P_t, is a step of considerable importance for the nowcasting–interpolation hybrid algorithm. The test area cannot be located behind the wind farm as multiturbine scattering effects may contaminate the data. Also, if the weather event is moving across the WTC region toward the chosen test area, it is likely that contaminated cells will translate into the test region reducing the number of test gates and therefore diminishing the usefulness of the entire testing procedure. To avoid this problem, a narrow (≈1 km) band of test cells is chosen, encompassing the three remaining sides of the farm.

d. Interpolation testing and results

Time series data for two weather events were used to test the interpolation algorithms on the KDDC WTC case. The first was an isolated cell recorded by KDDC on 30 March 2006 and the second was a squall line recorded by KTLX near Oklahoma City, Oklahoma, on 24 April 2007. The data were combined with KDDC WTC data collected on 30 March 2006 in the manner described earlier. Six interpolation schemes were used on each weather case over four scans of equal temporal distance. The four scans provide a variety of weather–WTC scenarios that include the weather event entering, overlapping, and exiting the WTC region. There are many techniques that can be used to quantify the quality of an image with respect to an original that take the human visual system (HVS) into consideration (Eskicioglu and Fisher 1995). However, for the sake of simplicity, a root-mean-square (RMS) error evaluation is used for this study. The values presented in Tables 1 and Tables 2 were obtained by calculating the RMS errors between the original and corrected reflectivity (Ẑ) and radial velocity (υ̂_r) PPI images for each weather case and interpolation technique. Only the interpolated region was considered in the RMS error analysis and a 5-dB SNR was required for the gate to be included in the interpolation or error analysis.

For the purpose of comparison, a one-dimensional linear regression fit was performed along the radials for each case study and the results are given in Tables 1 and Tables 2. In some instances, the linear regression technique outperforms the multiquadric method. For example, it appears that for scenarios in which the weather has passed or is overlapping the wind farm, the regression technique performs better, especially for the radial velocity fields, but only for the two-dimensional cases and one three-dimensional moment case. Linear regression does not outperform either the three-dimensional spectral or hybrid technique for any scenario. It is believed that multiquadric interpolation is more sensitive to the noise introduced by weak weather signals than linear regression and may account for this effect. While multiquadric interpolation is the primary technique examined here, it is shown by the linear regression comparison that other interpolation algorithms may prove more appropriate for particular fields, weather scenarios, or wind farms. However, in many cases, multiquadric interpolation provides more accurate corrections.

The application of the interpolation algorithms to the isolated cell case largely improved the reflectivity and radial velocity estimations as summarized in Table 1. However, assumptions that the spectral interpolation would significantly improve the radial velocity estimations do not hold. For most cases, the improvement does not justify the increase in computational complexity incurred by performing the interpolation on each spectral component. In fact, the two-dimensional spectral interpolation performs worse than the two-dimensional moment interpolation for scans at 2034:17 and 2040:04 UTC. Noisy data present in the PPI scan can cause inaccuracies in the interpolation output. In particular, gates near the border of the interpolation region pose a problem due to the fact that the weights determined by the multiquadric method are a function of distance as well as magnitude. The likelihood for corruption due to noise is greater for the spectral interpolation method since any signal present in a discrete frequency is considered for the interpolation, as compared to the moment interpolation where only a single value is considered for each gate. One solution to this problem is to expand the WTC exclusion zone to include gates that do not contain wind turbines but are affected by infrequent interference. Another possible solution involves smoothing the data prior to the interpolation, thus suppressing potential noise corruption (Nuss and Titley 1994). In contrast, the assumption that the three-dimensional interpolation would outperform the two-dimensional interpolation holds true for the isolated cell case. The inclusion of the higher elevations in the interpolation scheme enhances the accuracy of the algorithm. Finally, the nowcasting–interpolation hybrid algorithm outperformed the two-dimensional moment interpolation in each case presented in Table 1.

The squall-line case exhibits much of the same results as those of the isolated cell case and the results are shown in Table 2. The spectral interpolation does not provide an appreciable gain in velocity estimations but the three-dimensional interpolation does improve the estimates over the two-dimensional schemes. This is true for all but the 1836:26 UTC scan where the three-dimensional schemes actually perform worse than the two-dimensional schemes for reflectivity estimations. This may be due to the high gradient in the reflectivity values within the interpolation window or the higher elevations included in the algorithm may not accurately represent the 0.5° cut. Though the three-dimensional schemes do not perform as well as the two-dimensional schemes for this particular scan, it is important to note the improvement over the original corrupted image. The high weather reflectivity values for the squall-line case in the 1846:16 and 1856:07 UTC scans mask the interference caused by the blades, and the interpolation schemes actually increase the reflectivity estimation error by smoothing the dominate weather signal. However, for these same scans, the blade interference does bias the radial velocity estimates and the interpolation schemes provide adequate radial velocity error correction. The slow movement of the squall line did not allow many replacement gates to propagate into the WTC region. As a result, the weighted nowcasting values from the least squares combination act as a slight interference to the interpolation algorithm and increase the estimation error for the hybrid technique.

In both cases, the interpolation algorithms improve the accuracy of the reflectivity fields when the WTC bias is equal to or less than that of the weather. Strong weather reflectivity values (relative to the WTC) will mask contamination due to WTC and should therefore not be modified. Radial velocity values are much more likely to be affected by WTC and therefore more likely to benefit from interpolation. While the multiquadric method detects the high-frequency changes present in reflectivity values, this can potentially prove counterproductive for extremely smooth fields such as radial velocity. In some instances, it may be more appropriate to consider linear interpolation as opposed to the multiquadric method for smooth fields.

While a quantitative assessment of the mitigation schemes is essential to this work, a qualitative examination is also useful. Time-lapse images of the isolated cell reflectivity and radial velocity measurements, respectively, are provided in Figs. 6 and Figs. 7. The corrupted images are shown in the left-most columns of Figs. 6 and Figs. 7 and the corrected images in the right-most while the original weather data are displayed in the center. Listed on the right axis of each corrected image is the calculated RMS error. The storm traverses the interpolation window rapidly and exhibits weak reflectivity values. In fact, the WTC echoes are stronger than the weather in some gates. The leading and trailing edges of the isolated cell are just overlapping the WTC region in the 2028:31 and 2045:50 UTC scans, respectively, and the interpolation algorithm removes the majority of the WTC, but there are some gates with low residual reflectivity values. The overall improvement of the PPI images is notable.

The Doppler spectrum of each range gate for the 243° radial is shown in Fig. 8. The spectra have been filtered for stationary clutter and the black diamonds represent the radial velocity estimates for each gate. The wind farm occupies a continuous set of gates along the radial from 37 to 44 km. The weather signal is seen at approximately −10 m s⁻¹ at the bottom and shifts slightly to −15 m s⁻¹ at the top. The data were filtered for stationary clutter so the interference from the tower is removed but the blade interference remains and is visible in Fig. 8a. After the application of the interpolation algorithm, the shape of the weather signal is restored and the radial velocity estimates appear to follow a much more natural path. Some loss of resolution is visible in the time-lapse reflectivity images after the interpolation, but the quantitative and qualitative improvements are significant.

Shown in Fig. 9 are the time-lapse images of the squall-line case reflectivity again with the application of the three-dimensional spectral interpolation algorithm. The homogeneity of the radial velocity field in this case creates a qualitatively trivial exercise of the interpolation algorithm and for this reason the image is not shown. The first reflectivity scan, at 1836:26 UTC, shows the leading edge of a strong convective squall line as it arrives over the WTC region. Visually, the spectral interpolation maintains the leading boundary through the interpolated gates. The weather reflectivity values for 1846:16 and 1856:07 UTC are as high or much higher than the bias created by the turbine blades. Still, the algorithm provides a good representation of the true weather in these cases, albeit slightly smoothed.

The results of the nowcasting–interpolation hybrid method applied to the reflectivity field for the isolated cell case are presented in Fig. 10. Again, time-lapse images of the corrupted, original, and corrected data are shown in the left, center, and right columns, respectively. The rapid motion of the storm facilitates the accurate use of the nowcasting portion of the algorithm by translating many replacement or clean gates into the WTC region. Slower-moving weather events do not accomplish this and the interpolation portion of the algorithm is assigned a greater weight through the least squares operation. The hybrid algorithm shows improvement over the two-dimensional moment interpolation, indicating that the addition of the nowcasting holds some promise for future use. However, further refinement of the algorithm is necessary before it is ready for operational deployment.

e. Additional mitigation efforts

While the mitigation algorithms developed in this work focus on masking the contaminated weather data, other techniques are being explored that require collaborative efforts between government entities and the wind power industry. Careful consideration of wind turbine locations could enhance the effectiveness of interpolation techniques discussed here. One suggested arrangement of turbines mimics a checkerboard pattern with respect to the radar PPI grid. It is supposed that the number of uncontaminated gates within the wind farm would increase dramatically and thus, intuitively, so would the effectiveness of any interpolation scheme. While multipath effects, surface area requirements, and considerations for overlapping radar coverage patterns complicate the implementation of such strategies, the viability of alternative wind farm spatial patterns is being explored nevertheless.