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Keywords:

  • remote sensing;
  • signal processing;
  • instruments and techniques

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Computer Simulations
  5. 3. Simulation Results
  6. 4. Doppler Beam Swinging/Spaced Antenna (DBS/SA) Experiment
  7. 5. Discussion and Concluding Remarks
  8. Acknowledgments
  9. References

[1] In this paper we estimate the random errors in the spaced antenna (SA) winds by two techniques and compare them with measurements made by the Doppler technique. With a one spatial dimension computer simulation, we apply typical parameters for the middle and upper atmosphere (MU) radar without noise. Briggs [1984] full correlation analysis (FCA) is commonly applied to the SA technique, while Doviak et al. [1996] and Holloway et al. [1997] used another simple analytic form based on scattering theory to derive generalized expressions. This simple analytic form should have equivalent results to the Briggs FCA for the horizontal wind estimation. With our simulation results, this form generally shows similar results to the FCA, and sometimes shows better performance than the FCA although it needs simpler calculation than the FCA. The estimation error of this simple analytic form is better than that of the Doppler for large wind, and better than that of the FCA for small antenna spacing. MU radar observations are compared with these two analyses for the SA technique, and the simple analytic form also shows similar performance to the FCA.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Computer Simulations
  5. 3. Simulation Results
  6. 4. Doppler Beam Swinging/Spaced Antenna (DBS/SA) Experiment
  7. 5. Discussion and Concluding Remarks
  8. Acknowledgments
  9. References

[2] The quality of the horizontal wind velocity estimates made with the spaced antenna (SA) technique (hereafter called the “SA wind”) has been investigated through many kinds of experiments. The SA wind velocities have been compared with velocities measured by in situ and Doppler radar techniques. For example, comparisons with rocketsonde and radiosonde data were performed by Vincent et al. [1977, 1987]. Comparisons with the Doppler technique [Vincent et al., 1987; Van Baelen et al., 1990] and the interferometer technique [Sheppard et al., 1993; Brown et al., 1995] were also carried out. Hines et al. [1993] compared the SA wind collected during the Arecibo Initiative in Dynamics of the Atmosphere (AIDA'89) campaign with those obtained from an incoherent scatter radar, a meteor-wind radar, and a Fabry-Perot interferometer. Averaged wind profiles were compared by the authors and possible sources of systematic errors in the SA technique were discussed. Theoretical studies performed by Briggs [1980] showed that the Doppler and SA techniques use the same information on the scattering irregularities that produce the radar echoes. May [1990] compared the techniques from theoretical and experimental points of view and showed that give similar accuracies. The SA technique determines velocities from diffraction patterns on the ground by calculating the cross correlation and autocorrelation between signals received by spatial domain antennas; the velocities are twice the actual horizontal wind velocity. This velocity of diffraction patterns is calculated by estimating a temporal lag at the maximum cross correlation coefficient, and generally biases because spatial and temporal variations of the diffraction pattern are not considered, which is called as “apparent” velocity. The full correlation analysis (FCA) was proposed to estimate the true horizontal wind velocities with the SA technique [e.g., Briggs, 1984]. Accuracies of the FCA were investigated by many authors, and sometimes the FCA is found underestimates for small antenna spacing. Meek [1990] studied this defect, knowing as “triangle size effect”, and showed that noise is the sole cause of the triangle size effect. Computer simulations without noise for the FCA were also performed to investigate the random errors in wind estimation with the Doppler and the SA techniques [Tahara et al., 1997]. It was shown that, in some particular conditions, the performance of the FCA results can be better than that obtained with the Doppler technique when the horizontal wind velocity u ≥ 70 m s−1. However, the FCA results are worse for small antenna spacing although this simulation model did not include noise. Holdsworth [1995] also investigated the triangle size effect by using model-generated and experimentally obtained data, and reported that there are four possible sources that cause the triangle size effect; receiver noise, receiver characteristics differences, coarse digitization, and receiver saturation. The source of the triangle size effect was discussed in detail by Holdsworth [1999] and showed that the triangle size effect is reduced by minimization of these four sources. Doviak et al. [1996] showed generalized expressions for reduction to a simple analytic form related to the cross correlation/spectrum of signals in the SA technique to the turbulent diffraction flow based on scattering theory. Holloway et al. [1995, 1997] applied the simple analytic form for development of time domain and frequency domain algorithms. This form is an another approach of the FCA for the horizontal wind estimation, which should provide equivalent results given by the FCA. It is expected that, however, the FCA will be better performance than this simple analytic form because the FCA involves much more correlation functions in estimation. In this paper, we apply this another form in computer simulations of one spatial dimension and compare with the FCA. Simple hypotheses are used for these simulations: 1) the correlation function of the refractive index fluctuations within the scattering layer is taken to be Gaussian, 2) noise effects on the estimations are not taken into account. These hypotheses were also employed by Tahara et al. [1997] for the FCA. First we compare computer simulation results using this simple analytic form with the FCA results [Tahara et al., 1997], and then we show an experimental observation conducted with the middle and upper atmosphere (MU) radar. This paper is organized as follows. In Section 2, the FCA, this another form with the SA technique, and the method of the computer simulation used in this paper are presented. In Section 3, computer simulations of one spatial dimension are shown. Section 4 presents an experimental observation with the MU radar.

2. Computer Simulations

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Computer Simulations
  5. 3. Simulation Results
  6. 4. Doppler Beam Swinging/Spaced Antenna (DBS/SA) Experiment
  7. 5. Discussion and Concluding Remarks
  8. Acknowledgments
  9. References

2.1. Full Correlation Analysis

[3] The full correlation analysis (FCA) was proposed to estimate the “true” horizontal wind velocities in the SA technique [e.g., Briggs, 1984]. In this technique it is generally assumed that contours of equal correlation form a family of ellipsoids. In this paper, we consider cases of one spatial dimension. We further assume that the correlation function has a Gaussian shape of

  • equation image

where ξ is the spatial lag along the baseline between two antennas and τ is the temporal lag. V is the diffraction pattern velocity along ξ on the ground, which corresponds to twice the actual horizontal wind velocity u because of the point source effect [Briggs, 1984]. Temporal lag τ and spatial lag ξ in this equation show parameters of correlation distance and correlation time, respectively. The correlation time τ0.5 is defined to be the temporal lag at which the autocorrelation function is reduced to half; ρ(0, τ0.5) = 0.5. While the correlation distance ξ0.5 is defined to be the spatial lag at which the autocorrelation function is reduced to half of its maximum value; ρ(ξ0.5,0) = 0.5. A and K in the equation are constants described as A = ln 2/ξ0.52 and K = ln 2/T0.52, where T0.5 is correlation time measured from the coordinate system moving with the velocity of the diffraction pattern V. Then T0.5 has the relationship to τ0.5 written as follows,

  • equation image

It is known that the correlation distance ξ0.5 depends on the radar size and scattering process. Briggs [1992] derives the spatial correlation function as

  • equation image

where λ is the radar wavelength, and s0 is a constant written as

  • equation image

where θT and θR are the 1/e half-widths of the transmitting and receiving antenna beams, respectively, and θs is the aspect sensitivity of scatterers. θT and θR are constants defined by the sizes of the respective antennas. Knowing these, we can calculate the correlation distance ξ0.5. The shape of the correlation function ρ(ξ, τ) is determined by u, ξ0, ξ0.5, and T0.5.

[4] Next we develop the case for two spatial dimension. The correlation function is assumed to have Gaussian shape

  • equation image

where ξ and η are the spatial lags along two orthogonal directions, τ is the temporal lag and A, B, C, F, G, and H are constants. The relationships among the constants in (5) are

  • equation image
  • equation image

where Vx and Vy are velocities of the diffraction patterns on the ground along ξ and η, respectively. If we assume isotropic scatter, the third term on the right hand side of (4) can be ignored, and we can consider the correlation distance, ξ0.5 and η0.5 to have equal value when the transmitting and receiving polar diagrams have circularly symmetric. In the observations complex cross correlation and autocorrelation functions are calculated from the complex time series of data obtained at each receiving antenna. The constants in (1) and (5) are estimated by using the least squares fitting method for the FCA around correlation function maximum. In this paper, we apply this fitting to the correlation function greater than 0.6 of its maximum.

2.2. Alternative Analytic Form

[5] Doviak et al. [1996] showed a simple analytic form to derive generalized expressions based on scattering theory. Holloway et al. [1997] applies this analytic form to the spaced antenna for horizontally/vertically anisotropic scattering. For one spatial dimension, we obtain

  • equation image

by ρ(ξ, τi) = ρ(0, τi) from (1). For two spatial dimension, we can refer to (5). Call the cross correlation and autocorrelation function ρ(ξ, η, τ) and ρ(0, 0, τ), respectively, set τ = 0, then write the cross correlation functions for three antenna pairs as

  • equation image

where A, B, and H are constants to be derived from these equations. We take the crossover points τi of the cross correlation and autocorrelation functions by fitting a line across the lags either side of the intersections for the cross correlation and autocorrelation. Then obtain the crossover points τi of the cross correlation and autocorrelation, for example,

  • equation image
  • equation image

where ρ(0, 0, τi12) shows (ρ1(0) + ρ2(0))/2, we can obtain:

  • equation image
  • equation image

Therefore we can estimate the wind velocity Vx and Vy along two orthogonal directions. In the practical analysis, we can employ several pairs of subarrays, and we use two pairs of larger correlation function maxima. This formulation is an another approach and an alternative analytic form to the FCA; this form should derive equivalent results to that of the FCA. We compare these results by means of computer simulations. In this paper, for convenience, we call this analysis a “partial correlation analysis (PCA)”.

2.3. Simulation Model

[6] This simulation model uses the model presented by Tahara et al. [1997]. We examined 1000 sample models and estimated their standard deviations, and found that 100 samples is efficient for this simulation. Therefore we generate 100 sample model time series of data that obey given parameters and contain expected statistical fluctuation but no noise. We show a technique to generate time series data described by May [1988] for cases of one spatial dimension.

[7] First we make two complex time series, S1 and S2 generated from random numbers that having Gaussian distribution. Next we get a transformed time series, S1′ and S2′, which have temporal correlation with given parameter by convolving with Gaussian function. Then we can create two time series Em and En with a cross correlation, written as [May, 1988]:

  • equation image
  • equation image

where a maximum value of the cross correlation ρm occurs at the lag τm. In this simulation we generate 100 sample model time series with the same given parameters. We apply the FCA and the PCA to these model data, we calculate the estimation error of horizontal wind velocities for each technique as written as the root mean square (RMS) error,

  • equation image

where δu means the average offset of the estimated velocities from the given velocity, and σu is the standard deviation around δu.

3. Simulation Results

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Computer Simulations
  5. 3. Simulation Results
  6. 4. Doppler Beam Swinging/Spaced Antenna (DBS/SA) Experiment
  7. 5. Discussion and Concluding Remarks
  8. Acknowledgments
  9. References

[8] Simulation parameters are selected to correspond to typical stratosphere observations with the MU radar. In (4), θT = 2.16° and θR = 6.3°, then ξ0.5 = 48 m, assuming isotropic scatter. In (2), T0.5 ≈ 2 s for typical observations with the MU radar. Correlation times T0.5 of 1.0, 2.0, and 4.0 s provide turbulent velocities νv of 0.6, 0.3, and 0.15 m s−1, respectively, where νv is expressed as follows [Briggs, 1980],

  • equation image

where λ is the radar wavelength.

[9] Errors of horizontal wind estimation with the Doppler technique are derived from the results with computer simulation. Yamamoto et al. [1988] studied random errors in radial wind estimates without noise, proposed an equation for the estimation error εv of the radial velocity with the least square fitting as

  • equation image

where c is the speed of light, f0 is the radar frequency, σv is the standard deviation of the Doppler spectrum, and T is the observation period. The constant 0.63 is derived from their computer simulation results. With the Doppler technique, the horizontal wind is usually estimated from two oblique beams. When a uniform wind field is assumed over the radar, the horizontal wind velocity u parallel to the azimuth direction of the oblique beams is estimated as

  • equation image

where v1 and v2 are radial velocities measured in the oblique beams, and θz is a zenith angle of the oblique beams. Then estimation error of u is written by

  • equation image

Figure 1 shows variation of the estimation errors εu for the horizontal wind velocity. Because the record length of individual time series is fixed in our system, the observation period T changes with the number of incoherent integrations n. Coherent integration was performed over 38 samples, giving an effective sampling interval of 0.076 s. Time series of 256 complex data were then stored every 19.45 s, which corresponds to incoherent integration n = 1. In the radar observations, incoherent integrations of the correlation functions are performed. Figure 1 shows results for n = 3, 6, 9, 18, and 36, which correspond to the periods of 58.4, 116.7, 175.1, 350.1, and 700.2 s, respectively. Solid lines show εu estimated by the FCA, dashed lines show εu estimated by the PCA, and dotted lines show εu estimated by the Doppler technique (20). Each line is generally decreasing as observation period T is increasing. This effect is caused by the reduction in statistical fluctuation, which is proportional to equation image, therefore each line varies as equation image. This effect can be seen with the Doppler technique plotted by the dotted line [Yamamoto et al., 1988]. For larger T0.5, εu is smaller because the maximum of the cross correlation function is larger for larger T0.5. For T0.5 = 1.0 s, εu from the PCA is similar to that from the FCA for T ≤ 116.7 s, but is worse for T ≤ 175.1 s. For T0.5 = 2.0 s, εu from the PCA is slightly better than that from the FCA for all T. For T0.5 = 2.0 s, εu from the PCA is better than that from the FCA for all T, and the difference between the εu estimates is larger than that obtained for smaller value of T0.5.

image

Figure 1. Estimation error of horizontal wind velocities versus the observation period T. Circle, triangle, and cross marks show results for T0.5 = 1.0, 2.0, and 4.0 s, respectively. Solid and dashed lines show the results with the FCA and the PCA, respectively. Dotted lines show the estimation errors of the Doppler winds for the corresponding values of T0.5. Parameters used in this simulation are u = 30.0 m s−1, ξ0 = 50.0 m, and ξ0.5 = 50.0 m.

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[10] Figure 2 shows variation of εu due to the horizontal wind velocity u. For each value of T0.5, εu generally decreases with increasing u. Figure 3 shows examples of cross correlation functions with small (top panel) and large (bottom panel) winds. For a small wind, the maximum cross correlation is smaller than that for a larger wind, and the lag of the maximum cross correlation is larger than that for a larger wind. These effects cause εu to decrease as the wind increases. εu estimated by the Doppler technique (vertical dashed line) is larger for the large wind because its spectrum is wide; this is called the beam broadening effect [e.g., Hocking, 1983]. For T0.5 = 1.0 s, εu from the PCA is slightly better than that from the FCA but worse than that from the Doppler. For T0.5 = 2.0 s, εu from the PCA is smaller than that from the FCA. εu from the PCA is also better than that from the Doppler for winds over 70 m s−1 while εu from the FCA is better for winds over 75 m s−1. For T0.5 = 4.0 s, εu from the PCA is clearly smaller than that from the FCA, while εu from the PCA is better than that from the Doppler for winds over 42 m s−1; εu from the FCA is better for winds over 51 m s−1. These results support that the PCA estimation is better than the FCA estimation in most cases, but both are worse than the Doppler estimation for winds below 70 m s−1. Figure 4 shows the variation of εu with antenna spacing ξ0. In the top panel, for T0.5 = 1.0 s, εu of apparent velocity is always worse than εu from the PCA and the FCA because spatial and temporal variations of the diffraction pattern are not considered. εu from the FCA increases as ξ0 decreases at ξ0 < 20 m and again increases ξ0 increase at ξ0 > 100 m, while εu is stable in the region of 20 ≤ ξ0 ≤ 100 m. εu from the PCA is stable in the region of 20 ≤ ξ0 ≤ 100 m and increases as ξ0 increases at ξ0 > 100 m, which is quite similar to εu from the FCA, but still stable at ξ0 < 20 m. In the middle panel, for T0.5 = 2.0 s, εu from the FCA shows a stable region at 30 ≤ ξ0 ≤ 100 m, increases as ξ0 increases over 100 m and increases again as ξ0 decreases under ξ0 = 30 m. Note that εu is worse than that of the apparent velocity at ξ0 = 5 m. εu from the PCA is similar to that from the FCA at ξ0 > 30 m while it still remains stable at ξ0 < 30 m. In the bottom panel, for T0.5 = 2.0 s, εu from the FCA shows a stable region at 50 ≤ ξ0 ≤ 200 m, εu is quite worse than that of the apparent velocity at ξ0 < 20 m, while εu from the PCA shows a stable region for 5 ≤ ξ0 ≤ 70 m with values much better than the FCA values. Figure 5 shows variations of averaged velocity (top panel) and standard deviation (bottom panel) versus antenna spacing ξ0 for T0.5 = 2.0 s. The averaged velocity from the FCA is stable at 30 ≤ ξ0 ≤ 150 m but underestimated for larger antenna spacing. This defect for large antenna spacing is thought to be due to the small value of the maximum cross correlation for large ξ0. On the other hand, for small antenna spacing, the averaged velocity from the FCA is underestimated for small antenna spacing, but the averaged velocity from the PCA is stable. This underestimate for small antenna spacing seems to be caused by the triangle size effect [Meek, 1990]; however, this simulation model had not included noise. Holdsworth [1999] investigated the triangle size effect in detail and showed that the FCA velocity is constant for small antenna spacing without noise. We consider this may be due to our simplified simulation model, nevertheless, the PCA is almost constant for small antenna spacing. In the bottom panel, standard deviation from the FCA is large at ξ0 < 10 m and ξ0 > 150 m, while that from the PCA is stable at ξ0 < 120 m. These results indicate that the PCA is more stable in small antenna spacing in our simulation.

image

Figure 2. Estimation error of horizontal wind velocities versus wind velocity u. Circle, triangle, and cross marks show results for T0.5 = 1.0, 2.0, and 4.0 s, respectively. Solid and dashed lines show the results with the FCA and the PCA, respectively. Dotted lines show the estimation errors of the Doppler winds for the corresponding values of T0.5. Parameters used in this simulation are T = 175.1 s, ξ0 = 50.0 m, and ξ0.5 = 50.0 m.

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image

Figure 3. Examples of cross correlation functions for two different horizontal wind velocities for T0.5 = 4.0 s. Solid and dashed lines show the generated and fitted functions, respectively. Parameters are T = 175.1 s, ξ0 = 50.0 m, and ξ0.5 = 50.0 m.

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image

Figure 3. (continued)

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image

Figure 4. Estimation error of horizontal wind velocities versus antenna spacing ξ0 for T0.5 = 1.0 s (top panel), T0.5 = 2.0 s (middle panel), and T0.5 = 4.0 s (bottom panel). Solid and dashed lines show the results with the FCA and the PCA, respectively. Dotted lines show apparent velocities. Parameters used in this simulation are u = 30.0 m s−1, T = 175.1 s, and ξ0.5 = 50.0 m.

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image

Figure 4. (continued)

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image

Figure 4. (continued)

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image

Figure 5. Averaged velocity and standard deviation versus antenna spacing ξ0 for T0.5 = 2.0 s. Solid and dashed lines show the results with the FCA and the PCA, respectively. Dotted lines show apparent velocity. Other parameters are the same as in Figure 4.

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image

Figure 5. (continued)

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[11] Figure 6 shows variations of εu versus correlation distance ξ0.5. In (3), ξ0.5 depends on antenna size parameters, which are constants for a given array configuration and an aspect angle θs. In isotropic scatter, θs is ignored, ξ0.5 is 48 m, while for anisotropic scattering with the strong aspect sensitivity such as that observed in the lower stratosphere, θs = 2° [Hocking et al., 1986], which corresponds to ξ0.5 = 70 m. εu decreases as ξ0.5 decreases in Figure 6, which indicates that large θT and θR give better εu, which is consistent to the result by Briggs [1980], but this causes that signal to noise ratio to be poor, which must be taken into account for real observations. Within the region of actual observation parameters, 48 ≤ ξ0.5 ≤ 70 m, εu from the PCA is generally similar to that from the FCA.

image

Figure 6. Estimation error of horizontal wind velocities versus correlation distance ξ0.5. Solid and dashed lines show the results with the FCA and the PCA, respectively. Dotted lines show the estimation error of the Doppler winds for the corresponding values of T0.5. Parameters used in this simulation are T = 175.1 s, ξ0 = 50.0 m, and u = 30.0 m s−1.

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4. Doppler Beam Swinging/Spaced Antenna (DBS/SA) Experiment

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Computer Simulations
  5. 3. Simulation Results
  6. 4. Doppler Beam Swinging/Spaced Antenna (DBS/SA) Experiment
  7. 5. Discussion and Concluding Remarks
  8. Acknowledgments
  9. References

[12] This observation was conducted from 1830 local time (LT) on January 16 to 0300 LT on January 17, 1996 with the MU radar located at Shigaraki, Japan (34.51°N, 136.6°E, 375 m Mean Sea Level). The receiving antenna configuration for this experiment is shown in Figure 7, which has the triangle array configuration with a antenna spacing ξ0 = 52 m. The whole array of 475 Yagis was employed as transmitting antenna. With the active phased array system, the radar beam was steered every inter pulse period (IPP) through the vertical and four oblique directions (north, east, south, and west) at 10° off zenith. On the other hand, the receiving antenna array was divided into 4 subarrays forming 4 channels. Channel 1 was connected to the whole antenna array for the Doppler analysis in the 5 beam directions. Channels 2, 3, and 4 corresponded to three equally sized subarrays composed of 57 Yagi antennas for applying the SA technique on the signals received from the vertical beam. Signals received from the four channels were independently and simultaneously sampled at 64 heights every 150 m from the altitude range from 5.1 km to 14.55 km. Coherent integration was performed over 38 samples, giving an effective sampling interval of 0.076 s. Time series of 256 complex data were then stored every 19.45 s for Fast Fourier Transform. Incoherent integrations over 36 records were performed. Thus, we obtained the spectra and cross correlation and autocorrelation functions approximately every 12 minutes. the FCA and the PCA wind estimates were obtained by procedure already explained. On the other hand, the horizontal wind simultaneously estimated every 12 minutes with the Doppler technique. This observation is presented in detail by Kawano et al. [2001]. In this paper we calculate the horizontal wind only via FCA, PCA, and the Doppler techniques. Our simulation results shown in Figure 2 indicate that the estimation errors for the Doppler are smaller than that for the FCA/PCA, the estimation errors are then derived from differences between the FCA/PCA winds and Doppler winds. Figure 8 shows the difference εu between the FCA and Doppler winds and between the PCA and Doppler winds versus horizontal wind. The data are averaged into 10 m s−1 bins for this plot. εu from the FCA and the PCA in the observation show similar results and remain at constant level even in large wind. εu in the simulation show smaller for all winds than that in the observation. We consider some reasons; this is mainly caused by noise because our simulation does not take noise into account. In addition, εu in the observation are not smaller for large winds, which is not consistent to εu in the simulation. We take T0.5 = 2.0 and ξ0.5 = 52 m in this simulations shown in Figure 8 derived from corresponding observation results, but T0.5 and ξ0.5 are not constant during the observation. T0.5 is smaller for large winds in this observation, for examples, T0.5 ≃ 1.9 at u = 20 m s−1, T0.5 ≃ 0.6 at u = 50 m s−1, so that smaller T0.5 provides larger estimation errors. Therefore we consider that the meteorological conditions, such as a passage of a trough and gravity waves, could affect to the SA results more than stable conditions. Moreover, note that εu here is just the difference between the FCA and Doppler winds or between the PCA and Doppler winds, not an estimation error from a true velocity as shown in Figure 2. εu of this observation is derived from differences between the Doppler and the SA winds. The SA wind has estimation errors εuSA and the Doppler wind also has estimation error εuDPL. εu from the observation should be shown as equation image, which means that εu of this observation is larger than real estimation error of the SA. εuDPL is larger for large wind, which contributes to εu in larger wind. We consider that these cause the differences between observation and simulation results; however, the PCA shows similar εu to the FCA in this observation.

image

Figure 7. Receiver antenna configuration used for the simultaneous DBS/SA observation with the MU radar. The antenna spacing ξ0 = 52 m.

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image

Figure 8. Variations of the estimation error of the FCA (top panel) and the PCA (bottom) versus wind velocity. Cross marks show observation results with the MU radar; circle marks show simulation results. Parameters used in this simulation are ξ0 = 52 m, ξ0.5 = 52 m, T0.5 = 2.0 s, and T = 700.2 s. Dashed curves show the estimation error of the Doppler winds without noise. Error bars denote standard deviations of the results from the observations.

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image

Figure 8. (continued)

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5. Discussion and Concluding Remarks

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Computer Simulations
  5. 3. Simulation Results
  6. 4. Doppler Beam Swinging/Spaced Antenna (DBS/SA) Experiment
  7. 5. Discussion and Concluding Remarks
  8. Acknowledgments
  9. References

[13] In this paper we studied estimation errors of the horizontal wind with the spaced antenna technique. Full correlation analysis (FCA) is generally employed for the SA, while Holloway et al. [1997] applied the simple analytic form based on the scattering theory, which for convenience, we called “partial correlation analysis (PCA)”. This simple analytic form is the alternative approach to the Briggs' [1984] FCA; therefore this should have equivalent results to the FCA. We expected that, however, the FCA would be better because the FCA involves much more correlation functions. We compared with results from these two techniques for the SA and the Doppler technique. Typical observation parameters for the MU radar were applied for this simulation. The PCA generally shows similar performance to the FCA, and performed better for large winds, u > 70 m s−1 for T0.5 = 2.0 s, than the Doppler technique. For the variation of estimation error εu due to the antenna spacing ξ0, εu for the FCA increases as ξ0 decreases, at ξ0 < 40 m for T0.5 = 2.0 s; on the other hand, εu for the PCA is stable and performs better than the FCA for small ξ. Holdsworth [1999] showed that the FCA is constant for all antenna spacing; we consider our result may be due to simplified simulation model. For the small antenna spacing, the lag of cross correlation maximum is close to zero. If this position of the cross correlation maximum causes large estimation errors, it must provide similar results to the larger wind although the FCA and PCA show better performance for the large wind in Figure 2. Then we conduct the simulation for far larger wind, and find that u > 150 m s−1, which cannot be realized in the real observation in the troposphere and stratosphere; εu of the FCA increases as u increases, which is consistent to the results in the small antenna spacing. εu of the PCA also increase as u increases, but it is still better than that of the FCA as shown in Figure 9. This result indicates that the PCA is more stable when the cross correlation function is close to the autocorrelation function in our model. Finally we showed an observation result with the MU radar. The estimation differences of the FCA and the PCA were stable for all wind speeds. These results show that the PCA has similar performances to the FCA although the PCA needs simpler calculation than the FCA. We considered this simulation without noise; however, it is expected that noise would be one of the major sources of estimation errors for the SA technique as shown by Meek [1990], and this is a subject for our future works.

image

Figure 9. Estimation error of horizontal wind velocities versus wind velocity u for T0.5 = 2.0 s. Solid and dashed lines show the results with the FCA and the PCA, respectively. Dotted lines show the estimation errors of the Doppler winds for T0.5 = 2.0 s. Parameters used in this simulation are T = 175.1 s, ξ0 = 50.0 m, and ξ0.5 = 50.0 m.

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References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Computer Simulations
  5. 3. Simulation Results
  6. 4. Doppler Beam Swinging/Spaced Antenna (DBS/SA) Experiment
  7. 5. Discussion and Concluding Remarks
  8. Acknowledgments
  9. References
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  • Briggs, B. H., The analysis of spaced sensor record by correlation techniques, in Handbook for MAP, vol. 13, pp. 166186, Sci. Comm. on Sol.-Terr. Phys. Secr., Univ. of Ill., Urbana, 1984.
  • Briggs, B. H., Radar measurements of aspect sensitivity of atmospheric scatters using spaced-antenna correlation techniques, J. Atmos. Terr. Phys., 54, 153165, 1992.
  • Brown, W. O. J., G. J. Fraser, S. Fukao, and M. Yamamoto, Spaced antenna and interferometric velocity measurements with MF and VHF radars, Radio Sci., 30, 12811292, 1995.
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