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Keywords:

  • interferometry

Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. The STI Instruments
  5. Generation of Path Delay and Array Loss Statistics
  6. Examples of RMS Path Delay Statistics
  7. Analysis
  8. Conclusion
  9. Acknowledgments
  10. References

[1] Site test interferometers (STIs) have been deployed at two locations within the NASA Deep Space Network tracking complex in Goldstone, California. An STI measures the difference of atmospheric delay fluctuations over a distance comparable to the separations of microwave antennas that could be combined as phased arrays for communication and navigation. The purpose of the Goldstone STIs is to assess the suitability of Goldstone as an uplink array site and to statistically characterize atmosphere-induced phase delay fluctuations for application to future arrays. Each instrument consists of two ~1 m diameter antennas and associated electronics separated by ~200 m. The antennas continuously observe signals emitted by geostationary satellites and produce measurements of the phase difference between the received signals. The two locations at Goldstone are separated by 12.5 km and differ in elevation by 119 m. We find that their delay fluctuations are statistically similar but do not appear as shifted versions of each other, suggesting that the length scale for evolution of the turbulence pattern is shorter than the separation between instruments. We also find that the fluctuations are slightly weaker at the higher altitude site.

Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. The STI Instruments
  5. Generation of Path Delay and Array Loss Statistics
  6. Examples of RMS Path Delay Statistics
  7. Analysis
  8. Conclusion
  9. Acknowledgments
  10. References

[2] The role of the atmosphere in degrading interferometric measurements for radio astronomy and multiple-antenna arrays has been discussed by many investigators [D'Addario, 2005, 2008; Treuhaft and Lanyi, 1987; Zheng et al., 1990; Holdaway and Owen, 1995; Carilli and Holdaway, 1999; Butler et al., 2001]. In order to assess these effects at given sites, specialized instruments known as atmospheric phase interferometers or site test interferometers (STIs) have been utilized. An STI measures the difference in signal delay from a celestial source (typically a geostationary satellite) to two points on the Earth. Variations in that delay difference are primarily due to turbulence in the troposphere causing a difference in the mean refractive indices along the two paths. Such instruments have been used by radio astronomers to assess atmospheric conditions for scheduling astronomical observations [Kimberk et al., 2012; National Radio Astronomy Observatory (NRAO), 2013] and to evaluate sites for new instruments [Radford and Holdaway, 1998; Blundell et al., 2011].

[3] The Goldstone Deep Space Communications Complex located in the Mojave Desert in California is a potential site for a future array of smaller diameter antennas that could replace the aging monolithic structures of the current Deep Space Network (DSN) [Davarian, 2007]. For example, several existing 34 m diameter antennas could be arrayed to replace an existing 70 m antenna. This is already being done in the receiving direction, where the delay variations can usually be removed by adaptive signal processing, but no such adaptation is feasible in the transmitting direction, where performance is expected to be limited by the level of turbulence.

[4] Two STIs of different design have been deployed at the Goldstone complex, and their results are discussed in this paper. A duplicate of one of these has been deployed at the Canberra, Australia, DSN complex, and others have been recently deployed at the Madrid, Spain, DSN complex and at NASA's Kennedy Space Center (Florida) in 2013. Two more are in operation at sites of the future Square Kilometer Array radio telescope in Western Australia and South Africa [Millenaar, 2011]. These instruments consist of at least two small-diameter outdoor antennas and associated electronics with element separations of ~200 m. One of the Goldstone STIs now includes three antennas in a triangular configuration to allow two-dimensional characterization of the atmosphere. Only one of its three baselines will be considered here. That baseline has the same east-west orientation as that of the other Goldstone STI. The Canberra, Madrid and Kennedy Space Center STIs also have three antennas each. Optical fiber (or coaxial) connections carry local oscillator (LO) and intermediate frequency (IF) signals between each element and an indoor electronics rack. The antennas continuously observe signals emitted by geostationary satellites, and the phase difference of the received signals is measured. During postprocessing, long period trends due to satellite motion and instrumental drift are removed. The resulting phase delay residuals contain fluctuations dominated by the troposphere on timescales ranging from <1 s to several hundred seconds.

[5] The statistics of these delay fluctuations vary among sites due to climate and altitude and at any one site diurnally, seasonally, and with passage of weather systems. An STI should be operated for several years to obtain sufficient statistics for reliable characterization of a particular site. The long-term statistics can be used to determine the suitability of a site for hosting an array, or they can be used in communication link budgets of current or proposed missions using an array at the site. Short-term (intraday) statistics can be used to assist in scheduling communication links so that the best conditions are used for links with small margins, and conversely.

[6] Although an STI and a nearby communication array or radio telescope are expected to see the same short- and long-term statistical delay fluctuations, the instantaneous delay measured by the STI is generally not useful for correcting delay errors in the array because their targets are in different directions and their signals pass through different parts of the same turbulent distribution. Water vapor radiometers (WVRs) have sometimes been used for such real-time corrections, but their accuracy is not adequate for removing the array phasing loss at high microwave frequencies. A previous study compared an STI and a two-WVR system at Goldstone [Morabito et al., 2012a]. This paper is a significantly expanded study that was initially reported in Morabito et al. [2012b].

The STI Instruments

  1. Top of page
  2. Abstract
  3. Introduction
  4. The STI Instruments
  5. Generation of Path Delay and Array Loss Statistics
  6. Examples of RMS Path Delay Statistics
  7. Analysis
  8. Conclusion
  9. Acknowledgments
  10. References

[7] Radio astronomers have been studying the delay stability of the atmosphere using interferometric techniques for many years. One of the earliest efforts [Armstrong and Sramek, 1982] used the 27 antenna Very Large Array (VLA) radio telescope to observe the phase fluctuations from point-like natural sources as they passed near zenith, obtaining information on many spatial scales simultaneously. A microwave interferometer dedicated to atmospheric delay monitoring was first described in 1989 [Ishiguro et al., 1990]. Like nearly all of its successors, it used signals from a geostationary communication satellite in the 11.7–12.7 GHz band. A detailed description of such a design is given by Radford et al. [1996]; that instrument has been in nearly continuous use at the Atacama Large Millimeter/submillimeter Array telescope site in Chile since 1995. Other instruments using the same concept were later built for the Large Millimeter Telescope in Mexico [Hiriart and Valdez, 2002], the Australia Telescope Compact Array [Middelberg et al., 2006], and the VLA [NRAO, 2013]. All of these use narrow-bandwidth signal processing and rely on the satellite to transmit an unmodulated tone. Most geostationary communication satellites transmit a suitable CW beacon.

[8] In an attempt to obtain improved signal-to-noise ratio and to use smaller and less expensive dish antennas, a wide-bandwidth STI concept was developed by Lay [1998]. This used digitally modulated direct broadcast television signals, which are transmitted at much higher power levels than the CW beacons. Each satellite typically carries signals on multiple transponders of bandwidth 20 to 40 MHz spread over a 500 MHz band. For our purposes, the signals can be regarded as broadband noise. The STI is then slightly complicated by the need to equalize the signal delays from the satellite to the cross correlator, but overall the signal processing electronics is simpler than for the narrow-bandwidth architecture. A more advanced wide-bandwidth design intended to achieve higher-precision measurements was later developed by Kimberk et al. [2012] for the Submillimeter Array (SMA) in Hawaii.

[9] Table 1 gives the main parameters of the two STI instruments that we have deployed at the Goldstone complex. Geometric location information of the sites was obtained from Kwok [2010].

Table 1. Goldstone STI Instruments
ParameterVenusApolloNormalize
Longitude (°E)243.21243.13
Latitude (°N)35.0735.16
SatelliteANIK-F2Ciel 2
Signal frequency (GHz)20.212.45
Raw observablePhasePhaseDelay
Elevation angle (deg)48.547.090.0
Baseline length (m)256190190
Height (WGS84) (m)1070.4951.5951.5

[10] The first Goldstone STI was installed at the Venus antenna site in May 2007 [Nessel et al., 2008; Acosta et al., 2008], near the 34 m diameter DSN Research and Development antenna. It uses a narrow-bandwidth design and relies on an unmodulated tone at 20.2 GHz in the spectrum of the signal from a geostationary satellite. A detailed description of its design is given in Acosta et al. [2007]. The phase of each antenna's received signal is measured with respect to a common clock over each 1.0 s interval and then the two phases are subtracted. This phase difference is the raw observable. The results of the first year of phase stability measurements are presented in Nessel et al. [2008]. The ongoing data analysis for this instrument is a collaborative effort between propagation experimenters at the Glenn Research Center and Jet Propulsion Laboratory (JPL) NASA centers [Nessel et al., 2007, 2008; Acosta et al., 2008; Morabito et al., 2008; Acosta et al., 2007].

[11] A second STI was deployed at the Apollo antenna site in September 2010 and began routine operation in January 2011. The Apollo site is home to the operational beam waveguide subnet of the DSN consisting of three 34 m diameter antennas. This subnet is a candidate for uplink arraying and has been used for 7.15 GHz uplink array studies [Morabito and D'Addario, 2007; Vilnrotter et al., 2006, 2009]. The Apollo STI is located about 12.5 km northwest of the Venus STI (azimuth 324°).

[12] The Apollo STI is wide-bandwidth design and relies on direct broadcast TV signals near 12.45 GHz. To a large extent, it is a copy of the SMA design by the Harvard-Smithsonian Center for Astrophysics [Kimberk et al., 2012]. We provide an overview of the JPL version here. It uses two 0.84 m diameter reflector antennas and associated electronics to receive the broadband signals emitted by the Ciel 2 satellite (orbital longitude of 129°W) at an elevation angle of 47° and center frequency of 12.45 GHz. The received signals are mixed with LO signals carried on optical fiber from a common source located within a temperature-controlled building. The resulting IF signals are brought back to the building on separate optical fibers where they are cross-correlated using analog mixers to produce in-phase (I) and quadrature-phase (Q) components of the cross power. The outputs of the IQ mixers are digitized and averaged over 0.1 s intervals; these are the raw observables of the instrument. They are recorded in real time to a local disk drive and periodically transferred over the Internet to other computers for further processing and analysis. The four-quadrant phase of the complex cross-correlation I + jQ is calculated in off-line processing.

[13] The antenna separation (baseline) for both STIs has a roughly east-west orientation.

[14] Measurements from other instruments at the site (or nearby) are also available, including a water vapor radiometer (WVR) and meteorology station.

[15] Because the troposphere is nondispersive, the present observations (20.2 GHz for the Venus STI and 12.5 GHz for the Apollo STI) can be scaled to higher or lower frequencies such as those of the deep space communications links (7.2 and 32–40 GHz). The fluctuation statistics can also be estimated at antenna separations different from the STI baseline by extrapolating in accordance with turbulence theory, as discussed in section 3.

[16] The present paper presents and compares the phase delay statistics extracted from these two independent Goldstone STIs. Generally the results agree, which helps to validate each instrument's performance. But we do not find that each instrument's phase pattern is a delayed version of the other's, suggesting that the turbulence pattern evolves over the 12.5 km distance between them. We find that the RMS delay fluctuations at Venus are smaller than those at Apollo by a small but statistically significant amount, and we attribute this to the 118.9 m altitude difference of the sites.

[17] The data from both instruments will help assess the suitability of the Goldstone site to support widely distributed antenna systems for future RF communications.

[18] The data can also be used to extract physical parameters of the atmosphere, such as the thickness of the turbulent layer and its variation over diurnal cycles, seasons, and the passage of weather systems.

Generation of Path Delay and Array Loss Statistics

  1. Top of page
  2. Abstract
  3. Introduction
  4. The STI Instruments
  5. Generation of Path Delay and Array Loss Statistics
  6. Examples of RMS Path Delay Statistics
  7. Analysis
  8. Conclusion
  9. Acknowledgments
  10. References

[19] For both instruments, the phase time series is unwrapped to remove cycle ambiguities. This results in the time series ϕ(t) with sampling intervals of 1.0 s and 0.1 s for the Venus and Apollo instruments, respectively. An example of ϕ(t) over 24 h is plotted in Figure 1. The diurnal sinusoidal signature is due to satellite motion within its assigned “box” of the geostationary orbit, even though it remains within the beam of each fixed antenna.

image

Figure 1. Example of signal phase from the Apollo STI for a 1 day period (14 August 2011). Plot also includes the segments of fitted model phase over 600 s intervals (not discernible on this plot scale).

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[20] During postprocessing, the effects of satellite motion and other slow changes are removed as follows [Acosta et al., 2008]. A second degree polynomial model is fit over each 600 s block of data. The fitted model is subtracted from the data, and the resulting residuals Δφ(t) are presumed to be dominated by the troposphere. This removes instrumental phase drifts induced by temperature changes and component aging, as well as the effects of satellite motion. An example of the phase residuals for the data of Figure 1 is shown in Figure 2, and Figure 3 displays an expanded view covering 1 h.

image

Figure 2. Example of filtered phase residuals derived from the difference of measured and fitted phases in Figure 1 for 14 August 2011 (long-term nontropospheric trends removed).

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image

Figure 3. Expanded view of 1 h period of phase residual data of Figure 2, showing detailed character of phase residual behavior.

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[21] The statistics of the residual phase Δφ(t) are generated over intervals of T = 600 s for this study. This time interval was selected early in the operation of the Venus STI [Acosta et al., 2008] and was retained for consistency in all the studies presented here. The 600 s interval size is considered short enough to remove satellite motion and instrumental drift but long enough to retain the atmospheric contributions of interest. Future studies may employ different time intervals and filtering schemes.

[22] The standard deviation of the residual phase within each block is denoted σΔφ(tk), tk = t0 + kT, k = 0,…,N, where t0 is a reference start time. This time series is one data output of the STI with baseline rsti, frequency fsti, and elevation angle θsti. Typically σΔφ is smaller during nighttime and winter and larger during daytime and summer.

[23] To facilitate comparison of measurements from different STIs, the statistics from each can be normalized to values that would be measured under standardized conditions (Table 1). The line-of-sight σΔφ phase scatter measurements from each STI are converted to normalized delay scatter inline image by making appropriate adjustments for frequency, elevation angle, antenna element spacing, and height as follows. Let

  • display math(1)

where f, θ, r, and h are the measurement frequency, elevation angle, baseline length, and height above ellipsoid, respectively, of the STI instrument; and parameters γ, β, and H are discussed in the following paragraphs. Then inline image is the estimated RMS delay difference (independent of f) at elevation angle 90°, baseline length 190 m, and height 951.5 m. We have thus chosen to standardize the baseline and height to those of the Apollo STI.

[24] The RMS delay is just the RMS phase divided by angular frequency because the troposphere is nondispersive throughout the microwave spectrum (1–40 GHz, at least). So phase delay is the same as group delay, and both are independent of frequency. Even for frequencies that lie near the 22 GHz water absorption line, there is never enough water vapor present in the atmosphere to cause any significant dispersion. The ionosphere is dispersive, but at our observing frequencies near 12 GHz and 21 GHz, the ionosphere's delay fluctuations are well below those of the troposphere. During the most severe geomagnetic storms, the ionosphere's excess path gradient can be ~400 mm/km and move at several kilometers per second [Pullen et al., 2009]. This can in principle produce phase delay difference fluctuations of up to several ps at 12 GHz on our baselines. Since such events are rare, they should not affect the statistical results reported here. They occur mainly during solar maximum, and the data reported here were taken near solar minimum. We have looked for and do not see such effects. Further discussion is given in section 5.1.

[25] Delay fluctuations decrease with elevation angle as air mass 1/sinθ decreases. The dependence is linear (γ = 1 in equation (1)) if the turbulence along the two lines of sight is dominated by a few large inhomogeneities so that the instantaneous delay along each path is proportional to air mass. If the turbulence is dominated by many small, random inhomogeneities, then the number of them along the line of sight is proportional to air mass, and the RMS delays are proportional to the square root of that number inline image. The general case is between these and has a complicated dependence on the geometry, including the thickness of the turbulent layer Hw and the average distance between the two signal paths, where the latter depends on the baseline length r as well as the azimuth and elevation of the signal paths. A detailed analysis is given by Treuhaft and Lanyi [1987]. In our cases, the signal path azimuth is roughly perpendicular to the baseline so that the path separation is roughly r. Hw is typically 1 to 2 km [Treuhaft and Lanyi, 1987], so usually r ≪ Hw, which leads to inline image, but sometimes Hw is lower and γ approaches unity. For the analyses of this paper, we used inline image.

[26] The adjustment for baseline length r depends on the 3-D spatial structure function of the refractive index. Using the Kolmogorov theory of turbulence and integrating vertically through the turbulent layer [Coulman, 1991; Treuhaft and Lanyi, 1987] gives the power law dependence in (1) with inline image when r ≪ Hw (thick screen) and inline image when r ≫ Hw (thin screen). For this study, we used inline image.

[27] The adjustment for height h is based on the assumption that the delay fluctuations are proportional to the total delay and that the latter decreases exponentially with height along with the density of the air. The parameter H (different from Hw discussed previously) is an empirical constant, and we show later that H = 2 km fits the small systematic difference that we observe between the Venus and Apollo instruments whose heights differ by 118.9 m. Butler et al. [2001] found that two 8 km apart STIs in the high desert of Chile with a height difference of 250 m have long-term median delay fluctuations that are 12% smaller at the higher site, and this too fits the dependence in (1) with H = 2 km. We note that this empirical value for H is close to the typical value of the turbulent layer thickness Hw.

Examples of RMS Path Delay Statistics

  1. Top of page
  2. Abstract
  3. Introduction
  4. The STI Instruments
  5. Generation of Path Delay and Array Loss Statistics
  6. Examples of RMS Path Delay Statistics
  7. Analysis
  8. Conclusion
  9. Acknowledgments
  10. References

[28] The time series of the filtered STI phase delay scatter for each 600 s block of data for the winter month of December 2011 is shown in Figure 4. These data are representative of a quiet month marked by low turbulence. The data for August 2011 are shown in Figure 5. The average scatter for the colder month of December 2011 (Figure 4) is much smaller than that for the warmer month of August 2011 (Figure 5). The diurnal variation is also larger during the warmer month. Fluctuations usually peak within a couple hours of local noon, sometimes earlier and sometimes later. During cold months, the strongest fluctuations correspond to the passage of weather systems rather than day-night heating patterns. Sometimes the diurnal variation becomes insignificant (see period of 25–29 December in Figure 4).

image

Figure 4. December 2011 zenith path delay standard deviations over 600 s time intervals (blue points denote Apollo STI values, red points denote Venus STI values) [Morabito et al., 2012b].

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image

Figure 5. August 2011 zenith path delay standard deviations over 600 s time intervals (blue points denote Apollo STI values, red points denote Venus STI values) [Morabito et al., 2012b].

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[29] It is also apparent from Figures 4 and 5 that the time series of the phase delay statistics from the Apollo STI and Venus STI follow each other very well during quiet conditions and reasonably well during periods of higher turbulence. Differences are likely attributable to local terrain. The Venus site has a nearby group of high hills to the north, while the Apollo site is located in a nested valley.

[30] The instrumental noise floor of the data plotted in Figures 4 and 5 is about 0.1 ps. This noise is expected to be stationary or at least slowly varying and independent of the tropospheric delay fluctuations. It can be subtracted in a quadratic sense, leaving only the troposphere effects. It is somewhat higher for the Venus STI (0.158 ps was measured during zero-baseline tests prior to installation [Acosta et al., 2007]). Whereas the noise is usually small compared with the tropospheric fluctuations, we did not subtract it from any of the measurements presented in this paper.

Analysis

  1. Top of page
  2. Abstract
  3. Introduction
  4. The STI Instruments
  5. Generation of Path Delay and Array Loss Statistics
  6. Examples of RMS Path Delay Statistics
  7. Analysis
  8. Conclusion
  9. Acknowledgments
  10. References

Monthly Averages

[31] The statistics for several months of contemporaneous zenith path delay data for the Apollo and Venus STIs are summarized in Figure 6 which displays average RMS values among all 600 s blocks in each month after the standardizations discussed in section 3 were performed. The average values from each STI are very close in magnitude, providing support that the statistics are in reasonable agreement for the Goldstone complex despite being 13 km apart in differing terrain. A clearly dominant seasonal signature is also apparent.

image

Figure 6. Average STI zenith delay RMS scatter for each month extracted from the data from each STI.

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[32] The fact that the Apollo and Venus delay RMS signatures are comparable in magnitude suggests that any ionospheric contributions are negligible. For example, if a 2 ps delay RMS observed at Venus (20.2 GHz) were entirely due to the ionosphere, the delay RMS seen at Apollo (12.5 GHz) would be 5.2 ps, given the inverse frequency-squared dependence of the delay RMS due to ionosphere. We expect that ionospheric effects at these frequencies for midlatitude locations such as Goldstone should be negligible except possibly during the strongest geomagnetic storms. We examined the Apollo and Venus delay RMS signatures during the periods of the strongest geomagnetic storms that occurred during the data acquisition period from 2011 through 2012 and were unable to detect any discernible differences. Ionospheric effects in the form of anomalous fast fluctuations were detected on data collected by a similar instrument but located in an equatorial region at very high altitude [Hales et al., 2003]. In this case, these measurements were vulnerable to a phenomenon known as equatorial spread F where the very high altitude also resulted in much lower tropospheric contributions. Such a situation is not expected to occur at a midlatitude site such as Goldstone.

[33] Although we do not expect the time series of the RMS delay always to agree, their statistics over time are reasonably consistent. The statistics in Figure 6 are evaluated using data across common time periods for both STIs. Sometimes one STI had a period of missing data due to a power outage or similar issue; in such cases, the data from the other STI were removed from the statistics reflected in Figure 6.

[34] The maximum values for each month (not shown in Figure 6) were as high as 20 ps and are in good agreement between the instruments. The minimum value (not shown in Figure 6) is for most months near 0.1 ps for the Apollo STI and near 0.16 ps for the Venus STI, in agreement with the expected instrumental noise floor of each instrument. The Apollo STI has a lower noise floor than the Venus STI because the wideband satellite signal is stronger and because of its more noise-efficient signal processing. Higher minimum values occur during summer months, and these agree between the two instruments.

Cumulative Distributions

[35] The zenith delay RMS estimates from all 600 s intervals in a given month were combined and sorted in descending order in order to produce the cumulative distribution (CD) curve for that month. Thus, a 31 day month will have a maximum of 4464 intervals and a 30 day month will have a maximum of 4320 intervals. As an example, a delay RMS of 4 ps occurring at a CD of 90% means that 90% of the intervals for that month have delay RMS values that lie below 4 ps and 10% of the intervals have delay RMS values that lie above 4 ps.

[36] Figure 7a displays the monthly cumulative distribution curves of the zenith phase delay standard deviation from the Apollo and Venus STI instruments for January 2011 through December 2012. The distributions of the warmer months (summer) are shown in reddish colors, and the curves for the cooler months (winter) are shown in bluish colors. The curves for the intermediate months (spring and autumn) are shown in greenish-yellowish colors. As expected, the curves for the warmer months lie on the right side of the plot, while those of the cooler months lie on the left side of the plot. For each month, the two STI instruments (Apollo (solid curves) and Venus (dashed curves) in Figure 7a) follow each other fairly well, but there are a few differences that may be due to terrain.

image

Figure 7. (a) Cumulative distribution of filtered zenith delay standard deviation in 600 s blocks (includes height adjustment). (b) Cumulative distribution of filtered zenith delay standard deviation in 600 s blocks for selected summer and winter months (without height adjustment).

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[37] Figure 7b displays the cumulative distribution curves of the Apollo and Venus STIs for selected summer and winter months where the height adjustment (last factor in (1)) was not applied. For the summer months, the Venus curves lie significantly to the left of the Apollo curves, suggesting less turbulent conditions, whereas for the selected winter months, the difference is not as striking. The fluctuations are thus weaker at the higher altitude site. This was attributed to the fact that the Venus site is located at a higher altitude than the Apollo site and thus is subject to less turbulence than Apollo. The height difference of 118.9 m results in an adjustment factor of 1.06, which causes the curves to line up fairly well as seen in Figure 7a. Butler et al. [2001] reported a similar decrease in the strength of fluctuations with altitude for STI instruments with a similar separation, although that was at a much higher and dryer location in Chile.

Diurnal and Seasonal Variations

[38] Figure 8 is a color scale plot of the hourly average RMS zenith delay at the Apollo STI as a function of time of day and day of year. The plot includes data from both 2011 and 2012. Mean solar noon at Goldstone is at 19:47 UTC. There is little difference between day and night RMS delay during the colder months (first 80 days and last 50 days of the year), whereas the difference is more pronounced during the warmer months (days 150 through 260).

image

Figure 8. Color scale plot of composite 2011 and 2012 Apollo STI RMS zenith delay showing hourly averages as a function of time of day and day of year. Conversion scale between colors and ps values is shown at right. Mean solar noon occurs at 19:47 UTC.

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Structure Functions

[39] We examine the strength of the phase delay fluctuations as a function of timescale by making use of structure functions. The utility of the STI phase delay structure functions to provide information on site tropospheric characteristics such as boundary layer height looks promising. A wide variety of techniques have been employed by atmospheric researchers to infer boundary layer height [Seibert et al., 2000; Gryning, 2005]. The use of the structure function derived from STI RMS phase delay data provides information on the local site conditions such as level of turbulence and boundary layer height. The data acquired from the STI can be used to characterize the structure function, in terms of its level, exponent, and characteristic timescale (knee). We do this on a daily basis for the purpose of the intercomparison between the two STIs for each month. The structure functions for the phase delay scatter are evaluated every 600 s and then we evaluate and plot the average for each day each month from both STIs.

[40] If τ(x) is the zenith delay at location x on the Earth's surface, then its two-dimensional spatial structure function is defined as

  • display math(2)

where τ(x,t) is assumed to be a spatially and temporally stationary random variable and the angle brackets denote the ensemble average.

[41] An STI can directly determine this quantity at only one value of |r| = rsti, but it can measure the phase delay difference as a function of time, and from that we estimate the temporal structure function, defined as

  • display math(3)

where Δτ(t) = τ(x1,t) − τ(x2,t) and x1,x2 are the positions of the STI antennas.

[42] Dτ(r) and Dτ(t) are closely related if the “frozen flow” model holds. In this model, the atmosphere has a fixed distribution of refractive index which is moved across the Earth by the prevailing wind aloft. Then, roughly, the zenith delay is constant for all x = x0 + vt, where v is the average wind velocity in the turbulent layer. In this section, we examine estimates of Dτ(t) computed from STI observations by replacing the ensemble average with a time average using 600 s segments of Δτ(t) measurements at the sampling rate of each STI (1 s for Venus and 0.1 s for Apollo).

[43] Figure 9a displays the daily average temporal structure functions from both STIs measured for each day in August 2011. Figure 9b displays the same functions for December 2011. The raw measurements have been adjusted for elevation angle, baseline length, and site altitude, with the result that the Apollo and Venus curves lie on top of each other reasonably well. The faster sampling rate of the Apollo STI allows the structure function curves for Apollo to cover a wider range of time than the Venus curves. The time interval at which the structure function begins to flatten out corresponds to the time required for the wind to carry the tropospheric irregularities across the STI baseline and should be the component of baseline length along the wind direction divided by the wind speed. The level of turbulence is higher for the summer month (Figure 9a) than for the winter month (Figure 9b).

image

Figure 9. Structure functions for Goldstone Apollo (blue) and Venus (red) STIs for (a) August 2011 and (b) December 2011 referred to phase, baseline length, elevation angle, and height of Apollo baseline. Also plotted are the maximum (black) and minimum (green) slopes that the structure functions could achieve based on the theoretical thick model and thin model limits.

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[44] Below the flattening, the structure function typically has a power law behavior, with Dτ(t) proprotional to tβ. Turbulence theory [Coulman, 1985] predicts that inline image when the thickness of the turbulent layer is much less than the baseline length, h ≪ rsti (thin layer) and that inline image when h ≫ rsti (thick layer), just as it does for the RMS delay in (1).

[45] Figure 10 is a plot of the monthly average structure function exponents along with the monthly minimum and maximum values, for both instruments. The average surface air temperature from the Apollo site is also displayed. The Apollo STI structure function exponents are larger than those of the Venus STI during the warm months and closer to the thick layer model limit, while the curves for the cooler months are generally in better agreement. In almost all cases, the measured structure function exponents lie between the minimum (thin model) and maximum (thick model) theoretical limits. Note that during the hotter summer months the exponents lie closer and more compacted toward the upper limit, which is suggestive that the hotter temperatures cause increased boundary layer height even during nighttime, while during the colder months the range of exponent is larger with the minimum values lying right on (Venus) or near (Apollo) the lower theoretical limit. There is also a seasonal variation that correlates well with average air temperature. Venus being at a higher altitude may contribute to the fact that its structure function exponents do not reach values as high as those of the Apollo STI during the summer months.

image

Figure 10. Monthly average structure function exponent for each instrument over 2 years, along with the monthly maximum and minimum values and the average surface air temperature at the Apollo site. The black line (exponent inline image) is the thick model limit, and the yellow line is the thin model limit inline image.

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[46] We normally assume that the scaling exponent used in equation (1) would be inline image for baseline distances much smaller than 1000 m, a reasonable value for h [Morabito and D'Addario, 2007]. However, this assumption may not always hold, especially during cold winter nights when the height of the planetary boundary layer can be as low as ~100 m, which is smaller than our STI baseline length. The frozen flow assumption may not always hold for Goldstone or at least may be weakened since the prevailing wind direction (or at least the average of the wind direction measurements for Apollo) is within a few degrees of south, which is perpendicular to the baseline.

[47] The structure function slope fits within the theoretical limits for a thin and thick turbulent layer (see Figure 10). The temporal structure function measured from data for cold winter nights typically follows the τ2/3 slope for longer time scales up to tens of seconds (consistent with slow winds) and consistent with the turbulent layer taking on a height near its minimal value (smaller than the STI separation). A structure function measured for data from hot summer daytime periods approach the τ5/3 slope usually for shorter timescales ~ 10 s characteristic of higher wind speeds and where the height of the turbulent layer exceeds the interferometer spacing. A future study will examine the behavior of the structure function level, slope, and transition timescale for daytime-only and nighttime-only conditions for all of these data for each month and by season.

[48] Holdaway and Owen [1995] noted that early STI measurements of the slope of the structure function have a continuous distribution between the theoretical thin layer inline image and thick layer inline image limits. Our measurements show different distributions depending upon month and other conditions. Carilli and Holdaway [1999] have provided explanations for the intermediate values of this exponent including the likely fact that such values could simply indicate the transition between thick layer and thin layer turbulence.

Correlation Between Instruments

[49] If the frozen flow model holds over the 12.5 km distance between our two STI instruments, then under some circumstances the turbulence pattern seen over one instrument will be a delayed version of the pattern seen over the other. We have not observed such a delayed correlation in our data. To obtain such a result, the prevailing wind would need to be along the direction between the stations, and that is sometimes the case. At typical wind speeds, the delay would be more than an hour.

[50] We tentatively conclude that the length scale for the evolution of the turbulence pattern is typically shorter than the separation between the two STIs. There may be cases of delayed correlation when strong large-scale storm cells are carried through the region by the prevailing wind. However, the data acquired during the cases studied here are consistent with turbulence generated by local heating. The long-term statistics (daily or longer, as discussed in sections 5.1 through 5.4) are similar at the two locations, presumably because they are in similar desert terrain. The short-term turbulence patterns are different, perhaps because there are hills between the sites that break up a flow that would otherwise remain frozen.

Array Loss Calculated From RMS Phase Delay

[51] Atmospheric delay fluctuations over an element spacing of an array cause variations in the transmitted power of the uplink array as seen from a spacecraft. Morabito and D'Addario [2011] discuss scenarios and different approaches in estimating telemetry loss for an uplink array when there is concern about atmospheric fluctuation timescale versus that of logical elements of the signal (telemetry frame size, for example). A reasonable link budget can be constructed by using the mean value of loss (under a given set of conditions) along with the nominal values of other link parameters and then considering a range of adverse and favorable variations from the mean using methodology in Yuen [1983].

[52] The decibel equivalent loss discussed in Morabito and D'Addario [2011] was applied to the overall power (or power-to-noise ratio) of the link. Here the cumulative distributions of the array loss derived from the data for selected months that a two-element uplink array with 191 m baseline length located at Goldstone were examined. The STI delay data were adjusted to an elevation angle of 20° and a link frequency of 7.15 GHz. The value inline image (see equation (1)) was used to scale the Venus baseline length to that of the Apollo baseline, 191 m. A telecom link engineer can then use this estimated loss as one entry in a link budget table. Whereas the prediction is statistical, the engineer must also consider its probability distribution and its variation with season and time of day. We find that the monthly ninetieth percentile loss is always below 0.2 dB at 7.15 GHz in Goldstone. This is consistent with uplink array demonstrations that were conducted using the 34 m DSN antennas located at this site [Vilnrotter et al., 2006, 2008, 2009].

Conclusion

  1. Top of page
  2. Abstract
  3. Introduction
  4. The STI Instruments
  5. Generation of Path Delay and Array Loss Statistics
  6. Examples of RMS Path Delay Statistics
  7. Analysis
  8. Conclusion
  9. Acknowledgments
  10. References

[53] Site test interferometers (STIs) have been deployed at the Venus and Apollo antenna sites in Goldstone, California, to assess the suitability of Goldstone as an uplink array site and to statistically characterize atmospheric-induced phase fluctuations for application to potential Goldstone array link scenarios. We have presented preliminary results of phase delay statistics extracted from these two independent instruments located in Goldstone, California. Both STIs have been shown to present approximately equivalent results after adjusting for differences in their geometries. In addition, the delay RMS signatures for these instruments show very strong daily and seasonal variations. The comparison of two independent nearby STIs provides important data that will help assess the suitability of the Goldstone site to support widely distributed antenna systems for future Ka-band and optical communications. We also discussed array loss derived from these data and the structure functions of the residual RMS delay. Such information can also be used to extract parameters related to the physical atmospheric conditions, such as the level of atmospheric turbulence and atmospheric boundary layer height as well as their variation over different atmospheric conditions which is a focus of future study.

[54] We find that the fluctuations from both sites are statistically similar and do not appear as shifted versions of each other, suggesting that the length scale for evolution of the turbulence pattern is shorter than the separation between instruments. We also find that the fluctuations are weaker at the higher altitude Venus site than at the Apollo site.

Acknowledgments

  1. Top of page
  2. Abstract
  3. Introduction
  4. The STI Instruments
  5. Generation of Path Delay and Array Loss Statistics
  6. Examples of RMS Path Delay Statistics
  7. Analysis
  8. Conclusion
  9. Acknowledgments
  10. References

[55] We appreciate the assistance and cooperation of the NASA Deep Space Network and the DSS-13 station crew. We want to thank Faramaz Davarian, Steve Townes, and Barry Geldzahler for support of this work. We want to also thank Connie Dang of Exelis for providing the DSN weather station data and statistics used in the correlations with the STI data. Most of the design of the Apollo station STI was copied from the phase monitoring system of the Submillimeter Array on Mauna Kea, Hawaii, developed at the Harvard-Smithsonian Center for Astrophysics (CfA) [Kimberk et al., 2012]. We are grateful to Robert Kimberk, Steve Leiker, John Test, and Ray Blundell of CfA for sharing their detailed design information and software. The research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration.

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  2. Abstract
  3. Introduction
  4. The STI Instruments
  5. Generation of Path Delay and Array Loss Statistics
  6. Examples of RMS Path Delay Statistics
  7. Analysis
  8. Conclusion
  9. Acknowledgments
  10. References
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