An Improved Blackbody Calibration Cadence for CYGNSS

An improved blackbody calibration procedure is developed, implemented, and tested for the cyclone global navigation satellite system (CYGNSS). Previously, CYGNSS calibrated its receivers once every minute to account for temperature-induced gain fluctuations. The time spent making calibration measurements limited the duty cycle of wind-speed measurements to approximately 90%. The analysis presented here shows that the 1-min cadence was overly conservative and can be increased to once every 10 min with minimal impact to data quality, thereby improving the wind-speed duty cycle to 98%. A permanent change to the blackbody cadence was made for the complete eight-satellite constellation during July 27, 2021–August 3, 2021, and subsequent analysis verifies that the new cadence improves duty cycle without impacting science data quality, as expected.


I. INTRODUCTION
L AUNCHED in 2016, NASA's cyclone global navigation satellite system (CYGNSS) mission has been collecting global observations between ±38 • latitude with a technique known as global navigation satellite system (GNSS) reflectometry [1]. CYGNSS works by measuring the reflections of GNSS signals from the Earth's surface, in effect operating as an opportunistic bistatic radar. Designed to investigate the evolution and structure of tropical cyclones, CYGNSS is comprised of eight microsatellites in equatorial low Earth orbit [2]. With this architecture, CYGNSS measures the reflected power of GNSS signals from the Earth's surface with fast revisit time (2.8 h median and 7.2 h mean) that allows for rapid acquisition of dynamic weather events [3].
CYGNSS's utility is impaired by a suboptimal sampling cadence related to the satellite's onboard calibration system. The sequencing rate for sampling the onboard blackbody calibration target had been once every minute since launch, and each time this event occurred, the calibration would last approximately 4 s, inclusive of the time required to switch loads from the antenna source to the onboard blackbody target. As a result, CYGNSS occasionally missed sampling certain high-value targets.
Based on the analysis presented in the following, the flight software was updated in 2021 to modify the sampling cadence to once every 10 min, with a slightly increased dwell time of approximately 6 s. This improves the wind-speed retrieval duty cycle from 90% to 98% and shows no detectable deterioration in performance.

II. THEORY
CYGNSS measures ocean surface roughness as a proxy for ocean surface wind speed. Mean ocean surface roughness is estimated from the normalized bistatic radar cross section (NBRCS) measured at L-band (1575 MHz). The NBRCS is determined from the scattered power received at the CYGNSS satellite by [4] σ o = P g (4π) 3 L I R T R R 2 where σ o is NBRCS, P g is the received power, L is the atmospheric attenuation along the propagation path from the GPS satellite to the specular point and CYGNSS, I is a term to account for instrument losses, R T and R R are the ranges between the specular point and the transmitter and CYGNSS receiver, respectively, P T is the transmit power of the GPS satellite, G T is the antenna gain of the GPS satellite in the direction of the specular point, λ is the wavelength of the GPS L1 signal, G R is the gain of the CYGNSS nadir receive antenna in the direction of the specular point, and A is the effective scattering area. Note that P g and A vary as functions of the time delay and Doppler shift of the received signal. As a result, NBRCS also depends on delay and Doppler. The NBRCS determined at all sampled values of delay and Doppler is referred to as a delay Doppler map (DDM). NBRCS is directly related to the mean square slope (MSS) of ocean wave spectra via [5], [6] where θ is the angle of incidence of the scattering geometry and R(θ ) is the Fresnel reflection coefficient for the ocean surface at the specular point. Stronger received signals P g indicate smoother, more specular scattering of the ocean surface; weaker signals indicate This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ rough ocean surfaces associated with higher wind speed. CYGNSS's electronics measures received power in raw digital counts, and calibrated received signal power P g in units of watts is calculated by where G is the receiver gain in watts/count, C is the raw counts measured at delay-Doppler bins where a scattered signal is present, and C N is the mean raw counts for background noise without any scattered signal present. In practice, C N is an average over many delay-Doppler bins at delay coordinates shorter than that of the specular point. Shorter delays correspond to radar reflections from the atmosphere above the ocean surface, for which there is no appreciable scattering at L-band. CYGNSS satellites are in an equatorial low-Earth orbit with a period of approximately 95 min and experience significant variations in their thermal loads associated with their orbit. As each satellite crosses the terminator into sunlight, the body heats unevenly, causing thermal gradients across the structure. As the spacecraft enters the nightside, it cools suddenly and unevenly.
As the body of the structure changes temperature, so does the thermal environment of the CYGNSS receiver electronics. These dynamics induce variations in the gain of CYGNSS's receiver. Because the quality of wind speed retrieval depends on the consistency of receiver power, each satellite's nadir instruments have built-in onboard calibration equipment to account for thermal gain variations in the receiver amplifiers.
CYGNSS has two nadir science antennas, facing the satellite's port and starboard directions. The receiver connected to each nadir science antenna has its own blackbody calibration target. A thermistor adjacent to the target monitors its temperature in real time to determine the power in the blackbody thermal emission. During a blackbody calibration sequence, the input to the receiver is redirected from the science antenna to the blackbody load and the power emitted by the blackbody is recorded in raw counts for later processing. This sequence takes approximately 4 s because the calibration clock and the science data clock are not synchronized, and the switching of loads is not perfectly instantaneous. To ensure that a full reading of the blackbody is measured without contamination from the load switching process, samples immediately preceding and succeeding calibration are flagged out.
During data processing, the nearest calibration samples before and after a science sample are linearly interpolated to the time of the science sample to estimate gain variations between calibration looks. At launch, this sequence was scheduled to occur once every minute such that every science sample was within approximately 30 s of a receiver calibration event. This calibration sequence sets receiver gain for calculating received power as given by where C B is the counts measured while looking at the blackbody load, P B is the power from the blackbody as estimated from the thermocouple on the low noise amplifier, and P r is the receiver noise estimated from a temperature-dependent Fig. 1. Example of temperature influence on receiver gain. (Top) FM4's port receiver gain is plotted (blue) with the temperature at a nearby probe (red) for a full day starting at 0Z 12 APR 2019. Note that gain is inversely related to local temperature and that these swings are periodic, consistent with CYGNSS's 95-min orbital period. noise floor parameterization determined prelaunch. All three values vary as the spacecraft temperature fluctuates. The 1-min cadence was estimated to bound the one-sigma calibration error for the received power to 0.13 dB [7]. Fig. 1 shows how the spacecraft gain varies with temperature. The blue trace is the calibrated receiver gain in decibels, the red trace is variation in low-noise amplifier temperature in degrees Celsius. The gain varies approximately 0.4-0.6-dB peak-to-peak, whereas the absolute temperature of the low-noise amplifier varies approximately 8 • C peak-to-peak.
CYGNSS's thermal environment also varies due to the orientation of its orbit plane relative to the Sun. The relative time spent in sunlight or shade varies throughout the year as the orbital plane precesses about the Earth. This precession is conveniently characterized by the time-dependent nature of the angle between the orbit plane and a line from the Earth to the Sun, referred to as the orbit beta angle (see Fig. 2). In general, CYGNSS is exposed to the greatest temperature variations during low magnitudes of orbit beta angle, which implies that the spacecraft will spend the maximum amount of time in shade [8]. In addition, during periods at the highest beta angles, at approximately 50 • in magnitude and greater, the spacecraft are commanded into a roll configuration to maintain adequate solar radiance on the solar array panels.

III. METHODS
Decreasing the calibration frequency risks increases error caused by inaccurate compensation for time-varying receiver gain. Science data taken between blackbody calibration measurements are calibrated using linearly interpolated values of the nearest calibration data before and after the science measurement. If the temperature of the spacecraft receiver electronics changes in a nonlinear way between calibrations, it can result in significant errors due to improper corrections for gain variation. An on-orbit experiment was performed to explore how two fundamental CYGNSS data products, NBRCS and retrieved wind speed, degrade due to an increase in the time between blackbody samples. Three days of data from one satellite (FM4) were used, with days selected representing different characteristic beta angles to explore how different thermal cycling may impact the calibration sequence, as shown in Table I.
For all three days, science samples were collected and processed with normal 1-min blackbody sampling. This generated baseline measurements: the fully developed sea (FDS) wind-speed retrieval product u FDS1 , the young-seas limitedfetch (YSLF) wind-speed retrieval product u YSLF1 , and the NBRCS σ o 1 [9]. CYGNSS uses two separate geophysical model functions for wind-speed retrieval. Both retrievals are empirical fittings, but the YSLF differs from the FDS in its sensitivity to long-wave swell, which tends to be underdeveloped in high-wind, dynamic weather where wind direction is frequently changing, such as during tropical cyclones [10], [11]. The YSLF product is tuned to respond to higher windspeed conditions where measurement sensitivity is diminished and so will be more sensitive to possible degradation in calibration quality that results from the change in blackbody cadence.
These data were then reprocessed using every nth blackbody sample, where n is an integer that ranged from 2 to 45, representing sampling the blackbody once every n minutes. The maximum value considered corresponds to performing a blackbody calibration approximately once every half orbit. Between the blackbody samples used, the raw counts recorded by the blackbody were linearly interpolated. An additional case was considered in which the daily mean value of all blackbody samples was used to calibrate the entire day of science data. This case represents calibration without regard for short-term gain variations.
Degradation in calibration accuracy is assessed by examining the difference between science samples calibrated using every nth blackbody sample versus using blackbody samples every minute. These differences are given by where u n is the wind speed produced at a calibration period of n minutes, u 1 is the wind speed produced at the original calibration sequence, and u n is the difference in wind speed due to the increased calibration period of n minutes. If u 1 is assumed to be accurately calibrated, u represents the error that results from less-frequent blackbody calibration. Similar values can be produced for NBRCS and gain where σ o n is the NBRCS at n-minute calibrations, σ o 1 is the NBRCS produced during 1-min calibrations, σ o n is the NBRCS error induced by sampling at longer periods, G n is the receiver gain at n-minute calibrations, G 1 is the original gain at 1-min sampling, and G n is the error due to a longer calibration sequence at period n.
If the use of a particular (longer) sampling rate produces a measurable change in the derived CYGNSS data products relative to the 1-min baseline measurements, this is an indication of degradation in calibration accuracy.
To explore a "worst case" scenario, an additional comparison is made assuming that the satellite only calibrates the blackbody once per day using the daily average value. This provides a sense of how NBRCS and wind speed would degrade if the calibration was performed at timescales much slower than the orbit-induced changes in the thermal loading of the spacecraft.

A. Characterizing the Impact of Change in Cadence
Changing the period of calibration impacts the quality of the gain estimate in (4). If the nonlinear component of the thermal environment changes at timescales faster than the calibration period, the gain estimated by the calibration process will no longer be representative of the true gain. Fig. 3 shows the histograms of normalized gain changes due to increased blackbody sampling cadences. For every sample, both the original gain and the relative fraction of its change are calculated. At blackbody sampling rates close to 1 min, there is very little difference from the original gain, and the distribution of samples approaches a delta function. At longer sampling intervals, this distribution widens, illustrating how gain estimates degrade as the sampling cadence increases. At approximately two samples per orbit or n = 45, the gain variations can be up to ±5% of the baseline.
The results in Fig. 3 are shown for the impact on gain, but this behavior is observed across all derived products. To estimate the growth in error as a function of sampling cadence, the standard deviation is calculated for each distribution. Fig. 4 shows how the standard deviation grows as the sampling period increases.
Sampling every 2 min, the NBRCS error standard deviation is approximately 0.25 m 2 /m 2 . This grows to an error of just over 1 m 2 /m 2 at 45-min cadence. The error characteristics for sampling once per day resembles the 45-min scenario, as the sampling at every half-orbit maximizes error due to unrepresentative temperature-dependent gain corrections. The standard deviation of wind-speed error is approximately three times larger for the YSLF retrieval than the FDS retrieval. At the worst possible case, sampling once every day, the standard deviation of error on the wind-speed product approaches Fig. 3. Histograms of gain error at n = {5, 15, 25, 35, 45} min. The blue and red distributions represent data from the port and starboard antennas, respectively. At low n, the gain error approaches a delta function. As sampling cadence time increases, the distribution widens, illustrating the degradation from the original 1-min sampling cadence. 0.6 m/s. For context, the requirement for CYGNSS retrieval accuracy is a root-mean-square (rms) error of less than 2 m/s at wind speeds lower than 20 m/s and an rms error of less than 10% at winds greater than 20 m/s [6]. The error inventory for the mission suggests that the total L1 error will be 0.82 dB at low wind speeds and 0.70 dB at high winds [4]. Assuming a low-wind NBRCS of 100 and a high-wind NBRCS of 16, the once-daily sampling degrades the measurement by 0.04 and 0.28 dB, respectively. Therefore, even at this cadence, the magnitude of the standard deviation of error is still small enough to meet system requirements.
The standard deviation can, however, be a misleading metric, as it describes the behavior of the total distribution, as opposed to errors in high-value samples. Changes in NBRCS are much more significant at low values because NBRCS is inversely related to wind speed. In addition, large errors in wind-speed retrievals in high-wind areas such as hurricanes can be averaged out by the much more frequent and smaller errors over calm seas.
For this reason, a new metric is developed to appropriately capture how modifications in calibration cadence can impact the CYGNSS science products. This metric is named PCT1, which stands for the percent of samples with error magnitudes that are 1% or greater than its value when using the original 1-min calibration cadence. The PCT1 metric ranges from 0 to 1, with 0 indicating that no samples have errors greater than 1% and 1 indicating that every sample has an error that is at least 1%. PCT1 for the three data products is shown in Fig. 5. As the cadence period increases, the PCT1 rises, with an inflection point between 10 and 15 min. At that point, the increase in blackbody cadence significantly impacts the overall population of data. As expected, the YSLF windspeed retrieval is the most sensitive product to changes in the blackbody sampling rate.
To see how this relationship varies across different orbit beta angles and resulting thermal conditions, PCT1 for NBRCS is plotted across different orbit beta angles in Fig. 6. At lower beta angles, the errors are more pronounced, as the spacecraft spends more time in the shaded portion of the orbit, resulting in greater temperature variability.

B. Optimal Blackbody Sampling Cadence
Determining an optimal sampling cadence requires exploring the tradeoff between the potential benefit of increased science duty cycle over the cost of potentially poorer instrument performance. Fig. 6. PCT1 of NBRCS error as a function of sampling cadence period at various beta angles. At lower beta, the performance degradation is more pronounced.
For this analysis, the worst possible conditions are employed to provide an upper bound on potential impacts on downstream products. Because the low beta angle orbit has the greatest temperature variability, it leads to increased performance degradation, and because the YSLF wind-speed product is more sensitive to calibration errors than its FDS counterpart, the choice of blackbody sampling rate should be driven by the low beta YSLF error growth.
We chose an arbitrary YSLF PCT1 value of 0.05 as the optimal cutoff threshold, which means that the number of samples with greater than 1% error due to an increased sampling period could be no more than 5% of the total population. The largest sampling rate below the PCT1 cutoff for the YSLF data product is once every 10 min, as shown in Fig. 5. At 11 min, the PCT1 values exceed 0.05 during the low beta angle day.

IV. PERFORMANCE BY ORBIT SECTOR
The temperature gradients on CYGNSS are the largest as the spacecraft crosses the terminator. This implies that the performance degradation due to the increased sampling period should be greatest as the spacecraft crosses the terminator. To validate this theory, we calculate the standard deviation of the wind-speed anomaly as a function of sampling cadence as before and further segregate results by orbital phase.
The terminator crossing is approximated by utilizing the temperature traces of the low-noise amplifiers. The spacecraft is assumed to cross the terminator 5 min prior to each peak and valley of the temperature trace. After the terminator crossings are established, the time since crossing the terminator is segregated into five 10-min bins. Fig. 7 shows the standard deviation of the YSLF windspeed anomaly for the low beta case, separated by time since terminator crossing. The performance impact of increasing the sampling cadence is clearly dependent on orbital location, with the worst performance immediately following the terminator crossing and moderate impacts as the spacecraft enter a steady-state thermal environment. Standard deviation of YSLF wind-speed error as a function of sampling cadence period at various orbit sectors. The errors due to increased blackbody sampling rates are greatest immediately after crossing the terminator. This effect is largest at longer sampling periods.

V. DISCUSSION
As a result of this analysis, the CYGNSS operations team elected to transition science operations to the 10-min blackbody sampling cadence in August 2021.

A. Characterizing the Impact on Duty Cycle
To evaluate the utility of a refined sampling cadence, the preferred figure of merit is the duty cycle of high-quality ocean observations in which wind-speed retrievals are possible, as given by (8) where N good is the number of good-quality ocean observations capable of otherwise retrieving a wind-speed retrieval and N BB is the number of samples impacted by the blackbody calibration sequence. The original 1-min blackbody cadence took on average 4 s, inclusive of the time it took for the spacecraft to switch loads (1 s), sample the blackbody target (2 s), and switch back to the science antenna (1 s). This would suggest a nominal duty cycle of approximately 56/60 = 93.33% as computed in (8) without considering other factors.
For the 10-min sequence, the length of time observing the blackbody target was increased to 4 s to reduce variability due to sudden receiver excursions. When considering 2 s required for changing the antenna load to the target, an average blackbody measurement takes approximately 6 s. Theoretically, the duty cycle should improve to 594/600 = 99%.
CYGNSS L1 data files have several quality flags associated with each sample, and N good is determined by an "overall quality" indicator, which is the sum of several other flags with logical OR operations as described in the product data dictionary [12]. In practice, only about 60% of samples collected over the ocean are useful due to other quality control flags independent of the blackbody calibration. Therefore, any improvement in the raw duty cycle with a new blackbody sequence will have outsized impact on D fom . When accounting for this difference, the expected D fom in the naïve 1-min cadence where 6.67% data are lost is no longer 93%, but approximately 89% as 6.67%/0.6 = 11%. Similarly, the expected D fom for the improved blackbody sequence is 98%.
N BB is composed of logical ORs of flags associated with the blackbody sample itself plus flags, indicating that the instrument is reconfiguring in preparation for or immediately after a blackbody sample, adjusted for samples that occur only over the ocean. By implementing this modification, D fom increases from approximately 90% to 98%.

B. Characterizing the Impact on the Level 1A Error Budget
CYGNSS's Level 1 error budget described in the Algorithm Theoretical Basis Document is composed of the root sum of squares of individual error terms in the Level 1A equation [13]. Combining (3) and (4) shows the full Level 1A equation with each source term The individual error terms can be approximated by taking the partial derivative with respect to each individual term where q i represents an individual input parameter. The total error from the root sum of squares of individual error terms can be expressed as In this experiment, we modified the input parameter C B and held all other inputs constant. Therefore, we can calculate the specific contribution of error due to the blackbody sequence by plugging (9) into (10) and setting The latest Level 1A error budget estimates that the one-sigma E(C B ) is 0.05 dB [7]. With the change in blackbody cadence from 1 to 10 min, the one-sigma uncertainty becomes approximately 0.07 dB. The total error now follows by computing the root sum of squares in (11) with the other values specified in [7]. Prior to the blackbody calibration, the rolled-up Level 1A error budget was 0.225 dB, and after the change, it has increased to 0.232 dB.

C. Comparing Expected Results to Empirical Data
To demonstrate that wind-speed performance has not significantly deteriorated, a statistical comparison is performed with reanalysis data using the CYGNSS Climate Data Record Version 1.1. This product matches up MERRA-2 windspeed reanalysis with CYGNSS observations and generates an expected "modeled" NBRCS for a given ocean condition with the appropriate spectral corrections for CYGNSS. The performance of the CYGNSS retrieval is compared as the To account for variability in global wind-speed distributions, 24 prior samples at the 1-min cadence were selected in 2020 to account for any seasonal or subseasonal variability in the CYGNSS performance. Because year-round data are not available for the new sampling cadence, a week of data was collected to represent current behavior.
With these data, Student's T-test was performed with both the standard deviation and mean of σ o to evaluate whether there were any statistically significant changes in the performance of CYGNSS. Each day of the 1-min data serves as a realization of the prior distribution, and the week of 10-min data is a realization used in the significance test, where the parameters are shown in (14a)-(14d). To minimize the sensitivity to outliers, only values between the 5th and 95th percentiles of each dataset were utilized As shown in Table II, there are no statistically significant differences in the overall performance of CYGNSS, both in terms of the average absolute performance of the difference between observations and expected NBRCS values, as well as any appreciable increase in variability. The errors inherent in wind-speed model performance are several orders of magnitude greater than any expected deterioration that could be attributed to elongated blackbody sequence.

VI. SUMMARY AND CONCLUSION
This work explores an optimal blackbody sampling cadence for the CYGNSS constellation. Fundamentally, the calculus to modify sampling cadence weighs the potential deterioration of data quality as a result of less precise thermal gain variation knowledge against the potential utility of increased science collection coverage.
With this analysis, we show that the original design generally overestimated the effects of thermal gain variations on the end derived products and the calibration sequencing oversampled at the expense of science operations.
The most dynamic thermal environment for CYGNSS spacecraft occurs as they cross the terminator, and the most significant variations occur when the orbit is at its lowest beta angle when the spacecraft has the longest opportunity to cool in the Earth's shadow. Under those conditions, any changes to the blackbody cadence will have the most significant impact on the derived products. However, even considering CYGNSS's most sensitive product, the YSLF wind speed, the blackbody sampling rate can be increased tenfold to once every 10 min without degrading more than 5% of the data population by more than 1%.
With this modification, CYGNSS can improve its retrieval duty cycle from 90% to 98%, significantly improving the availability of data previously lost to excessive blackbody calibration.