Cross Validation of TEMPEST-D and RainCube Observations Over Precipitation Systems

This article presents cross validation of nearly simultaneous observations between the Temporal Experiment for Storms and Tropical Systems-Demonstration (TEMPEST-D) and Radar in a CubeSat (RainCube) satellite microwave sensors over precipitation systems. RainCube senses the atmosphere using a Ka-band nadir-pointing radar, and TEMPEST-D senses using multifrequency millimeter-wave radiometers. Nine precipitation systems were used in this cross-validation study. Occurring over nearly a two-year period, these storms were scattered over many regions of the world from the Tropics to the midlatitudes. A shift correction algorithm was developed to remove the uncertainty between the two sensors’ observations due to the time difference and the storm motion between the two instrument overpasses. Correlation coefficients were calculated between self-normalized, inverted RainCube cumulative reflectivity and self-normalized TEMPEST-D brightness’ temperatures. As expected, these correlation coefficients are consistently higher for the four TEMPEST-D high-frequency channels than for the single low-frequency channel. The shift correction algorithm improved the average correlation coefficient by 19% for the four high-frequency channels and by 58% for the single low-frequency channel. The average correlation coefficient after shift correction is 0.76 for TEMPEST-Ds four high-frequency channels and 0.54 for the single low-frequency channel. The comparisons demonstrated high consistency between the TEMPEST-D and RainCube observations, even though the two microwave sensors’ fundamental physics is different; one is passive, and the other is active.


I. INTRODUCTION
U NDERSTANDING cloud microphysics is essential for studying the formation and evolution of precipitation systems. The time scale of most cloud microphysics processes is short, and high temporal resolution measurements are needed to properly capture them. Ground weather radar networks can observe the atmosphere with very high temporal resolution [1]. Many studies [2], [3], [4] have used weather radar observations to analyze the evolution of cloud microphysical processes within storms. However, ground weather radars provide observations over land, and a few observations are available near coastal regions, but no ground weather radars provide coverage over the open ocean. The prediction skills of numerical weather and climate models mainly depend on the model's initial conditions [5], [6], [7] and physics parameterization schemes [8], [9], [10]. Open ocean observations are essential to generate acceptable initial conditions for numerical weather prediction (NWP) models, especially to predict severe weather events, such as hurricanes, typhoons, and tropical cyclones. In addition, open ocean measurements are required to validate and improve NWP models' physics parametrization schemes over the ocean. Open ocean observations are also crucial to analyze the variability of precipitation over the oceans. Knowledge of these variations is needed to study and predict climate change and inform environmental policies.
Weather satellite observations play an increasingly crucial role in providing critical oceanic observations on a global basis. Depending on the applications and requirements, weather satellites are deployed either in geosynchronous equatorial orbit (GEO) or low Earth orbit (LEO). Presently, weather sensors on GEO satellites provide observations only in the visible and infrared (IR) wavelength ranges. Visible and IR sensors measure only the locations of clouds and cloud top temperatures. They cannot penetrate the cloud to observe the cloud microphysics and surface precipitation. Sensors on LEO satellites also include microwave radiometers, either with or without IR and visible sensors. Microwave radiometers can penetrate the cloud to measure cloud microphysics and surface precipitation characteristics. However, the main limitation of LEO satellites is their low temporal resolution due to long revisit times. Therefore, it is challenging to study the growth and decay of individual storms using LEO satellites. A constellation of satellites could overcome these limitations by deploying identical sensors This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ with much more frequent revisit times [11]. However, when using traditional satellite technology, producing and deploying a satellite constellation is very expensive. Nevertheless, CubeSat technology has been recently demonstrated as a viable low-cost option. As of March 2022, more than 1594 CubeSats had been launched [12]. Since CubeSats' fabrication and launch costs are relatively low, including both spacecraft and instruments, it is possible to deploy a constellation of CubeSats in LEO to enable improved temporal resolution of global observations. However, before using CubeSat observations for operational product generation, merging their data with other traditional satellite observations or assimilating them into NWP models, it needs to be validated with equivalent traditional satellite observations and corresponding ground-based observations. Studies have assessed the performance of CubeSats using other observations. Berg et al. [13] conducted a calibration and validation study of Temporal Experiment for Storms and Tropical Systems -Demonstration (TEMPEST-D) observations with multiple well-calibrated sensors, including the Global Precipitation Measurement (GPM) Microwave Imager (GMI) as well as four Microwave Humidity Sounder (MHS) sensors aboard National Oceanic and Atmospheric Administration and European Space Agency/EUMETSAT MetOp satellites. Their analysis demonstrated that the absolute calibration accuracy of TEMPEST-D is within 1 K and calibration precision, or stability over time, is within 0.6 K for all five channels. Christophersen et al. [14] successfully assimilated the simulated radiances expected from future Time-Resolved Observations of Precipitation structure and storm Intensity with a Constellation of Smallsats (TROP-ICS) CubeSats and showed potential improvements in tropical cyclone prediction.
Radhakrishnan et al. [15] cross-validated TEMPEST-D and GPM GMI brightness temperature (TB) observations over precipitation systems and concluded that the two sets of observations have good agreement. Their analysis also showed that when TEMPEST-D observations are combined with those from GMI, this can double the number of observations and improve the temporal frequency of measurements over severe weather events.
Schulte et al. [16] retrieved atmospheric water vapor, cloud liquid water path, and cloud ice water path from TEMPEST-D TB observations. They showed that the retrieved products match well with the same products retrieved from similar but more expensive and larger MHS sensors' observations. Radhakrishnan et al. [17] used TEMPEST-D TB observations to successfully estimate surface rainfall. These studies showed that CubeSats could measure the atmosphere as well as traditional satellites. To continue the validation of CubeSat observations, this study cross-validated observations from two CubeSats, TEMPEST-D and radar in a CubeSat (RainCube).
The rest of this article is organized as follows. Section II describes the TEMPEST-D and RainCube missions. Section III discusses the methodology followed to compare the two observations. In Section IV, the data are presented, while in Section V, the results are presented. Finally, Section VI concludes this article.

II. TEMPEST-D AND RAINCUBE SATELLITE MISSIONS
Temporal Experiment for Storms and Tropical Systems (TEMPEST) is a 6U CubeSat mission concept to observe the evolution of cloud convective systems with high temporal resolution. The concept of TEMPEST constellation mission is to deploy six to eight identical 6U CubeSats in the same orbital plane with approximately 5-min spacing [18]. TEMPEST-D ("D" for demonstration) satellite is a single 6U CubeSat launched on May 21, 2018 and deployed into orbit on July 13, 2018. The TEMPEST-D radiometers measure at five millimeter-wave frequencies (87, 164, 174, 178, and 181 GHz) that provide detailed information on convection as well as the surrounding water vapor environment. The TEMPEST-D spatial resolution at nadir is 25 km for 87 GHz and 12.5 km at 181 GHz from a nominal orbital altitude of 400 km. A detailed description of the instrument and prelaunch calibrations are provided in [19]. Calibration and validation of the TEMPEST-D instrument have demonstrated equivalent performance to the traditional satellites, as discussed in [13]. RainCube is the first-ever radar instrument in a 6U CubeSat. It is a joint development between the Jet Propulsion Laboratory and Tyvak NanoSatellite Systems (Tyvak). RainCube has a 35.75 GHz (Ka-band) nadir-pointing precipitation profiling radar payload deployed from the ISS on July 13, 2018. The peak transmit power of RainCube's radar is 10 W, and it has a sensitivity of 13 dBZ. The horizontal resolution of RainCube radar at the surface is 7.9 km, and the vertical resolution is 120 m. The design and technical details of RainCube are described in [20] and the products are discussed in [21]. Fig. 1 shows a graphical view of RainCube (in blue) and TEMPEST-D (in red) overpasses. The National Aeronautics and Space Administration supported these two CubeSat missions for on-orbit validation of technology for studying the Earth's atmosphere.

III. METHODOLOGY
Cross comparison of TEMPEST-D and RainCube observations consists of two parts. The first part is to identify nearly simultaneous overpasses over precipitating systems by RainCube and TEMPEST-D. The second part is to determine parameters from two observations that are meaningful to compare and develop an algorithm to correct the shift between the two observations to maximize the correlation. In the first part, an automated algorithm has been developed to identify nearly simultaneous overpasses. The algorithm consists of the following four steps, as shown in detail in Fig. 2.
1) The first step is to read the RainCube overpass date and find the closest date of a TEMPEST-D overpass. If a TEMPEST-D overpass is available within ± one day of the RainCube overpass, then the algorithm proceeds to the second step. If not, the algorithm continues to the next RainCube overpass. 2) The second step is to determine the number of pixels (n 1 ) in which a geolocated distance between the two datasets is less than 100 km. If n 1 is not equal to zero, the algorithm proceeds to the third step. If none of the pixel distances are less than 100 km, the algorithm continues to the next RainCube overpass.
3) The third step is to calculate the time difference between two observations to determine the number of pixels (n 2 ), which have a time difference of less than 2 h. If n 2 is not equal to zero, the algorithm will proceed to the fourth step. If n 2 is equal to zero, the algorithm continues to the next RainCube overpass. 4) The fourth step is to store the detailed data for both the RainCube and TEMPEST-D overpasses and plot them to select precipitation events observed by both RainCube and TEMPEST-D. The second part of cross validation is to use the nearly simultaneous overpasses identified in the first part and performs cross comparisons. Fig. 3 shows the procedure followed for the cross-comparison process. The process consists of the following five steps to compare nearly simultaneous TEMPEST-D and RainCube observations.
1) The first step is to find the TEMPEST-D pixels nearest to RainCube pixels for collocation. the third step, each of these observations is self-normalized between 0 and 1. The TEMPEST-D TBs represent upwelling microwave radiation and decrease due to interaction with atmospheric liquid and frozen hydrometeors, cloud liquid water, water vapor, and oxygen. On the other hand, the reflectivity factor of RainCube increases due to the backscatter of microwave radiation [22]. To account for this physical difference between sensing modalities and to obtain a clear visualization for determining the cross correlation, the RainCube self-normalized values are "inverted," i.e., subtracted from unity. These self-normalized and inverted RainCube observations are used in further joint analysis with the self-normalized TEMPEST-D observations. 4) The fourth step is to perform a shift correction between the two observations. This shift correction eliminates the uncertainty due to the time difference between two observations and storm motion between the TEMPEST-D and RainCube observations. The shift correction algorithm optimally shifts the RainCube observations to match the location of lowest inverted self-normalized RainCube, Ref cum , to the lowest self-normalized TEMPEST-D TB location. The amount of shift correction is chosen to maximize the correlation between the inverted RainCube cumulative reflectivity and the TEMPEST-D TBs. The shift correction algorithm is performed separately for each case since the required shift correction depends on the time difference between TEMPEST-D and RainCube observations as well as the dynamics of the precipitation system. 5) The final step is to perform a cross comparison between collocated and shift corrected observations.

IV. DATA USED
The analysis presented here used publicly available TEMPEST-D Level 1b data (https://tempest.colostate.edu/ data/), containing calibrated, geolocated TBs, as well as Earth viewing angles, for all five TEMPEST-D channels. In addition, the publicly available RainCube data (https://tcis.jpl.nasa.gov/ data/raincube/) used here are calibrated, geolocated reflectivities as a function of altitude, as well as ground elevation data derived from digital elevation maps. All available observations from TEMPEST-D and RainCube are used in the study. Nine valid precipitation events were identified using the algorithm as nearly simultaneous overpasses. Fig. 4 shows the locations of the selected events on a global map, and Table I lists the event dates and regions of the world. The boxes, as shown in Fig. 4, indicate the regions considered for TEMPEST-D and RainCube overpasses over precipitation systems. These geographic areas are chosen to visualize the TEMPEST-D TBs at 164 GHz as well as the corresponding RainCube orbits, as shown in Figs. 5, 7, 9, and 11 . Only the pixels common to TEMPEST-D and RainCube data were used for cross validation between the two sensors. The storm observations for the events numbered 1, 2, 6, and 9, as highlighted in bold in Table I, are shown in detail in Fig. 5, Fig. 7, Fig. 9, and Fig. 11, respectively. However, all nine events are used in the quantitative cross comparisons, as listed in Tables II-IV. V. RESULTS AND DISCUSSION Nine cases over diverse regions of the world during nearly a two-year period were identified for cross comparison of TEMPEST-D and RainCube over precipitating systems. For these cases, validation analysis is performed, and results are reported for all five TEMPEST-D channels. For brevity, the TB maps and time series results using only the 164 GHz channel are provided here.  Fig. 5(b) shows the RainCube observed vertical reflectivity profile for the same storm. The time difference between the two observations was less than 12 min. For this storm case, both CubeSats were orbiting along nearly     parallel paths in the same direction, from southwest to northeast. The TEMPEST-D TB image shows multiple intense storm cells and two cells along the path of RainCube. The black dots on the TEMPEST-D images in Fig. 5(a) correspond to the black vertical dotted lines in Fig. 5(b). The RainCube vertical reflectivity profile shows two peaks, corresponding to locations of two substantial decreases in the TEMPEST-D TBs. The RainCube reflectivity indicates that both storm cells extended to 15 km above the surface. Fig. 5 shows that RainCube and TEMPEST-D observations agree well in terms of storm cell locations. Fig. 6 shows a comparison of range Ref cum observed by RainCube and 164 GHz TBs observed by TEMPEST-D. Fig. 6(a) shows the comparison on the original scale, and Fig. 6(b) shows the comparison on a self-normalized scale with inverted RainCube      II  CORRELATION COEFFICIENTS BETWEEN SELF-NORMALIZED AND INVERTED RAINCUBE CUMULATIVE REFLECTIVITY AND SELF-NORMALIZED TEMPEST-D TBS  BEFORE SPATIAL SHIFT CORRECTION   TABLE III  RainCube radar observes precipitation due to backscattering from hydrometeors. A substantial scattering signature is also clearly observed in the TEMPEST-D TB observations. The TB values decrease from 280 to 160 K over the precipitating regions.

A. Storm Over Mexico's Pacific Coast
Since both the TEMPEST-D and inverted RainCube time series decrease with increasing scattering, a correlation coefficient was calculated. Table II lists the correlation coefficients between self-normalized and inverted RainCube cumulative reflectivity (Ref cum-norm ) and self-normalized TEMPEST-D TB (TB norm ) for all five TEMPEST-D frequencies. In particular, the correlation coefficients for the 178, 174, and 164 GHz channels are at least 0.9, and the correlation coefficient for the 181 GHz channel is 0.85. In contrast, the 87 GHz channel has a low correlation coefficient of 0.6. The correlation coefficients are consistently higher for the four TEMPEST-D high-frequency channels than for the single low-frequency channel. This is expected since the low-frequency TEMPEST-D channel is mostly sensitive to the surface as well as integrated water vapor, which are not included in the radar at Ka-band signature. These qualitative and quantitative comparisons show that RainCube and TEMPEST-D data agree very well for this storm case, in terms of both location and intensity. Since the two measurements agree well, no shift correction was needed for this case.

B. Storm Over South Pacific Ocean
TEMPEST-D observations of a storm over the South Pacific Ocean near the Solomon Islands were performed on October 15, 2018 between 20:11 and 20:15 UTC, as shown in Fig. 7(a), along with the RainCube orbit path. Fig. 7(b) shows the Rain-Cube observations over the storm on October 15, 2018 between 20:00 and 20:02 UTC. The time difference between these two observations was about 13 min. Both CubeSats were orbiting in the same direction, from southwest to northeast. The two black dots in Fig. 7(a) correspond to the locations of the vertical dotted lines in Fig. 7(b). It can be observed that the storm heights extend to 10-15 km altitude. Fig. 8(a) shows a comparison of RainCube Ref cum and TEMPEST-D 164 GHz TB. The maximum value of Ref cum for this case was approximately 600 dBZ-km at the center of the storm cell. The lowest TB value for this case was 130 K, 30 K smaller than for event 1. The large decreases in TB correspond to the high reflectivity at the center of the cell. It can be clearly seen in Fig. 7(b) that a narrow portion of the storm reached a reflectivity value of 40 dBZ. Fig. 8(b) and (c) shows the comparison of Ref Cum-norm and TB norm before and after shift correction. Fig. 8(b) shows good match between the two observations with little shift. The shift correction algorithm is applied to the RainCube overpass data to match the TEMPEST-D overpass. The algorithm shifted the RainCube data by 28 km to the northeast to obtain a maximum correlation with TEMPEST-D observations. From event number 2 in Tables II and III, the correlation coefficients between self-normalized and inverted RainCube cumulative reflectivity (Ref cum-norm ) and self-normalized TEMPEST-D TB (TB norm ) have increased for all five TEMPEST-D frequencies after shift correction. For event number 2 in Table IV, the average correlation coefficient for the four TEMPEST-D high-frequency channels, i.e., 181, 178, 174, and 164 GHz, is 0.67. The shift correction algorithm increases the average correlation coefficient of the four highfrequency channels to 0.80, a 19% improvement. For the single low-frequency channel at 89 GHz, the correction algorithm improved the correlation coefficient from 0.5 to 0.67, a 34% improvement. Fig. 8(c) also shows good qualitative agreement between the self-normalized and inverted RainCube reflectivity and the self-normalized TB.

C. Storm Over Central African Republic
TEMPEST-D observations of a storm over the Central African Republic were performed on June 24, 2020 between 22:59 and 23:03 UTC, as shown in Fig. 9(a), along with the orbit path of RainCube. Fig. 9(b) shows the RainCube vertical reflectivity profiles for the storm on July 24, 2020 between 21:09 and 21:12 UTC. The time difference between these two observations was about 49 min. Both CubeSats were orbiting in the same direction, from southwest to northeast. The four black dots in Fig. 9(a) correspond to the four vertical dotted black lines in Fig. 9(b). The black dots and lines from Fig. 9(a) and (b) clearly show the shift in the time between the TEMPEST-D and RainCube observations. The correction algorithm corrected the shift of approximately 145 km by moving the RainCube observation in the southwest direction. The four red dots in Fig. 9(a) correspond to the four vertical dotted red lines in Fig. 9(b). The red dotted lines indicate the location of the storms from RainCube observations after the shift correction has been applied. The red dots and dotted lines in Fig. 9(a) and (b) clearly show that RainCube observed storm after shift correction matches the storm location observed by TEMPEST-D. The intensity pattern of the storm looks similar in the two observations. Fig. 10(a) shows a comparison of RainCube Ref cum and TEMPEST-D 164 GHz TB. For this case, the maximum value of Ref cum was approximately 700 dBZ-km, and the lowest TB value was approximately 140 K. Fig. 10(b) and (c) shows the comparison of the self-normalized inverted RainCube observations with the self-normalized TEMPEST-D 164 GHz TB. Fig. 10(b) clearly shows the shift between the two observations, and Fig. 10(c) shows that the two storm locations match after the shift of approximately 145 km has been corrected by the correction algorithm. From event number 6 in Tables II and III, the correlation coefficients between self-normalized and inverted RainCube cumulative reflectivity (Ref cum-norm ) and self-normalized TEMPEST-D TB (TB norm ) have increased for all five TEMPEST-D frequencies after shift correction. For event number 6 in Table IV, the average correlation coefficient value over the four TEMPEST-D high-frequency channels is 0.25 before correction, and it increased to 0.72 after shift correction, an increase of 192%. For this case, the two observations, as shown in Fig. 9, agree well in terms of storm location and intensity.

D. Hurricane Laura
Hurricane Laura was a deadly and destructive Category 4 hurricane that made landfall in Cameron, Louisiana, on August 27, 2020. TEMPEST-D observations of Hurricane Laura over the Cayman Islands were performed on August 24, 2020, between 15:50 to 15:53 UTC, as shown in Fig. 11(a), along with the orbit path of RainCube. Fig. 11(b) shows the corresponding RainCube vertical reflectivity profile. Similar to previous cases, the two instruments were orbiting in the same direction except in a descending orbit, i.e., from northwest to southeast. The time difference between the two overpasses is 1 h and 52 min. The two black dots in Fig. 11(a) correspond to the two vertical dotted lines in Fig. 11(b). Fig. 12(a) shows a comparison of RainCube Ref cum and TEMPEST-D 164 GHz TB. For this case, the maximum value of Ref cum was approximately 500 dBZ-km, and the lowest TB value was approximately 190 K. Fig. 12(b) and (c) shows the comparison of the self-normalized inverted RainCube observations with the self-normalized TEMPEST-D 164 GHz TB. Fig. 12(b) clearly shows the shift between the two observations, and Fig. 12(c) shows that the two storm locations match after the shift of approximately 120 km has been corrected by the correction algorithm. From event number 9 in Tables II and III, the correlation coefficients between self-normalized and inverted RainCube cumulative reflectivity (Ref cum-norm ) and self-normalized TEMPEST-D TB (TB norm ) have increased for all five TEMPEST-D frequencies after shift correction. The comparison maps show that the pattern of the two observations looks similar. For event number 9 in Table IV, the average correlation coefficient value over the four TEMPEST-D high-frequency channels is 0.50 before correction, and it increased to 0.57 after shift correction, an increase of 14%. The average correlation coefficient value is lower than the previous cases due to the relatively long time between the RainCube and TEMPEST-D overpasses compared with the other cases. In addition to the storm motion between the two overpasses, Hurricane Laura also evolved between the RainCube and TEMPEST-D observations.

E. Regression Analysis
A regression model has been developed to determine the trend of the correlation coefficient with respect to the time difference between TEMPEST-D and RainCube observations. The averaged correlation coefficient values over the four TEMPEST-D high-frequency channels for all nine cases are used in the regression analysis. Table IV lists the averaged correlation coefficient value and the time difference between TEMPEST-D and Rain-Cube observations for each of the nine cases. Fig. 13 shows the averaged correlation coefficient values for all nine cases as a function of the time difference between the two observations, along with the best-fit linear regression. The regression analysis clearly shows that the averaged correlation coefficient decreases as the time difference between TEMPEST-D and RainCube observations increases. When the regression line is extended to zero time difference, corresponding to a RainCube radar and a TEMPEST-D radiometer on the same small satellite, the averaged correlation coefficient is 0.81.

VI. CONCLUSION
Cross validation is performed between RainCube and TEMPEST-D microwave observations to study their physical consistency using nine storm cases scattered over many regions of the globe during a nearly two-year period. The results of this validation study demonstrate that RainCube and TEMPEST-D CubeSat observations are in very good qualitative and quantitative agreement. The correlation coefficient between the selfnormalized and inverted RainCube cumulative reflectivity and the self-normalized TEMPEST-D TBs is greater for the four TEMPEST-D high-frequency channels near the water vapor absorption line at 183.31 GHz than for the low-frequency imaging channel near 90 GHz. This is expected since the low-frequency channel is mostly sensitive to the surface and integrated water vapor, which are not measured by the RainCube radar. A correction algorithm was developed to remove the uncertainty between RainCube and TEMPEST-D observations due to the time difference and the storm motion between the two sensors' overpasses. The correction algorithm improved the correlation coefficient averaged over all nine cases from 0.64 to 0.76 for the four TEMPEST-D high-frequency channels, a 19% increase on average. For the single TEMPEST-D low-frequency channel (87 GHz), the correction algorithm improved the correlation coefficient from 0.35 to 0.55, an increase of 58%. Regression analysis demonstrated that the averaged correlation coefficient decreases as the time difference between TEMPEST-D and RainCube increases. Extrapolation of the regression line to zero time difference leads to a correlation coefficient of 0.81 for a potential future deployment of a TEMPEST-D radiometer and a RainCube radar on the same small satellite.

ACKNOWLEDGMENT
The authors would like to thank T. Gaier, S. Brown, S. Padmanabhan, and B. Lim of JPL for producing the TEMPEST-D radiometer instrument and providing calibrated, geolocated brightness' temperatures, and P. Millar, G. Komar, B. Bauer, and S. Babu for their on-going support, encouragement, and program management. TEMPEST-D is a collaborative program with Caltech/NASA Jet Propulsion Laboratory and Blue Canyon Technologies. A part of this research was performed at the Jet Propulsion Laboratory, under contract with the National Aeronautics and Space Administration.