REFRACTIVITY MEASUREMENTS FROM GROUND CLUTTER USING THE NATIONAL WEATHER RADAR TESTBED PHASED ARRAY RADAR

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1 8A.3A 1 REFRACTIVITY MEASUREMENTS FROM GROUND CLUTTER USING THE NATIONAL WEATHER RADAR TESTBED PHASED ARRAY RADAR B. L. Cheong 1,, R. D. Palmer 1, C. D. Curtis 2,3, T.-Y. Yu 4, D. Zrnić 3 and D. Forsyth 3 1 ool of Meteorology, The University of Oklahoma,, U.S.A. 2 Cooperative Institute of Mesosale Meteorologial Studies (CIMMS) 3 NOAA/OAR National Severe Storms Laboratory 4 ool of Eletrial and Computer Engineering, The University of Oklahoma,, U.S.A. 1. INTRODUCTION In warm seasons, onvetive preipitation initiation heavily depends on moisture near the surfae [e.g., Dabberdt and latter, 1996; Koh et al., 1997]. A neessary ondition for an aurate predition of onvetive rainfall is a good foreast of where and when onvetion will develop. Both predition and understanding of onvetion is limited by the lak of high spatial and temporal resolution of water vapor measurements [Wekwerth and Parsons, 23]. Radiosondes that launh twie a day simply do not supply the measurements at the desired level of temporal and spatial resolution. Near surfae measurements were deemed neessary but are expensive to implement on a dense network. A more attrative approah would be to use some kind of remote sensing tehnique near the surfae. Pioneering work by Fabry et al. [1997] attempted to use ground targets to measure refrativity, whih is losely related to humidity. Initial experiments were onduted in Montreal, Canada, demonstrating the potential of the tehnique [Fabry et al., 1997; Fabry and Creese, 1999]. In addition, extensive experiments were onduted during the International H 2 O Projet 2 (IHOP 2) ampaign [Fabry and Pettet, 22; Wekwerth and Parsons, 23]. The tehnique estimates refrativity from phase measurements of radar ehoes by inversely onstruting the refrativity field based on the relationship between refrativity and phase. Based on this approah [Fabry, 24], a similar refrativity retrieval algorithm was reently developed at the University of Oklahoma and applied to the Phased Array Radar (PAR), whih is the enterpiee of the National Weather Radar Testbed (NWRT) that is operated and maintained by the National Severe Storms Laboratory (NSSL). Here, we will exploit the agile beam steering apability of the PAR system for refrativity retrieval. Extremely short dwell times (down to 18 ms for a 9 overage) are tested and the results are presented here. If the Multi-Funtion PAR [MPAR, Weber et al., 25] onept is to beome a reality, rapid aquisition of refrativity fields would be an attrative omponent of the system. Corresponding author address: Boon Leng Cheong, University of Oklahoma, ool of Meteorology, 12 David L. Boren Blvd., Rm 464,, OK ; boonleng@ou.edu 2. NATIONAL WEATHER RADAR TESTBED The Navy s AN/SPY-1A radar system [Sensi, 1988] has reently been adopted for meteorologial researh by NSSL. The system is also referred to as the PAR system in the NWRT [Forsyth et al., 25]. The PAR operates at 3.2 GHz and utilizes an array of 4352 elements and a flexible data aquisition system. Real-time beamforming is used to eletronially steer the beam for sanning the atmosphere. In addition, raw time-series data from the PAR an be stored for off-line proessing. One of the attrative features of the PAR system is the agile beam steering apability that allows for extremely rapid sanning. In addition, image-smearing effets that are inherent in the standard WSR-88D due to antenna motion are eliminated in the PAR system. 3. BASICS OF REFRACTIVE INDEX AND RADIO WAVES Refrative index, n, of a medium is defined as the ratio of the speed of light in a vauum to the speed of light in the medium. For the air near the surfae of the earth, this number is typially around 1.3 and hanges are on the order of 1 5 [Bean and Dutton, 1968]. For onveniene, a derived quantity referred to as refrativity is used in many sientifi studies, and is mathematially formulated as follows N = 1 6 (n 1) (1) Refrativity is related to meteorologial parameters as shown below [Bean and Dutton, 1968] N = 77.6 p e T T 2 (2) where p represents the air pressure in millibar (mb), T represents the absolute air temperature in Kelvin (K) and e represents the vapor pressure in mb. The first term in equation (2) is proportional to pressure p and is, therefore, related to the air density. The seond term is proportional to vapor pressure e, whih is dominated by moisture. The two terms are often referred to as the dry and wet terms, respetively. Near the surfae of the earth with relatively warm temperatures, most of the spatial variability in N results from the hange in the seond term (refer to Figure 1). Quantitatively, given the pressure and temperature (that tends to be relatively homogeneous) over the radar overage, humidity is expeted to be estimated with reasonable

2 Temperature ( F) 8A.3A 2 Temperature ( C) RH = % p = 1 mb Funtion of Refrativity in Temperature and Relative Humidity RH = 25% RH = 5% RH = 75% RH = 1% Refrativity (N units) If the refrativity field of the referene san is known, the measurement of the hange of refrativity allows us to obtain the absolute refrativity map simply by adding the differene to the referene map. By performing a range derivative in equation (3), it an be shown that d dr [φ(r, t 1) φ(r, t )] = 4πf [n(r, t 1 ) n(r, t )]. (5) Figure 1: Refrativity N as a funtion of temperature T and relative humidity (derived from T and e). At a surfae pressure of 1 mb and temperature above 1 C, refrative index hanges predominantly based on the relative humidity (vapor pressure). As temperature inreases, N beomes more sensitive to the hange of e and thus an be used as a proxy to estimate the water vapor near the surfae. This method may be espeially useful during warm seasons. auray. At a fixed air pressure, say a typial surfae pressure around 1 mb, refrativity N beomes a funtion of e and T and is depited in Figure 1. As temperature inreases, refrativity hange beomes more sensitive to vapor pressure than to temperature and pressure. One an readily see that vapor pressure e is the dominant fator that hanges the refrativity and, thus, refrativity mapping near the surfae an be used as a proxy to estimate the spatial distribution of water vapor near the surfae. 4. SUMMARY OF OU S REFRACTIVITY RETRIEVAL AL- GORITHM Based on the work by Fabry [24], a separate platform for proessing phase measurements to refrativity map is being developed here at the University of Oklahoma (OU). In theory, given that the reeived phase from stationary targets is an integral funtion of the refrative index, this quantity an be obtained by performing the derivative operator on both sides of the equation. The reeived phase is desribed as follows φ(r) = 4πf r n(γ)dγ (3) where f represents the frequeny, represents the speed of light (299,792,458 m s 1 ) and r is the range. In pratie, the radar wavelength that is on the order of m and n 1, so the phase wraps many times within a resolution volume depth whih makes deriving refrativity diretly from a single san (equation 3) problemati. To mitigate this phase wrapping problem, Fabry et al. [1997] proposed that the hange of refrativity between two sans an be obtained instead, i.e., φ(r) = φ(r, t 1 ) φ(r, t ) = 4πf r [n(γ, t 1 ) n(γ, t )] dγ. (4) Usually measurement at time t is referred to as the referene, i.e., referene phase and referene refrativity. Fortunately for our studies, Oklahoma has a reliable, highquality network of surfae stations, known as the OK Mesonet [Brok et al., 1995]. We will use this network to provide an estimate of the referene refrativity map. Under onditions where the spatial struture of refrativity is not omplex, the OK Mesonet allows us to derive an aurate referene refrativity map. Figure 2 depits a flowhart of refrativity retrieval algorihtm. First, a map of referene phase measurements from the radar, assoiated with the time of the referene refrativity from OK Mesonet are olleted. In general, we would like the struture of the field to be relatively simple, so that the oarse sampling of the Mesonet an be used to produe an aurate referene refrativity map. During normal sanning time, a map of phase measurement is obtained and subsequently used to derive a map of phase differene from the referene. Then, regions without good ground targets (based on ground lutter overage and its quality) are masked out to retain only those phase measurements that are useful for refrativity retrieval. A proess of spatial interpolation and smoothing is applied to this masked phase-differene map in order to fill the map. By omputing radial derivatives (refer to equation (5)) of this smoothed phase-differene map, refrativity hange an be obtained. Another smoothing is applied to this refrativity hange map to redue the inherent unertainty in the measurement and derivative operation. Finally, absolute refrativity an be obtained by adding the referene refrativity map to the refrativity hange map. 5. EXPERIMENTAL RESULTS An experiment was onduted on September 28, 25 using the PAR system for refrativity retrieval. The radar was onfigured to operate at a pulse repetition time (PRT) of 1 ms. 64 samples were olleted for eah beam position. The array was set faing north and sanning at an elevation angle of.5. The olletion parameters resulted in a temporal resolution of approximately 5.76 s. During the olletion period, there was a strong low-level northerly wind of approximately 8 m s 1 ausing a light dust storm.

3 8A.3A Phase measurement for a map of referene phase Phase Change φ (rad) 2 Purell 2 4 A map of phase differene: Image proessing: lutter quality, masking, smoothing Radial gradient Phase measurement during operation time Refrativity Change N Proessed φ (rad) 2 Figure 2: Proedure of refrativity retrieval Oklahoma Mesonet : 28 Sep 25 19: 19:25 UTC 4 (1) 19: (2) 19:5 (3) 19: (4) 19:15 (5) 19: (6) 19: Purell 1 2 Purell Figure 4: Refrativity field derived from surfae measurements of the OK Mesonet serves as the ground truth for validation of refrativity retrieval using the NWRT PAR. The solid 9- setor line indiates the area of interest for the PAR- Mesonet omparison Validation with OK Mesonet Sine the algorithm estimates the hange of refrativity, validation is also onduted on this quantity. By using the refrativity field from the OK Mesonet at the beginning of the experiment as referene, hange of refrativity field is derived for omparison. The measurements from the OK Mesonet will be used as ground truth to validate the estimates from the PAR measurements. Figures 4 shows a sequene of images of refrativity hange from the OK Mesonet. Figure 3 shows a similar plot but from the PAR measurements. More images are available but only a subset is shown here. The temporal resolution of the measurements from the OK Mesonet is 5 min, whih is the same temporal spaing between eah image in the most-left olumn of Figure Refrativity Change N (N unit) From this omparison between the PAR and the OK Mesonet, we are onfident that the refrativity field an be estimated with reasonable auray by applying the retrieval algorithm to the S-band PAR. In the next setion, rapid sanning using the PAR will be disussed by exploiting the agile beam steering apability of this eletroni sanning system First Results from the NWRT In this setion, the refrativity fields (derived from 64-pulse dwell) will be used as the ground-truth field. Subsets of ontiguous pulses will be extrated from eah san to simulate refrativity fields derived from shorter dwells, whih would result in faster san times. The goal is to investigate refrativity estimates from extremely short dwell-times. Here, 32, 16, 8, 4 and 2-pulse dwells will be tested and ompared against the referene (64-pulse dwell). It must be noted that 1-sample dwell was not tested beause radial veloity estimation would not be possible and is key for the determination of the usefulness of ground targets. Figure 5 illustrates an example of suh a omparison, where the number of pulses is indiated in parenthesis in the upper-left orner. The lower-right panel of Figure 5 shows the quality partitioning of the refrativity estimates. During the proess of deriving the refrativity field, the phase differene map needs be interpolated and smoothed (refer to Setion 4). In the smoothing proess, the phase values are first onverted into omplex form exp(jφ), with appropriate values set to zero for regions with poor ground targets. Subsequently, the real and imaginary omponents are proessed separately through a weight-and-sum proedure in order to ahieve the interpolation and smoothing. Smoothing in this manner avoids the abrupt phase wrapping and diffiulties with smoothing over suh transitions. While phase of this interpolated-and-smoothed map is used for refrativity alulation, the magnitude is used as our quality metri for refrativity field partitioning. For our statistial omparisons, three partitions have been reated to represent regions with high, mid and low quality of estimates. Different quality of refrativity fields are partitioned and extrated for performane evaluation. Figure 6 shows a plot of the root-mean-squared (RMS) differene (from the 64-point dwell) for various number of samples. As one would expet, for a partiular number of samples, the RMS error inreases as the quality metri dereases. On the other hand, as the number of samples inreases toward 64, the RMS differene dereases. These results show that refrativity retrieval is usable even for a 2-sample dwell time! Note that the RMS differene and its standard deviation at this small number of samples is only 1 N-unit and less than 1-N-unit, respetively, despite the noisy measurements available during the dust storm. A possible explanation for this exeptional performane is that the signal-to-noise (SNR) of the ground tar-

4 8A.3A 4 PAR (EL =.51 ) 28 Sep 25 19: 19:24 UTC N (N unit) (1) 19: UTC (2) 19:1 UTC (3) 19:2 UTC (4) 19:3 UTC (5) 19:4 UTC (6) 19:5 UTC (7) 19:6 UTC (8) 19:7 UTC (9) 19:8 UTC (1) 19:9 UTC (11) 19:1 UTC (12) 19:11 UTC (13) 19:12 UTC (14) 19:13 UTC (15) 19:14 UTC (16) 19:15 UTC (17) 19:16 UTC (18) 19:17 UTC (19) 19:18 UTC (2) 19:19 UTC (21) 19:2 UTC (22) 19:21 UTC (23) 19:22 UTC (24) 19:23 UTC (25) 19:24 UTC Figure 3: Time history of the refrativity hange field retrieved using the PAR measurements shows similar spatial and temporal hange from the refrativity fields derived from the OK Mesonet. During this 25-min period, one an see an inrease in the refrativity field in the north-western region but a derease in the region nearer the radar.

5 8A.3A 5 PAR (EL =.51 ) 28 Sep 25 19:15 UTC 4 64 samples 32 samples 16 samples 8 samples samples 2 samples N (N unit) Grouping High Mid Low Quality Grouping 2 2 Figure 5: Using the weight-and-sum phase values within the smoothing window, the resulted magnitude is used as a metri to indiate the quality of derived field. Here, the field is partitioned into three regions with different quality index (high, mid and low) for omparison. Root mean square error (N unit) Performane Index: Sep 28, 25 High Mid Low Number of points Figure 6: RMS error from Refrativity fields retrieved for various dwell times using the 64-sample ase as the referene. The RMS differene of the fields with smaller number of samples are evaluated to ompare them against the referene. gets is suffiiently high. SNR values of 4-6 db an still easily be found within the overage and represent the partiular targets used for the extration of refrativity retrieval. As suh, even a 2-sample dwell time (with spatial smoothing) suffies for the neessary phase measurements. of the phase estimate with smaller number of samples. This 2- sample dwell with a PRT of 1 ms translates into an extremely rapid 18 ms san for a 9 overage. 6. CONCLUSIONS In this artile, it has been shown that refrativity retrieval is viable using phase measurements from the S-band PAR of the NWRT. The refrativity fields were ompared and validated with surfae measurements from the OK Mesonet and were found to be in good agreement. Subsets of the raw samples from the PAR system were extrated to simulate faster san rates. From this proedure, it has been shown that refrativity retrieval an be aomplished suessfully with as little as two samples. If the MPAR system is to beome a reality, rapid refrativity retrieval is ertainly attrative and would add an important apability to the system. Referenes Bean, B. R., and E. J. Dutton, 1968: Radio Meteorology. Dover Publiations. Brok, F. V., K. C. Crawford, R. L. Elliott, G. W. Cuperus, S. J. Stadler, H. L. Johnson, and M. D. Eilts, 1995: The Oklahoma Mesonet: a tehnial overview. J. Atmos. Oeani Tehnol., 12, Dabberdt, W. F., and T. W. latter, 1996: Researh opportunities from emerging atmospheri observing modeling apabilities. Bull. Amer. Meteor. So., 77, Fabry, F., 24: Meteorologial value of ground target measurements by radar. J. Atmos. Oeani Tehnol., 21(4), Fabry, F., and C. Creese, 1999: If fine lines fail, try ground targets. in 29th Conf. Radar Meteor., pp , Montreal, Canada. Amer. Meteor. So. Fabry, F., C. Frush, I. Zawadzki, and A. Kilambi, 1997: On the extration of near-surfae index of refration using radar phase measurements from ground targets. J. Atmos. Oeani Tehnol., 14(4), Fabry, F., and C. Pettet, 22: A primer to the interpretation of refrativity imagery during IHOP 22. IHOP 22 Refrativity Manual. Forsyth, D. E., J. F. Kimpel, D. S. Zrnić, R. Ferek, J. F. Heimmer, T. MNellis, J. E. Crain, A. M. apiro, R. J. Vogt, and W. Benner, 25: The National Weather Radar Testbed (phased array). in 32nd Conf. Radar Meteor., p. CDROM 12R.3, Albuquerque, New Mexio. Amer. Meteor. So. Koh, S. E., A. Aksakal, and J. T. MQueen, 1997: The influene of mesosale humidity and evapotranspiration fields on a model foreast of a old-frontal squall line. Mon. Weather Rev., 125, Sensi, Jr., J., 1988: The AEGIS system. in Aspets of Modern Radars, pp Arteh House. Weber, M., J. Cho, J. Flavin, J. Herd, and M. Vai, 25: Multifuntion phased array radar for U.S. ivil-setor surveillane needs. in 32nd Conf. Radar Meteor., pp , Albuquerque, New Mexio. Amer. Meteor. So. Wekwerth, T. M., and D. B. Parsons, 23: An overview of the International H 2 O Projet (IHOP 22). Bull. Amer. Meteor. So., 85(2),