REFRACTIVITY RETRIEVAL USING THE CASA X-BAND RADARS

Transcription

1 P8B.9 1 REFRACTIVITY RETRIEVAL USING THE CASA X-BAND RADARS B. L. Cheong 1,, K. Hardwik 2, J. Fritz 3, P. S. Tsai 2, R. D. Palmer 1, V. Chandrasekar 3, S. Frasier 2, J. George 3, D. Brunkow 4, B. Bowie 4 and P. Kennedy 4 1 Shool of Meteorology, University of Oklahoma, Norman, Oklahoma, USA 2 Department of Eletrial and Computer Engineering, University of Massahusetts, Amherst, Massahusetts, USA 3 Department of Eletrial and Computer Engineering, Colorado State University, Fort Collins, Colorado, USA 4 Department of Atmospheri Siene, Colorado State University, Fort Collins, Colorado, USA Abstrat For most weather radars, suh as the WSR-88D, refletivity, radial veloity and spetrum width are the only parameters estimated. Reently, a tehnique to retrieve near-surfae refrativity has been developed by Fabry et al. [1997]. The tehnique relies on the returned phase from ground lutter whih hanges aording to the refrativity of the atmosphere. Until reently, most refrativity measurements have been foused on S-band radars. These radars are usually designed, however, to observe long ranges and are therefore limited in range by the earth urvature effet. As part of the CASA NSF Engineering Researh Center, higher-frequeny X- band radars have been designed for observations of the lower atmosphere. The initial network (IP-1) onsists of four radars and is loated in south-west Oklahoma. Beause of the loser spaing of these radars (approximately 3 km), in omparison to the WSR-88D network, the IP-1 network is less suseptible to the earth urvature effet and an provide more omplete overage of estimated refrativity. A signifiant hallenge arises, however, with shorter wavelength radars in the implementation of refrativity retrieval. The refrativity retrieval tehnique relies on the phase hange between two radar sans. One is referred to as the referene san and the other as the measurement san. A typial field of phase-hange between these two sans exhibits a phase wrapping signature that depends on the refrativity hange between the two sans and the radar wavelength. For X-band radars, the phase obviously wraps more frequently in omparison to S-band radars, whih makes subsequent proessing steps problemati. To mitigate this problem, we have proposed an algorithm alled Differential Refrativity Retrieval (DRR), whih aumulates phase differenes from san-to-san rather than over a longer time period, as is urrently the pratie. As a result, typial atmospheri hanges over suh Corresponding author address: Boon Leng Cheong, University of Oklahoma, Shool of Meteorology, 12 David L. Boren Blvd., Rm 464, Norman, OK ; boonleng@ou.edu a short time (less than 5 min) do not ause a signifiant hange in signal phase, minimizing phase wrapping. As a possible drawbak, error aumulation aused by the DRR algorithm will be investigated as a limitation of the tehnique. A field experiment was onduted during REFRACTT-26 using a mobile X-band radar (XPOL) developed by the University of Massahusetts. Results from the XPOL radar and the CASA IP-1 network will be presented to illustrate the feasibility of refrativity retrieval using X-band radars. 1. INTRODUCTION Often suggested as a proxy to estimate the surfae moisture, the refrativity field retrieved from radars have reently reeived inreasing attention in the meteorologial ommunity. The moisture field near the earth s surfae is highly related to onvetive preipitation initiations [e.g., Dabberdt and Shlatter, 1996; Koh et al., 1997]. The auray of onvetive rainfall predition an be improved by having an aurate foreast of when and where onvetion will develop. Using the surfae refrativity from radars, higher spatial and temporal resolution an be ahieved ompared to the measurements from existing surfae instruments. For example, radiosonde networks provide hourly measurement but this is insuffiient for predition and understanding of fast evolving onvetive proesses [Wekwerth and Parsons, 23]. Based on the onept by Fabry [24], a similar but independent refrativity retrieval algorithm has been developed here at the University of Oklahoma [Cheong et al., 27] and has been tested on X-band radars. For the X-band magnetron-based radars, the algorithms were modified in order to aommodate the ompliations indued by the shorter wavelengths, i.e., more frequent phase wraps in omparison to S-band radars, and, thus, ompliates the subsequent proessing. A proposed algorithm referred to as Differential Refrativity Retrieval (DRR) aumulates refrativity hange over a short period of time, e.g., a 3-minute sanning yle

2 P8B.9 2 that is urrently used by the CASA IP-1 network, to mitigate the rapid phase wrapping phenomena. As a result, relatively small atmospheri hanges over suh a short time do not ause a signifiant hange in the signal phase, whih minimizes phase wrapping. A possible and pertinent drawbak of the DRR is the aumulation of error over a long period of time. 2. OVERVIEW OF RADAR REFRACTIVITY RE- TRIEVAL (SAME AS P8B.8) 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 T e T 2 (2) where p represents the air pressure in hetopasal (hpa), 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. 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. In theory, given that the reeived phase from stationary targets is a path-integrated funtion of the refrative index, whih 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) If the refrativity field of the referene san (t ) 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) where 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, high-quality network of surfae stations, known as the OK Mesonet [Brok et al., 1995; MPherson et al., 27]. 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. A flowhart of refrativity retrieval algorithm is provided in Figure 1. 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 phasedifferene 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. 3. DIFFERENTIAL REFRACTIVITY RETRIEVAL Using X-band radars in omparison to S-band, the shorter wavelength introdues a rapid phase wrapping

3 P8B Reno 2 kasha Phase measurement for a map of referene phase Proessed φ (rad) 2 Oklahoma City KOUN/PAR Norman Purell KTLX Sh 2 4 A map of phase differene: Image proessing: lutter quality, masking, smoothing Radial gradient Phase measurement during operation time 4 Reno 2 kasha 4 Reno 2 Phase Change φ (rad) 2 Oklahoma City KTLX KOUN/PAR Norman Purell Sh 2 4 Refrativity Change N kasha Oklahoma City Figure 1: Proedure of refrativity retrieval 1 2 KTLX KOUN/PAR Norman Purell Sh 2 4 in the map of phase differene (refer to Equation (4)). The interpolation and smoothing proess (refer to Setion 2) often fails when phase wrapping is too rapid. In order to mitigate the rapid phase folding, DRR was proposed given that atmospheri hange over a short amount of time is expeted to be minimal and, thus, the phase wrapping is minimized [Palmer et al., 26]. By aumulating the refrativity hange over these short time intervals, a total hange is obtained. An obvious drawbak of this tehnique is that estimation error/bias an aumulate over time whih would diverge the estimate far away from the true values. Another ompliation from using the XPOL and the IP- 1 radars is the frequeny drift of the magnetron osillator. During the REFRACTT-26 ampaign, the mobile XPOL radar from University of Massahusetts was used for initial test of refrativity retrieval using an X- band radar. At that time, the effets of frequeny drifts on the refrativity retrieval algorithm were not well understood. Therefore, raw phase measurements and the frequeny of the magnetron were monitored and stored in the hope of re-proessing the data later in order to aount for the effets indued by the drifting frequeny. Later, however, we learned that even without orretion of frequeny drift, the estimates of refrativity hange were well ompared with the surfae measurements. To resolve this issue, we began by investigating the proedure of retrieving refrativity hange, whih an be desribed as N = 1 6 d 4πf dr [φ(r, t 1) φ(r, t 2 )]. (6) One an see that Equation (6) is simply a rearrangement and onversion from refrative index to refrativity of Equation (5). In pratie, the derivative operator in Equation (6) is applied as a finite-differene operator desribed by Equation (7). Due the frequeny drift of the magnetron, additional phase offsets are introdued from time t to time t 1 at the phase measurements. Here, we represent the phase offsets as φ f and φ ǫ in Equation (8). Note that the amount of phase offset due to frequeny drift are lose to eah other for range bins (r r) and r. That is, range bin (r r) and r both have the total phase offsets of φ f and φ f +φ ǫ, respetively. As suh φ f anels due to the derivative operator in the refrativity algorithm and we are left with the residual term φ f, whih is small and insignifiant for the DRR method. This residual phase offset an be desribed mathematially as ǫ φ = 4π f r. (1) The 3-minute frequeny differene of the magnetron of XPOL as an example frequeny drift expeted from a 3- minute volume sanning onfiguration is shown in Figure 2. As mentioned earlier, this amount of frequeny drift results in negligible effets using DRR. For example, given r = 3 m, λ =.3 m and f = 1 khz, the resultant phase error is merely.72 (.126 rad), whih is muh less than the typial measurement noise. Therefore, the refrativity hange from DRR should be in agreement with the surfae measurements from radiosonde without any ompensation for the frequeny drift of the magnetron. Frequeny in khz Minute Frequeny Differene 25 : :1 :2 :3 :4 :5 1: Time in Hour Figure 2: A typial 3-minute frequeny differene of the magnetron of XPOL obtained by alulating the total basedband frequeny drift within a 3-minute running window. Similar but a less severe frequeny-drifting behavior an be expeted from IP-1 radars sine the magnetron is housed inside a temperature-onditioned environment. 4. EXPERIMENTAL RESULTS AND FINDINGS As part of the REFRACTT 26 ampaign, an experiment was onduted during July 26 using the XPOL radar, whih is an X-band, magnetron-based mobile radar developed by the University of Massahusetts, Amherst. Real-time raw data were proessed for phase

4 P8B.9 4 d dr [φ(t 1) φ(t )] 1 r {[φ t 1 (r) φ t (r)] [φ t1 (r r) φ t (r r)]} (7) d dr [φ(t 1) φ(t )] 1 r {[φ t 1 (r) φ t (r) + φ f + φ ǫ ] [φ t1 (r r) φ t (r r) + φ f ]} (8) = 1 r {[φ t 1 (r) φ t (r) + φ ǫ ] [φ t1 (r r) φ t (r r)]} (9) measurements and the standard moment for refrativity retrieval. Frequeny drift of the magnetron was reorded via the transmit pulse in the raw data for later postproessing. As mentioned earlier in Setion 3, however, frequeny drift orretion is negligible for DRR proessing and, thus, results from this setion are not frequeny orreted. Another investigation was onduted using the dataset olleted on September 17, 26 using two CASA radars of the IP-1 network. At the present time, the CASA IP-1 allows for user input for the operation of the system. Eah yle is at an inrement of 3-seond interval, or a so-alled heartbeat [Brotzge et al., 26]. Depending on the volume overage pattern, eah elevation maybe revisited every 5 heartbeats, i.e., the lowest elevation an be expeted to be revisited no longer than 3 minutes and, thus, the frequeny drifting behavior should be less severe than the 3-minute differene of the XPOL s magnetron mentioned in Setion Results from REFRACTT 26 Using XPOL Sine the ore of the refrativity retrieval algorithm derives refrativity hange, omparisons with other instruments are essential. Using one of the longest ontiguous dataset olleted during REFRACTT 26 with XPOL, i.e., a 6-hour ontiguous data from July 27, 26, we ompare the refrativity hange derived from the XPOL radar and values of refrativity hange derived from surfae measurements (via Equation (2)) from the nearby radiosonde (RAOB) stations. These RAOB stations are loated approximately 2 km and 3 km away from the XPOL radar, respetively. During this time period, a refrativity hange of more than 2 N units was reorded and an be seen to be in good agreement in Figure Preliminary Results From IP-1 Network From the dataset reorded on September 17, 26 with the CASA IP-1 network, a 2-hour ontiguous subset with two radars operating simultaneously from 13:55 to 15:55 N unit Refrativity Change from XPOL 27 Jul 26 XPOL RAOB KGXY RAOB KFNL 3 17: 18: 19: 2: 21: 22: 23: UTC Time Figure 3: A 6-hour N retrieved using the XPOL and from the surfae measurement of nearby radiosonde are in good agreement. The two RAOB stations KGXY and KFNL are approximately 2 km and 3 km, respetively, away from the XPOL radar. UTC were seleted for the investigation with the DRR. During this time period, a weak storm was passing from the west of the domain. Differential refrativity fields are aumulated for the total hange of refrativity sine 13:55 UTC and is shown in the time history plot in the top half of Figure 4. The same quantity is derived from the surfae measurements of the OK Mesonet and is shown in the bottom half of Figure 4. From this omparison, one an easily see a general agreement between the measurements from IP-1 network and OK Mesonet during this 2-hour period. More importantly, an apparent spatial struture annotated in ovals an be seen from both measurements. With this omparison, we an see the promising potential of retrieving refrativity using the CASA IP-1 network. 5. CONCLUSIONS In this projet, the possibility of retrieving refrativity using CASA X-band radars were investigated and found to show signifiant potential. The field experiment during the REFRACTT-26 using the XPOL radar provided us an opportunity to learn that DRR produes refrativity hange that is onsistent with the surfae measurement despite the frequeny drifting behavior inherent in the magnetron osillator. The DRR algorithm was developed with the goal to overome rapid phase wrapping using shorter wavelengths suh as the CASA X-

5 P8B.9 5 IP 1 (EL =. ) 17 Sep 26 13:55:8 15:55:16 UTC (1) 13:55:8 UTC KCYR KSAO KRSP (2) 14:5:9 UTC (3) 14:15:9 UTC (4) 14:25:1 UTC (5) 14:35:11 UTC (6) 14:45:11 UTC (7) 14:55:12 UTC (8) 15:5:12 UTC (9) 15:15:13 UTC (1) 15:25:14 UTC (11) 15:35:14 UTC (12) 15:45:15 UTC (13) 15:55:16 UTC Refrativity Change N (N unit) Oklahoma Mesonet : 17 Sep 26 13:55 15:55 UTC (1) 13:55 Anadarko KSAO Chikasha KCYR KRSP (2) 14:5 (3) 14:15 (4) 14:25 (5) 14: (6) 14:45 (7) 14:55 (8) 15:5 (9) 15:15 (1) 15: (11) 15:35 (12) 15:45 (13) 15:55 Refrativity Change N (N unit) Figure 4: Total refrativity hange sine 13:55 UTC using the phase measurements from IP-1 network and surfae measurements from the OK Mesonet are in agreement. By using the DRR method, frequeny drift effets is minimal.

6 P8B.9 6 band radars. In addition, in this paper, we revealed that by using the DRR algorithm, moderate frequeny drift, e.g., 1 khz in 3 minutes for the XPOL radar, an be negleted if the DRR algorithm is applied. Future work inlude the investigation of error propagation using the DRR method. Referenes Palmer, R. D., B. L. Cheong, K. Hardwik, P. S. Tsai, S. J. Frasier, B. Bowie, P. Kennedy, D. Brunkow, and V. Chandrasekar, 26: Refrativity retrieval using X- band radars: Mitigation of rapid phase wrapping. in PIERS 26, 2-5 August, Tokyo, Japan. 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), 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, Brotzge, J. A., K. K. Droegemeier, and D. J. MLaughlin, 26: Collaborative Adaptive Sensing of the Atmosphere (CASA): New radar system for improving analysis and foreasting of surfae weather onditions. J. Transport. Res. Board, 1948, Cheong, B. L., R. D. Palmer, C. D. Curtis, T.-Y. Yu, D. S. Zrnić, and D. Forsyth, 27: Refrativity retrieval using the phased array radar: First results and potential for multi-funtion operation. J. Atmos. Oeani Tehnol., to be submitted. Dabberdt, W. F., and T. W. Shlatter, 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., 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), 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, MPherson, R. A., C. A. Fiebrih, K. C. Crawford, R. L. Elliott, J. R. Kilby, D. L. Grimsley, J. E. Martinez, J. B. Basara, B. G. Illston, D. A. Morris, K. A. Kloesel, S. J. Stadler, A. D. Melvin, A. J. Sutherland, H. Shrivastava, J. D. Carlson, J. M. Wolfinbarger, J. P. Bosti, and D. B. Demko, 27: Statewide monitoring of the mesosale environment: A tehnial update on the Oklahoma Mesonet. J. Atmos. Oeani Tehnol., 24(3),