13A.3 ASSIMILATION OF POLARIMETRIC RADAR DATA USING ENSEMBLE KALMAN FILTER: EXPERIMENT WITH SIMULATED DATA. University of Oklahoma, Norman OK 73019

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1 13A.3 ASSIMILATION OF POLARIMETRIC RADAR DATA USING ENSEMBLE KALMAN FILTER: EXPERIMENT WITH SIMULATED DATA Youngun Jung 1,2, *, Ming Xue 1,2, and Jerry M. Straka 1 1 School of Meteorology and 2 Center for Analyi and Prediction of Storm Univerity of Oklahoma, Norman OK Introduction Since the ue of differential reflectivity for rainfall etimation a firt propoed by Seliga and Bringi (1976), many tudie have hon that polarimetric meaurement can improve precipitation type claification and quantitative precipitation etimate (Straka et al. 2000). Moreover, the polarimetric radar (PR) upgrade plan of the National Weather Service (NWS) for the operational WSR-88D netork radar ill undoubtedly motivate more active reearch on the utilization of PR data. A more accurate etimate of the amount of hydrometeor uing PR data can contribute to the improvement and verification of microphyical parameterization in cloud and meocale model. It can provide a ueful mean for the initialization of hydrometeor type and amount for torm-cale and meocale NWP model, and help the verification of quantitative precipitation forecat (QPF). Such etimation can alo help enhance our undertanding of the interaction beteen microphyic and kinematic in evere torm and meocale ytem (Straka et al. 2000). Polarimetric radar alo hould be helpful for torm-cale model initialization through data aimilation. Initialization of convective torm uing radar data ithin a numerical model ha enjoyed reaonable ucce in recent year, uing method uch a the complex cloud analyi, 4DVAR and more recently the enemble Kalman filter (EnKF). The firt paper hich invetigate the potential of EnKF to aimilate Doppler radar data into cloud model ith a arm rain microphyic only i Snyder and hang (2003). In their tudy, tate variable not directly oberved are uccefully retrieved uing EnKF. The recent tudie of Tong and Xue (2005, TX05 hereafter) and Xue et al. (2005, hereafter XTD05) alo ho that the cloud field, including microphyical pecie aociated ith a 3-ice microphyic cheme, can be accurately retrieved uing the EnKF method from imulated radial velocity and reflectivity data. It i expected that the analyi reult can be further * Correponding author addre: Youngun Jung, School of Meteorology, Univerity of Oklahoma, Norman OK youngun.jung@ou.edu improved hen additional polarimetric parameter are aimilated. The parameter include differential reflectivity ( dr ), pecific differential phae (K dp ) and poibly ome other parameter for hydrometeor claification. Wu et al. (2000) ued dr indirectly in a cloudcale 4DVAR data aimilation ytem; the reflectivity () and differential reflectivity ere firt converted to rain and ice mixing ratio hich are ubequently aimilated together ith the radial velocity (V r ) data. In thi tudy, the direct aimilation of dual polarization radar data uing an enemble Kalman filter i explored for the firt time. Forard obervation operator for the polarimetric radar meaurement that are conitent ith microphyic cheme ith varying degree of aumption are firt developed and their enitivitie to the aumption are examined. Thee obervational operator are then ued to create imulated data et from a model torm, and the impact of thee data are examined through Oberving Sytem Simulation Experiment (OSSE). 2. Decription of aimilation experiment a. The aimilation cheme and prediction model The particular variant of enemble Kalman filter ued in thi tudy i the enemble quare-root filter (EnSRF) after Whitaker and Hamill (2002). The OSSE frameork ued in thi tudy i decribed in detail by XTD05. The phyical domain ued for the experiment i km 3 ith a horizontal pacing of 1.5 km and a vertically tretched grid ith a minimum grid pacing of 100m near the urface. The Advanced Regional Prediction Sytem (ARPS) i ued in both imulation and analyi and i documented in Xue et al. (2000; 2001; 2003). The truth imulation i initialized in the ame ay a for the lo-moving ytem in the mall domain of XTD05. The environmental ounding ued to for the truth imulation i that of the 20 May 1977 Del City, Oklahoma upercell torm. Our experiment are an extenion of experiment named TLX decribed in XTD05, ith the addition of polarimetric data meaurement. b. Obervation operator The et of forard obervation operator that link the 1

2 dual polarization meaurement ith the model tate variable are firt developed and effort are made to enure their conitency ith the ARPS 3-ice microphyic cheme baed on Lin et al. (1983). Thee obervation operator are then incorporated into our EnSRF ytem to aimilate the correponding polarimetric parameter. The equivalent reflectivity of raindrop for horizontal and vertical polarization are, baed on hang et al. (2001), repectively, and at around x = -18 and y = 14 km, here the reflectivitie are at a maximum. Thee maxima are due to high concentration of hail in thee precipitation core, here the aociated dr i eak; thi behavior i conitent ith our dr formulation (4). rh rv 4 λ α a n0 (2β a + 1) = Λ Γ(2β + 1) (1) a π K 4 ) λ α b n0 (2β b + 1 = Λ Γ(2β + 1) (2) b π K here λ = 10.7 cm i the avelength, that of the WSR- 88D radar, n 0 = m -4 i the intercept parameter of the exponential drop ize ditribution, K = 0.93 i the dielectric factor for ater, and α a = , α b = , β a = 3.02, and β b = 2.69 are nondimenional coefficient. For dry no, the equivalent reflectivity equation given belo folloing Ryzhkov et al. (1998) replace Eq. (5) of TX05: a1 Γ(2δ + 1) 2 2δ + 1, dry = γ D Γ( δ + 1) 2 n n, (3) 9 K Γ( δ + 1) here a 1 = 7.3, δ = 1.9, γ = π, n = m -4. D n i the characteritic diameter defined a the invere of lope parameter Λ. In thi formula, the denity of no i a function of ize (Locatelli and Hobb 1974), o it i not exactly conitent ith the ARPS microphyic that aume a ingle denity for no. Thi formula give ignificantly maller reflectivity value at high altitude here mot ice crytal are mall. In the future, e ill eek to upgrade the ARPS microphyic for the no denity to depend on particle diameter. The formula for et no and dry and et hail are the ame a thoe given in TX05. Thoe equivalent reflectivitie for different pecie are combined to give differential reflectivity hh rh + + h = 10 log = 10 10log. (4) vv rv + + h dr 10 Here, hh and vv are the reflectivitie at horizontal and vertical polarization, repectively. The firt ubcript r, and ingle ubcript and h denote rainater, no and hail, repectively. An example of imulated and dr at the 1.5 km altitude at 90 minute of truth torm i preented in Fig. 1. We ho the 1.5-km level becaue dr i uually greater at loer altitude here the hydrometeor are motly raindrop. In contract to the reflectivity field, dr ho to minima near the center of domain Fig. 1. The reflectivity at horizontal polarization (upper panel) and differential reflectivity dr (loer panel) at 1.5 km altitude at 90 min of truth torm. c. The experiment deign A in XTD05, initial enemble member are initialized at t=20 min of model time by adding random perturbation of Gauian ditribution to the initially horizontal homogeneou firt gue defined by a ounding. The preure and microphyical variable are not perturbed. The firt aimilation of imulated obervation i performed at 25 min of model time and the analye are repeated every 5 min until 100 min. The filter ue 40 enemble member. A ingle WSR-88D radar that can 2

3 the model atmophere i located to the northeat at about 90 km from the center of model grid. We examine in particular the impact of aimilating differential reflectivity ( dr ) and reflectivity at vertical polarization ( vv ), in addition to radial velocity (V r ) and reflectivity at horizontal polarization ( hh ), on the analyi and prediction of the thundertorm. It i aumed that dr i only available here it value i equal to or greater than 0 db. Thu, dr i aimilated only here it value i greater than 0 db. vv i aimilated only here hh i greater then 10 db to ave computation hile hh data ithin the entire radar range are aimilated. For more detailed information on the configuration of the aimilation experiment, the reader i referred to XTD05. d. Obervation A Gauian poer-gain eighting function decribed in XTD05 i alo ued to imulate hh, vv, and V r obervation on the radar elevation plane from the gridded field of the truth imulation. Operational polarimetric WSR-88D radar ill meaure hh and vv from the ame pule. A a reult, ome of the error in hh and vv hould be correlated, hich hould reduce the error in dr becaue dr i related to the ratio of hh and vv. We therefore model the error in hh and vv uing o hh o vv t = hh + ε c + ε, h t = + ε + ε, (5) vv c v here upercript t and o denote the truth and imulated obervation, repectively. ε c repreent the correlated part of error and ε h and ε v are uncorrelated error for hh and vv, repectively. For example, random error ε c and ε h (and ε v ) are independently ampled from Gauian ditribution of zero mean and tandard deviation of 3.0 db and 0.22 db, repectively and added to the truth. Thi et of error reult in hh error of about 2.2 db and dr error of about 0.2 db hen calculated for the data collected over the entire domain for the entire aimilation time in term of tandard deviation. The error of vertically polarized reflectivity are treated in a imilar ay. Thee error ize hould be valid for ell-calibrated radar (A. Ryzhkov, peronal communication, 2005). Standard deviation of V r error i aumed to be 2 m -1. The tandard deviation of error aumed for and V r are 5 db and 1 m -1, repectively, in XTD05 and TX Reult Out of curioity, e firt tried aimilating dr data alone, ithout radial velocity or regular reflectivity data. The reult of analyi ere poor (not hon). Thi i not urpriing becaue dr mainly carrie the information on the difference beteen reflectivitie of horizontal and vertical polarization; it doe not provide much information on the magnitude of the reflectivity, and i therefore by itelf not able to analyze the mixing ratio of cloud and hydrometeor field. Hoever, a ill be hon, dr ha a poitive impact on analyi hen combined ith reflectivity and radial velocity data. We further examined the impact of aimilating both hh and vv. It i found that aimilating vv in addition to hh and V r ha almot no impact ith the tandard deviation of obervational error pecified earlier (not hon). The impact of aimilating vv hen the error in hh and V r are increaed ill be explored further in a later tudy. Fig. 2 ho the root-mean-quare (rm) error curve for each model tate variable during the aimilation period. It can be een that aimilating additional polarimetric meaurement, dr, improve the analye. Improvement motly dramatic in rain ater mixing ratio, q r, a the correponding black curve ho loer error. The vertical profile of rm error at the end of the aimilation cycle, i.e., at 100 min, are plotted in Fig. 3. It i een that the error in vertical velocity are decreaed at all level by aimilating dr among the ind field. Again, the reduction of error i larget for q r. Thi i reaonable becaue dr i mot trongly tied to raindrop. It hould be noted that becaue the analyi uing V r and hh a already very good, there i not too much room for further improvement, ithin the current OSSE frameork ith the perfect model aumption. For real data cae here model error and data quality problem do exit, the extra information content afforded by the polarimetric data i expected to produce larger impact. Thi ill be examined in the future. We have alo examined the enitivity of analyi to obervational operator ith larger reflectivity error. We performed the experiment in hich the reflectivity obervation are generated uing the formula in XTD05 hile the aimilation i performed uing the equation preented in thi paper and vice vera. The reult ho that EnSRF i not enitive to the difference beteen thee to et of obervation operator hen V r i aimilated along ith hh. When hh i aimilated alone, the difference in q field i noticeable (not hon). Thi agree ith the dicuion in ection 2b. We ill reviit thi iue hen conidering the cae here more uncertaintie in the obervational operator and/or hen the prediction model error are preent. 4. Summary and dicuion In thi tudy, e extended our enemble quare-root Kalman filter to aimilate, in addition to regular reflec- 3

4 tivity and radial velocity, the imulated differential reflectivity and the reflectivity at vertical polarization, for a upercell torm. It i found that the aimilation of dr, in addition to conventional reflectivity and radial velocity, improve the analyi, and among the tate variable, the poitive impact i larget for q r. A poitive impact can be een in even though it i not very ignificant. Future ork ill include the aimilation of additional parameter uch a pecific differential phae. Due to the lack of the relationhip beteen polarimetric variable except for dr and different type of hydrometeor including raindrop, hail, graupel, no and crytal, ne formula may need to be derived. One poible approach i to ue radar cattering model and T-matrix method to derive the relationhip. Thee obervation operator ill alo be refined baed on obervational evidence and for them to be coupled ith more ophiticated microphyic. For horter avelength radar, uch a the X-band radar to be intalled by the ne NSF Engineering Reearch Center for Collaborative Adaptive Sening of the Atmophere (CASA), the project that upport the current ork, attenuation i an iue that ha to be dealt ith. An appropriate attenuation correction for the polarimetric meaurement need to be built into the obervation operator and/or applied to the data. We hope the additional polarimetric radar meaurement to be helpful for improving attenuation correction alo, a it help to improve the analyi of hydrometeor content. Future tudie ill alo include an aement of the ability of our aimilation ytem for quantitative precipitation etimation (QPE). Acknoledgement The author thank Mingjing Tong for many her help on the initial ue of the Kalman filter code. We alo thank Dr. Alexander Ryzhkov for many ueful dicuion on polarimetric radar meaurement. Thi ork a primarily upported by NSF grant EEC Ming Xue a alo upported by NSF grant ATM , ATM , ATM and ATM The computation ere performed at the Pittburgh Supercomputing Center upported by NSF. Reference Lin, Y.-L., R. D. Farley, and H. D. Orville, 1983: Bulk parameterization of the no field in a cloud model. J. Climate Appl. Meteor., 22, Locatelli, J. D. and P. V. Hobb, 1974: Fall peed and mae of olid precipitation particle. J. Geophy. Re., 79, Ryzhkov, A. V., D. S. rnic, and B. A. Gordon, 1998: Polarimetric method for ice ater content determination. J. Appl. Meteor., 37, Seliga, T. A. and V. N. Bringi, 1976: Potential ue of radar differential reflectivity meaurement at orthogonal polarization for meauring precipitation. J. Appl. Meteor., 15, Snyder, C. and F. hang, 2003: Aimilation of imulated Doppler radar obervation ith an enemble Kalman filter. Mon. Wea. Rev., 131, Straka, J. M., D. S. rnic, and A. V. Ryzhkov, 2000: Bulk hydrometeor claification and quantification uing polarimetric radar data: Synthei of relation. J. Appl. Meteor., 39, Tong, M. and M. Xue, 2005: Enemble Kalman filter aimilation of Doppler radar data ith a compreible nonhydrotatic model: OSS Experiment. Mon. Wea. Rev., Whitaker, J. S. and T. M. Hamill, 2002: Enemble data aimilation ithout perturbed obervation. Mon. Wea. Rev., 130, Wu, B., J. Verlinde, and J. Sun, 2000: Dynamical and microphyical retrieval from Doppler radar obervation of a deep convective cloud. J. Atmo. Sci., 57, Xue, M., K. K. Droegemeier, and V. Wong, 2000: The Advanced Regional Prediction Sytem (ARPS) - A multicale nonhydrotatic atmopheric imulation and prediction tool. Part I: Model dynamic and verification. Meteor. Atmo. Phyic, 75, Xue, M., M. Tong, and K. K. Droegemeier, 2005: An OSSE frameork baed on the enemble quareroot Kalman filter for evaluating impact of data from radar netork on thundertorm analyi and forecat. J. Atmo. Ocean Tech., Accepted. Xue, M., D.-H. Wang, J.-D. Gao, K. Breter, and K. K. Droegemeier, 2003: The Advanced Regional Prediction Sytem (ARPS), torm-cale numerical eather prediction and data aimilation. Meteor. Atmo. Phyic, 82, Xue, M., K. K. Droegemeier, V. Wong, A. Shapiro, K. Breter, F. Carr, D. Weber, Y. Liu, and D.-H. Wang, 2001: The Advanced Regional Prediction Sytem (ARPS) - A multicale nonhydrotatic atmopheric imulation and prediction tool. Part II: Model phyic and application. Meteor. Atmo. Phy., 76, hang, G., J. Vivekanandan, and E. Brande, 2001: A method for etimating rain rate and drop ize ditribution from polarimetric radar meaurement. IEEE Tran. Geoci. Remote Sen., 39. 4

5 Fig. 2. The rm error of enemble-mean forecat and analyi, averaged over point at hich the reflectivity i greater than 10 db for: a) u, b) v, c) and d) perturbation potential temperature θ', e) perturbation preure p', f) cloud ater q c, g) rainater q r, h) ater vapor q v (the curve ith larger value), cloud ice q i (the curve ith loer value), i) no q, and j) hail q h, for the experiment that ue V r and only (red dahed), and the experiment that aimilate in addition dr (thin black). The drop of the error curve at pecific time correpond to the reduction of forecat error by analyi. Fig. 3. The vertical profile of rm error of EnSRF analyi at 100 min averaged over the entire horizontal domain for: a) u, b) v, c), d) θ', e) p', f) q c, g) q r, h) q v, i) q, and j) q h, for the experiment that ue V r and only (red dahed), and the experiment that aimilate dr (thin black). 5