3.01 ASSIMILATION OF DOPPLER RADAR OBSERVATIONS USING WRF/MM5 3D-VAR SYSTEM AND ITS IMPACT ON SHORT-RANGE QPF

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1 3.01 ASSIMILATION OF DOPPLER RADAR OBSERVATIONS USING WRF/MM5 3D-VAR SYSTEM AND ITS IMPACT ON SHORT-RANGE QPF Qingnong Xiao 1*, Ying-Hwa Kuo 1, Juanzen Sun 1, Jianfeng Gu 2, Euna Lim 3, Dale M. Barker 1, Wen-Cau Lee 1, and Yong-run Guo 1 1. National Center for Atmosperic Researc, Boulder, Colorado, USA 2. Sangai Weater Forecast Center, Sangai, Cina 3. Korean Meteorological Administration, Seoul, Korea 1. INTRODUCTION Altoug tere ave been marked improvements in recent years, quantitative precipitation forecasting (QPF) is still a callenging problem for mesoscale and microscale weater prediction. One of te fundamental underlying reason for tis callenge is tat precipitation is often concentrated in convective cells, or mesoscale bands or clusters wic are difficult to be presented in te model s initial conditions from te large-scale analysis. An immediate step in addressing tis problem is to develop a mesoscale and microscale data assimilation system and utilize observations wic matc te spatial and temporal scales of tunderstorms and oter samll scale weater features. During te past several years, NCAR developed te capabilities to assimilate Doppler radial velocity (Xiao et al. 2005) and reflectivity (Xiao et al. 2004) data using te WRF/MM5 tree dimensional variational (3D-Var) data assimilation system (Barker et al. 2004). Te major development of te Doppler radar data assimilation in te WRF/MM5 3D-Var system is inclusion of te analyses (increments) for vertical velocity and cloud water and rainwater mixing ratios. Altoug te 4D-Var approac is usually used for retrieving all tese fields (Sun and Crook, 1997; 1998), 3D-Var as advantages due to its computational efficiency. In te continuous cycling mode, 3D-Var can also integrate te model nonlinearity into te analysis. We will present te metodology for te WRF/MM5 3D-Var System to generate vertical velocity increments, as well as increments of cloud water and rainwater mixing ratios. We will also describe te observation operators for Doppler radial velocity and reflectivity in te WRF/MM5 3D-Var system. Te results of te 3D- Var radar data assimilation system in case studies of an IHOP squall line case of 13 June 2002 in te United States, a eavy *Corresponding autor address: Qingnong Xiao, National Center for Atmosperic Researc, Boulder, CO , USA, siao@ucar.edu. rainfall case in East Asia, and operational applications in Korea Meteorological Administreation (KMA) will be sown. We obtain positive impacts of te Doppler radar data assimilation on te sort-range quantitative precipitation forecasting (QPF). 2. METHODOLOGY 2.1 WRF/MM5 3D-Var Te configuration of te WRF/MM5 3D-Var system is based on te multivariate incremental formulation. Te preconditioned control variables in tis study are stream function, velocity potential, unbalanced pressure and total water mixing ratio q t. Te background error statistics can be carried out via NMC-metod (Paris and Derber 1992) or ensemble metod (Fiser et al., 1999). Horizontally isotropic and omogeneous recursive filters are applied to te orizontal components of background error. Te vertical component of background errors is projected onto climatologically averaged (in time, longitude, and optionally latitude) eigenvectors of te estimated vertical error. A detailed description of te 3D-Var system can be found in Barker et al. (2004). 2.2 Vertical velocity increments Based on Ricardson (1922), a balance equation tat combines te continuity equation, adiabatic termodynamic equation, and ydrostatic relation is derived and expressed as: w γ p = γ p v + v p g (ρv) dz (1) z z were w is vertical velocity, v is te vector of orizontal velocity (components u and v), γ te ratio of specific eat capacities of air at constant pressure/volume, p pressure, ρ density, T temperature, c p specific eat capacity of air at constant pressure, z eigt, and g te acceleration due to gravity. For simplicity, ereafter Eq. (1) will be referred to as te Ricardson s equation. For te future applications, latent eat term wic uses

2 convective parameterization can be included. Linearizing Eq. (1) by writing eac variable in terms of a basic state (overbar) plus a small increment (prime) gives: w w uur uur uur γ p = γ p γ p v γ p v v p z z uur uur uur v p+ g ( ρv ) dz+ g ( ρ v ) dz z z (2) Te basic state (overbar) variables satisfy Eq. (1). Tey also satisfy te continuity equation, adiabatic equation and ydrostatic equation. Te linear and adjoint of Ricardson s equation are incorporated into te 3D-Var system, wic serve as a bridge between te 3D-Var analyses and te vertical velocity component of te Doppler radial velocity observations. 2.3 Partition of moisture and water ydrometeor increments Because total water mixing ratio q t is used as a control variable, partitioning of te moisture and water ydrometeor increments is necessary in te 3D-Var system. A sopisticated micropysical process would be necessary to do te partitioning. However, development of te adjoint sceme for suc process is not trivial. In tis study, a simple warm rain process is introduced into te WRF/MM5 3D-Var system. Te warm rain process includes condensation of water vapor into cloud (P CON ), accretion of cloud by rain (P RA ), automatic conversion of cloud to rain (P RC ), and evaporation of rain to water vapor (P RE ). Te autoconversion term, P RC, is represented by k ( ), 1 qc qcrit qc qcrit PRC =, (3) 0, qc < qcrit were q c is te cloud water mixing ratio. According to Kessler (1965), k1 = 10 s, qcrit = 0.5g kg. Te accretion of cloud water by rain is parameterized by 1 Γ (3 + b) PRA = πρaqcen, (4) 0 3 b 4 λ + were Γ is te gamma-function, E is te collection efficiency. N 0 =8X10 6 m -4, a= and b=0.8. Te evaporation of rain can be determined from te equation: 5 + b Γ( ) 2 π N0( S 1) f1 aρ 1/2 1/3 PRE f 2 (5) = + 2 2( ) Sc 5+ b A+ B λ µ 2 λ were f 1 =0.78, f 2 =2. P CON, te condensation is determined by qv qvs, (6) PCON = 2 Lv qvs 1+ 2 RC T v pm were q vs is saturated water vapor mixing ratio, L v, R v and C pm are latent eat of condensation, gas constant for water vapor and specific eat at constant pressure for moist air, respectively. Details of te warm rain process are referred to te Appendix of Dudia (1989). Te tangent linear and its adjoint of te sceme are developed and incorporated into te 3D-Var system. Altoug te control variable is q t, te q v, q c and q r increments are produced troug te partitioning procedure during te 3D-Var analysis. Te warm rain parameterization builds a relation among rainwater, cloud water, moisture and temperature. Wen rainwater information (from reflectivity) enters into te minimization iteration procedure, te forward warm rain process and its backward adjoint distribute tis information to te increments of oter variables (under te constraint of te warm rain sceme. Once te 3D-Var system produces q c and q r increments, te assimilation of reflectivity is straigtforward. 2.4 Observation operator for Doppler radial velocity and reflectivity Te observation operator for Doppler radial velocity is: x xi y yi z zi Vr = u + v + ( w vt ), (7) ri ri ri were (u, v, w) are te wind components, (x, y, z) are te radar location, (x i, y i, z i ) are te location of te radar observation, r i is te distance between te radar and te observation, and v T is terminal velocity. Following te algoritm of Sun and Crook (1998), 25 vt = 5.40a q. (8) r Te quantity a is a correction factor defined by a = ( p0 / p), (9) were p is te base-state pressure and p 0 is te pressure at te ground. Te observation operator for Doppler radar reflectivity is (Sun and Crook 1997): Z = log( ρq r ), (10) were Z is reflectivity in te unit of dbz and q r is te rainwater mixing ratio. 3. CASE STUDIES 3.1 IHOP squall line case A squall line case was observed during te IHOP experiment on June 12-13, Tis squall line was documented by more tan eleven WSR-88D radars in Oklaoma and Kansas and several oter observing platforms. At 2200 UTC 12 June 2002, a convective line extended from

3 western Oklaoma to te Texas panandle. Te squall line was well developed from souteast Kansas to te Texas panandle at around 0000 UTC 13 June. It gradually moved souteastward and finally dissipated at around 1000 UTC 13 June. Figure 1 sows te observed 3- rainfall at 0300, 0600, 0900 and 1200 UTC 13 June based on NCEP/OH Stage IV data. Fig. 1: 3- accumulated precipitation derived from te National Stage-IV Precipitation Analysis (from NCEP) for (a) UTC, (b) UTC, (c) UTC and (d) UTC 13 June Te inner box is used for te treat score calculation. Te radar station of KVNX (solid triangle) is sown in (d). Doppler radar data assimilation wit te WRF 3D-Var system is carried out for tis case. 12- WRF forecast is conducted from te Doppler radar data enanced initial conditions at 0000 UTC 13 June. Te domain covers a 1600X1600 km 2 area wit grad-spacing of 4km (outer domain of Fig. 1). Te experiments are started from 2100 UTC 12 June, wit te firstguess interpolated from NCEP eta analysis. We conduct 3- cycling of observations until 0000 UTC 13 June. Here we sow te QPF skills of tree experiments: GTS: Only conventional GTS observations are assimilated in tis experiment; RVRF_ALL: In addition to te conventional GTS observations, te Doppler radar data from all 11 radar stations in te area are assimilated; RVRF_VNX: Same as RVRF_ALL, but te Doppler radar data from only 1 radar station KVNX (sown in Fig. 1d) are assimilated. To evaluate te QPF skills of te designed experiments, treat score (TS) of precipitation forecast in eac experiment, verified against 3- accumulated precipitation from te NCEP/OH Stage IV precipitation analysis, is calculated. Figure 2 sows TS scores of te tree experiments wit te tresold of 1 mm (Fig. 2a) and 10 mm (Fig. 2b). It is clearly indicated tat RVRF_ALL gives consistently iger scores for bot ligt and eavy rainfall. If te radar data from only one radar station KVNX are assimilated (RVRF_VNX), te scores are lower tat tose of RVRF_ALL, but iger tan tose of GTS. Tis set of experiments suggests tat te WRF 3D-Var system can extract useful

4 information from Doppler radar data assimilation, and improve te QPF skill for tis squall line case. Witout te Doppler radar data, te experiment GTS obtains te lowest TS score. Wit more Doppler radar data from one radar station to eleven radar stations, te TS scores are increased. Te verification results are valid for 9 ours for tis case. Te squall line was dissipated after 0900 UTC 13 June. (a) TS Score wit Tresold=1mm (b) TS Score wit Tresold=10mm THREAT SCORE GTS RVRF_ALL RVRF_VNX THREAT SCORE GTS RVRF_ALL RVRF_VNX FORECAST TIME (HR) FORECAST TIME (HR) Fig. 2: Te treat scores of te 3- accumulated precipitation forecasts verified against te Stage IV precipitation analysis for tresold of (a) 1 mm and (b) 10 mm 3.2 A eavy rain case in East Asia On 10 June 2002, a eavy rainfall event wit a mesoscale cyclone occurred in Sout Korea. Te KMA Automatic Weater Station (AWS) network observed tat te rain-band started around 06 UTC 10 June Its maximum 1-r rainfall occurred at 15 UTC 10 June 2002 (34 mm). Te observed maximum 3-r rainfall reaced 54.8mm ending at 18 UTC 10 June 2002 (Figure omitted). Te eavy rainfall cell was located at te soutwestern tip of Korea at 15 UTC, but it moved inland to te norteast at 18 UTC 10 June Tis rain-band moved souteastward along wit te cold front of te mesoscale cyclone and crossed Sout Korea at around 00 UTC 11 June During te rainband movement, te KMA Jindo radar captured te rainfall structures of te system over most of te period wile te rain-band was in Sout Korea. Te 3D-Var system is set up in a 3-r cycling mode. In addition to te conventional GTS data and AWS (Automatic Weater Station) surface observations, te Doppler velocities from Korean Jindo radar station are processed (quality control and preprocessing) and included in te 3D-Var analysis. Te model configuration is te same as te KMA operational design wit grid-spacing of 10 km. Tere are 33 layers in te vertical. Te MM5 model is used for tis case study. We conducted six experiments: 3D-Var wit only conventional data (3DV_C1000, 3DV_C0912, 3DV_C0700), and wit conventional data plus Doppler radar radial velocity data (RDR_C1000, RDR_C0912, RDR_C0700). Te conventions _C1000, _C0912, and _C0700 denote te 3D- Var cold start times at 0000 UTC 10, 1200 UTC 9 and 0000 UTC 7 June 2002, respectively. All te numerical forecasts (following te assimilation) start from 1200 UTC 10 June More details of te experiment design and overview of te case can be found in Xiao et al. (2005). Using KMA ig-resolution AWS ourly rainfall observations, we calculated treat scores for te QPF of te six experiments. Figure 3 sows te treat scores for 3- accumulated rainfall wit tresolds of 5 mm and 10 mm for 3D-Var experiments wit and witout Doppler radial velocity assimilation. Te treat scores for experiments wit radar data assimilation are iger tan tose witout radar data assimilation (RDR_C1000 vs. 3DV_C1000; RDR_C0912 vs. 3DV_C0912; and RDR_C0700 vs. 3DV_C0700, respectively). Te positive impact of Doppler velocity assimilation exists mainly in te first six ours of forecast. It is not clear if te positive impact can last longer tan six ours because te main rainfall event moves to te sea and te AWS network captures far less rainfall after 2100 UTC 10 June However, te TS scores in te first 6-r forecasts clearly suggest tat te Doppler radial velocity data assimilation is beneficial to sort-range precipitation forecasts. Te positive impact of Doppler velocity data assimilation on sort-range rainfall forecast can be seen in almost every pair of experiments wit and witout radar data assimilation.

5 (a) Tresold=5.0mm (b) Tresold=10mm Treat Score DV_C1000 3DV_C0912 3DV_C0700 RDR_C1000 RDR_C0912 RDR_C0700 Treat Score DV_C1000 3DV_C0912 3DV_C0700 RDR_C1000 RDR_C0912 RDR_C0700 Time (UTC) Time (UTC) Fig. 3: Comparison of treat scores between experiments wit and witout Doppler velocity assimilation for te eavy rainfall case in Korea. (a) Tresold=5mm; (b) Tresold=10mm Results from tese experiments also sow te impact of continuous assimilation troug update cycles for te rainfall forecast. During te 3D-Var update cycling procedure, te forecast from te previous cycle serves as te background for te next cycle wen te AWS data and Jindo radar radial velocity data are assimilated. A better dynamic balance among te analysis variables can be acieved wit continuous assimilation troug update cycles. It is sown tat a longer assimilation window can results in a iger TS score (Fig. 3). 4. REAL-TIME VERIFICATIONS Te 3D-Var Doppler radar data assimiulation capability was tested in real time at te Korean Meteorological Administration (KMA) for te period of 26t August 28t September 2004 before it was implemented in KMA operational applications. Te KMA operational model is MM5 wit orizontal resolution of 10 km. Te Doppler radar data from four radar stations are included in te 3D-Var assimilation cycles (every tree ours) during te real time verifications ~ Tresold = mm (a) ~ Tresold = 5.0mm (b) CSI BIAS TIME TIME Fig. 4: Treat score (bars) and bias (solid lines) of te MM5 forecasts for KMA 10km, 3 ourly cycling WRF/MM5 3D- Var. Blue = no radar data assimilation, Red = wit radail velovity and reflectivity bot assimilated. (a) Tresold = mm and (b) Tresolod = 5 mm Verified against te KMA AWS precipitation data, treat scores and bias scores of te 3- accumulated precipitation for tresolds of mm and 5 mm in te 24- prediction are calculated and sown in Figure 4. Te verifications are performed for te 10 km, 3 ourly cycling 3D-Var wit Doppler radar data from 26t August troug 28t September For te ligt precipitation (tresold of mm), te TS scores are all increased wit Doppler radar data assimilation, but bias are also increased at 12, 15 and 18- QPF (te bias scores are furter deviated from 1). For te eavier precipitation (tresold of 5 mm), in general, Doppler radar data assimilation also improves te QPF skills, except tat te TS score is decreased at 6- and te bias is furter deviated from 1 at 12- predictions. Overall, Figure 4 indicates a statistically-significant positive impact of te Doppler radar data assimilation on te sort-range QPF (0-24 ours).

6 5. SUMMARY AND CONCLUSIONS Te unified 3D-Var system for WRF and MM5 wit te capability of assimilating Doppler radial velocity and reflectivity data as been developed. Numerical experiments are conducted for several selected cases. We also implement real-time applications in Korea. It is indicated tat: Assimilation of Doppler radial velocity and/or reflectivity data improves te QPF skills for squall line, mesoscale cyclone and tropical cyclone cases. Assimilation of multiple Doppler radar observations can furter improve te QPF skills compared wit te experiment wit assimilation of single Doppler radar data. We conducted 3D-Var cycling of te Doppler radar data every tree ours up to 3 days. It is sown tat te QPF skills are improved wit te 3D-Var cycling mode. Furter experiments wit larger cycling window and iger update frequency is underway. Real-time applications wit te KMA operational model indicate a statisticallysignificant positive impact of Doppler radar data assimilation on te sort-range QPF (0-24 ours). adjoint. Part I: Model development and simulated data experiments. J. Atmos. Sci., 54, Sun, J., and N. A. Crook, 1998: Dynamical and micropysical retrieval from Doppler radar observations using a cloud model and its adjoint. Part II: Retrieval experiments of an observed Florida convective storm. J. Atmos. Sci., 55, Xiao, Q., Y.-H. Kuo, Juanzen Sun, Wen-Cau Lee, Euna Lim, Y.-R. Guo, D. M. Barker, 2005: Assimilation of Doppler radar observations wit a regional 3D-Var system: Impact of Doppler velocities on forecasts of a eavy rainfall case. J. Appl. Meteor, 44, Xiao, Q., Y.-H. Kuo, J. Sun. W.-C. Lee, D. M. Barker, and Euna Lim, 2004: Assimilation of Doppler radar observations and its impacts on forecasting of te landfalling typoon Rusa (2002), Proceedings of te Tird European Conference on Radar in Meteorology and Hydrology (ERAD), Vol. 2, Acknowledgements: Tis researc is supported by te USWRP project and Korea Meteorological Administration. Reference Barker, D. M., W. Huang, Y.-R. Guo, A. Bourgeois and Q. Xiao, 2004: A treedimensional variational (3DVAR) data assimilation system for use wit MM5: Implementation and initial results. Mon. Wea. Rev., 132, Dudia, J., 1989: Numerical study of convection observed during te winter monsoon experiment using a mesoscale twodimensional model. J. Atmos. Sci., 46, Fiser, M., 1999: Background Error Statistics derived from an Ensemble of Analyses. ECMWF Researc Department Tecnical Memorandum No 79, 12 pp. Paris, D. F., and J. Derber, 1992: Te National Meteorological Center s spectral statisticalinterpolation analysis system. Mon. Wea. Rev., 120, Ricardson, L. F., 1922: Weater Prediction by Numerical Process. Cambridge University Press, London, 1922, 236pp. Sun, J., and N. A. Crook, 1997: Dynamical and micropysical retrieval from Doppler radar observations using a cloud model and its