Retrievals along connecting lines

Transcription

1 Precipitation and Attenuation Estimates from a High Resolution Weather Radar Network Retrievals along connecting lines X-band Weather Radar Workshop Delft 2011 Nicole Feiertag, Marco Clemens and Felix Ament University of Hamburg

2 2 WHAT is the purpose of the Project PATTERN? It will show that a Network of HRWR systems could overcome the drawback of attenuation and improve the accuracy of rain rate estimates. HOW could a network accomplish this aim? Overlapping observing areas provides more Information. three different radars three different observed reflectivities three different specific attenuation three different information about same measuring area HAMBURG REQUIREMENTS? A retrieval that combines all radar information to ONE improved rain estimate.

3 3 FIRST STEP towards a retrieval of two-dimensional rain fields is to consider an IDEALIZED ONE-DIMENSIONAL setup along connecting lines. radar A radar B Idealized generated Rain Field GOOD? Intrinsic Reflectivity Calculated Reflectivity Forward Operator Observed Reflectivity Retrieval

4 4 Creation of idealized rain field Intrinsic reflectivity is calculated using relation between reflectivity and rain rate Assumption: Marshall-Palmer Distribution Simulation of observed reflectivity Discretized by a finite element basis

5 5.Retrieval estimates intrinsic reflectivity Three different methods are tested Method CL08 is related to the retrieval published by Chandrasekar & Lim (2008) Method LES is based on a linear system of equations Method ANY is the analytical solution of the intrinsic reflectivity Due to the idealized Forward Operator all settings are exactly known Detailed studies on the accuracy of each method are possible. CHANDRASEKAR V., S. LIM, 2008: Retrieval of Reflectivity in a Networked Radar Environment. J. Atmos. Oceanic Tech., 25,

6 6 Method CL08 related to the retrieval published by Chandrasekar & Lim (2008) based on the solution of the specific attenuation distribution k using the common relations k r = Z r b b ζ r m 1 (1) I r 0 ;r m b ζ r m 1 I r;r m ζ r m = 10log 10 Z r m 10log 10 Z r m (2) k = a Z r b (3) r I r 0 ; r m = 0.46 m Z s b ds (4) r 0 Nicole CHANDRASEKAR Feiertag V., S. LIM, 2008: Retrieval of Reflectivity X-band in a Weather Networked Radar Radar Workshop Environment. Delft J. Atmos. Oceanic Tech., 25, /11/15

7 7 Method CL08 related to the retrieval published by Chandrasekar & Lim (2008) based on the solution of the specific attenuation distribution k using the common relations k r = Z r b b ζ r m 1 (1) I r 0 ;r m b ζ r m 1 I r;r m ζ r m = 10log 10 Z r m 10log 10 Z r m (2) k = a Z r b (3) r I r 0 ; r m = 0.46 m Z s b ds (4) r 0 FIRST GUESS observed reflectivity (on gridpoint r m ) Nicole CHANDRASEKAR Feiertag V., S. LIM, 2008: Retrieval of Reflectivity X-band in a Weather Networked Radar Radar Workshop Environment. Delft J. Atmos. Oceanic Tech., 25, /11/15

8 8 Method CL08 related to the retrieval published by Chandrasekar & Lim (2008) based on the solution of the specific attenuation distribution k using the common relations k r = Z r b b ζ r m 1 (1) I r 0 ;r m b ζ r m 1 I r;r m ζ r m = 10log 10 Z r m 10log 10 Z r m (2) k = a Z r b (3) r I r 0 ; r m = 0.46 m Z s b ds (4) r 0 Nicole CHANDRASEKAR Feiertag V., S. LIM, 2008: Retrieval of Reflectivity X-band in a Weather Networked Radar Radar Workshop Environment. Delft J. Atmos. Oceanic Tech., 25, /11/15

9 9 Method CL08 k r = Z r b b ζ r m 1 I r 0 ;r m b ζ r (1) m 1 I r;r m STEP 1 calculation of k and Z along the path of radar A required: first guess STEP 2 calculation of k and Z along the path of radar B required: retrieved intrinsic reflectivity from Step 1 STEP 3 calculation of cost function STEP 4 iterative optimization of first guess value; repetition of Step 1-3 until minimum of cost function is reached

10 10 Method LES based on a linear system of equation derived from equation: z = z 2Bk (5) B := beam matrix describes geometry of radar beam time independent measured reflectivities from radar A and B could summarized in the observation vector x o = z A,1,, z A,N, z B,1,, z B,N intrinsic reflectivities and specific attenuations along the line stored in unknown analysis vector x a = z 1,, z N, k 1,, k N for two radars the linear system of equation can be written as: x o = Fx a (6) F = 1 N B A 1 N B B 1 N := identity matrices

11 11 Method ANY analytical solution of the intrinsic reflectivity z z = z 2 k dr (7) A(r) is defined as half of the difference in observed reflectivity by the two radars A r 0.5 z A r z B r (8) after some algebra the integral solution can be expressed by the path integrated attenuation PIA as PIA r 1, r 2 = 0.5 A r 1 A r 2 (9) for method ANY equation (9) is used

12 Without Perturbations 12 CL08 LES almost similar results Currently global drawbacks: CL08 iterative process costs time ANY LES even numbers of grid points needed, otherwise solution is singular ANY differences between neighbouring grid points, results in boundary problems

13 With Perturbations 13 Method CL08 local events local effects Good results, even with noise Robust method

14 With Perturbations 14 Method LES local events local effects Noise results in Bias Perturbations can results in negative attenuation

15 With Perturbations 15 Method ANY local events global effects Noise results in Bias

16 RMSE BIAS & NOISE 16 [dbz] CL08 LES [dbz] Method CL08 is very robust Method LES & ANY ANY Noise of >1.5 Bias is not relevant

17 Summary 17 Method CL08 Shows good results even with perturbations Input of unknown parameter b Is very time-consuming Method LES Time-saving Has problems with uneven numbers of rainy grid points Perturbations can result in negative attenuation Probably an iterative solution method will be more efficient Method ANY Time-saving Local perturbations results in global effects

18 Outlook 18 Next steps will be: enhance each method CL08: speed up LES: include iterative solution ANY: enhanced consideration of boundaries adaption from 1-dim to 2-dim retrieval

19 Precipitation and Attenuation Estimates from a High Resolution Weather Radar Network Thank you for your attention! Any Questions? Contact: n.feiertag@zmaw.de