1. 3D Multi-Radar Reflectivity Mosaic
Jian Zhang
CIMMS/NSSL
I’m very glad to have this opportunity to present our 3D multi-radar mosaic work. More importantly, this is a good opportunity for us to get inputs from users and potential users of the 3D high-resolution radar mosaic data. Please feel free to ask questions at anytime. And I would really appreciate your comments and inputs.
April 21, 2003
FAA Project Review

2. OUTLINE Motivation Challenges WSR-88D data characteristics
Demo of various gridding schemes
Demo of various mosaicking schemes
Summary
This is a list of the topics that I’ll be talking about today.
11/30/2018

3. Why Mosaic Single radar has limited coverage
Weather systems span over multiple radar umbrellas
FAA ARTCCs span multiple radar umbrellas (multiple states)
Multi-sensor storm algorithms require radar data on a common grid as other data (e.g., satellite, lightning, etc)
The reasons for gridding and mosaicking multi-radar data are rather simple. Single radar has limited coverage and weather often span over multiple radar umbrellas. In addition, the regions for which warning decision makers are responsible often require multiple radar coverage.
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4. Why 3D Mosaic
2D radar mosaic products have been very useful and efficient in many operational weather decision making processes
Adding high resolution vertical structure data can:
Provide more info about aviation hazardous weather
Help develop more and better aviation weather products
More efficient air traffic routing and improved aviation safety
Other:
Help improve storm growth and decay analysis
More accurate QPE
Help improve convective scale numerical weather prediction
There are many existing 2D radar mosaic products and they have been very useful and very efficient in operational weather applications. But to further improve the weather forecast and warning decisions, vertical structure is very important. The CRAFT project has demonstrated feasibility of disseminating high-resolution base radar data in real-time. And the rapid advance in computer power makes it possible to do high-resolution multi-radar mosaic in real-time. By adding the high resolution vertical structure, we can provide more info about storms and can thus improve air traffic safety.
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5. Challenges for 3D Multi-radar Mosaic
Extremely non-uniform data resolution
Different weather types/regimes
Non-weather echo contamination/quality control
Calibration differences
Synchronization among radars
Computational efficiency in real-time application
We’ve run into many challenges with gridding and mosaicking radar data. For single radar data gridding, we need to deal with: extremely non-uniform radar data resolution, different weather regimes/scales. For mosaicking multiple radar data, we encountered synchronization and calibration problems among radars. And even with the ever-increasing computer power, the computational efficiency remains a challenge due to the mass volume of radar data, especially when we deal with large domains and fine grids such as the FAA northeast corridor.
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6. Choose a Filter for Gridding: Uniform or Adaptive?
Uniform: (Trapp and Doswell, 2000, JTECH, 17)
Scale uniformity
Adaptive: (Askelson et al. 2000, MWR, 128)
Minimize RMS error
Retain high-resolution info in radar data
Depends on radar data characteristics and applications
There have been two point of views when choosing a gridding schem for radar data. One prefers a uniform scaled filter, and the other adaptive filter. Here adaptive means the filter’s space scale is adaptive to the radar data spatial resolution. The reason for a uniform filter is mainly the scale uniformity which would simplify model simulations. And the argument for an adaptive filter is the large non-uniformity of the radar data resolution. But the filter is really dependent on the data resolution. So next we’ll look at the spatial resolution of radar data.
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7. WSR-88D Radar Beam Propagation
Effective earth’s radius model (Doviak and Zrnic,1984):
All our beam propagation calculations are based on the four/third effective earth’s radius model shown in Doviak and Zrnics book: <<Doppler radar and weather observations>>. Here h is the height of the beam above the earth surface, s is the distance from radar to a gate along the earth surface. R is the slant range, ae is the effective earth radius, and theta-e is the elevation angle.
h: height above the earth surface
r: slant range
s: distance along the earth surface
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8. Radar Beam Propagation
Assumptions:
Spherically stratified atmosphere
Refractive index of air, n(h), linearly changes with height, h;
|n-1|<< 1
Predicts beam height with sufficient accuracy for exponential reference atmosphere
Severe departures at lower atmosphere (“AP”):
Temperature inversions
Large moisture gradients
The assumptions behind the model are: … Doviak and Zrnic have compared the four-third earth radius model with an exponential reference atmosphere and found that the effective earth radius model predicts beam height with sufficient accuracy. The exceptions exist at the very lower part of the atmosphere when there are T-inversions and large moisture gradients.
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9. WSR-88D Beam Geometry (VCP 11)
This is a plot of the radar beam geometry for the NEXRAD VCP 11. Note that the size of radar beams expand with range rapidly. At a range of 200km, the beam is more than 3km wide.
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10. Power Density Distribution (VCP 11)
This plot shows the WSR-88D radar power density distribution. Basically the power density function shows that targets at the center of radar beams contribute to the return power more than targets that are at the edge of the beams. The edge is the region shown in green and cyan.
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11. WSR-88D Beam Geometry (VCP 21)
And this is a same plot for VCP21. In addition to the expand of the beam size, we also notice the large gaps between high tilts.
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12. Power Density Distribution (VCP 21)
This is a plot showing power density function for VCP 21.
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13. WSR-88D Data Resolution Spatial resolution of radar data:
In spherical coordinates:
~1x 1km x 1 at lower tilts (azimuth:range:elevation)
higher tilts are as far as 5 apart
Power density distribution  not point data
“Effective” spatial resolution of radar data:
Physical distance between centers of adjacent radar bins in space
As you see, radar data are not point data, rather they are a weighted mean of all targets in a resolution volume. The weight is dependent on radar power density function. The center of the resolution volumes are approximately 1km by 1deg apart on a cone plane. In the vertical direction, the tilts can be as far as 5 degrees apart. For easy describe the data distribution, we define “effective” spatial resolution by using the physical distance between centers of the radar resolution volume scans (or radar bins).
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14. WSR-88D Azimuthal Resolution
This is a plot showing the distance between two adjacent radials on the same tilt, we call it “azimuthal resolution”. The red arrow indicates the range where the resolution become worse than 1km. 
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15. WSR-88D Azimuthal Resolution (VCP11 and VCP21)
Range (km) 50
100
150
200
300
460
Distance (km)
0.8
1.7
2.5
3.3
4.9 8
This table just lists a few values read from the previous plot.
Azimuthal resolution is worse than
1km beyond 60 km range
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16. WSR-88D Elevational Resolution (VCP11)
This plot shows the distance between two adjacent tilts at the same range and same azimuth. Majority of the centers of data bins are more than 1km apart, many are more than 5km apart. To achieve an uniform filtered field, we must use the worst resolution (longest wavelength) in the data. That means at least 5km in horizontal (azimuthal) and 10km in vertical. This would not be acceptable storm-scale applications. 
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17. WSR-88D Elevational Resolution (VCP21)
Same as previous plot but for VCP 21. The resolution is even worse. Therefore, the WSR-88D data is not really ideal for studying stratiform weathers. 
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18. Choose a Filter: Uniform or Adaptive?
Our choice: adaptive
Largely different spatial resolution
An adaptive filter is needed for gridding radar data in order to retain high resolution info in radar data
Data sampling resolution are worse than 1km in most places:
Grid resolution of 1km is sufficient
From previous discussion, we found that an adaptive filter is needed for gridding radar data, especially for high-resolution grid such as of 1km.
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19. Demo of Gridding Schemes
“Resolution volume mapping”
Nearest neighbor
Vertical interpolation (adaptive)
Vertical interpolation plus gap-filling
Cases:
convective, 6/25/02, 2036Z, KIWX
stratiform, 2/15/98, 0859Z, KIWA
From previous discussion, we found that an adaptive filter is needed for gridding radar data, especially for high-resolution grid such as of 1km.
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20. Convective Case 1: KIWX, 6/25/02, 2036Z
Now we begin to demonstrate our 3D mosaic project using real cases. The first case is a convective storm case in the CIWS domain and this image shows the composite reflectivity from North Webster or Fort Wayne radar on June 25, The white circle lines are range rings 50km apart and straight lines are azimuth lines 45 degrees apart. The x- and y- axis show distance in kilometers from the radar. There are strong convective cells at both near radar ranges and far ranges. The color table is shown at the upper right and it will be used for all our images unless mentioned otherwise.
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21. Stratiform Case 2: KIWA, 2/15/98, 0859Z
The second case is a stratiform winter storm case in the state of Arizona. And the image shows the composite reflectivity from KIWA (Phoenix) radar at about 9Z on Feb. 15, 1998.
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22. Gridding Scheme I: Resolution Volume Mapping
Assuming each radar bin (resolution volume) size =1x 1km x 1
Resample on Cartesian grid
Usually 1km x 1km x 500m
For any given grid cell, if the center of the grid cell is inside a radar bin volume, then the grid cell will take the value of the radar bin.
Like nearest neighbor, but within the beam width. Gaps may exists.
The first gridding scheme we developed is to simply map the radar resolution volumes assuming the size of the volume is 1x 1km x 1. We’ll show some results together with the second scheme, nearest neighbor remapping.
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23. Gridding Scheme II: Nearest Neighbor
For each grid cell:
If the center is above (below) the highest (lowest) elevation angle, but within half of a beam width, then it will take the value of the nearest bin value on the highest (lowest) tilt.
If the center is in between the lowest and highest elevation angles, then it will take the value of the nearest radar bin.
No gaps between the lowest and highest tilts
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24. Convective Case1: RHI, 263° Resolution Volume Mapping Nearest Neighbor
RHI images of the case 1 from bin volume mapping and the nearest neighbor remapping. The systems are characterized by large vertical scales and small horizontal scale. Note the beam spreading and the discontinuities in the vertical due to the power density function.
Resolution Volume Mapping
Nearest Neighbor
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25. Convective Case1: RHI, 173° Resolution Volume Mapping Nearest Neighbor
RHI images from a different azimuth angle, with a longer range. Again it shows the small horizontal scale and large vertical scale.
Resolution Volume Mapping
Nearest Neighbor
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26. Convective Case1: CAPPI, 5km
These are CAPPI images from the convective case. It is basically a horizontal cross section cut at a constant height with the same assumptions taken for the previous RHI images. The height here is defined with respect to the mean sea level. The image look quite consistent and smooth, even with the gaps between the tilts. It appears that a simple horizontal interpolation would fix the gaps.
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Resolution Volume Mapping
Nearest Neighbor

27. Convective Case1: CAPPI, 12km
Another CAPPI taken at 12km. This near the top of the system, therefore some of the arc shaped discontinuities are due to lack of data for interpolation.
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Resolution Volume Mapping
Nearest Neighbor

28. Stratiform Case 2: RHI, 0° Resolution Volume Mapping Nearest Neighbor
Now let’s look at the RHI images for the case 2. The discontinuity between tilts are much more pronounce, indicating that there are strong vertical gradients. When there are strong vertical gradients, the difference between centers of adjacent tilts are larger. Thus when fill in the whole radar bin volumes with the gate values, the discontinuity at the boundary is more noticeable.
11/30/2018
Resolution Volume Mapping
Nearest Neighbor

29. Stratiform Case2: CAPPI, 2.3km
CAPPI image for the winter case. The gaps are filled by the vertical expand of the radar beams. However, the ring-shaped discontinuities still exist.
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Resolution Volume Mapping
Nearest Neighbor

30. Stratiform Case2: CAPPI, 5km
Another CAPPI taken at 5km.
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Resolution Volume Mapping
Nearest Neighbor

31. Gridding Scheme I Summary: Resolution Volume Mapping
Shows raw data distribution
Gaps between high tilts
Ring-shaped discontinuities, especially for stratiform echoes. Caused by the coarse vertical resolution.
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32. Gridding Scheme II Summary: Nearest Neighbor
No smoothing
Gaps are filled
Ring-shaped discontinuities
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33. Gridding Scheme III: Vertical Adaptive Barnes
For each grid cell:
If the center is above (below) the highest (lowest) elevation angle, same as the nearest neighbor.
If the center is in between the lowest and highest elevation angles, then it will take the weighted mean of the two nearest radar bin values, one at the tilt above and one at below.
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34. Convective Case1: RHI, 263° Nearest Neighbor Vertical Adaptive Barnes
The vertical interpolation provide a continuous and more consistent reflectivity field.
Nearest Neighbor
Vertical Adaptive Barnes
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35. Convective Case1: RHI, 173° Nearest Neighbor Vertical Adaptive Barnes
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Nearest Neighbor
Vertical Adaptive Barnes

36. Convective Case1: CAPPI, 5km
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Nearest Neighbor
Vertical Adaptive Barnes

37. Convective Case1: CAPPI, 12km
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Nearest Neighbor
Vertical Adaptive Barnes

38. Stratiform Case 2: RHI, 0° Nearest Neighbor Vertical Adaptive Barnes
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39. Stratiform Case2: CAPPI, 2.3km
Another CAPPI taken at 10km. Note the gaps between different tilts.
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Nearest Neighbor
Vertical Adaptive Barnes

40. Stratiform Case2: CAPPI, 5km
Vertical interpolation smoothed this field.
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Nearest Neighbor
Vertical Adaptive Barnes

41. Gridding Scheme III Summary: Vertical Adaptive Barnes
Filled gaps
Alleviated discontinuities
Bright-band rings still exist
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42. Gridding Scheme IV: Adaptive Barnes + Gap Filling
For each grid cell:
If the center is above (below) the highest (lowest) elevation angle, same as the nearest neighbor.
If the center is in between the lowest and highest elevation angles, then it will take the weighted mean of four radar bin values on the tilt above and below, all at the same azimuth. Two of the radar bins are at the same range and two others are at the same height as the grid cell (See Figure next)
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43. Gridding Scheme IV: Adaptive Barnes + Gap Fillingo o + o o
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44. Stratiform Case 2: RHI, 0° Vertical Adaptive Barnes
Now a RHI image for the case 2. The discontinuity between tilts are much more pronounce, indicating that there are strong vertical gradients. When there are strong vertical gradients, the difference between centers of adjacent tilts are larger. Thus when fill in the whole radar bin volumes with the gate values, the discontinuity at the boundary is more noticeable.
Vertical Adaptive Barnes
Adaptive Barnes + Gap Filling
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45. Stratiform Case2: CAPPI, 2.3km
Another CAPPI taken at 10km. Note the gaps between different tilts.
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Vertical Adaptive Barnes
Adaptive Barnes + Gap Filling

46. Convective Case1: RHI, 263° Vertical Adaptive Barnes
Artifacts show horizontal interpolation is not suited for convective storms.
Vertical Adaptive Barnes
Adaptive Barnes + Gap Filling
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47. Gridding Scheme IV Summary: Adaptive Barnes + Gap Filling
Filled gaps
Eliminated discontinuities
Alleviated bright-band rings
Not suited for upright convective systems, so….
Solution:
Apply gap filling component only when bright-band is identified (Gourley and Calvert 2003)
Constraints:
h/s > scale_ratio;
range < range_limit;
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48. Mosaic
Data from individual radars have now been gridded (resampled on Cartesian grid)
Now we need to combine or mosaic data from multiple radars
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49. Mosaic Scheme I: Nearest Neighbor
At each grid cell:
If there is only one radar’s grid value, then the value is used
If there are multiple radar values, then the value from the nearest radar is used.
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50. Mosaic Scheme II: Maximum
At each grid cell:
If there is only one radar’s grid value, then the value is used
If there are multiple radar values, the the maximum value among the multiple radars is used.
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51. Mosaic Scheme III: Distance Weighted Mean
At each grid cell:
If there is only one radar’s grid value, then the value is used
If there are multiple radar values, then a weighted mean of the multiple values is used. The weighting function is dependent on the distance from the grid cell to the radars.
R is the radius of influence; d is the distance between radar and the given grid cell.
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52. Convective Case 1: 6/25/02, 2036Z KLOT and KIWX
Is KLOT radar too cold or KIWX radar too hot?
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CREF_KLOT
CREF_KIWX

53. Composite Reflectivity Difference KIWX-KLOT
Statistics along the equidistance line (white):
Mean: 7.7dBZ
Min: -9.5dBZ
Max: 26dBZ
Blue line is for a vertical cross section shown next
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54. RHI for Reflectivity Difference KIWX-KLOT
Blue line shows the equidistance.
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55. Convective Case 1: Nearest Neighbor
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56. Convective Case 1: Maximum
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57. Convective Case 1: Distance Weighted Mean
An exponential function with 50km scale radius provide “better” mosaicking.
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58. Convective Case 1: Distance Weighted Mean
Cressman weighting function with 300km radius of influence damped intensity for this case.
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59. Mosaic Scheme Summary Nearest Neighbor: Taking maximum value:
Produces discontinuities when there are calibration differences
Taking maximum value:
Retain highest intensity everywhere
Giving 100% weight to the “hot” radars
May expand bright-band features at far ranges
Weighted mean:
Retain highest intensity at near ranges
Weighting function based on distance -- giving high weight to closer range observations
Smoothing
Smoothing (“cold” radar can damp echo intensity at mid-ranges)
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60. Summary
An adaptive filter is required to retain highest possible resolution in the data.
Interpolation in vertical direction produces smooth and consistent reflectivity analysis.
A gap-filling is needed for stratiform precip echoes with strong vertical gradient, especially when there is bright-band.
Weighted mean mosaicking helps alleviate calibration discontinuities and provide continuity in the mosaic field.
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61. Future Work Further improve data QC Apply advection when mosaicking
Alleviate synchronization problems among radars
Incorporate TDWR, ASR-9, and other radar data
Develop toward a 4D dynamic grid
Demo of preliminary results
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62. Current 3D mosaic comp. refl. (every 5 min)
01:20Z - 01:30Z,
KTLX
KFDR
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63. Rapid update mosaic comp. refl. (every 10s)
01:20Z - 01:30Z,
KTLX
KFDR
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64. Lines for vertical cross sections2 1
01:20Z - 01:30Z,
KTLX 2
KFDR 1
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65. Cross section-1 loop (~ every 10 s)
01:17:00Z - 01:30:01Z,
KTLX
KFDR
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66. Cross section 2 loop (~every 10s)
01:17:00Z - 01:30:01Z,
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67. 3D Multi-Radar Mosaic Thank You! Questions? Email: Jian.zhang@noaa.gov
This ppt file is available at:
ftp://ftpnssl.nssl.noaa.gov/pub/jzhang/FAA_PR/
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