Intro to threp
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The document describes Threp, a lightweight remapping framework for use in Earth system models. Threp aims to provide a flexible, readable, and efficient framework for remapping data between different grid types, including regular, rectilinear, curvilinear, and unstructured grids. It supports operations like interpolation, masking, and extrapolation between source and destination grids. Threp uses a two-stage process of first generating interpolation weights and then applying those weights to remap data values. It is designed for parallel computation and to be easily extensible to support new interpolation methods and grid types.
![Two Stage
Stage 1: Weights Generation Stage 2: Regridding Data
𝑘
𝑤11 𝑤12 … 𝑤1𝑘
𝑤21 𝑤22 … 𝑤2𝑘 𝑑𝑎𝑡𝑎 𝐴 𝑗 = 𝑤 𝑖 ∙ 𝑑𝑎𝑡𝑎(𝑃𝑖 )
A= … 𝑖=1
𝑤 𝑗1 𝑤 𝑗2 … 𝑤 𝑗𝑘
…
𝑑𝑎𝑡𝑎 𝑑𝑠𝑡_𝑖𝑛𝑑𝑥 = 𝐴 ∙ 𝑑𝑎𝑡𝑎[𝑠𝑟𝑐_𝑖𝑛𝑑𝑥]
𝐴 𝑗 (on dst grid)
𝑃1 , 𝑃2 … 𝑃 𝑘 (on src grid)
𝑤1, 𝑤2 … 𝑤 𝑘 (wgts)](https://image.slidesharecdn.com/introtothrep-130310231032-phpapp02/85/Intro-to-threp-10-320.jpg)
![Still Two Stage
𝑓 𝑥1, 𝑦1 = 𝑎 + 𝑏𝑥1 + 𝑐𝑦1 + 𝑑𝑥1 𝑦1 𝑓 = 𝑓 𝑥1, 𝑦1 𝑓 𝑥1, 𝑦1 𝑓 𝑥1, 𝑦1 𝑓 𝑥1, 𝑦1 𝑇
𝑓 𝑥2, 𝑦2 = 𝑎 + 𝑏𝑥2 + 𝑐𝑦2 + 𝑑𝑥2 𝑦2
𝑓 = 𝐶𝑦 1 𝑥1 𝑦1 𝑥1 𝑦1
𝑓 𝑥3, 𝑦3 = 𝑎 + 𝑏𝑥3 + 𝑐𝑦3 + 𝑑𝑥3 𝑦3
1 𝑥2 𝑦2 𝑥2 𝑦2 𝑇
𝑓 𝑥4, 𝑦4 = 𝑎 + 𝑏𝑥4 + 𝑐𝑦4 + 𝑑𝑥4 𝑦4 𝐶= 𝑦= 𝑎 𝑏 𝑐 𝑑
1 𝑥3 𝑦3 𝑥3 𝑦3
1 𝑥4 𝑦4 𝑥4 𝑦4 4×4
Solving inversion of a 4×4
Matrix C
𝑓 𝑥 𝑘 , 𝑦 𝑘 = 𝑎 + 𝑏𝑥 𝑘 + 𝑐𝑦 𝑘 + 𝑑𝑥 𝑘 𝑦 𝑘 𝑓 𝑘 = 𝑧𝑦
𝑓 𝑘 = 𝑧𝐶 −1 𝑓 𝑧 = [1 𝑥 𝑘 𝑦 𝑘 𝑥 𝑘 𝑦 𝑘 ]
𝑓 𝑘 = 𝑤𝑓 𝑤 = 𝑧𝐶−1](https://image.slidesharecdn.com/introtothrep-130310231032-phpapp02/85/Intro-to-threp-31-320.jpg)
Intro to threp
- 1. Threp A Lightweight Remap Framework for the Earth System Model 吴竑 (Xunzhang) xunzhangthu@gmail.com 2013/03/09
- 2. Background Data management between components in the Earth System Model(coupler) Data exchange between grids in each Models(atmosphere, land, ocean, ice, ...) Grids have become diverse(triple pole, hexagon, unstructured) Interpolation algorithms have become complex(mixed/coupled, special handling)
- 3. Motivation Current popular universal remapping libraries: ESMF-Regridding
- 4. Motivation Current popular universal remapping libraries: Inflexible data structure(latitude bin, local traverse) 3D Cartesian coordinates Tooold(SCRIP1.4 released at 2001) Unstructured grid supported Serial Parallel ESMF-Regridding
- 5. Motivation Current popular universal remapping libraries: Inflexible data structure(latitude bin, local traverse) Appeared as a app, no interface supplied 3D Coords Tooold(SCRIP1.4 released at 2001) Complicated hierarchy, really hard to improve Unstructured grid supported Serial Thoughtless readability Parallel ESMF-Regridding
- 6. Motivation More versatility, flexible data structure Remapping programming model in the Earth System Model(throw details to Threp) Readable, lightweight, efficient remapping framework
- 7. Goal of Threp Universal(Earth System Model) Users develop just like building blocks More grids(regular, rectilinear, curvilinear, unstructured) supported Mask supported(source, destination) Extrapolation supported(e.g., border of land and sea) Parallel and Scalable
- 9. Outline Remapping on a sphere Design of Threp Implementation Bilinear in action Demo Future work
- 10. Two Stage Stage 1: Weights Generation Stage 2: Regridding Data 𝑘 𝑤11 𝑤12 … 𝑤1𝑘 𝑤21 𝑤22 … 𝑤2𝑘 𝑑𝑎𝑡𝑎 𝐴 𝑗 = 𝑤 𝑖 ∙ 𝑑𝑎𝑡𝑎(𝑃𝑖 ) A= … 𝑖=1 𝑤 𝑗1 𝑤 𝑗2 … 𝑤 𝑗𝑘 … 𝑑𝑎𝑡𝑎 𝑑𝑠𝑡_𝑖𝑛𝑑𝑥 = 𝐴 ∙ 𝑑𝑎𝑡𝑎[𝑠𝑟𝑐_𝑖𝑛𝑑𝑥] 𝐴 𝑗 (on dst grid) 𝑃1 , 𝑃2 … 𝑃 𝑘 (on src grid) 𝑤1, 𝑤2 … 𝑤 𝑘 (wgts)
- 11. Search Neighbors IDW: nearest k points Bilinear: nearest quadrangle Bicubic: nearest quadrangle or nearest 16 points find nearest k + select Patch: nearest patch Least Square Method: nearest k points
- 12. Matrix-Vector Multiply 𝑤11 𝑤12 … 𝑤1𝑘 𝑤21 𝑤22 … 𝑤2𝑘 𝑘 × 𝑛𝑢𝑚 𝑑𝑠𝑡 Sparse matrix A = … , sparsity = . 𝑛𝑢𝑚 𝑠𝑟𝑐 ×𝑛𝑢𝑚 𝑑𝑠𝑡 𝑤𝑗1 𝑤𝑗2 … 𝑤𝑗𝑘 … 𝑛𝑢𝑚 𝑠𝑟𝑐 ×𝑛𝑢𝑚 𝑑𝑠𝑡 𝑇 dst_𝑖𝑛𝑑𝑥 = 1 1 … 1 2 2 … 2 … … 𝑛𝑢𝑚 𝑑𝑠𝑡 𝑛𝑢𝑚 𝑑𝑠𝑡 … 𝑛𝑢𝑚 𝑑𝑠𝑡
- 13. Outline Remap model in the Earth System Model Design of Threp Implementation Bilinear in action Demo Future work
- 15. Nearest neighbor search in a 2d tree demo Average: 𝑙𝑜𝑔𝑁 Worse: 𝑁
- 16. Remap on a sphere Periodic Boundary Construct left ghost boundary: (lon, 0.5) -> (lon, -0.5) Construct right ghost boundary: (lon, 359.5) -> (lon, 360.5) Index recovery map/table: index of (lon, ghost_lat) ->index of (lon, lat) Left ghost right ghost boundary boundary
- 17. Remap on a sphere Pole Singularities if highest lat(dst grid)> highest lat(src grid): use north pole region interp pnts continue if lowest lat(dst grid)< lowest lat(src grid): use south pole region interp pnts continue normal case…
- 18. A Map-Reduce application Map: Stage1 Reduce: Stage 2
- 19. Outline Remap model in the Earth System Model Design of Threp Implementation Bilinear in action Demo Future work
- 20. Architecture bilinear idw patch conserve interp search solver prediction geometry io NetCDF MPI/TCP-IP Pydoop clusters
- 21. Embrace Python User friendly(geoscience user) Recursive efficiency: Easy to code, easy to read loop version of kd-tree More integrated libraries(no more repeated wheels) Auto type checking:
- 22. Embrace Python < 4000 LOC! (so far) 12th day, available!
- 23. Grid File SCRIP Grid Format 2D lat/lon coords(degrees/radians units supported) Atmosphere grid with mask or no mask
- 24. Nearest k + Select Heuristic
- 25. Solver -solve weights for each dst grid pnt Class +__init__() +solve_quadratics() +select_legal_root() Idw_Solver Bilinear_Solver Bilinear_Solver -solve idw weights -solve bilinear weights -solve bilinear weights +__init__() +solve() +__init__() +solve() +__init__() +solve() Solver Bilinear Interp -Bilinear remapping -Interpolation management class class +__init__() +__init__() +local_functions() +interp() +interp() +remap() +remap() +check_wgt() +check_wgtsum() +check_all_masks() +dst_distribute() Interp +dst_merge() Idw +indx_recovery() -Idw remapping class +compact_remap_matrix() +__init__() +learn() +local_functions() +deliver() +interp() +remap() Predictor Bilinear_Predictor -Preditor class -Bilinear predictor class Predictor +__init__() +__init__() +predict() +predict()
- 26. MPI Python MPI library: mpi4py Linear speedup(stage1) 4min->2min->1min->30sec->…(not complete) Very fast for serial stage2, <0.2sec. necessary to parallelize? callback of MPI_Reduce interface?
- 28. Outline Remap model in the Earth System Model Design of Threp Implementation Bilinear in action Demo Future work
- 29. Bilinear Algorithm 𝑓 𝑥, 𝑦 = 𝑎 + 𝑏𝑥 + 𝑐𝑦 + 𝑑𝑥𝑦 𝑓 𝑥 𝑘 , 𝑦 𝑘 = 𝑓 0,0 1 − 𝑥 𝑘 (1 − 𝑦 𝑘 ) + 𝑓 1,0 𝑥 𝑘 (1 − 𝑦 𝑘 ) + 𝑓 0,1 𝑦 𝑘 1 − 𝑥 𝑘 + 𝑓 1,1 𝑥 𝑘 𝑦 𝑘 𝑓 𝑥 𝑘 , 𝑦 𝑘 = 𝑓 0,0 𝑤1 + 𝑓 1,0 𝑤2 + 𝑓 0,1 𝑤3 + 𝑓 1,1 𝑤4 For irregular bilinear box, a similar way to calculate𝑤1, 𝑤2, 𝑤3, 𝑤4 (2011/8, wuhong)
- 30. Extrapolation Case Source grid masked atm2ocn & ocn2atm Destination grid masked ignore Coupled bilinear Can extrapolation as accurate as interpolation? Yes, a property that…
- 31. Still Two Stage 𝑓 𝑥1, 𝑦1 = 𝑎 + 𝑏𝑥1 + 𝑐𝑦1 + 𝑑𝑥1 𝑦1 𝑓 = 𝑓 𝑥1, 𝑦1 𝑓 𝑥1, 𝑦1 𝑓 𝑥1, 𝑦1 𝑓 𝑥1, 𝑦1 𝑇 𝑓 𝑥2, 𝑦2 = 𝑎 + 𝑏𝑥2 + 𝑐𝑦2 + 𝑑𝑥2 𝑦2 𝑓 = 𝐶𝑦 1 𝑥1 𝑦1 𝑥1 𝑦1 𝑓 𝑥3, 𝑦3 = 𝑎 + 𝑏𝑥3 + 𝑐𝑦3 + 𝑑𝑥3 𝑦3 1 𝑥2 𝑦2 𝑥2 𝑦2 𝑇 𝑓 𝑥4, 𝑦4 = 𝑎 + 𝑏𝑥4 + 𝑐𝑦4 + 𝑑𝑥4 𝑦4 𝐶= 𝑦= 𝑎 𝑏 𝑐 𝑑 1 𝑥3 𝑦3 𝑥3 𝑦3 1 𝑥4 𝑦4 𝑥4 𝑦4 4×4 Solving inversion of a 4×4 Matrix C 𝑓 𝑥 𝑘 , 𝑦 𝑘 = 𝑎 + 𝑏𝑥 𝑘 + 𝑐𝑦 𝑘 + 𝑑𝑥 𝑘 𝑦 𝑘 𝑓 𝑘 = 𝑧𝑦 𝑓 𝑘 = 𝑧𝐶 −1 𝑓 𝑧 = [1 𝑥 𝑘 𝑦 𝑘 𝑥 𝑘 𝑦 𝑘 ] 𝑓 𝑘 = 𝑤𝑓 𝑤 = 𝑧𝐶−1
- 32. Piece of Results T42 -> POP43: are: 8.74e-5 mre: 0.00596 Better than idw! POP43->T42: Better than idw mixed bilinear! are: 0.000238 mre: 0.0829
- 33. Outline Remap model in the Earth System Model Design of Threp Implementation Bilinear in action Demo Future work
- 34. Discussion Unstructured grid source Periodic boundary problem of unstructured grid Specificity conservative remapping High dimensional remapping Restart Threp
- 35. Outline Remap model in the Earth System Model Design of Threp Implementation Bilinear in action Demo Future work
- 36. Roadmap Performance: More sub modules in Threp: PyPy interpreter derivation C extension of kernel code integral mapreduce version of Threp More algorithms: More grids: patch triple poles bicubic unstructured conservative(first & second) Graduate!!
- 37. Conclusion Threp abstract remapping model in the Earth System Model Threp is a parallel remapping framework, supports masked/unstructured grid Threp is lightweight, easy to start A extrapolation coupled bilinear algorithm implemented in Threp, better accuracy High performance scalability Embrace Threp!!
- 39. Acknowledge Google.com Stackoverflow.com Lanning Wang< wangln@bnu.edu.cn > Shunqiang Song< pinewall@gmail.com > Li Liu< liuli03@mails.tsinghua.edu.cn > Yushu Chen<>
- 40. Thank you! Questions?