NCAR HPC Spatial Data Analysis

1. High performance computing and spatial data: an overview of recent work at NCAR Dorit Hammerling Analytics and Integrative Machine Learning Group Technology Development Divison National Center for Atmospheric Research (NCAR) Joint work with Sophia Chen, Joseph Guinness, Marcin Jurek, Matthias Katzfuss, Daniel Milroy, Douglas Nychka, Vinay Ramakrishnaiah, Yun Joon Soon and Brian Vanderwende February 13, 2018 Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 1 / 45

2. Introduction and Motivation Outline 1 Introduction and Motivation 2 Application benchmarking study example 3 Other examples and future work Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 2 / 45

3. Introduction and Motivation The National Center for Atmospheric Research (NCAR) • A federally federally funded research and development center • Mission: To understand the behavior of the atmosphere and related Earth and geospace systems Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 3 / 45

4. Introduction and Motivation NCAR’s Community Earth System Model • a “virtual laboratory” to study past, present and future climate states • describes interactions of the atmosphere, land, river runoﬀ, land-ice, oceans and sea-ice • complex! Large code base: approx. 1.5 Millions lines of code Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 4 / 45

5. Introduction and Motivation Earth System Models • Computationally very demanding, diﬀerential equations are solved for millions of grid boxes. → Require HPC infrastructure. • Approximately 200 variables, many in 3-D, are saved to describe the state of the atmosphere, land, river runoﬀ, land-ice, oceans and sea-ice for every grid cell. → Massive amounts of data and storage requirements, lots of science questions. Work with scientists to gain insights from massive data sets, ideally without moving the data. Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 5 / 45

8. Introduction and Motivation Analyzing large spatial data: initial considerations • What is the scientiﬁc question and what statistical or machine learning modeling framework can we use to answer it? • Is the analysis inherently parallel or does the model allow for parallelization? • What software? Where and how is the data stored? • How can we optimize the execution on our HPC infrastructure? Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 6 / 45

12. Application benchmarking study example Outline 1 Introduction and Motivation 2 Application benchmarking study example 3 Other examples and future work Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 7 / 45

13. Application benchmarking study example Study of Precipitation extremes: a typical example • daily data for 35 years: 12,775 values per grid cell • 288 longitudes × 192 latitudes: 55,296 grid cells • 12,775 × 55,296 = 706,406,400 data points (2.83 GB) Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 8 / 45

14. Application benchmarking study example Fitting a Generalized Pareto distribution • This is a complementary approach to block maxima for Extreme Value Analysis • For data above a given threshold (µ) ﬁt a probability density with the form: f (x) = 1 σ[1 + ξ(x−µ) σ ](1/ξ+1) for x ≥ µ. • σ – scale parameter, ξ – shape parameter • We are ignoring all the data below the threshold to just ﬁt the tail. • Having selected the threshold, estimate σ and ξ by maximum likelihood. Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 9 / 45

15. Application benchmarking study example Fitting a Generalized Pareto distribution: R code tailProb<- .01 # tail probability used in extremes fitting returnLevelYear <- 100 # Years used for return level Y<- dataset[lonindex,latindex] threshold<- quantile(Y, 1- tailProb) frac<- sum(Y > threshold) / length(Y) GPFit<- fevd(Y, threshold=threshold, type="GP",method="MLE") ReturnLevel<- return.level(GPFit,returnLevelYear, do.ci=TRUE) Depending on your machine takes somewhere from 0.3 to 1 second. Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 10 / 45

16. Application benchmarking study example Fitting a Generalized Pareto distribution: R code tailProb<- .01 # tail probability used in extremes fitting returnLevelYear <- 100 # Years used for return level Y<- dataset[lonindex,latindex] threshold<- quantile(Y, 1- tailProb) frac<- sum(Y > threshold) / length(Y) GPFit<- fevd(Y, threshold=threshold, type="GP",method="MLE") ReturnLevel<- return.level(GPFit,returnLevelYear, do.ci=TRUE) Depending on your machine takes somewhere from 0.3 to 1 second. Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 10 / 45

17. Application benchmarking study example Why use HPC systems for statistical computing? Doing repetitive tasks can take a lot of time. Even short tasks add up quickly: • 0.33 seconds for one location corresponds to approx. 5 hours for 55,000 locations. • 1 second for one location corresponds to approx. 15 hours for 55,000 locations. And that is for a single data set. Often we want to analyze hundreds of data sets and test diﬀerent parameters. Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 11 / 45

20. Application benchmarking study example NCAR’s high performance computing (HPC) systems Yellowstone (previous system (decommissioned at the end of 2017) ): • 1.5 petaﬂops peak • 72,256 cores • 145 TB total memory • 56 Gb/s interconnects Cheyenne (new system: evolutionary increase) • 5.34 petaﬂops peak • 145,152 cores • 313 TB total memory • 100 Gb/s interconnects Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 12 / 45

21. Application benchmarking study example Cores and nodes on HPC systems • Usually cores on one node share memory (cache). • Memory between nodes is typically not shared, but can be accessed. • Understanding the basics of the architecture and interconnects can be really helpful! Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 13 / 45

22. Application benchmarking study example Relevant details: Memory and parallelization tools Memory available on compute nodes Two classes of nodes on Cheyenne: • Standard nodes have 64 GB of memory (46 GB usable). • Large memory nodes with 128 GB of memory (110 GB usable). • Data Analysis cluster: 1TB (!) of memory (1000 GB usable) • But very diﬀerent network architecture, not meant for working across nodes! You need to know what is installed and how it is conﬁgured! • Rmpi: • Limits on workers? • What physical interconnect is it using? • Matlab Distributed Computing server • Spark for Python or Scala Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 14 / 45

23. Application benchmarking study example Relevant details: Memory and parallelization tools Memory available on compute nodes Two classes of nodes on Cheyenne: • Standard nodes have 64 GB of memory (46 GB usable). • Large memory nodes with 128 GB of memory (110 GB usable). • Data Analysis cluster: 1TB (!) of memory (1000 GB usable) • But very diﬀerent network architecture, not meant for working across nodes! You need to know what is installed and how it is conﬁgured! • Rmpi: • Limits on workers? • What physical interconnect is it using? • Matlab Distributed Computing server • Spark for Python or Scala Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 14 / 45

24. Application benchmarking study example Application benchmarks Even if one knows the architecture very well and has data on low-level benchmarks, application benchmarking is critical. Application benchmarking: benchmarking that uses code as close as possible to the real production code (including I/O operations!). For our application we use a quarter (approximately 14,000 grid cells) of the full data for initial benchmarking. Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 15 / 45

27. Application benchmarking study example Double for loop: code sketch # outer loop over latitude for (latindex in 1:dim(lat)) { # inner loop over longitude for (lonindex in 1:dim(lon)) { Y<- dataset[latindex,lonindex,] # extract data ...... EXTREME VALUE ANALYSIS (EVA) CODE outSummary[latindex,lonindex,]<-EVA RESULTS ...... print(lonindex) # Counter } # end of inner loop print(latindex) # Counter } # end of outer loop Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 16 / 45

28. Application benchmarking study example Setup for Application benchmarking Experimental design: • What kind of cluster i.e. communication protocol and network? • What loop to parallelize: inner or outer? Or nested? • What to put in the inner/outer loop: latitude or longitude? • How to read in the data? All at once, one latitude/longitude band at a time, one grid cell at a time? • How does the application scale with more cores and nodes? Additional consideration: • Do we want our code to run as fast as possible or as eﬃciently as possible? Total execution time vs. time per core? Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 17 / 45

29. Application benchmarking study example Setup for Application benchmarking Experimental design: • What kind of cluster i.e. communication protocol and network? • . . . • . . . • . . . • . . . Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 18 / 45

30. Application benchmarking study example Physical networks and communication protocols • TCP/IP is the protocol on which the internet is based. Connections can be high bandwidth but also high latency, partially because the protocol is designed to work in lossy networks. Logical endpoints of TCP/IP connections are called sockets. • Ethernet is a physical network designed to support TCP/IP connections. • InﬁniBand is a physical network designed to support MPI message passing. The physical connections are very high bandwidth, very low latency, and very expensive. • MPI (Message Passing Interface) is a library written to enable message passing on compute clusters. It employs algorithms that optimize communication eﬃciency and speed on clusters. It works best with a high bandwidth, low latency and near lossless physical network, but can work on Ethernet via TCP/IP as well. Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 19 / 45

31. Application benchmarking study example Remote Direct Memory Access (RDMA) • RDMA allows data to be written/read to/from other nodes’ memories. • In a sense, the nodes behave like a single aggregate node. Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 20 / 45

32. Application benchmarking study example Cluster setup in R To run foreach in parallel, a cluster needs to be set up. • Starting an R PSOCK cluster sets up TCP/IP connections (without RDMA) across the Ethernet network (and can be tricked to work over InﬁniBand). • Starting an MPI cluster sets up MPI communications with RDMA across the InﬁniBand network. library(Rmpi) library(doMPI) ##### Cluster setup ##### cl <- startMPIcluster(numCores) # Create MPI cluster registerDoMPI(cl) # Register parallel backend for foreach Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 21 / 45

33. Application benchmarking study example Cluster setup in R To run foreach in parallel, a cluster needs to be set up. • Starting an R PSOCK cluster sets up TCP/IP connections (without RDMA) across the Ethernet network (and can be tricked to work over InﬁniBand). • Starting an MPI cluster sets up MPI communications with RDMA across the InﬁniBand network. library(Rmpi) library(doMPI) ##### Cluster setup ##### cl <- startMPIcluster(numCores) # Create MPI cluster registerDoMPI(cl) # Register parallel backend for foreach Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 21 / 45

34. Application benchmarking study example Setup for Application benchmarking Experimental design: • What kind of cluster i.e. communication protocol? • What loop to parallelize: inner or outer? Or nested? • What to put in the inner/outer loop: latitude or longitude? • . . . • . . . Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 22 / 45

35. Application benchmarking study example Parallelizing for loops: the “foreach” package • foreach provides a looping construct using binary operators, which can be easily parallelized. • hyprid between standard for loop and lapply, evaluates an expression, not a function (as lapply). • returns a value rather than “causing side-eﬀects”. • needs a parallel backend, most commonly doParallel Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 23 / 45

39. Application benchmarking study example Code sketch for inner loop parallelization library(doParallel) # loads foreach, parallel and iterators # outer loop over latitude for (latindex in 1:numLat) { dataset <- getData(latindex) # load data for specific latitu # inner loop over longitude (executed in parallel) outSummary[latindex,,]<- foreach (lonindex = 1:dim(lon), .combine=rbind,.packages=c("extRemes")) %dopar% { Y<- dataset[lonindex,] # extract Y for specific longitude ...... EXTREME VALUE ANALYSIS (EVA) CODE ...... c(threshold,GPFit$results$par,frac = frac,ReturnLevel ) #print(lonindex) # Counter DON’T use in parallel execution } print(latindex) # Counter to monitor progress } Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 24 / 45

40. Application benchmarking study example One latitude at a time: inner loop over longitude Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 25 / 45

43. Application benchmarking study example One longitude at a time: inner loop over latitude Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 26 / 45

46. Application benchmarking study example Code sketch for outer loop parallelization # outer loop over latitude (executed in parallel) outSummary <- foreach(latindex = 1:numLat,lat_count = icount() .combine = rbind,.packages=c("extRemes", "ncdf4","foreach", "iterators")) %dopar% { dataset <- getData(latindex) # inner loop over longitude (executed sequentially) foreach(lonindex = 1:dim(lon), lon_count = icount(), .combine = rbind,.packages=c("extRemes", "foreach")) %do% { Y<- dataset[lonindex,] ...... EXTREME VALUE ANALYSIS (EVA) CODE ...... c(threshold,GPFit$results$par,frac = frac,ReturnLevel) } } Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 27 / 45

47. Application benchmarking study example Setup for Application benchmarking Experimental design: • What kind of cluster i.e. communication protocol and network? • What loop to parallelize: inner or outer? Or nested? • What to put in the inner/outer loop: latitude or longitude? • How to read in the data? All at once, one latitude/longitude band at a time, one grid cell at a time? • . . . Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 28 / 45

48. Application benchmarking study example Options of reading in the data • All the data at once • One latitude or longitude band at a time • One grid cell at a time Trade-oﬀ between the number of I/O calls and ﬁlling up memory. Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 29 / 45

49. Application benchmarking study example Options of reading in the data • All the data at once • One latitude or longitude band at a time • One grid cell at a time Trade-oﬀ between the number of I/O calls and ﬁlling up memory. Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 29 / 45

50. Application benchmarking study example Application Benchmarking Results Experiment 1: Inner Loop Parallelization Across Longitude for 48 Latitudes reading in the data by latitudinal band Cluster numCores ptile numNodes Run Time (seconds) IPoIB 16 16 1 375 IPoIB 32 16 2 523 IPoIB 48 16 3 543 mpi 16 16 1 2955 mpi 32 16 2 3206 mpi 48 16 3 3277 Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 30 / 45

51. Application benchmarking study example Application Benchmarking Results cont. Experiment 2: Inner Loop Parallelization Across Longitude for 48 Latitudes reading all the data at once Experiment 3: Inner Loop Parallelization Across Latitude for 48 Longitudes reading in the data by longitudinal band Experiment 4: Inner Loop Parallelization Across Latitude for 48 Longitudes reading all the data at once • Results equivalent or worse for experiments 2 through 4. • The inner loop parallelization does NOT scale across nodes and can run out of memory when reading in all the data at once. • R does not have variable slicing, meaning each worker needs to be sent the full data and then worker-speciﬁc-data is extracted. [Diﬀerent in Matlab!] Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 31 / 45

55. Application benchmarking study example Application Benchmarking Results cont. Experiment 5: Outer Loop Parallelization Across Latitude for 48 Latitude Values reading in the data by latitudinal band Cluster numCores ptile numNodes Run Time (seconds) IPoIB 16 16 1 198 IPoIB 32 16 2 172 IPoIB 48 16 3 101 mpi 16 16 1 208 mpi 32 16 2 129 mpi 48 16 3 80 Much better scaling than innner loop parallelization. Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 32 / 45

56. Application benchmarking study example Application Benchmarking Results cont. Experiment 5: Outer Loop Parallelization Across Latitude for 48 Latitude Values reading in the data by latitudinal band Cluster numCores ptile numNodes Run Time (seconds) IPoIB 16 16 1 198 IPoIB 32 16 2 172 IPoIB 48 16 3 101 mpi 16 16 1 208 mpi 32 16 2 129 mpi 48 16 3 80 Much better scaling than innner loop parallelization. Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 32 / 45

57. Application benchmarking study example Application Benchmarking Results cont. Experiment 7: Outer Loop Parallelization Across Longitude for 72 Longitude Values reading in the data by longitudinal band Cluster numCores ptile numNodes Run Time (seconds) IPoIB 16 16 1 214 IPoIB 32 16 2 152 IPoIB 48 16 3 116 mpi 16 16 1 209 mpi 32 16 2 146 mpi 48 16 3 101 Much better scaling than innner loop parallelization. Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 33 / 45

58. Application benchmarking study example Application Benchmarking Results cont. Experiment 7: Outer Loop Parallelization Across Longitude for 72 Longitude Values reading in the data by longitudinal band Cluster numCores ptile numNodes Run Time (seconds) IPoIB 16 16 1 214 IPoIB 32 16 2 152 IPoIB 48 16 3 116 mpi 16 16 1 209 mpi 32 16 2 146 mpi 48 16 3 101 Much better scaling than innner loop parallelization. Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 33 / 45

59. Application benchmarking study example Application Benchmarking Results cont. Experiment 5: Outer Loop Parallelization Across Latitude for 48 Latitude Values reading in the data by latitudinal band Cluster numCores ptile numNodes Run Time (seconds) mpi 16 16 1 208 mpi 32 16 2 129 mpi 48 16 3 80 Experiment 7: Outer Loop Parallelization Across Longitude for 72 Longitude Values reading in the data by longitudinal band Cluster numCores ptile numNodes Run Time (seconds) mpi 16 16 1 209 mpi 32 16 2 146 mpi 48 16 3 101 Outer loop parallelization over latitude somewhat faster. Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 34 / 45

60. Application benchmarking study example Application Benchmarking Results cont. Experiment 5: Outer Loop Parallelization Across Latitude for 48 Latitude Values reading in the data by latitudinal band Cluster numCores ptile numNodes Run Time (seconds) mpi 16 16 1 208 mpi 32 16 2 129 mpi 48 16 3 80 Experiment 7: Outer Loop Parallelization Across Longitude for 72 Longitude Values reading in the data by longitudinal band Cluster numCores ptile numNodes Run Time (seconds) mpi 16 16 1 209 mpi 32 16 2 146 mpi 48 16 3 101 Outer loop parallelization over latitude somewhat faster. Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 34 / 45

61. Application benchmarking study example Application Benchmarking Results cont. Experiment 5: Outer Loop Parallelization Across Latitude for 48 Latitude Values reading in the data by latitudinal band Cluster numCores ptile numNodes Run Time (seconds) mpi 16 16 1 208 mpi 32 16 2 129 mpi 48 16 3 80 Experiment 6: Outer Loop Parallelization Across Longitude for 72 Longitude Values reading in the data only once Cluster numCores ptile numNodes Run Time (seconds) mpi 16 16 1 220 mpi 32 16 2 123 mpi 48 16 3 93 Data read options provide similar results for this data size. Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 35 / 45

64. Application benchmarking study example Application Benchmarking Results for FULL data Experiment 5: Outer Loop Parallelization Across Latitude for 192 Latitude Values reading in the data by latitudinal band Cluster numCores ptile numNodes Run Time (seconds) IPoIB 16 16 1 719 IPoIB 32 16 2 521 IPoIB 48 16 3 352 IPoIB 64 16 4 279 IPoIB 80 16 5 252 IPoIB 96 16 6 192 IP (Socket) clusters have a limit of 128 workers within R. Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 36 / 45

65. Application benchmarking study example Application Benchmarking Results for FULL data Experiment 5: Outer Loop Parallelization Across Latitude for 192 Latitude Values reading in the data by latitudinal band Cluster numCores ptile numNodes Run Time (seconds) IPoIB 16 16 1 719 IPoIB 32 16 2 521 IPoIB 48 16 3 352 IPoIB 64 16 4 279 IPoIB 80 16 5 252 IPoIB 96 16 6 192 IP (Socket) clusters have a limit of 128 workers within R. Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 36 / 45

66. Application benchmarking study example Application Benchmarking Results for FULL data Experiment 5: Outer Loop Parallelization Across Latitude for 192 Latitude Values reading in the data by latitudinal band Cluster numCores ptile numNodes Run Time (seconds) mpi 16 16 1 658 mpi 32 16 2 354 mpi 48 16 3 233 mpi 64 16 4 206 mpi 80 16 5 187 mpi 96 16 6 154 mpi 192 16 12 88 Fastest setup overall. About one and a half minutes for the entire data set. Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 37 / 45

67. Application benchmarking study example Application Benchmarking Results for FULL data Experiment 5: Outer Loop Parallelization Across Latitude for 192 Latitude Values reading in the data by latitudinal band Cluster numCores ptile numNodes Run Time (seconds) mpi 16 16 1 658 mpi 32 16 2 354 mpi 48 16 3 233 mpi 64 16 4 206 mpi 80 16 5 187 mpi 96 16 6 154 mpi 192 16 12 88 Fastest setup overall. About one and a half minutes for the entire data set. Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 37 / 45

68. Application benchmarking study example Technical Report, Data and Code available Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 38 / 45

69. Other examples and future work Outline 1 Introduction and Motivation 2 Application benchmarking study example 3 Other examples and future work Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 39 / 45

70. Other examples and future work Think globally - act locally (Doug Nychka’s latest work) • A global statistical model for a spatial field provides seamless inference across a spatial domain • A local analysis of spatial data avoids large memory requirements and simplifies parallel computation Goal is to combine these two ideas. • Compute on local neighborhoods of the spatial field but assemble the results into a global model. • The local computations are embarrassingly parallel and so easily scale to many cores. Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 40 / 45

71. Other examples and future work Emulation of model output • Pattern scaling is based on a linear relationship between local temperatures and the global mean. • Derived from a long coupled climate model run. Mean scaling pattern Variation in 8 pattern scaling fields Goal: Simulate additional fields cheaply that reflect the properties of the ensemble. Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 41 / 45

72. Other examples and future work Parameters of local spatial models −140 −100 −60 −40−200204060 2 4 6 8 10 14 Range (degrees) −140 −100 −60 −40−200204060 0.05 0.15 0.25 Sigma (C) −140 −100 −60 −40−200204060 0.00 0.02 0.04 0.06 Tau (C) • Parallel ﬁts using Rmpi on moving 11×11 pixel windows • Demonstrated linear scaling to at least 1000 cores • Highly nonstationary! Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 42 / 45

73. Other examples and future work Emulation of the model output • Encode the local parameter estimates into a global Markov Random field model (LatticeKrig). • Fast simulation due to sparsity of the LatticeKrig precision matrix and basis functions Top row: 4 model fields Bottom row: 4 simulated fields −0.5 0.0 0.5 Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 43 / 45

74. Other examples and future work Other spatial work using HPC infrastructure • Comparison of Python and Matlab implementation of the Multi-resolution approximation • Statistical compression algorithms using half-spectral models for spatio-temporal data, parallelization over temporal frequencies • Bayesian climate change detection and attribution models, parallelization over number of basis functions • . . . Thanks! Any questions? Dorit Hammerling (dorith@ucar.edu) Hammerling et al. (NCAR) HPC for spatial data February 13, 2018 44 / 45

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