Adaptive Lossy Compression of Complex Environmental Indices Using Seasonal Auto-Regressive Integrated Moving Average Models

Significant increases in computational resources have enabled the development of more complex and spatially better resolved weather and climate models. As a result the amount of output generated by data assimilation systems and by weather and climate simulations is rapidly increasing e.g. due to higher spatial resolution, more realisations and higher frequency data. However, while compute performance has increased significantly because of better scaling program code and increasing number of cores the storage capacity is only increasing slowly. One way to tackle the data storage problem is data compression. Here, we build the groundwork for an environmental data compressor by improving compression for established weather and climate indices like El Niño Southern Oscillation (ENSO), North Atlantic Oscillation (NAO) and Quasi-Biennial Oscillation (QBO). We investigate options for compressing these indices by using a statistical method based on the Auto Regressive Integrated Moving Average (ARIMA) model. The introduced adaptive approach shows that it is possible to improve accuracy of lossily compressed data by applying an adaptive compression method which preserves selected data with higher precision. Our analysis reveals no potential for lossless compression of these indices. However, as the ARIMA model is able to capture all relevant temporal variability, lossless compression is not necessary and lossy compression is acceptable. The reconstruction based on the lossily compressed data can reproduce the chosen indices to such a high degree that statistically relevant information needed for describing climate dynamics is preserved. The performance of the (seasonal) ARIMA model was tested with daily and monthly indices

Parallel Implementation of Lossy Data Compression for Temporal Data Sets

Many scientific data sets contain temporal dimensions. These are the data storing information at the same spatial location but different time stamps. Some of the biggest temporal datasets are produced by parallel computing applications such as simulations of climate change and fluid dynamics. Temporal datasets can be very large and cost a huge amount of time to transfer among storage locations. Using data compression techniques, files can be transferred faster and save storage space. NUMARCK is a lossy data compression algorithm for temporal data sets that can learn emerging distributions of element-wise change ratios along the temporal dimension and encodes them into an index table to be concisely represented. This paper presents a parallel implementation of NUMARCK. Evaluated with six data sets obtained from climate and astrophysics simulations, parallel NUMARCK achieved scalable speedups of up to 8788 when running 12800 MPI processes on a parallel computer. We also compare the compression ratios against two lossy data compression algorithms, ISABELA and ZFP. The results show that NUMARCK achieved higher compression ratio than ISABELA and ZFP.Comment: 10 pages, HiPC 201

Significantly Improving Lossy Compression for Scientific Data Sets Based on Multidimensional Prediction and Error-Controlled Quantization

Today's HPC applications are producing extremely large amounts of data, such that data storage and analysis are becoming more challenging for scientific research. In this work, we design a new error-controlled lossy compression algorithm for large-scale scientific data. Our key contribution is significantly improving the prediction hitting rate (or prediction accuracy) for each data point based on its nearby data values along multiple dimensions. We derive a series of multilayer prediction formulas and their unified formula in the context of data compression. One serious challenge is that the data prediction has to be performed based on the preceding decompressed values during the compression in order to guarantee the error bounds, which may degrade the prediction accuracy in turn. We explore the best layer for the prediction by considering the impact of compression errors on the prediction accuracy. Moreover, we propose an adaptive error-controlled quantization encoder, which can further improve the prediction hitting rate considerably. The data size can be reduced significantly after performing the variable-length encoding because of the uneven distribution produced by our quantization encoder. We evaluate the new compressor on production scientific data sets and compare it with many other state-of-the-art compressors: GZIP, FPZIP, ZFP, SZ-1.1, and ISABELA. Experiments show that our compressor is the best in class, especially with regard to compression factors (or bit-rates) and compression errors (including RMSE, NRMSE, and PSNR). Our solution is better than the second-best solution by more than a 2x increase in the compression factor and 3.8x reduction in the normalized root mean squared error on average, with reasonable error bounds and user-desired bit-rates.Comment: Accepted by IPDPS'17, 11 pages, 10 figures, double colum

Optimizing Lossy Compression Rate-Distortion from Automatic Online Selection between SZ and ZFP

With ever-increasing volumes of scientific data produced by HPC applications, significantly reducing data size is critical because of limited capacity of storage space and potential bottlenecks on I/O or networks in writing/reading or transferring data. SZ and ZFP are the two leading lossy compressors available to compress scientific data sets. However, their performance is not consistent across different data sets and across different fields of some data sets: for some fields SZ provides better compression performance, while other fields are better compressed with ZFP. This situation raises the need for an automatic online (during compression) selection between SZ and ZFP, with a minimal overhead. In this paper, the automatic selection optimizes the rate-distortion, an important statistical quality metric based on the signal-to-noise ratio. To optimize for rate-distortion, we investigate the principles of SZ and ZFP. We then propose an efficient online, low-overhead selection algorithm that predicts the compression quality accurately for two compressors in early processing stages and selects the best-fit compressor for each data field. We implement the selection algorithm into an open-source library, and we evaluate the effectiveness of our proposed solution against plain SZ and ZFP in a parallel environment with 1,024 cores. Evaluation results on three data sets representing about 100 fields show that our selection algorithm improves the compression ratio up to 70% with the same level of data distortion because of very accurate selection (around 99%) of the best-fit compressor, with little overhead (less than 7% in the experiments).Comment: 14 pages, 9 figures, first revisio

Improving Performance of Iterative Methods by Lossy Checkponting

Iterative methods are commonly used approaches to solve large, sparse linear systems, which are fundamental operations for many modern scientific simulations. When the large-scale iterative methods are running with a large number of ranks in parallel, they have to checkpoint the dynamic variables periodically in case of unavoidable fail-stop errors, requiring fast I/O systems and large storage space. To this end, significantly reducing the checkpointing overhead is critical to improving the overall performance of iterative methods. Our contribution is fourfold. (1) We propose a novel lossy checkpointing scheme that can significantly improve the checkpointing performance of iterative methods by leveraging lossy compressors. (2) We formulate a lossy checkpointing performance model and derive theoretically an upper bound for the extra number of iterations caused by the distortion of data in lossy checkpoints, in order to guarantee the performance improvement under the lossy checkpointing scheme. (3) We analyze the impact of lossy checkpointing (i.e., extra number of iterations caused by lossy checkpointing files) for multiple types of iterative methods. (4)We evaluate the lossy checkpointing scheme with optimal checkpointing intervals on a high-performance computing environment with 2,048 cores, using a well-known scientific computation package PETSc and a state-of-the-art checkpoint/restart toolkit. Experiments show that our optimized lossy checkpointing scheme can significantly reduce the fault tolerance overhead for iterative methods by 23%~70% compared with traditional checkpointing and 20%~58% compared with lossless-compressed checkpointing, in the presence of system failures.Comment: 14 pages, 10 figures, HPDC'1

Compression and Conditional Emulation of Climate Model Output

Numerical climate model simulations run at high spatial and temporal resolutions generate massive quantities of data. As our computing capabilities continue to increase, storing all of the data is not sustainable, and thus it is important to develop methods for representing the full datasets by smaller compressed versions. We propose a statistical compression and decompression algorithm based on storing a set of summary statistics as well as a statistical model describing the conditional distribution of the full dataset given the summary statistics. The statistical model can be used to generate realizations representing the full dataset, along with characterizations of the uncertainties in the generated data. Thus, the methods are capable of both compression and conditional emulation of the climate models. Considerable attention is paid to accurately modeling the original dataset--one year of daily mean temperature data--particularly with regard to the inherent spatial nonstationarity in global fields, and to determining the statistics to be stored, so that the variation in the original data can be closely captured, while allowing for fast decompression and conditional emulation on modest computers