1. Modeling Problems & Signals
IN21A-1416: Representation of Uncertainty in GPS Data Product Earth System Data Records (ESDRs)
Melinda B Squibb1, Yehuda Bock1, Brendan W Crowell1, Danan Dong2, Peng Fang1, Sharon Kedar2, Zhen Liu2, Diego Melgar-Moctezuma1, Angelyn W. Moore2, Susan E Owen2, Louis Ratzesberger1, Frank Webb2
1Scripps Institution of Oceanography, University of California-San Diego, La Jolla, CA
2Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA
Abstract
SOPAC and JPL have collaborated through the MEaSUREs SESES project to provide Level 1A ESDR's of automated weekly-updated, long-term (from 1995 to the present) raw geodetic position time series of over 1800 stations in the Western U.S. (including all PBO sites) and global stations. In addition, JPL and SOPAC provide Level 1B ESDR's of automated weekly updates of calibrated, validated, and filtered time series for stations in the Western U.S. based on the combined solutions of independent JPL and SOPAC analyses. We also provide Level 2 ESDR's consisting of velocity field and velocity field histories in various geodetic reference frames. Strain and strain rate fields, Level 3 ESDR's, will also shortly be in production. All products are available to the public through NASA's GPS Explorer Gridsphere-based data portal. A new set of geodeticML schemas and a downloadable metadata viewer are being developed which allow the inclusion of processing metadata and versioning information in addition to other data quality information, such as outliers and chi-squared and rms values of the overall combination process. The incremental chi-squared fit of each subnetwork, adjustment value and sigma for each site are calculated and used to tag as anomalous those sites with 3 times the formal uncertainty. Another set of files generated weekly as part of our recursive processing and evaluation of the time series, detects signals such as postseismic decays, outliers and trends still apparent in the adjustment residuals.
Modeling Problems & Signals
Outlier Detection Algorithm
Trend Detection Algorithm
Geophysical Anomalies
The algorithms we developed successfully detect many GPS time series that exhibit geophysical anomalies, which often occur in the form of anthropogenic effects (such a groundwater removal and oil extraction), volcanic signals, or postseismic deformation.
San Gabriel basin
Los Angeles basin
Problem: A model that does not consistently fit the data constitutes a modeling problem. Similarly, data that deviates away from the model in a particular pattern represents a signal.
Problem: Outliers are problematic because they skew the data, and in turn, they can bias the model. Extreme outliers must be removed.
Problem: A detrended series that still exhibits significant trend indicates that the data contains unaccounted for information and/or modeling.
Santa Ana basin
Method: Using the correlation coefficient, r, we can measure the strength of the linear association between time (X) and distance (Y) in GPS data. Since -1<r <1, with a value of 0 representing no linear association, and a value close to 1 or -1 representing a strong linear association, we determined that a value greater than .7 or less than -.7 signifies trend.
Anthropogenic effects: The algorithms detect anomalous sites (in orange) in the Los Angeles basin, Santa Ana basin, and San Gabriel basin, which are regions where anthropogenic effects occur.
Method: Create a threshold for each residual series that is equal to 5 times the interquartile range (IQR). The IQR is a very robust estimator of the spread of the series since it is more resistant to outliers than the standard deviation. Thus, residuals that cross this threshold correspond to outliers.
Method: Search each GPS site for existence of eight-month windows during which the residual series does not change sign, and therefore does not resemble white noise. This signifies a lack of important, but unaccounted for, model terms.
Overview of ESDRs
The level 0 ESDRs are RINEX files archived at SOPAC including PBO, SCIGN, BARD, PGC and PANGA stations.
We generate several sets of daily position time series for over 1800 global and regional GPS stations, with the majority of stations in Western North America.
We use a common source of metadata available through the SOPAC database to reduce systematic errors – available publically in XML and “IGS log file” formats.
Yellowstone
Mount St. Helens
Long Valley Caldera
Volcanic Signals: Volcanoes affect ground motion in patterns that the anomaly detection algorithms consistently recognize, which is seen above as concentrations of detected sites in volcanic regions (Mt. St. Helens, Long Valley Caldera, and Yellowstone).
Level 1A ESDRs: Unfiltered individual time series based on independent SOPAC (GAMIT) and JPL (GIPSY) analyses of GPS data
Level 1B ESDRs: Unfiltered combined time series
Level 1C ESDRs: Filtered individual (SOPAC and JPL) and combined time series that have gone through a Principal Component Analysis (PCA) and quality control, and corresponding time series of residuals.
Level 2 ESDRs: One of the byproducts of Level 1 are velocity time series for the GPS stations, representing the long-term tectonic motion.
Parkfield Earthquake
Time Series Modeling and Uncertainties
Hector Mine & Landers Earthquakes
Evaluation of uncertainties in metadata and Level 1-2 ESDRs is complicated by the following:
Modeling Problems: These are seen when the model does not represent the data well. This happens either because the model is lacking an important model term(s), or because the data has gaps and jumps that mislead the model.
Signals: Many signals such as postseismic decays, anthropogenic effects, and volcanic signals are recognized as data that deviate away from the model in particular patterns.
Outliers: Outliers are caused by many different sources. If the outliers are extreme, they can distort the model, and it is therefore very important to detect and remove them from the data.
Trend: Due to geophysical forces, GPS time series inherently contain a linear velocity (trend). Thus, the series are detrended before further analysis is performed. Nevertheless, some series may contain a significant trend, especially when two or more trends are estimated. The existence of trend in a detrended series signifies the need for further modeling of the data, and so trend detection is critical.
The daily position time series are analyzed with the now standard fitting of:
slopes (velocities)
offsets (coseismic, equipment change, etc.)
periodic (annual and semiannual terms) terms
postseismic (exponential or logarithmic) parameters
While the parameters that make the time series model are excellent for most stations, some are poorly modeled, have bad data or contain nonlinear effects not taken into account. For the purposes of evaluation of realistic uncertainties, quality control and detection of interesting signals in the time series, we have developed a few simple algorithms to scan the time series every week to detect instances when the model does not represent the data well. Our algorithms look for the following:
outliers
“signals”
residual linear trends
The flagged stations are posted on the GPS Explorer data portal where we look for spatial clustering to gain insight into any un-modeled geophysical or other physical effects.
San Simeon Earthquake
El Mayor-Cucapah Earthquake
Postseismic Deformation: The algorithms effectively detect post-seismic deformation, which is the anomalous trademark of medium to large earthquakes (1992 Mw=7.3 Landers, 1999 Mw= 7.1 Hector Mine, 2003 Mw=6.5 San Simeon, and 2004 Mw= 6.0 Parkfield). The epicenter for each earthquake is circled in red on the map above. The 2010 Mw 7.2 El Mayor Earthquake affected nearly all stations in southern California.