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Kimberly Slinski

Colorado School of Mines

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ABSTRACT:

This dataset contains total water storage anomalies (TWSAs) over East Africa predicted from observations from the Gravity Recovery and Climate Experiment (GRACE) mission using a Bayesian spatiotemporal mixed effects model. The model was also used to estimate missing observations from the GRACE mission. We obtained the RL05M.1 CRI Filtered Version 2 (Wiese et al., 2016, Watkins et al., 2015) monthly mass grids of the NASA JPL global mascon solution from the JPL’s GRACE TELLUS site. TWSAs for 40 mascons covering East Africa were extracted from the dataset for May, 2002 through August, 2016. This dataset did not contain data for several months due to missing observations in the global mascon solution dataset. The missing values were predicted by the model.

The following Bayesian spatiotemporal mixed effects model was used to generate the modeled dataset. The GRACE TWSA data can be represented by the spatiotemporal mixed effects model: Zt = Xtβ + Yt + εt; where Zt is a vector of TWSAs observations at time t, Xt is a matrix of fixed seasonal affects, β is a vector of fixed covariate values for the seasonal affects, Yt is a vector of the true, underlying process, and εt is a vector of errors error terms.

The true TWSAs at time t can be modeled by the autoregressive process: Yt = ΦYt-1 +ηt; where Φ defines the spatial-temporal structure of the GRACE TWSA and ηt is a vector of errors error terms. However, estimating Φ is computationally difficult because of its high dimensionality.

Empirical orthogonal function (EOF) analysis (Cressie & Wikle, 2011) can be used to identify the principal spatial structures in the GRACE TWSA data. The dimensionality of the model is reduced by modeling the spatial structure using EOFs: Yt = Mut +ηt; ut = Ξut-1 + ζt; where M is a matrix of fixed, time-invariant basis functions defined as the first p empirical orthogonal functions (EOFs) of the data, ut is a vector representing a rank reduced process at time t, Ξ is a diagonal matrix defined as diag(ξ1.. ξp), representing the eigenvalues corresponding to the EOFs, and ζt is a vector of random errors error terms. EOF analysis greatly reduces the computation burden of estimating the spatial-temporal structure of the GRACE TWSA.

A Bayesian approach is used to estimate the stochastic distributions for the model parameters ut , u0 , σ2ζ , β , and ξj. Bayesian priors are chosen for each parameter and Monte Carlo Makov Chain methods are used to estimate the distribution parameters following the algorithm:
I. Initialize the parameter values
II. Gibs sampler draws from the posterior conditional for parameters ut , σ2ζ , u0, and β
III. Slice sampler draws from the posterior conditional for the parameter ξj
IV. Repeat II and III until the Markov chain converges to a stationary distribution

The calculations to implement the model are provided as part of the data archive.

The SI dataset contains the following fields:
• ID: mascon ID assigned by NASA JPL
• Year: year of the TWSA
• Month: month of the TWSA
• Day: day of the TWSA
• TWSA_Obs: observed TWSA (NA if missing) in cm
• TWSA_Mod: observed TWSA in cm
• CI05: lower limit of the 90% credible interval for the modeled value in cm
• CI95: upper limit of the 90% credible interval for the modeled value in cm

This dataset was created on April 28, 2017.

Cressie, N., & Wikle, C. K. (2011). Statistics for Spatio-Temporal Data. Hoboken, New Jersey: John Wiley & Sons, Inc.
Watkins, M. M., Wiese, D. N., Yuan, D.-N., Boening, C., & Landerer, F. W. (2015). Improved methods for observing Earth’s time variable mass distribution with GRACE using spherical cap mascons: Improved Gravity Observations from GRACE. Journal of Geophysical Research: Solid Earth, 120(4), 2648–2671. https://doi.org/10.1002/2014JB011547
D. N. Wiese, D.-N. Yuan, C. Boening, F. W. Landerer, M. M. Watkins. 2016. JPL GRACE Mascon Ocean, Ice, and Hydrology Equivalent Water Height RL05M.1 CRI Filtered Version 2. Ver. 2. PO.DAAC, USA. Dataset accessed [2017-02-07] at http://dx.doi.org/10.5067/TEMSC-2LCR5.

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ABSTRACT:

This dataset contains total water storage anomalies (TWSAs) over East Africa predicted from observations from the Gravity Recovery and Climate Experiment (GRACE) mission using a Bayesian spatiotemporal mixed effects model. The model was also used to estimate missing observations from the GRACE mission. We obtained the RL05M.1 CRI Filtered Version 2 (Wiese et al., 2016, Watkins et al., 2015) monthly mass grids of the NASA JPL global mascon solution from the JPL’s GRACE TELLUS site. TWSAs for 40 mascons covering East Africa were extracted from the dataset for May, 2002 through August, 2016. This dataset did not contain data for several months due to missing observations in the global mascon solution dataset. The missing values were predicted by the model.

The following Bayesian spatiotemporal mixed effects model was used to generate the modeled dataset. The GRACE TWSA data can be represented by the spatiotemporal mixed effects model: Zt = Xtβ + Yt + εt; where Zt is a vector of TWSAs observations at time t, Xt is a matrix of fixed seasonal affects, β is a vector of fixed covariate values for the seasonal affects, Yt is a vector of the true, underlying process, and εt is a vector of errors error terms.

The true TWSAs at time t can be modeled by the autoregressive process: Yt = ΦYt-1 +ηt; where Φ defines the spatial-temporal structure of the GRACE TWSA and ηt is a vector of errors error terms. However, estimating Φ is computationally difficult because of its high dimensionality.

Empirical orthogonal function (EOF) analysis (Cressie & Wikle, 2011) can be used to identify the principal spatial structures in the GRACE TWSA data. The dimensionality of the model is reduced by modeling the spatial structure using EOFs: Yt = Mut +ηt; ut = Ξut-1 + ζt; where M is a matrix of fixed, time-invariant basis functions defined as the first p empirical orthogonal functions (EOFs) of the data, ut is a vector representing a rank reduced process at time t, Ξ is a diagonal matrix defined as diag(ξ1.. ξp), representing the eigenvalues corresponding to the EOFs, and ζt is a vector of random errors error terms. EOF analysis greatly reduces the computation burden of estimating the spatial-temporal structure of the GRACE TWSA.

A Bayesian approach is used to estimate the stochastic distributions for the model parameters ut , u0 , σ2ζ , β , and ξj. Bayesian priors are chosen for each parameter and Monte Carlo Makov Chain methods are used to estimate the distribution parameters following the algorithm:
I. Initialize the parameter values
II. Gibs sampler draws from the posterior conditional for parameters ut , σ2ζ , u0, and β
III. Slice sampler draws from the posterior conditional for the parameter ξj
IV. Repeat II and III until the Markov chain converges to a stationary distribution

The calculations to implement the model are provided as part of the data archive.

The SI dataset contains the following fields:
• ID: mascon ID assigned by NASA JPL
• Year: year of the TWSA
• Month: month of the TWSA
• Day: day of the TWSA
• TWSA_Obs: observed TWSA (NA if missing) in cm
• TWSA_Mod: observed TWSA in cm
• CI05: lower limit of the 90% credible interval for the modeled value in cm
• CI95: upper limit of the 90% credible interval for the modeled value in cm

This dataset was created on April 28, 2017.

Cressie, N., & Wikle, C. K. (2011). Statistics for Spatio-Temporal Data. Hoboken, New Jersey: John Wiley & Sons, Inc.
Watkins, M. M., Wiese, D. N., Yuan, D.-N., Boening, C., & Landerer, F. W. (2015). Improved methods for observing Earth’s time variable mass distribution with GRACE using spherical cap mascons: Improved Gravity Observations from GRACE. Journal of Geophysical Research: Solid Earth, 120(4), 2648–2671. https://doi.org/10.1002/2014JB011547
D. N. Wiese, D.-N. Yuan, C. Boening, F. W. Landerer, M. M. Watkins. 2016. JPL GRACE Mascon Ocean, Ice, and Hydrology Equivalent Water Height RL05M.1 CRI Filtered Version 2. Ver. 2. PO.DAAC, USA. Dataset accessed [2017-02-07] at http://dx.doi.org/10.5067/TEMSC-2LCR5.

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ABSTRACT:

This dataset contains standardized drought indexes (SIs) over East Africa derived from total water storage anomaly (TWSA) observations from the Gravity Recovery and Climate Experiment (GRACE) mission. We obtained the RL05M.1 CRI Filtered Version 2 (Wiese et al., 2016, Watkins et al., 2015) monthly mass grids of the NASA JPL global mascon solution from the JPL’s GRACE TELLUS site. TWSAs for 40 mascons covering East Africa were extracted from the dataset for May, 2002 through August, 2016. Observations collected between the 10th and 20th day of the month were retained as the SI dataset. The resulting SI dataset did not contain data for several months due to missing observations in the global mascon solution dataset or because the observation for the month was not between the 10th and 20th day of the month. The missing values were interpolated and the final SI dataset contains a TWSA value for each mascon for each month from May, 2002 through August, 2016. 1-month, 3-month, and 6-month standardized drought indexes were calculated following the nonparametric approach described by Farahman and AghaKouchak (2015). This methodology derives the SI using the empirical Gringorten plotting position (Gringorten, 1963).

The SI dataset contains the following fields:
• ID: mascon ID assigned by NASA JPL
• Year: year of the SI
• Month: month of the SI
• SI1Mo: one-month SI
• SI3Mo: three-month SI
• SI6Mo: six-month SI

This dataset was created on April 20, 2017. Figures mapping the drought indices by year are presented with the dataset.

Farahmand, A., & AghaKouchak, A. (2015). A generalized framework for deriving nonparametric standardized drought indicators. Advances in Water Resources, 76, 140–145. https://doi.org/10.1016/j.advwatres.2014.11.012
Gringorten, I. I. (1963). A plotting rule for extreme probability paper. Journal of Geophysical Research, 68(3), 813–814. https://doi.org/10.1029/JZ068i003p00813
Watkins, M. M., Wiese, D. N., Yuan, D.-N., Boening, C., & Landerer, F. W. (2015). Improved methods for observing Earth’s time variable mass distribution with GRACE using spherical cap mascons: Improved Gravity Observations from GRACE. Journal of Geophysical Research: Solid Earth, 120(4), 2648–2671. https://doi.org/10.1002/2014JB011547
D. N. Wiese, D.-N. Yuan, C. Boening, F. W. Landerer, M. M. Watkins. 2016. JPL GRACE Mascon Ocean, Ice, and Hydrology Equivalent Water Height RL05M.1 CRI Filtered Version 2. Ver. 2. PO.DAAC, USA. Dataset accessed [2017-02-07] at http://dx.doi.org/10.5067/TEMSC-2LCR5.

Show More

ABSTRACT:

This dataset contains standardized drought indexes (SIs) over East Africa derived from total water storage anomaly (TWSA) observations from the Gravity Recovery and Climate Experiment (GRACE) mission. We obtained the RL05M.1 CRI Filtered Version 2 (Wiese et al., 2016, Watkins et al., 2015) monthly mass grids of the NASA JPL global mascon solution from the JPL’s GRACE TELLUS site. TWSAs for 40 mascons covering East Africa were extracted from the dataset for May, 2002 through August, 2016. Observations collected between the 10th and 20th day of the month were retained as the SI dataset. The resulting SI dataset did not contain data for several months due to missing observations in the global mascon solution dataset or because the observation for the month was not between the 10th and 20th day of the month. The missing values were interpolated and the final SI dataset contains a TWSA value for each mascon for each month from May, 2002 through August, 2016. 1-month, 3-month, and 6-month standardized drought indexes were calculated following the nonparametric approach described by Farahman and AghaKouchak (2015). This methodology derives the SI using the empirical Gringorten plotting position (Gringorten, 1963).

The SI dataset contains the following fields:
• ID: mascon ID assigned by NASA JPL
• Year: year of the SI
• Month: month of the SI
• SI1Mo: one-month SI
• SI3Mo: three-month SI
• SI6Mo: six-month SI

This dataset was created on April 20, 2017. Figures mapping the drought indices by year are presented with the dataset.

Farahmand, A., & AghaKouchak, A. (2015). A generalized framework for deriving nonparametric standardized drought indicators. Advances in Water Resources, 76, 140–145. https://doi.org/10.1016/j.advwatres.2014.11.012
Gringorten, I. I. (1963). A plotting rule for extreme probability paper. Journal of Geophysical Research, 68(3), 813–814. https://doi.org/10.1029/JZ068i003p00813
Watkins, M. M., Wiese, D. N., Yuan, D.-N., Boening, C., & Landerer, F. W. (2015). Improved methods for observing Earth’s time variable mass distribution with GRACE using spherical cap mascons: Improved Gravity Observations from GRACE. Journal of Geophysical Research: Solid Earth, 120(4), 2648–2671. https://doi.org/10.1002/2014JB011547
D. N. Wiese, D.-N. Yuan, C. Boening, F. W. Landerer, M. M. Watkins. 2016. JPL GRACE Mascon Ocean, Ice, and Hydrology Equivalent Water Height RL05M.1 CRI Filtered Version 2. Ver. 2. PO.DAAC, USA. Dataset accessed [2017-02-07] at http://dx.doi.org/10.5067/TEMSC-2LCR5.

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ABSTRACT:

This dataset consists of InSAR-measured line-of-sight surface deformation over the Ara watershed (located in northern Benin) for two dry seasons (November 2015-June 2016 and November 2016-June 2017). Thirty-six single look complex (SLC) images acquired by the Sentinel 1 mission were obtained from the Alaska Satellite Facility (ASF) Distributed Active Archive Centers (DAAC; http://www.asf.alaska.edu/). 12-, 24-, and 36-day interferograms were generated using the open source (GNU General Public License) Generic Mapping Tools 5 Synthetic Aperture Radar (GMT5SAR) processing system (Sandwell et al 2016, Massonnet and Feigl 1998). GMT5SAR geometrically aligns Sentinel TOPSAR images to a single master image with centimeter accuracy, maps topography into phase, and forms a stack of complex interferograms (Sandwell et al 2016). The Generic Mapping Tools- (GMT-) (Wessel et al 2013) based GMT5SAR postprocesser filters the interferogram and generates phase, coherence, and phase gradient products. GMT5SAR unwraps the interferograms using the well-known snaphu algorithm (Chen and Zebker 2000). Filter and decimation parameters for the inSAR processing were chosen to produce relatively high resolution interferograms, considering the computational cost of phase unwrapping. Lighter filtering and decimation improves interferogram resolution, but increases the computational time for phase unwrapping. Pixels were decimated by a factor of 8 in the range and 2 in the azimuth directions, generating interferograms with a pixel size of approximately 18.4 x 28.2 meters (range x azimuth). A 100 meter Gaussian filter was selected for the Ara study area. Enhances spectral diversity was used to reduce phase mismatch at the burst boundary (Sandwell et al 2016). The new small baseline subset(NSBAS) technique (Doin et al 2011) was used was used to generate a time series analysis of deformation across the study area. The NSBAS algorithm was applied using the Generic InSAR Analysis Toolbox (GIAnT; Agram et al 2012, 2013). The GIAnT tool box stacked the geometrically-aligned phase-unwrapped interferograms, estimated and applied corrections for residual long‐wavelength errors due to imprecise orbits, and estimated line-of-sight displacements using the NSBAS technique.

Agram P S, Jolivet R, Riel B, Lin Y N, Simons M, Hetland E, Doin M-P and Lasserre C 2013 New Radar Interferometric Time Series Analysis Toolbox Released Eos Trans. Am. Geophys. Union 94 69–70
Chen C W and Zebker H A 2000 Network approaches to two-dimensional phase unwrapping: intractability and two new algorithms J Opt Soc Am A 17 401–414
Doin M-P, Guillaso S, Jolivet R, Lasserre C, Lodge F, Ducret G and Grandin R 2011 Presentation of the small baseline NSBAS processing chain on a case example: the Etna deformation monitoring from 2003 to 2010 using Envisat data Proceedings of the Fringe Symposium (ES) pp 3434–3437
Massonnet D and Feigl K L 1998 Radar interferometry and its application to changes in the Earth’s surface Rev. Geophys. 36 441–500
Sandwell D, Mellors R, Tong X, Wei M and Wessel P 2016 Gmtsar: An insar processing system based on generic mapping tools (second edition)
Wessel P, Smith W H, Scharroo R, Luis J and Wobbe F 2013 Generic mapping tools: improved version released Eos Trans. Am. Geophys. Union 94 409–410

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ABSTRACT:

The “active-passive surface water classification” (APWC) method leverages cloud-based computing resources and machine learning techniques to merge Sentinel 1 synthetic aperture radar and Landsat observations and generate monthly 10-meter resolution waterbody maps. Merging data from two sensor types reduces the impact of errors associated with the individual sensors. The skill of the APWC method is demonstrated by mapping surface water change over the Awash River basin in Ethiopia from October 2014 through March 2017. This period corresponds to the 2015 East African regional drought and 2016 localized flood events. Errors of omission and commission in the case study area are 7.16% and 1.91%, respectively. These data were generated using the APWC method on August 18, 2017.

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Composite Resource Composite Resource

ABSTRACT:

This dataset consists of InSAR-measured line-of-sight surface deformation over the Ara watershed (located in northern Benin) for two dry seasons (November 2015-June 2016 and November 2016-June 2017). Thirty-six single look complex (SLC) images acquired by the Sentinel 1 mission were obtained from the Alaska Satellite Facility (ASF) Distributed Active Archive Centers (DAAC; http://www.asf.alaska.edu/). 12-, 24-, and 36-day interferograms were generated using the open source (GNU General Public License) Generic Mapping Tools 5 Synthetic Aperture Radar (GMT5SAR) processing system (Sandwell et al 2016, Massonnet and Feigl 1998). GMT5SAR geometrically aligns Sentinel TOPSAR images to a single master image with centimeter accuracy, maps topography into phase, and forms a stack of complex interferograms (Sandwell et al 2016). The Generic Mapping Tools- (GMT-) (Wessel et al 2013) based GMT5SAR postprocesser filters the interferogram and generates phase, coherence, and phase gradient products. GMT5SAR unwraps the interferograms using the well-known snaphu algorithm (Chen and Zebker 2000). Filter and decimation parameters for the inSAR processing were chosen to produce relatively high resolution interferograms, considering the computational cost of phase unwrapping. Lighter filtering and decimation improves interferogram resolution, but increases the computational time for phase unwrapping. Pixels were decimated by a factor of 8 in the range and 2 in the azimuth directions, generating interferograms with a pixel size of approximately 18.4 x 28.2 meters (range x azimuth). A 100 meter Gaussian filter was selected for the Ara study area. Enhances spectral diversity was used to reduce phase mismatch at the burst boundary (Sandwell et al 2016). The new small baseline subset(NSBAS) technique (Doin et al 2011) was used was used to generate a time series analysis of deformation across the study area. The NSBAS algorithm was applied using the Generic InSAR Analysis Toolbox (GIAnT; Agram et al 2012, 2013). The GIAnT tool box stacked the geometrically-aligned phase-unwrapped interferograms, estimated and applied corrections for residual long‐wavelength errors due to imprecise orbits, and estimated line-of-sight displacements using the NSBAS technique.

Agram P S, Jolivet R, Riel B, Lin Y N, Simons M, Hetland E, Doin M-P and Lasserre C 2013 New Radar Interferometric Time Series Analysis Toolbox Released Eos Trans. Am. Geophys. Union 94 69–70
Chen C W and Zebker H A 2000 Network approaches to two-dimensional phase unwrapping: intractability and two new algorithms J Opt Soc Am A 17 401–414
Doin M-P, Guillaso S, Jolivet R, Lasserre C, Lodge F, Ducret G and Grandin R 2011 Presentation of the small baseline NSBAS processing chain on a case example: the Etna deformation monitoring from 2003 to 2010 using Envisat data Proceedings of the Fringe Symposium (ES) pp 3434–3437
Massonnet D and Feigl K L 1998 Radar interferometry and its application to changes in the Earth’s surface Rev. Geophys. 36 441–500
Sandwell D, Mellors R, Tong X, Wei M and Wessel P 2016 Gmtsar: An insar processing system based on generic mapping tools (second edition)
Wessel P, Smith W H, Scharroo R, Luis J and Wobbe F 2013 Generic mapping tools: improved version released Eos Trans. Am. Geophys. Union 94 409–410

Show More
Composite Resource Composite Resource
GRACE-based Standardized Drought Indices over East Africa for 2002-2016
Created: March 10, 2019, 8:10 p.m.
Authors: Kimberly Slinski · Terri Hogue · John McCray

ABSTRACT:

This dataset contains standardized drought indexes (SIs) over East Africa derived from total water storage anomaly (TWSA) observations from the Gravity Recovery and Climate Experiment (GRACE) mission. We obtained the RL05M.1 CRI Filtered Version 2 (Wiese et al., 2016, Watkins et al., 2015) monthly mass grids of the NASA JPL global mascon solution from the JPL’s GRACE TELLUS site. TWSAs for 40 mascons covering East Africa were extracted from the dataset for May, 2002 through August, 2016. Observations collected between the 10th and 20th day of the month were retained as the SI dataset. The resulting SI dataset did not contain data for several months due to missing observations in the global mascon solution dataset or because the observation for the month was not between the 10th and 20th day of the month. The missing values were interpolated and the final SI dataset contains a TWSA value for each mascon for each month from May, 2002 through August, 2016. 1-month, 3-month, and 6-month standardized drought indexes were calculated following the nonparametric approach described by Farahman and AghaKouchak (2015). This methodology derives the SI using the empirical Gringorten plotting position (Gringorten, 1963).

The SI dataset contains the following fields:
• ID: mascon ID assigned by NASA JPL
• Year: year of the SI
• Month: month of the SI
• SI1Mo: one-month SI
• SI3Mo: three-month SI
• SI6Mo: six-month SI

This dataset was created on April 20, 2017. Figures mapping the drought indices by year are presented with the dataset.

Farahmand, A., & AghaKouchak, A. (2015). A generalized framework for deriving nonparametric standardized drought indicators. Advances in Water Resources, 76, 140–145. https://doi.org/10.1016/j.advwatres.2014.11.012
Gringorten, I. I. (1963). A plotting rule for extreme probability paper. Journal of Geophysical Research, 68(3), 813–814. https://doi.org/10.1029/JZ068i003p00813
Watkins, M. M., Wiese, D. N., Yuan, D.-N., Boening, C., & Landerer, F. W. (2015). Improved methods for observing Earth’s time variable mass distribution with GRACE using spherical cap mascons: Improved Gravity Observations from GRACE. Journal of Geophysical Research: Solid Earth, 120(4), 2648–2671. https://doi.org/10.1002/2014JB011547
D. N. Wiese, D.-N. Yuan, C. Boening, F. W. Landerer, M. M. Watkins. 2016. JPL GRACE Mascon Ocean, Ice, and Hydrology Equivalent Water Height RL05M.1 CRI Filtered Version 2. Ver. 2. PO.DAAC, USA. Dataset accessed [2017-02-07] at http://dx.doi.org/10.5067/TEMSC-2LCR5.

Show More
Composite Resource Composite Resource

ABSTRACT:

This dataset contains standardized drought indexes (SIs) over East Africa derived from total water storage anomaly (TWSA) observations from the Gravity Recovery and Climate Experiment (GRACE) mission. We obtained the RL05M.1 CRI Filtered Version 2 (Wiese et al., 2016, Watkins et al., 2015) monthly mass grids of the NASA JPL global mascon solution from the JPL’s GRACE TELLUS site. TWSAs for 40 mascons covering East Africa were extracted from the dataset for May, 2002 through August, 2016. Observations collected between the 10th and 20th day of the month were retained as the SI dataset. The resulting SI dataset did not contain data for several months due to missing observations in the global mascon solution dataset or because the observation for the month was not between the 10th and 20th day of the month. The missing values were interpolated and the final SI dataset contains a TWSA value for each mascon for each month from May, 2002 through August, 2016. 1-month, 3-month, and 6-month standardized drought indexes were calculated following the nonparametric approach described by Farahman and AghaKouchak (2015). This methodology derives the SI using the empirical Gringorten plotting position (Gringorten, 1963).

The SI dataset contains the following fields:
• ID: mascon ID assigned by NASA JPL
• Year: year of the SI
• Month: month of the SI
• SI1Mo: one-month SI
• SI3Mo: three-month SI
• SI6Mo: six-month SI

This dataset was created on April 20, 2017. Figures mapping the drought indices by year are presented with the dataset.

Farahmand, A., & AghaKouchak, A. (2015). A generalized framework for deriving nonparametric standardized drought indicators. Advances in Water Resources, 76, 140–145. https://doi.org/10.1016/j.advwatres.2014.11.012
Gringorten, I. I. (1963). A plotting rule for extreme probability paper. Journal of Geophysical Research, 68(3), 813–814. https://doi.org/10.1029/JZ068i003p00813
Watkins, M. M., Wiese, D. N., Yuan, D.-N., Boening, C., & Landerer, F. W. (2015). Improved methods for observing Earth’s time variable mass distribution with GRACE using spherical cap mascons: Improved Gravity Observations from GRACE. Journal of Geophysical Research: Solid Earth, 120(4), 2648–2671. https://doi.org/10.1002/2014JB011547
D. N. Wiese, D.-N. Yuan, C. Boening, F. W. Landerer, M. M. Watkins. 2016. JPL GRACE Mascon Ocean, Ice, and Hydrology Equivalent Water Height RL05M.1 CRI Filtered Version 2. Ver. 2. PO.DAAC, USA. Dataset accessed [2017-02-07] at http://dx.doi.org/10.5067/TEMSC-2LCR5.

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Composite Resource Composite Resource
Total Water Storage Anomalies over East Africa Predicted by a GRACE-Based Bayesian Spatiotemporal Mixed Effects Model
Created: March 10, 2019, 8:35 p.m.
Authors: Kimberly Slinski · Terri Hogue · John McCray · Aaron Porter

ABSTRACT:

This dataset contains total water storage anomalies (TWSAs) over East Africa predicted from observations from the Gravity Recovery and Climate Experiment (GRACE) mission using a Bayesian spatiotemporal mixed effects model. The model was also used to estimate missing observations from the GRACE mission. We obtained the RL05M.1 CRI Filtered Version 2 (Wiese et al., 2016, Watkins et al., 2015) monthly mass grids of the NASA JPL global mascon solution from the JPL’s GRACE TELLUS site. TWSAs for 40 mascons covering East Africa were extracted from the dataset for May, 2002 through August, 2016. This dataset did not contain data for several months due to missing observations in the global mascon solution dataset. The missing values were predicted by the model.

The following Bayesian spatiotemporal mixed effects model was used to generate the modeled dataset. The GRACE TWSA data can be represented by the spatiotemporal mixed effects model: Zt = Xtβ + Yt + εt; where Zt is a vector of TWSAs observations at time t, Xt is a matrix of fixed seasonal affects, β is a vector of fixed covariate values for the seasonal affects, Yt is a vector of the true, underlying process, and εt is a vector of errors error terms.

The true TWSAs at time t can be modeled by the autoregressive process: Yt = ΦYt-1 +ηt; where Φ defines the spatial-temporal structure of the GRACE TWSA and ηt is a vector of errors error terms. However, estimating Φ is computationally difficult because of its high dimensionality.

Empirical orthogonal function (EOF) analysis (Cressie & Wikle, 2011) can be used to identify the principal spatial structures in the GRACE TWSA data. The dimensionality of the model is reduced by modeling the spatial structure using EOFs: Yt = Mut +ηt; ut = Ξut-1 + ζt; where M is a matrix of fixed, time-invariant basis functions defined as the first p empirical orthogonal functions (EOFs) of the data, ut is a vector representing a rank reduced process at time t, Ξ is a diagonal matrix defined as diag(ξ1.. ξp), representing the eigenvalues corresponding to the EOFs, and ζt is a vector of random errors error terms. EOF analysis greatly reduces the computation burden of estimating the spatial-temporal structure of the GRACE TWSA.

A Bayesian approach is used to estimate the stochastic distributions for the model parameters ut , u0 , σ2ζ , β , and ξj. Bayesian priors are chosen for each parameter and Monte Carlo Makov Chain methods are used to estimate the distribution parameters following the algorithm:
I. Initialize the parameter values
II. Gibs sampler draws from the posterior conditional for parameters ut , σ2ζ , u0, and β
III. Slice sampler draws from the posterior conditional for the parameter ξj
IV. Repeat II and III until the Markov chain converges to a stationary distribution

The calculations to implement the model are provided as part of the data archive.

The SI dataset contains the following fields:
• ID: mascon ID assigned by NASA JPL
• Year: year of the TWSA
• Month: month of the TWSA
• Day: day of the TWSA
• TWSA_Obs: observed TWSA (NA if missing) in cm
• TWSA_Mod: observed TWSA in cm
• CI05: lower limit of the 90% credible interval for the modeled value in cm
• CI95: upper limit of the 90% credible interval for the modeled value in cm

This dataset was created on April 28, 2017.

Cressie, N., & Wikle, C. K. (2011). Statistics for Spatio-Temporal Data. Hoboken, New Jersey: John Wiley & Sons, Inc.
Watkins, M. M., Wiese, D. N., Yuan, D.-N., Boening, C., & Landerer, F. W. (2015). Improved methods for observing Earth’s time variable mass distribution with GRACE using spherical cap mascons: Improved Gravity Observations from GRACE. Journal of Geophysical Research: Solid Earth, 120(4), 2648–2671. https://doi.org/10.1002/2014JB011547
D. N. Wiese, D.-N. Yuan, C. Boening, F. W. Landerer, M. M. Watkins. 2016. JPL GRACE Mascon Ocean, Ice, and Hydrology Equivalent Water Height RL05M.1 CRI Filtered Version 2. Ver. 2. PO.DAAC, USA. Dataset accessed [2017-02-07] at http://dx.doi.org/10.5067/TEMSC-2LCR5.

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Composite Resource Composite Resource
Total Water Storage Anomalies over East Africa Predicted by a GRACE-Based Bayesian Spatiotemporal Mixed Effects Model
Created: March 10, 2019, 9:06 p.m.
Authors: Kimberly Slinski · Terri Hogue · John McCray · Aaron Porter

ABSTRACT:

This dataset contains total water storage anomalies (TWSAs) over East Africa predicted from observations from the Gravity Recovery and Climate Experiment (GRACE) mission using a Bayesian spatiotemporal mixed effects model. The model was also used to estimate missing observations from the GRACE mission. We obtained the RL05M.1 CRI Filtered Version 2 (Wiese et al., 2016, Watkins et al., 2015) monthly mass grids of the NASA JPL global mascon solution from the JPL’s GRACE TELLUS site. TWSAs for 40 mascons covering East Africa were extracted from the dataset for May, 2002 through August, 2016. This dataset did not contain data for several months due to missing observations in the global mascon solution dataset. The missing values were predicted by the model.

The following Bayesian spatiotemporal mixed effects model was used to generate the modeled dataset. The GRACE TWSA data can be represented by the spatiotemporal mixed effects model: Zt = Xtβ + Yt + εt; where Zt is a vector of TWSAs observations at time t, Xt is a matrix of fixed seasonal affects, β is a vector of fixed covariate values for the seasonal affects, Yt is a vector of the true, underlying process, and εt is a vector of errors error terms.

The true TWSAs at time t can be modeled by the autoregressive process: Yt = ΦYt-1 +ηt; where Φ defines the spatial-temporal structure of the GRACE TWSA and ηt is a vector of errors error terms. However, estimating Φ is computationally difficult because of its high dimensionality.

Empirical orthogonal function (EOF) analysis (Cressie & Wikle, 2011) can be used to identify the principal spatial structures in the GRACE TWSA data. The dimensionality of the model is reduced by modeling the spatial structure using EOFs: Yt = Mut +ηt; ut = Ξut-1 + ζt; where M is a matrix of fixed, time-invariant basis functions defined as the first p empirical orthogonal functions (EOFs) of the data, ut is a vector representing a rank reduced process at time t, Ξ is a diagonal matrix defined as diag(ξ1.. ξp), representing the eigenvalues corresponding to the EOFs, and ζt is a vector of random errors error terms. EOF analysis greatly reduces the computation burden of estimating the spatial-temporal structure of the GRACE TWSA.

A Bayesian approach is used to estimate the stochastic distributions for the model parameters ut , u0 , σ2ζ , β , and ξj. Bayesian priors are chosen for each parameter and Monte Carlo Makov Chain methods are used to estimate the distribution parameters following the algorithm:
I. Initialize the parameter values
II. Gibs sampler draws from the posterior conditional for parameters ut , σ2ζ , u0, and β
III. Slice sampler draws from the posterior conditional for the parameter ξj
IV. Repeat II and III until the Markov chain converges to a stationary distribution

The calculations to implement the model are provided as part of the data archive.

The SI dataset contains the following fields:
• ID: mascon ID assigned by NASA JPL
• Year: year of the TWSA
• Month: month of the TWSA
• Day: day of the TWSA
• TWSA_Obs: observed TWSA (NA if missing) in cm
• TWSA_Mod: observed TWSA in cm
• CI05: lower limit of the 90% credible interval for the modeled value in cm
• CI95: upper limit of the 90% credible interval for the modeled value in cm

This dataset was created on April 28, 2017.

Cressie, N., & Wikle, C. K. (2011). Statistics for Spatio-Temporal Data. Hoboken, New Jersey: John Wiley & Sons, Inc.
Watkins, M. M., Wiese, D. N., Yuan, D.-N., Boening, C., & Landerer, F. W. (2015). Improved methods for observing Earth’s time variable mass distribution with GRACE using spherical cap mascons: Improved Gravity Observations from GRACE. Journal of Geophysical Research: Solid Earth, 120(4), 2648–2671. https://doi.org/10.1002/2014JB011547
D. N. Wiese, D.-N. Yuan, C. Boening, F. W. Landerer, M. M. Watkins. 2016. JPL GRACE Mascon Ocean, Ice, and Hydrology Equivalent Water Height RL05M.1 CRI Filtered Version 2. Ver. 2. PO.DAAC, USA. Dataset accessed [2017-02-07] at http://dx.doi.org/10.5067/TEMSC-2LCR5.

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