Mass-change experiment in West-Greenland.

Note on computational experiments in West-Greenland, from Nov., 2013.

The purpose of the investidation is to see if GOCE gradient data can be used for the estimation of mass changes in Greenland, specifically Western-Greenland, where data from Jakobshavn Isbraae are available from Joanna Levinsen.
Initially only GOCE Tzz TRF data were used, but the error-estimates were very large. Then we added ground-gravity at the coast, at points where we did not expect any mass change.
This lowered the error-estimate along the coast, see Error-estimates of predicted gravity anomalies (mgal)
Then FC was used to compute differences
The computations were repeated, because the differences clearly were not significant. The error-estimate was decreased by computing a new empirical covariance function for a smaller area.
New error-estimates and differences were computed, now putting the error-associated with the Tzz-grf values to 0.004 EU and the error of the fixed gravity to 1 mgal.
New figures were plotted of the differences and of the errors.
The output files are geocol_grgrf_240d.out and geocol_grwgrf_240d.out.
There is still one problem left, namely that the model standard deviation of Tzz at 250000 km is 0.00064 EU, i.e. it is too small. This makes the signal/noise ratio wrong.
On the other hand, when predicting the gap91 airborne gravity at 3900 m, the differences and the error-estimates agreed very well. For 232 values the mean of the differences was 0.15 mgal and the st.dev. 7.14 mgal, where the mean of the error-estimates was 6.86 mgal. For the other period the numbers are -0.58, 8.37 and 6.85.
Differences at 3900 m.
Then the combination Tyy, Txx was tried. The error estimates became slightly smaller.. The differences increased.
All data, job and output-files are kept in the directory /home/gfy-gut/cct/cct1/jsg03.
A Summary has been prepared for the seminar at DMI, 2014-01-07.

Data:

The Dir3 spherical harmonic model has been used to degree 120, 150 and 240.
NAME OF FILE HOLDING COEFFICIENTS: ../dgravsoft/go_cons_gcf_2_dir_r3.gfc
Two GOCE TRF datasets were used:
DATA INPUT FROM UNIT 25, FILE=Tzz-Dir3-240green_Winter2009.dat
DATA INPUT FROM UNIT 25, FILE=Tzz-Dir3-240green_Summer2012.dat
Subsets of the data were used, e.g. bounded by 68,72,-52,-47.
Two GOCE GRF data-sets were used covering the same time-interval: gogrfw.dat (4510 obs) and gogrfw.dat, respectively.
The program ../dgravsoft/reformat1.f was modified in order to extract the data from GO_GRF-ITG_Tzzc.dat in dgravsoft.

Local ground data were used:

DATA INPUT FROM UNIT 26, FILE=/home/cct/cct1/dgap91/dg_fixed.dat, totally 109 values.
The values were compared to Dir3 to 240 and predicted from the gap91 data-set mentioned below. The result showed large outliers:
0 OBSERVATIONS PREDICTIONS DIFFERENCE ERROR ESTIMATES
MEAND -32.326 -25.625 -6.700
ST.DEVI. 34.249 25.479 29.122
MAX 47.390 14.946 74.016
MIN -104.730 -76.512 -66.336
Consequently the data were subtituted with the values predicted from the gap91 data-set, and stored in a file named dg_fixed_gap91b.dat in column 9.
GAP91 airborne data were used:
DATA INPUT FROM UNIT 27, FILE=gap91-dir3.dat , The values were compared to the Dir3 model to 240:
NUMBER: 232, units: mgal.
0 OBSERVATIONS PREDICTIONS DIFFERENCE ERROR ESTIMATES
MEAND -14.883 -17.138 2.255
ST.DEVI. 23.782 26.390 12.912
MAX 26.600 37.188 33.440
MIN -72.880 -80.668 -26.647
In subsequent calculations, a major issue has been that the values predicted and compared to the gap91 dataset should not have a larger standard deviation of the differences than 13 mgal.

Empirical covariance computation.

empcov_gap91.job was used with output empcov_gap91_120b.out for data bounded by 68,71,-52,-47. The covariance function was output to
COVARIANCE FUNCTION TABLE OUTPUT TO FILE gap91-dir3120b.cov
The computation was repeated with the differences to the model to degree 240,
The covarinces are in empcov_gap91b.out, with a table named gap91-dir3240b.cov.

Covfit:

The covariance function was fitted, covfit_gap91_120.job. and subsequently covfit_gap91240.job with output covfit_gap91240.out.
The essential parameteres were estimated to: a=0628, RE-RB 6.22069 km and VAR(dg)=418.02 (mgal**2).

Prediction jobs using Tzz.

Prediction using data in TRF:
geocol_gr120.job, geocol_grw120.job, with corresponding *.out..
Reduced normal-equations were stored in neqz120s and neqz120w. After this the introduction of track-biases will be tried.
The jobs with terrestrial gravity data added were executed,
geocol_gr120f.job, geocol_grw120f.job.
Prediction with data in GRF:
The covariance parameteres determined from the gap91 values were used with the GRF data in jobs geocol_grgrf.job and geocol_grwgrf.job with output with suffix _240.out.
The differences with respect to the GAP91 data-set was stored in gap91_dif_grf_240.dat and gap91_difw_grf_240.dat.
The mean and standard deviations were 0.3, 7.7 mgal, and 0.1, 7.3 mgal, respectively, i.e. the agreement was as expected improved (since th fixed data were used as input).
The differences between the gridded output files at h=0 in a 0.25 deg grid were computed by fc,
/home/cct/cct1/dgravsoft/pyGravsoft/bin/fc
gr0km_s20120.1igrfw.dat
gr0km_s20120.1igrf.dat
gr0km_dif0.1grf.dat
1 1 5.0
using fc_0km.job with output fc_0kmgrf.out. The difference file was called gr0km_dif0.1grf.dat.

Plotting.

Jobs grplotdgrf.gmt plotted the differences, dgplote0grf.gmt the errors and the data-location, see above.

Computation with track bias-parameters.

The differences were clearly much too large, and would correspond to mass changes of several 100 m equivalent water. Data of actual changes were received from Joanna. They are based on the NASA Airborne Topographic Mapper in the Icebridge project.
An indication of the noise in the Tzz data were that the covariance function predicted a data standard deviation of 0.001 mE, while the estimated standard deviation was 0.01 mE.
This indicated the presence of correlated errors, or that all information above deg. 240 was noise. Therefore we used the Dir3 only to degree 120, to be sure that some signal was left.
A new covariance function was estimated with much more reasonable parameters, AA=0.3004, dR=-2798 m, VARG= 576.19 (mgal**2). The model stdev. for Tzz was 0.009812 corresponding to the observed one of 0.016. For each period a new gravity prediction was made, using Tzz from which track-bias parameters had been subtracted. Then gravity anomalies were computed at 2 km altitude and the result from the two periods subtracted. . Error estimates are still large and have to be multiplied by sqrt(2) for the differences.
Then gravity anomalies were computed at 10 km altitude and the result from the two periods subtracted. . Error estimates are still large and have to be multiplied by sqrt(2) for the differences.
Then gravity anomalies were computed using an error of Tzz at 0.004 E at 10 km altitude and the result from the two periods subtracted. . Error estimates are still large and have to be multiplied by sqrt(2) for the differences.
Experiment with 12 month dataset, 2010, 2012. Dg at 2 km.
differences .
errors .
Experiment with 12 month dataset, 2010, 2011. Dg at 2 km.
differences .
errors .
Last update 2014-03-25 by cct