Kriged Sea Level Rise

Guest post by AJ

Kriged Sea Level Rise

May 14, 2019

Introduction

This post shows a reconstruction of sea level rise (SLR) derived by kriging tide gauge data corrected for vertical land velocity.  Kriging is a statistical interpolation method which takes into account how observations differ over distance.  This method is employed widely in the mining industry to estimate the mineral concentrations of ore bodies.  It has also been used to create global surface temperature reconstructions such as those produced by “Berkeley Earth” and “Cowtan and Way”.

Results

Here is the reconstruction from 1900 to 2017:

Figure 1.  Kriged Sea Level Reconstruction 1990-2017. black: 1900 onward trend, red: 1960 onward trend.

The overall linear trend is 2.3 [2.2 to 2.4] mm/yr.  The trend from 1960 onward is 2.5 [2.4 to 2.6] mm/yr.  The linear trend since 1993 is 2.5 [2.3 to 2.7] mm/yr.  This is significantly less than the 3.3 mm/yr trend estimated by satellite altimetry data.  No significant acceleration or deceleration was found in either regression.

The 20th century SLR was about 23 cm.  The predicted 21st century SLR is 22 cm and 26 cm using the 1900 and 1960 onward quadratic regressions respectively.

The reconstructed values are available here.

Methods

First the tide gauge observations were obtained from the Permanent Service for Mean Sea Level (PSMSL).  Specifically, the Annual Revised Local Reference (RLR) dataset was used.  Stations that were marked with a quality flag and yearly data that was flagged for attention were excluded.

The tide gauge stations were then matched up to the closest GPS stations listed on the vertical land velocity table from SONEL.  The combined data was filtered so that only gauge stations with a GPS station within 80 km were retained.

The combined data was also filtered to exclude stations where the vertical velocity was outside the two standard deviation range (+/- 5 mm/yr) or if the associated uncertainty was more than 0.5 mm/yr.  This was to exclude observations from what might be unstable ground.  Here is a map of the remaining tide gauges:

Figure 2. Sampled Tide Gauge Stations

From the map we can see that the coverage is uneven.  This unevenness is further exacerbated when we consider temporal coverage.  When kriging, stations will not be of equal effective weight.  Stations which do not share much overlapping range with others are more significant.  For example, isolated stations in the Southern Ocean will be relative heavyweights compared to the lightweights in the densely packed North Atlantic.

The difference between consecutive years was then taken on the remaining observations and adjusted for vertical land velocity.  This was then further filtered to only retain values that were within two standard deviations of each year’s mean.  Using this data, the following variogram was generated:

Figure 3. SLR Variogram. black: spherical fit, red: exponential fit

This variogram is actually an average of four recent years of observations (2013-2016).  The spherical fit was subsequently used to krig the reconstruction.  This shows that the observations between neighboring stations are highly correlated, with a y-intercept (nugget) of zero.  The observations show a relative prediction skill out to a range of about 2150 km.  The maximum distance for kriging was limited to this range.

One reason why the “GPS within 80 km” rule was chosen was that beyond this value the nugget crept above zero.  A non-zero nugget indicates a measurement error in the observations.

Initially this post was going to use a variogram derived from Aviso satellite altimetry data.  This idea was abandoned after the following variogram was generated, which again was an average of four recent years:

Figure 4. Aviso Pacific SLR Variogram. black: spherical fit, red: exponential fit

The relatively high nugget value suggests a large measurement error in the observations.  Maybe this is due to the wavy roughness of the ocean surface?  Perhaps the shear number of observations cancels out this noise?  It is noted that an exponential fit works best with this dataset.

The Aviso data was used to compute a 5×5 degree grid of ocean coordinates.  This was a lower resolution version of the 0.25 degree grid provided.  This is the result:

Figure 5. 5×5 Ocean Grid

This grid looks entirely suitable for kriging.  There are a couple of anomalies (Caspian Sea, North Pole), but nothing that would materially impact the results.

Kriging was then performed using the filtered observations, spherical fit, and grid.  In addition to the reconstruction displayed at the top of this post, the number of observations for each year and the percentage of the Earth’s oceans kriged was also tallied:

Figure 6. Number of observations per year

Figure 7. Percentage of oceans kriged

It is noted that the number of observations follows a smoother trend than the percentage of oceans kriged.  This is an indication of the impact of heavyweight stations as observations become available or unavailable.  Additionally, the small sample sizes in the early portion of the time frame explains the associated noise in the reconstruction.

Conclusion

This post calls into question the narrative that SLR is accelerating.  It demonstrates that it is possible to create a linear timeline by employing a suitable method and making reasonable parameter choices.  This may also explain why many tide gauges do not show acceleration.

Of course there were many arbitrary choices made in this analysis, so confirmation bias is a concern.  Due to the various filters, only about a quarter of the PSMSL observations were used, mostly because a suitable match to a GPS station was not found.

One example of how a choice can impact the results is shown by what value is given to the maximum distance parameter used for kriging.  This reconstruction used the range taken from the variogram fit (~2150 km) as this was considered the maximum predictive distance that an observation had relative to other observations.  By varying this parameter one can see how this impacts the predicted 21st century SLR:

Figure 8. Predicted 21st Century SLR based on 1960 onward regressions given different values of maxdist parameter used in krige() function.

This shows the predictive sensitivity to this parameter’s value and brings up the question of what value is most appropriate.  This post will not examine that question.  It is simply noted that parameter choices can significantly impact the results.  This is probably a factor in any tide gauge SLR reconstruction.

Thank-you for your time.

Links

The R source code and Intermediary files can be found here

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References

1. Permanent Service for Mean Sea Level (PSMSL), 2019, “Tide Gauge Data”, Retrieved 01 Apr 2019 from http://www.psmsl.org/data/obtaining/.
   Simon J. Holgate, Andrew Matthews, Philip L. Woodworth, Lesley J. Rickards, Mark E. Tamisiea, Elizabeth Bradshaw, Peter R. Foden, Kathleen M. Gordon, Svetlana Jevrejeva, and Jeff Pugh (2013) New Data Systems and Products at the Permanent Service for Mean Sea Level. Journal of Coastal Research: Volume 29, Issue 3: pp. 493 – 504. doi:10.2112/JCOASTRES-D-12-00175.1.
2. SONEL: Santamaría-Gómez A., M. Gravelle, S. Dangendorf, M. Marcos, G. Spada, G. Wöppelmann (2017). Uncertainty of the 20th century sea-level rise due to vertical land motion errors. Earth and Planetary Science Letters, 473, 24-32.
3. Aviso: The altimeter products were produced by Ssalto/Duacs and distributed by Aviso+, with support from Cnes (https://www.aviso.altimetry.fr).