- Email: [email protected]
Short term comparison of climate model predictions and satellite altimeter measurements of sea levels
Coastal Engineering 60 (2012) 319–322
Contents lists available at SciVerse ScienceDirect
Coastal Engineering journal homepage: www.elsevier.com/locate/coastaleng
Short communication
Short term comparison of climate model predictions and satellite altimeter measurements of sea levels Alberto A. Boretti School of Science and Engineering, University of Ballarat, Ballarat, Victoria, Australia
a r t i c l e
i n f o
Article history: Received 30 June 2011 Received in revised form 21 October 2011 Accepted 21 October 2011 Available online 10 November 2011 Keywords: Climate models Sea level rise Satellite altimeter measurements Statistical analysis Curve fitting
a b s t r a c t Climate models (http://climatecommission.govspace.gov.au/files/2011/05/4108-CC-Science-Update-PRINTCHANGES.pdf, 2011; http://www.ipcc.ch/publications_and_data/publications_ipcc_fourth_assessment_report_ synthesis_report.htm, 2011; Rahmstorf, 2007, 2010) calculate that temperatures are increasing globally and sea level rises are increasing due to anthropogenic carbon dioxide emissions. More recent predictions (http://climatecommission.govspace.gov.au/files/2011/05/4108-CC-Science-Update-PRINT-CHANGES.pdf, 2011; Rahmstorf, 2007, 2010) have forecasted that sea level rises by 2100 will be higher than the 2007 projections by the Intergovernmental Panel on Climate Change (http://www.ipcc.ch/publications_and_data/ publications_ipcc_fourth_assessment_report_synthesis_report.htm, 2011), with projected sea level rises increasing from 18–59 cm to 100 cm. In this brief communication, the predictions of Rahmstorf (2007) are validated against the experimental evidence over a 20 year period. The University of Colorado Sea Level satellite monitoring shows that the rate of rise of the sea level is not only well below the values computed in http://climatecommission.govspace.gov.au/files/2011/05/4108-CC-Science-Update-PRINTCHANGES.pdf (2011) and Rahmstorf (2007, 2010), but actually reducing rather than increasing (http://sealevel. colorado.edu/, 2011b; 10,11). These results suggest that sea level predictions based solely on the presumed temperature evolution may fail to accurately predict the long term sea levels at the end of the century. © 2011 Elsevier B.V. All rights reserved.
1. Introduction In their report published in 2007, the Intergovernmental Panel on Climate Change projected that sea level is likely to rise between 18 and 59 cm by 2100, threatening the homes and livelihoods of millions who live in low-lying and deltaic regions (http://www.ipcc.ch/ publications_and_data/publications_ipcc_fourth_assessment_report_ synthesis_report.htm, 2011). This focus draws together studies of past and present sea-level change, and predictions for future fluctuations, as well as presenting insights into the challenges facing coastal communities. The Australian Federal Government's Climate Commission (http://climatecommission.govspace.gov.au/files/2011/05/ 4108-CC-Science-Update-PRINT-CHANGES.pdf, 2011) has warned that global warming could cause global sea levels to rise higher than previously thought by up to 100 cm by the end of the century. The predictions of a more than 100 cm increase in sea levels by 2100 (for example Rahmstorf, 2007, 2010) do not have the consensus of all those in the scientific community supporting the existence of global warming attributed to carbon dioxide emissions. For the most part the model-based analyses performed recently have predicted much higher sea level rise for the twenty-first century than the Intergovernmental Panel on Climate Change (http://www.ipcc.ch/
E-mail address: [email protected]. 0378-3839/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.coastaleng.2011.10.005
publications_and_data/publications_ipcc_fourth_assessment_report_ synthesis_report.htm, 2011), exceeding 100 cm if greenhouse gas emissions continue to escalate. Some recent papers have also provided sea level rise (SLR) numbers that contrast the 100 cm SLR by 2100 based both on experiments or modelling in this latter case obviously with different assumptions (Holgate, 2007; Houston and Dean, 2011; Wenzel and Schröter, 2010; Wunsch et al., 2007). Their findings contradict the general perception that SLR is escalating at present. Analysis of nine long and nearly continuous sea level records over one hundred years (1903–2003) provided a mean value of SLR of 1.74 mm/year with higher values in the earlier part of the 20th century compared to the latter part in Holgate (2007). Detailed simulations with a 23-layer general circulation ocean model, which include different types of data, provided an estimate of SLR as 1.6 mm/year for the period 1993–2004 (Wunsch et al., 2007). Tide gauge records over the period 1900–2006 provided a mean value of 1.56 mm/year with no statistically significant acceleration in sea level rise (Wenzel and Schröter, 2010). Same paper shows rates immediately before 2007 had been achieved or exceeded over similar time periods at other points during the 20th century, with some decades even revealing a fall in global sea level over that period. Analysis of 57 tide gauge records each with a record length of 80 years, which include 25 gauges with data from 1930 to 2010,
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A.A. Boretti / Coastal Engineering 60 (2012) 319–322
provided no evidence of acceleration in SLR, but instead a small average deceleration of −0.0014 and −0.0123 mm/year2 (Houston and Dean, 2011). The measurements from the TOPEX and Jason series of satellite radar altimeters are used here to better understand if the SLR is accelerating, stable or decelerating by applying simple statistics to the 20 years of data to validate the climate model predictions of Rahmstorf (2007). 2. Sea level rises from TOPEX, Jason-1 and Jason-2 data The best source of global sea level data is the University of Colorado (http://sealevel.colorado.edu/, 2011b). Since 1993, measurements from the TOPEX and Jason series of satellite radar altimeters have allowed accurate estimates of the global mean sea level (MSL). These measurements are continuously calibrated against a network of tide gauges. When seasonal and other variations are subtracted, they allow estimation of the global mean sea level rate. As new data, models and corrections become available, these estimates are continuously revised (about every two months) to improve their quality. Fig. 1 presents the global MSL Time Series (data from (http:// sealevel.colorado.edu/, 2011b), 2011 Release 3 (2011-09-19)). Fig. 1
also presents the predictions of Rahmstorf (2007) for MSL (data from Fig. 4 of Rahmstorf, 2007 covering the range of temperatures provided as an input to the simple semi empirical model). The satellite data are shifted upwards of a constant to obtain tangency of the 2nd order polynomial trend line with the curve “Rahmstorf mean” in January 1993. Polynomial trend lines are used to understand the behaviour. Linear, 2nd and 3rd order polynomial curve fittings of all the data available are considered first (first record December 1992, last record July 2011). The linear fitting of MSL data permits to determine the averaged SLR. The 2nd order polynomial curve fitting of MSL data is the minimum order that permit to estimate an acceleration of sea levels that is constant over the observation period. The 3rd order polynomial curve fitting of MSL data permits to estimate linear changes in acceleration of sea levels over the observation period. These fitting provide the following curves for the MSL (Y is the MSL in mm and X is the year): – Y1 = 3.1640 · X − 6.2919 · 10 3 (R 2 = 9.3377 · 10 − 1) – Y2 = − 5.8185 · 10 − 2 · X 2 + 2.3617 · 10 2 · X − 2.3957 · 10 5 (R 2 = 9.4120 · 10 − 1) – Y3 = − 1.3132 · 10 − 2 · X 3 + 7.8828 · 10 1 ∙ X 2 − 1.5772 · 10 5 · X + 1.0518 · 10 8 (R 2 = 9.4957 · 10 − 1).
Fig. 1. Comparison of MSL predictions from Rahmstorf (2007) with measurements from http://sealevel.colorado.edu/ (2011b), top is Fig. 4 of Rahmstorf (2007). The min and max curves are the lower and the higher boundaries of the grey area of Fig. 4 of Rahmstorf (2007). The mean curve is the average of these curves. The model predictions clearly do not agree with the experimental evidence in the short term.
A.A. Boretti / Coastal Engineering 60 (2012) 319–322
321
Fig. 1 (continued).
This translates in the following constant and linear or 2nd order SLR equations (Y is now the SLR in mm/year): – Y1 = 3.1640 – Y2 = − 11.637 · 10 − 2 · x + 2.3617 · 10 2 – Y3 = − 3.9396 · 10 − 2 · x 2 + 15.7656 · 10 1 · x − 1.5772 · 10 5. Finally, the constant or linear acceleration of sea levels (Y is now the acceleration of sea levels in mm/year 2) are given by: − Y2 = − 11.637 · 10 − 2 − Y3 = − 7.8792 · 10 − 2 · x + 15.7656 · 10 1. The average SLR over the almost 20 year period of observation is 3.1640 mm/year. The SLR is reducing over the period of observation −11.637 · 10 − 2 mm/year 2. The acceleration of sea level rises is reducing −7.8792 · 10 − 2 mm/year 3. Focusing on shorter periods of time (last 10 years or last 5 years) the deceleration of sea level rises is even stronger, as shown by the other pictures. The SLR is clearly reducing significantly. Worthy of note is the huge deceleration of SLR over the last 10 years that is clearly the opposite of what is being predicted by the models. The SLR's reduction is even more pronounced during the last 5 years.
Even more interesting is the fact that from 1992 to 2005 there was an increase each year of the SLR. 2006 was the first year to show a reduction in the global SLR. 2010 is the second year to show a decrease in the SLR. Increases in SLR are much smaller than the 10 mm/year necessary to produce a rise of 100 cm over a century and also highlights the reduction over the last 10 years. In order for the prediction of a 100 cm increase in sea level by 2100 to be correct, the SLR must be almost 11 mm/year every year for the next 89 years. Since the SLR is dropping, the predictions (http://climatecommission.govspace.gov.au/files/2011/05/4108-CCScience-Update-PRINT-CHANGES.pdf, 2011; Rahmstorf, 2007, 2010) become increasingly unlikely. Not once in the past 20 years has the SLR of 11 mm/year ever been achieved. The average SLR of 3.1640 mm/ year is only 20% of the SLR needed for the prediction of a 1 m rise to be correct. The average SLR over the last 5 years is also much smaller than the average rate of rise over the last 20 years. These already small SLR numbers are reducing, not exponentially increasing and this is a consistent trend over the last 5 years. Global satellite data is therefore showing something similar to the longer tide gauge records of Wenzel and Schröter (2010) in terms of SLR variability. The measured MSL and SLR follow a trend completely different from the prediction of Rahmstorf (2007).
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3. Conclusions The oceans are truly the best indicator of climate that is driving the world's weather patterns, and reductions in the ocean SLR show that there is still much to learn. The estimate of over 100 cm and higher rise in sea level by 2100 (in the next 90 years) is unrealistic when analysed in the context of present sea level rise. The linear fitting of the Colorado SLR data in Fig. 1 shows a 2011 value of 2.4691 mm/year and a clear component of deceleration in SLR. For the global sea level to rise by over 100 cm in the next 90 years would require an acceleration in SLR of up to 0.28 mm/year 2, which seems highly unlikely at present with the SLR actually decreasing. The assumption that SLR is proportional to the temperature rise, and that this temperature rise is proportional to the anthropogenic carbon dioxide emission of Rahmstorf (2007, 2010), is certainly too simplistic to represent a reality where there are other driving forces that do need attention. As a matter of fact, the SLR measured with the accurate TOPEX and Jason series of satellite radar altimeters has decelerated and not accelerated over the last 20 years.
References Holgate, S.J., 2007. On the decadal rates of sea level change during the twentieth century. Geophysical Research Letters 34, L01602. Houston, J.R., Dean, R.G., 2011. Sea-level acceleration based on U.S. tide gauges and extensions of previous global-gauge analyses. Journal of Coastal Research 27, 409–417. http://climatecommission.govspace.gov.au/files/2011/05/4108-CC-Science-Update-PRINTCHANGES.pdf. 2011[Internet]. [Cited 2011 May 20]. http://sealevel.colorado.edu/. 2011[Internet]. [Cited 2011 October 20]. http://www.ipcc.ch/publications_and_data/publications_ipcc_fourth_assessment_report_ synthesis_report.htm. 2011[Internet]. [Cited 2011 May 20]. Rahmstorf, S., 2007. A semi-empirical approach to projecting future sea-level rise. Science 315, 368–390. Rahmstorf, S., 2010. A new view on sea level rise: has the IPCC underestimated the risk of sea level rise. Nature Reports Climate Change. doi:10.1038/climate.2010.29. Published online: 6 April. Wenzel, M., Schröter, J., 2010. Reconstruction of regional mean sea level anomalies from tide gauges using neural networks. Journal of Geophysical Research — Oceans 115, C08013. Wunsch, C., Ponte, R., Heimbach, P., 2007. Decadal trends in sea level patterns: 1993–2004. Journal of Climatology 5889–5911.
Contents lists available at SciVerse ScienceDirect
Coastal Engineering journal homepage: www.elsevier.com/locate/coastaleng
Short communication
Short term comparison of climate model predictions and satellite altimeter measurements of sea levels Alberto A. Boretti School of Science and Engineering, University of Ballarat, Ballarat, Victoria, Australia
a r t i c l e
i n f o
Article history: Received 30 June 2011 Received in revised form 21 October 2011 Accepted 21 October 2011 Available online 10 November 2011 Keywords: Climate models Sea level rise Satellite altimeter measurements Statistical analysis Curve fitting
a b s t r a c t Climate models (http://climatecommission.govspace.gov.au/files/2011/05/4108-CC-Science-Update-PRINTCHANGES.pdf, 2011; http://www.ipcc.ch/publications_and_data/publications_ipcc_fourth_assessment_report_ synthesis_report.htm, 2011; Rahmstorf, 2007, 2010) calculate that temperatures are increasing globally and sea level rises are increasing due to anthropogenic carbon dioxide emissions. More recent predictions (http://climatecommission.govspace.gov.au/files/2011/05/4108-CC-Science-Update-PRINT-CHANGES.pdf, 2011; Rahmstorf, 2007, 2010) have forecasted that sea level rises by 2100 will be higher than the 2007 projections by the Intergovernmental Panel on Climate Change (http://www.ipcc.ch/publications_and_data/ publications_ipcc_fourth_assessment_report_synthesis_report.htm, 2011), with projected sea level rises increasing from 18–59 cm to 100 cm. In this brief communication, the predictions of Rahmstorf (2007) are validated against the experimental evidence over a 20 year period. The University of Colorado Sea Level satellite monitoring shows that the rate of rise of the sea level is not only well below the values computed in http://climatecommission.govspace.gov.au/files/2011/05/4108-CC-Science-Update-PRINTCHANGES.pdf (2011) and Rahmstorf (2007, 2010), but actually reducing rather than increasing (http://sealevel. colorado.edu/, 2011b; 10,11). These results suggest that sea level predictions based solely on the presumed temperature evolution may fail to accurately predict the long term sea levels at the end of the century. © 2011 Elsevier B.V. All rights reserved.
1. Introduction In their report published in 2007, the Intergovernmental Panel on Climate Change projected that sea level is likely to rise between 18 and 59 cm by 2100, threatening the homes and livelihoods of millions who live in low-lying and deltaic regions (http://www.ipcc.ch/ publications_and_data/publications_ipcc_fourth_assessment_report_ synthesis_report.htm, 2011). This focus draws together studies of past and present sea-level change, and predictions for future fluctuations, as well as presenting insights into the challenges facing coastal communities. The Australian Federal Government's Climate Commission (http://climatecommission.govspace.gov.au/files/2011/05/ 4108-CC-Science-Update-PRINT-CHANGES.pdf, 2011) has warned that global warming could cause global sea levels to rise higher than previously thought by up to 100 cm by the end of the century. The predictions of a more than 100 cm increase in sea levels by 2100 (for example Rahmstorf, 2007, 2010) do not have the consensus of all those in the scientific community supporting the existence of global warming attributed to carbon dioxide emissions. For the most part the model-based analyses performed recently have predicted much higher sea level rise for the twenty-first century than the Intergovernmental Panel on Climate Change (http://www.ipcc.ch/
E-mail address: [email protected]. 0378-3839/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.coastaleng.2011.10.005
publications_and_data/publications_ipcc_fourth_assessment_report_ synthesis_report.htm, 2011), exceeding 100 cm if greenhouse gas emissions continue to escalate. Some recent papers have also provided sea level rise (SLR) numbers that contrast the 100 cm SLR by 2100 based both on experiments or modelling in this latter case obviously with different assumptions (Holgate, 2007; Houston and Dean, 2011; Wenzel and Schröter, 2010; Wunsch et al., 2007). Their findings contradict the general perception that SLR is escalating at present. Analysis of nine long and nearly continuous sea level records over one hundred years (1903–2003) provided a mean value of SLR of 1.74 mm/year with higher values in the earlier part of the 20th century compared to the latter part in Holgate (2007). Detailed simulations with a 23-layer general circulation ocean model, which include different types of data, provided an estimate of SLR as 1.6 mm/year for the period 1993–2004 (Wunsch et al., 2007). Tide gauge records over the period 1900–2006 provided a mean value of 1.56 mm/year with no statistically significant acceleration in sea level rise (Wenzel and Schröter, 2010). Same paper shows rates immediately before 2007 had been achieved or exceeded over similar time periods at other points during the 20th century, with some decades even revealing a fall in global sea level over that period. Analysis of 57 tide gauge records each with a record length of 80 years, which include 25 gauges with data from 1930 to 2010,
320
A.A. Boretti / Coastal Engineering 60 (2012) 319–322
provided no evidence of acceleration in SLR, but instead a small average deceleration of −0.0014 and −0.0123 mm/year2 (Houston and Dean, 2011). The measurements from the TOPEX and Jason series of satellite radar altimeters are used here to better understand if the SLR is accelerating, stable or decelerating by applying simple statistics to the 20 years of data to validate the climate model predictions of Rahmstorf (2007). 2. Sea level rises from TOPEX, Jason-1 and Jason-2 data The best source of global sea level data is the University of Colorado (http://sealevel.colorado.edu/, 2011b). Since 1993, measurements from the TOPEX and Jason series of satellite radar altimeters have allowed accurate estimates of the global mean sea level (MSL). These measurements are continuously calibrated against a network of tide gauges. When seasonal and other variations are subtracted, they allow estimation of the global mean sea level rate. As new data, models and corrections become available, these estimates are continuously revised (about every two months) to improve their quality. Fig. 1 presents the global MSL Time Series (data from (http:// sealevel.colorado.edu/, 2011b), 2011 Release 3 (2011-09-19)). Fig. 1
also presents the predictions of Rahmstorf (2007) for MSL (data from Fig. 4 of Rahmstorf, 2007 covering the range of temperatures provided as an input to the simple semi empirical model). The satellite data are shifted upwards of a constant to obtain tangency of the 2nd order polynomial trend line with the curve “Rahmstorf mean” in January 1993. Polynomial trend lines are used to understand the behaviour. Linear, 2nd and 3rd order polynomial curve fittings of all the data available are considered first (first record December 1992, last record July 2011). The linear fitting of MSL data permits to determine the averaged SLR. The 2nd order polynomial curve fitting of MSL data is the minimum order that permit to estimate an acceleration of sea levels that is constant over the observation period. The 3rd order polynomial curve fitting of MSL data permits to estimate linear changes in acceleration of sea levels over the observation period. These fitting provide the following curves for the MSL (Y is the MSL in mm and X is the year): – Y1 = 3.1640 · X − 6.2919 · 10 3 (R 2 = 9.3377 · 10 − 1) – Y2 = − 5.8185 · 10 − 2 · X 2 + 2.3617 · 10 2 · X − 2.3957 · 10 5 (R 2 = 9.4120 · 10 − 1) – Y3 = − 1.3132 · 10 − 2 · X 3 + 7.8828 · 10 1 ∙ X 2 − 1.5772 · 10 5 · X + 1.0518 · 10 8 (R 2 = 9.4957 · 10 − 1).
Fig. 1. Comparison of MSL predictions from Rahmstorf (2007) with measurements from http://sealevel.colorado.edu/ (2011b), top is Fig. 4 of Rahmstorf (2007). The min and max curves are the lower and the higher boundaries of the grey area of Fig. 4 of Rahmstorf (2007). The mean curve is the average of these curves. The model predictions clearly do not agree with the experimental evidence in the short term.
A.A. Boretti / Coastal Engineering 60 (2012) 319–322
321
Fig. 1 (continued).
This translates in the following constant and linear or 2nd order SLR equations (Y is now the SLR in mm/year): – Y1 = 3.1640 – Y2 = − 11.637 · 10 − 2 · x + 2.3617 · 10 2 – Y3 = − 3.9396 · 10 − 2 · x 2 + 15.7656 · 10 1 · x − 1.5772 · 10 5. Finally, the constant or linear acceleration of sea levels (Y is now the acceleration of sea levels in mm/year 2) are given by: − Y2 = − 11.637 · 10 − 2 − Y3 = − 7.8792 · 10 − 2 · x + 15.7656 · 10 1. The average SLR over the almost 20 year period of observation is 3.1640 mm/year. The SLR is reducing over the period of observation −11.637 · 10 − 2 mm/year 2. The acceleration of sea level rises is reducing −7.8792 · 10 − 2 mm/year 3. Focusing on shorter periods of time (last 10 years or last 5 years) the deceleration of sea level rises is even stronger, as shown by the other pictures. The SLR is clearly reducing significantly. Worthy of note is the huge deceleration of SLR over the last 10 years that is clearly the opposite of what is being predicted by the models. The SLR's reduction is even more pronounced during the last 5 years.
Even more interesting is the fact that from 1992 to 2005 there was an increase each year of the SLR. 2006 was the first year to show a reduction in the global SLR. 2010 is the second year to show a decrease in the SLR. Increases in SLR are much smaller than the 10 mm/year necessary to produce a rise of 100 cm over a century and also highlights the reduction over the last 10 years. In order for the prediction of a 100 cm increase in sea level by 2100 to be correct, the SLR must be almost 11 mm/year every year for the next 89 years. Since the SLR is dropping, the predictions (http://climatecommission.govspace.gov.au/files/2011/05/4108-CCScience-Update-PRINT-CHANGES.pdf, 2011; Rahmstorf, 2007, 2010) become increasingly unlikely. Not once in the past 20 years has the SLR of 11 mm/year ever been achieved. The average SLR of 3.1640 mm/ year is only 20% of the SLR needed for the prediction of a 1 m rise to be correct. The average SLR over the last 5 years is also much smaller than the average rate of rise over the last 20 years. These already small SLR numbers are reducing, not exponentially increasing and this is a consistent trend over the last 5 years. Global satellite data is therefore showing something similar to the longer tide gauge records of Wenzel and Schröter (2010) in terms of SLR variability. The measured MSL and SLR follow a trend completely different from the prediction of Rahmstorf (2007).
322
A.A. Boretti / Coastal Engineering 60 (2012) 319–322
3. Conclusions The oceans are truly the best indicator of climate that is driving the world's weather patterns, and reductions in the ocean SLR show that there is still much to learn. The estimate of over 100 cm and higher rise in sea level by 2100 (in the next 90 years) is unrealistic when analysed in the context of present sea level rise. The linear fitting of the Colorado SLR data in Fig. 1 shows a 2011 value of 2.4691 mm/year and a clear component of deceleration in SLR. For the global sea level to rise by over 100 cm in the next 90 years would require an acceleration in SLR of up to 0.28 mm/year 2, which seems highly unlikely at present with the SLR actually decreasing. The assumption that SLR is proportional to the temperature rise, and that this temperature rise is proportional to the anthropogenic carbon dioxide emission of Rahmstorf (2007, 2010), is certainly too simplistic to represent a reality where there are other driving forces that do need attention. As a matter of fact, the SLR measured with the accurate TOPEX and Jason series of satellite radar altimeters has decelerated and not accelerated over the last 20 years.
References Holgate, S.J., 2007. On the decadal rates of sea level change during the twentieth century. Geophysical Research Letters 34, L01602. Houston, J.R., Dean, R.G., 2011. Sea-level acceleration based on U.S. tide gauges and extensions of previous global-gauge analyses. Journal of Coastal Research 27, 409–417. http://climatecommission.govspace.gov.au/files/2011/05/4108-CC-Science-Update-PRINTCHANGES.pdf. 2011[Internet]. [Cited 2011 May 20]. http://sealevel.colorado.edu/. 2011[Internet]. [Cited 2011 October 20]. http://www.ipcc.ch/publications_and_data/publications_ipcc_fourth_assessment_report_ synthesis_report.htm. 2011[Internet]. [Cited 2011 May 20]. Rahmstorf, S., 2007. A semi-empirical approach to projecting future sea-level rise. Science 315, 368–390. Rahmstorf, S., 2010. A new view on sea level rise: has the IPCC underestimated the risk of sea level rise. Nature Reports Climate Change. doi:10.1038/climate.2010.29. Published online: 6 April. Wenzel, M., Schröter, J., 2010. Reconstruction of regional mean sea level anomalies from tide gauges using neural networks. Journal of Geophysical Research — Oceans 115, C08013. Wunsch, C., Ponte, R., Heimbach, P., 2007. Decadal trends in sea level patterns: 1993–2004. Journal of Climatology 5889–5911.