Global Mean Sea Level Rise



Global Mean Sea Level Rise
It was becoming patently obvious that a linear fit/trend line was not the most appropriate fit to the global sea rise , given by Jason-2 and on public access site
http://www.aviso.altimetry.fr/en/data/products/ocean-indicators-products/mean-sea-level/products-images.html




 Projections of Global SLR compared to IPCC emissions scenario
As of August 2021. The green curve is about midway between 4.5 RPC and 8.5RPC of then plots on page 40 of 139 of Chapter 04 of the IPCC 2021 report , https://www.ipcc.ch/site/assets/uploads/sites/3/2019/11/SROCC_FOD_Ch04_Final.pdf , . For 2019.0 to 2020.0 from those curves 5mm of increase for the green, 5.3mm for the red and 4.3mm for the black curves. For 2100 the projection of the green is 80.4cm , 105.4cm for the red and 61.9cm for black.
Data to 2021.9517 public output 01 Mar 2022, 697 datapoints from 2003.0 (from 2003 to avoid the 10 years post-Pinatubo recovery in geodata, and earlier than 1993 was near enough linear SLR anyway) Linear (no acceleration) y = 1.36+ 0.387977 *x where x is year minus 2000, and y is cm in Aviso terms to 2100, 40.16cm exponential (rising acceleration) y= 2.19 -6.027664 *(1-e^(0.039026 *x)) To 2100, 2.947 metres quadratic (constant acceleration) y=2.35 +0.190819 *x+ 0.007902*x^2 To 2100, 100.45cm indicial (falling acceleration) Best fit by goodness of fit R^2 ranking of curve-fitting y= 2.65+ 0.078770*x^1.482199 Global SLR to year 2100 = 75.216cm From that curve 2021.0 to 2022.0 = 5.13 mm in the last year again marginally lower than the previous such determination of 75.54cm to 2100, looks to have bottomed-out. Assuming the Earth is coming out of the double La Nina early 2022, will mean the next such century-long SLR determination will return to 80cm or so prediction. Using ftp://ftp.aviso.altimetry.fr/pub/oceano/AVISO/indicators/msl/MSL_Serie_MERGED_Global_AVISO_GIA_Adjust_Filter2m.txt data from http://www.aviso.altimetry.fr/en/data/products/ocean-indicators-products/mean-sea-level/products-images.html Background. Using an online curve fitting site to try different functions and weightings, the highest R^2 values were for an exponential fit, followed by a quadratic fit. Black dots, 6-month filtered, seasonality removed used in the following. Even historical assessment of SLR, its an exponential that is best fit https://robertscribbler.com/2015/05/04/global-sea-level-rise-going-exponential-new-study-records-big-jump-in-ocean-surface-height/ and long term piece-wise "exponential " https://robertscribbler.files.wordpress.com/2015/05/hansen-sea-level-rise.png Exponential was best fit with R^2 value of 0.998 for that historic plot adjusting for Aviso x and y axes y = 1.57 - (24.8942)*(1 - e^(+0.011*x)) for 2010,y=4.46 cm for 2020, y = 7.70 cm , reached in reality Dec 2016 Unfortunately exponentials soon run away with themselves, for historic or Jason-2 data and outrun the amount of Greenland and Antarctic land based ice , before 2100. So hard splitting into 2 functions at arbitrarily year 2030. (there seems to be no high resolution ,decadal level,indications from the geological record for a representative year for a presumed return to steady state, as too long ago, 120kya) For Aviso/Jason-2 data as of 20 Dec 2016, public access 13 March 2017 easily changed calculator using exponential best fit for 19 datapoints of the Aviso plot (y cm as in Aviso plots and scaling, and x=0 for year 2000) y=2.1465 - (2.00209)*(1 - e^(+0.07779*x)) then quadratic best fit, for the 2008 to Dec 2016 Jason-2 quadratic best fit and assumed to apply later in the century of new normal returning y = 3.0329 - 0.03173*x + 0.01787*x^2 (starting at where E(30) finished, the exponential to year 2030) year Sea Level cm (Aviso/Jason-2 scaling) , decadal difference 2010 4.502 2020 9.632 5.13 2030 20.798 11.166 2040 32.99 12.192 2050 48.76 15.77 2060 68.1 19.34 2070 91.01 22.91 2080 117.5 26.49 2090 147.56 30.06 2100 181.2 33.64 (2010 not quite hitting the Aviso plot figure as using a fitted curve to their plot) I'll return to this at next update, perhaps 23 March 2017, and an updated best fit , to see what ,if any, effect it has on these projections, hence retention of 3 decimal places. I doubt it but a quadratic may become the best fit again and the uptick of late 2016 was just a blip. With all the satellite-era record breaking 3 metrics of global, arctic and antarctic sea-ice , I doubt it was a blip. The previous sharp rise in the Jason-2 plot 2012 was also a time of sea-ice record-breaking. Not that sea-ice affects SLR but as a global measure of temperature rise and hence thermal expansion of the oceans and/or increased glacial run-off. Hindcast back-testing of the Aviso Jason-2 data for years 2013 to 2017 http://diverse.4mg.com/jason2+hincast.jpg (light blue straight line is the Aviso 4.44 mm/yr gradient) exp, 2013 for "predicting" to end of 2014 y = 3.29668 - (.19468)*(1 - e^(+0.195876*x)) to end of 2015 y = 2.97247 - (0.4954)*(1 - e^(+0.14052*x)) to end 2016 exp y = 3.184 - (.28907)*(1 - e^(+0.17071*x)) then to end of 2017 y = 2.6829 - 0.8798*(1 - e^(+0.11216*x)) (best fit curve with 30 Dec 2016 data and R^2=0.9724 ) QUADRATIC 2014 y = 3.826216 - 0.1681465*x + 0.02356196*x^2 to 2015 y = 3.097 - 0.03005*x + 0.01715*x^2 to 2016 quad, y = 5.24956 - 0.41661*x + 0.034044*x^2 2016 to 2017 y = 3.0329 - 0.03173*x + 0.01787*x^2 to 2018 y = 3.0329 - 0.03173*x + 0.01787*x^2 This is the changed matrix of the inverse factors, to modify to the hindcast predictive curves , each year to connect with reality. ie applying each year-end , would end up with the real data for the end of 2016. This time in polarised terms of subtraction or addition percentages. E exp, Q quad. 2014 E -35%,-5.37 , Q -11%, -4.68 2015 E +33%,+5.33 , Q +73% , +4.67 2016 E -51%, -6.96, Q -38%, -6.39 So percentages to decrease or increase the predictions on best curve types each end of year and gradients in mm/deci-year where, the sign is determined by the gradient of rise in the last deci-year of each year. 2014, 1.4 mm/deciyear 2015 2.4 2016 0.8 2017 3.3 in the last deci-yr of the year ,so divisor is 1.9mm / deci-yr, less gives negative sign giving "correlation" curve for the exponentials y = -.30169 * x^2 + 6.343 * x + 7.762 y is the percentage and x is the gradients with added signs, and for the quadratics y = -0.6153 * x^2 + 8.9778 * x + 44.49 (3 points will always give a curve though, so specious "accuracy") So what of 2017 for predicting 2018 E ?%, +6.33 , Q ? %, +5.60 now becomes 2017 E +36%,+6.33 , Q 75%, +5.60 Giving 2 sort of predictive adjustments to the 2017 to 2018 increments (not absolute, ie removing 2017 curve-fit evaluations ) of height of the previous best curve-fits , E and Q, 8.68cm and 9.28cm. then by curve fit to those projected points for exponential, in and beyond 2017 y = 2.8121 - (0.6917)*(1 - e^(+0.12367*x)) for quadratic, in and beyond 2017 y = 7.10098 - 0.7044*x + 0.04453*x^2 y is the Jason-2 height in Aviso cm and x is the year minus 2000 so new projections into the future, or the trash can , if someone comes up with a more reasonable hindcast correlation structure Again these curves do not pass through real or projected datapoints, so differences at Aviso update points during 2017 (allowing for the 3month dither) for the exponential curve 10day 0.02cm 20day 0.04 30day 0.06 60day 0.12 120day 0.23 180day 0.36 240day 0.48 300day 0.61 2020 10.32cm 2030 30.38 2050 337.38, or 33.8m 2100 is seriously off the planet for the quadratic curve 10day 0.02cm 20day 0.04 30day 0.07 60day 0.13 120day 0.27 180day 0.41 240day 0.55 300day 0.69 year 2020 10.82cm 2030 26.0 2050 83.2 2100 382= 3.82m If I was on the Jason team, in the UK. I'd get permission to mount a flapper plate wave generator at one end of Lake Windermere , prior to a Jason overpass. Time the start so just one passage of waves for the overpass, to get a calibration for the wave-compensation algorithm as distinct to the simple flat level. Repeat for different wave amplitudes and frequencies, and repeat on the other lakes used around the world. Enough data now,2018, on Jason-3 plot to continue monitoring after the orbit shift and break to Jason-2 data. http://diverse.4mg.com/jason1+2+3r.jpg Ignoring the first and last six months of Jason 1,2 and 3 plots, scaling, hovering transparent at the joins. The central parts of the overlap curves agree, but with a vertical displacement of about 2mm . Seems odd querying 2mm when dealing with the slippery commodity that is sea level. From one of the team on the Jason project, they use land-locked lakes like Windermere in Cumbria, other such lakes around the world and also active transponders they can place anywhere before overpasses, for calibrating and therefore cross-calibrating different satellite outputs. So I assume the end result is that there is smooth transition in the outputted results from J1 to J3 and the jumps have some technical justification. Anyway concattenating the 3 plots from the Aviso site , ignoring the transistion steps , continous from 2003 to end 2017 and 46 datapoints for curve-fitting . At least exponential is no longer the best fit in the rankings from Linear, Exponential, Quadratic and Fractional Indicial, any other curve-type suggestions? Linear Y= cm of sea-level as per Aviso output and x=0 for year 2000 Y = 1.446098 + 0.331877*x R^2= 0.978086 RMS Error = 0.244821 projecting into the future year 2030 11.402 cm SL rise 2050 18.04 cm 2100 34.63cm Exponential Y = 1.948854 -6.880730*(1-Exp(0.033013*x)) R^2 = 0.981571 RMS Error = 0.227110 projections 2030 13.593 cm 2050 30.919 cm Quadratic Y = 2.023609 + 0.204265*x + 0.005656*x^2 R^2 = 0.981740 RMS Error = 0.226064 projections 2030 13.242cm 2050 26.377cm Indicial, approx 4/3 fractional indicial power Best fit on R^2 and RMS Y = 2.252107 + 0.104773*x^1.355666 R^2 = 0.981919 RMS Error = 0.224954 2030 13.058cm 2050 23.313 cm 2100 , 56.15 cm (21.5cm more than linear , the official standpoint) Then staying with indicial curve type , chopping off later data and curve-fitting for an idea of trend over time. The fractional index to near end of 2017 ,1.355666 to mid 2017 , 1.378523 to 2017.0 , 1.571937 to 2016.0 , 1.730158 to 2015.0, 1.449256 to 2014.0, 1.428276 so knocked back from the year 2016, when things looked to be going fully exponential. update 27 June 2018 Y = year (minus 2000) , x is cm SLR in Aviso.Altimetry terms for Jason-3 output up to 05 April 2018, publically outputed 26 June 2018, for various optimised curve fits and concattenated 52 datapoint data for Jason1+2+3 Linear y= 1.427594 + 0.334124x r*r = 0.981312 year Sea Level Rise 2020 8.11cm 2050 18.133 2100 34.839 Exponential Y = 1.926243 -7.467664*(1-Exp(0.031073*x)) r*r = 0.984443 year Sea Level 2020 8.36 cm 2050 29.77 cm 2100 161.4m Quadratic Y= 1.998822 +0.210329 * x +0.005367 * x^2 r*r = 0.984598 year Sea Level 2020 8.352cm 2050 25.932 2100 76.701 Best still on R*R goodness, Indicial Y= 2.232609 +0.109142 * x^1.342432 r*r = 0.984789 about 4/3 power year Sea Level Rise 2020 8.321 cm 2050 23.065 2100 55.059 I got into this global monitoring about October 2016. It became obvious that the global sea-ice anomaly was going seriously negative. This metric got corrupted, from a duff datafeed, in early 2016 but it is the only one I've found in terms of the simple millions of sq km rather than the time varying standard-deviations. The lower trace of http://arctic.atmos.uiuc.edu/cryosphere/IMAGES/global.daily.ice.area.withtrend.jpg For 20 years no one had asked let alone answered the simple question , why with all the different weather, oceanography and geography between north and south poles ,should that plot have only required fixed bounds of +3 to -3. In fact for 28 years +/-2 was sufficient. Only when it started going seriously off the plot last year did anyone start asking , what global "hand of Gaia" had kept things in balance for all that time. I've only been able to access NSIDC sea-ice extent rather than area data since then, so about .3 million sq km jump, between the 2 metrics, in early 2016. Continuing that lower plot onwards , as extent rather than (slightly different) area terms, tabulated in units of 10^6 km^2 using, north and south extent measures on http://nsidc.org/arcticseaicenews/charctic-interactive-sea-ice-graph/ 01 March 2016 -1.29 01 May -1.616 01 July -1.63 01 Aug -2.445 01 nov -3.465 record minimum 0f -4.376 on 22 Nov 2016 01 Dec -3.907 then continuing recovery eg 15 April 2017 stood at -2.441 First the dies-anno, day of the year , all satellite era global anomaly record fell , then the simple global sea-ice minimum record fell, then the Antarctic minimum record fell, then the lowest maximum Arctic record fell My theory to explain the elevated , beyond linear, of the Jason-2 record , it could be associated with the latterly downwards trend in that global sea-ice amount since about 2000 as a global proxy for temp increase and thermal expansion of the oceans. A curvefit to that trend is y= -0.12532 * e^(0.111934 * x) where x is the year -2000 and y is the negative amount in units of 10^6 km^2 For the curvefit to the Jason2 plot of y = 2.6829 - 0.8798*(1 - e^(+0.11216*x)) and the gradient at mid 2008 , the start of Jason2, 2.56mm/yr linear trend. Subtract that linear trend (to account for the long term , nearer linear, climate change global temperature increase) y=0.256*x +1.91 from the exponential fit values and produce a table of differences for 2009 to 2017 Then for a potential transfer/conversion function of K=2.9381 * L^0.996964 + 0.00066 R^2 goodness of fit 0.999999 where L is the negative of the global sea-ice anomaly in 10^6 sq km since 2009 so less by .343 area units of the year 2000 anomaly from that curve , and K is the global sea level rise , to be added to the linear 2.56mm/yr rise . It will be interesting to see what Jason-2 makes of end of 2016 spike , if any, if the sea-ice anomaly does reflect a proxy global themometer . Also interesting to see if there is any correlation , should there be a new normal for the cryosphere and global sea-ice figures fail to recover. Also considering the ENSO plot and the Jason-2 plot, I had a go graphically overlaying one over the other. It looks as though a proper mathematical treatment might remove a lot of the , beyond annual+seasonal lumps from the Jason2 plot. Enso plot on https://www.esrl.noaa.gov/psd/enso my overlay image (may require URL copy and paste) http://diverse.4mg.com/jason2+enso_overlay2.jpg Because of rotating the Aviso image 23 degrees, the peaks move to the right and so the overlay is shifted to the left and scaled and hovered for best visual overlay . The lower 2 red squares are for mid 2008 and start of 2017. The purple squares are the exponential fit referred to above. The blue line is the Aviso 4.44 mm/yr "trend" line. The lowest image I could not perfectly bend the plot , so the exponential line is only nearer flat, not flat. The Aviso blue straight line is now curved. For the GRACE curve for Greenland, on http://polarportal.dk/fileadmin/polarportal/mass/ in 2018 http://polarportal.dk/fileadmin/polarportal/mass/Grace_curve_La_EN_20170100.png a curve fit for that (2017) is y = -0.0164 * x^2 - 2.469 * x + 42.779 where x is year - 2000, and y =0 for -2400 GT Using mass-loss conversion of 458 GigaTons to 1.45mm of global sea level rise, the anomalous 2010 to 2012 mass-loss leading to a peak of about 1.4mm / yr, then dropping back to recent somewhat insignificant .4mm /yr. I've not taken into account , as overall , at the moment the Greenland effect is not too significant compared to thermal expansion of the world's oceans. Getting back to this with resumption of Jason2 outputs , Dec 2017. Best curve fit for data updated to 08 May 2017 y = 2.443701 - 1.3509295*(1 - e^(+0.09227284*x)) R^2 = 0.96787 was y = 2.8121 - (0.6917)*(1 - e^(+0.12367*x)) y=2.1465 - (2.00209)*(1 - e^(+0.07779*x)) For Jason3 data output of 05 Feb 2018, publically available about 10 Apr 2018. Best fit exponential, R^2 = 0.983876 1.995164 -5.721914*(1-Exp( 0.037837*x)) 2020 8.468cm 2050 34.218cm 2100 2.479m Best fit linear 1.407961 + 0.336498*x , R^2 = 0.97938 year Sea Level 2020 8.137cm 2050 18.232cm 2100 35.057cm Best fit quadratic, R^2= 0.984018 2.080588 + 0.189329*x + 0.006446*x^2 year Sea Level 2020 8.445cm 2050 27.662cm 2100 85.473cm Best fit indicial power, best R^2= 0.984105 y= 2.311576 +0.090898*x^1.403844 year Sea Level 2020 8.406cm 2050 24.373cm 2100 60.688 cm Y = year (minus 2000) , x is cm SLR in Aviso.Altimetry terms for Jason-3 output up to 25 May 2018, publically outputed approx 23 July 2018, for various optimised curve fits and concattenated 54 datapoint data for Jason1+2+3, ranked in terms of R*R Linear Y= 1.440160 + 0.332706 * x R^R=0.981621 so linear rate 3.327mm per year , compares very well with the Aviso Reference value of 3.32mm /year from 1993 to 2018, using a lot more datapoints year Sea Level Rise , cm 2020 8.094 2050 18.075 2100 34.71 Exponential Y = 1.885012 -8.885318*(1-Exp(0.027178*x)) r*r = 0.984062 year Sea Level Rise ,cm 2020 8.301 2050 27.58 2100 127.585 Quadratic Y= 1.949468 +0.222901 * x +0.004728 * x^2 r*r = 0.984207 year Sea Level Rise , cm 2020 8.298 2050 24.914 2100 71.519 Best still on R*R goodness, Indicial Y= 2.182871 +0.121504 * x^1.306716 r*r = 0.984447 still about 4/3 power, projection still falling year Sea Level Rise , cm 2020 8.273 2050 22.35 2100 52.073 58 datapoints to 02 Aug 2018 updated on 01 Dec 2018 https://www.aviso.altimetry.fr/en/data/products/ocean-indicators-products/mean-sea-level/products-images.html Linear Y= 1.449671 + 0.331635 * x R*R = 0.982318 year Sea Level Rise (cm) 2020 8.082 2050 18.031 2100 34.613 (So linear "fit " gradient of 3.32 mm per year much as Aviso reference value as a simple validity check on the relatively small set of datapoints ) Exponential Y = 1.838701 -10.950351*(1-Exp(0.023025*x)) R*R = 0.984114 year Sea Level Rise (cm) 2020 8.243 2050 25.514 2100 100.382 Quadratic Y= 1.894041+0.236818 * x +0.004035 * x^2 R^2 = 0.984237 year Sea Level Rise (cm) 2020 8.244 2050 23.822 2100 65.925 Best curvefit still by R*R goodness, by a whisker, Indicial Y= 2.125981+ 0.136320 * x^1.268834 R^2 = 0.984511 year Sea Level Rise (cm) 2020 8.226 2050 21.636 2100 49.14 Still on the downward trend Another output 07 Dec 2018 ,data up to 01 Sep 2018 on https://www.aviso.altimetry.fr/en/data/products/ocean-indicators-products/mean-sea-level/products-images.html No wonder anti-climate change bods shout foul in such circumstances. Usually with these updates, because of the 6-month filter and seasonality, its a matter of revisiting some of the previous datapoints as well as the update points. This time the revisionists had been at work and the whole Jason-3 curve has been "adjusted" , nothing seen about it in the accompanying notes, presumably the reason for the paucity of data until the latest 2 updates. So had to revisit all Jason-3 datapoints. Creating a transparent masque of the latest data and rescaling+hovering over an earlier Jason-3 output , it was impossible to align the early sections of the curves. Also took the opportunity to make transparent overlay masque of the pixel to time and height conversions plotted out , to check for any errors there on my part. http://www.diverse.4mg.com/jason3_01oct+02aug.jpg Combined image with the later 01 Oct 2018 data, showing the revisioning, brown is the earlier version. Revisioning certainly back to start of 2017 and probably back to the mission start. With the cross-over from J2 to J3 data, as used before, gave a linear "fit" of 3.34 mm/year when rounded. Aviso reference figure is 3.33 now, not 3.32 . Undefined coming out and in of the filters for J2 and J3, over the cross-over period, betwixt and between. I'd previously used a mean for the heights in that period. Otherwise arbitrarily making the 2 datapoints both 1mm lower, brought the liner "fit" here when rounded to 3.33 (gradient 0.333). Retained as part of the suite of now 68 datapoints for the remaining 3 curve-fit assesments. Linear Y = 1.434539 + 0.333266*x r*r = 0.983702 year Sea Level Rise (cm) 2020 8.099 2050 18.097 2100 34.761 A basic exponential curve, worse fit than the following exponential form by R^2 but less projected rise to 2100 Y = -8.243462 +10.097411 * 1.024902 ^x r*r = 0.984998 year Sea Level Rise (cm) 2020 8.27 2050 26.296 2100 109.909 Exponential Y = 1.86385 -9.780226*(1-e^(0.025191*x)) r*r = 0.985743 year Sea Level Rise (cm) 2020 8.27 2050 26.547 2100 113.528 Quadratic Y = 1.92383 + 0.229431*x + 0.004391*x^2 r*r = 0.985864 year Sea Level Rise (cm) 2020 8.268 2050 24.372 2100 68.776 Best curvefit still by R*R goodness, Indicial Y = 2.15921 + 0.127719*x^1.289983 r*r = 0.986091 year Sea Level Rise (cm) 2020 8.248 2050 22.015 2100 50.712 upward trend again for the likely start of El Nino cycle 70 datapoints for the complete Jason1+2+3 concattenated dataset to 01 October 2018, public output on Aviso 18 Jan 2019 Linear Y= 1.426891 + 0.334249 *x goodness R*R = 0.98329 year Sea Level Rise (cm) 2020 8.111 2050 18.139 2100 34.851 Exponential Y = 1.861067 -9.801611*(1-e^(0.025179*x)) R*R= 0.985352 year Sea Level Rise (cm) 2020 8.277 2050 26.578 2100 113.624 Interesting that the previous processing gave 113.528, virtually the same, no idea if any significance to that. Quadratic Y = 1.921387 + 0.229779*x + 0.004398*x^2 R*R = 0.985472 year Sea Level Rise (cm) 2020 8.276 2050 24.405 2100 68.879 Best curvefit still by R*R goodness, Indicial Y = 2.158700 + 0.127525*x^1.290962 R*R = 0.985697 year Sea Level Rise (cm) 2020 8.256 2050 22.06 2100 50.857 upward trend still Tried another curve form , converged on to (1.835379+ 0.233802*x)/(1 -0.106677*x) and R^2 goodness better than linear but worse than exponential. But was not well behaved beyond 2050. There is no "business as usual" Trump-land curve in the Nature paper, https://www.nature.com/articles/s41467-018-02985-8 , for the early 21C situation, like on here http://www.realclimate.org/index.php/archives/2013/10/sea-level-in-the-5th-ipcc-report/comment-page-5/ Gives such a projection as 52cm for 2050 and 98cm for 2100 From that Nature paper ,taking 2035 peak net-zero CO2 plot as a close stand-in for business-as-usual and the state of early 21C, gives 22cm for 2050 and 55cm for 2100. My analysis ,projecting on from the Jason data over one cycle of up and down trend and best curve-fitting to the 2003 to 2018 data, from 2000 =0 cm. Minimum 22cm rise to 2050 and 49cm for 2100 Maximum 24cm rise to 2050 and 61cm for 2100 so far , nearer the more benign "2035" scenario, still woese than the other CO2/GHG scenarios. Whichever way you look at these projections, a rise of the yearly rate of global sea level rise, from the non Jason or projection fitting linear 3.3/3.4 mm per year. I don't trust the Saral/Attica project as its "calibrated" against tide-gauges which go up and down with geological rates of the mm/year rate much as sea level rates, via isostatic rebound, tectonic plate movement, human-led local water abstraction under the tide-gauges etc I like the final line of this paper https://www.researchgate.net/profile/Adam_Parris/publication/328380647_Evolution_of_21st_Century_Sea-level_Rise_Projections/links/5be4488892851c6b27afee36/Evolution-of-21st-Century-Sea-level-Rise-Projections.pdf " As awareness grows that other aspects of the climate system may be characterized by deep uncertainty as well (e.g., Lenton et al., 2008), examples of how the SLR and coastal risk communities have integrated different types of information and projection approaches over time may prove instructive. " I'd not found that paper using "meta study" (term for medical multiple comparison papers only?) as they seemed to have used the odd term "evolution". Interesting to get a wider handle to my analysis , assuming it has some validity. From their assessed papers of 2016/17/18 only of Table S1, and taking my best fit , so far, middle projected SLR of +0.55m on 2000 global level to 2100 and their conversion table S2. 2016 RCP4.5 = 2.4 RCP4.5 =2.4 RCP4.5 =2.4 RCP4.5 = 2.4 2deg C above pre-industrial warming 2017 RCP2.6 = 1.5 2 APIW < RCP8.5 scaled to 3.5 between RCP 4.5 and 6.0 = 2.7 RCP2.6 = 1.5 450ppm stabilisation = 2.0 RCP2.6 = 1.5 2018 1.5 deg APIW converts to 1.9 2 deg APIW Simple average of all those converted to APIW is 2.3 degree above pre-industrial warming. Also from IPCC AR5 55cm in 2100 is the RCP2.5 scenario, which from the S2 table equates to 2.4 degrees APIW. Latest projection for global sea level rise , from Jason 3 data to 29 Nov 2018, public output 02 Feb 2019 on https://www.aviso.altimetry.fr/en/data/products/ocean-indicators-products/mean-sea-level/products-images.html via best (RMS optimisation) curve-types and curve-fit of 73 datapoints concattenated to Jason2 and Jason3 data back to 2003. The Jason-3 filtered (dotted line) output plot is above 8cm for the first time. Linear y= 1.394804 + 0.337655 * x R^2 = 0.983013 year Sea Level Rise (cm) 2020 8.147 2050 18.277 2100 35.16 Exponential y= 1.925352 -7.599908*(1-e^(0.030612 * x)) R^2 = 0.986048 year Sea Level Rise (cm) 2020 8.343 2050 29.444 2100 156.607 Quadratic y= 1.996267 + 0.211446*x + 0.005277*x^2 R^2 = 0.986157 year Sea Level Rise (cm) 2020 8.335 2050 25.761 2100 75.91 Indicial y=2.238733 + 0.108241*x^1.344403 R^2 = 0.986287 year Sea Level Rise (cm) 2020 8.313 2050 23.059 2100 55.107 Upward trend still, for the best curve-fit by R*R goodness factor, by only a whisker from the quadratic fit. Resume of these projections from the Aviso Jason3 updates concattenated to the Jason 1 and Jason 2 data, for the best-fit of indicial power curves and global sea level rise for the rest of the century, based purely on the Jason altimetry data . to year 2100 using Dec 2017 data , 56.15 cm data to 05 Feb 2018 to 2100 , 60.7 cm data to 25 May 2018 to 2100 , 52.1 cm data to 02 Aug 2018 to 2100 , 49.1 cm Update to 01 Sep 2018, public output 07 Dec 2018 to year 2100 , 50.7 cm Update to 01 Oct 2018, public output 18 Jan 2019 to year 2100 , 50.9 cm Update to 29 Nov 2018, public output 02 Feb 2019 to year 2100 , 55.1 cm Revised summary in Feb 2019, with revised J1/J2/J3 overlap datapoints to year 2100 using Dec 2017 data of May2017 , J1+J2 only , so not revisited data to 05 Feb 2018 SLR to 2100 , 56.2 data to 25 May 2018 to 2100 , 57.1 cm data to 02 Aug 2018 to 2100 , 50.5 cm Update to 01 Sep 2018, public output 07 Dec 2018 to year 2100 , 49.0 cm Update to 01 Oct 2018, public output 18 Jan 2019 to year 2100 , 50.9 cm Update to 29 Nov 2018, public output 02 Feb 2019 to year 2100 , 77.4 cm So between 49cm and 77cm SLR to 2100. Well above the 35.6cm of linear "fit". Shame about to the disjunctures between them, but the x,y axes are the Jason 1 image ones extended on to 8cm and 2020. For the disjunctures, with no other info about the filters, a matter of avoiding the last or first 6 months of a mission, compare with the Aviso Reference image and check the slope of a linear "fit" near enough agrees with the reference slope , being aware that theirs also includes the early T/P mission , which I've not included in all this. The original blue gradient lines retained of the 3 images. Comparison between Aviso Reference and individual Jason plots, no idea why the vertical displacement, ref always higher. Where there is overlap of missions , avoiding first and last 6 months . As of the public Aviso output of 02 Feb 2019, updated to 2018.93, I make the equation of their reference plot to be y= 0.334 *x - 1.51 for x=0 of 1990 and y in cm. I'd not realised before , the Aviso reference curve includes 0.3mm per year contribution of isostatic rebound correction or GIA glacial isostatic adjustment. I'd thought there was too much disagreement over the degree of GIA contribution to SLR, for anyone to use it for primary reference purposes, more like a matter of faith rather than science. Only the one paper by Peltier put a figure to it of 0.3mm/year, then the University of Colorado decided to include that 0.3mm /yr figure in their outputs. Despite loads of assumptions relating to the known unknowns of the oceans sub-bottom geology. Anyway I'd thought the answer lay in the term isostatic, ie all balanced out, swings and roundabouts. For example , in a minor way and simplified (no account of groundwater abstraction near tide gauges or long term change of current-streams etc) for just the UK recovering from the last ice-age. From BODC data for Lerwick tide gauge, between 1957 and 1999 mean sea level has risen 30 mm relative to the rising land there. But for Portsmouth between 1962 and 2002, the sea level relative to isostatic sinking Portsmouth ,had a 170mm rise. Unfortunately no BODC long term tide gauge data for "middle " England ports. But simply taking the average of 30 and 170mm and over about 40 years, gives a ball-park figure of SLR around the UK over those decades to be about 2.5mm per year, much like the global figure for those decades. Anyway the Aviso reference data is simply the Jason data plus 0.3mm per year added. I still have no explantion for the mismatch of curves on the overlaps of J1 and J2, then J2 and J3 missions. But removing the yearly pro-rata GIA amounts from the Aviso reference plots , for the periods of overlap, is very much the lowest values, wheras previously I'd taken the average, as I had no info on how to handle the transitions of missions. This now exagerates the knee of the concattenated J1+J2+J3 plots, revised image showing the greater deviation from linear and more balanced passes through the plots, http://diverse.4mg.com/jason1+2+3_29nov2018.jpg , more of a curve and so higher projected global SLR to 2100. It is possible to transparent masque across the reference plot onto that J1+J2+J3 image, with only x and y rescaling, to confirm the lower datapoints in the transition periods. For year 2010 on that plot, 2 pixels difference between indicial and quadratic but 13 pixels to exponential curve , but decided not to overlay another curve on that plot. Same ranking order via R^2 value , same J-3 data to 29 Nov 2018, but higher projected SLR. x= year minus 2000, y = Aviso global SLR 73 datapoints linear y=1.272075+ 0.343219*x r*r = 0.976375 year Sea Level Rise (cm) 2020 8.136 2050 18.433 2100 35.593 Exponential y=2.095669 -3.722926*(1-Exp(0.049906*x)) r*r = 0.984341 year Sea Level Rise (cm) 2020 8.473 2050 43.514 2100 545.734 = 5.46m same r*r and SLR for this alternative manipulation of that expression y= -1.630970 + 3.726249*1.051143^x to sensible number of iterations for the curve-fit quadratic y = 2.270613 + 0.133686*x + 0.008761*x^2 r*r = 0.984705 year Sea Level Rise (cm) 2020 8.448 2050 30.857 2100 103.249 = 1.03m indicial power y=2.483612 + 0.053029*x^1.575023 r*r = 0.984834 year Sea Level Rise (cm) 2020 8.421 2050 27.627 2100 77.397 So 11.8mm per year rise by year 2100 For turn of year J3 data output in early 2020, I'll have to remember to check whether this prediction was nearer the 8.1cm of linear or 8.4cm of the curves. Now J3 plot is approaching the longer term gradient, I'll move to checking my linear fit to J3 only compared to Aviso gradient or mm/yr, as they are getting closer. Current Aviso J3 0.312 gradient cm/yr, my reduced datapoint gradient 0.327 revisiting previous Jason 3 data assesments to decimal year 2018.685, aviso 0.247 gradient, me 0.192 to 2018.441, aviso 0.246 gradient, me 0.196 to 2017.964, aviso 0.241 gradient, me 0.205 The only other curve-fit I've found is Prof Steven Nerem , https://cires.colorado.edu/council-fellows/r-steven-nerem , and his processing giving <>10mm/yr for year 2100 but for data only up to year 2017.42. For best curve-fit at end of 2017 I had 7.3mm/yr for year 2100. and https://www.pnas.org/content/pnas/115/9/2022.full.pdf In email with him, variability around the curve is much due to changes in terrestrial water storage. I make the equation of his quadratic curve, to graphical/pixel resolution. y= 42.05 + 2.925*x + 0.042* x^2 (y = mm and x = year minus 2005) I'll be using Enso+Pinatubo adjustment plot to modify the Aviso J1,J2,J3 data 2003 to 2017 and reign-in the otherwise hareing-off of SLR now we are well into the next El Nino for the latest Jason3 data . Maybe the curve type of best fit will become quadratic rather than indicial. I'd not considered acceleration. I'd dismissed linear (acceleration=0) and exponential (rising acceleration) SLR as worst goodness of fit and cubic (with change of time index) converged but poor fit and not well-behaved beyond year 2030. Leaving quadratic (constant acceleration) and indicial (falling acceleration) with little difference in goodness between them and applying his "green" correction could well move the curve-form to quadratic best fit, as well as expected reduction in SLR projection to 2100. Taking D2y of my indicial form , I get acceleration of 0.48 * x ^(-0.425) (in mm terms where x = year -2000) for 2018.0 acceleration 0.14 2030 , 0.11 2050, 0.091 2100, 0.068 From the last seven years of the Nerem plot I get his adjusted SLR near enough 0.5 difference between his curve fit line and the Jason data, so taking 0.5 or the average of my curve fit and Jason data, hoping not too much self-fulfilling as only a couple of pixels in it. Adjusting the Jason3 data fully in line with his adjusted curve , to the end of his plot so from 2003.0 to 2017.0 and using the 0.5 factor to adjust the latest data 2017.0 out to 2018.9 , beyond his plot, until a better adjustment emerges, possibly involving phase between SST and SLR Applying to the latest Jason-3 data of 29 Nov 2018 . Reduced SLR to 2100 but moved the best fit curve-type to exponential unfortuately, not the quadratic or indicial. So I'll change my policy and go for the most conservative rather than best R^R goodness of fit, to the least SLR to 2100 , the indicial form. Y=Aviso structure cm and x=year - 2000 linear Y = 1.538367 + 0.32577 *x , R^2 = 0.98385 year Sea Level Rise (cm) 2020 8.053 2050 17.8 2100 34.1 exponential y= 2.320390 -3.537474 *(1-Exp(0.049866*x)) r*r = 0.991467 year Sea Level Rise (cm) 2020 8.373 2050 41.59 2100 516.8 quadratic y = 2.440064 +0.136559 *x + 0.007911 *x^2 r*r = 0.991447 year Sea Level Rise (cm) 2020 8.335 2050 29.045 2100 95.205 indicial y = 2.655903 + 0.054672*x^1.548546 r*r = 0.991309 year Sea Level Rise (cm) 2020 8.311 2050 26.028 2100 71.024 compared to 77.4cm without "Nerem" adjustment acceleration in mm terms and self-limiting 0.46441 * x^(-0.451454) 2020, 0.12 2030 , 0.1 2050, 0.08 2100, 0.058 Update September 2019 In the intervening 6 months I'd forgotten, until seeing my concattenated Jason1+2+3 plot again and the SLR of 77cm, in future I intended using the more representative data set . Originally I could not make sense of the mission cross-over periods and decided to arbitrarily use a conservative, ie the few datapoints in the cross-over subsets that would flatten out any curve to some extent. Then I realised it would be more logical to use the Aviso reference plot, even though low resolution, for datapoints in the J1 to J2 crossover and J2 to J3 crossover periods. When I eventually realised that the Aviso reference plot simply had 0.3mm/year GIA figure somewhat spuriously added to the underlying data . 83 datapoints to 26 june 2019 public output 07 sep 2019 on Same ranking from R^2 , indicial is still best fit , giving SLR to 2100 of 80cm compared to linear "fit " SLR of 36cm linear and r*r= 0.977453 Y= Sea level in Aviso terms and x = year minus 2000 Y = 1.219 + 0.348509 *x year Sea Level Rise (cm) 2020 8.19 2030 11.67 2050 18.64 2100 36.07 exponential and r*r = 0.986480 y= 2.107 -3.61507*(1- e^(0.050817*x)) year Sea Level Rise (cm) 2020 8.48 2030 15.09 2050 44.37 2100 580.69 = 5.8 metres quadratic and r*r = 0.986767 Y = 2.292 + 0.128753*x + 0.008981* x^2 year Sea Level Rise (cm) 2020 8.46 2030 14.24 2050 31.18 2100 104.98 indicial and r*r = 0.986839 Y = 2.509 + 0.049363*x^1.598526 year Sea Level Rise (cm) 2020 8.44 2030 13.85 2050 28.17 2100 80.21 Quadratic may become the best curve-fit type on the next output as R^2 ratio for quadratic to indicial for the previous was 0.999869 and for this output 0.999927 .
Update for 02 Nov 2019 public output, data to 25 July 2019. So much backwards revision and especially being able at last to download the ftp files from the Aviso site, I decided to try big number crunching of 610 datapoints. Firstly from the files ftp://ftp.aviso.altimetry.fr/pub/oceano/AVISO/indicators/msl/MSL_Serie_MERGED_Global_AVISO_GIA_Adjust_Filter2m.txt , and ftp://ftp.aviso.altimetry.fr/pub/oceano/AVISO/indicators/msl/MSL_Serie_MERGED_Global_AVISO_NoGIA_Adjust_Filter2m.txt, No-GIA data excludes 0.3mm per year from "zero" of about 1993.173659 but only up to 2017 and approximate , needs more insight to unravel fully. 610 datapoints from 2003.002659 to 2019.589818 , again I've ignored the early altimetry missions because of the instrument drift but mainly it took about a decade for the SLR suppression by Mount Pinatubo , to drop out of consideration, effectively linearising any would-have-been acceleration in SLR ( see the work of Stephen Nerem). It also allows a convenient time axis zero of year 2000. Starting after the beginning of Jason1, to avoid some of the cross-over mismatch. Using a www curve-fit number cruncher on those 610 datapoints, so anyome else with access to a curve-fitter could check my results, hopefully using a different agency. For the following y is cm of global SLR in Aviso terms and x is the decimal year minus 2000. Again ranking in terms of "goodness" R^2 indicial form remains the best fit. linear, R^2 =0.969321 y= 1.394912 + 0.369895 *x For year 2100 SLR 38.28cm exponential, R^2= 0.982114 y= 2.258757 -3.814849*(1-e^(x*0.052559)) For 2100 7.292metres quadratic, R^2= 0.982546 y= 2.447193 + 0.14249 *x + 0.010067 * x^2 For 2100 1.17metres indicial, R^2, = 0.982663 y = 2.678741 + 0.056302*x^1.590879 For 2100, SLR 88.24cm Plotted out as
 Global SLR
Producing a masque of this and scaling/hovering over the Aviso reference picture is coincident, so a check against a degree of processing error. Someone else agrees with the linear regression processing to linear equation of the 610 Aviso datapoints , but his math package allowed only linear fits. In terms of acceleration of SLR, using second differentials Quadratic constant 0.20mm/yr2, more than double the figure for the 1993 to 2018 determination in the paper , http://www.pnas.org/content/early/2018/02/06/1717312115 Indicial acceleration for 2020.0 , 0.156mm/yr/yr Indicial for 2100.0, 0.805 mm/yr/yr self-limiting, unlike constant acceleration of quadratic, hareing-off for exponential and zero acceleration for linear. Its not so clear cut between quadratic and indicial. There is so much revisionism going on of these current and past altimetry measurements , its impossible to compare the history of this curve-fitting, comparing apples and pears. But chopping back the latest output of heavily revised data. The only thing set is stone is the GIA , precisely the thing that is not set in stone literally and figuratively, because of the unknown unknowns relating to the stone underlying the world's oceans, let alone the known unknowns. At least with all that revisionism , it makes me more comfortable starting my processing at 2003.0 , not 1993 the actual start of the altimetry SLR era, so excluding a decade of the post-Pinatubo recovery years. Perhaps 0.88m projection SLR for 2100 is about the minimum to expect. The next Aviso public output is likely to be about 2 months time. 588 datapoints 2003 to 2019.0 Quadratic y=2.467318 + 0.137333*x +0.010339*x^2 for 2100 , 1.196m indicial y= 2.688470 +0.054761*x^1.600479 for 2100, 0.897m *********** 551 datapoints 2003 to 2018.0 quadratic y= 2.620858 +0.096916*x +0.012545*x^2 For 2100, 1.378m indicial y=2.795849 +0.039033*x^1.719367 For 2100, 1.090m ********** 514 datapoints 2003 to 2017.0 quadratic y=2.794919 +0.049351*x + 0.015264*x^2 For 2100, 1.604m indicial y=2.9154 +0.024716*x^1.88367 For 2100, 1.476m ********* ratioing quad/indicial century SLR, to the latest 1.17/0.882= 1.326 to 2019.0, 1.334 to 2018.0, 1.264 to 2017.0, 1.087 and R^2 values for indicial and quadratic are very close and for the 2003 to 2018.0 processing, by R^2, the quadratic was actually the better fit compared to the indicial. ******** Decided to see what adding a sine "correction" to the curve would produce. y= 2.672865 + 0.056919*x^1.587456 -0.054064 * sin (x *3.422537 +0.331269) nominal 1.8 year tidal cycle optimised to 1.836 years in the curve-fitting and R*R improved to 0.983109. Giving a nice wiggle to the curve but otherwise marginal change out at year 2100, less SLR by all of half a centimetre Now having confidence with this on-line curve-fit resource, I decided to try the full set of 977 datapoints of Aviso altimetry from 2003 to mid 2019, including GIA adjustment. Taking 1990 as x=0. Firstly for linear "fit" , still the worst R*R goodness of fit of 0.98545, but the gradient of 0.337585 agrees with Aviso 0.338 cm/yr when rounded or 3.38mm/yr. Y= 0.337585 *x -1.564251 For year 2100, 35.57cm Next best fit, indicial curve type, R*R=0.989097 Y=-0.630654 +0.126134(x*1.271910) For 2100 ,49.18cm Next best fit, quadratic,R*R=0.98973 Y= -0.894056+0.231924*x +0.003240*x^2 For 2100, 63.82cm Presumably via the flattening 1993 to 2003, due to the 1993 Mount Pinatubo eruption cooling the planet, the best curve-fit is exponential, R*R= 0.98998 Y= -0.912529 -11.847747*(1-e^(0.020309*x)) For 2100, SLR of 97.86cm (The double-negative form of the exponential because for some unknown reason the curve-fit does not always converge using the normal positive form of an exponential, ie Y= -12.760276 + 11.847747*e^(0.020309*x) So in summary , best fit from the known data so far, global SLR to 2100 between 88cm from post-Pinatubo 2003 to 2019 data only and 98cm for the whole satellite altimetry era data.
For the updated Jason altimetry data output on Aviso , 11 January 2020 https://www.aviso.altimetry.fr/en/data/products/ocean-indicators-products/mean-sea-level/products-images.html For the best curve-fit, indicial, with my chosen dataset of 2003 to 2019 gives 88cm SLR to 2100 and little different for the complete set 1993 to 2019, exponential best fit, 80cm. Datapoints from decimal-year 2003.002659 to 2019.806999 , from 2003 to exclude false "flattening" of SLR over the 10 years from 1993 after the Mt Pinatubo eruption and also instrument drift uncertainty on the early satellites. Linear, y cm of global SLR as per Aviso and x is year minus 2000 y= 1.276 +0.372 *x SLR to year 2100 , 38.5cm r*r = 0.969777 Exponential y= 2.259 -3.813162*(1-Exp(0.052571*x)) SLR to 2100, 7.30m (not cm) r*r = 0.982885 Quadratic y= 2.451 + 0.141679*x + 0.010107*x*2 SLR to 2100, 1.177m r*r = 0.983298 Indicial, best fit by r^2 RMS goodness of fit ranking y= 2.684 + 0.055567*x^1.595349 SLR to 2100, 88.11cm r*r = 0.983404 Previous Aviso output 02 Nov 2019 ,for 2003.002659 to 2019.589818 SLR to 2100 linear, 38.28cm exponential, 7.292m quadratic, 1.17m indicial, 88.24cm (best curve-fit) ******** For the complete Aviso 985 datapoint set 1993 to 2019 x=year minus 1990 (because of negative x and the exponential curve-type , if 2000 for x=0) Linear (gradient rounds to the Aviso value of 3.39mm per year as a simple check on my processing) y=-1.5797 + 0.338891 *x SLR to 2100, 35.469cm r*r = 0.985296 Indicial y= -0.606 +0.121291*x^1.283533 SLR to 2100, 44.154cm r*r = 0.989253 Quadratic y=-0.878 +0.228824*x + 0.003353*x^2 SLR to 2100, 55.534cm r*r = 0.989915 Exponential (best curve-fit by RMS R^2 ranking) y= -0.898478 --11.375953*(1-e^(x*0.020952)) SLR to 2100, 80.179cm r*r = 0.990186
Update 16 Feb 2020 Summary global sea level rise by year 2100 between 103 and 117cm, from the current known data. As even to the eye, a linear " fit" is totally inappropriate, so a matter of what sort of curve is the best fit to the data, via on-line curve-fit utility. Jason altimetry data to 01 Dec 2019 output to the public 15 Feb 2020 For the complete Aviso 989 datapoint set 1993 to 2019, GIA included, 4 curve-types with zero acceleration, constant acceleration, negative acceleration and positive acceleration and best curve-fit ranking, hence projection of future sea level rise, determined by the "goodness of fit" R^2 values. x=year minus 1990, y= Aviso assigned sea level Linear y=-1.586 + 0.339446 *x (rounds to the Aviso gradient of 3.39mm/year and the .339446 cm/year figure for anyone else checking these results) SLR to 2100, 36cm r*r = 0.9853 Indicial y= -0.596 +0.119426*x^1.28812 SLR to 2100, 50cm r*r = 0.9894 Quadratic y=-0.871 + 0.227659*x + 0.003394*x^2 SLR to 2100, 65cm r*r = 0.9900 Exponential (best curve-fit by RMS R^2) y= -0.893 -11.218653*(1-e^(x*0.021174)) SLR to 2100, 103cm r*r = 0.9903 622 datapoint subset of Aviso Jason record from 2003 to avoid early Jason altimeter drift era and the false flattening of the SLR curve by the 10 years of recovery from Mount Pinatubo eruption 1993. x=year minus 2000 Linear y=1.368 + 0.373114 *x SLR to 2100, 39cm r*r = 0.9702 Exponential y= 2.256 -3.848634*(1-e^(x*0.052256)) SLR to 2100, 714cm= 7.14m r*r = 0.9833 Indicial y= 2.683 + 0.055731*x^1.594306 SLR to 2100, 89cm r*r = 0.9838 Quadratic (best curve-fit by RMS R^2) y=2.448 + 0.142361*x + 0.01007*x^2 SLR to 2100, 117cm r*r = 0.9918
Update 01 March 2020 624 datapoints from year 2003.002659 to year 2019.9699 ,data from aviso.altimetry.fr output to the public 29 Feb 2020. Starting from 2003 to avoid the earlier altimeter drift problem and false flattening of the curve for approx 10 years after the 1993 Mount Pinatubo eruption x=year minus 2000 y = Aviso sea level ranking by r^2 linear y=1.364 +0.373531*x SLR to year 2100 38.7cm r*r = 0.983499 exponential y=2.254 -3.878231*(1-e^(0.051999*x)) SLR to 2100 701cm or 7metres r*r = 0.983499 quadratic y=2.446+0.143071*x + 0.010034*x^2 SLR to 2100, 117cm r*r = 0.983912 indicial y=2.681+ 0.05599*x^1.592718 SLR to 2100, 88.5cm r*r = 0.984025 Change from previous is the R^2 ranking , reverting to indicial as best fit to the data , so dropping back to 88 cm SLR from the previous such assessment For completeness, processing the full 991 datapoint set from 1993 to near end of 2019, similarly 81.5cm SLR to 2100 x = year minus 1990 ranked by goodness-of-fit r^2 Linear y= -1.59 + 0.339733+x (rounds to 0.340 cm/yr or 3.40mm/yr of the Aviso Reference plot as confirmation of no silly errors to this stage of linear only) r*r = 0.985297 SLR to year2100= 32.4cm Indicial y=-0.592 +0.118672*x^1.289997 r*r = 0.989438 SLR to year 2100= 45.7cm Quadratic y= -0.869 + 0.227209*x +0.003410*x^2 r*r = 0.990111 SLR to year 2100=56cm Exponential y= -0.892 -11.162847*(1-e^(x*0.021255)) r*r = 0.990392 SLR to year 2100= 81.5cm
Update 21 July 2020 Site with page is now back working after an absence of a month or two. Firstly using all 1007 datapoints of the Reference plot from 1993 to 2020.404245 , as a partial check on my processing and as a check for anyone else repeating this. Linear "fit" , here y is cm as Aviso and x=0 for year 1990.0000 (to avoid problems if using an exponential or indicial curve-type, but just the linear here) y= 0.341193*x -1.607415 R^2= 0.98572 Agreeing with the rounded to 3.41, as mm/year, of the Aviso plot As explained below , I prefer to start from 2003 and just the Jason missions. Ranking of fit by R*R, ie closest to 1 is best curve fit. x=0 for year 2000.0000 and for the following curves Linear y= 0.3751*x + 1.35 R*R=0.972487 SLR to 2100, 38.9cm Exponential y=2.20 -4.47675*(1-exp(0.04735*x)) R^2=0.984027 slr to 2100 = 5.05metres Quadratic y=2.38 + 0.15843*x + 0.009259*x^2 R^2= 0.98450 slr to 2100= 110.82cm Indicial (best fit) y=2.64 + 0.06310*x^(1.55207) R^R= 0.984715 SLR to 2100 = 82.87cm
Update 07 October 2020 From data otherwise , when working as still unavailable , from website aviso.altimetry.fr For the 1011 datapoints 1993 to 2020 , for when the Aviso graphic emerges of the Reference plot, gradient should be 3.42mm/year to 2 decimal places, if I've not made an error, 3.41646 before rounding. For my preferred time-span of 2003.0 to latest 2020.512835 , output to the public probably in Sept 2020. 644 datapoints, avoiding early Jason and Mount Pinatubo problems and being able to choose x=0 for year 2000. The following ranked in terms of R^2 or r2 goodness of fit Linear "fit" r*r = 0.977796 y= 0.375292*x + 1.35 SLR to 2100= 37.9cm Exponential r*r = 0.984118 y= 2.20 -4.495443*(1 - e^(x*0.047218) ) SLR to 2100 = 5.029m (sic, not cm) Quadratic r*r = 0.984591 y= 2.38 + 0.158836*x + 0.009238 * (x)^2 SLR to 2100 = 1.106m Best fit as previous results, in the range 80 to 89 cm rise from 2000 to 2100 Indicial r*r = 0.984807 y=2.63+ 0.063277* (x)^1.551148 SLR to 2100 = 86.6cm ***** Global Sea Level rise from satellite altimetry from the latest aviso.altimetry.fr data release, from datafile at Processing below is for my preferred time-span of 2003.0 to latest 2020.702868 (13 September 2020 ), output to the public ,28 November 2020. Using 651 datapoint subset, avoiding early Jason and Mount Pinatubo problems and being able to choose x=0 for year 2000 and y is cm of global SLR in Aviso terms. The following curve-fits ranked in terms of R^2 goodness of fit and curve-forms with, second differentials; zero acceleration, increasing acceleration, constant acceleration and the indicial form with decreasing acceleration again as the best fit. Linear r*r = 0.97374 y= 0.376521*x + 1.34 SLR to 2100= 40.0cm In Aviso terms, 3.77mm/year of GSLR . Bear in mind that gradient is based on 2003 to 2020 data. If/when Aviso sorts out the javascript problem on their site, myself and others have enquired but no change for months, I'll redo with the full dataset 1993 to 2020 . But without their linear "fit", little point in me doing so, the previous such comparisons of the gradient have agreed. Exponential r*r = 0.98464 y= 2.18 -4.808622*(1 - e^(x*0.045144) ) SLR to 2100 = 4.36m (sic, not cm) Quadratic r*r = 0.985125 y= 2.35 + 0.165837*x + 0.008889 * (x)^2 SLR to 2100 = 1.078m Best fit as previous results, in the last 1.5 years, in the range 80 to 89 cm rise from 2000 to 2100 Indicial r*r = 0.985384 y=2.61+ 0.066640 * (x)^1.533651 SLR to 2100 = 80.4cm SLR 5.2mm per year for mid year 2020 to mid 2021 For anyone wishing to repeat this execise , the curve-fitter I use is once the source page is saved to disc, it's a stand alone javascript coding routine. (Reminder to self: when reloading the source file from disc, enable genearal default javascript in the browser as its not a website and so no white-listable, check it works , then disable javascript in the browser and it will continue working) As above, the full dataset linear processing has previously agreed to Aviso to 2 decimal places of the gradient on their plots. The cumbersome form of the exponential is more comfortable for converging with that curve-fitter than the simpler transformation of it. Aviso website has come back again, so I returned to the full dataset of 1018 datapoints x=0 for year 1990, y is cm in Aviso terms y= 0.342338*x -1.621 So gradient 0.342338 cm /year Rounding to the latest Aviso graphic , dated 04 Dec 2020 to their gradient of 3.42mm/year
October 2021 Aviso and NOAA continue to use a linear "fit" to their data, but even to visual inspection of the plots , a curve is more appropriate principally above the straight line 1990s and 2020s but below the line 2010s , but which curve fits the data best, for projecting on into the 21st century. Aviso https://www.aviso.altimetry.fr/en/data/products/ocean-indicators-products/mean-sea-level/products-and-images-selection-without-saral-old.html used to output about every 2 months with data to 2 months before that, but nothing for nearly a year now. So while awaiting an Aviso update using and converting the NOAA data for the last year Using seasonally adjusted NOAA SLR dataset off the SLR part of https://www.star.nesdis.noaa.gov 651 Aviso+ 37 NOAA Jason3 only datapoints from 2003.002659 to 2021.6978 using transform of NOAA mm data NOAA *0.1 + 1.892 + 0.03*x cm (where x= year minus 2000 ) With 1.892 value , the offset error between NOAA (no GIA) and Aviso (with 0.3mm/yr GIA) at 2020.7 made to be 0 mm, 2003 difference error is then 0.6mm and at 1993 is 1.5mm . Firstly forming a consistent dataset for the NOAA data, simply choosing the data from the most recent satellite data at overlaps for all 1993 to 2021 produces a gradient of 3.03 mm/yr compared to NOAA linear "fit" of 3.02 so pretty good and kept to that dataset. NOAA presumably used a proportioned value at the transitions coming in and out of the filters. Then repeating for the Aviso dataset , then back to NOAA with a "GIA" factor of 0.33mm /yr gave a best linear fit, so settled with 0.3mm/year and the 1.892cm bridging the datasets at year 2020.7 Curve fitting ,least RMS , ranking by "goodness of fit" R*R using statpages.info excellent off-line 8 parameter, high data capacity (>3400 datapoints possible with Opera javascript) and function complexity (eg >240 sin terms in one function) curve fitter. x= year -2000, y = sea level in Aviso cm terms For Aviso 2003 to 2020.7 plus the transformed NOAA to 2021.7 below 20.7048, 9.2221 20.7319, 9.1930 20.7590, 9.2708 20.7862, 9.4346 20.8115, 9.4493 20.8413, 9.5952 20.8676, 9.4310 20.8948, 9.0748 20.9219, 9.4177 20.9490, 9.2825 20.9762, 9.3483 21.0034, 9.4161 21.0305, 9.6179 21.0577, 9.6357 21.0848, 9.8355 21.1119, 9.4844 21.1390, 9.3122 21.1662, 9.1520 21.1934, 9.3468 21.2205, 9.4616 21.2477, 9.7214 21.2748, 9.8202 21.3015, 9.8290 21.3291, 9.4419 21.3562, 9.5847 21.3834, 9.7175 21.4105, 9.6333 21.4377, 9.3381 21.4649, 9.7259 21.4920, 9.7708 21.5192, 9.6806 21.5463, 9.5914 21.5735, 9.8052 21.6005, 9.9270 21.6278, 9.9488 21.6549, 9.5216 21.6821, 9.6345 21.6978, 9.6819 in cm terms and including GIA Linear (zero acceleration) r*r = 0.977234 y= 1.305473 + 0.380060 *x SLR to 2100= 39.3 cm Exponential (increasing acceleration) r*r = 0.985902 y= 2.086881 -6.216526*(1 - e^(x*0.037839) ) SLR to 2100 = 2.69 m (sic, metres not cm) Quadratic (fixed acceleration) r*r = 0.986379 y= 2.242356 + 0.192407 *x + 0.007595 * (x)^2 SLR to 2100 = 97.4 cm Indicial (reducing acceleration ) best curve fit r*r = 0.986786 y= 2.531871 + 0.080958 * (x)^1.468615 SLR to 2100 = 72.6 cm current SLR from that curve 4.95 mm per year for mid year 2020 to mid 2021
Related topic , CO2 increase over this century Mauna Loa CO2 data (most recent updated before 08 of the month ) https://gml.noaa.gov/webdata/ccgg/trends/co2_trend_mlo.png https://gml.noaa.gov/dv/data/index.php?parameter_name=Carbon%2BDioxide&type=Insitu&site=MLO https://gml.noaa.gov/aftp/data/trace_gases/co2/in-situ/surface/mlo/ https://gml.noaa.gov/aftp/data/trace_gases/co2/in-situ/surface/mlo/co2_mlo_surface-insitu_1_ccgg_MonthlyData.txt and IPCC CO2 RCP plots https://en.wikipedia.org/wiki/Representative_Concentration_Pathway Again unbalanced above and below the line if a straight line is fitted, suggesting a curve is the better fit Firstly fitting the 4 simple curve types and the order of best fit with statpages.info least RMS curve-fitter was again linear, exponential, quadratic , indicial. But adding a sine term for the NH temperate forest annual cycle was too tempting. A sine of periodicity of about 2*Pi , amplitude of about half the annual swing so about 3ppm and phase of about 0 or 2*Pi as mid cycle was about turn of the year. That much improved the, RMS error and r*r factor but now the quadratic was best fit ie maximal r*r, next indicial, exponential and linear worst of course. I decided that allowing for industrial recession about 2008 and 2020 that annual cycle amplitude seemed to be increasing slightly over time, so added the final term in this 7 parameter optimised fit function. Starting from 2003.0 again to 2021.67,x = year minus 2000 , y = ppm CO2. y = 370.168 + 1.626878*x + 0.025487*x^2 +2.872285*sin(6.288333*x+6.187070)*(1+0.003680*x) Unfortunately the RCP plots are contrary, less is more, up to mid century for CO2. So for 2050, excluding the sine term , Y= 512.2 ppm so RCP is the better , ie higher presumably,side of RCP 4.5 (508 ppm) so perhaps about RCP 4.2 From SLR and the previous procesing, sugests a 2100 RCP of about 5.5 The following may be total bollocks, I've not read around the subject, just my speculation. Perhaps the mid-century RCP cross-over business is a positive feedback effect. As human derived CO2 levels go up, the NH temperate forests put on more growth and so deeper annual swings in the global CO2 curve until thermal or water stress of climate change starts to kill them off. In future years , rolling monitoring the Mauna Loa outputs and such processing as this, the change of the 2.87 and 0.0037 numbers in the above might be useful signals of worsening or improvement. Although 0.0037 ppm is a very small figure per year, it might be a sign of notable leverage . For the added October CO2 datapoint on https://gml.noaa.gov/webdata/ccgg/trends/co2_trend_mlo.png requiring revisioning back to 2021.0 and optimising the 226 datapoints on curve Y=a + b*x + c*x^2 +d*sin(e*x+f)*(1+g*x) where Y is MLO CO2 in ppm and x is year minus 2000 a= 370.168 b= 1.626926 b= 0.025485 c= 2.862351 d= 6.287995 e= 6.190249 f= 0.004065 Ignoring the sine component , the increase to 2050 up from last month processing 512.2 to 515.2 ppm Again a quadratic (constant acceleration) curve is the best fit by R*R compared to Indicial or Exponential, let alone linear. Baseline annual arboreal sine amplitude (c) 2.872 down to 2.862 and annual arboreal sine amplitude increment factor (f) 0.003680 up to 0.004065 No indication that anyone took any notice of upcoming COPout26.
Repeating the process for Ocean Heat Content. Borrowing Humpty Dumpty's maxim. When I use a mathematical process, I choose where to apply it, nothing more, nothing less. Curve-fitting, best RMS fit, to current available data and projecting the curve to 2100 and comparing that figure to the various IPCC RCP emissions scenarios for this century. This time for the global ocean heat content, monthly data, this time Chinese data, summing 0 to 700m and 700m to 2000m datapoints. http://159.226.119.60/cheng/images_files/IAP_OHC_estimate_update.txt R^2 goodness of fit for the 3 curve types exponential, quadratic and indicial only varying 0.9670 to 0.9671 with exponential being the better ,marginally . But choosing the most conservative one for the 2100 figure, indicial y= -7.74+ 0.320009 * (t)^1.316999 Where y is OHC in IAP terms and t is year minus 2000 ZetaJoule = 10^21 Joules IPCC By 2100, the top 2,000m of the ocean are projected to take up 57 times more heat under RCP8.5 (or 24 times more under RCP2.6) wrt 1970 to 2019 heating. So by the latest data to year 2021.25 gives an RCP of about 3.5 by simple ratioing Previous such determinations with the latest monthly data Mauna Loa CO2 rise About RCP 4.2 Global Sea Level Rise by altimetry About 5.5 RPC
Repeating the process for Methane 223 datapoints from 2003.0 , from MLO https://gml.noaa.gov/ccgg/trends_ch4/ and https://gml.noaa.gov/webdata/ccgg/trends/ch4/ch4_mm_gl.txt Quadratic is best fit , just Y= 1772.5 -0.752915*x +0.292574*x^2 Giving 2466 ppb in 2050 essd.copernicus.org/"essd-12-1561-2020-f02-web.png" about the same as SSP3 (7.0 W/m^2 ) for 2050 Update 09 Dec Quadratic is best fit by r^2 ranking of linear, quadratic, exponential and indicial , just best over indicial Y= 1772.43 -0.737780*x + 0.291955*x^2 where x is year minus 2000 last month was 2466.0 ppb for 2050 now 2465.43 ppb , marginally lower , and comparing to projections at essd.copernicus.org "essd-12-1561-2020-f02-web.png" about SSP3 (7.0 W/m^2 ) Indicial fit gives 2480.06ppb for 2050
Repeating curve-fitting for N20 data Mauna Loa monthly N2O data , 218 monthly datapoints https://gml.noaa.gov/aftp/data/hats/n2o/insituGCs/CATS/monthly/mlo_N2O_MM.dat and comparing 2050 projections from the copernicus site SSP page gmd-13-3571-2020-t05-web.png taking MLO data as representative of global concentrations Linear y= 314.43 + 0.919095* x y is MLO N2O ppb and x is year minus 2000, starting from year 2003 again For 2050 gives 360.388 ppb exponential fit y=315.81 -24.505271 (1- e^( 0.026832*x)) For 2050 gives 385.04 Quadratic fit y = 315.93 + 0.617959 *x + 0.012290 * x^2 For 2050 gives 377.55 Indicial fit y= 316.60 + 0.334002 * x ^1.303565 For 2050 gives 371.36 By R^2 , goodness-of-fit, exponential is the best fit , but even taking the indicial figure for 2050 , the most conservative, is about 7W/sq m of the SSP scenarios. It would take a lot of revisionism downwards for the last 1.5 years of data to bring the SSP projection down to the 5 to 6 W/sq m region, unlikely as the trend from the other labs around the world is much the same. Update Linear For 2050 previously 360.388 ppb with 01 Dec data 360.65 ppb exponential fit For 2050 previously 385.04 ppb with 01 Dec data 386.54 ppb Quadratic fit For 2050 previously 377.55 ppb with 01 Dec data 378.38 ppb Indicial fit For 2050 previously 371.36 ppb with 01 Dec data 372.14 ppb
Repeating for global temperature. I thought it would be too noisey but giving global temp a go. Again restricting to a start from 2003.0 when visually the plot starts to curve upwards from straighish GLOBAL Land-Ocean Temperature Index GHCN-v4 https://data.giss.nasa.gov/gistemp/tabledata_v4/GLB.Ts+dSST.txt Linear y= 0.46 +0.023509 * x 2050, 1.63 deg C 2100, 2.81 deg C exponential y= 0.52 -0.224928 * (1- e^(0.052914 * x)) 2050, 3.47 deg C 2100, 50 deg C Quadratic a + b*x + c*Power(x,2) y= 0.56 +0.002076 * x + 0.000860 * x^2 2050 , 2.82deg C 2100 , 9.37 deg C Indicial y= 0.56 + 0.001816 * x^1.790003 The best curve fit by R^2 goodness_of_fit To 2050 , 2.56 deg C minus 1.00 for 21.5 (= decimal_year 2021.5) of that curve ,so +1.56 above present 2100 , 6.90 deg C minus 1.00 ,so +5.9 *************** To give Earth more of a chance, I repeated with the 742 datapoints from 1960 to the present Linear y = -1.207 + 0.017189 *x y as before and x is year minus 1900 for 2050, 1.48 deg C for 2100, 2.23 for 2021.5, 0.88 Did not bother with exponential Quadratic, Best fit on R*R y= -0.0058 -0.010286 * x + 0.000151 *x^2 for 2050 , 1.85 deg C for 2100, 3.98 for 2021.5, 0.97 from that curve Indicial y = -0.292 + 0.00000548427 * x^2.573040 p1= -0.292152 +/- 0.047306; p= 0.0000 For 2050, 1.92 deg C For 2100, 4.28 For 2021.5, 0.98
History of the SLR results, ranking by R*R, goodness of fit, for best curve type each time usually the indicial form and decreasing acceleration , using 2003 to the latest datapoint to avoid the early altimeter calibration problem and post-Pinatubo recovery SLR flattening and including the 1993 to 2003 tranche does not actually make much difference to projections, going by previous full and partial dataset processing. Initially melding together the separate J1,J2 and J3 plots and then since 2019 using the Aviso Reference data as the small GIA component is getting less and less significant and less and less confidence in the mission cross-over/overlap data, going in and out of the filters. SLR to year 2100 using Dec 2017 data of May2017 , J1+J2 only , 56.2cm data to 25 May 2018 to 2100 , SLR 57.1 cm data to 02 Aug 2018 to 2100 , SLR 50.5 cm Update data to 01 Sep 2018, public output 07 Dec 2018 SLR to year 2100 , 49.0 cm Update data to 01 Oct 2018, public output 18 Jan 2019 SLR to year 2100 , 50.9 cm Update data to 29 Nov 2018, public output 02 Feb 2019 SLR to year 2100 , 77.4 cm Update data to 26 June 2019, public output 07 September 2019 SLR to year 2100 , 80.2 cm Update to 25 July 2019, 02 Nov 2019 public output, SLR to 2100, 88.2cm Update 11 January 2020 for data 2003.002659 to 2019.806999, SLR to 2100 , 88cm 01 Dec 2019 output to the public 15 Feb 2020 SLR to 2100, 117cm (quadratic was the best fit that time, otherwise indical was 89cm) 624 datapoints from year 2003.002659 to year 2019.9699 output to the public 29 Feb 2020. SLR to 2100, 88.5cm 640 datapoints 2003.002659 to 2020.404245 website back working on 20 July 2020 SLR to 2100 = 82.9cm 644 datapoints 2003.002659 to 2020.512835 , output to the public probably in Sep 2020, update here of 07 Oct 2020 Global SLR to year 2100 = 86.6 cm 651 datapoints 2003.002659 to 2020.702868 or 14 Sep 2020 , output to the public 28 Nov 2020. Global SLR to year 2100 = 80.4cm 685 datapoints from 2003.002659 to 21.625885 or 17 Aug 2021 public release 12 Oct 2021 Global SLR to year 2100 = 76.06cm Update 12 October 2021 (decimal year 2021.78877), ,public output on 30 Nov 2021 Indicial (reducing acceleration ) best curve fit r*r =0.986942 y= 2.65 + 0.077111* (x)^1.489312 SLR to 2100 = 76.06cm current SLR from that curve 5.1 mm per year for year 2021.0 to 2022.0 compared to linear "fit " trend of 3.51 mm/yr

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