Uncertainty of sea level rise, rankings etc.

First some results on the temperature hiatus

Simulated KS- distribution

Effect of anomalies Anomalies wrt different reference period are computed by subtracting off the average over the new period from the old anomalies When looking at an ensemble of anomalies (for each member a different reference mean has been taken out) the standard deviation over the reference period is too small

Effect on KS statistics

Measuring tides Connected to sea in bottom of well. Eliminates wave action and enables measurement under ice. A GPS measures station altitude.

Sea level data

Global mean sea level Each point in the global mean sea level (GMSL) time series plots is the area-weighted mean of all of the sea surface height anomalies measured by the altimeter of the TOPEX A/B satellite in a single, 10-day satellite track repeat cycle (time for the satellite to begin repeating the same ground track).

Difference between gauges and satellite Land motion glacial rebound (millenial scale) tectonic activity (decadal scale) Altimeter drift orbital drift instrument drift

A simple model Change in sea level height Cumulative change in temperature (slow response) Change in temperature (quick response)

Robustness of fit C2006R07 GISS0.36 (0.11) Current GISS0.31 (0.10) HadCRUT40.31 (0.08) C2006 ResR07 GISS0.46 (0.09) Current GISS0.40 (0.07) HadCRUT40.40 (0.09) C2011R07 GISS0.19 (0.08) Current GISS0.16 (0.07) HadCRUT40.17 (0.07) C2011 ResR07 GISS0.31 (0.07) Current GISS0.27 (0.07) HadCRUT40.28 (0.07) (0.28,0.64 ) (0.02,0.30)

Sea level projections Use projected temperatures instead of observed in the formula Each climate model/scenario will give a different projected sea level rise. Uncertainty? Comes from Estimation uncertainty Model uncertainty Scenario uncertainty

Simultaneous confidence bands 2100 CI (38-56) w/res (52-80) AR5 (33-68)

Downscaling Find a statistical relationship between global sea level change and local sea level change Apply this relationship to global sea levels estimated from projected temperatures Uncertainties?

Sweden

Model for sea level projections for Sweden Overall projection is mixture of Gaussian processes, used to calculate joint uncertainty

Uncertainty bands

Time until given level 25 cm 50 cm RCP5%median95% > > > > >2100

Scenario comparison

Uncertainty components 2075

Issues Global – should we relate sea level to historical climate model temperatures instead of observations? Gothenburg – ocean level and river level both important Archipelago – need spatial sea level model. Data? Satellite data may help?

Seasons Göteborg just hit Autumn on Oct 17. SMHI defines this as the first time five consecutive days have DMT< 10°C Other definitions: Astronomical: Equinox Sep 22 Climatological: Sep 1 Tropical seasons: wet and dry Southern hemisphere Effect of climate change

17/10 Winter Temp <0°C A Autumn Temp <10°C Summer

A statistical approach Maximize the difference in temperature distribution Algorithm: Pick four cutoffs Compute KS-distance for distribution of temperatures between cutoffs Change cutoffs. Recompute distance

Data

Results for Swedish network

Trends

State of the Climate 2008 rwrwrw

Shen et al. (2012) 1921, 4 th warmest 2 nd warmest 14 th warmest

How does one assess the uncertainty in ranks? Draw independent normal random numbers with the right mean and sd for each year Rank Repeat to get an ensemble of paths

Rank distribution

But aren’t years dependent? Structure ARMA(3,1)

Effect of dependence Independent Dependent

Rank sd

Back to State of the Climate “ was the warmest year in the period of record for the nation.”

Need to extrapolate standard error se(2012) ≈ 0.08 anomaly(2012) = 1.7 anomaly(1998) = /0.08 ≈ 6 !!!

And the uncertainty in the ranking of 2012 is...