A simple statistical method for estimating the - PowerPoint Presentation

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A simple statistical method for estimating theeffect of systematic errors in climate data sets of long-term sea-surface temperature change

John Kennedy

10 June 2016, 13

th

IMSC,

Canmore

, Canada

The Problem – Part Ilots of little problems2004

Further Exploring and Quantifying Uncertainties for Extended Reconstructed Sea Surface Temperature (ERSST) Version 4 (v4)B. Huang, P.W. Thorne, T.M. Smith, W. Liu, J. Lawrimore, V.F. Banzon, H-M. Zhang, T.C. Peterson, and M. Menne Journal of Climate 2016 29:9, 3119-3142 The Problem – Part IIBIG problems

Possible

artifacts of data biases in the recent global surface warming hiatus, T.R. Karl, A. Arguez,

B.

Huang,

J.H

.

Lawrimore

,

J.R

. McMahon,

M.J

.

Menne

,

T.C

. Peterson,

R.S

.

Vose

,

H. Zhang,

Science

26

Jun 2015 : 1469-1472

The solution?I will be using coarsely gridded SST data5 degree latitude by 5 degree longitude monthlyModel the global SST field as a multivariate Gaussian random fieldSST ~ N(0, C)

The solution?

Spatial Covariance

Error Covariance

Subsampler

DATA

Solution

The solution!

DATA

Solution

Estimate of error

The really nice thing about R is that you can break it down into separate components: individual ships, all German ships, all ships using a particular measurement system

Karspeck, A. R., Kaplan, A. and Sain, S. R. (2012), Bayesian modelling and ensemble reconstruction of mid-scale spatial variability in North Atlantic sea-surface temperatures for 1850–2008. Q.J.R. Meteorol. Soc., 138: 234–248. doi: 10.1002/qj.900

Spatial covariance a simple function of the zonal and meridional separation between points Construct spatially-varying length scale and variance Using method of Karspeck et al. 2012

Spatial

Covariance

Error covariance (R)Observation=

SSTUncorrelated error

+

Errors which affect each measurement differently

Error covariance (R)Observation=

SSTUncorrelated error

Micro bias

+

+

Errors which affect each ship differently

Error covariance (R)Observation=

SSTUncorrelated error

Micro bias

Macro bias

+

+

+

Errors which affect the whole global fleet of ships

Two step assimilation of dataGrid data at 5 degree, monthly resolutionMake prior covarianceAssimilate high-quality (e.g. buoy) data

Update mean and covarianceAssimilate ship dataEstimate macro and micro bias terms

Compare ship data to reliable satellite estimates

Estimated micro bias

SST retrievals from the Along Track Scanning Radiometer instruments as processed in the ARC project (ATSR Reanalysis for Climate)

Merchant, C. J., et al. (2012), A 20 year independent record of sea surface temperature for climate from Along-Track Scanning Radiometers, J.

Geophys

. Res., 117, C12013, doi:

10.1029/2012JC008400

.

In situ SST Quality Monitor (iQuam)Feng Xu and Alexander Ignatov. Journal of Atmospheric and Oceanic Technology 2014 31:1, 164-180 Compare to other estimates of ship biases

IQUAM uses a combined satellite and in situ background field to estimate ship biases

Recent reduction in macro biasesEstimated bias (degC)

Pushing further back in time

Atkinson, C. P., N. A. Rayner, J. J. Kennedy, and S. A. Good (2014), An integrated database of ocean temperature and salinity observations, J. Geophys. Res. Oceans, 119, 7139–7163, doi:10.1002/2014JC010053

.

Summary…A simple error model and……a simple interpolation schemeUsed to estimate biases in SST dataBiases have likely led to a slight underestimate of recent global SST trends, tentatively consistent with the Karl et al. result

…and a plea for help

If you have more powerful methods for solving these kinds of problems it would be great to hear from you

j

ohn.kennedy@metoffice.gov.uk