The relevance of the reference depth

Our 5 reconstructions use gridded data from data sets of which 3 contain full depth data (Carton et al.,2000,Ingleby and Huddleston,2007,Smith and Murphy,2007), one is to 1500 m (Ishii and Kimoto,2009) and one to 700m (Levitus et al.,2009). The steric height is evaluated from an assumed level of no motion. This is the deepest level available and is termed the reference depth. By recalculating the steric height using reference depths of 700 m, 1500 m and full depth only, we can evaluate the impact of the reference depth on the steric calculation. Figures (4.12a,

4.12b, 4.12c and 4.12d) show the results of the steric zonal average calculation

when referenced to levels 700 m, 1500 m and full depth. The model environment of the Carton et al. (2000) data set in figure (4.12d) shows the least variability

−80 −60 −40 −20 0 20 40 60 80 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5 3 3.5

Ingleby and Huddleston (2007)

Latitude Trend (mm yr −1) Full 1500 700

(a) Ingleby and Huddleston(2007)

−80 −60 −40 −20 0 20 40 60 80 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5 3 3.5

Smith and Murphy (2007)

Latitude Trend (mm yr −1 ) Full 1500 700

(b) Smith and Murphy(2007)

−80 −60 −40 −20 0 20 40 60 80 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5 3 3.5 Latitude Trend (mm yr −1)

Ishii and Kimoto (2009) 1500

700

(c) Ishii and Kimoto (2009)

−80 −60 −40 −20 0 20 40 60 80 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5 3 3.5 Carton et al (2000) Latitude Trend (mm yr −1) Full 1500 700 (d) Carton et al.(2000) −80 −60 −40 −20 0 20 40 60 80 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5 3 3.5

Steric Mean of 5 data sets

Latitude Trend (mm yr −1 ) Full 1500 700 Mean of all 5

(e) Steric Mean of 5 data sets

Figure 4.12: The relevance of the reference depth was evaluated using the

steric height calculated from an assumed level of no motion at 700 m (cyan), 1500 m (green) and full depth (blue). The error shown is one standard error for

each 10 degree latitude band. Figure (4.12e) shows the zonal mean between all

data sets for each of the 3 reference depths where data is available for trends during 1993 to 2010. The bold blue line compares the steric zonal average when the maximum reference depth available for each data set is used. (This is the

between this change in reference depth. Ingleby and Huddleston (2007),Ishii and

Kimoto (2009), Smith and Murphy (2007) data sets (figures (4.12a - 4.12c)) all

show slightly more variability, mostly within one standard error. The steric trend using a 700 m reference depth (cyan) shows regional trends that are generally lower than trends where the reference depth is 1500 m or full depth. This makes sense as we would expect some of the trend signal to come from deeper within the water column. The differences in trend outside of one standard error are generally located in the Southern Hemisphere.

Figure (4.12e)shows the steric mean of the 5 data sets for each reference depth. The bold blue line is the mean of the 5 data sets to their individual maximum depth. The 3 deepest steric zonal mean trends are within error and therefore we have confidence that the mean of 5 data sets referenced to their deepest level is well representative of the zonal average, but caution should be used when using steric trends which are not referenced to full depth. It should also be noted that the observations which go into the gridded products is very limited below 2000 m (and even at this depth only since ARGO floats). Therefore, even a gridded product which is to full depth will have large errors when giving values for the deep ocean. In order to quantify the true steric component to sea level trends more full depth observations are needed.

4.8

Summary

ˆ The steric component of sea level is calculated from the specific volume anomaly using temperature and salinity data and the equation of state. Ex- amined in this chapter are 5 temperature and salinity gridded data sets, which are used to evaluate and compare the steric height.

ˆ The new equation of state, TEOS-10 is used. TEOS-10 introduces the vari- able Conservative Temperature and uses Absolute Salinity to produce a ther- modynamically consistent set of equations to describe sea water and reduce errors in heat content and steric height calculations.

ˆ The IPCC AR5 states that the steric contribution to sea level trends account for 0.7 ±0.3 mm yr−1 to sea level rise between 1993 to 2010 (Stocker et al.,

2013). The IPCC AR4 had previously suggested that the steric contribution was closer to 50% of the contribution to total sea level rise (Bindoff et al.,

2007, Lombard et al., 2005), showing that there is still some uncertainty

regarding sea level trends and the sea level budget. This uncertainty is further complicated by the lack of historical data making it hard to calculate long term trends and the lack of deep ocean observations.

ˆ Five data sets have been examined to compare the steric trends calculated from temperature and salinity data. There are considerable differences, as well as some similarities, between the data sets. This is true when the data sets are examined as isothermal layer depths, global average time series, regional average trends for 1993 to 2010 and zonal averages of trends for 1993 to 2010. The data sets tend to agree on the more prominent steric signals such as deepening of the 14o _{C isotherm in the Atlantic (figure (4.6b)) and}

the East and West opposing steric trends in the Pacific Ocean between 1993 and 2010 (figures (4.9a, 4.9b, 4.9c, 4.9d and 4.9e) ). The data sets differ in terms of the time scale of the variability, as seen in the global average steric trends time series (figure (4.8)).

ˆ While the regional trends look similar in their spatial pattern, the magnitude of the zonal averages can vary between 1 and 2 mm yr−1_{. For this reason}

the mean of the zonal average of the 5 data sets is used in Chapter 6 to estimate the mass component of sea level trends. The variance between the zonal average of the steric trends from the 5 data sets is used to estimate

the error. The steric mean of the zonally averaged trends calculated using 5 temperature and salinity data sets is 0.83 ± 0.52 mm yr−1 for the years

1993 to 2010 in this study. The significance of unobserved trends from the deep ocean should not be under-estimated. If the model analysis from Song

and Colberg (2011), suggesting that an unobserved 1.1 mm yr−1 _{could have}

contributed to the steric trend between 1993 and 2008, is accurate then this would have a significant on both the steric zonal average and the calculated errors. This large steric trend from the deep ocean has not yet been observed with instruments and would need the deep ARGO floats (up to 6,000 m deep) to have global coverage before it could be detected on a regional scale.

Sea Level Trends from Altimeter

Measurements

The aim of this Chapter is to provide a view of sea surface height which is not constrained to be at the coast. The results will then subsequently be used to diagnose mass contributions from this sea surface height, after correction for the

GIAresponse has been applied. The aim in this Chapter is also to assess the skill of our tide gauge analysis, which is known to have spatial bias. The constraint of the altimetry data is the comparatively short time scale for which there is data. In this Chapter the spatial and zonal averages of trends from altimetry data are calculated for the time period 1993 to 2010. Changes in the gravity and global average V LD as a result of GIA are removed, so that the results can be used to compare with trends calculated from tide gauges in Chapter 3. We also compare regional and zonally averaged trends to the regional trends from our steric analysis over the same time period in Chapter4and we present the residual as an estimate for the mass component from the difference between these altimetry and steric trends.

5.1

Absolute sea level

T = Dynamic Topography

Go = Geoid

G = Gravitational equipotential surface

τ = Augmented Dynamic Topography

V LD = Vertical Land Displacement

ASL = Absolute Sea Level

RSL = Relative Sea Level

Absolute sea level (ASL) is defined as the height of the sea surface above a refer- ence ellipsoid measured from the centre of mass of the Earth. ASLis the definition of the sea surface that we measure with altimetry (figure (5.1)). Altimeters cal- culate the ASL by measuring the distance from the satellites to the ellipsoid (H) minus the distance to the sea surface (R).

The definition of G is also measured from the ellipsoid as the distance to the equipotential surface. This equipotential surface describes where the ocean would settle in equilibrium in the absence of wind, currents or change through time in the density structure of the water column.

Altimetry measurements differ from tide gauge measurements (in Chapter 3) in that measurements are from a high orbit (over 1,300 km) and therefore the alti- metric measurements are not affected by vertical land displacement V LD. Tide gauges and altimetry are related through V LD such that

ASL=RSL+V LD (5.1)

While the altimeter instrument is not moving up and down with any vertical land displacement, the sea surface can still be influenced by the movement of the ocean floor. There is a direct influence (if the ocean floor gets deeper on average then the global mean absolute sea level will fall) and an indirect influence as the land movement changes the mass distribution of the whole Earth. This can be taken into account by the fact that there will be a subsequent change in the equipotential surface G, as dynamic topography T is defined as the distance of the sea surface fromG. There is only modelled output available for changes toG. Gravity satellite GRACE does observe changes in G but currently only has data available for half of the altimetry period. We use a combined modelled solution for the change inG

reference ellipsoid

Earth’s

crust

Ocean surface

G

T

Altimeter

ASL

H

R

ASL = T + G

ASL = H - R

Figure 5.1: Schematic to show definitions and measurements from satellite

altimetry. The reference ellipsoid (black dotted line) is the reference for ASL

measurements. The geoid Go (black dashed line) is the exact equipotential

surface from which the dynamic topographyT is measured to the ocean surface

(blue line). Go and G are referenced to the reference ellipsoid. The Earth’s

crust (brown line) is from whereRSL is measured to the ocean surface.

and mean V LD due to the effects of GIA provided by Mark Tamisiea (National Oceanography Centre, Liverpool) (Tamisiea et al.,2001). Data for any changes in

G unrelated to GIA, which includes recent melting, have not been corrected for. We use this remaining G and V LD response to compare our estimates with the fingerprints in Chapter 6.

In addition, we define dynamic topography (T) as the distance of the sea sur- face from the potential surface G and the dynamic topography is used to infer geostrophic currents (Hughes and Bingham, 2008). The three variables ASL, T

and G relate to one another as in equation (5.2) and (2.5).

ASL=T +G (5.2)

When we consider the augmented dynamic topography, τ, we are using the dy- namic topography T plus the mean global relative sea level RSL. As set out in Chapter 2 equation 2.9, this allows for change in the dynamic topography plus change in the the water column from G to the crust.

τ =T +RSL. (5.3)

Substituting T from equation 5.2 and using a substitution for RSL from a time average of equation 5.1 we can rewrite equation 5.3 as

τ =ASL−G+ASL−V LD

where

ASL≈G and G′=G−G

where G′ _{is the equipotential surface undulation, we then find that}

τ =ASL− (G′+V LD) (5.4)

This Chapter takes absolute sea level as measured by altimetry and, using model output for the change in G plus the mean crustal displacement (of the sea floor)

(Tamisiea et al., 2001), corrects for changes due to GIA. The resulting approx-

imate augmented dynamic topography will then be compared with approximate augmented dynamic topography as calculated from tide gauges in Chapter3, steric reconstructions from Chapter 4 and used to evaluate the mass component to sea level in Chapter 6. The augmented dynamic topography (τ) is approximate be- cause we have only corrected for GIA and not other sources of V LD or G dis- placement. These effects will be accounted for in the fingerprint calculation in Chapter 6.