Chapter3is a concise study of the effects that different choices make on the results of tide gauge derived trends and provides justification of the choices made within this study over following chapters, especially Chapter6, where we use selected tide gauge trends combined with steric trends to imply zonally averaged mass trends. Tide gauge data is provided by the Permanent Service for Mean Sea Level (PSMSL)
(Holgate et al.,2012) using the research quality data from the Revised Local Ref-
erence (RLR) set. Because tide gauges are all levelled to different bench marks, when comparing gauges on a global level we use annual trends as opposed to sea levels themselves. Only data which has eleven out of twelve months per year is considered sufficient to form their annual average. The RLR data set currently involves 1357 gauges. Each gauge within the tide gauge network is individually managed. They can be influenced locally by natural events such as earthquakes, but also can be affected by human intervention such as gauge upgrading and repo- sitioning while retaining the same name. PSMSL record any local event on their website and the effects of these individual factors has been assessed during this analysis. Data from gauges which do not meet the strict RLR criteria is still avail- able from the metric data set. Figure (3.1) shows the locations of all RLR tide gauges (black circles) and those with data (70% complete, so at least 12 of the 18 years) over the altimetry period within this study of 1993 to 2010 (red dots). The
V LD correction was applied to the trend in annual mean (mm yr−1) in each case.
Some studies attempt to overcome the question of spatial selection by choosing gauges which represent well either longer trends (Holgate, 2007), or are globally well spaced (Merrifield et al., 2009). There are valid reasons for gauge selecting and so in this Chapter we look at how 4 different gauge choices affect our zonal average results. These 4 choices are: all tide gauges, long records of 70 years, a set
0 45 90 135 180 225 270 315 360 −90 −60 −30 0 30 60 90
Figure 3.1: Map showing locations of all tide gauges in the PSMSL database
(black circles) and those with data during 1993 - 2010 (red).
created for uniform spatial coverage and 500 gauges for optimal spatial-temporal coverage. Chapter 3 therefore displays a range of results for 3 VLD solutions for 4 sets of tide gauge.
Sea level responds to changes in air pressure where sea level will rise and fall in response to changes in pressure from the atmosphere. The sea level will rise (fall) in response to a decrease (increase) in local air pressure by approximately 1 cm / mbar
(Pugh and Woodworth, 2014) and can reach around ±15 cm. Correcting for this
response to atmospheric pressure is termed the Inverse Barometer (IB). Tide gauge corrections are available via atmospheric pressure data from the National Centers for Environmental Prediction (NCEP) reanalysis model as monthly gridded global fields. The correction should be applied using the relation in equation 3.1
∆z= ∆Pa
ρg (3.1)
where ∆z represents the change in sea level (m), ∆Pa denotes the deviation of
atmospheric pressure (mb) from the mean, ρ is the density of seawater and g is the acceleration due to gravity. Average values of 1026 kg m−3 and 9.81 m s−1 are
assumed forρ and Grespectively. Church et al.(2004) estimate that the pressure correction results in an increase of the global sea level rise rate (1950–2000) of about 0.16 mm yr−1. Inverse barometer corrections were not applied to tide gauges
0 45 90 135 180 225 270 315 −60 −30 0 30 60 −0.04 −0.02 0 0.02 0.04
(a) Inverse barometer trend 1993-2010 (mm yr−1).
−80 −60 −40 −20 0 20 40 60 80 −0.02 −0.015 −0.01 −0.005 0 0.005 0.01 0.015 Latitude Trend mm yr −1
NCEP zone average
NCEP zone average at tide gauges
(b) Zonally averaged inverse barometer trend 1993-
2010 (mm yr−1).
Figure 3.2: Map of the inverse barometer correction for 1993-2010 calculated
using equation 3.1 using data downloaded from NCEP (figure (3.2a)). Shown
also as zonal averages (figure (3.2b)) both at all grid points (blue) and at tide
gauge locations (red).
in the present study under the assumption that the effect would be small over the long time period. This may not be true latitudinally if there were a shift in atmospheric pressure over the southern hemisphere during this time period, for instance. The IB trend between 1993-2010 was therefore examined as a global map (figure (3.2a)) and from this the zonal average in trend was found (figure (3.2b)). Annual mean values were calculated from monthly averages and the trend of the deviation in atmospheric pressure from the mean was calculated and applied to
3.1
The IB trend shows a regional distribution which varies from ±0.04 mm yr−1.
IB trend between -50o S and 40o N is practically zero. Northern high latitudes
see an overall negative IB trend by up to -0.015 mm yr−1 and zonally averaged
southern high latitudes see an overall increase by 0.01 mm yr−1 (blue line in figure
(3.2b)). When the zonal average of the atmospheric trend is calculated only from tide gauge locations with trends that are 70% complete during 1993-2010 (i.e. the tide gauges that would need to be IB corrected for this study), the result is seen from the red line in figure (3.2b) where values vary between approximately
±0.005 mm yr−1 except at 50o N - 60o N where the trend value reaches -0.01 mm
yr−1. Due to the small magnitude of the IB trend as a function of latitude during
the 1993-2010 period it was concluded that the tide gauge results would not be affected by the IB correction.
3.2.1
Calculating tide gauge trends
Trends have been calculated over 18 years. Recent trends for the 18 year period 1993 to 2010 were used to show zonal averages as a function of latitude. This time period was used to minimise the influence of short time scale variability while maximising the available data from altimetry (Chapter 5). This study aims ultimately to determine any changes to the distribution of ocean mass trends and so by using the 18 year trend we filter out much of the daily, seasonal, annual and inter annual variability (Jevrejeva et al., 2008) as well as to dampen any decadal variability (Holgate, 2007).
We note that the nodal tide does have a period of 18.6 years, which is the same length as the trends calculated here. However we expect the nodal tide effect to be small (up to 2 mm in absolute height and therefore associated trends will be much smaller than this) and so do not include the nodal tide correction here (Haigh
et al., 2011,Woodworth,2011). Global trends were calculated as the sum of area
weighted zonal means (weighted by the area of ocean within each 10o latitude
zone) of 18 year trends and plotted as running means centred on the middle year. Trends were only included if the records met our criterion of being 70% complete within the 18 year period. The length of this trend meant that exclude shorter tide gauges from the study. Where errors are plotted they represent ±1 standard
error (σ) and are the statistical error based purely on the quality of fit. Where there were gaps in the data, if the gap appeared at the beginning or the end of the 18 year time this did influence the magnitude of the trend value. This will have an
influence on a small number of gauges, especially when all tide gauges were used, however although this is noted, no correction was applied for the influence of end points.