Flechtner F.M., Gruber Th., G?ntner A., Mandea M., Rothacher M., Sch?ne T., Wickert J. (Eds.) System Earth via Geodetic-Geophysical Space Techniques

Подождите немного. Документ загружается.

344 H. Reinhardt et al.

information from neighbouring gauge stations into data gaps. Our method of pref-

erence is based on Multi-Channel-Singular-Signal-Analysis (MSSA) as explained

in detail in Kondrashov and Ghil (2006). Here the inserted information in the data

gaps comes from the spatio-temporal covariance structure of the other gauges in the

same region.

The procedure begins with inserting zeros instead of the data gaps (though one

gets the same results when inserting random numbers or linear trends). We use a

two-fold iteration. The inner iteration uses the following steps:

1. Calculate the leading RC of the new time-series (with inserted zeros) using

MSSA.

2. At the position of the data gap insert the values of the RC.

3. Recalculate the leading RC again and insert these (new) values at the data-gaps.

4. Carry out these operations until convergence of the new (inserted) values is

reached.

5. Perform the same with the next RC by starting with the resulting reconstructed

time-series of the previous RC.

When a sufﬁcient number of RCs is calculated, we get a ﬁrst gap-ﬁlled signal.

This result is then again inserted in step 1. We perform this outer iteration until

convergence is reached. This is done for each region of gauges separately.

Best Parameters: The dominant oscillation of the plain time series is the annual

cycle. In our study we only are interested in multi-annual oscillations and the lin-

ear trend. Therefore the annual cycle is removed by subtracting the mean of all

Januarys from each January and accordingly with the other months. In order to have

a common frame of variance, all variances where normalized to var = 1.

As shown in Kondrashov and Ghil (2006) the ideal window length M depends on

the type of signal to be reconstructed. Since we are interested in multi-year oscilla-

tions and trends, we choose multiples of 1 year i.e. M = 12; 24; 36; 48 months. A

larger M would reduce the ratio of ﬁlter epoch versus total time and consequently

the degrees of freedom.

We want to reconstruct only the dominant behaviour of the signal in the data gaps.

It turns out that only the ﬁrst two RCs need to be considered. In Fig. 2 an example is

shown as a test case. Into the measurements at tide gauge Fort Myers/Florida shown

in grey (right panel) a large artiﬁcial gap from 1967 to 1975 is introduced. The left

panel shows time s eries of the RC’s for this gap where our method of reconstructing

sea level from surrounding station data is tested. The measurements at the artiﬁcial

gap were withheld from the analysis and ﬁlled with our method depicted as black

curve in Fig. 1 (left). Comparison with the original data shows good agreement.

The correlation between both, original and ﬁlled gap, is 0.97. Thus the gap ﬁlling

method appears to be reasonable and successful.

Signal ﬁltering: MSSA can also be used to split the signal in trend, oscillations

and high-frequent noise. In the gauge data (without annual cycle) the dominant sig-

nal is the trend. Time series analysis of the 1st RC shows that low f requencies (i.e.

a linear trend) dominate the signal. In higher RCs the major frequencies are in the

Sea Level Rise in North Atlantic Derived from Gap Filled Tide Gauge Stations 345

Fig. 2 The left panel shows in grey the sum of RCs 1 and 2 of the original time series of gauge Fort

Myers/Florida (M = 12). An artiﬁcial gap for the years 1967 to 1975 was ﬁlled with our method

(black). The correlation between both for the years 1967–1975 is 0.97. The right panel shows the

full measured time (grey) and the how the original data gaps were ﬁlled (black)

annual to sub-annual scale. This is depicted in Fig. 3 the 1st RC (black) and 2nd

RC (grey) are displayed together with their respective trends. The window length is

M = 60.

In the following section we calibrate the sea surface height of IFEOM model with

the time series of the reconstructed tide gauges. The IFEOM ﬁelds are provided as

pentads (5 year means) from 1950 to 1994 which result from an analysis of historic

ﬁelds of temperature and salinity (Lozier et al., 1995). Accordingly, gap-ﬁlled tide

gauge time series are smoothed with MSSA using a window length M = 60 for

the gap-ﬁlled time span of 1950–2006. We used the resulting smoothed time-series

from 1950–1994 to calibrate IFEOM. In Fig. 3 the trend of the gap ﬁlled time series

Fig. 3 The gap ﬁlled time series at gauge Fort Myers/Florida, the 1. RC (black) and 2. RC (grey)

and their respective trends. The window length is M = 60. The trend is conﬁned to 1. RC

346 H. Reinhardt et al.

is conﬁned completely to 1st RC. Including only the 1st RC for calibration of 5-year

mean values seems to be reasonable.

4 Reduced Number of Gauges and Calibration of IFEOM

Next we consider a series of results from the Inverse Finite Element Ocean Model

(IFEOM) which was applied to hydrographic data to obtain a sequence of dynamic

topography (Sidorenko et al., 2008). The series consists of nine realisations which

are available as means for the periods from 1950–1954 to 1990–1994. The model

circulation is in equilibrium with spatial gradients of dynamic topography. A bias or

shift in the surface reference has no dynamic consequence and cannot be determined

by the inverse model. The bias was therefore arbitrarily set to zero mean for each of

the pentads. Thus an undetermined shift exists from one realisation to another. The

tide gauge data were now used to determine the interpentadal shifts.

For calibration of IFEOM we want to rely on stable tide gauges only. We per-

formed reconstructions of data gaps using different window lengths M = 12; 24;

36; 48 months. All gauges with correlation below 0.8 (20 gauges) and difference

in regression greater 0.5 (22 gauges) for different window lengths where omitted.

Six gauges of the region Texas where discarded because they possess strong posi-

tive trends, different from all other gauges. This could be explained by local land

subduction due to oil exploitation, which cannot be corrected by the PGR model

of Peltier. Every station containing less than 25% of data between 1950 and 1994

was omitted (26 gauges). Two remaining African stations (Santa Cruz de Tenerife

and Takoradi) were excluded from calibration due to signiﬁcant variance in the tide

gauges resulting from unaccounted land-movements. This and the large ratio (see

Fig. 1) are the reasons for gap-ﬁlling to fail here. All together 53 gauges remain for

calibration from the 129 gauges originally used for gap ﬁlling (see Fig. 4).

Fig. 4 Correlation and regression between 53 consistent tide gauges and calibrated IFEOM model.

Good agreement is seen on the American coast, where the model input data resolution is also

the best

Sea Level Rise in North Atlantic Derived from Gap Filled Tide Gauge Stations 347

The calibration was carried out by ﬁtting pentadal differences of IFEOM at gauge

locations to the tide gauges series in the least squares sense. The area mean recon-

structions show the trend in dynamic topography of 1.18; 1.18; 1.19; 1.19 mm/year

for the window lengths M = 12; 24; 36; 48 months, respectively.

Figure 4 shows the correlation and regression between the consistent tide gauges

and the calibrated IFEOM model. Good agreement is seen along the American coast

where hydrographic data used by IFEOM are dense. The gauges on the Canary

Islands and the African coast differ largely, possibly as a consequence of poor data

coverage in temperature and salinity ﬁelds.

A few time series of the gauges and the calibrated IFEOM Model (for the exact

locations see right side of Fig. 4) are shown in Fig. 5. The signal variance is gener-

ally greater in the Western Atlantic (St. Georges and Argentia). Gauge Portsmouth

is also well represented by IFEOM, whereas gauge Fishguard is anticorrelated to

IFEOM. This is perhaps due to the limited capabilities of IFEOM in the Irish Sea or

to undiscovered movement of the tide gauge.

The regional distribution of sea level rise calculated from calibrated IFEOM is

shown in Fig. 6 (left). The resulting mean is 1.18 mm/year sea level rise (SLR) for

the period of 1950–1994.

Fig. 5 Time series of tide gauges (black) and calibrated IFEOM Model (grey) at selected locations

(see Fig. 4 right)

348 H. Reinhardt et al.

Fig. 6 The sea level rise of calibrated IFEOM for 1950–1994 (left). The mean sea level rise for

the complete model area is 1.18 mm/year. The right ﬁgure shows the trend of steric height with a

mean of 0.31 mm/year

The right panel in Fig. 6 shows the 0.31 mm/year in SLR due to steric effects.

The trend in ocean bottom pressure with a mean of 0.87 mm/year is depicted in

Fig. 7 (left) . It is to a large extent equally distributed over the model domain with

notable exceptions near the boundaries. In the right panel of Fig. 7 the mean of the

pentads for sea level, steric height and ocean bottom pressure is plotted. The fourth

curve is the mean sea level calculated from all gauges directly, which leads to a trend

in SLR of 1.54 mm/year. This is signiﬁcantly larger than the 1.18 mm/year in SLR

from the calibrated IFEOM.

Fig. 7 The left panel shows the trend of bottom pressure (surface height minus steric height) with

a mean of 0.87 mm/year. The right panel shows the mean of the pentads for the calibrated sea level

of the IFEOM model (blue), the ocean bottom pressure (black), and the steric height (green)and

for comparison the mean sea level of all gauges (red).

Sea Level Rise in North Atlantic Derived from Gap Filled Tide Gauge Stations 349

5 Conclusions

Gap ﬁlling of observed sea level data can be performed with the MSSA method and

is stable with respect to different window length when long time scales are con-

sidered. MSSA can also be used for low pass ﬁltering of the gap ﬁlled time series.

Our method of calibrating the basin wide sea surface topography derived from the

inverse ocean circulation model IFEOM with gauge data leads to reasonable results.

The trend in SLR, calculated directly from the tide gauges used for calibration,

is 1.54 mm/year. Our calibration converts this to a basin wide sea level rise of

1.18 mm/year which shows that coastal and regional sea level trends may differ

substantially (see also Holgate and Woodworth, 2004). In our results 0.31 mm/year

SLR are due to steric expansion while 0.87 mm/year are due to mass increase in the

North Atlantic.

References

Church JA, White NJ, Coleman R, Lambeck K, Mitrovica JX (July 2004) Estimates of the regional

distribution of sea level rise over the 1950–2000 period. J. Clim. 17(13), 2609\u20132625.

Ghil M, Allen MR, Dettinger MD, Ide K, Kondrashov D, Mann ME, Robertson AW, Saunders A,

Tian Y, Varadi F, Yiou P (August 2002) Advanced spectral methods for climatic time series.

Rev. Geophy. 40(1), 1003.

Holgate SJ, Woodworth PL (April 2004) Evidence for enhanced coastal sea level rise during the

1990s. Geophys. Res. Lett. 31(7), L07305.

Jevrejeva S, Grinsted A, Moore JC, Holgate S (September 12, 2006) Nonlinear trends and

multiyear cycles in sea level records. J. Geophys. Res. Oceans 111, C9.

Kondrashov D, Ghil M (2006) Spatiotemporal ﬁlling of missing points in geophysical data sets.

Nonlinear Processes Geophys. 13(2), 151\u2013159.

Lozier MS, Owens WB, Curry RG (1995) The climatology of the North Atlantic. Prog. Oceanogr.

36, 1–44.

Peltier WR (November 1998) Postglacial variations in the level of the sea: implications for climate

dynamics and solid-earth geophysics. Rev. Geophys. 36(4), 603\u2013 689.

Sidorenko D, Danilov S, Schröter J (2008) Inverse solution for pentadal variability in the North

Atlantic. Geophys. Res. Lett. 35, L02603.

Snay R, Cline M, Dillinger W, Foote R, Hilla S, Kass W, Ray J, Rohde J, Sella G, Soler T (April

25, 2007) Using global positioning system-derived crustal velocities to estimate rates of abso-

lute sea level change from North American tide gauge records. J. Geophys. Res. Solid Earth

112(B4).

Zervas C (2001) Sea level variations of the United States 1854–1999, NOAA Technical Report

NOS CO-OPS 036, Version July 2001.

Using ARGO, GRACE and Altimetry

Data to Assess the Quasi Stationary

North Atlantic Circulation

Falk Richter, Dimitry Sidorenko, Sergej Danilov, and Jens Schröter

1 Introduction

In the last years, two major observation systems have become operational. The ﬁrst,

satellite altimetry, maps the ocean surface quasi synoptically, and by referencing

sea surface height to the GRACE geoid ocean currents are diagnosed. The second

observing system is the Global Array of Proﬁling Floats (ARGO) adding in situ

subsurface temperature and salinity data. Both types of measurements are consistent

with each other to such an extent that altimetry can be used to check the quality and

performance of individual temperature and salinity proﬁles measured by ARGO

(see e.g. Ivchenko et al., 2007; Guinehut et al., 2009). It is shown that both types

of measurements complement each other and a joint analysis is required in order to

fully exploit the information content.

We combine the two sources of data in the context of an ocean inverse general

circulation model. In this way we make use of dynamical rather than statistical cor-

relations between the data and analyse ocean currents and transports simultaneously

with the observations.

Generally, numerical ocean circulation models produce ﬁelds which differ from

observations. The bias is a result of many factors, which are in both, models and

measurements. On one hand models produce uncertainties due to the lack of suf-

ﬁcient information on the surface forcing and errors in model dynamics. On the

other hand, the measurements themselves are contaminated by measurement errors

and include transient effects of the ocean dynamics which are not resolved by mod-

els. Assimilating all available information into an ocean circulation model could

serve the purpose of ﬁnding the compromise between model and data and obtaining

improved patterns of ocean circulation. This has been successfully demonstrated

in a series of works (Wenzel and Schröter, 1998; Wenzel et al., 2001; Wenzel and

Schröter, 2002; Stammer et al., 2002, 2003; Losch and Schröter, 2004; Kivman

et al., 2005).

F. Richter (B)

Alfred-Wegener-Institute for Polar- and Marine Research, D-27570 Bremerhaven, Germany

e-mail: Falk.Richter@awi.de

351

F. Flechtner et al. (eds.), System Earth via Geodetic-Geophysical Space Techniques,

Advanced Technologies in Earth Sciences, DOI 10.1007/978-3-642-10228-8_29,



Springer-Verlag Berlin Heidelberg 2010

352 F. Richter et al.

2 Model Setup and Data

The model used for the present study is an inverse ﬁnite-element ocean circulation

model (IFEOM) which has been described in Sidorenko et al. (2005). The model

solves the stationary momentum equations for velocity ﬁeld and sea surface height,

and treats the advective-diffusive tracer balances as soft constraints. IFEOM seeks

for the temperature (T) and salinity (S) ﬁelds which give minimum to its objective

function. The latter penalizes residuals in the tracer equations, deviations of model

variables from data available and also the misﬁt between the diagnosed deep pres-

sure gradient and the pressure gradient of a prognostic model run. The experiments

reported below take into account several data sources. Gouretsky and Koltermann

(2004) climatology is used in all experiments as a background for temperature and

salinity.

The other dataset includes T and S proﬁles for the years 2005–2006 from the

ARGO project, available from the ofﬁcial ARGO web site (www.ARGO.ucsd.edu).

The ARGO data comes from a set of proﬁling buoys which contains seasonal and

transient signals. Because of a poor spatial coverage of ARGO data on a monthly

basis we restrict our results to annual model solutions. We use the annual mean of

ARGO data in our experiments with the seasonal signal removed.

Altimetry data is optionally taken as gridded maps of absolute dynamic topog-

raphy (MADT) provided by AVISO (Archiving, Validation and Interpretation of

Satellite Oceanographic data). Absolute dynamic topography is the sum of sea

level anomaly (SLA) and a mean dynamic topography (MDT). Following AVISO

the Rio05 MDT is used here. The Rio05 mean dynamic topography (Rio and

Hernandez, 2004 and Rio et al., 2005) is the combined product of large scale

MDT, using the CLS01 mean sea surface (MSS) and the EIGEN-GRACE 03S

geoid (Reigber et al., 2005), and hydrographic and Lagrangian data together with

altimeter SLA over t he 1993–2002 period. CLS01 shows the mean shape of the sea

surface during the period covered by t he altimetry data. It is corrected from sea-

sonal variations and corresponds to the sum of geoid + mean elevation in response

to ocean circulation. The annual means of MADT have been computed for the years

2005–2006.

Three experiments have been performed for each year for the period 2005–2006.

First, solutions are obtained by assimilating only the ARGO data (ARGO05-

ARGO06). Second, solutions that use only altimetry data (Alt05-Alt06) are found.

Finally, solutions using both, ARGO and altimetry are computed (AltARGO05-

AltARGO06). In the following, the adjustments produced by IFEOM in temperature

and salinity ﬁelds and the resulting circulation patterns are analysed.

3 Results

The sea surface elevation corresponding to the analysis of ARGO data with the

altimeter information included (AltARGO05) is presented in Fig. 1 for 2005. It

exhibits all major features of the North Atlantic dynamic topography, i.e. the warm

Using ARGO, GRACE and Altimetry Data t o Assess the Quasi Stationary 353

Fig. 1 Left panel: Modelled sea surface elevation (dynamic height) of the AltARGO05 experi-

ment. Right panel: the corresponding barotropic stream function

pool with a strong gradient toward the subpolar Gyre south of Greenland, the loop

current in the Caribbean basin, a strong Labrador current which continues around

the Grand Banks, a northward extension of the North Atlantic Current after its sep-

aration from the American coast at Cape Hatteras, and the Azores Current. Ocean

currents are in agreement with the conventional oceanic knowledge and are used for

the further analysis of the North Atlantic circulation and its interannual changes.

We analyse the impact of using altimetry on the model solution. Comparing

ARGO05, the experiment that excludes altimetry, with the independent altimeter

sea surface (Fig. 2, left panel ) we observe a large scale shift of about 80 cm, from

the Caribbean Sea to the subpolar gyre which shows that the circulation derived

from hydrographic data alone is far from the observed reality. Using only ocean

subsurface data produces a sea surface height with large scale spatial differences

to altimeter and geoid observations. Thus, the additional information on the ocean

circulation is necessary, and the obvious choice is to account for altimetry data in

the model. The success of this choice (AltARGO05) is demonstrated in Fig. 2,

Fig. 2 Difference of modelled sea surface elevation and altimetry data in 2005. Based on ARGO

only (left panel; ARGO05) and after including altimetry (right panel; AltARGO05)

354 F. Richter et al.

Fig. 3 Difference in modelled sea surface change based on ARGO only (left panel; ARGO06-

ARGO05) and after including altimetry (right panel; AltARGO06-AltARGO05)

right panel. It shows the differences of AltARGO05 to altimetric data which are

an order of magnitude smaller than those for ARGO05. Referenced altimetry and

the dynamic topography of the inverse model can be matched by small adjustments

inTandStoanRMSmisﬁtof3cm.

One of the improvement by including altimetry is seen at an oceanographic sec-

tion at 24

◦

N. The heat transport across this line computed from AltARGO05 is

1.24 PW what compares perfectly with the values estimated by Lumpkin and Speer

(2007) and Ganachaud and Wunsch (2003). Their estimates are 1.24 ±0.25 PW

and 1.27±0.15 PW, respectively. ARGO05 underestimates the heat transport across

◦

N providing a value of only 0.89 PW.

In order to estimate the variability contained in ARGO and altimetry data the

intercomparison of temporal change in modelled topography between years 2005

and 2006 is presented in Fig. 3. The left panel shows s ea surface variability

based on ARGO (ARGO06-ARGO05), and the right panel displays the difference

(AltARGO06-AltARGO05) when all data are used.

Both patterns suggest a sea level rise of about 5 cm in Nordic seas. The Gulf

Stream region and its extension are characterized by large activity. The inter-annual

differences are up to 20 cm. The differences in variability between the two plots

are obviously due to the poor spatial sampling of ARGO data in comparison to

altimetry. The corresponding change in the solution AltARGO06-AltARGO05 is

similar to that of altimetry data (Fig. 4). It contains slightly smaller and less sharp

local anomalies, but takes into account a signiﬁcant part of variability contained in

the data.

The model solution allows studying other characteristics of the circulation. We

discuss the transport and its variability. Barotropic stream function has been deter-

mined for the inverse solution using all data (AltARGO05) and is depicted in Fig. 1

right panel. The gyre structures are well developed, the strength of the subpolar

gyre is 50 Sv and is on the upper limit of most forward modelling studies (see

e.g. Treguier et al., 2005). Considering the temporal changes 2006–2005 we notice

differences of about 20 Sv with the maximum in Gulf Stream region seen in both

ARGO and AltARGO experiments (Fig. 5, left and right panels, respectively) with