A newly reconciled data set for identifying sea level rise and variability in Dublin Bay

We provide an updated sea level dataset for Dublin for the period 1938 to 2016 at yearly resolution. Using a newly collated sea level record for Dublin Port, as well as two nearby tide gauges at Arklow and Howth Harbour, we perform data quality checks and calibration of the Dublin Port record by adjusting the biased high water level measurements that affect the overall calculation of mean sea level (MSL). To correct these MSL values, we use a novel Bayesian linear regression that includes the Mean Low Water values as a predictor in the model. We validate the re-created MSL dataset and show its 5 consistency with other nearby tide gauge datasets. Using our new corrected dataset, we estimate a rate of 1.08 mm/yr sea level rise at Dublin Port during 1953-2016 (95% CI from 0.62 to 1.55 mm/yr), and a rate of 6.48 mm/yr during 1997-2016 (95% CI 4.22 to 8.80 mm/yr). Overall sea level rise is in line with expected trends but large multidecadal variability has led to higher rates of rise in recent years.

nual Dataset were used to evaluate agreement with the older dataset. There was approximately 1 cm difference between high water values. Low water values agreed to within millimetric accuracy. Data are reported relative to LAT. With particular respect to the Greene dataset, prior to the availability of digital data in 2003, the high water values for each day were extracted from the tidal charts. This was completed by the generation of tables for each year, with two available cells for each day, these values were read off and inputted into the designated cell. The data from the period 1968-1976 was 70 converted from feet and inches to meters. Data post 1998 were already digitised at 15 minute time intervals, post 2004 this data's frequency increased to 1 minute intervals. To locate the two high tides, each month was split into days, sorted with the highest value being extracted for high tide 1. The second-high tide occurred between 12 and 13 hours after the first high tide, therefore by using the time component within the dataset, this value was extracted. A summary of the datasets is shown in While no overlaps exist between the Harbourmaster dataset and the Port Authority dataset, the Greene dataset overlaps the Port Authority, Harbourmaster, and NTGN datasets. Figure 1 shows MHW from the monthly Port Authority, Harbourmaster, NTGN, and Greene datasets. There is good agreement between the data indicative of consistent datums. We find a residual 0.008m difference between the Greene dataset and the Port Authority Monthly dataset and the NTGN Dataset. We thus add 8 85 mm to the Greene dataset as the final datum adjustment.  France. Figure 2 shows the locations of the tide gauges. The recordings, when taken together, have different time spans and different sampling frequencies. Table 2 provides the details of the datasets.     Figure 3 and Table 3  To find the period of time over which to train the regression model, we use a change point model (Carlin et al., 1992 with ω 1 = 2π 18.61 , ω 2 = 2π 4.4 where (M SL) t is MSL in year t, µ t is the mean process, σ 2 is the residual variance, β 0 is the intercept, β 1 is the MLW coefficient, β 2 and β 3 are the amplitudes of the cosine and sine functions of the 18.6-year lunar nodal modulation respectively, and β 4 and β 5 are the amplitudes of the cosine and sine functions of the 4.4-year modulation respectively. We fitted the model using the JAGS software (Denwood, 2016) and R (R Core Team, 2020) and used 3 Markov Chain Monte 120 Carlo chains, 2000 iterations per chain with 1000 as burn-in and a thinning value of 1. Convergence was assessed using the R-hat diagnostic (Brooks and Gelman, 1998;Gelman and Rubin, 1992). All R-hat values associated with β and σ were close

Sea level rise at Dublin Port and nearby gauges
We now use the Dublin Port corrected data to calculate rates of sea level rise. We use the yearly MSL data from Brest and Newlyn for comparison. We first removed the atmospheric effects following Diabaté et al. (2021) and Frederikse et al. (2017).
Atmospheric data are accessed via the RNCEP package (Kemp et al., 2012) in the R programming language which accesses the

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of Energy Reanalysis I & II datasets (Kalnay et al., 1996;Kanamitsu et al., 2002). Figure 6 shows the atmospherically corrected MSL data of Dublin Port, Brest and Newlyn superimposed for comparison.
To calculate the SLR rates, as before, we use a Bayesian multivariate linear regression including an intercept, a linear trend, and a harmonic function with periods of 18.6 years and 4.4 years. The model is fitted in JAGS with the same settings and convergence requirements as previously described. We write the model as: µ t = β 0 + β 1 t + β 2 cos(ω 1 t) + β 3 sin(ω 1 t) + β 4 cos(ω 2 t) + β 5 sin(ω 2 t) with ω 1 = 2π 18.61 , ω 2 = 2π 4.4  where (M SL) t is MSL at time t, µ t is the mean process, σ 2 t is the fixed variance at time t extracted from the posterior distribution of the calibration model to account for the uncertainty in modelling the MSL introduced in the previous section, σ 2 is the residual variance, β 0 is the intercept, β 1 is the rate in mm/yr, β 2 and β 3 are the amplitudes of the cosine and sine functions 140 of the 18.6-year lunar nodal modulation respectively, and β 4 and β 5 are the amplitudes of the cosine and sine functions of the 4.4-year modulation respectively. We use the same approach (but without the fixed measurement error) for estimating the rates of rise at Brest and Newlyn.
The estimated rates with their associated 95% posterior credible intervals are given in Table 4 which shows that, between 1953 and 2016, the rate of SLR at Dublin Port has mean estimate of 1.08 mm/yr, consistent with the estimated rate of 1.06 145 mm/yr at Brest and that of 1.4 mm/yr at Newlyn. However in more recent years, specifically between 1997 and 2016, Dublin has experienced a greater SLR of 6.48 mm/yr, larger than that of 2.59 mm/yr at Brest, and 3.69 mm/yr at Newlyn. Figure 6 also suggests that sea level in Dublin Port has experienced larger decadal fluctuations and is not as secular as the sea level at the two other locations.  Taken over the full time period of observations, 1953 to 2016, the estimated sea level rise of 1.08 mm/yr in Dublin is consistent with that of Brest and Newlyn, both located at the western European coastline. The rates of rise for earlier periods are less than 1.08 mm/yr (Carter, 1982;Woodworth et al., 1991) are consistent with the findings here and were lower due to the decades of larger sea level rise and variability (1980s, 2000s) not being included in the trend estimation. Elsewhere in Ireland Orford et al. (2006) investigated tide gauge records in Malin Head (1958( -1998( ) and Belfast harbour (1918( -2002 where they reported 155 substantial annual variation for both sites with overall negative trends of -0.2 mm/yr for Belfast and -0.16 mm/yr for Malin Head. Both Belfast and Malin Head, being in the north of the country, are in regions of Glacial Isostatic Uplift, which will reduce relative sea level rise there (Bradley et al., 2011). However, Dublin is in a region of neutral Glacial Isostatic Uplift so these long term effects of post-glacial land motion should be negligible and hence greater consistency with the global figure is expected and ultimately found.

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More surprising is the large decadal variability revealed. This study has found a rate of sea level rise for Dublin of 3.41 mm/yr for the period 1975-1985 followed by a negative sea level trend in the next decade (-9.8 mm/yr during 1986-1996)

Conclusions
We have collated multiple sources of tide gauge data for Dublin Port, and subsequently corrected them for bias in the MHW level. We have then shown that these corrected MSL measurements agree with both Howth Harbour and Arklow to a far higher 185 degree than the raw data. A longer term comparison with Brest and Newlyn also indicates overall agreement. There remains a difference between the data during the 1970s and 1980s where a large cyclic disparity in Dublin contrasts with the other two records. Our final adjusted dataset estimated the rate of SLR to be 1.08 mm/yr between 1953 and 2016, and 6.48 mm/yr between 1997 and 2016 at Dublin Port.
The work we present here is part of a broader aim to improve sea level records in Ireland through the multi-centre Aigéin,

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Aeráid, agus athrú Atlantaigh (A4) project. A recent example is that of the now corrected tide gauge record in Cork City (Pugh et al., 2021). We hope to report elsewhere on further records which may provide a fuller picture of SLR in Ireland.
where y t is the absolute difference between the measured mean sea level at Dublin Port and Newlyn at time t (t = 1, 2, . . . , T ).
We assume y t to be normally distributed with mean µ t and variance σ 2 . The mean is set to α 1 if t < t c and α 1 + α 2 otherwise, and t c is the time of the change point. The function u(t) is the unit step function. We used vague prior distributions for all parameters: 1938,2016) σ 2 ∼ U nif (0, 100) The model output is shown in figure A1. The vertical red line indicates the year of the change point and so marks the end of 200 the calibration period as described in Section 3.