A Look Behind the Letters:
Where Once
the Waters
In 1941, oceanographer Beno Gutenberg first reported that sea levels were rising. Observations over recent decades agree. We now know that without doubt sea level rise is accelerating. According to the Intergovernmental Panel on Climate Change, global sea level (calculated from mean annual tide gauge readings and altimetry observations) increased from 1.4mm per year between 1901–1990, to 2.1mm per year over the period 1970–2015, to 3.2mm per year over the period 1993–2015, to 3.6mm per year over the period 2006–2015. And that ‘the dominant cause of global mean sea level rise since 1970 is anthropogenic forcing’ (IPCC Special Report: Special Report on the Ocean and Cryosphere in a Changing Climate, chapter 4).
This acceleration will continue – warming is now locked-in for many decades. But these are mean global figures. In fact, changes in sea levels range considerably around the world, from coast to coast and from month to month. The National Ocean Service tells us ‘…just as the surface of the Earth is not flat, the surface of the ocean is also not flat – in other words, the sea surface is not changing at the same rate at all points around the globe. Sea level rise at specific locations may be more or less than the global average due to many local factors: subsidence, ocean currents, variations in land height, and whether the land is still rebounding from the compressive weight of Ice Age glaciers.’
For a variety of reasons, sea levels along our Earth’s coasts are often quite different from those at nearby open waters, too. Fluctuations occur as freshwater meets saltwater (as rivers meet the sea at estuarial points); as a result of the depth of the water at the coast; or indeed because of human activity at the coast.
The readings reported in Where Once the Waters focus on the coast. The project’s aim has been to find out how much the water level (and indeed coastal height) at our nearest seaside points have changed across our lifetimes. For it is the coast that so many of us identify with. It is the coast that we visit, the shoreline that we might know better than the open ocean.
Tide stations around the globe tell us what is happening at that local level. These mareographs record the height of the water relative to land. Readings from tide-gauge stations have been used in this project. The title Where Once the Waters, could therefore be taken as “where once the waters reached at your closest coast.”
Something that’s troubled me whilst working on this project is that – in many cases – we should take the readings given in each letter artwork as a minimum. Some of the tide-gauge stations consulted in this project (though this was certainly not the general rule) base their calculations on historic readings, as opposed to current data, and so a minimum (nominal) global average figure has been combined with historical data to bring these readings up to date.
Each one of these readings has been calculated as thoroughly as possible. Though, because each is based on the level of sea relative to land, because of issues such as erosion and subsidence, because of differences in interpreting the data, each must be rendered approximate. Where Once the Waters is a creative project and must not be taken as scientific fact, nor advice.
Looking to the future, if we continue to use fossil fuels at the current rate, global warming could exceed up to 5 degrees above pre-industrial levels in the worst case. As a result, sea levels could be between 61cm and 1.1m higher by 2100, according to the IPCC (at the time of writing in early 2021). This chapter of the project does not look to the future, rather, it works backward from today, at a period that can be reasonably charted.
In many ways this project should be seen as a prototype, a model. The figures provided are as close to accurate as myself and my small team have been able to generate, with the available tide-gauge data. We’ve reached out to scientists and a mathematician. Yet, many readings remain as estimates. How much more deeply would each of us engage with climate related issues if each aspect was personalised in this manner? If our carbon footprint was more easily counted; if changes in our nearby sea temperature was reported as part of our weather news; if dying sea kelp could be seen in our parks and gardens…
Calculating Local Sea-Rise
The sea level readings provided in Where Once the Waters have been calculated using tide-gauge data from the PSMSL / Permanent Service for Mean Sea Level’s Data Explorer resource and the NOAA / National Oceanic & Atmospheric Administration’s Sea Level Trends service. These services list coastal readings from around the world, mostly over a period of decades. The data can be interpreted in several ways. The following explains the process(es) undertaken to reach personalised figures for Where Once the Waters.
Case 1: In cases where a reasonable pattern of local sea rise has been observed year on year (where three or more sets of three-year readings demonstrate a sequential rise) PSMSL annual tide-gauge data has been used. Calculations have been made by subtracting the earliest year available from the most recent; subtracting the earliest reading value from the most recent; dividing the calculated level of rise by the number of years measured, to reach a mean annual figure which can then be multiplied by the participant’s age. Each result generated in this manner has been listed as ‘approximate’ or using the term ‘around’, for the method of calculation arrives at an average figure.
Case 2: In cases where PSMSL tide-gauge readings fluctuate year on year, or where only a short period is charted (less than fifteen years) NOAA data interpretations have been used. NOAA uses selected PSMSL stations in generating their annual local sea level figures. Their interpretations use a least squares method which makes for more precise results and therefore has been the preferred option throughout. Even in these cases however – and even when using data from the most up-to-date stations – one must be aware that these are indicative figures presented as part of a creative project. The results generated using this formula are not all listed as ‘approximate’ yet must still be treated with caution despite being the most trusted throughout the creation of the artwork.
Case 3: There are considerably more PSMSL stations around the globe than there are NOAA data interpretations. In cases where no up-to-date NOAA records have been found within a reasonable distance of a participant’s birthplace, a PSMSL station has been used – even if that station shows fluctuating or short-term measurements. Readings have been calculated in these cases using the arithmetic average of case 1 (above). This type of method works well if the data is relatively stable and consistent (this formula is reasonable in case 1, where the figures show a pattern year-on-year) but the result can only ever be taken as a token figure in cases where the data fluctuates severely. Each result generated in this way has been listed as ‘approximate’ or ‘around’.
Case 4: This case relates specifically to Venice, Italy; the location of the exhibition and focus of Cass’ ongoing artwork. NOAA data for Venice ends in 2000, and so PSMSL data must be used to bring this location up to date. In some letters written to participants born in Venice, both low and high estimates are provided. The higher estimate comes from a least squares study of PSMSL data; the lower comes from NOAA data, with an additional 1mm/yr to account for sea level rise acceleration.
According to the 2018 Bulletin of the American Meteorological Society (BAMS) State of the Climate report, acceleration in sea level rise during the post-1993 period is increasing by 1mm per year. Other sources state an acceleration of between 1 and 3 extra millimetres across the same period. The readings listed in this project have taken this recently observed acceleration into account but have used only the minimum figure of 1mm for the sake of consistency. For example, an extra 3mm has been added to Edinburgh (Leith) to account for the years 2018, 2019 and 2020, as this station only showed clear readings up to the end of 2017, though these – it should be noted – are still ‘approximate’.
Participants’ birth years have been calculated using late 2020, all of 2021, and early 2022 as the present, depending on when the letter was written. Dates are listed on each letter. While the letters were written between 2020 and 2022, the original intention was to present the exhibition in 2021 rather than 2022. The project was postponed by a year as a result of the coronavirus pandemic. For that reason, formulas used do not take findings of late 2021 or 2022 into account.
Participants were invited to take part in a project which would see their personal “sea level reading” added to an artwork. Where participants were not born at or near a coast, the closest reading-station (as the crow flies) has been located. Where participants rest equidistant between two or more stations, an average figure has been calculated and combined from each. Again, these are listed as ‘approximate’.
Why Sea Levels are not Uniform Globally
Sea level change is not uniform around the world. Several factors influence the rate at which sea levels are fluctuating. For example, changes in ocean temperature and salinity cause wide-ranging regional fluctuations. Overall, sea levels are rising. But, some locations (albeit a lower portion of the whole) see no rise, or indeed an apparent lowering in sea level (relative to land). This can be, in part, as a result of the land itself rising (due to melting glaciers – or the loss of glaciers which once occupied the land – which also influences the shape and gravitational field of the Earth) and is mostly witnessed in the seas surrounding the Arctic circle.
“Post Glacial Rebound” or “Land Uplift” are terms to describe the slow bouncing-back of land. Sweden, for example, has itself been rising for some 10,000 years. During the last Ice Age, massive glaciers formed all over Scandinavia, so heavy that their weight warped the surface of the Earth, pushing it down into the viscous mantle. When the ice melted, glacial rebound began, and Scandinavia is still rising at a rate of about 9mm per year.
Below is a list of key factors which influence the rate at which sea levels are rising:
Temperatures | Hot water is more voluminous than cold water, hence sea level may rise more in the Tropics.
Winds | The dominant winds in a region affect the shape of the seas.
Tectonic Settings | Plate shifting can affect the response of a given location to sea level change.
Coastlines | The shape of the coastline plays a role.
Currents | Global warming can cause changes in oceanic currents, which would have a direct impact on local sea level rise.
Meltwater | Currents change as meltwater pours in from land-based glaciers.
Ocean Floor | At our poles, changes in the topography at the bottom of the sea occur as the ice resting on top of it melts away.
Distribution | Earth's rotation plays a significant role in the distribution of ocean water.
Differences at the Coast & Off-Shore
We reached out to Prof. Phil Woodworth of the National Oceanography Centre. In summary, he told us that the main reasons for differences at the coast and offshore are fairly straightforward. By definition, the land provides a fixed barrier to propagation of processes in the ocean (what ocean modellers call a “boundary condition”) and the fact that the dynamics (physics) of many of those processes depends on water depth, which goes to zero at the coast.
As an example – the magnitude of storm surges depends on something called wind stress (basically the square of the wind speed) divided by water depth. So, you get bigger surges where wind blows over shallow waters (such as the southern North Sea). Similarly, the wavelengths of tides depend on depth. Wind driven waves break as they move into shallow water from the open ocean. Thus, it is not surprising that sea level varies between coast and open ocean.
Calculation Examples
Baltimore, USA
Between 1902 and 2019, Baltimore station shows a rise of 377.6mm
So, over 118 years, Baltimore saw local (relative) sea rise of 3.2mm per year
An extra 1mm is added to the final personalised calculation (to 2020) to account for global average acceleration
From data gathered by the National Oceanic & Atmospheric Administration (NOAA) using formula (case) 2
Christchurch, New Zealand
Between 1924 and 2018, Port Lyttelton station shows a rise of 262.2mm
So, over 95 years, Christchurch saw local (relative) sea rise of 2.76mm per year
An extra 2mm is added to the final personalised calculation (to 2020) to account for global average acceleration
From data gathered by the National Oceanic & Atmospheric Administration (NOAA) using formula (case) 2
Edinburgh, Scotland
Between 1956 and 1971, reading station Leith I shows an average rise of 80mm
Then, between 1989 and 2017, station Leith II shows an average rise of 17mm
So, over 45 years, Leith, Edinburgh saw local (relative) sea rise of 97mm, or, 2.15mm per year (on average)
An extra 3mm is added to the final personalised calculation (to 2020) to account for global average acceleration
From data gathered by the Permanent Service for Mean Sea Level (PSMSL) using formula (case) 1
New York City, USA
In the city
Between 1856 and 2019, The Battery station shows a rise of 470.7mm
So, over 164 years, New York saw local (relative) sea rise of 2.87mm per year
An extra 1mm is added to the final personalised calculation (to 2020) to account for global average acceleration
From data gathered by the National Oceanic & Atmospheric Administration (NOAA) using formula (case) 2
At the coast
Between 1932 and 2019, Sandy Hook station shows a rise of 362.6mm
So, over 88 years, New York saw local (relative) sea rise of 4.12mm per year
An extra 1mm is added to the final personalised calculation (to 2020) to account for global average acceleration
From data gathered by the National Oceanic & Atmospheric Administration (NOAA) using formula (case) 2
Venice, Italy
In most cases, for Venice, we need to offer both a higher and lower reading, as there’s no clear way to decode sea level rise for Venice using tide-gauges
To calculate the lower estimate, using an average reading for the second part of the calculation:
Between 1872 and 2000, Punta della Salute station saw local (relative) sea rise of 2.44mm per year
Then, between 2002 and 2015, Venezia II station shows average local sea rise of 9.5mm per year
Participants’ ages are divided* to combine readings from both stations, as the periods of measurement differ
An extra 6mm (to 2021) is added to the final personalised calculation to account for global average acceleration
From data gathered by the National Oceanic & Atmospheric Administration (NOAA) and Permanent Service for Mean Sea Level (PSMSL) using formulas 1 & 2
*Example:
If someone was born in 1980; a reading from 1980-2000 is added to a reading using the most current data from 2001-2021
20 years at 2.44mm = 48.8mm
20 years at 9.5mm = 190mm (+ 6mm)
244.8 over the last 40 years
In theory, one year is missing from this result. However, as the split is not 50/50, and we do not know the participant’s birth month, we must exclude these months
To calculate the higher estimate, using a least squares method for the second part of the calculation:
Between 1872 and 2000, Punta della Salute station saw local (relative) sea rise of 2.44mm per year
Then, between 2002 and 2015, Venezia II station could provide a least-squares figure of rise at 14.29mm per year (workings can be seen in this PDF)
Participants’ ages are divided* to combine readings from both stations, as the periods of measurement differ
No additional millimetres are added to this total as it’s already higher than is likely
From data gathered by the National Oceanic & Atmospheric Administration (NOAA) and Permanent Service for Mean Sea Level (PSMSL) using formulas 1 & 2
*Example:
If someone was born in 1980; a reading from 1980-2000 is added to a reading using the most current data from 2001-2021
20 years at 2.44mm = 48.8mm
20 years at 14.29mm = 285.8mm
334.6 over the last 40 years
In theory, one year is missing from this result, to account for Januarys through Decembers. However, as the split is not 50/50, it’s simpler to exclude these months
For those born around the later data set (any year from 2000), only that one is used:
If someone was born in 2001
2021-2001 = 20
Low: 20 x 9.5 + 6 = 196mm
High: 20 x 14.29 = 285.8mm
The result is then expressed along the lines of: “since your birth sea level has risen (relative to land) by between _ and _, on average”
For those born before around 1970, only the lower estimate is used
Selected Stations
Tide-gauge stations are chosen on a case by case basis. For locations (birthplaces) without their own reading station, or one nearby; or their own reliable reading station, examples follow:
Arbroath (Scotland) uses Edinburgh + Aberdeen (NOAA)
Artemida (Greece) uses Khalkis North (NOAA)
Belfast (N.I) uses Portpatrick (NOAA)
Bilbao (Spain) uses Santander (NOAA)
Chicago (USA) uses Washington (NOAA)
Chimanimani (Zimbabwe) uses Maputo (NOAA)
Cork City (Ireland) uses Dublin (NOAA)
Dundee (Scotland) uses Leith (NOAA+PSMSL)
Essen (Germany) uses Maassluis (NOAA)
Fort William (Scotland) uses Millport (NOAA)
Fraserburgh (Scotland) uses Aberdeen (NOAA)
Harare (Zimbabwe) uses Maputo (NOAA)
Johannesburg (South Africa) uses Richards Bay (NOAA)
Lancaster (England) uses Heysham (NOAA)
London (England) uses Tower Pier (NOAA)
London (England) suburbs / surrounding area uses Sheerness (NOAA)
Mbale (Uganda) uses Mombasa (NOAA)
Meknes (Morocco) uses Ceuta (NOAA)
Montego Bay (Jamaica) uses Gibara (NOAA)
Peterborough (England) uses Lowestoft (NOAA)
Poznań (Poland) uses Kolobrzeg (NOAA)
Sacramento (USA) uses Port Chicago (NOAA)
Santiago (Chile) uses Talcahuano (NOAA)
Tbilisi (Georgia) uses combined data from Batumi and Poti (NOAA)
Please contact info@davidcass.art if you would like to suggest edits
The participants’ data used for these letters was gathered on this website, on social media and in person, with agreement that it be used as part of an artwork, stating first names only (for the sake of privacy) between 2019 & 2022. The letters themselves were written in late 2020, during the whole of 2021, and early 2022.