Background

Why 2050?

Looking to the future in a warmer world, we have good reason to expect rising seas. That has been made clear by the work of the Intergovernmental Panel on Climate Change (IPCC) and the results presented in its latest assessment report—a guide to risks we will likely face by the year 2100.

Predicting water levels as far forward as 2100—an appropriate horizon for the global considerations addressed by the IPCC—requires the use of physics-based models, as sea-level observations alone cannot be "extrapolated" to the end of the century with any certainty. However, if we choose a closer target—the year 2050—we find there is sufficient historical data to allow inferences based on observed trends. This is the approach that we at the Virginia Institute of Marine Science have adopted in our sea-level report cards. We chose 2050 as an appropriate time frame for use in planning by citizens, property owners, and municipalities.

Why 1969?

Most of the tide-gauge stations that provide the data used in our sea-level report cards began operation in the first few decades of the 1900s or even earlier. However, many stations—particularly along the U.S. East Coast—show evidence of a non-linear change or acceleration beginning in 1987, at the center of a 36-year sliding window beginning in 1969—thus setting the start date for our sea-level report cards. In short, we use post-1969 data because the linear sea-level trends of earlier decades do not accurately predict the sea-level changes that are most likely to occur given more recently observed acceleration in the rate of sea-level rise.

MMSL (Monthly Mean Sea Level)

We obtain the monthly mean sea-level measurements for our report cards from official tidal stations operated by the National Oceanic and Atmospheric Administration (NOAA). We do so because these measurements represent the value we are most concerned with—the rate of sea-level change relative to piers, buildings, homes, and streets.

NOAA’s monthly measurements of "relative mean sea level" (RMSL) account not only for global changes in the volume of sea water—driven by factors such as thermal expansion of the ocean and melting of ice sheets, but also local movements of the land as shorelines rise, sink, or remain stable in response to groundwater removal, glacial isostatic adjustment, and other factors.

We obtain the RMSL data for our selected U.S. tide stations from the NOAA/National Ocean Service at www.tidesandcurrents.noaa.gov. The site offers its users a choice of tidal datums—a base elevation used as a reference from which to reckon the tidal height. We use mean sea level (MSL), a reference defined at U.S. primary tide stations as the average water level over a series of years (currently 1983-2001). The MSL datum approximates where sea level stood mid-series in the year 1992. Sea-level values are negative if below the height of mean sea level during this year.

Linear Trend

Public projections of sea-level change most commonly use a linear trend—a straight line fitted to a time-series plot of monthly (or annual) mean sea level heights. The trend is the slope of the line expressed (usually) in millimeters per year (mm/yr). A positive slope, if statistically different from zero, implies a constant rise in sea level at the rate shown for the period given; a significant negative slope implies that sea level is falling at a constant rate for the given period.

Whereas use of a linear trend may be an appropriate approach for concerns about sea-level rise in the near term and for regional, national, and global scales, it has several drawbacks:

• A linear trend is rarely constant for very long and, in fact, may not be—even though the fit to the data appears to be a good one judging by the small confidence interval placed on the trend obtained through a routine linear analysis.
• Confidence intervals invariably become smaller as the series analyzed gets longer and longer (see sea level trends at websites operated by NOAA and PSMSL) though the trend may vary slightly with each passing year.

For these and other reasons, we have chosen to base our sea-level projections on non-linear, exponential trends as explained in the following section. We display the linear trend in our sea-level report cards to help clarify that linear projections result in a significantly lower sea level in future years than we expect given recent observations of an accelerating rate of sea-level rise at many tidal stations.

Quadratic Trend/Best Estimate

If the best fit to a series of monthly mean sea-level data is a non-linear trend, it implies that sea level has either accelerated or decelerated during the given period. If acceleration or deceleration is assumed constant, then the curve fitted is described by a quadratic equation. A conventional analysis fitting a quadratic curve yields two coefficients, symbolized here by β1 and β2. β1 represents sea-level rise (or fall if negative) in millimeters per year (mm/year), whereas β2 represents acceleration (deceleration if negative) in mm/year².

For each report card, we have analyzed the quadratic trend to determine whether either coefficient is statistically significant (different from zero). The precaution about a linear trend (β1) not remaining constant with time is doubly important in the case of a non-linear trend where acceleration (β2) is likely to be much more variable.

Where a pattern of non-linear change can be seen it is well worth noting because, if it persists, a very different outcome could result compared to that derived from a strictly linear projection of sea level forward in time.

For further details, read Evidence of Sea Level Acceleration at U.S. and Canadian Tide Stations, Atlantic Coast, North America (Boon 2012).

QHi95 & QLo95 Confidence Intervals

The confidence intervals used in VIMS’ Sea-Level Report Cards are based on the standard deviation of the individual monthly observations, and encompass approximately 95% of those observations—whether above (QHi95) or below (QLo95) the monthly mean. When extended, the confidence intervals show the range within which 95% of all future values of monthly RMSL height are likely to be found, including those expected in 2050. In other words, extending these intervals forward implies that sea level could exceed or fall short of the projected best (quadratic) estimate for sea-level height by an equal amount during any future month.

Decadal Signal

Different forces affect sea level at different rates. A growing ice sheet can draw sea level downward over millions of years, while hurricanes and nor’easters can raise water levels in a matter of hours or days.

Between these extremes are forces—typically caused by interactions between the ocean and atmosphere—that raise and lower sea level on time scales of several years to decades.

Isolating and defining these decadal signals, as we have done in our sea-level report cards, can help better understand and predict sea-level trends on longer timescales. For example, a projection of sea-level trends to 2050 made during an upturn in a decadal signal will be higher than it would be if the projection was made during a period when decadal signal was nearing or at a low. An upturn in a decadal signal can amplify a projection of long-term sea-level rise due to global warming, while a downturn in a decadal signal can temper that projection.

Examples of decadal signals include El Niño-La Niña (aka El Niño Southern Oscillation or ENSO), the North Atlantic Oscillation, the Atlantic Decadal Oscillation, and the Pacific Decadal Oscillation.

Learn more about the long- and short-term processes that influence sea level.

How to Interact

Move your cursor over a chart to reveal individual data values. To move between the Linear chart and Acceleration chart, click an index tab.

Annual Linear Rate

Each year when we release our Sea-Level Report Cards, the linear rate of sea-level rise or fall will very likely change due to variations in the decadal signal and the sea-level heights observed during the intervening 12 months. The values in this plot record the linear-rate values at this station for each past year since 2004, with the time-series analysis beginning in 1969 (for a minimum series length of 36 years: 1969-2004). The linear rate is in millimeters per year (mm/yr).

Annual Acceleration Rate

Each year when we release our Sea-Level Report Cards, the rate of acceleration or deceleration will very likely change due to variations in the decadal signal and the sea-level heights observed during the intervening 12 months. The values in this plot record the non-linear rate of sea-level change at this station for each year since 2004, with the time-series analysis beginning in 1969 (for a minimum series length of 36 years: 1969-2004). The rate of acceleration or deceleration is in millimeters per year per year (mm/yr²).