The Question Is: How Much Acceleration Is Involved In SLR?

Downtown Tomorrow

I. Introduction

The question is not "is sea level rise accelerating?"

The consensus is that sea level rise (SLR) is accelerating.

The answer, then, is based on a three-fold spectrum: "how much was there in the past?", "how much is there now?", and "how much will there be in the future?"

Any historical or current data is ok to use to build upon, because we really need to use a known base from which to calculate prospective acceleration.

II. Data Sources & Reasons

To set the stage for the reasoning, which is basic to the foundation of the software architecture currently being constructed and enhanced, I am using the following posts and papers from various sites, to establish the gist of the initial factors involved: Wikipedia, Current Sea Level Rise, Is sea level rise accelerating?, Sea Level Rise Accelerating Faster Than Thought, Discovery, Nature, Study Reveals Scary New Facts About Sea Level Rise, Gulf Stream Impact, Exceptional twentieth-century slowdown in Atlantic Ocean overturning circulation.

The purpose for using the three-fold spectrum, mentioned above, is to develop a potential for a narrower, and more tightly focused solution.

When contemplating the writing of software algorithms, which can reasonably project expectations of future SLR, it helps to not only properly design the initial system, but further, that design should also facilitate ongoing improvements and enhancements as they become necessary.

IMO, that involves a data driven system, with data entry windows, which are used to more easily update the associated database.

A database from which the current values are loaded into the computer by the software, where the software then uses that dynamic data to make increasingly accurate SLR projections.

Any software models of future SLR are speculation engines, but speculation is what all weather forecasting models do quite well now, all things considered.

III. Basic Approach

The basic approach I took was to first establish four melt zones for the three melt locations, which locations are "non-polar", "Greenland", and "Antarctica."

Fig. 1 (click to enlarge)

The latter two are the major future sources of water from melting ice.

Those four melt zones were described in earlier posts as "Coastal", "Inland 1", "Inland 2", and "No Melt" (Will This Float Your Boat - 7).

In the evolving model, each melt zone has its own beginning phase, rate of delay, rate of melt, rate of acceleration of melt, volume of ice, and total possible contribution to SLR.

Those factors are shown in Fig. 1, where X_n is the beginning (CO₂ emission) and delay phase of the sequence, triggered by an initial CO₂ emission temperature increase.

Then Y_n represents the end of the delay phase, if any, as well as the beginning of the melt phase.

Finally, Z_n represents the end of the melt phase.

So, X_1,Y_1, and Z₁ represent the Coastal Zone, X_2,Y_2,and Z₂ represent the Inland 1 Zone, X_3,Y_3, and Z₃ represent the Inland 2 Zone, and X_4,Y_4, and Z₄ represent the No Melt Zone.

Fig. 2 (click to enlarge)

As you can see, at any time the four zones could be in separate phases, or could be in the same phase.

They can also be in the same phase at a particular time, then change to separate phases as the relevant environmental factors change.

Each zone's phase sequencing depends on warming, delay, ice volume, and acceleration, each as they impact upon that particular zone.

The same goes for the three ice source locations (Non-polar, Greenland, Antarctica), however, not to the same degree (locations overall are generally more stable than zones).

For example, the Non-polar zone (non polar glaciers, snow capped peaks, high altitude frozen lakes, etc.) went into AGW induced melt phases that affect SLR first, Greenland second, and Antarctica last.

Where the math efficiency comes in is directly applying the volume of melt (500 cu. km) to the total volume of SLR for a zone.

Fig. 3 (click to enlarge)

Fig. 2 has the SLR for each location and sub-location.

That is, the volume in terms of km³ can be directly related to SLR by percentage.

Dividing the annual 500 km³ of current melt by the total volume for those locations (e.g. Greenland, 75%) renders the SLR value immediately (as shown in Fig. 3), but the reality is only grasped when it is projected out at that rate of acceleration.

Fig. 4 (click to enlarge)

I graphed it (Fig. 4) at the raw 14.87% acceleration rate to show how the initial figures can throw us off.

That is because they seem insignificant when viewed without the concept of acceleration applied to them.

The initial low numbers are deceptive, because, at that raw acceleration rate, a three foot SLR (catastrophic!) takes place in only about ten years, and a 21.49 SLR takes place in only about 30 years.

And, as is indicated on the graph, that only includes Greenland, not Antarctica which has about ten times more ice than Greenland.

Thus, as this post declares, the rate of acceleration must be known, and applied circumspectly, if mature risk management and risk aversion is to be realized.

The 14.87% rate is based on a melt of 250 km³  in 2009 becoming 500 km³ at the end of 2013 (only five years) as measured directly by the Cryosat-2 satellite.

That is why the zone concept, with altering rates of acceleration of melt, can implement a more realistic view of the impact that acceleration has on the amount of future melt.

A. The Rates of Melt & Acceleration

There are four basic rates of melt: "fast", "medium", "low", and "lowest."

In each zone in general, rates at first will tend to be: Coastal=fast, Inland 1=medium, Inland 2=low, and No melt=lowest.

Fig. 5 (click to enlarge)

Also, those rates can change as a zone phases through to reach the downhill slope of melt (Y_n - Z_n), especially as it nears the end of its ice melt.

Coastal zones are initially rated as "fast" because they are subject to warmer water and winds, since they are close to the ocean, nearer to sea level, and away from cooler, high altitudes.

In the locations with by far the most ice (Greenland, Antarctica), those factors change more slowly, on a longer time-scale, as we move inland and upward.

That is because, generally, as the height above sea level increases the ice is thicker, as we move up to higher elevations with colder temperatures.

Of course there are exceptions, such as when Greenland surface melt takes place even in the higher elevations ("Measurements from three satellites showed that on July 8, about 40 percent of the ice sheet had undergone thawing at or near the surface. In just a few days, the melting had dramatically accelerated and an estimated 97 percent of the ice sheet surface had thawed by July 12" NASA 2012).

Compare Fig. 4 with Fig. 5 to see how the model uses zones to normalize the raw acceleration rate, converting it to a zone specific acceleration, making acceleration fit the real world scenario more accurately.

IV. Selecting The Zones by Topography Factors

The four zones were selected based on the notion that the melt, for the most part, is moving from the coast into the interiors of Greenland and Antarctica.

Should that reality change at any time in any location (volcano, earthquake changed heights, etc.), the database can be updated.

Then, the software program can process the newest data to generate more current projections.

V. Selecting Acceleration Rates

The initial values should be produced by a combination of historical values with current values, AND likewise should be produced with an understanding that neither the past world, nor today's world, axiomatically control the future world.

All three (past, present, and future) are distinct, each with its own peculiarities and dynamics.

Future acceleration, then, is a product of how the future is going to be different from the past, and from the present, not how it is going to be the same.

And finally, keep in mind that acceleration, by definition, is an increase over the present rate.

That said, there are times when acceleration can be very near zero, and there are even times when there can be deceleration, so do not confuse the two (Good Nomenclature: A Matter of Life and Death).

Frequent updates of data, bringing the database very current and up to date, will insure that any scenario, and subsequent software-model projection based on it, is done on a robust location by location, and zone by zone analysis.

VI. Selecting the Initial Phase Values

I intend to select the initial phase based upon global temperature data compared to and fused with global SLR data (in terms of seeding the initial data).

In other words, the global-temperature-increases data and graphs will also be used to determine when the initial SLR increases took place year by year.

The initial global warming beginnings (X_n), the subsequent beginning rates of SLR, and finally the rates of acceleration of SLR, will be based on a common sense analysis of both historical and present values.

VII. Conclusion

Having done the above, if the projections cause someone to mess their pants, so be it.

Now, let me go finish the coding so we can try it out and discuss it some more (The Evolution of Models, 2, 3, 4).

The next post in this series is here.