Sea Level Rise Models – IV

So far, I’ve established that the qualitative results of Rahmstorf (R) and Grinsted (G) can be reproduced. Exact replication has been elusive, but the list of loose ends (unresolved differences in data and so forth) is long enough that I’m not concerned that R and G made fatal errors. However, I haven’t made much progress against the other items on my original list of questions:

  • Is the Grinsted et al. argument from first principles, that the current sea level response is dominated by short time constants, reasonable?
  • Is Rahmstorf right to assert that Grinsted et al.’s determination of the sea level rise time constant is shaky?
  • What happens if you impose the long-horizon paleo constraint to equilibrium sea level rise in Rahmstorf’s RC figure on the Grinsted et al. model?

At this point I’ll reveal my working hypotheses (untested so far):

  • I agree with G that there are good reasons to think that the sea level response occurs over multiple time scales, and therefore that one could make a good argument for a substantial short-time-constant component in the current transient.
  • I agree with R that the estimation of long time constants from comparatively short data series is almost certainly shaky.
  • I suspect that R’s paleo constraint could be imposed without a significant degradation of the model fit (an apparent contradiction of G’s results).
  • In the end, I doubt the data will resolve the argument, and we’ll be left with the conclusion that R and G agree on: that the IPCC WGI sea level rise projection is an underestimate.

Continue reading “Sea Level Rise Models – IV”

Sea Level Rise Models – III

Starting from the Rahmstorf (R) parameterization (tested, but not exhaustively), let’s turn to Grinsted et al (G).

First, I’ve made a few changes to the model and supporting spreadsheet. The previous version ran with a small time step, because some of the tide data was monthly (or less). That wasted clock cycles and complicated computation of residual autocorrelations and the like. In this version, I binned the data into an annual window and shifted the time axes so that the model will use the appropriate end-of-year points (when Vensim has data with a finer time step than the model, it grabs the data point nearest each time step for comparison with model variables). I also retuned the mean adjustments to the sea level series. I didn’t change the temperature series, but made it easier to use pure-Moberg (as G did). Those changes necessitate a slight change to the R calibration, so I changed the default parameters to reflect that.

Now it should be possible to plug in G parameters, from Table 1 in the paper. First, using Moberg: a = 1290 (note that G uses meters while I’m using mm), tau = 208, b = 770 (corresponding with T0=-0.59), initial sea level = -2. The final time for the simulation is set to 1979, and only Moberg temperature data are used. The setup for this is in change files, GrinstedMoberg.cin and MobergOnly.cin.

Moberg, Grinsted parameters

Continue reading “Sea Level Rise Models – III”

Sea Level Rise Models – II

Picking up where I left off, with model and data assembled, the next step is to calibrate, to see whether the Rahmstorf (R) and Grinsted (G) results can be replicated. I’ll do that the easy way, and the right way.

An easy first step is to try the R approach, assuming that the time constant tau is long and that the rate of sea level rise is proportional to temperature (or the delta against some preindustrial equilibrium).

Rahmstorf estimated the temperature-sea level rise relationship by regressing a smoothed rate of sea level rise against temperature, and found a slope of 3.4 mm/yr/C.

Rahmstorf figure 2

Continue reading “Sea Level Rise Models – II”

Sea Level Rise Models – I

A recent post by Stefan Rahmstorf at RealClimate discusses a new paper on sea level projections by Grinsted, Moore and Jevrejeva. This paper comes at an interesting time, because we’ve just been discussing sea level projections in the context of our ongoing science review of the C-ROADS model. In C-ROADS, we used Rahmstorf’s earlier semi-empirical model, which yields higher sea level rise than AR4 WG1 (the latter leaves out ice sheet dynamics). To get a better handle on the two papers, I compared a replication of the Rahmstorf model (from John Sterman, implemented in C-ROADS) with an extension to capture Grinsted et al. This post (in a few parts) serves as both an assessment of the models and a bit of a tutorial on data analysis with Vensim.

My primary goal here is to develop an opinion on four questions:

  • Can the conclusions be rejected, given the data?
  • Is the Grinsted et al. argument from first principles, that the current sea level response is dominated by short time constants, reasonable?
  • Is Rahmstorf right to assert that Grinsted et al.’s determination of the sea level rise time constant is shaky?
  • What happens if you impose the long-horizon paleo constraint to equilibrium sea level rise in Rahmstorf’s RC figure on the Grinsted et al. model?

Paleo constraints on equilibrium sea level

Continue reading “Sea Level Rise Models – I”

I'm Shovel Ready

Lots of carping on the ‘net about the likely slow pace of stimulus spending. Nevermind the pace, I want to know what’s in it. You actually have to dig quite a bit to get the details of the package (especially with the CBO web site down today). Fortunately, I always keep my shovel handy. Here’s what I see:

9702bc96-e756-11dd-adce-000255111976 Blog_this_caption(Click through to the live version to see the labels)

A few observations:

  • There’s $90 billion in unstated spending.
  • Infrastructure grabs the headlines, but education and health actually get the lion’s share.
  • The “green” portion of the stimulus looks rather small in context. It also seems out of balance – more $ for energy supply than energy efficiency. I’m not convinced that energy supply subsidies are very green.
  • The distribution of half the tax credits is unstated. How do you know the magnitude without knowing the components? Could it be that business tax credits constitute the majority? If so, that would be highly regressive.

Where’s the consulting sector in all this?

Some Links I Won't Have Time to Blog About

Paul Krugman’s letter to Obama

Reasoning-from-conclusions-to-assumptions? (a perspective on modeling)

Sell-off drops EUAs to $11.60/TonCO2

Via Nature, a google search doesn’t really produce 7 grams of carbon, and you can’t build carbon infrastructure to get to a low-carbon future.

Four new CCSP reports from the last days of the Bush administration:
Final Report of Synthesis and Assessment Product 4.1 (Coastal Sensitivity to Sea-Level Rise: A Focus on the Mid-Atlantic Region)
Final Report of Synthesis and Assessment Product 4.2 (Thresholds of Climate Change in Ecosystems)
Final Report of Synthesis and Assessment Product 2.3 (Aerosol properties and their impacts on climate)
Final Report of Synthesis and Assessment Product 1.2 (Past Climate Variability and Change in the Arctic and at High Latitudes)
Plus last month’s USGS report on abrupt climate change, buried over the holidays.

Are We Slaves to Open Loop Theories?

The ongoing bailout/stimulus debate is decidedly Keynesian. Yet Keynes was a halfhearted Keynesian:

US Keynesianism, however, came to mean something different. It was applied to a fiscal revolution, licensing deficit finance to pull the economy out of depression. From the US budget of 1938, this challenged the idea of always balancing the budget, by stressing the need to boost effective demand by stimulating consumption.

None of this was close to what Keynes had said in his General Theory. His emphasis was on investment as the motor of the economy; but influential US Keynesians airily dismissed this as a peculiarity of Keynes. Likewise, his efforts to separate capital projects from ordinary budgets, balanced if possible, found few echoes in Washington, despite frequent mention of his name.

Should this surprise us? It does not appear to have disconcerted Keynes. ‘Practical men were often the slaves of some defunct economist,’ he wrote. By the end of the second world war, Lord Keynes of Tilton was no mere academic scribbler but a policymaker, in a debate dominated by second-hand versions of ideas he had put into circulation in a previous life. He was enough of a pragmatist, and opportunist, not to quibble. After dining with a group of Keynesian economists in Washington, in 1944, Keynes commented: ‘I was the only non-Keynesian there.’

FT.com, In the long run we are all dependent on Keynes

This got me wondering about the theoretical underpinnings of the stimulus prescription. Economists are talking in the language of the IS/LM model, marginal propensity to consume, multipliers for taxes vs. spending, and so forth. But these are all equilibrium shorthand for dynamic concepts. Surely the talk is founded on dynamic models that close loops between money, expectations and the real economy, and contain an operational representation of money creation and lending?

The trouble is, after a bit of sniffing around, I’m not seeing those models. On the jacket of Dynamic Macroeconomics, James Tobin wrote in 1997:

“Macrodynamics is a venerable and important tradition, which fifty or sixty years ago engaged the best minds of the economics profession: among them Frisch, Tinbergan, Harrod, Hicks, Samuelson, Goodwin. Recently it has been in danger of being swallowed up by rational expectations, moving equilibrium, and dynamic optimization. We can be grateful to the authors of this book for keeping alive the older tradition, while modernizing it in the light of recent developments in techniques of dynamic modeling.”
’”James Tobin, Sterling Professor of Economics Emeritus, Yale University

Is dynamic macroeconomics still moribund, supplanted by CGE models (irrelevant to the problem at hand) and black box econometric methods? Someone please point me to the stochastic behavioral disequilibrium nonlinear dynamic macroeconomics literature I’ve missed, so I can sleep tonight knowing that policy is informed by something more than comparative statics.

In the meantime, the most relevant models I’m aware of are in system dynamics, not economics. An interesting option (which you can read and run) is Nathan Forrester’s thesis, A Dynamic Synthesis of Basic Macroeconomic Theory (1982).

Forrester’s model combines Samuelson’s multiplier accelerator, Metzler’s inventory-adjustment model, Hicks’ IS/LM, and the aggregate-supply/aggregate-demand model into a 10th order continuous dynamic model. The model generates an endogenous business cycle (4-year period) as well as a longer (24-year) cycle. The business cycle arises from inventory and employment adjustment, while the long cycle involves multiplier-accelerator and capital stock adjustment mechanisms, involving final demand. Forrester used the model to test a variety of countercyclic economic policies, commonly recommended as antidotes for business cycle swings:

Results of the policy tests explain the apparent discrepancy between policy conclusions based on static and dynamic models. The static results are confirmed by the fact that countercyclic demand-management policies do stabilize the demand-driven [long] cycle. The dynamic results are confirmed by the fact that the same countercyclic policies destabilize the business cycle. (pg. 9)

It’s not clear to me what exactly this kind of counterintuitive behavior might imply for our current situation, but it seems like a bad time to inadvertently destabilize the business cycle through misapplication of simpler models.

It’s unclear to what extent the model applies to our current situation, because it doesn’t include budget constraints for agents, and thus doesn’t include explicit money and debt stocks. While there are reasonable justifications for omitting those features for “normal” conditions, I suspect that since the origin of our current troubles is a debt binge, those justifications don’t apply where we are now in the economy’s state space. If so, then the equilibrium conclusions of the IS/LM model and other simple constructs are even more likely to be wrong.

I presume that the feedback structure needed to get your arms around the problem properly is in Jay Forrester’s System Dynamics National Model, but unfortunately it’s not available for experimentation.

John Sterman’s model of The Energy Transition and the Economy (1981) does have money stocks and debt for households and other sectors. It doesn’t have an operational representation of bank reserves, and it monetizes the deficit, but if one were to repurpose the model a bit (by eliminating the depletion issue, among other things) it might provide an interesting compromise between the two Forrester models above.

I still have a hard time believing that macroeconomics hasn’t trodden some of this fertile ground since the 80s, so I hope someone can comment with a more informed perspective. However, until someone disabuses me of the notion, I have the gnawing suspicion that the models are broken and we’re flying blind. Sure hope there aren’t any mountains in this fog.