State Space Models

All state space models are written and estimated in the R programming language. The models are available here with instructions and R procedures for manipulating the models here here.

Monday, July 7, 2025

World-System (1950-2100+) Global Temperature Projections


May 26, 2026 Scientist Ditch Scary Climate Scenario Goodbye RCP8.5 (see below).

A Recent Paper in Nature Communications: Earth and Environment was titled Warming of +1.5 °C is too high for polar ice sheets.** In terms of projections from my models (above), this would mean that if we reach the 15.5 temperature level, it will be too late for the Polar Ice Caps to maintain their integrity and sea level rise will inundate most countries around the World (to include Mar-a-Lago, President Trumps Empire). Does this mean catastrophe for the World-System

The first projection to consider is the Random Walk (RW). If Global Temperature were a  Random Walk it would mean that it cannot be forecast, a result that would please Climate Change Deniers. Given the high variability of the Global Temperature data, it should be no surprise that, in the short-run year-to-year, Global Temperature is a RW given the Akaike Information Criterion [-77.33, AIC=-65.15,-55.0]. However, in the long-run there is a clear trend. The issue is how far into the future can the trend be carried.

In the Stokes (2025) Global Sea Level article the conclusion is that, to prevent destabilizing the Arctic Ice Caps, Global Temperature should return to the levels somewhere around the 1980's. The graphic above plots a forecast of the Temperature WL203 BAU model that has no inputs (no radiative forcings). Without forcings from human systems (anthropogenic forcings) the model would say within the "safe" zones. Unfortunately, isolating Global Temperature from human systems seems impossible.



The next one of my models to consider simply uses CO2 emissions to predict global temperature, something similar to the endpoint of the Kaya Impact Model (graphed above) used by the IPCC. The model projects a linear increase in temperature that eventually reaches a steady state (the model is stable). Using the Akaike Information Criterion (smaller is better) [170.2,AIC=198.3 217.1], it is not a strong competitor.

Another important model involves the technical coefficients of the Kaya Impact Model (q, e, c, t in the graphic above). The model is important because improvements in Kaya Technology (efficiency) such as renewable energy, etc. should ultimately reduce Global Temperature. The model shows continuing increases in Global Temperature, but because the model is stable, a steady state will eventually be reached but at a higher Global Temperature than 15.5 degrees (dotted red line in first graphic). In other words, even though technological change can moderate temperatures, it will not be enough to prevent melting of the Polar Ice Caps. Still, the model is a good competitor using the Akaike Information Criterion [-47.94, AIC=14.95, 67.81].*** 

Finally, driving Global Temperature with the state of the World System using two different models (the dashed blue line and the pink line in the graphic at the beginning of this post), produce growth-and-collapse modes and keep global temperature below 15.5 degrees. The WL203 model (dashed blue line) is the best model (beyond the RWusing the Akaike Information Criterion  [-70.95, AC=-10.41, 34.52] compared to the WL20W model [-4.007, AIC=64.63, 107.9].

You can experiment with the stable WL203 model (here) or the unstable WL20W model (here).


Notes

WL203 Measurement Model


The measurement model for the World System has three historical environmental controllers: W1=(Growth-LivingPlanet), W2=(LivingPlanet-TEMP) and W3=(P.Oil.-TotalFootprint).  Information about the indicators (LivingPlanet index, Global TEMP, TotalFootprint), etc. can be found in the Boiler Plate.

** Recent data from NASA's CRES (Clouds and Earth’s Radiant Energy System) satellite data also indicates that Earth's Albedo (ability to reflect sunlight and reduce warming) is decreasing!

*** There is another type of Technological change that involves productivity (the dashed black line in the graphic at the beginning of this article). It shows a similar, if somewhat worse, time path than Kaya Technology and reaches 15.5 degrees earlier in time.


RCP2.6 to RCP8.5


Although there has been a lot of controversy surrounding RCP8.5 (Scientist Ditch Scary Climate Scenario), one point to make about the graphic above is that there is no Unlimited-Exponential-Growth-Forever scenario which seems to be what Climate Deniers predict will happen. Neoclassical Economists (see the DICE model) argue that growth will be limited when Technological change (Productivity) and Population growth reach  steady state (See the Solow-Swan Neoclassical Growth Model below).


Solow-Swan Growth Model





The Solow-Swan Neoclassical Growth Model (It is the basis for the DICE model) is one of the most important macro models in economics (along with the AS-AD Supply-Demand model). The directed graph above shows that the two exogenous causal variables are Population (N) and Technology (TECH). If either of these variables stop growing, the system will reach a Steady State Economy. It may be surprising to students of Economics to learn that, from a causality standpoint), Labor (L), Production (Q) and Capital Stock (K) are purely dependent variables and are not the primary drivers of growth.

UN Population projections currently anticipate that Population will peak at 10.3 Billion people in 2084. In order to reach steady steady, the  DICE model has to also assume (arguably) that Technology Change will also peak at some time in the future.


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