(added note: this is the initial post covering the CSALT model, index to other posts)
It would be nice to have a simple climatology tool that illustrates the trend of modern-day global warming, while also providing a view of the underlying mechanisms. What I came up with is the CSALT model, which is based on some of the analysis from a recent blog post titled Climate Variability and Inferring Global Warming.
What CSALT does right now is act as a reverse weather forecaster that can hindcast the global average temperature accurately without using any direct measures of temperature.
All CSALT requires is historical time-series of these characteristics:
- CO2 concentration in the atmosphere
- SOI (Southern Oscillation Index) as defined by the difference in values of atmospheric pressure in Tahiti and Darwin
- Aerosol concentration in the atmosphere as generated by volcanic events (and potentially man-made events such as armed conflicts).
- LOD (Length-of-Day) as defined by the correction in the Length Of Day measure in seconds. (edit: this is related to the Stadium Wave hypothesis of Wyatt&Curry)
- TSI (Total Solar Irradiance) as a measure of the variation in solar insolation due to quasi-periodic sunspot activity.
The parameters form the mnemonic CSALT, with the CO2 acting as the main driving force to the rising temperature trend (the "control knob" ) and the other SALT terms adding fluctuations (i.e. natural uncertainty) to the trend.
The CSALT model works very well over a time period stretching back to 1880. You can try it out here and play with the tuning parameters:
Foundation of the CSALT model
As always physics rules when it comes to defining natural behavior, and so we start by looking at energy balance. Consider a Gibbs energy formulation as a variational approach:
where S can describe heat capacity terms and the extra energy terms can represent external forces such as EM and induced terms such as the GHG effect reducing the radiative outflow.
So we have:
LOD representing differential internal free energy of the spinning planet as it gains or releases angular momentum → dG
SOI representing a pressure differential → V dP
Aerosols representing a reflective EM → dEa
TSI representing an external EM driving force → dEb
ln(CO2) representing a suppressive EM → dEc
Temperature and heat capacity (S) combine → S dT
We then have enough information to try to solve the first equation as a variational problem, where each of the terms needs to be scaled to get the best fit.
[ $ latex LOI = SOI - S dT - TSI - Aerosols - ln(CO2) $ ]
or rearranging to make it more convenient to a solver
That turns into multiple linear regression problem as we use data from each month from 1880-2013 to give a best fit with respect to the coefficients ci.
That is essentially what goes into the R linear model solver, where we use the data from a temperature time-series such as GISS for dT and appropriate data sets for the other factors:
lm( dT ~ C + S + A + L + T )
and then out pop the coefficients, c1 ... c5
The reconstructed function is created from these coefficients applied to the individual data sets.
So to do a good job of forecasting climate in the future, all we need is a good projection of CO2 levels to get the elevated temperature anomaly and the SALT parameters to get at the possible fluctuations.
In summary, the basic premise of the CSALT model is that are using a variational energy balance approach and then perturbing the system by looking at the energy differential with respect to various contributions to the system. Nature will then pick a path that has a stationary point of action that conserves energy, essentially treating the summed energy components as an invariant. One only has to account for all the ways that energy can transform so as not to lose track of any of the major pathways.
The residual, or what is left over, is noise. This noise is either systemic (caused by measurement errors, etc) or aleatory which consists of contributions from everything else we don’t yet fully comprehend, or can’t because of the shear number of other paths.
This is not the optimal situation, as not knowing all the combinations makes it an incomplete solution, but picking up the most significant patterns is very useful. It is indeed remarkable how well dT can be reconstructed from the other energy constituents.
The Tunable Parameters are mainly exponentially damped responses to the datasets. A lag of this kind gives the energy term time to propagate to the rest of the earth, or if its a discrete event the amount of time it takes to dissipate.
- SOI lag → 6 months to model the propagation across the earth
- Aerosol lag → Between 2 to 3 years to dissipate an individual discrete event, otherwise use the Sato dataset from GISS
- LOD lag → About 7-8 years for the internal energy to propagate and disperse from the deep ocean or where ever it may be originating .
- TSI lag → another short lag to model response from latent and transient energy stores.
- CO2 → no lag on this because it is a continuous increase in globally dispersed atmospheric concentration.
The Fitted Parameters are what the solver finds as scaling factors for the lagged regressor variables.
- SOI scaling → This is scaled to fit most of the subdecadal fluctuations
- Aerosol scaling → This is scaled to fit the major volcanic events such as Pinatubo, which result in a temporary transient reduction in temperature.
- LOD scaling → A subtle factor which effects the ocean temperatures (2× to 4×) more than the land. This captures the PDO effect which impacts SST.
- TSI scaling → This turns out to agree with that predicted from the proportional radiative heating, about 0.05C heating due to a 1 W/m^2 change in solar irradiance at the top of the atmosphere
- ln(CO2) scaling → This drops out to agree with the accepted value of TCR=2°C for global warming and 3°C for land.
Again, all the fitted parameters are due to the solution of the multiple regression. The scaling factors of the fitted parameters are shown at the top of the graph in blue cells. A correlation coefficent for the goodness of fit is also included.
If the surface of the earth releases aerosols in the air as a discrete event or impulse from a volcanic eruption, the effect will temporally lag from the action as the aerosols disperse. This has to be in a direction that obeys causality.
As a rough approximation we can always say that the lag function is an exponential damped response on the stimulus. The term lag is used to describe an "exponentially damped response" or "first-order impulse response function" .
The October 1943 spike is the single anthro effect I added apart from CO2. You can turn that on/off by the anthro aerosols checkbox. I added that because since the overall agreement is so good, one can really start to look at particular points in time for further evaluation.
All the lags can be modified by the user. You can turn all of them off by setting the lags to zero. The agreement is still good.
The application of the LOD (length of day) is crucial as a proxy for multidecadal oscillations. This ensures conservation of energy and conservation of momentum according to work by Dickey et al at NASA JPL . The fluctuations in kinetic energy have to go somewhere and of course changes in temperature are one place for this dissipation. So as of now, the LOD is in the category of a phenomenological behavior that can be described by a heuristic of a ~60 year cycle. If the cycle does not reoccur in the future, that heuristic will get shot down. But that is the nature of a heuristic, in that it is a stop-gap measure to describe something that is not yet completely understood.
Some insight to the relative importance of the LOD is seen by its impact depending on the temperature series used. If we use a global series such as GISS-LOTI or HadCrut, then the LOD influence is clearly there. However, if we use the Land-based CruTEM or BEST or GISS-land (dTs) series, the LOD influence is a factor of 2× to 4× lower in strength.
In fact, the contribution of the LOD is still there because many of the land observations are near the ocean but it is suppressed. Yet, bottomline, the LOD does not seem to have as big an impact on land temperatures as on SST.
As far as volcanic disturbances, I initially took the 10 significant events from the BEST spreadsheet of Muller  and then later added Sato's optical depth profile for volcanic activity .
Also note that several different temperature time series are included, and combined in various ways. A low-pass first-order exponential smoothing filter is provided to see how well the model works when the remaining red noise is removed.