ARIMA theory of climate change

I have just uploaded a manuscript to the preprint archive viXra. ViXra is an interesting alter-ego to the other preprint archive arXiv. The goals of viXra are:

It is inevitable that viXra will therefore contain e-prints that many scientists will consider clearly wrong and unscientific. However, it will also be a repository for new ideas that the scientific establishment is not currently willing to consider. Other perfectly conventional e-prints will be found here simply because the authors were not able to find a suitable endorser for the arXiv or because they prefer a more open system. It is our belief that anybody who considers themselves to have done scientific work should have the right to place it in an archive in order to communicate the idea to a wide public. They should also be allowed to stake their claim of priority in case the idea is recognised as important in the future.

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0 thoughts on “ARIMA theory of climate change

  1. Why not, so long as the volume can be controlled ans well as a minimum quality standard that does not repress new ideas but does cull those that have been tested thoroughly enough for dismissal. Imagine the number of papers that would pour in from bush lawyers if the legal profession did this.
    David, I’ve lost 5 years of email address books. Might you please send an email to me to help with the rebuilding as I don’t even have a current for you? Also any other readers who would have been in there in the past.

  2. Accumulation of forcing over extended periods may indeed be rather important. I wonder if you have seen this:

    http://earthweb.ess.washington.edu/roe/GerardWeb/Publications_files/Roe_Milankovitch_GRL06.pdf

    It seems to suggest that the rate of change of climate is related to the orbital forcing. Mathematically this is the same thing as say that the forcing integrates over time.

    Of course, why Northern Hemisphere summer insolation correlates with the rate of change of global ice is still puzzling.

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  5. Someone pointed me to your work and told me it proved that the GHE doesn’t exist. While trying to prove your work was incorrect (the GHE does exist), I found that much of it made sense – but that your accumulation theory wasn’t radically different from traditional approaches.

    One section of your first unpublished manuscript (http://vixra.org/pdf/1108.0004v1.pdf) says:

    “A linear regression can be used to estimate the parameters of the system with the form:

    T_i = aT_i−1 + bS_i−1 + c

    where a is the AR coefficient, S is the solar irradiance at the TOA, b is the effect of changes in solar irradiance on global temperature T, and c is the intercept that allows us to calculate the equilibrium value. The result of fitting the HadCRU annual temperature to the solar irradiance from Lean et.al. (2001) are as follows:

    a = 0.89 ± 0.04; b = 0.063 ± 0.029C/W m2; c = −86.2 ± 39; R2 = 0.8603

    The solar effect on temperature is 0.06 ± 0.03C/W m2/yr. The volume of water that would rise by 0.06C after one year of even heating by 1 Watt has a depth of 159 meters, corresponding to the midpoint depth of the tropical ocean thermocline. We can also calculate the equilibrium value of 86.2/0.063 = 1365.9W/m2 as found previously.”

    What this equation appears to say is that the current year’s temperature anomaly will be: a) 89% of last year’s anomaly PLUS b) the temperature change expected for heating 159 m of ocean mixed layer with last year’s incoming solar radiation MINUS c) a 86.2 degC fudge factor. From a physics perspective, the equation initially appeared to be nonsense: 1) Radiative cooling varies with the fourth power of absolute temperature, not linearly with temperature anomaly. 2) The mixed layer is unreasonably deep. However, those problems can be fixed.

    Let’s start by using your formula to calculate the temperature change (dT) for any year:

    dT = T_i – T_i−1 = aT_i−1 + bS_i−1 + c – T_i−1
    dT = -(1-a)*T_i−1 + bS_i−1 + c

    Now let’s calculate dT from first principles. Incoming power from the sun is S, but it needs to be corrected for albedo and the view factor (the ratio of surface area of a sphere to a disk); something you ignore. Outgoing power is given by the S-B equation. In your notation, T is the temperature anomaly, so we need to add the average temperature Ta that was subtracted to calculate the anomaly. The radiative flux imbalance (W) is therefore:

    W = 0.7*S/4 – o(Ta+T)^4
    W = 0.7*S/4 – oTa^4 – (4Ta^3)T + …

    Ignoring the negligible terms with lower powers of Ta, convert to the annual energy imbalance (dE) by multiplying by the number of seconds (n) per year.

    dE = -(4noTa^3)*T + (n*0.7/4)*S – noTa^4

    Then we convert to temperature change by dividing the heat capacity per unit area, which is the heat capacity over water (C, in J/m3) times the depth of the mixed layer (d).

    dT = -(4noTa^3/Cd)*T + (n*0.7/4Cd)*S – noTa^4/Cd

    Eureka! We have an equation that looks like yours, but which provides a physical explanation for the coefficients you found by empirical fitting. Since the coefficient for S depends only on the depth of the mixed layer, we can use your value (0.063) to solve for d and get 29.9 m. This is much closer to the usual estimate for the depth of the mixed layer and the observed depth of seasonal warming. (If I didn’t correct S, d = 171 m. For heat capacity, I assumed that 70% of the earth was covered by water and ignored everything else. The real heat capacity is somewhat larger. You may have made slightly different assumptions.)

    Knowing the depth of the mixed layer, we can solve for Ta using your empirical value for c (86.2). Ta turns out to be 254.9 degK, which I’m sure you recognize as the blackbody equivalent temperature for the earth – the temperature at which post-albedo incoming and outgoing radiation are equal. So, your constant term arises from the fact that you chose to work with temperature anomalies instead of absolute temperature. (Of course, the temperature where the average photon is escaping to space is emitted is far more relevant to the planet’s energy balance than surface temperature.)

    Using these values for Ta and d, 1-a turns out to be 1.35, not 0.11. In essence, you are assuming that the mixed layer that the temperature anomaly diffuses into is 12-fold bigger than the mixed layer associated with the solar radiation. That can’t be right. We do know that some heat does escape into the deeper ocean (a two-compartment model) and your empirical model appears to be trying to correct for this problem. You can see why a two compartment model is needed here: http://rankexploits.com/musings/2012/pinatubo-climate-sensitivity-and-two-dogs-that-didnt-bark-in-the-night/

    In this exercise, you have corrected the input solar radiation for interference from volcanic aerosols. You should also explore what happens when you correct for the interference from GHGs and other anthropogenic aerosols. I suspect you can do a better job of fitting both the first and second halves of the temperature record for the 20th century if you take GHGs into account. However, any model without two compartments can’t deal with the problem that the ocean has a top compartment that is rapidly mixed by the wind and a deeper compartment that is slowly mixed by downwelling/upwelling and by eddy diffusion associate currents moving along the ocean floor.

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