Earth's climate responds to solar energy dominantly as a mechanical tapped delay line, and so is sympathetic to certain delays in the solar output, to reinforce some but suppress others. This phenomenon occurs first because the atmosphere is a by product of the ocean. The ocean dominates the climate response because it is dark to absorb short wave radiation, because it has a high heat capacity, and because ocean currents cause delays to neutralize or reinforce solar patterns.

The Intergovernmental Panel on Climate Change (IPCC) asks the question, "Can the Warming of the 20th Century be Explained by Natural Variability?" IPCC's answer can be read as affirmative, but with no more than 10% certainty. AR4, FAQ 9.2, p. 702. IPCC's data on which it relied show that the answer is "Yes" with high confidence, and that the cause of the variability is the Sun. IPCC's own data analysis techniques, applied more frequently and its own preferred data, reveal the patterns, and reveal IPCC's error in computing the radiative forcing of Total Solar Irradiance (TSI).

IPCC's Fatal Errors, the previous paper in the Journal, showed a number of errors within IPCC's Anthropogenic Global Warming Model, each of which was sufficient to invalidate AGW based on internal errors. That paper relied on no new data, nor any alternative in data analysis or modeling by IPCC, but the result was negative with respect to the climate model. This paper relies on IPCC's preferred data expressed in its Reports, but is affirmative, advancing an alternative model for global warming in which the Sun is the cause.

This Solar Global Warming model is a competing model to AGW, based on the same data. It necessarily contradicts several more arguments, claims and derivations made by IPCC. Each is analyzed here.

This paper in part confirms and extends the analysis of Dr. Nicola Scafetta. (See references.) The starting points and end points are similar, but this study adheres to IPCC's data and methods to debunk IPCC's model on its own terms, and to minimize any tendency to produce an alternative and competing climate model from the infinity of possible candidates.

IPCC's modeling is far less mathematical than Scafetta's, and relies on patterns evidenced in graphs rather than computed correlation values. To be sure, either graphical or computational correlation methods can guide the creation of scientific models, but in the end, models must produce fully quantified predictions to compare with scientific facts. The patterns shown and discussed in this paper are exclusively objective.

II. SUN IMPRINT ON EARTH'S TEMPERATURE

A. Temperature Data

IPCC has considered an abundance of published temperature records:

Of IPCC's sources, the Brohan record, identified as HadCRUT3, is the longest and broadest, and serves as IPCC's standard. That source also provides a graph of annual temperatures:

The Brohan record is next with the error bands removed, and IPCC's 11-year smoothed trace superimposed in blue:

The Brohan record is similar to the NOAA monthly record, shown overlaid next in red:

IPCC separately provides the global temperature series, taken from Brohan and shown next:

IPCC uses variations of the global surface temperature to make its forecasts. The next figure contains several examples. Note that the differences in the anomaly zero points, 1961-1990 vs. 1980-1999.

Adjusting for the difference in the zero points, the average temperature record used in the simulations overlays the global HadCRUT3 series in the later years and in 1900, but the simulation average is missing the temporary warming feature centered in 1940. The simulation average temperature record is shown as the green overlay in the next figure.

IPCC, it would seem, only requires its models have the correct amplitude and slope at the end point of the current temperature. This is reinforced by considering IPCC's radiative forcing paradigm in which a response to added forcings is linearly added to the previous climate history. However, this study depends on the shape of the temperature history.

B. Solar Irradiance Data

IPCC provides the following chart for the history of solar radiation:

The references are to the journal paper Wang, Y.-M., J.L. Lean, and N.R. Sheeley, Jr., Modeling the Sun's Magnetic Field and Irradiance since 1713, Astrto.J., 625:522-538, 5/20/05 (Wang, et al. (2005)) and to the journal letter, Lean, J.L., Evolution of the Sun's Spectral Irradiance Since the Maunder Minimum, Geophs.Res.Ltrs, V. 27, No. 16, pp. 2425-2428, 8/15/00 (Lean (2000)). Peculiarly but more informatively, Wang et al. (2005) sports a second title on each page: Secular Evolution of the Sun's Magnetic Field.

IPCC's reconstruction is lifted from the following chart in Wang:

The violet line in Figure 9 (AR4 Figure 2.17) is a thick, painted region bounded by the upper pair of curves from Wang. The blue region in that figure is a similarly filled region bounded by two curves. IPCC's lower bound is Wang's lower curve, as originally published in Lean (2000), but extended and reduced about 0.97 Wm^-2 and more in the 20th Century to as much as 1.6 Wm^-2:

The upper bound in blue in IPCC's Figure 2.17 (Figure 9) is the upper curve from IPCC's Third Assessment Report, shown below, shifted down by an average of 5.7 Wm^-2 and more in the 20th Century. TAR, Figure 6.5, p. 382, attributed to Lean et al. (1995):

IPCC provides little if any explanation for its preparation of the Total Solar Irradiance model in its Figure 2.17. Lean (2000) introduces her letter by saying,

The observation in Lean (2000) is still valid: no empirical evidence exists beyond a few decades to compare the accuracy of these models. Regardless, the modeling in Wang et al. (2005) is a substantial improvement in rigor. They divided the Sun's surface in two: an active region comprising the sunspots and faculae, plus a separable ephemeral or background region. They represented the active region by as many as 600 large, closed loop dipoles, called Bipolar Magnetic Regions (BMRs), randomly placed over the sphere. They matched the resulting magnetic field to the annual sunspot number, the polarity switching phenomenon, and the solar wind aa index. They also adopted empirical relationships from the literature, and substantially reduced the facular background used in Lean (2000).

Wang, et al. recognize that their secular (background) trend is substantially smaller than found in previous models. However they make no claim that their model is more accurate beyond accounting for implications from an arbitrary scaling of the aa index, recorded since 1868, and empirical relationships involving the index. While any model of sophistication would agree with modern measurements, the question is how well a model represents the evolution of the Sun's irradiance to the present, as Wang, et al. stated at the outset was their objective. While the absolute value of the trend remains relatively uncertain, the Wang model represents the state-of-the-art in representing solar irradiance, optimum to account for the fine structure of TSI variability because it is an emulation of physical phenomena, constrained by the long records of sunspot numbers and the solar wind.

The Total Solar Irradiance used in this paper is the Wang et al. (2005) model, digitized from the violet trace in IPCC�s Figure 2.17.

C. Data Analysis Methods

Finding patterns is the essence of scientific discovery, leading to assumptions about cause and effect for modeling. Coherence and cross-correlation are two mathematical methods found in the literature for quantifying the similarity between two records. The coherence function is the cross-spectral density normalized by the product of the standard deviations of the individual processes. Empirically, the coherence function is problematic because it includes estimates of noisy processes in the denominator, making it an unstable statistic. The word coherent in this paper is to mean the appearance of a pattern with attributes similar to those known to be due to a signal or to a common source in noise (e.g., "coherent patterns of statistically significant trends", AR4 �3.8.2.2, p. 302), and incoherent to mean having the attributes of a pattern due to noise alone.

Correlation appears in the literature most often as a single point calculation, but the cross-correlation function is essential to establish leads and lags. It is the point correlation with one record shifted with respect to the other by a variable amount. The cross-correlation function is the method by which CO2 is known to be the effect of temperature and not its cause in the Vostok record. See The Acquittal of Carbon Dioxide in the Journal.

Cross-correlation generally requires detrending of records to remove the mean, and where, as here, a substantial and perhaps significant trend exists in the means of both the candidate cause and the candidate effect, the prospects for intensive and esoteric computations are not promising.

Spectral analysis and principal component analysis (PCA) are cross-correlation methods. In these techniques, a data record is cross-correlated not with another record, but with a set of mutually uncorrelated functions to decompose the record into a scalar sum of the components. In spectral analysis, sinusoids provide a standard set of component functions. In PCA, the investigator chooses the functions to use, the first being arbitrary, and the subsequent functions residue functions, forced to be uncorrelated with each of the preceding functions.

Spectral analysis is not particularly helpful in the climate problem. While the solar intensity model appears to have a powerful sinusoidal signal from the solar cycle, the cycle is irregular, varying between 9 and 13 years. AR4, Glossary, p. 952. This irregularity creates a broad response around the center period of about 10.5 to 11 years instead of producing a single line and a single coefficient.

Even more important is that beyond the average power contributed, the 11-year cycle is noise to climate. The temperature record appears to contain no 11 year component, and in fact 11-years is marginally too short with respect to climate so it would tend to be classified as weather.

D. Representing Signal Sources According to Receiver Responses

Sinusoids are important in electromagnetics because the sources and receptors are molecular oscillators that naturally produce or resonate to sinusoids. These arise in climate with respect to measuring solar activity by the calcium molecule lines I and II, and again in atmospheric absorption spectra due to molecules of water vapor, CO2, and the other greenhouse gases.

Sinusoids are also important in electrical and mechanical systems because of what is called simple harmonic motion, a process in which energy alternates between kinetic and potential forms at natural frequencies. This does not exist in thermodynamic systems because, while heat can be converted and stored, it has no kinetic form. That is, heat lacks inertia, and when inertia is used in climate jargon, it signifies heat capacity. These considerations go to the heart of the modeling problem: a clue to how one might profitably decompose a candidate source of energy lies into characteristic responses of the receptor. The receiver favors or rejects certain forms of input, so decomposing the source in similar forms can be a fruitful pursuit.

Electrical and mechanical systems can also be tuned without inductors by delay lines. Narrowband, high-pass and low-pass reactions produced by tapped delay lines are common in the literature, although the utility of such filters is often limited by the challenge in designing long, low loss delay lines. However, in the case of climate, the ocean provides short to extremely long delay lines by subsurface absorption and deep water circulation patterns such as the Thermohaline Circulation, better called the "conveyor belt", and the Gulf Stream. The observed common pattern between the Sun and Earth's temperature leads to the conjecture that these oceanic phenomena tune Earth's climate to prefer some lag times and reject others within solar radiation.

The hypothesis tested here is whether the Sun is responsible for the observed climate variability. In the climate problem, the primary concern is the global average surface temperature (GAST). It is of special interest on the scale of a few centuries because of the span of available scientific measurements, and because of the conjecture that man has influenced climate during the industrial age. Furthermore, the record shows no obvious sensitivities on the scale of the solar cycle, either at 11 years or 22 years.

E. IPCC Interprets Its Charter To Defend Manmade Climate Changes.

The United Nations Environment Programme (UNEP) says,

Accordingly, IPCC implements its model, committed to the radiative forcing paradigm, in a number of individual global climate models, selected and tuned by IPCC for agreement with its conjecture that Earth's climate must be caused by man through his CO2 emissions. By application of that flawed and biased model, IPCC determined that the Sun is not the cause of Earth's climate variability.

IPCC claims to stimulate science, not actually to do science, but to define the problem and then to rely on the "best available science", meaning that agreeable science published in peer-reviewed publications. AR4, �1.2 The Nature of Earth Science, p. 95, below. However, its investigators indicate that they accept as peer-reviewed only material from journals which publish no articles skeptical about anthropogenic climate change. The investigators reject other journals and other media, and boycott, intimidate, or ridicule editors and sources not in the camp.

At the same time, the recent Himalayan glacier incident demonstrates the willingness of IPCC to rely on a student paper, based solely on that paper's favorable support of IPCC's conjecture.

IPCC has influenced genuine papers that have negligible bearing on the anthropogenic conjecture to be salted with immaterial phrases to acknowledge dutifully the significance of anthropogenic global warming, and to reference immaterial or biased papers that form a network for a belief system. So IPCC has isolated its work from scientists who respect the virtue of skepticism, from public criticism, and from the review of its superiors in science.

F. IPCC Omits Cloud Albedo

IPCC's resulting climate model, reflected in the GCMs, is open loop with respect to Bond albedo, the total shortwave reflectance of Earth. The simplest of computations show planetary albedo due to the hydrological cycle to be the overwhelming negative feedback in climate. Cloud albedo stabilizes Earth in its warm state, and surface albedo from ice and snow locks Earth into its cold state ("cold glacial times and � warm interglacials", AR4 FAQ 6.2, p. 465). Cloud albedo mitigates warming from any cause, and because of its power it is unfriendly to the greenhouse effect.

IPCC not only omits albedo from its table of what it knows, but from its models. Because it is unable to model cloud cover, IPCC parameterizes it:

G. Simulating Cloud Albedo

Cloud albedo dominates surface albedo by its magnitude and its location, and by eclipsing surface reflectance and absorbance.

IPCC admits that cloud cover, and hence cloud albedo and Bond albedo, is known to be dependent on specific humidity and the availability of cloud condensation nuclei (CCN). That humidity is further admitted by IPCC to be dependent on surface temperature, completing a negative feedback mechanism omitted from its GCMs.

Svensmark postulated that galactic cosmic rays supply a significant number of CCNs, and further that the solar wind modulates GCR intensity. In his model, increased solar activity causes warming by sweeping away GCRs and hence CCNs to decrease cloud cover. It is supported by some evidence that cloud cover is negatively correlated with solar activity. IPCC rejected the Svensmark model:

While the results of this paper are consistent with the GCR model, they suggest yet another hypothesis: cloud cover, and hence Bond albedo, is dependent on shortwave radiant absorption and warming at cloud level. At one point in its Reports, IPCC touches on a link between shortwave (solar) radiation and cloud cover. It says,

As IPCC shows from Kiehl and Trenberth (1997), 20% of incoming solar radiation, almost as much as is reflected back into space, is absorbed by the atmosphere. AR4 FAQ Figure 1.1, p. 96, shown modified below. That shortwave absorption will warm the atmosphere and tend to reduce cloud cover. In brief, and from multiple possible causes, Earth responds to the Sun in part through increased solar activity decreasing cloud cover. All the elements of this model are represented in the GCMs or IPCC's supporting theory, but the Panel has yet to connect them and to activate them. The time has passed to introduce Kiehl & Trenberth v. 2.0:

In this revision to the initial model for climate, available CCN and specific humidity combine to form clouds, dependent on the temperature at altitude. The model allows for the Svensmark effect, and links total solar activity directly and indirectly to the extent of cloud cover.

As a result of its selective and incomplete modeling, IPCC determined, with an admittedly low level of scientific understanding, that solar radiation is insignificant compared to its chartered model. Using its ambiguous standard of radiative forcing (RF), IPCC calculates that the RF from the Sun is 0.12 [0.06 to 0.30] Wm^-2, only 7% of the 1.66 [1.49 to 1.83] Wm^-2 it attributes to CO2 (AR4, Figure TS.5, p. 32), all based on a constant Bond albedo. IPCC puts the total solar RF at a third of just the uncertainty in CO2 forcing. That figure of 0.12 Wm^-2 approximates the best fit linear increase in solar radiation since 1750 using the model of Wang, et al. (2005), but after applying 11-year smoothing. Id., �2.7.1.2.2, above. In a popular spread sheet, the best fit straight line is the trend, a lexographically efficient synonym adopted here.

Why did IPCC first apply 11-year smoothing, and then model the Sun by a single trend covering almost twice the span of temperature measurements? The answer to the smoothing question is that Earth does not respond to the 11-year cycle. That large component dominating the solar pattern is noise with respect to climate, and it masks underlying patterns. IPCC chose the 250 year trend to minimize any pattern in the solar output, thus reinforcing its conjecture that CO2 is the cause global warming. It is the illusionary handle of a hockey stick.

Conversely IPCC created those Earthly hockey stick patterns to support its thesis. IPCC's transcending argument is that if multiple records are similarly unprecedented, then they must have a common cause; and if any one of them is arguably manmade, then all must be. Applied to the Sun, IPCC urges that the current solar irradiance is not unprecedented, being within 0.05% of its level just 250 years ago. Therefore, IPCC concludes the Sun is not among the parameters with a common cause, and so it ruled out the Sun as a cause.

IPCC says,

If the Sun had no effect on albedo, or any other amplifying process, IPCC's calculation would put to rest any consideration that solar variability might be the cause of the modern temperature variations. IPCC's mistake is to abandon consideration of the Sun as the instrument of climate change based on its first-order forcing calculation with everything else held constant. Albedo, for example, is not constant.

H. Albedo Dependence on Solar Radiation & Humidity

Cloud albedo is a positive feedback that amplifies solar radiation while at the same time it is a negative feedback that mitigates warming from any cause. Increased solar activity initially causes more shortwave energy to be absorbed in the atmosphere. This warms the atmosphere, reducing cloud cover at a constant humidity, and thus increasing insolation at the surface. Only later does the resulting warming of the surface increases humidity as the ocean absorbs the higher insolation. The ocean is both the primary agent and a slow agent because of its high heat capacity. The increased humidity increases cloud cover, provided a surplus of cloud condensation nuclei is available, increasing cloud albedo, and mitigating the entire effect. The concept is in this illustration:

The steady state effects are seen by examining the first order changes in Albedo, A, Humidity, H, and surface temperature, T, here attributed to the Ocean. Representing the terms by small changes near their nominal values, produces the following linear values, where k_i ≥ 0:

Let Equations (5) and (6) be represented by

For the albedo and temperature, respectively

Instead with the Cloud Albedo Model, the sensitivity of albedo to humidity, k_O, is the negative cloud albedo feedback in Equation (16) multiplying ΔS and in Equation (17), a factor of ΔS². The albedo sensitivity to solar radiation is an amplifier, appearing in Equation (17) as a cofactor of k_T to multiply ΔS².

Albedo is similarly represented by

This model is approximately linear over a wide range of useful values for the constants, which remain to be optimized. With increasing solar output, Earth's temperature and atmospheric humidity increase while albedo decreases. Here is a sample set:

	CLOUD COVER MODEL PARAMETERS
#	Parameter	Value	Comments
1	A0	0.3	Nominal current value
2	T0	133.4	For anomalies
3	H0	30%	Nominal current value
4	kH	0.0001	Nominal current value
5	kO	0.1
6	kS	0.1
7	kH	31	For T = 1.1�C @ ΔS = 0.055

Between 1862 and 1998, temperature rose 1.1�C (Figure 5) while TSI increased 0.22 Wm^-2 (Figure 9, bold). Dividing by 4 for the geometric effect on Earth, the solar input increased by 0.055.

This cloud albedo model amplifies the Sun in the short term, and introduces the Earthly lags in the long term that tune the climate, making it selective to long term variations on the Sun.

I. Patterns in the Sun

The next task is to search for a pattern in the Sun irradiance much longer than the solar cycle. A robust pattern is sought similar to that characterizing the instrument record for temperature, which spans about 150 years. Instead of a single, best fit criterion from end-to-end, the problem suggests analyzing the solar irradiance varying the trend span from 11 years to 150 years. Instead of analyzing the solar pattern at the single point of today, it needs to be assessed at every point in the modern instrument record, from 150 years ago to the present. For every span and every point in time, this filtering provides a running record of the trend of the solar intensity.

IPCC began a similar analysis of the global surface temperature, shown next.

IPCC characterizes the present day temperature response by measuring the rate of temperature increase from trends for four time spans of interest. This choice dramatizes the hockey stick effect by showing that the angle to the tip of the stick blade gets steeper when viewed closer to the blade.

IPCC urges its readers to read a significance into the latest temperature trends, those going back from 25 to 150 years. It doesn't explore how those trends appeared at other times past. For example, the next figure shows the 25 year trend lines as they might have characterized temperature, drawn every five years.

1. IPCC vernacular

IPCC says of the trend method,

Mathematical models have poles, meaning singularities at which a dependent parameter becomes infinite or undergoes perpetual oscillation. These are instabilities, and a stable system or a stable state is always finite, and any oscillations are damped. The most violent of natural phenomena, supernova in astronomy, and volcano eruptions in geology, are the largest witnessed events in their fields, but in the end are finite in energy, in time, and in space. Man has observed nothing infinite or infinitesimal. Things become infinite in models that employ rates or densities in which the denominators vanish. Nature doesn't give a fig about man's models.

IPCC is not particular enough about definitions, as discussed above or in the Journal for equilibrium, residence time, cloud albedo, and now for stable or linearity. It defines nonlinear as the absence of a "simple proportional relation between cause and effect." AR4, Glossary, p. 949. The word simple qualifies and blunts a promising definition. But the existence ever of cause and effect is an axiom in science, notwithstanding some painfully obvious counterexamples. Linearity has a precise definition in mathematics and system theory. A system is linear if the response to a linear combination of inputs is that same linear combination of the individual responses. What might be linear in, say, cylindrical coordinates, becomes nonlinear in Cartesian coordinates. The Beer-Lambert Law states that absorbance by a gas is linear in the product of concentration and the distance traveled (from the probability of a collision), but it also expresses gas radiative forcing as the non-linear complement of an exponential in gas concentration. A linear relationship in the macroparameters of thermodynamics is likely nonlinear on smaller scales, that is, in mesoparameter or microparameter spaces. Linearity is a state of mathematical being, and is not continuously measurable. It exists or not. A system cannot be "highly nonlinear". That "the climate system exhibits highly nonlinear behavior" (AR4, Appendix 3A, p. 336) is doubly meaningless.

2. Systems science principles

IPCC's reconstructions are built on measurements with extremely low signal-to-noise ratio. The trend line will indeed be noisy, not unstable. It might be vertical, meaning that the rate or slope is infinite, but that doesn't mean that the line ceases to exist, or that correlation has vanished. The trend line inherits its noise from the underlying measurements, and by its very nature is less noisy than the data, making it most useful in detection and estimation.

The trend line is always less noisy than the data it fits, but it can still be highly variable. This can be overcome by measuring it frequently, whether in time or space. A good filter has the property of being reversible. This means that the input can be reconstructed from the output without loss, given a sufficiency of initial conditions. That the linear trend line is a reversible filter may be a conjecture, but given the initial conditions and the trend line at each data point, the original data appear to be reproducible. The complete record of the trend line may be a lossless representation of the input data at every width or span of calculation. It is certainly objective, a scientific necessity. A tangential conjecture or assumption here is that the representation by a complete set of trend samples retains all the information in the original signal.

What is important here in solar radiation is Earth's response to the driving energy. By its nature, climate on the largest scale is a low pass system in response to that energy. And because Earth returns energy back to space but most importantly not instantaneously, it should be well modeled by finite delay lines.

Oceans, because of their mass, their heat capacity, and their color, are the dominant mechanism of Earth's energy balance between the Sun and space. The atmosphere as a reservoir plays a minute role, and is well-represented as a byproduct of the ocean. And the ocean is the distributor of the carbon cycle, the hydrological cycle, and the energy cycle. The ocean's complex patterns of circulation across the surface, and between the surface and the deeper ocean, produce a pattern of delays, with some cycle times exceeding a millennium. These are evident in the concentration of CO2 cross-correlated with temperature. Consequently, temperature might be best modeled as a set of relatively narrowband accumulators of solar energy. An analog to this process in electronics and signal processing is the tapped delay line.

If Earth's climate had resonators that responded to sinusoids, the best characterization of solar energy might be its Fourier spectrum. The point is that how a system responds can be a guide to how best to characterize its driving inputs. This is the physical reason IPCC denied existed. The conjecture that climate temperature responds with one or more finite delays suggests characterizing solar energy with finite time filters. The fixed span trend line is a first-order finite time filter. It finds regular use as the first step in signal analysis, often discarded under the name of detrending, but sometimes, as here, containing the wanted information. IPCC repeatedly states that it seeks no more than a first order effect with its radiative forcing paradigm. See for example, TAR, Ch. 6 Radiative Forcing of Climate Change, Executive Summary, p. 351.

This paper reports the successful search for Earth's temperature pattern using the trend line applied to the noisy source, Total Solar Irradiance, as modeled by Wang, et al. (2005). The parameter of interest is the increase in solar radiation over the term of the span, normalized by the value at the start of the span. It is the ratio expressed as the percentage increase. This is analogous to IPCC's determination that over 250 years, the Wang model increased 0.05%. For each span, a computer routine computes the maximum sampled ratio since 1900. Equation (12). The set of all such maxima produces a curve, shown in Figure 17:

The curve has labels for the 11-year point, and three local maxima, 20, 119, and 199 years. The search for maxima since 1900 is to avoid uncompensated start up effects. Because this trend model only looks back in time, it is what is known as a realizable or causal filer. This means that the real Earth or an emulating model could have actually responded to the data included in the filter.

To the contrary, IPCC employs centered symmetrical filters for its data records, which are unrealizable, meaning filters that are aware of the future. IPCC's results are thus subjectively attractive, but to the extent that it applies such filtered to data to its models, its work is physically problematic and not objective. A prime example is IPCC's unquantified attribution of the glacial cycles to the Milankovitch cycles (AR4 FAQ 6.1, with the humorous title "What Caused the Ice Ages and Other Important Climate Changes Before the Industrial Era", bold added). Wikipedia falls in line, but steps over it to say, "Past and future Milankovitch cycles. VSOP [Variations S�culaires des Orbites Plan�taires] allows prediction of past and future orbital parameters with great accuracy." Bold added. Wikipedia puts the lie to its claim by saying the Milankovitch Climate model is "not perfectly worked out" (as if perfection were ever achieved in any science), listing eight named problems, which IPCC minimizes. See for example AR4 �6.7 Concluding Remarks on Key Uncertainties, p. 483. Among those problems are a mismatch between the magnitudes of the orbital forcings and the climate response, and a causal problem with the penultimate glacial cycle. IPCC tries to salvage its AGW theory by making CO2 an agent of the Milankovitch theory, amplifying the variations without triggering them. AR4 Ch. 6, Executive Summary, p. 435. When the CO2 proves insufficient as a positive feedback, IPCC adds water vapor as the next, most important, and as clouds, the least understood feedback. AR4 FAQ 1.3 What is the Greenhouse Effect?, p. 116; AR4, Ch. 8, Executive Summary, p. 593; AR4 �8.6.3.2 Clouds, p. 636. This cascade of speculation about causes and effects arises out of a lack of causality coupled into a model for Earth's climate that is only conditionally stable, on the cusp of being triggered into a new state by an unidentified event, or crossing a model "tipping point". Nature doesn't have systems balanced on a knife edge, round boulders perched on the sides of hills, or cones standing on their tips. To be objective, investigators should model Earth as deeply stable, that is, requiring by definition cataclysmic events to dislodge it from its conditionally stable state, and instead responding gradually to causal forces.

Following are examples of a search for causal extractions of Total Solar Irradiation (TSI). Each chart contains a set of three running linear trends, used as a check for anomalous behavior. The traces include uncompensated end effects allowed to go off scale.

The important new result occurs at a span of 134 years, shown next, now co-plotted with the modern temperature record.

The 134-year solar running trend alone provides an excellent model for the global average surface temperature over its entire instrument record, as shown next in Figure 23:

J. Implications on Climate Processes & Further Study.

Demonstrated filtering of solar intensity exposes a strong signal in the best available model for the Sun, a signal that closely approximates the best available record of climate temperature, and one spanning 160 years. These same sources relied upon by IPCC are the Wang, et al. TSI model of AR4 Figure 2.17 (Figures 9 and 10, above), and the HadCRUT3 temperature record of AR4 Figure 3.6 (Figures 1 and 6, above). Certainly the signal on the Sun was caused neither by the industrial revolution nor any greenhouse effect; it does not bear the fingerprint of humans.

The Sun is the only significant cause for Earth's climate to have ranged from a few degrees Celsius to a maximum of about 17�C (an anomaly range of about -9�C to 3�C). The new results here constitute the only evidence showing more specifically that the Sun is also the cause of the observed variations of Earth's surface temperature over the last century and a half, the entire instrument record, and more than likely the cause over the geological record.

This model for the Sun is an � posteriori model, meaning that it is based on experiment, as was the Wang, et al. model. It provides opportunities for further improvements. For example, a modeler might discover a better filter than the trend, especially one based on physical processes on Earth, in the fashion that Wang, et al. matched experimental data with a randomized collection of solar eruptions called Bipolar Magnetic Regions (BMRs). A sum of mutually orthogonal (uncorrelated) waveforms might provide a superior filter, and a coefficient for each to best fit Earth's temperature record. Regardless, a fine model for Earth's Global Average Surface Temperature is immediately available that fits well within the uncertainty of measuring and estimating the unmeasurable macroparameter of the global average surface temperature, and the uncertainty in the TSI model.

To develop an � priori model, a model from physical reasoning, a link is needed to account for the relative small energy in the otherwise well-formed solar signal. The secular scale factor adopted by Wang should be re-examined. An amplifier in the climate is needed, and albedo is the obvious choice and it remains to be theoretically quantified. The radiant heating model, balancing the net shortwave radiation in and the long wave radiation out, is still valid. However, the parameter of consequence is not the radiative forcing of the Sun located somewhere between the top and the bottom of the troposphere and under a clear sky. What counts is the insolation at the surface, averaged over all possible cloud covers, suitably weighted.

This experimental model for Sun-induced climate variability arose out of consideration of the ocean's multiple, finite delays in energy distribution. This opens several avenues for future supporting studies. One is to investigate the class of problems in which a source might be characterized as it is manifest on a receiver. The second is to model the energy distribution of the ocean as a tapped delay line. For additional future work, see Conclusions, below.

III. FINGERPRINTS

A model in which the Sun impresses its energy pattern on Earth's climate is plainly inconsistent with IPCC's three-pronged argument for patterns of human activities to have imprinted the observed warming. IPCC urges (1) that the depletion of atmospheric oxygen matches the rate of increase of atmospheric CO2, (2) that the decline in the isotopic weight of atmospheric CO2 matches fossil fuel emissions, and (3) the sudden rise in gas concentrations and temperature match the onset of the industrial era, the family of hockey stick graphs. Of these imprint patterns, only one is strong, extensive, complex, and genuine: the Sun's fingerprint on Earth's temperature.

A. Oxygen Depletion & δ13C Lightening Do Not Match Human Activities.

IPCC asks and answers this "frequently asked question":

IPCC here states its foremost reason for ascribing the recent CO2 increase to man: unprecedented increases. It finds additional support for its anthropogenic model through isotopic lightening, never presenting the requisite mass balance analyses for the isotopic ratio and the commensurate oxygen depletion. IPCC quantifies neither model, but relies for both on a compact, duplex demonstration by graphic sophistry, shown in Figure 27.

IPCC shifted and scaled both the O2 and the δ¹³CO2 traces to give the false appearance in (a) that O2 is anti-parallel to the growth in CO2, and in (b) that δ¹³CO2 parallels the estimate of carbon emissions. Even at that, IPCC did not draw the O2 trace exactly parallel, as revealed in the next figure, shown in graph coordinates, O2 now reversed. IPCC's scale was arbitrary, and is shown here in inches following conversion of a pdf version of the original report.

IPCC's argument is that the decline in O2 matches the rise in CO2 and therefore the latter is from fossil fuel burning. Every molecule of CO2 created from burning in the atmosphere should consume one molecule of O2 decline, so the traces should be drawn identically scaled in parts per million (1 ppm = 4.773 per meg (Scripps O2 Program)). Corrected to remove the graphical bias, the data diverge as shown next.

Carbon's isotopic ratio fairs no better. Under the banner of "The Human Fingerprint on Greenhouse Gases", IPCC gushed:

IPCC manufactured two parallel traces out of the rate of CO2 emissions and the history of δ13C by graphical shifting and scaling. IPCC Figure 2.3(b), (Figure 27 above). First, look at the fraudulent technique, as shown next, even though no physical reason exists for these two records to be parallel.

The graph is in pdf inches, converted from IPCC's AR4 Figure 2.3, above. IPCC scaled the isotopic trace to be parallel in the ACO2 rate trace with respect to the two five year trends shown. It shifted the isotopic trace to lie just below the ACO2 rate so it was easy to see how parallel they were. Had IPCC not shifted and scaled one trace with respect to the other, and instead objectively used the full available range of the chart, the figure might have appeared as shown next:

A relationship does exist between δ13C and ACO2, but only indirectly between it and the rate of emissions, ACO2 rate. The relationship is not complicated, once the traditional delta ratio, a legacy from a time long before computers, is simplified. The definition of the ratio is straightforward, although the reference point, the PeeDee belemnite ratio R_PDB, is a bit obscure and even ambiguous.

With these relations,

With these results, the ergonomic but esoteric δ13C can disappear, and the graph of IPCC's Figure 2.3 or Figure 34 immediately scaled in terms of the ratio of 13C, r:

The value of δ13C becomes evident � it solves the human problem of dealing with changes in the fifth significant figure. In other words, the isotopic ratio solves the problem humans have coping with the first four significant figures being insignificant.

With the value of r for the atmosphere, r_a, at any time and the value for the ACO2, principally attributed to fossil fuel burning, r_f, a new value of r_a or, equivalently, δ13C can be readily derived for the a slug of ACO2 added to the atmosphere and well-mixed. However in spite of the importance, values for δ13C_a and δ13C_f are rare in the literature. IPCC cites neither, and apparently used neither. Battle, et al., (2000) provided the following estimates:

These equations yield

These definitions and equations reduce to the following equation:

Following are four possible solutions to the mass balance problem.

	ACO2 ISOTOPIC FINGERPRINT IS NOT A MATCH
#	Parameter	Value	Source
1	G0	762	AR4 Fig. 7.3, p. 515 C cycle
2	g(2003)	133.4	AR4 Fig. 2.3, p. 138
3	δ13C0	-7.592�	AR4 Fig. 2.3, p. 138
4	r0	0.011028894	Eq. (7)
5	δ13Cf	-29.4�	Battle, et al.
6	rf	0.010789151	Eq. (7)
7	k	50%	AR4 TS p.025
8	r(2003)	0.011009598	Eq. (12)
9	δ13C	-9.348�	Eq. (6)
10	δ13Cfinal	-8.080�	AR4 Fig. 2.3, p138

IPCC provides all the parameter values but the one from Battle, et al. Those values with the equations derived above establish the ACO2 fingerprint on the bulge of CO2 measured at MLO, as if it were a well-mixed, global parameter as IPCC assumes.

IPCC does not provide δ13C_f, the parameter found in Battle, et al., suggesting IPCC may have never made this simple mass balance calculation. A common value for that parameter in the literature is around 25�. The figure from Battle, et al., being published with a tolerance, earns additional respect. As will be shown, the number is not critical. The result is a mismatch with IPCC's data at year 2003 by a difference of 1.3�, more than twice the range of measurements, which cover two decades.

This discrepancy is huge, and is sufficient to reject the hypothesis that the surge in CO2 seen in the last century was caused by man. The CO2 added to the atmosphere is far heavier than the weight attributed to ACO2.

	CO2 SURGE IS TOO HEAVY TO BE ACO2
#	Parameter	Value	Source
1	G0	762	AR4 Fig. 7.3, p. 515 C cycle
2	g(2003)	133.4	AR4 Fig. 2.3, p. 138
3	δ13C0	-7.592�	AR4 Fig. 2.3, p. 138
4	r0	0.011028894	Eq. (7)
5	δ13Cf	-13.657�	Eq. (12)
6	rf	0.010962235	Eq. (7)
7	k	50%	AR4 TS p25
8	r(2003)	0.011023529	Eq. (7)
9	δ13C	-8.080�	AR4 Fig. 2.3, p. 138
10	δ13Cfinal	-8.080�	AR4 Fig. 2.3, p. 138

This computation is the first of three to examine other parameter values that would have rendered IPCC's fingerprint test affirmative: ACO2 was the cause of the CO2 lightening. The isotopic ratio for fossil fuel would have had to be considerably heavier, -13.657� instead of -29.4�, for the increase in atmospheric CO2 to have been caused by man.

	OR, ATMOSPHERIC CO2 IS OVER 1400 PPM
#	Parameter	Value	Source
1	G0	2913.9	Eq. (12)
2	g(2003)	133.4	AR4 Fig. 2.3, p. 138
3	δ13C0	-7.592�	AR4 Fig. 2.3, p. 138
4	r0	0.011028894	Eq. (7)
5	δ13Cf	-29.4�	Battle, et al.
6	rf	0.010789151	Eq. (7)
7	k	50%	AR4 TS p.025
8	r(2003)	0.011023529	Eq. (7)
9	δ13C	-8.080�	AR4 Fig. 2.3, p. 138
10	δ13Cfinal	-8.080�	AR4 Fig. 2.3, p. 138

For ACO2 at the stated rate and retention to have caused the small drop measured in atmospheric δ13C, the initial atmosphere concentration would have had to be 2,913.9 GtC, 3.8 times the figure used by IPCC. This is equivalent to 1,453 ppm of CO2 instead of 380 ppm.

	OR, 13%, NOT 50%, OF ACO2 REMAINS IN THE ATMOSPHERE
#	Parameter	Value	Source
1	G0	762	AR4 Fig. 7.3, p515 C cycle
2	g(2003)	133.4	AR4 Fig. 2.3, p. 138
3	δ13C0	-7.592�	AR4 Fig. 2.3, p. 138
4	r0	0.011028894	Eq. (7)
5	δ13Cf	-29.4�	Battle, et al.
6	rf	0.010789151	Eq. (7)
7	k	13.1%	Eq. (12)
8	r(2003)	0.011023529	Eq. (7)
9	δ13C	-8.080�	AR4 Fig. 2.3, p. 138
10	δ13Cfinal	-8.080�	AR4 Fig. 2.3, p. 138

The mass balance will agree with the measurements if the atmosphere retains much less than 50% of the estimated emissions. The necessary retention is 13.1%, a factor again of 3.8 less than supplied by IPCC.

These results apply to IPCC's model by which it adds anthropogenic processes to natural processes assumed to be in balance. Instead, the mass flow model must include the temperature-dependent flux of CO2 to and from the ocean to modulate the natural exchanges of heat and gases. The CO2 flux between the atmosphere and the ocean is between 90 and 100 GtC of CO2 per year. This circulation removes lightened atmospheric CO2, replacing it with heavier CO2 along many paths, some accumulated several decades to over 1000 years in the past. The mass flow model is a mechanical tapped delay line.

B. Custom Carved Hockey Sticks.

From IPCC's standpoint, its hockey stick constructions are too good not to be true. They support its logic of the unprecedented proving causation. Of course, and lest any further misunderstanding arise, the proposition is neither logical nor a theory. Unprecedented establishes nothing but odds, and proof is for mathematics and logic, not science. The Sun does not account for the hockey sticks, those IPCC artifacts of data mishandling, whether intentional or a consequence of IPCC's admitted "low level of scientific understanding."

IPCC urges emergency action from world government to stop global warming, because the present climate is already the warmest in over a millennium and is increasing rapidly due to man�s CO2 emissions. Founded in 1988 specifically to advance climate science, later interpreted by IPCC as a charter to promote AGW, IPCC's crowning achievement is featured as the 1^st graph of the 1^st section of its Third Assessment Report, Climate Change 2001, Summary for Policymakers. TAR, p. 3. It is the history of global average temperatures for the past millennium, the Hockey Stick. The Handle of the Stick is the benign, even cooling, past, and the Blade is the unprecedented rapid rise in the 20th Century.

Michael E. Mann, lead author of Mann et al. (1999), the credited source of the Hockey Stick, was � coincidentally -- a Lead Author of TAR Chapter 2.

IPCC here practices not science but hucksterism. It put proxy in quotes as if to say "not that there's anything wrong with that"; or, everyone knows proxy temperature data are as good as thermometer readings. What should be set off in quotes are data and calibrated. IPCC unabashedly includes in calibration shifting records to coincide (throwing away the mean), and scaling them to match (wrecking the variance and standard deviation), all for visual effects and never quantified. What IPCC produces are no longer data records, but illusions.

The next piece of the AGW story is corroboration of the link between temperature increasing and the mechanism by which man has caused it. The evidence comprises the chemical hockey sticks in the next figure for Policymakers in the Third Assessment Report:

For its Fourth Assessment Report, IPCC polished the gas story for policymakers, adding multiple ice core records, presumably "calibrated":

IPCC above made chemical hockey sticks by cutting the records in half (20 kyr reduced to 10 kyr) in the parent chart, Figure 6.4, below:

The gray bars, representing the past 650 kyr, are from the extended Vostok ice cores, where the measured CO2 concentration ranged between 180 and 300 ppm. TAR, Figure 3.2(a), p. 201. If IPCC had shown the full reconstructed range, the gray bar for CO2 would have exceeded 6,000 ppm. Id., Figure 3.2(f). These data contradict the unprecedented argument. Measured gas concentrations and proxy estimates have undergone peak-to-peak changes at least as great as those determined from modern instruments. And considering the long averaging time of ice cores, here admitted by IPCC to be in the range of 20 to 200 years, the hockey stick story loses any validity.

Furthermore with respect to CO2, ice core samples accumulate inside the cold water oceanic sinks at the headwaters for the thermohaline circulation, while the MLO record, "the master time series documenting the changing composition of the atmosphere", above, sits in the plume of the dominating outgassing of CO2 from the Eastern Equatorial Pacific (EEP). Changes in the mean atmospheric concentration of CO2 will measure higher at MLO than they do in polar regions because of this source-sink bias. Instead of estimating the bias, IPCC assumed it away with its well-mixed conjecture.

C. Well-mixed confusion.

IPCC's well-mixed notion is its determination made so that gas concentrations, especially CO2 from Mauna Loa, will be global, and certainly not regional distortions from sources or sinks. It arises out of its assumption that the surface layer of the ocean is in equilibrium, causing the chemical equations of equilibrium to create a bottleneck to the dissolution of CO2. This novel back pressure on solubility causes CO2 to accumulate in the atmosphere until space is made to dissolve it in the ocean. IPCC makes the solubility pump stand in queue behind the extremely slow sequestering processes known as the organic carbon pump and the CaCO3 counter pump, collectively the biological pumps. See AR4, Figure 7.10, p. 530. To rely on the surface layer being in equilibrium, IPCC has to be blind to turbulence, currents, circulations, life processes, wave actions, wind, entrained air, and heat transfer. Nor does the Panel offer any explanation for the natural flux of CO2 proceeding apace at the rate of about 100 GtonsC/year under different solubility parameters than those it presumes for manmade CO2.

Nevertheless, under IPCC's equilibrium model for the surface layer, anthropogenic CO2 is slow to be dissolved, and when it is, it shifts the surface layer to a more acidic, less environmentally friendly, state. This is another plus for the alarmists. And while ACO2 is being slowly absorbed, atmospheric circulations cause it to become well-mixed. Then being well-mixed, IPCC can calibrate every CO2 measuring station in the network to agree with MLO. And as discussed at length in the Journal, MLO sits in the plume of the ocean's massive Eastern Equatorial Pacific outgassing, ripe to be modulated by slow changes in the lie of the plume from seasonal winds or shifts accompanying changes in processes like the Southern Oscillation.

Unfortunately for the AGW movement, IPCC contradicts its well-mixed assumption in its reports:

And of course IPCC's speculation about a northern sink for CO2 is confirmed in its Takahashi diagram. AR4, Figure 7.8, p. 523; see discussion and recalibration, On Why CO2 Is Known Not To Have Accumulated in the Atmosphere, etc., Journal, Figures 1 and 1A. That sink turns into the headwaters of the thermohaline circulation, where the water, dense from the cold and heavy with a full load of CO2, plunges to depths, emerging to outgas a millennium later mostly in the Eastern Equatorial Pacific. Carbon dioxide cannot be well-mixed while exhibiting gradients, lumpiness, circulations, and patterns.

D. The Fallacy of Unprecedented.

IPCC's hockey stick charts comprise its "unprecedented argument" by which it hopes to persuade the public that a catastrophic global warming, caused by man through his greenhouse gas emissions, is underway. It floats on a raft of logical fallacies. What is unprecedented in these records, the brief blades of the hockey sticks, cannot be said never to have happened, but only that they have yet to be sampled among a small number of widely spaced ice core samples, or are yet to be estimated from highly uncertain proxy reductions. What is unprecedented in our observations does not establish impossibilities before man. Having gases and temperatures appear to rise together is a correlation, and elementary in science is that correlation does not imply cause and effect. In the theory of causation, the lack of a correlation rules out a cause and effect, and a lagging process cannot be the cause of a leading process. Graphical appearances are not measures of correlation, much less estimates of leads and lags.

While man must be ruled out as a factor in climate pre-1750, that adds no weight to the hypothesis that he must be a cause of change post-1750. Could be does not imply is. Accepting a hypothesis by eliminating some but not all competing plausible hypothesis is an error in causality, sometimes known as the hidden factor fallacy. Man cannot be accepted as the cause unless the Sun is ruled out, and the Sun cannot be ruled out based on a constant albedo model until albedo is shown not to vary in some significant, dependent way, directly or indirectly, on solar activity.

E. Gas Hockey Stick Misunderstanding.

As a matter of physics, ice core gas records would not connect to modern instrument counterparts. The paleo records and especially the modern records are variable, but the measured variability between the two should differ by a factor of 6,000 or more. In the modern methods, technicians collect gas in a flask by sealing a sample from a continuous flow in a matter of one minute in the manual mode, or less. Ice core data are open to the air for a period reportedly as brief as 20 years, but more frequently cited to be on the order of 70 years to a millennium or two. The air in the snow has to be compressed from the weight of the snow above into firn, and then the firn compressed and frozen into ice before it can be measured in ice cores.

The time to closure depends on the rate of snow fall and other parameters, and varies by site. One authority puts the time at 20 years to 600 years (Kohler, et al. (2006), p. 528), and another puts it at more than 2000 years in central Antarctica (Readinger (2006), p. 8).

The minimum close off period of 20 years is over 10 million minutes, and the variability in standard deviations is proportional to the square root of the relative sample size. Consequently, ice core data should have one three-thousandth, and taking Bender's Δage to be the close-off period, perhaps as little as one sixty-thousandth the variability evident in the modern record. Of course, the air before close off is not well circulated and close-off is a process of slowly decreasing porosity. Regardless, ice core data are the measure of very long term averages, while modern instrument records are relatively instantaneous. Ice core processes are an extensive low pass filter mechanism that introduces two effects: a lag, and a variance reduction. Investigators routinely take into account the lag as the ice age, but have yet to take into account the variance reduction. What is witnessed in the modern readings over a half to one-and-a-half centuries is an event that, if repeated, would be lost in the noise of ice core data.

Either the modern records all coincidentally match the multi-decade averages at the start, or someone has doctored the records to make matches where none exists. Of course if the concentrations of all these gases undergoes an increase from the same cause beginning 350 to 250 years ago, for example as from the Sun, then the records might have fortuitously merged somewhere around 1750 to 1850. However, that, too, would defeat the model that man is causing the increases.

F. Temperature Hockey Stick Fraud

The hockey stick temperature reduction met with controversy at its outset in 1998, and it now enjoys a complicated history all its own. A few times, investigators have declared it dead from one fatal disease or another, but its author, Michael Mann, has emphatically proclaimed its death to be greatly exaggerated. Contrary to the opinion of several observers, Mann denies that IPCC discarded the Hockey Stick reconstruction in its Fourth Assessment Report, but instead expanded upon it.

On 11/26/09, Mann told Daily Kos that "Mike's Nature trick" to "Hide the decline" in the purloined CRU email was a reference to the "divergence problem", namely that tree-ring data ran opposite to instrument data after 1960. This, he says, arose in work by Keith Briffa, and that he (Mann) was "not directly associated with" it. On 12/4/04 Mann had claimed a dozen reductions support his Hockey Stick, but to the contrary on 2/5/07 that the other reductions "show no similarity to each other".

Steve McIntyre provides an analysis of those emails, and a chronology of the events leading to IPCC's acceptance and publication of the Hockey Stick. See especially "IPCC and the 'Trick'", 12/10/09. http://climateaudit.org/2009/12/10/ipcc-and-the-trick/ and the links from there. McIntyre also shows evidence he uncovered in the CRU documents of a specific proxy decline that the authors deleted from one of files. "The Deleted Portion of the Briffa Reconstruction", 11/26/09. McIntyre's approach is prospective. Relying on the emails, he shows signs of an agreement to commit fraud by altering data to fit the doctrine. His trail of evidence includes cuttings and insertions of data, but not the publication that completes the act.

A number of critics have written about a now infamous "fudge factor", a comment naming a piece of code in a program intended for proxy reductions and discovered in the appropriated CRU documents. This little subroutine is not a filter to smooth data objectively, but instead is a ramp that exaggerates 20th century temperatures from tree-ring studies so that they look more like the instrument record. This by any standards is a fraud. It has met with two related but different responses from IPCC supporters. First is that the section of code is "commented out", meaning that it is tagged to prevent execution at run time. However, the same code without tags also appears among the CRU documents.

The second criticism is the more important. It is a facile denial that the program with the fudge factor was ever used in published results. If true, the code could amount to no more than a scientific experiment, a normal what-if analysis aiding the investigator in understanding the behavior of tree-ring reductions. If true, it would also be a complete defense against a legal charge of conspiracy where the law requires an overt act in furtherance of the agreement.

Whatever the nature of the agreement, whether by a specific piece of computer code, or simply collective acknowledgement that someone is going to jigger the data, this paper examines the published reports for evidence of the overt act. The Journal complements McIntyre's prospective analysis, adding a retrospective or forensic view to discover from the Reports what IPCC did publish as data.

Michael E. Mann was one of eight lead authors to Chapter 2, "Observed Climate Variability and Change", of IPCC's Third Assessment Report, Climate Change 2001. This is the section that reported his 1999 Hockey Stick reconstruction for the past 1000 years. See Figure 33, above. Mann's reconstruction appears again in the Fourth Assessment Report, buried in a dozen other traces, now extending back 1300 years:

IPCC defends its reconstructions as follows:

IPCC said,

But when Mann's Hockey Stick reconstruction (TAR Figure 2.20, p. 134) came under criticism (AR4 �6.6.1.1 What Do Reconstructions Based on Palaeoclimatic Proxies Show?, p. 466), IPCC retained it, but buried in the spaghetti graph of 11 other reconstructions as if those reconstructions validated Mann's. Why didn't IPCC follow Mann's "notable advance" by creating a single, super multi-proxy reconstruction out of the 11 others? Here's how that appears as an average with equal weights:

Should these proxy data actually measure a Medieval Warm Period, honors would be due the investigators for a scientific breakthrough. IPCC treats the MWP (and for that matter the Little Ice Age (LIA), as well) as anecdotal, or even apocryphal, referring to it in quotation marks, "the 'Medieval Warm Period'", and as the "so-called Medieval Warm Period" (AR4 �6.6.1.1, p. 466). IPCC credits Lamb (1965) for coining the phrase MWP, then describes his work as lacking precision, predating formal statistical methods, and based on evidence difficult to interpret. AR4 Box 6.4: Hemispheric Temperatures in the 'Medieval Warm Period', p. 468. It concludes,

However, IPCC describes the multi-proxy reconstructions as containing data from "terrestrial (tree ring, ice core and historical documentary indicator[s]) and marine (coral)" sources, "calibrated against dominant patterns of 20th century global surface temperature", including boreholes, in one instance using "largely independent data". TAR, �2.3.2.2 Multi-proxy synthesis of recent temperature change, p. 133. With respect to the MWP, the historical documentary indicators are not quantitative. Consequently, to the extent that historical indicators of the MWP influenced the multi-proxy reconstructions, the results would be contaminated by investigator subjectivity.

The concept of a proxy seems easily understood, but difficult to define. IPCC says a proxy is a measurement by which the value of a parameter is inferred through a model.

The failure of a reconstruction might be due to arbitrary weights the investigator assigned to the various proxy sources, or perhaps to his calibration method. IPCC doesn't provide enough information to reproduce its results.

IPCC says,

IPCC investigators forced these dozen reconstructions to overlie one another by mean shifting and variance scaling. Since IPCC offers these traces as reconstructions of the same temperature from the same time period, the reconstructions should share patterns. In particular they should exhibit a pattern related to temperature as well as to other, confounding patterns related to processing.

The construction of synthetic records reveals and helps identify patterns due to signal, noise, and processing. Here is an example of two such records:

Low pass filtering of each synthetic record is next, as occurs in most measuring. Sensing energy or matter requires a collection time, even to count events. The filter applied is the elementary single pole filter, called an alpha-filter with α = 0.93. It is a causal filter. At this point, the bandwidth of the filter is relevant, but not its shape. The result is shown in the next figure.

Correlation, and in particular the cross-correlation function, would be a standard statistical technique for measuring how well such proxies match one another, and hence how well they might represent the temperature they are supposed to measure. Raw records are not available, and IPCC's smoothing causes the cross-correlation function to be masked by the dominant effects of the smoothing filter.

Another of an abundance of techniques is analysis of pairwise behavior beginning with a graph known as a scatter diagram. It is useful where two or more records rely a common parameter, such as time or space, and rely in a way to yield coincident samples. Then cross-plotting one record against the other produces the diagram.

IV. Signal Analysis

A. Synthetic Signal Analysis

Analysis of a pair of synthetic signals with known characteristics helps calibrate the method.

In the next scatter diagram, the same two synthetic signals in noise passed through identical low-pass filters. Low-pass filtering might be applied by the investigator to improve the signal to noise ratio, but it is also a natural consequence of measurement and of real objects. The collection time for instruments is on the order of one minute, for tree rings about one year, and for ice core records, a couple of decades to over a millennium.

Next the two records received 41-point Gaussian filtering.

B. Real Signal Analysis

The results of the synthetic signal analysis provide an understanding of the real signals. Next is the scatter diagram for Mann's Hockey Stick compared to the long record of Mann & Jones, 2003, as published in the Fourth Assessment Report.

After about 1910, the loopiness all but vanishes, and the pattern switches from incoherent to coherent. The red dots are still visible, now shown connected. Coming out of the last loop, the records jointly head for the future high temperatures of the instrument record. IPCC's records are preposterously prescient. The dots move further apart showing an acceleration in anticipation of the future. This acceleration was evident as an end effect in the synthetic signal analysis, but in the real records it is a transition effect, suggesting separate Gaussian filtering of the proxy data before appending the instrument record.

The comparison of the reconstructions reveals two distinct patterns. The first before 1910 agrees with a low signal to noise ratio model, where the signal might be temperature or a shared data source. The second after 1910 is the instrument record, somewhat altered, but unlike the tree-ring reductions from the preceding 12 centuries.

The transition is from a very low signal-to-noise ratio of about -14 dB to a extremely high signal-to-noise ratio that measures about +30 dB. The data processing was substantially different before 1910 than it was afterwards, suggesting a switch from proxy calculations to fudging or dry-labbing.

1. Strong correlation.

The strong correlation of 71.3% could be an artifact of the data processing, or the result of a common data source shared by the two reductions. The common cause might be proxy records used by both Mann et al. (1999) and Mann & Jones (2003) in their reductions. Or the common cause might actually be Earth's global average surface temperature, as IPCC claims. Two are possible, and the third is improbable.

The data records 1999 and 2003 records above are typical of all the records in that the investigators scaled and shifted the multi-proxy reductions to blend smoothly into the appended instrument record. Having the proxy part match the instrument part in amplitude and slope where they meet is a highly improbable coincidence. It is not credible once, much less for all 12 multi-proxy reconstructions. The investigators or later editors shifted and scaled every multi-proxy record causing each to be correlated with the instrument record.

As a usual consequence of measurement, the last of the proxy records should have a step to the beginning of the instrument record, and a discontinuity in slope. Scaling would serve to minimize the slope change, and shifting, the step. The trick is to shift and scale so that the discontinuities are small enough to be erased by a smoothing filter mild enough to preserve some character to the reconstructions.

The fact that the graphs become coherent, beginning in anticipation of the future, is a result of investigator filtering with what is called an unrealizable filter. A realizable or causal filter is one that does not look into the future, and so could be applied to data in real time. Neither tree-rings nor climate can anticipate the future.

2. Non-causal filtering

IPCC frequently uses n-point filters symmetric about the instant position, and hence produces an unrealizable result. For its temperature records in Figure 6-10(b) (Figure 37, above), it applied "a Gaussian-weighted filter to remove fluctuations on time scales less than 30 years". AR4, Figure 6-10 caption, p. 467. IPCC describes two smoothing filters with weights of 1-2-3-2-1 and 1-6-19-42-71-96-106-96-71-42-19-6-1. AR4, Appendix 3.A, p. 336. The problematic fudge factor filter discovered in the e-mails is not directly of this class, so is not implicated. Some of IPCC's filters are obviously symmetric, and without introducing a rather meaningless lag, they bring future data into the present to change what was measured. They are mostly of subjective value, good for marketing to policymakers, but not for science.

Real world patterns are the essence of scientific discovery, and often produce some of the most productive scientific models. But so are events, rare occurrences that break expected patterns, like distorted sunspot cycles or switching of the thermohaline circulation. Smoothing can reveal real world patterns, or produce them where none of any significance exists. Smoothing may aid discovery of events, but may destroy their traces in the measurements. Modeling the causes and behavior of stock market crashes is an exercise in futility if the stock index is overly smoothed.

Causation by reason, and almost by definition, rules out the future. Scientific models embody everything known about cause and effect. A valid scientific model and science can rely neither on the supernatural nor the crystal ball.

3. Pairwise comparisons of temperature reconstructions.

The scatter diagram above between Mann's Hockey Stick and Mann & Jones 2003 reconstruction is typical of all 12 reconstructions, whether compared with Mann & Jones long record, or with the short instrument record. (The 2005 reconstruction by Moberg et al. is somewhat exceptional.) These two sets of 13 graphs, which includes the instrument record, are shown in the following 26 figures drawn to the same scale to accommodate the largest variability in the set.

4. Comparisons of temperature reconstructions to instrumental record.

Finally for reference, here are comparisons of each of IPCC's reconstructions compared with the instrument record of the last century and a half.

All 12 reconstructions are coherent with the temperature instrument record, indicating that the reconstructions are biased by inclusion of the instrumental record. Any information the tree-ring proxy reconstructions might have produced about Earth's temperature was destroyed when the means were shifted and the variance scaled. What is left in the spaghetti graph is indistinguishable from a millennium of noise smoothly blended into the modern record of the last 150 years or so.

In trying to defend Mann's Hockey Stick, IPCC has provided evidence that proxy reconstructions relying on tree ring data provide no valid temperature data.

V. CONCLUSIONS

A. Solar Radiation Pattern Matches Earth's Temperature

The imprint of the Sun is on Earth's climate. The signal is unusually strong among the class of all climate signals, matching the entire record of global average surface temperature based on data from instruments. The imprinted signal is not visible in the broadband, Total Solar Irradiation model, but can be seen by filtering, much as spectral analysis reveals significant sinusoidal frequency components. And what is significant depends not on the source � the Sun -- but on the receiver � Earth. Moreover, because the problem is thermodynamic, and the medium, heat, has capacity but not inertia, temperature will not contain natural frequencies to resonate with a source.

B. Earth's Natural Responses Dictate What Is Important from the Sun.

The ocean dominates the natural climate processes on Earth, and its three dimensional currents have the effect of storing and releasing energy and gases after a number of finite delays. According to this model, Earth should selectively reinforce and suppress finite delays within the structure of solar radiation. Application of the most elementary finite-time filter, the fixed time, running trend, reveals a pair of components of solar radiation, one major (S₁₃₄) and one minor (S₄₆), that combine linearly in the ratio of 5:1 to match Earth's temperature history as known by instruments.

C. Signal Selection & Amplification.

For the conclusions reached in this paper, the energy in S₁₃₄ is sufficient by itself. However, it is not sufficient as a radiative forcing were it to be received at the surface of Earth to have a measurable affect on climate. However, the accuracy of the model in matching Earth's temperature record indicates that an amplifying process must operate on solar radiation.

1. Albedo Amplification

The obvious choice for the amplifier of solar radiation is cloud albedo, neglected in GCMs, but easily shown to be the most powerful temperature feedback in Earth's climate. Furthermore, the conventional model for Earth's radiation budget contains open-loop processes known to affect the extent of cloud cover, and hence cloud albedo. Most significant among these processes is atmospheric absorption of incoming solar radiation. This absorption affects the temperature lapse rate to warm the atmosphere, but heretofore climate studies did not apply this short wave effect to the extent of cloud cover. The model advanced for Earth's variable response to solar radiation is empirical, but requiring few coefficients to match the long records of temperature on Earth to appropriately filtered solar energy.

2. Fast & slow albedo feedback

In consideration of all the processes and observations, cloud albedo must be modeled with both a fast reaction, positive feedback, and a slow reaction, negative feedback. The fast reaction is a positive feedback with respect to solar insolation, amplifying variations in solar radiation as it imparts energy to Earth's surface, including the surface layer of the ocean. The slow reaction is a negative feedback with respect to surface temperature. It operates through the increase in humidity that accompanies a rise especially in ocean surface layer temperature. The fast reaction amplifies TSI, while at the same time the slow reaction mitigates warming, including that from the TSI it amplified.

Not recognized by IPCC is that feedback exists with respect to a flow variable. This fact is not even recognizable within IPCC's radiative forcing paradigm because it has no flow variables. Consequently, IPCC models feedback loops as correlations between variables (e.g., TAR Figures 7.4, 7.6, 7.7, & 7.8, pps. 439, 445, 448, & 454 respectively), and not as confluences in energy, mass, or information flow between sources external and internal to the system. Cloud albedo fast response operates on short wave radiation directly through the parameter of the temperature at cloud level. Cloud albedo slow response operates on surface temperature indirectly through the parameter of humidity, especially as released by the ocean.

D. Climate Change Is Not Anthropogenic.

On the scale of the instrumental record of Earth's surface temperature over the last 160 years, humans have had no effect, and the Solar Global Warming model advanced here would predict none. To the extent that IPCC might presume that human activities have altered Earth's temperature record, the effect is imaginary, absent some sentient extraterrestrial force that managed to keep the Sun synchronized with Earth's average surface temperature.

IPCC claims to have evidence of the fingerprint of man on Earthly gas and temperature processes are unsubstantiated. Each has a basis in graphical trickery. Two of these claims falsely demonstrate relationships known mathematically: the rate of CO2 increase compared to the rate of O2 decrease, and the rate of fossil fuel emissions compared to the rate of decrease in the isotopic weight of atmospheric CO2 based on mass balance principles. Other claims rely on investigator-manufactured data from ancient records blended into modern records, where the former are averages by a process requiring a year to centuries, while the latter are relatively instantaneous. The records requiring a year are tree ring reductions, while the others are measurements from ice cores that average gas concentrations over a range of couple of decades to a millennium and a half.

E. Greenhouse Gases Do Not Cause Climate Change.

Just as the Earth's temperature record following the Sun eliminates humans from the climate equation, so is the fate of the greenhouse effect. To the extent that the greenhouse effect is correlated with Earth's temperature history, the cause must link from the Sun to the greenhouse gases. The alternative is the silly proposition that solar radiation variations might be caused by changes in greenhouse gas concentrations.

F. AGW post-mortem.

AGW is dead. Here are some topics for the post-mortem. Forensic analysis of proxy reductions for correlations caused by data set sharing, and subjective smoothing into the instrument record. Forensic analysis of whether proxy temperature reductions have any validity. An � priori model for the tapped delay line representation of climate based on ocean currents. An � priori model for cloudiness as it responds to short wave radiation.

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© 2010 JAGlassman. All rights reserved.

INTRODUCTION

Global surface temperature is the essence of global climate, and by definition the only sensible measure of Global Warming. Global temperature is influenced in part by the solar wind, according to a chain of connections admitted by the IPCC in its Third Assessment Report (TAR). The Consensus on Climate, which finds its voice in the IPCC reports, recognizes (1) a dependence of global temperature on clouds, (2) a positive correlation between clouds and galactic cosmic rays, and (3) the physics of cosmic ray flux modulation by the solar wind. Nonetheless, the Consensus refuses to adopt this three part model into its climate models for lack of evidence. Climate Change 2001, ¶6.11.2.2, pp. 384-385. More importantly, the TAR never uses the record of solar wind measurements, a record longer than the record of temperature from thermometers.

According to the Consensus, Earth’s surface temperature is strongly affected by the El Niño/Southern Oscillation (ENSO), so named because of the strong indication of El Niño events in the Southern Oscillation Index (SOI), a continuous variable. The Consensus is convinced that ENSO causes human suffering, and that on some time scales it is the cause of the strongest natural fluctuations in the climate. Climate Change 2001, Box 4, p. 52. However, the Global Circulation Models, formerly known as Global Climate Models but more aptly named Global Catastrophe Models, (GCMs), have yet to demonstrate sufficient accuracy in replicating ENSO to even answer the pointed question posed by the Consensus: whether anthropogenic greenhouse gases cause a positive feedback by precipitating warming El Niño events. Climate Change 2001, p. 151; ¶7.6.5, pp. 453-455. The SOI sample record is substantial, but the TAR uses it merely to remark on its variability and to label the El Niño events for qualitative discussion.

These issues are well-suited to ordinary signal analysis of the three time series because the method can recognize signals at the threshold of detectability. It can, among other things, locate events in the record, and measure the correlation and lead or lag between temperature and the other parameters, all key to model building. That analysis, not reported in the IPCC and apparently never addressed by the Consensus, is initiated here for what it reveals, and as background for upcoming climate studies.

DATA SOURCES

Records are available on-line of monthly measurements of the Temperature anomaly, the Southern Oscillation Index, and Solar Wind Index.

Temperature anomaly

The Temperature anomaly is the subject of several reductions by the IPCC (e.g., Fourth Assessment Report, Summary for Policy Makers, p. 14, Fig. 5; Climate Change 2001, Fig. 2.7c, p. 114. See also http://svs.gsfc.nasa.gov/vis/a000000/a001000/a001008/a001008_pre.jpg), including the infamous reduction for the Northern Hemisphere (Climate Change 2001, Fig. 2.20, p. 134) known derisively outside the IPCC reports as the Hockey Stick reconstruction. The phrase solar wind appears just once in the TAR, and that is in the title of a reference about cloud creation. However, the TAR uses not a single datum from the solar wind database. The Fourth Assessment Report also mentions the solar wind, but again just once, and that is to say that the effects of solar wind fluctuations are ambiguous. Id., ¶2.7.1.3, p. 192.

Global temperature data are available from January, 1880. http://data.giss.nasa.gov/gistemp/tabledata/GLB.Ts.txt. (see also ftp://ftp.ncdc.noaa.gov/pub/data/anomalies/monthly.land_and_ocean.90S.90N.df_1901-2000mean.dat.) The global temperature as reported by the IPCC extracted from Figure 2.7(c) is shown in Figure 1. The report states without elaboration that the data are an “optimum average”.

Figure 1

IPCC Data Distribution Center

Southern Oscillation Index

The available Southern Oscillation Index (SOI) data, designated “aa”, begin January, 1876. ftp://ftp.bom.gov.au/anon/home/ncc/www/sco/soi/soiplaintext.html. {Begin rev. 7/10/07} The Third Assessment Report charts them in Figure 7.9 after subtracting the average for the first 100 years. A copy is Figure 2, below. The offset by the average has little effect; it is trivial because by design, the Index is nominally zero. {End rev. 7/10/07}

Figure 2

Solar Wind Index