Tests of sunspot number sequences: 3. Effects of regression procedures on the calibration of historic sunspot data

We use sunspot group observations from the Royal Greenwich Observatory (RGO) to investigate the effects of intercalibrating data from observers with different visual acuities. The tests are made by counting the number of groups RB above a variable cut-off threshold of observed total whole-spot area (uncorrected for foreshortening) to simulate what a lower acuity observer would have seen. The synthesised annual means of RB are then re-scaled to the full observed RGO group number RA using a variety of regression techniques. It is found that a very high correlation between RA and RB (rAB > 0.98) does not prevent large errors in the intercalibration (for example sunspot maximum values can be over 30 % too large even for such levels of rAB). In generating the backbone sunspot number (RBB), Svalgaard and Schatten (2015, this issue) force regression fits to pass through the scatter plot origin which generates unreliable fits (the residuals do not form a normal distribution) and causes sunspot cycle amplitudes to be exaggerated in the intercalibrated data. It is demonstrated that the use of Quantile-Quantile (“Q  Q”) plots to test for a normal distribution is a useful indicator of erroneous and misleading regression fits. Ordinary least squares linear fits, not forced to pass through the origin, are sometimes reliable (although the optimum method used is shown to be different when matching peak and average sunspot group numbers). However, other fits are only reliable if non-linear regression is used. From these results it is entirely possible that the inflation of solar cycle amplitudes in the backbone group sunspot number as one goes back in time, relative to related solar-terrestrial parameters, is entirely caused by the use of inappropriate and non-robust regression techniques to calibrate the sunspot data.

A new calibrated sunspot group series since 1749: statistics of active day fractions

Although the sunspot-number series have existed since the mid-19th century, they are still the subject of intense debate, with the largest uncertainty being related to the "calibration" of the visual acuity of individual observers in the past. Daisy-chain regression methods are applied to inter-calibrate the observers which may lead to significant bias and error accumulation. Here we present a novel method to calibrate the visual acuity of the key observers to the reference data set of Royal Greenwich Observatory sunspot groups for the period 1900-1976, using the statistics of the active-day fraction. For each observer we independently evaluate their observational thresholds [S_S] defined such that the observer is assumed to miss all of the groups with an area smaller than S_S and report all the groups larger than S_S. Next, using a Monte-Carlo method we construct, from the reference data set, a correction matrix for each observer. The correction matrices are significantly non-linear and cannot be approximated by a linear regression or proportionality. We emphasize that corrections based on a linear proportionality between annually averaged data lead to serious biases and distortions of the data. The correction matrices are applied to the original sunspot group records for each day, and finally the composite corrected series is produced for the period since 1748. The corrected series displays secular minima around 1800 (Dalton minimum) and 1900 (Gleissberg minimum), as well as the Modern grand maximum of activity in the second half of the 20th century. The uniqueness of the grand maximum is confirmed for the last 250 years. It is shown that the adoption of a linear relationship between the data of Wolf and Wolfer results in grossly inflated group numbers in the 18th and 19th centuries in some reconstructions.

Disparity-defined objects moving in depth do not elicit three-dimensional shape constancy

Observers generally fail to recover three-dimensional shape accurately from binocular disparity. Typically, depth is overestimated at near distances and underestimated at far distances [Johnston, E. B. (1991). Systematic distortions of shape from stereopsis. Vision Research, 31, 1351–1360]. A simple prediction from this is that disparity-defined objects should appear to expand in depth when moving towards the observer, and compress in depth when moving away. However, additional information is provided when an object moves from which 3D Euclidean shape can be recovered, be this through the addition of structure from motion information [Richards, W. (1985). Structure from stereo and motion. Journal of the Optical Society of America A, 2, 343–349], or the use of non-generic strategies [Todd, J. T., & Norman, J. F. (2003). The visual perception of 3-D shape from multiple cues: Are observers capable of perceiving metric structure? Perception and Psychophysics, 65, 31–47]. Here, we investigated shape constancy for objects moving in depth. We found that to be perceived as constant in shape, objects needed to contract in depth when moving toward the observer, and expand in depth when moving away, countering the effects of incorrect distance scaling (Johnston, 1991). This is a striking example of the failure of shape con- stancy, but one that is predicted if observers neither accurately estimate object distance in order to recover Euclidean shape, nor are able to base their responses on a simpler processing strategy.

A moving observer in a three-dimensional world

For many tasks, such as retrieving a previously viewed object, an observer must form a representation of the world at one location and use it at another. A world-based 3D reconstruction of the scene built up from visual information would fulfil this requirement, something computer vision now achieves with great speed and accuracy. However, I argue that it is neither easy nor necessary for the brain to do this. I discuss biologically plausible alternatives, including the possibility of avoiding 3D coordinate frames such as ego-centric and world-based representations. For example, the distance, slant and local shape of surfaces dictate the propensity of visual features to move in the image with respect to one another as the observer’s perspective changes (through movement or binocular viewing). Such propensities can be stored without the need for 3D reference frames. The problem of representing a stable scene in the face of continual head and eye movements is an appropriate starting place for understanding the goal of 3D vision, more so, I argue, than the case of a static binocular observer.