Abstract:
We report that the Atlantic Multi-Decadal Oscillation (AMO) shows the same phase-locked states of period 2 and 3 years that have been reported in many other climate indices. In addition, we find that the report by Muller, Curry et al. of an oscillation in the AMO of 9.1 years is a misinterpretation of a maximum in the Fourier spectrum.

Abstract:
There is great interest in knowing when a future El Niño will occur. Most physical models forecast the future based on climate data from the recent past—about a year. The forecasted future is also a fraction of a year. This approach to predicting the future does not use the fact that the climate system may be in a phase-locked state in which sinusoidal oscillations of 2 or 3 years are observed. These states can last many cycles. Thus, if the climate system is in a phase-locked state, one may be able to make definite statements about the future independent of physical models. Douglass, Knox, Curtiss, Geise and Ray (DKCGR) have used the fact that the climate system is presently in a phase-loxked state of period 3 years to state (December 2016) that the next El Niño episode may show a maximum at about November of 2018. We present an updated analysis and state (September 2018) that if the climate system remains in a phase-locked state of period 3 years there will be an El Niño maximum at about November 2018. If that happens, there could be another El Niño maximum at about November 2021.

Abstract:
This paper discusses why model predictions of El Niño events fail. We begin by commenting on a recent retrospective about the failed prediction of an El Niño during 1975 McPhaden et al. state that “for all the advances in seasonal forecasting over the past 40 years, the fundamental problem of skillfully predicting the development of ENSO events and their consequences still challenges the scientific community.” In a second paper McPhaden, this time alone, discusses the case of a “monster” El Niño “that failed to materialize in 2014”. Unbeknown to McPhaden, these two climate “nonevents” have already been discussed and “explained” in some details in papers that report that the climate system consists of a series of finite time segments bounded by abrupt climate shifts. These finite time segments are phase-locked to the 2^{nd} or 3^{rd} subharmonic of an annual forcing. This paper will be an updated review of these “explanations”. Additionally, we note that the climate system is presently (August 2017) in a phase-locked state of period 3 years that began in 2009 to make a qualified prediction: The next El Niño will occur during boreal winter of 2018 unless this phase-locked state terminates before then.

Abstract:
Geophysical signals N of interest are often contained in a parent signal G that also contains a seasonal signal X at a known frequency f_{X}. The general issues associated with identifying N and X and their separation from G are considered for the case where G is the Pacific sea surface temperature monthly data, SST3.4; N is the El Niño/La Niña phenomenon and the seasonal signal X is at a frequency of 1/(12 months). It is shown that the commonly used climatology method of subtracting the average seasonal values of SST3.4 to produce the widely used anomaly index Nino3.4 is shown not to remove the seasonal signal. Furthermore, it is shown that the climatology method will always fail. An alternative method is presented in which a 1/f_{X} (= 12 months) moving average filter F is applied to SST3.4 to generate an El Niño/La Niña index N_{L} that does not contain a seasonal signal. Comparison of N_{L} and Nino3.4 shows, among other things, that estimates of the relative magnitudes of El Niños from index N_{L} agree with observations but estimates from index Nino3.4 do not. These results are applicable to other geophysical measurements.

Abstract:
A recently published estimate of Earth’s global warming trend is 0.63 ± 0.28 W/m2, as calculated from ocean heat content anomaly data spanning 1993-2008. This value is not representative of the recent (2003-2008) warming/cooling rate because of a “flattening” that occurred around 2001-2002. Using only 2003-2008 data from Argo floats, we find by four different algorithms that the recent trend ranges from –0.010 to –0.161 W/m2 with a typical error bar of ±0.2 W/m2. These results fail to support the existence of a frequently-cited large positive computed radiative imbalance.

Abstract:
It was shown by Faltings and Hriljac that the N\'eron-Tate height of a point on the Jacobian of a curve can be expressed as the self-intersection of a corresponding divisor on a regular model of the curve. We make this explicit and use it to give an algorithm for computing N\'eron-Tate heights on Jacobians of hyperelliptic curves. To demonstrate the practicality of our algorithm, we illustrate it by computing N\'eron-Tate heights on Jacobians of hyperelliptic curves of genus from 1 to 9.

Abstract:
We use Arakelov theory to define a height on divisors of degree zero on a hyperelliptic curve over a global field, and show that this height has computably bounded difference from the N\'eron-Tate height of the corresponding point on the Jacobian. We give an algorithm to compute the set of points of bounded height with respect to this new height. This provides an `in principle' solution to the problem of determining the sets of points of bounded N\'eron-Tate heights on the Jacobian. We give a worked example of how to compute the bound over a global function field for several curves, of genera up to 11.

Abstract:
We investigate to what extent the theory of N\'eron models of jacobians and of abel-jacobi maps extends to relative curves over base schemes of dimension greater than 1. We give a necessary and sufficient criterion for the existence of a N\'eron model. We use this to show that, in general, N\'eron models do not exist even after making a modification or even alteration of the base. On the other hand, we show that N\'eron models do exist outside some codimension-2 locus.

Abstract:
The jacobian of the universal curve over $\mathcal{M}_{g,n}$ is an abelian scheme over $\mathcal{M}_{g,n}$. Our main result is the construction of an algebraic space $\beta\colon \tilde{\mathcal{M}}_{g,n} \rightarrow \bar{\mathcal{M}}_{g,n}$ over which this jacobian admits a N\'eron model, and such that $\beta$ is universal with respect to this property. We prove certain basic properties, for example that $\beta$ is separated, locally of finite presentation, and satisfies a certain restricted form of the valuative criterion for properness. In general, $\beta$ is not quasi-compact. We relate our construction to Caporaso's balanced Picard stack $\mathcal{P}_{d,g}$.