Estimating Population Attribute Values in a Table: “Get Me Started in” Iterative Proportional Fitting

Iterative proportional fitting (IPF) is a technique that can be used to adjust a distribution reported in one data set by totals reported in others. IPF is used to revise tables of data where the information is incomplete, inaccurate, outdated, or a sample. Although widely applied, the IPF methodology is rarely presented in a way that is accessible to nonexpert users. This article fills that gap through discussion of how to operationalize the method and argues that IPF is an accessible and transparent tool that can be applied to a range of data situations in population geography and demography. It offers three case study examples where IPF has been applied to geographical data problems; the data and algorithms are made available to users as supplementary material.     

Collapse‐induced fluidization structures in the Lower Cretaceous Athabasca Oil Sands Deposit,Western Canada

Unique vertical fluidization structures from the Lower Cretaceous Athabasca Oil Sands Deposit in Western Canada are described. The multi‐metre long structures resulted from ascending Devonian karst aquifer waters injected into the overlying unconsolidated sands of the McMurray Formation (Aptian). The dissolution removal of 100–200 m of Middle Devonian salt beds caused the collapse and fragmentation of the 200 m of Upper Devonian limestones underlying the Cretaceous sands. Hypogene karst aquifer waters fingered upwards along the faults and fractures. Disintegrated muddy wall rock sourced hydroplastic mud flows along fractures in the limestone beds below the floor of the central Bitumount Trough. These dykes widened and lengthened collapse‐induced Upper Devonian fault blocks that differentially subsided due to salt dissolution. Conduits plugged by these mud flows diverted over‐pressured aquifer waters upwards along remaining open pipes, some of which vented on the trough floor. Aquifer waters injected into the McMurray sand and mud beds accumulated on the trough floor generated several types of collapse‐induced fluidization structures: (1) stronger aquifer flows mobilized sands into tens‐of‐metres high sand dykes consisting of multiple vertical pipes of fluidized sand contorted around and intertwined with fragmented muddy wall rock; (2) smaller aquifer jets resulted in 1–2 m high sand‐rich pillars on the trough floor; and (3) narrower high‐pressure jets flowed muddy waters along multi‐metre long, 3–5 cm wide, vertical pipes that cross‐cut and wrapped around fragmented in situ beds. The velocity gradient between these narrow but multi‐metre long water pipe flows and the ambient velocity in the surrounding sediments caused water infiltration to radiate outwards. This plugged porosity along the outer wall of the pipe, diminished drainage into the wall rock, and stabilized concentric growth ring depositions along the length of the pipe. These pipe fills appear as unique striped ribbon fabrics when viewed in longitudinal section.     

Dependence of inferred magnetic sector structure upon geomagnetic and solar activity

Inferred solar sector polarity given by the AC index of Svalgaard, has been intensively studied as a single time series and as a time series correlated with geomagnetic and solar activity. Power auto-spectra of the AC index yield a highly significant harmonic series with fundamental at 27 days period and possessing clear harmonics up to the sixth; and a very prominent peak at a period of 1 yr. The 27 day harmonic series clearly indicates the solar control of the index while the 1-yr period might be taken as confirmation of the work of Rosenberg and Coleman to the effect that the sector pattern observed on Earth depends upon Earth's heliographic latitude which has a 1-yr period.Cross correlation analysis and superposed epoch analysis are used to show that sectors inferred to be positive or away are associated with low geomagnetic and solar activity whereas sectors inferred to be negative or toward exhibit significantly enhanced geomagnetic and solar activity.These results appear to be in conflict with superposed epoch analyses by Wilcox and Ness using satellite observed sector polarities which showed that geomagnetic activity increased after passage of a sector boundary, independent of the nature, whether + ? or ? + of the boundary.The conflict is resolved here by noting that the yearly correlation coefficient, at zero time lag, between inferred sector structure and geomagnetic activity averaged about 0·5 for the year 1927–1958, dropped to low values by 1960, recovered by 1962 and then dropped sharply in 1963 by an order to magnitude; the correlation has remained essentially zero ever since. Thus, the satellite results, all obtained post 1963, would not show increased activity during either sector sign.The results cast doubt upon the accuracy of the early ‘inferred’ sector polarities because it is felt that the only simple explanation for the strange behavior of the correlation coefficient lies in some artifact of the data.     

The interrelationship between cosmic dust and the microwave background

Attention is given to the radiation of microwaves by charged dust in space. Presently-used particle distributions do not restrict the presence in space of large numbers of small (r<10^–6 cm) silicate grains, but it is shown that such densities (10^–25–10^–26 g cm^–3) of small grains would produce a microwave background with an energy density of the same order of magnitude as the energy density of the (presumed) cosmological 3 K background. Limits set by the isotropy of the latter are: (HI clouds)10^–26, (Galactic plane)10^–30, (Halo)10^–32, (Local Group)10^–34 g cm^–3. These limits imply that either there is a cutoff in particle distributions atr10^–6 cm, or that the density of silicate grains in space has been generally overestimated, or that cosmic rays have broken up a lot of grains so that they now form a population of grains of very small size (10^–7 cm) which are difficult to detect by conventional methods. One way to look for the latter population is by studying expected distortions of the 3 K spectrum to the short wavelength side of the portion hitherto observed (grains may have a size distribution able to give an approximate black-body curve for radiation from larger grains of 10^–6 cm size), and by testing the effective energy density of the 3 K field in other galaxies.     

Untersuchung über die Wirkungsweise des Solarigraphen Moll-Gorczynski

Zusammenfassung Die Wirkungsweise des zur Messung der Himmels- und der Globalstrahlung verwendeten SolarigraphenMoll-Gorczynski wird theoretisch und experimentell untersucht. Die Wärmebilanz derMollschen Thermosäule wird aufgestellt und gezeigt, welche Größen in den Eichfaktor eingehen und wie die Temperatur- und Intensitätsabhängigkeit des Eichfaktors zustande kommt. Der Einfluß der Thomson-, Joule- und Peltier-Wärmen erweist sich als praktisch vernachlässigbar. Der Temperaturkoeffizient des Eichfaktors beträgt zirka 0,2% pro Grad C. Auf Grund der spektralen Verteilung der terrestrischen Sonnenstrahlung und der Himmelsstrahlung läßt sich zeigen, daß die durch die Absorptions- und Reflexionsverluste in den Deckgläsern bedingten Empfindlichkeitsänderungen höchstens ±0,4% betragen. Es wird untersucht, welche Fehler entstehen, wenn bei der Berechnung der Strahlungswerte die Abhängigkeit des Eichfaktors von der Winkelhöhe der einfallenden Strahlung nicht berücksichtigt wird. Auf Grund der vonReitz beobachteten Abweichungen vom Cosinusgesetz ergibt sich in den Himmelsstrahlungswerten bei gleichmäßig strahlendem Himmel ein Fehler von zirka 0,5%, während der Fehler in den Werten der Globalstrahlung für Sonnenhöhen über 15° höchstens 2,6% beträgt. Die durch die Eichmethode, die Schaltung und das Registrierinstrument bedingten Fehler werden diskutiert und der Einfluß der langwelligen Ausstrahlung der Glashüllen (Nullpunktsdepression) untersucht. In einer zusammenfassenden Fehlerdiskussion wird die Genauigkeit der unter Berücksichtigung der Temperatur- und Intensitätsabhängigkeit des Eichfaktors berechneten Strahlungswerte auf ±1 bis 2% geschätzt; die je nach Instrument verschieden großen Fehler, welche durch die Abweichungen vom Cosinusgesetz erzeugt werden, sind in dieser Abschätzung nicht inbegriffen.

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Summary The author examines by experiments and in the theory the principle of working of the solarigraphMoll-Gorczynski, used for measuring the sky radiation and the global radiation of sun and sky. He develops the heat-balance ofMoll's thermopile and shows the factors entering into the calibration factor and in which manner this factor is depending on temperature and intensity of radiation. The influence of the Thomson-, Joule-, and Peltier-effects can practically be neglected. The temperature coefficient of the calibration factor is about 0,2%/°C. As regards the spectral distribution of solar and sky radiation it can be shown that the modifications of sensitivity as caused by the loss by absorption and reflexion in the cover-glasses of the solarigraph amount to ±0,4% in the maximum. Furthermore the errors are examined which occur with the calculation of the radiation intensities if the dependency of the calibration factor from the angle of height of incoming radiation is not taken into consideration. Due to the deviations from the law of cosine as observed byReitz, it can be concluded that the error of the values of the sky radiation (with uniform sky) is of about 0,5%, whereas the error of the values of the global radiation for solar altitudes above 15° is 2,6% in the maximum. The errors resulting from the calibration method, the electric connexions and the recording instrument are discussed, as well as the influence of outgoing long-wave radiation of the cover-glasses (zero depression). In a summarizing discussion the accuracy of the calculated values of radiation is estimated at ±1 to 2%, taken into consideration the dependency from the temperature and intensity of the calibration factor. The errors caused by the deviations from the cosine-law varying according to the instrument, are not included in this estimation.

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Résumé On étudie du point de vue théorique et pratique le fonctionnement du solarigrapheMoll-Gorczynski utilisé pour la mesure du rayonnement céleste et global. On établit le bilan thermique de la pile thermoélectrique deMoll et on montre quels sont les grandeurs intervenant dans le facteur d'étalonnage et comment ce facteur dépend de la température et de l'intensité du rayonnement. L'influence des effets Thomson, Joule et Peltier se révèle pratiquement négligeable. Le coefficient de température du facteur d'étalonnage s'élève à env. 0,2% par degré centigrade. Considérant la distribution spectrale du rayonnement solaire et céleste, on peut montrer que les variations de sensibilité dues aux pertes par absorption et réflexion dans les enveloppes de verre protectrices s'élèvent à ±0,4%. On recherche quelles sont les erreurs commises en négligeant l'effet sur le facteur d'étalonnage de l'angle d'incidence des rayons lors du calcul des valeurs de rayonnement. Se fondant sur les écarts à la loi du cosinus observés parReitz, on constate que l'erreur pour la valeur du rayonnement céleste (ciel uniforme) est d'environ 0,5%, et que celle du rayonnement global pour des hauteurs solaires supérieures à 15° est au plus de 2,6%. On discute les erreurs résultant de la méthode d'étalonnage, du montage du circuit électrique et de l'enregistreur lui-même, ainsi que l'effet du rayonnement propre à grande longuer d'onde des écrans de verre (dépression du zéro). II résulte de toute la discussion des erreurs possibles que l'exactitude des valeurs calculées du rayonnement, en tenant compte de l'influence de la température et de l'intensité sur le facteur de sensibilité, est estimée à ±1 à 2%; les erreurs, variables suivant les appareils, provenant des écarts à la loi du cosinus ne sont pas prises en considération dans ce chiffre.

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Mit 20 Textabbildungen.     

Beitrag zur Frage einer solaren Steuerung geophysikalischer Vorgänge

Zusammenfassung Die starke Abhängigkeit der zeitlichen Folge erdmagnetischer Störungen und Erdbehen von einer Periode 34 ^d .19 wird an den Diagrammen der Figg. 1–5 veranschaulicht. Nach der harmonischen Analyse tritt die Periodenwelle in zwei bestimmten, um 180° gegeneinander versetzten Phasenlagen auf. Ein Vergleich der Amplituden mit derSchusterschen Expektanz lässt erkennen, dass ein Walten des Zufalls hierbei praktisch ausgeschlossen sein sollte. Die Periode ist identisch mit der vom Verfasser früher abgeleiteten Rotationsdauer 34 ^d .19 eines hypothetischen Sonnenkerns. Auch Perioden der Form treten auf ( _p =Umlaufszeit der einzelnen Planeten), wie hier nur an einem Beispiel für den Merkur (Fig. 7) gezeigt wird.

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Summary It is shown in the diagrams Figg. 1–5, that the temporal sequences of terrestrial magnetic storms and earthquakes are largely dependent from a period of 34.19 days. The harmonic analyse demonstrates, that there are two waves of this period with a difference of 180° between them. The comparison of the amplitudes of waves with the expectance as defined byA. Schuster shows, that the period should be a reality. This period is identical with the period of 34.19 days for the rotation of an hypothetical sun-core, discovered earlier by the author. It is illustrated only at the example of the planet Mercury (Fig. 7), that there exist also periods of the form: ( _p =period of the revolution of the single planet).

     

Sur l'influence de la loi de répartition des densités à l'intérieur de la Terre dans les variations luni-solaires de la gravité en un point

Résumé Les observations des variations luni-solaires de la gravité en divers points du globe ne donnent pas des valuers très concordantes pour le facteur lié au module de rigidité de la Terre. On démontre ici que la répartition croissante des densités vers le centre de la Terre a pour conséquence d'amplifier encore les effets dus à l'élasticité. En adoptant la répartition deBullen, on aurait =1+0.244h>1, (h étant le premier nombre deLove). En outre une relation simple lie les facteurs et (déviations de la verticale). La valuer deh déduite de telles observations ne peut conduire directement à une valeur significative du module de rigidité du globe car il faut encore tenir compte des variations de la période et de l'amplitude du mouvement chandlérien du pôle.

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Summary Observations of luni-solar variations of gravity at various points of the Earth do not give values in agreement for the factor bound to the Earth's modulus of rigidity. It is shown here that the law of increasing of density toward the center of the Earth emphasizes the effect of elasticity: following the law ofBullen, we should have =1+0.244h>1, (h is the firstLove's number). Further, there is a simple relation between the factors and (deviations of the vertical). The value ofh deduced from such observations could not give directly a significative value of the modulus of rigidity because we must take into account the variations of period and amplitude of the chandlerian motion of the pole.

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Riassunto Le osservazioni delle variazioni luni-solari della gravità in diversi punti della Terra non dànno valori concordanti per il fattore legato al modulo di rigidità del Globo. Si dimostra che la ripartizione crescente della densità verso il centro della Terra ha per conseguenza di amplificare ancora gli effetti dell'elasticità; adottando la legge diBullen, abbiamo =1+0.244h>1, (h essendo il primo numero diLove). Inoltre, una semplice relazione lega i fattori e (deviazioni della verticale). Il valore dih dedotto da tali osservazioni non può condurre ad un valore significativo del modulo di rigidità del Globo poiché bisogna considerare anche le variazioni del periodo e dell'ampiezza del moto polare diChandler.