Was there a ‘medieval warm period’, and if so,where and when?

It has frequently been suggested that the period encompassing the ninth to the fourteenth centuries A.D. experienced a climate warmer than that prevailing around the turn of the twentieth century. This epoch has become known as theMedieval Warm Period, since it coincides with the Middle Ages in Europe. In this review a number of lines of evidence are considered, (including climatesensitive tree rings, documentary sources, and montane glaciers) in order to evaluate whether it is reasonable to conclude that climate in medieval times was, indeed, warmer than the climate of more recent times. Our review indicates that for some areas of the globe (for example, Scandinavia, China, the Sierra Nevada in California, the Canadian Rockies and Tasmania), temperatures, particularly in summer, appear to have been higher during some parts of this period than those that were to prevail until the most recent decades of the twentieth century. These warmer regional episodes were not strongly synchronous. Evidence from other regions (for example, the Southeast United States, southern Europe along the Mediterranean, and parts of South America) indicates that the climate during that time was little different to that of later times, or that warming, if it occurred, was recorded at a later time than has been assumed. Taken together, the available evidence does not support aglobal Medieval Warm Period, although more support for such a phenomenon could be drawn from high-elevation records than from low-elevation records.The available data exhibit significant decadal to century scale variability throughout the last millennium. A comparison of 30-year averages for various climate indices places recent decades in a longer term perspective.     

Enhancing the credibility of ecology: Interacting along and across hierarchical scales

A wide range of space and time scales characterize the processes and phenomena which interact to shape environmental condition and trends. Important perspectives of environmental space and time include the role of terrestrial and astronomical factors in shaping climatic change, insights to be gained from the pre-historical record, relations between disturbance and biotic responses, episodic extreme events and large-scale phenomena, cumulative impacts, fast — slow processes and memory reservoirs. Scales in physical, chemical and biological phenomena have parallels in human driving forces, societal relations and decision — making processes, and environmental scales of space and time thus have perceptual as well as physical (objective) dimensions. Scale is clearly more than just size and dimension, and there is a growing body of examples on how zooming along and across hierarchical scales can help in seeking explanation (how) and significance (why), and in revealing emergent properties. Scaling can also act as a motor for new approaches to scientific cooperation. Such evolving scales in scientific cooperation are examined in relation to three international research programmes (IBP, MAB, IGBP), to various sub-disciplines of ecology and biogeography, and to the restructuring of a largish research institute in Montpellier (France). An overall conclusion is that scaling issues may provide a stimulus to increased coherence within the science of ecology itself, and may facilitate mutually supportive links with other scientific domains and society at large.The views expressed are those of the authors and not necessarily those of the authors' employers.     

Late cretaceous and tertiary history and the dynamic crushing of cobbles, black butte area, southwestern Montana

Black Butte is an early Miocene basaltic volcanic neck that forms a prominent landmark as the highest peak of the Gravelly Range, southwestern Montana. The intrusion cuts mid-Cenozoic and older sedimentary rocks near the eastern margin of the Overthrust Belt.

After erosional removal of the Late Cretaceous Frontier Formation, quartzite-rich detritus from ultimate sources probably far to the west was deposited in the area and now forms a diamicton that rests on striated bedrock. This unit, previously interpreted as a till and as a mudflow deposit, probably represents Upper Cretaceous or lower Tertiary, syntectonic alluvial-fan sediments. These were deposited after the Gravelly Arch had begun to rise and were deformed during overthrusting from the west or possibly during mass movement as the basal part of a landslide.

Scattered cobbles of hard quartzite in the diamicton are crushed. If this crushing occurred within aggregates of coarse clasts that were momentarity in point contact with one another, it does notrequire either overthrusting or mass movement of extremely thick depositional overburden. But if a major thrust sheet did move over the diamicton, the leading edge of the Overthrust Belt must extend considerably further east of where it is currently recognized in this area.

Volcanic and volcaniclastic rocks were deposited in the area throughout much or all of Oligocene time. These include tuffaceous mudstone as much as 265 m thick that contains vertebrate fossils of Chadronian through Whitneyan age. The KAr age of biotite in an airfall tuff within this section at nearby Lion Mountain is 31.4 Ma, and the KAr age of an alkaline basaltic flow at the top of the Lion Mountain section is 30.8 Ma. These tuffaceous rocks and basalt on Lion Mountain correlate with volcaniclastics in Wyoming and as far east as Nebraska and the Dakotas.

Eruptions at Black Butte, dated previously at 22.9 Ma, begun with phreatomagmatic explosions that deposited tuff across an irregular topographic surface cut in the section of tuffaceous mudstone into which the Black Butte plug was emplaced. The alkali basalt magma differentiated to yield the relatively rare rock typetephritic phonolite during fractional crystallization and segregation in situ of potassic late liquids.

Lava flows from Black Butte and the nearby Lion Mountain volcanic center may have covered much of this part of the Gravelly Range but have been mostly removed owing to erodability of the thick blanket of mudstone on which they rested.

Removal of mudstone that contained the Black Butte intrusion involved massive slumping. Mass movement of the diamicton beneath the mudstone is occurring today as an earthflow down the west-dipping structural and topographic slope of the range.     

Crustal geomagnetic field: two-dimensional intermediate-wavelength spatial power spectra

Two-dimensional Fourier spatial power spectra of equivalent magnetization values are presented for a region that includes a large portion of the western United States. The magnetization values were determined by inversion of POGO satellite data, assuming a magnetic crust 40 km thick, and were located on an 11 × 10 array with 300 km grid spacing. The spectra appear to be in good agreement with values of the crustal geomagnetic field spatial power spectra given by McLeod and Coleman (1980) and with the crustal field model given by Serson and Hannaford (1957). The spectra show evidence of noise at low frequencies in the direction along the satellite orbital track (N-S), indicating that for this particular data set additional filtering would probably be desirable. These findings illustrate the value of two-dimensional spatial power spectra both for describing the geomagnetic field statistically and as a guide for diagnosing possible noise sources.     

Orthogonality of spherical harmonic coefficients

An essentially arbitrary function V(θ, λ) defined on the surface of a sphere can be expressed in terms of spherical harmonics $\text{V(θ, Λ) = a}\text{∑}\text{n=1}\text{∞}\text{∑}\text{m=0}\text{n}\text{p}{}^{\mathrm{m}}{}_{\mathrm{n}}\text{(cos θ) (g}{}^{\mathrm{m}}{}_{\mathrm{n}}\text{cos mΛ + h}{}^{\mathrm{m}}{}_{\mathrm{n}}\text{sin mΛ)}$ where the P_n^m are the seminormalized associated Legendre polynomials used in geomagnetism, normalized so that $\text{〈[P}{}^{\mathrm{m}}{}_{\mathrm{n}}\text{(cos θ) cos mΛ]〉}{}^2\text{=1/}\text{(2n+1)}$ The angular brackets denote an average over the sphere. The class of functions V(θ, λ) under consideration is that normally of interest in physics and engineering. If we consider an ensemble of all possible orientations of our coordinate system relative to the sphere, then the coefficients g_n^m and h_n^m will be functions of the particular coordinate system orientation, but $\text{〈:(g}{}^{\mathrm{m}}{}_{\mathrm{n}}\text{)}{}^2\text{〉) = 〈(h}{}^{\mathrm{m}}{}_{\mathrm{n}}\text{)}{}^2\text{=}\text{S}{}_{\mathrm{n}}\text{/}\text{(2n=1)}$ where $\text{S}{}_{\mathrm{n}}\text{=}\text{∑}\text{m=0}\text{n}\text{[(g}{}^{\mathrm{m}}{}_{\mathrm{n}}\text{)}{}^2\text{+ (h}{}^{\mathrm{m}}{}_{\mathrm{n}}\text{)}{}^2\text{]}$ for any orientation of the coordinate system (S_n is invariant under rotation of the coordinate system). The averages are over all orientations of the system relative to the sphere. It is also shown that 〈g^m_ng^l_p〉 = 〈h^m_nh^l_p〉 = 0 for l ≠ m or p ≠ n and 〈g^m_nh^l_p〉 = 0 fro all n, m, p, l.     

Spatial power spectra of the crustal geomagnetic field and core geomagnetic field

Lowes (1966, 1974) has introduced the function R_n defined by $\text{R}{}^{\mathrm{n}}\text{=(n + 1)}\text{∑}\text{m=0}\text{∞}\text{[(g}{}^{\mathrm{m}}{}_{\mathrm{n}}\text{)}{}^2\text{+ (h}{}^{\mathrm{m}}{}_{\mathrm{n}}\text{)}{}^2\text{]}\text{where}\text{g}{}_{\mathrm{n}}{}^{\mathrm{m}}\text{and}\text{h}{}_{\mathrm{n}}{}^{\mathrm{m}}$ are the coefficients of a spherical harmonic expansion of the scalar potential of the geomagnetic field at the Earth's surface. The mean squared value of the magnetic field B = ??V on a sphere of radius r > α is given by $\text{〈}\text{B}\text{·〉 =}\text{∑}\text{n=1}\text{∞}\text{R}{}^{\mathrm{n}}\text{(}\text{a/}\text{r}\text{)}{}^{\mathrm{2n=4}}\text{where}\text{a}$ is the Earth's radius. We refer to R_n as the spherical harmonic spatial power spectrum of the geomagnetic field.In this paper it is shown that Rⁿ = R^M_n = R^C_n where the components R_n^M due to the main (or core) field and R_n^C due to the crustal field are given approximately by $\text{R}{}^{\mathrm{M}}{}_{\mathrm{n}}\text{= [}\text{(n =1)/}\text{(n + 2)}\text{](1.142 × 10}{}^9\text{)(0.288}{}^{\mathrm{n}}\text{Λ}{}^2\text{R}{}^{\mathrm{C}}{}_{\mathrm{n}}\text{= [}\text{(n =1){[1 — exp(-n/290)]/}\text{(n/290)} 0.52 Λ}{}^2\text{where}\text{Iγ = 1 nT}$. The two components are approximately equal for n = 15.Lowes has given equations for the core and crustal field spectra. His equation for the crustal field spectrum is significantly different from the one given here. The equation given in this paper is in better agreement with data obtained on the POGO spacecraft and with data for the crustal field given by Alldredge et al. (1963).The equations for the main and crustal geomagnetic field spectra are consistent with data for the core field given by Peddie and Fabiano (1976) and data for the crustal field given by Alldredge et al. The equations are based on a statistical model that makes use of the principle of equipartition of energy and predicts the shape of both the crustal and core spectra. The model also predicts the core radius accurately. The numerical values given by the equations are not strongly dependent on the model.Equations relating average great circle power spectra of the geomagnetic field components to R_n are derived. The three field components are in the radial direction, along the great circle track, and perpendicular to the first two. These equations can, in principle, be inverted to compute the R_n for celestial bodies from average great circle power spectra of the magnetic field components.     

Geomagnetic field mapping from a satellite: Spatial power spectra of the geomagnetic field at various satellite altitudes relative to natural noise sources and instrument noise

For a low-level geomagnetic satellite survey, for which the motion of the satellite converts spatial variation into temporal variation, the limit on accuracy may well be background temporal fluctuations. The sources of the temporal fluctuations are current systems external to the Earth and include currents induced in the Earth due to these sources. The internal sources consist primarily of two components, the main geomagnetic field with sources in the Earth's core and a crustal geomagnetic field.Power spectra of the vertical geomagnetic field internal component that would be observed by a spacecraft in circular orbit at various altitudes, due to satellite motion through the spatially varying geomagnetic field, are compared to power spectra of the natural temporal fluctuations of the geomagnetic field vertical component (natural noise) and to the power spectrum for typical fluxgate magnetometer instrument noise. The natural noise is shown to be greater than this typical instrument noise over the entire frequency range for which useful measurements of the geomagnetic field may be made, for all geomagnetic latitudes and all times. Thus there would be little benefit in reducing the instrument noise below the typical value of 10^?4 gamma² Hz^?1 plus a 1/f component of 10 milligamma rms decade^?1.For a given satellite altitude, there is a maximum frequency above which the natural noise is greater than the power spectrum of the crustal geomagnetic field vertical component. Below this maximum frequency, the situation is reversed. This maximum frequency depends on geomagnetic latitude (and to a lesser extent on time of day and season of year), being lower in the auroral zone than at lower latitudes. The maximum frequency is also lower at higher satellite altitudes. The maximum frequency determines the spatial resolution obtainable on a magnetic field map. The spatial resolution (for impulses) obtainable at low latitudes for a 100-km satellite altitude (possibly achievable by tethering a small satellite at this altitude to a space vehicle at a higher altitude) is 60 km, while at the auroral zone the obtainable spatial resolution is 100 km. At the higher satellite altitude of 300 km the obtainable spatial resolution is 230 km at low latitudes and 530 km at the auroral zone. At 500-km satellite altitude, the obtainable spatial resolution is 500 km at low latitudes, while maps cannot be made at all for the auroral zone unless the data are selected for “quiet” days.For the lower satellite altitudes, greater spatial resolution can be obtained than at higher altitudes. Furthermore since the crustal geomagnetic field power spectrum is larger at lower altitudes, the relative error due to the natural noise is less than for higher altitudes.