Power law or power flaw?

Since its introduction by Svensson in 1959, the power law curve y = ax^b (where x and y are horizontal and vertical direction, respectively) has been widely used in morphological analysis of glacial trough cross-profiles. The numerical constants a and b are obtained by a linear regression analysis of the logarithmic form of the power law curve (ln y = ln a + b ln x). The value b then gives a measure for the form of the cross-section. However, over the years this form of the power law has endured a lot of criticism. This criticism is well founded, since this particular form of the power law is not suitable for curve fitting in morphological analyses. In this paper a general power law is proposed, of the form y − y₀ = a|x − x₀|^b (where x₀, y₀ are the coordinates of the origin of the cross-profile). A unique and unbiased solution for this equation is obtained with a general least-squares method, thereby minimizing the error between the cross-profile data and the curve, and not between the logarithmic transform of the data and its regression line. This provides a robust way to characterize trough cross-section forms. © 1998 John Wiley & Sons, Ltd.     

Morphometric Analysis on the Size, Shape and Areal Distribution of Glacial Cirques in the Maritime Alps (Western French-Italian Alps)

The morphometry of 432 glacial cirques in the Maritime Alps (Western French‐Italian Alps), studied over several years of fieldwork, was analysed with the use of a geographical information system. Some of the parameters automatically evaluated from digital elevation models required an objective and relatively new definition. In particular, cirque length was measured along a line that, from the threshold midpoint, splits the cirque into two equivalent surfaces; cirque width was automatically drawn as the longest line inscribed in the cirque and perpendicular to the length line. Significant correlations were found among the different factors and parameters analysed. In particular, cirque shape analysis showed that cirques develop allometrically in the three dimensions, i.e. more in length and width than in altitudinal range. Nevertheless cirques of the Maritime Alps have a regular, almost circular shape (mean L/W value = 1.07). The correlations among length, width and area are all very high (r²= 0.8–0.9). In terms of size, cirques show a wide range in area from 0.06 to 5.2 km² with a mean value of 0.4 km². The largest cirques are found on SSW‐facing slopes and at high elevations. Small cirques can be found at all altitudes but all those at high elevation are part of compound cirques at the main head valleys. Most cirques (37%) are characterized by a northern aspect; NE and SW are also frequent directions.     

Glaciers,rock avalanches and the ‘buzzsaw’ in cirque development: Why mountain cirques are of mainly glacial origin

It has been proposed that most cirques are source-area depressions of large, deep-seated rock-slope failures. Yet the close relation between cirques and climate is convincing evidence of the dominance of glacial erosion, rather than rock-slope failure, in mountain cirque development and distribution. Cirque floor altitudes have a lower limit that varies with snowfall by 1000 m or more between windward and leeward sides of mountain systems. Glaciation levels and equilibrium line altitudes implied by cirques vary in parallel with those for modern glaciers. Cirques are often found mainly on the poleward or leeward slopes of individual mountain ranges, as are modern small glaciers (because of solar radiation and wind effects on ablation and accumulation). Most rock-slope failures (RSFs: rock slides, rock avalanches and gravitational deformations) do not involve the deep-seated rotational movement that would produce a cirque form. Although some deep-seated RSFs with arcuate head scars may be confused with cirques, identification as a glacial cirque is more confident as the floor is longer, wider and more gently sloping. Some scars from major RSFs may resemble poor or moderately developed cirques, but tend to have steeper floors, to be more scattered and closely related to geology, whereas glacial cirques develop on all rock types. Deep-seated RSFs high on slopes can be associated with seismic shaking, but cirques develop without relation to seismicity. Degree of cirque development can be related to duration of exposure to glaciation. Often RSFs are found adjacent to cirques, or in glacial transfluences; only a proportion are well situated to develop into glacial cirques. Valley-head cirques are continued down-valley by glacial troughs. The ‘overdeepening’ (rock basins with reversed slopes) found in a large minority of cirques is not due to rock avalanching, fluvial or periglacial erosion. The RSF proposal should therefore be rejected in favour of the traditional glacial explanation, without any nivation stage being necessary. Rock-slope failure is one of several possible ways of initiating hollows for glacier accumulation, as well as an ancillary process of cirque extension or widening through collapse of glacially oversteepened slopes. Headward extension of adjacent cirques on a ridge leads to displacement of the divide, sometimes by 2 km or more, lowering ridge and summit altitudes and producing the ‘glacial buzzsaw’ effect. Where a relatively lower snowline has led to cirque erosion on all sides of a mountain, cirque intersection lowers summits further. The buzzsaw hypothesis is not applicable, however, where remnants of a preglacial summit surface survive. © 2020 John Wiley & Sons, Ltd.     

New formulae for estimating lava flow volumes at Mt. Etna Volcano, Sicily

 A new data set of Etna lava flows erupted since 1868 has been compiled from eight topographic maps of the volcano published at intervals since then. Volumes of 59 flows or groups of flows were measured from topographic difference maps. Most of these volumes are likely to be considerably more accurate than those published previously. We cut the number of flow volumes down to 25 by selecting those examples for which the volume of an individual eruption could be derived with the highest accuracy. This refined data set was searched for high correlations between flow volume and more directly measurable parameters. Only two parameters showed a correlation coefficient of 70% or greater: planimetric flow area A (70%) and duration of the eruption D (79%). If only short duration (<18 days) flows were used, flow length cubed, L³, had a correlation coefficient of 98%. Using combinations of measured parameters, much more significant correlations with volume were found. Dh had a correlation coefficient of 90% (h is the hydrostatic head of magma above the vent), and  , 92% (where W is mean width and E is the degree of topographic enclosure), and a combination of the two , 97%. These latter formulae were used to derive volumes of all eruptions back to 1868 to compare with those from the complete data set. Values determined from the formulae were, on average, lower by 16% (Dh), 7% (, and 19% . Received: 30 November 1998 / Accepted: 20 June 1999     

Dynamics of salt marsh margins are related to their three-dimensional functional form

The three-dimensional configuration of sedimentary landforms in intertidal environments represents a major control on regional hydrodynamics. It modulates the location and magnitude of forces exerted by tidal currents and waves on the landform itself and on engineered infrastructure such as sea walls or coastal defences. Furthermore, the effect is reflexive, with the landforms representing an integrated, long-term response to the forces exerted on them. There is a strong reciprocal linkage between form and process (morphodynamics) in the coastal zone which is significantly lagged and poorly understood in the case of cohesive, vegetated sediments in the intertidal zone. A method is presented that links the geometric properties of the tidal flat–salt marsh interface to the history and potential future evolution of that interface. A novel quantitative classification scheme that is capable of separating marsh margins based on their functional form is developed and is applied to demonstrate that relationships exist between landform configuration and morphological evolution across a regional extent. This provides evidence of a spatially variable balance between self-organized and external controls on morphodynamic evolution and the first quantitative basis for a quick assessment procedure for likely future dynamism. © 2019 John Wiley & Sons, Ltd.     

Phase Changes in Linear Solar-Terrestrial Relationships and a Review of the Electrification Hypothesis

It appears that relatively strong linear relationships between solar activity and various weather phenomena are forthcoming only if the analyses relate to specific solar periods or are con ducted for specific geographic locations. Solar periods in this instance are defined according to the amplitude of the 11-year sunspot cycle. The sign for correlation coefficients between weather ele ments under investigation and solar activity often change according to solar amplitude. However, these phase changes may not weaken arguments in favor of sun-weather hypotheses.

Atmospheric teleconnection provides a logical explanation for phase changes over space within specific time frames, and variations in solar-amplitude relate to reversals in phase with space held constant. Previous research of large pressure systems in the tropics and mid-latitudes as well as re gional variations in annual precipitation outlined in this research indicate that a change in sign for the linear sun-weather relationship occurred between 1930 and 1940. Between 1930 and 1940, the amplitude of the solar cycle also changed. The incredibly complex nature of the climatic change equation along with the lack of an explicit physical link between solar-activity and the lower atmo sphere are serious deterrents for broad acceptance of a solar-weather connection. It is suggested, however, that recent research on a possible electrical stimulus might go far in establishing the solar hypothesis as a credible one.     

Predicting oxygen in small estuaries of the Baltic Sea: a comparative approach

Coastal eutrophication, manifested as hypoxia and anoxia, is a global problem. Only a few empirical models, however, exist to predict bottom oxygen concentration and percentage saturation from nutrient load or morphometry in coastal waters, which are successfully used to predict phytoplankton biomass both in lakes and in estuaries. Furthermore, hardly any empirical models exist to predict bottom oxygen from land-use. A data set was compiled for 19 estuaries in the northern Baltic Sea, which included oxygen concentration and percentage saturation, water chemistry, estuary morphometry, and land-use characteristics. In regression analyses, bottom oxygen was predicted both as a function of the percentage of watershed under agriculture and of mean depth. These models accounted for ca. 55% of the variation in oxygen. Additionally, oxygen was linked to fetch (diameter of the area in the direction of the prevailing wind), which accounted for 30% of the variation in oxygen. This suggests that shallow Finnish estuaries are wind-sensitive. In ‘pits’ (sub-thermocline waters of deep basins), near-bottom total nitrogen strongly correlated with oxygen percentage saturation (R²=0.81). Neither chlorophyll a, total phosphorus nor nutrient loading explained oxygen variation in entire estuaries or in ‘pits’, probably mainly due to annual sedimentation/sediment–water flux dynamics. On the basis of the results of cross-validation, the models have general applicability among Finnish estuaries.