Complexity and non-linearity in earth surface processes - concepts, methods and applications

Complexity has long been recognized and is increasingly becoming mainstream in geomorphology. However, the relative novelty of various concepts and techniques associated to it means that ambiguity continues to surround complexity. In this commentary, we present and discuss a variety of recent contributions that have the potential to help clarify issues and advance the use of complexity in geomorphology.

The role of upper-level dynamics and surface processes for the Pakistan flood of July 2010

In July and August 2010 floods of unprecedented impact afflicted Pakistan. The floods resulted from a series of intense multi-day precipitation events in July and early August. At the same time a series of blocking anticyclones dominated the upper-level flow over western Russia and breaking waves i.e. equatorward extrusions of stratospheric high potential vorticity (PV) air formed along the downstream flank of the blocks. Previous studies suggested that these extratropical upper-level breaking waves were crucial for instigating the precipitation events in Pakistan. Here a detailed analysis is provided of the extratropical forcing of the precipitation. Piecewise PV inversion is used to quantify the extratropical upper-level forcing associated with the wave breaking and trajectories are calculated to study the pathways and source regions of the moisture that precipitated over Pakistan. Limited-area model simulations are carried out to complement the Lagrangian analysis. The precipitation events over Pakistan resulted from a combination of favourable boundary conditions with strong extratropical and monsoonal forcing factors. Above-normal sea-surface temperatures in the Indian Ocean led to an elevated lower-tropospheric moisture content. Surface monsoonal depressions ensured the transport of moist air from the ocean towards northeastern Pakistan. Along this pathway the air parcel humidity increased substantially (60–90% of precipitated moisture) via evapotranspiration from the land surface. Extratropical breaking waves influenced the surface wind field substantially by enhancing the wind component directed towards the mountains which reinforced the precipitation.

Lithium isotope constraints on crust–mantle interactions and surface processes on Mars

Lithium abundances and isotope compositions are reported for a suite of martian meteorites that span the range of petrological and geochemical types recognized to date for Mars. Samples include twenty-one bulk-rock enriched, intermediate and depleted shergottites, six nakhlites, two chassignites, the orthopyroxenite Allan Hills (ALH) 84001 and the polymict breccia Northwest Africa (NWA) 7034. Shergottites unaffected by terrestrial weathering exhibit a range in δ7Li from 2.1 to 6.2‰, similar to that reported for pristine terrestrial peridotites and unaltered mid-ocean ridge and ocean island basalts. Two chassignites have δ7Li values (4.0‰) intermediate to the shergottite range, and combined, these meteorites provide the most robust current constraints on δ7Li of the martian mantle. The polymict breccia NWA 7034 has the lowest δ7Li (−0.2‰) of all terrestrially unaltered martian meteorites measured to date and may represent an isotopically light surface end-member. The new data for NWA 7034 imply that martian crustal surface materials had both a lighter Li isotope composition and elevated Li abundance compared with their associated mantle. These findings are supported by Li data for olivine-phyric shergotitte NWA 1068, a black glass phase isolated from the Tissint meteorite fall, and some nakhlites, which all show evidence for assimilation of a low-δ7Li crustal component. The range in δ7Li for nakhlites (1.8 to 5.2‰), and co-variations with chlorine abundance, suggests crustal contamination by Cl-rich brines. The differences in Li isotope composition and abundance between the martian mantle and estimated crust are not as large as the fractionations observed for terrestrial continental crust and mantle, suggesting a difference in the styles of alteration and weathering between water-dominated processes on Earth versus possibly Cl–S-rich brines on Mars. Using high-MgO shergottites (>15 wt.% MgO) it is possible to estimate the δ7Li of Bulk Silicate Mars (BSM) to be 4.2 ± 0.9‰ (2σ). This value is at the higher end of estimates for the Bulk Silicate Earth (BSE; 3.5 ± 1.0‰, 2σ), but overlaps within uncertainty.

Modelling raindrop impact and splash erosion processes within a spatial cell: a stochastic approach

A new approach is proposed to simulate splash erosion on local soil surfaces. Without the effect of wind and other raindrops, the impact of free-falling raindrops was considered as an independent event from the stochastic viewpoint. The erosivity of a single raindrop depending on its kinetic energy was computed by an empirical relationship in which the kinetic energy was expressed as a power function of the equivalent diameter of the raindrop. An empirical linear function combining the kinetic energy and soil shear strength was used to estimate the impacted amount of soil particles by a single raindrop. Considering an ideal local soil surface with size of I m x I m, the expected number of received free-failing raindrops with different diameters per unit time was described by the combination of the raindrop size distribution function and the terminal velocity of raindrops. The total splash amount was seen as the sum of the impact amount by all raindrops in the rainfall event. The total splash amount per unit time was subdivided into three different components, including net splash amount, single impact amount and re-detachment amount. The re-detachment amount was obtained by a spatial geometric probability derived using the Poisson function in which overlapped impacted areas were considered. The net splash amount was defined as the mass of soil particles collected outside the splash dish. It was estimated by another spatial geometric probability in which the average splashed distance related to the median grain size of soil and effects of other impacted soil particles and other free-falling raindrops were considered. Splash experiments in artificial rainfall were carried out to validate the availability and accuracy of the model. Our simulated results suggested that the net splash amount and re-detachment amount were small parts of the total splash amount. Their proportions were 0.15% and 2.6%, respectively. The comparison of simulated data with measured data showed that this model could be applied to simulate the soil-splash process successfully and needed information of the rainfall intensity and original soil properties including initial bulk intensity, water content, median grain size and some empirical constants related to the soil surface shear strength, the raindrop size distribution function and the average splashed distance. Copyright (c) 2007 John Wiley & Sons, Ltd.

Isotopic Assessment of Sources of Surface Water Nitrate within the Oldman River Basin, Southern Alberta, Canada

Concentrations and isotopic compositions of NO-3 from the Oldman River (OMR) and some of its tributaries (Alberta, Canada) have been determined on a monthly basis since December 2000 to assess temporal and spatial variations of riverine NO-3 sources within the OMR basin. For the OMR sites, NO-3 -N concentrations reached up to 0.34 mg L-1, d15N-NO-3 values varied between –0.3 and +13.8‰, and d18O-NO-3 values ranged from –10.0 to +5.7‰. For the tributary sites, NO-3 -N concentrations were as high as 8.81 mg L-1, d15N-NO-3 values varied between –2.5 and +23.4‰, and d18O-NO-3 values ranged from –15.2 to +3.4‰. Tributaries in the western, relatively pristine forested part of the watershed add predominantly NO-3 to the OMR with d15N-NO-3 indicative of soil nitrification. In contrast, tributaries in the eastern agriculturally-urban-industrially-used part of the basin contribute NO-3 with d15N-NO-3 values of about +16‰ indicative of manure and/or sewage derived NO-3. This difference in d15N-NO-3 values of tributaries was found to be independent of the season, but rather indicates a spatial change in the NO-3 source, which correlates with land use changes within the OMR basin. As a consequence of tributary influx, d15N-NO-3 values in the Oldman River increased from +6‰ in the downstream direction (W to E), although [NO-3 -N] increased only moderately (generally

Response of surface horizons in an oak forest to prescribed burning

The reduction of forest floor ground cover and litter layers by prescribed fires may alter the morphology (field and micro) and physical properties of surface horizons. This study determined long-term (35 yr) changes in surface horizon bulk density, organic matter concentration and content, and morphology in response to periodic (5 yr) and annual (1 yr) prescribed fires. Soils were fine-silty, siliceous, thermic Glossic Fragiuldults, supporting mixed oak vegetation in middle Tennessee. Upper mineral soils (0- to 2-cm and 0- to 7.6-cm depths) were sampled and detailed field descriptions made. Periodic and control plots had a thin layer of Oi, Oe, and Oa horizons 5 yr after the 1993 burn, whereas on annual burn plots a 1- to 2-cm charred layer was present. Significant reductions in organic matter concentration and mean thickness of the A horizon were found from burning (A horizons thicknesses were 6.4, 4.6, and 2.9 cm in control, periodic, and annual plots, respectively). Periodic burns did not significantly alter the organic matter and bulk density of the upper 7.6 cm of mineral soil; however, annual burns did result in significantly higher bulk densities (1.01, 1.07, and 1.29 Mg m-3 in control, periodic, and annual plots, respectively) and lower organic matter concentrations and contents. Microscopic investigations confirmed that compaction was increased from annual burning. Thin sections also revealed that the granular structure of the A horizons in control and periodic plots resulted from bioterbation of macro and mesofauna, fungi, and roots. Long-term annual burning greatly affected surface soil properties, whereas periodic burning on a 5-yr cycle had only limited effects.

Dynamical instability in surface permeability characteristics of building sandstones in response to salt accumulation over time

This paper explores how the surface permeability of sandstone blocks changes over time in response to repeated salt weathering cycles. Surface permeability controls the amount of moisture and dissolved salt that can penetrate in and facilitate decay. Connected pores permit the movement of moisture (and hence soluble salts) into the stone interior, and where areas are more or less permeable soluble salts may migrate along preferred pathways at differential rates. Previous research has shown that salts can accumulate in the near-surface zone and lead to partial pore blocking which influences subsequent moisture ingress and causes rapid salt accumulation in the near-surface zone.

Two parallel salt weathering simulations were carried out on blocks of Peakmoor Sandstone of different volumes. Blocks were removed from simulations after 2, 5, 10, 20 and 60 cycles. Permeability measurements were taken for these blocks at a resolution of 20 mm, providing a grid of 100 permeability values for each surface. The geostatistical technique of ordinary kriging was applied to the data to produce a smoothed interpolation of permeability for these surfaces, and hence improve understanding of the evolution of permeability over time in response to repeated salt weathering cycles.

Results illustrate the different responses of the sandstone blocks of different volumes to repeated salt weathering cycles. In both cases, after an initial subtle decline in the permeability (reflecting pore blocking), the permeability starts to increase — reflected in a rise in mean, maximum and minimum values. However, between 10 and 20 cycles, there is a jump in the mean and range permeability of the group A block surfaces coinciding with the onset of meaningful debris release. After 60 cycles, the range of permeability in the group A block surface had increased markedly, suggesting the development of a secondary permeability. The concept of dynamic instability and divergent behaviour is applied at the scale of a single block surface, with initial small-scale differences across a surface having larger scale consequences as weathering progresses.

After cycle 10, group B blocks show a much smaller increase in mean permeability, and the range stays relatively steady — this may be explained by the capillary conditions set up by the smaller volume of the stone, allowing salts to migrate to the ‘back’ of the blocks and effectively relieving stress at the ‘front’ face.

Dinoflagellate cyst-based reconstructions of mid to late Holocene winter sea-surface temperature and productivity from an anoxic fjord in the NE Pacific Ocean

Published contemporary dinoflagellate distributional data from the NE Pacific margin and estuarine environments (n = 136) were re-analyzed using Canonical Correspondence Analysis (CCA) and partial Canonical Correspondence Analysis (pCCA). These analyses illustrated the dominant controls of winter temperature and productivity on the distribution of dinoflagellate cysts in this region. Dinoflagellate cyst-based predictive models for winter temperature and productivity were developed from the contemporary distributional data using the modern analogue technique and applied to subfossil data from two mid to late Holocene (~5500 calendar years before present–present) cores; TUL99B03 and TUL99B11, collected from Effingham Inlet, a 15 km long anoxic fjord located on the southwest coast of Vancouver Island that directly opens to the Pacific Ocean through Barkley Sound. Sedimentation within these basins largely comprises annually deposited laminated couplets, each made up of a winter deposited terrigenous layer and spring to fall deposited diatomaceous layer. The Effingham Inlet dinoflagellate cyst record provides evidence of a mid-Holocene gradual decline in winter SST, ending with the initiation of neoglacial advances in the region by ~3500 cal BP. A reconstructed Late Holocene increase in winter SST was initiated by a weakening of the California Current, which would have resulted in a warmer central gyre and more El Niño-like conditions.

Near-surface temperature cycling of stone and its implications for scales of surface deterioration

Many previous studies into internal temperature gradients within stone have assumed smooth, exponential increases and decreases in sub-surface temperatures in response, for example, to diurnal patterns of heating and cooling and these have been used to explain phenomena such as large-scale contour scaling. This high-resolution experimental study, in which a porous limestone block was subjected to alternate surface heating and cooling using an infrared lamp, demonstrates that internal temperature gradients in response to short-term environmental cycles (measured in minutes) can in fact be complex and inconsistent. Results confirm the significance of very steep temperature/stress gradients within the outer 10 mm or less of exposed stone. Below this the data indicate complex patterns of temperature reversals, the amplitudes of which are attenuated with depth and which are influenced in their intensity and location by variations in the relative duration of heating and cooling phases. It is suggested that the reversals might represent ‘interference patterns’ between incoming and outgoing thermal waves, but whatever their origin they are potentially important because they occur within the zone in which many stone decay processes, especially salt weathering, operate. These processes invariably respond to temperature and moisture fluctuations, and short-term interruptions to insolation could, for example, trigger these fluctuations on numerous occasions over a day. In particular, the reversals occur at a scale that is commensurate with decay by multiple flaking and could indicate an underlying control on this previously little-researched pattern of weathering. In the context of this publication, however, the main lesson to be learned from this study is that differing scales of behaviour require different scales of enquiry.