Multiscale Soil Investigations: Physical Concepts And Mathematical Techniques

Soil variability has often been considered to be composed of “functional” (explained) variations plus random fl uctuations or noise. However, the distinction between these two components is scale dependent because increasing the scale of observation almost always reveals structure in the noise (Burrough, 1983). Soils can be seen as the result of spatial variation operating over several scales, indicating that factors infl uencing spatial variability differ with scale. Th is observation points to variability as a key soil attribute that should be studied

Predicting microbial water quality with models: Over-arching questions for managing risk in agricultural catchments

The application of models to predict concentrations of faecal indicator organisms (FIOs) in environmental systems plays an important role for guiding decision-making associated with the management of microbial water quality. In recent years there has been an increasing demand by policy-makers for models to help inform FIO dynamics in order to prioritise efforts for environmental and human-health protection. However, given the limited evidence-base on which FIO models are built relative to other agricultural pollutants (e.g. nutrients) it is imperative that the end-user expectations of FIO models are appropriately managed. In response, this commentary highlights four over-arching questions associated with: (i) model purpose; (ii) modelling approach; (iii) data availability; and (iv) model application, that must be considered as part of good practice prior to the deployment of any modelling approach to predict FIO behaviour in catchment systems. A series of short and longer-term research priorities are proposed in response to these questions in order to promote better model deployment in the field of catchment microbial dynamics

Super-diffusive Transport Processes in Porous Media

The basic assumption of models for the transport of contaminants through soil is that the movements of solute particles are characterized by the Brownian motion. However, the complexity of pore space in natural porous media makes the hypothesis of Brownian motion far too restrictive in some situations. Therefore, alternative models have been proposed. One of the models, many times encountered in hydrology, is based in fractional differential equations, which is a one-dimensional fractional advection diffusion equation where the usual second-order derivative gives place to a fractional derivative of order α, with 1 < α ≤ 2. When a fractional derivative replaces the second-order derivative in a diffusion or dispersion model, it leads to anomalous diffusion, also called super-diffusion. We derive analytical solutions for the fractional advection diffusion equation with different initial and boundary conditions. Additionally, we analyze how the fractional parameter α affects the behavior of the solutions

Predicting microbial water quality with models: Over-arching questions for managing risk in agricultural catchments

The application of models to predict concentrations of faecal indicator organisms (FIOs) in environmental systems plays an important role for guiding decision-making associated with the management of microbial water quality. In recent years there has been an increasing demand by policy-makers for models to help inform FIO dynamics in order to prioritise efforts for environmental and human-health protection. However, given the limited evidence-base on which FIO models are built relative to other agricultural pollutants (e.g. nutrients) it is imperative that the end-user expectations of FIO models are appropriately managed. In response, this commentary highlights four over-arching questions associated with: (i) model purpose; (ii) modelling approach; (iii) data availability; and (iv) model application, that must be considered as part of good practice prior to the deployment of any modelling approach to predict FIO behaviour in catchment systems. A series of short and longer-term research priorities are proposed in response to these questions in order to promote better model deployment in the field of catchment microbial dynamics

Can a Species Keep Pace with a Shifting Climate?

Consider a patch of favorable habitat surrounded by unfavorable habitat and assume that due to a shifting climate, the patch moves with a fixed speed in a one-dimensional universe. Let the patch be inhabited by a population of individuals that reproduce, disperse, and die. Will the population persist? How does the answer depend on the length of the patch, the speed of movement of the patch, the net population growth rate under constant conditions, and the mobility of the individuals? We will answer these questions in the context of a simple dynamic profile model that incorporates climate shift, population dynamics, and migration. The model takes the form of a growth-diffusion equation. We first consider a special case and derive an explicit condition by glueing phase portraits. Then we establish a strict qualitative dichotomy for a large class of models by way of rigorous PDE methods, in particular the maximum principle. The results show that mobility can both reduce and enhance the ability to track climate change that a narrow range can severely reduce this ability and that population range and total population size can both increase and decrease under a moving climate. It is also shown that range shift may be easier to detect at the expanding front, simply because it is considerably steeper than the retreating back

Effects of branching spatial structure and life history on the asymptotic growth rate of a population

Author Posting. © The Author(s), 2009. This is the author's version of the work. It is posted here by permission of Springer for personal use, not for redistribution. The definitive version was published in Theoretical Ecology 3 (2010): 137-152, doi:10.1007/s12080-009-0058-0.The dendritic structure of a river network creates directional dispersal and a hierarchical arrangement of habitats. These two features have important consequences for the ecological dynamics of species living within the network.We apply matrix population models to a stage-structured population in a network of habitat patches connected in a dendritic arrangement. By considering a range of life histories and dispersal patterns, both constant in time and seasonal, we illustrate how spatial structure, directional dispersal, survival, and reproduction interact to determine population growth rate and distribution. We investigate the sensitivity of the asymptotic growth rate to the demographic parameters of the model, the system size, and the connections between the patches. Although some general patterns emerge, we find that a species’ mode of reproduction and dispersal are quite important in its response to changes in its life history parameters or in the spatial structure. The framework we use here can be customized to incorporate a wide range of demographic and dispersal scenarios.Funding for this work came from the James S. McDonnell Foundation (EEG, HJL, WFF). MGN was supported by grants from the National Science Foundation (CMG-0530830, OCE-0326734, ATM-0428122)

Development and analysis of the Soil Water Infiltration Global database.

In this paper, we present and analyze a novel global database of soil infiltration measurements, the Soil Water Infiltration Global (SWIG) database. In total, 5023 infiltration curves were collected across all continents in the SWIG database. These data were either provided and quality checked by the scientists who performed the experiments or they were digitized from published articles. Data from 54 different countries were included in the database with major contributions from Iran, China, and the USA. In addition to its extensive geographical coverage, the collected infiltration curves cover research from 1976 to late 2017. Basic information on measurement location and method, soil properties, and land use was gathered along with the infiltration data, making the database valuable for the development of pedotransfer functions (PTFs) for estimating soil hydraulic properties, for the evaluation of infiltration measurement methods, and for developing and validating infiltration models. Soil textural information (clay, silt, and sand content) is available for 3842 out of 5023 infiltration measurements (~76%) covering nearly all soil USDA textural classes except for the sandy clay and silt classes. Information on land use is available for 76% of the experimental sites with agricultural land use as the dominant type (~40%). We are convinced that the SWIG database will allow for a better parameterization of the infiltration process in land surface models and for testing infiltration models. All collected data and related soil characteristics are provided online in *.xlsx and *.csv formats for reference, and we add a disclaimer that the database is for public domain use only and can be copied freely by referencing it. Supplementary data are available at https://doi.org/10.1594/PANGAEA.885492 (Rahmati et al., 2018). Data quality assessment is strongly advised prior to any use of this database. Finally, we would like to encourage scientists to extend and update the SWIG database by uploading new data to it