Comparison of derivative-free optimization methods for groundwater supply and hydraulic capture community problems

Management decisions involving groundwater supply and remediation often rely on optimization techniques to determine an effective strategy. We introduce several derivative-free sampling methods for solving constrained optimization problems that have not yet been considered in this field, and we include a genetic algorithm for completeness. Two well-documented community problems are used for illustration purposes: a groundwater supply problem and a hydraulic capture problem. The community problems were found to be challenging applications due to the objective functions being nonsmooth, nonlinear, and having many local minima. Because the results were found to be sensitive to initial iterates for some methods, guidance is provided in selecting initial iterates for these problems that improve the likelihood of achieving significant reductions in the objective function to be minimized. In addition, we suggest some potentially fruitful areas for future research.     

Aeolian activity at a giant sandstone weathering pit in arid south‐central Utah

Aeolian abrasional, depositional and deflational features indicate exceptionally strong southwesterly winds in a giant sandstone weathering pit in Grand Staircase Escalante Monument, about 22 km southeast of Escalante, Utah. The 60 m wide, 5–20 m deep pit has developed near the summit of a broad, barren 160‐m‐high dome on the Lower Jurassic Navajo Sandstone. Unlike other giant weathering pits (10–30 m diameter) in the region, the bedrock floor of this pit is undulatory, and there is a cylindrical, 10‐m‐high rock pedestal in the centre of the pit. An active dune surrounds the central pedestal and at times has as much as 8 m of local relief. The dune shifts considerably over brief (<1 year) periods of time. Fine‐grained (<250 µm) dunal sand on the pit floor is periodically removed by deflation, leaving coarser sand (>250 µm) trapped in the pit. Dunal sand is typically derived from external sources (other than the pit walls and floor). Centimetre to metre‐scale abrasional features such as grooves, flutes and dedos occur on the bedrock walls and floor of the pit. These dedos and other streamlined aeolian sculpted host‐rock features occur in clusters and typically form in the lee of iron concretions. The dedos are similar to the controversial stalked blueberries on Mars. Above the western rim of the pit there is a 29‐m‐long, 5‐m‐wide aeolian groove with a fluted bedrock floor. A 1·2‐km‐long bedrock valley descends to the southwest from the pit and groove, amplifying southwesterly winds. Data from hand‐held anemometers suggest that southwesterly winds can be accelerated 200–300 per cent or more by local topography. Copyright © 2008 John Wiley and Sons, Ltd.     

Nekton Use of Flooded Salt Marsh and an Assessment of Intertidal Creek Pools as Low-Tide Refuges

Patterns of nekton occurrence on the salt marsh surface at high tide and in an adjacent intertidal creek pool at low tide were used to investigate movements of nekton in an intertidal basin. Paired collections were made in North Inlet estuary, SC on 67 dates over 9 years. Comparisons of high- and low-tide total abundance indicated that what remained in the creek pool at low tide was representative of the nekton on the flooded marsh. Of the 64 taxa collected, the same 8 species ranked in the top 10 in both the high- and low-tide collections. Abundances of most resident species were positively correlated with the area of marsh flooded, but mummichog (Fundulus heteroclitus), the most abundant resident, was not. Abundances of young-of-the-year transient species were not related to the extent of tidal flooding. Some transient species used the flooded marsh but did not occupy the pool at low tide, and others found in the pool did not use the marsh. Differences in abundance, biomass, and length between the marsh and pool collections indicated differences in the tendency of species and life stages to retreat downstream of the pool to the subtidal channel. Proportionately more of the nekton that were present on the flooded marsh left the intertidal basin when large changes in temperature and salinity occurred between high and low tides. More transients left the basin following higher tides, but more residents did not. The results demonstrate a wide range of taxonomic and ontogenetic patterns among nekton using intertidal salt marsh basins and the underappreciated importance of intertidal creek pools as alternative low-tide refuges.     

Ecological criteria, participant preferences and location models: A GIS approach toward ATV trail planning

This paper presents a geographic information system (GIS)-based method for recreational trail location for all-terrain vehicles (ATVs) which considers environmental factors, as well as rider preferences for trail attributes. The method utilizes the Least-Cost Path algorithm within a GIS framework to optimize trail location. The trail location algorithm considered trail impacts and benefits associated with water bodies, slope, land ownership, noise, trail separation, views, and rider preferences for vegetation types and loop trails. Alternative trails were generated to highlight the influence of different preferences for trail attributes and to demonstrate the capabilities of the Least-Cost Path algorithm as applied to trail location. The method shows promise for use in generating ATV trails, as well as other types of recreational trails, for consideration in recreational planning and analysis.     

Effects of nitrate and phosphate on growth and C2 toxin productivity of Alexandrium tamarense CI01 in culture

Growth and C2 toxin productivity of a marine dinoflagellate, Alexandrium tamarense CI01 (ATCI01) which predominantly produces C2 toxin, were studied in unialgal batch cultures to optimize the concentrations of nitrate and phosphate for a maximal toxin yield. A range of start concentrations of the two major nutrients was determined in which algal growth was proportional to the nutrient concentrations used. The highest concentrations of nitrate and phosphate in this growth-enhancing range were 264 and 20 μM, respectively. In this concentration range, the C2 toxin yield (μg/l) and cellular toxin content (Qt, fmole per cell) reached a maximum at the lowest end of phosphate (5 μM) and the highest end of nitrate (264 μM). Further increase in the supply of nitrate continued to enhance the toxin yield. Our results indicated that the growth and toxin productivity of this algal strain in batch cultures had distinctly different optimal ranges of nitrate and phosphate concentrations. For a maximum toxin yield, a judicious use of phosphate under a nitrate-replete condition is called for.     

Use of a particle-tracking model for predicting entrainment at power plants on the Hudson River

A major assumption of the Empirical Transport Model (ETM), widely adopted by both electric utilities and regulatory agencies for estimating the effects of entrainment mortality on fish populations in estuaries, is that the fraction of ichthyoplankton entrained varies only in response to changes in water withdrawals, not to changes in freshwater flow. We evaluated this assumption using a particle-tracking model to estimmate the probability of entrainment at power plants on the Hudson River during low and high freshwater flow periods and comparing those probabilities with estimates calculated from the ETM. We found that freshwater flow had a profound effect on the probability of entrainment. Both the number of river regions from which particles were entrained and the probabilities of entrainment for particles in those river regions differed between low-flow and high-flow periods. During high flow, particles spent less time in the grid box next to the intakes, reducing the probability of entrainment for particles released in the river region of each power plant and the average probability of entrainment across all regions at three power plants. The reduced probability of entrainment for particles released in the river regions of two power plants was offset by higher entrainment for particles upriver of these power plants. Although the average probabilities of entrainment across all river regions estimated with the particle-tracking model and the ETM were relatively similar for some power plants at high flow, low flow, or both, the probabilities for each river region differed considerably between the models. The number of river regions from which particles were entrained using the ETM was consistently undersestimated, resulting in probabilities for regions where entrainment occurred that were biased high compared with the particle-tracking model.     

Distributed velocity method of solving the convective-dispersion equation: 1. Introduction,mathematical theory,and numerical implementation

This is the first part of a two-part paper presenting a new method for treating convective-dispersive transport. The motivation for developing this technique arises from the demands of performing a risk assessment for a nuclear waste repository. These demands include computational efficiency over a relatively large range of Peclet numbers, the ability to handle chains of decaying radionuclides with rather extreme contrasts in both solution velocities and half lives, and the ability to treat leach- or solubility-limited sources. To the extent it has been tested to date, the distributed velocity method (DVM) appears to satisfy these demands. This part contains an overall introduction and presents the mathematical theory, numerical implementation, and example results.