Spatial analysis of the error in a model of soil nitrogen

Models of the dynamics of nitrogen in soil (soil-N) can be used to aid the fertilizer management of a crop. The predictions of soil-N models can be validated by comparison with observed data. Validation generally involves calculating non-spatial statistics of the observations and predictions, such as their means, their mean squared-difference, and their correlation. However, when the model predictions are spatially distributed across a landscape the model requires validation with spatial statistics. There are three reasons for this: (i) the model may be more or less successful at reproducing the variance of the observations at different spatial scales; (ii) the correlation of the predictions with the observations may be different at different spatial scales; (iii) the spatial pattern of model error may be informative. In this study we used a model, parameterized with spatially variable input information about the soil, to predict the mineral-N content of soil in an arable field, and compared the results with observed data. We validated the performance of the N model spatially with a linear mixed model of the observations and model predictions, estimated by residual maximum likelihood. This novel approach allowed us to describe the joint variation of the observations and predictions as: (i) independent random variation that occurred at a fine spatial scale; (ii) correlated random variation that occurred at a coarse spatial scale; (iii) systematic variation associated with a spatial trend. The linear mixed model revealed that, in general, the performance of the N model changed depending on the spatial scale of interest. At the scales associated with random variation, the N model underestimated the variance of the observations, and the predictions were correlated poorly with the observations. At the scale of the trend, the predictions and observations shared a common surface. The spatial pattern of the error of the N model suggested that the observations were affected by the local soil condition, but this was not accounted for by the N model. In summary, the N model would be well-suited to field-scale management of soil nitrogen, but suited poorly to management at finer spatial scales. This information was not apparent with a non-spatial validation. (c),2007 Elsevier B.V. All rights reserved.

A review and implementation of swarm pattern formation and transformation models

Purpose: The purpose of this paper is to address a classic problem – pattern formation identified by researchers in the area of swarm robotic systems – and is also motivated by the need for mathematical foundations in swarm systems. Design/methodology/approach: The work is separated out as inspirations, applications, definitions, challenges and classifications of pattern formation in swarm systems based on recent literature. Further, the work proposes a mathematical model for swarm pattern formation and transformation. Findings: A swarm pattern formation model based on mathematical foundations and macroscopic primitives is proposed. A formal definition for swarm pattern transformation and four special cases of transformation are introduced. Two general methods for transforming patterns are investigated and a comparison of the two methods is presented. The validity of the proposed models, and the feasibility of the methods investigated are confirmed on the Traer Physics and Processing environment. Originality/value: This paper helps in understanding the limitations of existing research in pattern formation and the lack of mathematical foundations for swarm systems. The mathematical model and transformation methods introduce two key concepts, namely macroscopic primitives and a mathematical model. The exercise of implementing the proposed models on physics simulator is novel.

A mathematical model, implementation and study of a swarm system

The work reported in this paper is motivated towards the development of a mathematical model for swarm systems based on macroscopic primitives. A pattern formation and transformation model is proposed. The pattern transformation model comprises two general methods for pattern transformation, namely a macroscopic transformation method and a mathematical transformation method. The problem of transformation is formally expressed and four special cases of transformation are considered. Simulations to confirm the feasibility of the proposed models and transformation methods are presented. Comparison between the two transformation methods is also reported.

A phylogenetic mixture model for detecting pattern-heterogeneity in gene sequence or character-state data

We describe a general likelihood-based 'mixture model' for inferring phylogenetic trees from gene-sequence or other character-state data. The model accommodates cases in which different sites in the alignment evolve in qualitatively distinct ways, but does not require prior knowledge of these patterns or partitioning of the data. We call this qualitative variability in the pattern of evolution across sites "pattern-heterogeneity" to distinguish it from both a homogenous process of evolution and from one characterized principally by differences in rates of evolution. We present studies to show that the model correctly retrieves the signals of pattern-heterogeneity from simulated gene-sequence data, and we apply the method to protein-coding genes and to a ribosomal 12S data set. The mixture model outperforms conventional partitioning in both these data sets. We implement the mixture model such that it can simultaneously detect rate- and pattern-heterogeneity. The model simplifies to a homogeneous model or a rate- variability model as special cases, and therefore always performs at least as well as these two approaches, and often considerably improves upon them. We make the model available within a Bayesian Markov-chain Monte Carlo framework for phylogenetic inference, as an easy-to-use computer program.

Problems with binary pattern measures for flood model evaluation

As the calibration and evaluation of flood inundation models are a prerequisite for their successful application, there is a clear need to ensure that the performance measures that quantify how well models match the available observations are fit for purpose. This paper evaluates the binary pattern performance measures that are frequently used to compare flood inundation models with observations of flood extent. This evaluation considers whether these measures are able to calibrate and evaluate model predictions in a credible and consistent way, i.e. identifying the underlying model behaviour for a number of different purposes such as comparing models of floods of different magnitudes or on different catchments. Through theoretical examples, it is shown that the binary pattern measures are not consistent for floods of different sizes, such that for the same vertical error in water level, a model of a flood of large magnitude appears to perform better than a model of a smaller magnitude flood. Further, the commonly used Critical Success Index (usually referred to as F<2 >) is biased in favour of overprediction of the flood extent, and is also biased towards correctly predicting areas of the domain with smaller topographic gradients. Consequently, it is recommended that future studies consider carefully the implications of reporting conclusions using these performance measures. Additionally, future research should consider whether a more robust and consistent analysis could be achieved by using elevation comparison methods instead.

A high-order arbitrarily unstructured finite-volume model of the global atmosphere: tests solving the shallow-water equations

Simulations of the global atmosphere for weather and climate forecasting require fast and accurate solutions and so operational models use high-order finite differences on regular structured grids. This precludes the use of local refinement; techniques allowing local refinement are either expensive (eg. high-order finite element techniques) or have reduced accuracy at changes in resolution (eg. unstructured finite-volume with linear differencing). We present solutions of the shallow-water equations for westerly flow over a mid-latitude mountain from a finite-volume model written using OpenFOAM. A second/third-order accurate differencing scheme is applied on arbitrarily unstructured meshes made up of various shapes and refinement patterns. The results are as accurate as equivalent resolution spectral methods. Using lower order differencing reduces accuracy at a refinement pattern which allows errors from refinement of the mountain to accumulate and reduces the global accuracy over a 15 day simulation. We have therefore introduced a scheme which fits a 2D cubic polynomial approximately on a stencil around each cell. Using this scheme means that refinement of the mountain improves the accuracy after a 15 day simulation. This is a more severe test of local mesh refinement for global simulations than has been presented but a realistic test if these techniques are to be used operationally. These efficient, high-order schemes may make it possible for local mesh refinement to be used by weather and climate forecast models.

An eclectic morphostratigraphic model for the sedimentary response to Holocene sea-level rise in northwest Europe

The improved empirical understanding of silt facies in Holocene coastal sequences provided by such as diatom, foraminifera, ostracode and testate amoebae analysis, combined with insights from quantitative stratigraphic and hydraulic simulations, has led to an inclusive, integrated model for the palaeogeomorphology, stratigraphy, lithofacies and biofacies of northwest European Holocene coastal lowlands in relation to sea-level behaviour. The model covers two general circumstances and is empirically supported by a range of field studies in the Holocene deposits of a number of British estuaries, particularly, the Severn. Where deposition was continuous over periods of centuries to millennia, and sea level fluctuated about a rising trend, the succession consists of repeated cycles of silt and peat lithofacies and biofacies in which series of transgressive overlaps (submergence sequences) alternate with series of regressive overlaps (emergence sequences) in association with the waxing and waning of tidal creek networks. Environmental and sea-level change are closely coupled, and equilibrium and secular pattern is of the kind represented ideally by a closed limit cycle. In the second circumstance, characteristic of unstable wetland shores and generally affecting smaller areas, coastal erosion ensures that episodes of deposition in the high intertidal zone last no more than a few centuries. The typical response is a series of regressive overlaps (emergence sequence) in erosively based high mudflat and salt-marsh silts that record, commonly as annual banding, exceptionally high deposition rates and a state of strong disequilibrium. Environmental change, including creek development, and sea-level movement are uncoupled. Only if deposition proceeds for a sufficiently long period, so that marshes mature, are equilibrium and close coupling regained. (C) 2002 Elsevier Science B.V. All rights reserved.

The interannual variability of energy transports within and over the Atlantic Ocean in a coupled climate model

To gain a new perspective on the interaction of the Atlantic Ocean and the atmosphere, the relationship between the atmospheric and oceanic meridional energy transports is studied in a version of HadCM3, the U.K. Hadley Centre's coupled climate model. The correlation structure of the energy transports in the atmosphere and Atlantic Ocean as a function of latitude, and the cross correlation between the two systems are analyzed. The processes that give rise to the correlations are then elucidated using regression analyses. In northern midlatitudes, the interannual variability of the Atlantic Ocean energy transport is dominated by Ekman processes. Anticorrelated zonal winds in the subtropics and midlatitudes, particularly associated with the North Atlantic Oscillation (NAO), drive anticorrelated meridional Ekman transports. Variability in the atmospheric energy transport is associated with changes in the stationary waves, but is only weakly related to the NAO. Nevertheless, atmospheric driving of the oceanic Ekman transports is responsible for a bipolar pattern in the correlation between the atmosphere and Atlantic Ocean energy transports. In the Tropics, the interannual variability of the Atlantic Ocean energy transport is dominated by an adjustment of the tropical ocean to coastal upwelling induced along the Venezuelan coast by a strengthening of the easterly trade winds. Variability in the atmospheric energy transport is associated with a cross-equatorial meridional overturning circulation that is only weakly associated with variability in the trade winds along the Venezuelan coast. In consequence, there is only very limited correlation between the atmosphere and Atlantic Ocean energy transports in the Tropics of HadCM3

North Atlantic Oscillation response to transient greenhouse gas forcing and the impact on European winter climate: a CMIP2 multi-model assessment

This study investigates the response of wintertime North Atlantic Oscillation (NAO) to increasing concentrations of atmospheric carbon dioxide (CO2) as simulated by 18 global coupled general circulation models that participated in phase 2 of the Coupled Model Intercomparison Project (CMIP2). NAO has been assessed in control and transient 80-year simulations produced by each model under constant forcing, and 1% per year increasing concentrations of CO2, respectively. Although generally able to simulate the main features of NAO, the majority of models overestimate the observed mean wintertime NAO index of 8 hPa by 5-10 hPa. Furthermore, none of the models, in either the control or perturbed simulations, are able to reproduce decadal trends as strong as that seen in the observed NAO index from 1970-1995. Of the 15 models able to simulate the NAO pressure dipole, 13 predict a positive increase in NAO with increasing CO2 concentrations. The magnitude of the response is generally small and highly model-dependent, which leads to large uncertainty in multi-model estimates such as the median estimate of 0.0061 +/- 0.0036 hPa per %CO2. Although an increase of 0.61 hPa in NAO for a doubling in CO2 represents only a relatively small shift of 0.18 standard deviations in the probability distribution of winter mean NAO, this can cause large relative increases in the probabilities of extreme values of NAO associated with damaging impacts. Despite the large differences in NAO responses, the models robustly predict similar statistically significant changes in winter mean temperature (warmer over most of Europe) and precipitation (an increase over Northern Europe). Although these changes present a pattern similar to that expected due to an increase in the NAO index, linear regression is used to show that the response is much greater than can be attributed to small increases in NAO. NAO trends are not the key contributor to model-predicted climate change in wintertime mean temperature and precipitation over Europe and the Mediterranean region. However, the models' inability to capture the observed decadal variability in NAO might also signify a major deficiency in their ability to simulate the NAO-related responses to climate change.

Understanding projections of sea level rise in a Hadley Centre coupled climate model

Sea level changes resulting from CO2-induced climate changes in ocean density and circulation have been investigated in a series of idealised experiments with the Hadley Centre HadCM3 AOGCM. Changes in the mass of the ocean were not included. In the global mean, salinity changes have a negligible effect compared with the thermal expansion of the ocean. Regionally, sea level changes are projected to deviate greatly from the global mean (standard deviation is 40% of the mean). Changes in surface fluxes of heat, freshwater and wind stress are all found to produce significant and distinct regional sea level changes, wind stress changes being the most important and the cause of several pronounced local features, while heat and freshwater flux changes affect large parts of the North Atlantic and Southern Ocean. Regional change is related mainly to density changes, with a relatively small contribution in mid and high latitudes from change in the barotropic circulation. Regional density change has an important contribution from redistribution of ocean heat content. In general, unlike in the global mean, the regional pattern of sea level change due to density change appears to be influenced almost as much by salinity changes as by temperature changes, often in opposition. Such compensation is particularly marked in the North Atlantic, where it is consistent with recent observed changes. We suggest that density compensation is not a property of climate change specifically, but a general behavior of the ocean.

Later Pleistocene evolution of the Exe valley: a chronostratigraphic model of terrace formation and its implications for Palaeolithic archaeology

This paper presents the first systematic chronostratigraphic study of the river terraces of the Exe catchment in South West England and a new conceptual model for terrace formation in unglaciated basins with applicability to terrace staircase sequences elsewhere. The Exe catchment lay beyond the maximum extent of Pleistocene ice sheets and the drainage pattern evolved from the Tertiary to the Middle Pleistocene, by which time the major valley systems were in place and downcutting began to create a staircase of strath terraces. The higher terraces (8-6) typically exhibit altitudinal overlap or appear to be draped over the landscape, whilst the middle terraces show greater altitudinal separation and the lowest terraces are of a cut and fill form. The terrace deposits investigated in this study were deposited in cold phases of the glacial-interglacial Milankovitch climatic cycles with the lowest four being deposited in the Devensian Marine Isotope Stages (MIS) 4-2. A new cascade process-response model is proposed of basin terrace evolution in the Exe valley, which emphasises the role of lateral erosion in the creation of strath terraces and the reworking of inherited resistant lithological components down through the staircase. The resultant emergent valley topography and the reworking of artefacts along with gravel clasts, have important implications for the dating of hominin presence and the local landscapes they inhabited. Whilst the terrace chronology suggested here is still not as detailed as that for the Thames or the Solent System it does indicate a Middle Palaeolithic hominin presence in the region, probably prior to the late Wolstonian Complex or MIS 6. This supports existing data from cave sites in South West England.

Integrating socio-economics and ecology: a taxonomy of quantitative methods and a review of their use in agro-ecology

Answering many of the critical questions in conservation, development and environmental management requires integrating the social and natural sciences. However, understanding the array of available quantitative methods and their associated terminology presents a major barrier to successful collaboration. We provide an overview of quantitative socio-economic methods that distils their complexity into a simple taxonomy. We outline how each has been used in conjunction with ecological models to address questions relating to the management of socio-ecological systems. We review the application of social and ecological quantitative concepts to agro-ecology and classify the approaches used to integrate the two disciplines. Our review included all published integrated models from 2003 to 2008 in 27 journals that publish agricultural modelling research. Although our focus is on agro-ecology, many of the results are broadly applicable to other fields involving an interaction between human activities and ecology. We found 36 papers that integrated social and ecological concepts in a quantitative model. Four different approaches to integration were used, depending on the scale at which human welfare was quantified. Most models viewed humans as pure profit maximizers, both when calculating welfare and predicting behaviour. Synthesis and applications. We reached two main conclusions based on our taxonomy and review. The first is that quantitative methods that extend predictions of behaviour and measurements of welfare beyond a simple market value basis are underutilized by integrated models. The second is that the accuracy of prediction for integrated models remains largely unquantified. Addressing both problems requires researchers to reach a common understanding of modelling goals and data requirements during the early stages of a project.

An integrative model of amino acid metabolism in the liver of the lactating dairy cow

The objective of this work was to construct a dynamic model of hepatic amino acid metabolism in the lactating dairy cow that could be parameterized using net flow data from in vivo experiments. The model considers 22 amino acids, ammonia, urea, and 13 energetic metabolites, and was parameterized using a steady-state balance model and two in vivo, net flow experiments conducted with mid-lactation dairy cows. Extracellular flows were derived directly from the observed data. An optimization routine was used to derive nine intracellular flows. The resulting dynamic model was found to be stable across a range of inputs suggesting that it can be perturbed and applied to other physiological states. Although nitrogen was generally in balance, leucine was in slight deficit compared to predicted needs for export protein synthesis, suggesting that an alternative source of leucine (e.g. peptides) was utilized. Simulations of varying glucagon concentrations indicated that an additional 5 mol/d of glucose could be synthesized at the reference substrate concentrations and blood flows. The increased glucose production was supported by increased removal from blood of lactate, glutamate, aspartate, alanine, asparagine, and glutamine. As glucose Output increased, ketone body and acetate release increased while CO2 release declined. The pattern of amino acids appearing in hepatic vein blood was affected by changes in amino acid concentration in portal vein blood, portal blood flow rate and glucagon concentration, with methionine and phenylalanine being the most affected of essential amino acids. Experimental evidence is insufficient to determine whether essential amino acids are affected by varying gluconeogenic demands. (C) 2004 Published by Elsevier Ltd.

Seeds of growth? Agricultural productivity and the transitional dynamics of the Ramsey model

A two-sector Ramsey-type model of growth is developed to investigate the relationship between agricultural productivity and economy-wide growth. The framework takes into account the peculiarities of agriculture both in production ( reliance on a fixed natural resource base) and in consumption (life-sustaining role and low income elasticity of food demand). The transitional dynamics of the model establish that when preferences respect Engel's law, the level and growth rate of agricultural productivity influence the speed of capital accumulation. A calibration exercise shows that a small difference in agricultural productivity has drastic implications for the rate and pattern of growth of the economy. Hence, low agricultural productivity can form a bottleneck limiting growth, because high food prices result in a low saving rate.

Shock persistence in a dual economy model of India

This article examines shock persistence in agricultural and industrial output in India. Drawing on the dual economy literature, the linkages between the sectors through the terms of trade are emphasised. However different dual economy models make differing assumptions regarding the categorisation of variables as being either endogenous or exogenous and this distinction is crucial in explaining the pattern of shock persistence. Using annual data for 1955-95, our results show that shocks to both output series are permanent while those to the terms of trade are transient.