The effect of the equivalent-weights particle filter on dynamical balance in a primitive equation model

The disadvantage of the majority of data assimilation schemes is the assumption that the conditional probability density function of the state of the system given the observations [posterior probability density function (PDF)] is distributed either locally or globally as a Gaussian. The advantage, however, is that through various different mechanisms they ensure initial conditions that are predominantly in linear balance and therefore spurious gravity wave generation is suppressed. The equivalent-weights particle filter is a data assimilation scheme that allows for a representation of a potentially multimodal posterior PDF. It does this via proposal densities that lead to extra terms being added to the model equations and means the advantage of the traditional data assimilation schemes, in generating predominantly balanced initial conditions, is no longer guaranteed. This paper looks in detail at the impact the equivalent-weights particle filter has on dynamical balance and gravity wave generation in a primitive equation model. The primary conclusions are that (i) provided the model error covariance matrix imposes geostrophic balance, then each additional term required by the equivalent-weights particle filter is also geostrophically balanced; (ii) the relaxation term required to ensure the particles are in the locality of the observations has little effect on gravity waves and actually induces a reduction in gravity wave energy if sufficiently large; and (iii) the equivalent-weights term, which leads to the particles having equivalent significance in the posterior PDF, produces a change in gravity wave energy comparable to the stochastic model error. Thus, the scheme does not produce significant spurious gravity wave energy and so has potential for application in real high-dimensional geophysical applications.

Social and ecological drivers of success in agri-environment schemes: the roles of farmers and environmental context

1. Agri-environment schemes remain a controversial approach to reversing biodiversity losses, partly because the drivers of variation in outcomes are poorly understood. In particular, there is a lack of studies that consider both social and ecological factors. 2. We analysed variation across 48 farms in the quality and biodiversity outcomes of agri-environmental habitats designed to provide pollen and nectar for bumblebees and butterflies or winter seed for birds. We used interviews and ecological surveys to gather data on farmer experience and understanding of agri-environment schemes, and local and landscape environmental factors. 3. Multimodel inference indicated social factors had a strong impact on outcomes and that farmer experiential learning was a key process. The quality of the created habitat was affected positively by the farmer’s previous experience in environmental management. The farmer’s confidence in their ability to carry out the required management was negatively related to the provision of floral resources. Farmers with more wildlife-friendly motivations tended to produce more floral resources, but fewer seed resources. 4. Bird, bumblebee and butterfly biodiversity responses were strongly affected by the quantity of seed or floral resources. Shelter enhanced biodiversity directly, increased floral resources and decreased seed yield. Seasonal weather patterns had large effects on both measures. Surprisingly, larger species pools and amounts of semi-natural habitat in the surrounding landscape had negative effects on biodiversity, which may indicate use by fauna of alternative foraging resources. 5. Synthesis and application. This is the first study to show a direct role of farmer social variables on the success of agri-environment schemes in supporting farmland biodiversity. It suggests that farmers are not simply implementing agri-environment options, but are learning and improving outcomes by doing so. Better engagement with farmers and working with farmers who have a history of environmental management may therefore enhance success. The importance of a number of environmental factors may explain why agri-environment outcomes are variable, and suggests some – such as the weather – cannot be controlled. Others, such as shelter, could be incorporated into agri-environment prescriptions. The role of landscape factors remains complex and currently eludes simple conclusions about large-scale targeting of schemes.

Twin experiments with the equivalent weights particle filter and HadCM3

This paper investigates the use of a particle filter for data assimilation with a full scale coupled ocean–atmosphere general circulation model. Synthetic twin experiments are performed to assess the performance of the equivalent weights filter in such a high-dimensional system. Artificial 2-dimensional sea surface temperature fields are used as observational data every day. Results are presented for different values of the free parameters in the method. Measures of the performance of the filter are root mean square errors, trajectories of individual variables in the model and rank histograms. Filter degeneracy is not observed and the performance of the filter is shown to depend on the ability to keep maximum spread in the ensemble.

Geotechnical systems that evolve with ecological processes

Geotechnical systems, such as landfills, mine tailings storage facilities (TSFs), slopes, and levees, are required to perform safely throughout their service life, which can span from decades for levees to “in perpetuity” for TSFs. The conventional design practice by geotechnical engineers for these systems utilizes the as-built material properties to predict its performance throughout the required service life. The implicit assumption in this design methodology is that the soil properties are stable through time. This is counter to long-term field observations of these systems, particularly where ecological processes such as plant, animal, biological, and geochemical activity are present. Plant roots can densify soil and/or increase hydraulic conductivity, burrowing animals can increase seepage, biological activity can strengthen soil, geochemical processes can increase stiffness, etc. The engineering soil properties naturally change as a stable ecological system is gradually established following initial construction, and these changes alter system performance. This paper presents an integrated perspective and new approach to this issue, considering ecological, geotechnical, and mining demands and constraints. A series of data sets and case histories are utilized to examine these issues and to propose a more integrated design approach, and consideration is given to future opportunities to manage engineered landscapes as ecological systems. We conclude that soil scientists and restoration ecologists must be engaged in initial project design and geotechnical engineers must be active in long-term management during the facility’s service life. For near-surface geotechnical structures in particular, this requires an interdisciplinary perspective and the embracing of soil as a living ecological system rather than an inert construction material.

Linking classroom learning and research to advance ideas about social-ecological resilience

There is an increasing demand in higher education institutions for training in complex environmental problems. Such training requires a careful mix of conventional methods and innovative solutions, a task not always easy to accomplish. In this paper we review literature on this theme, highlight relevant advances in the pedagogical literature, and report on some examples resulting from our recent efforts to teach complex environmental issues. The examples range from full credit courses in sustainable development and research methods to project-based and in-class activity units. A consensus from the literature is that lectures are not sufficient to fully engage students in these issues. A conclusion from the review of examples is that problem-based and project-based, e.g., through case studies, experiential learning opportunities, or real-world applications, learning offers much promise. This could greatly be facilitated by online hubs through which teachers, students, and other members of the practitioner and academic community share experiences in teaching and research, the way that we have done here.

The pitfalls of ecological forecasting

Ecological forecasting is difficult but essential, because reactive management results in corrective actions that are often too late to avert significant environmental damage. Here, we appraise different forecasting methods with a particular focus on the modelling of species populations. We show how simple extrapolation of current trends in state is often inadequate because environmental drivers change in intensity over time and new drivers emerge. However, statistical models, incorporating relationships with drivers, simply offset the prediction problem, requiring us to forecast how the drivers will themselves change over time. Some authors approach this problem by focusing in detail on a single driver, whilst others use ‘storyline’ scenarios, which consider projected changes in a wide range of different drivers. We explain why both approaches are problematic and identify a compromise to model key drivers and interactions along with possible response options to help inform environmental management. We also highlight the crucial role of validation of forecasts using independent data. Although these issues are relevant for all types of ecological forecasting, we provide examples based on forecasts for populations of UK butterflies. We show how a high goodness-of-fit for models used to calibrate data is not sufficient for good forecasting. Long-term biological recording schemes rather than experiments will often provide data for ecological forecasting and validation because these schemes allow capture of landscape-scale land-use effects and their interactions with other drivers.

A Variance-Minimizing Filter for Large-Scale Applications

A truly variance-minimizing filter is introduced and its per for mance is demonstrated with the Korteweg– DeV ries (KdV) equation and with a multilayer quasigeostrophic model of the ocean area around South Africa. It is recalled that Kalman-like filters are not variance minimizing for nonlinear model dynamics and that four - dimensional variational data assimilation (4DV AR)-like methods relying on per fect model dynamics have dif- ficulty with providing error estimates. The new method does not have these drawbacks. In fact, it combines advantages from both methods in that it does provide error estimates while automatically having balanced states after analysis, without extra computations. It is based on ensemble or Monte Carlo integrations to simulate the probability density of the model evolution. When obser vations are available, the so-called importance resampling algorithm is applied. From Bayes’ s theorem it follows that each ensemble member receives a new weight dependent on its ‘ ‘distance’ ’ t o the obser vations. Because the weights are strongly var ying, a resampling of the ensemble is necessar y. This resampling is done such that members with high weights are duplicated according to their weights, while low-weight members are largely ignored. In passing, it is noted that data assimilation is not an inverse problem by nature, although it can be for mulated that way . Also, it is shown that the posterior variance can be larger than the prior if the usual Gaussian framework is set aside. However , i n the examples presented here, the entropy of the probability densities is decreasing. The application to the ocean area around South Africa, gover ned by strongly nonlinear dynamics, shows that the method is working satisfactorily . The strong and weak points of the method are discussed and possible improvements are proposed.

Analysis Scheme in the Ensemble Kalman Filter

This paper discusses an important issue related to the implementation and interpretation of the analysis scheme in the ensemble Kalman filter . I t i s shown that the obser vations must be treated as random variables at the analysis steps. That is, one should add random perturbations with the correct statistics to the obser vations and generate an ensemble of obser vations that then is used in updating the ensemble of model states. T raditionally , this has not been done in previous applications of the ensemble Kalman filter and, as will be shown, this has resulted in an updated ensemble with a variance that is too low . This simple modification of the analysis scheme results in a completely consistent approach if the covariance of the ensemble of model states is interpreted as the prediction error covariance, and there are no further requirements on the ensemble Kalman filter method, except for the use of an ensemble of sufficient size. Thus, there is a unique correspondence between the error statistics from the ensemble Kalman filter and the standard Kalman filter approach

Assimilation of Geosat Altimeter Data for the Agulhas Current Using the Ensemble Kalman Filter with a Quasigeostrophic Model

The ring-shedding process in the Agulhas Current is studied using the ensemble Kalman filter to assimilate geosat altimeter data into a two-layer quasigeostrophic ocean model. The properties of the ensemble Kalman filter are further explored with focus on the analysis scheme and the use of gridded data. The Geosat data consist of 10 fields of gridded sea-surface height anomalies separated 10 days apart that are added to a climatic mean field. This corresponds to a huge number of data values, and a data reduction scheme must be applied to increase the efficiency of the analysis procedure. Further, it is illustrated how one can resolve the rank problem occurring when a too large dataset or a small ensemble is used.

Variability in life-history and ecological traits is a buffer against extinction in mammals

Anthropogenic degradation of the world's ecosystems is leading to a widespread and accelerating loss of biodiversity. However, not all species respond equally to existing threats, raising the question: what makes a species more vulnerable to extinction? We propose that higher intraspecific variability may reduce the risk of extinction, as different individuals and populations within a species may respond differently to occurring threats. Supporting this prediction, our results show that mammalian species with more variable adult body masses, litter sizes, sexual maturity ages and population densities are less vulnerable to extinction. Our findings reveal the role of local variation among populations, particularly of large mammals, as a buffering mechanism against extinction, and emphasise the importance of considering trait variation in comparative analyses and conservation management.

Environmental and ecological economics in the 21st century: an age adjusted citation analysis of the most influential articles, journals, authors and institutions

We investigate the influence of articles, authors, journals and institutions in the field of environmental and ecological economics. We depart from studies that investigated the literature until 2001 and include a time period that has witnessed an enormous increase of importance in the field. We adjust for the age effect given the huge impact of the year of an article's publication on its influence and we show that this adjustment does make a substantial difference — especially for disaggregated units of analysis with diverse age characteristics such as articles or authors. We analyse 6597 studies on environmental and ecological economics published between 2000 and 2009. We provide rankings of the influential articles, authors, journals and institutions and find that Ecological Economics, Energy Economics and the Journal of Environmental Economics and Management have the most influential articles, they publish very influential authors and their articles are cited most. The University of Maryland, Resources for the Future, the University of East Anglia and the World Bank appear to be the most influential institutions in the field of environmental and ecological economics.