Assessing the vulnerability of blanket peat to climate change using an ensemble of statistical bioclimatic envelope models

We assessed the vulnerability of blanket peat to climate change in Great Britain using an ensemble of 8 bioclimatic envelope models. We used 4 published models that ranged from simple threshold models, based on total annual precipitation, to Generalised Linear Models (GLMs, based on mean annual temperature). In addition, 4 new models were developed which included measures of water deficit as threshold, classification tree, GLM and generalised additive models (GAM). Models that included measures of both hydrological conditions and maximum temperature provided a better fit to the mapped peat area than models based on hydrological variables alone. Under UKCIP02 projections for high (A1F1) and low (B1) greenhouse gas emission scenarios, 7 out of the 8 models showed a decline in the bioclimatic space associated with blanket peat. Eastern regions (Northumbria, North York Moors, Orkney) were shown to be more vulnerable than higher-altitude, western areas (Highlands, Western Isles and Argyle, Bute and The Trossachs). These results suggest a long-term decline in the distribution of actively growing blanket peat, especially under the high emissions scenario, although it is emphasised that existing peatlands may well persist for decades under a changing climate. Observational data from long-term monitoring and manipulation experiments in combination with process-based models are required to explore the nature and magnitude of climate change impacts on these vulnerable areas more fully.

Optimal linearization trajectories for tangent linear models

We examine differential equations where nonlinearity is a result of the advection part of the total derivative or the use of quadratic algebraic constraints between state variables (such as the ideal gas law). We show that these types of nonlinearity can be accounted for in the tangent linear model by a suitable choice of the linearization trajectory. Using this optimal linearization trajectory, we show that the tangent linear model can be used to reproduce the exact nonlinear error growth of perturbations for more than 200 days in a quasi-geostrophic model and more than (the equivalent of) 150 days in the Lorenz 96 model. We introduce an iterative method, purely based on tangent linear integrations, that converges to this optimal linearization trajectory. The main conclusion from this article is that this iterative method can be used to account for nonlinearity in estimation problems without using the nonlinear model. We demonstrate this by performing forecast sensitivity experiments in the Lorenz 96 model and show that we are able to estimate analysis increments that improve the two-day forecast using only four backward integrations with the tangent linear model. Copyright © 2011 Royal Meteorological Society

Conditional mean functions of non-linear models of US output

We compare a number of models of post War US output growth in terms of the degree and pattern of non-linearity they impart to the conditional mean, where we condition on either the previous period's growth rate, or the previous two periods' growth rates. The conditional means are estimated non-parametrically using a nearest-neighbour technique on data simulated from the models. In this way, we condense the complex, dynamic, responses that may be present in to graphical displays of the implied conditional mean.

Forecasting economic and financial time series with non-linear models

In this paper we discuss the current state-of-the-art in estimating, evaluating, and selecting among non-linear forecasting models for economic and financial time series. We review theoretical and empirical issues, including predictive density, interval and point evaluation and model selection, loss functions, data-mining, and aggregation. In addition, we argue that although the evidence in favor of constructing forecasts using non-linear models is rather sparse, there is reason to be optimistic. However, much remains to be done. Finally, we outline a variety of topics for future research, and discuss a number of areas which have received considerable attention in the recent literature, but where many questions remain.

Forecasting US output growth with non-linear models in the presence of data uncertainty

We consider the impact of data revisions on the forecast performance of a SETAR regime-switching model of U.S. output growth. The impact of data uncertainty in real-time forecasting will affect a model's forecast performance via the effect on the model parameter estimates as well as via the forecast being conditioned on data measured with error. We find that benchmark revisions do affect the performance of the non-linear model of the growth rate, and that the performance relative to a linear comparator deteriorates in real-time compared to a pseudo out-of-sample forecasting exercise.

Impacts of pollution and climate change on ombrotrophic Sphagnum species in the UK: analysis of uncertainties in two empirical niche models

A significant challenge in the prediction of climate change impacts on ecosystems and biodiversity is quantifying the sources of uncertainty that emerge within and between different models. Statistical species niche models have grown in popularity, yet no single best technique has been identified reflecting differing performance in different situations. Our aim was to quantify uncertainties associated with the application of 2 complimentary modelling techniques. Generalised linear mixed models (GLMM) and generalised additive mixed models (GAMM) were used to model the realised niche of ombrotrophic Sphagnum species in British peatlands. These models were then used to predict changes in Sphagnum cover between 2020 and 2050 based on projections of climate change and atmospheric deposition of nitrogen and sulphur. Over 90% of the variation in the GLMM predictions was due to niche model parameter uncertainty, dropping to 14% for the GAMM. After having covaried out other factors, average variation in predicted values of Sphagnum cover across UK peatlands was the next largest source of variation (8% for the GLMM and 86% for the GAMM). The better performance of the GAMM needs to be weighed against its tendency to overfit the training data. While our niche models are only a first approximation, we used them to undertake a preliminary evaluation of the relative importance of climate change and nitrogen and sulphur deposition and the geographic locations of the largest expected changes in Sphagnum cover. Predicted changes in cover were all small (generally <1% in an average 4 m2 unit area) but also highly uncertain. Peatlands expected to be most affected by climate change in combination with atmospheric pollution were Dartmoor, Brecon Beacons and the western Lake District.

The effects of different knowledge-dissemination interventions on the mastitis knowledge of Tanzanian smallholder dairy farmers

We developed three different knowledge-dissemination methods for educating Tanzanian smallholder farmers about mastitis in their dairy cattle. The effectiveness of these methods (and their combinations) was evaluated and quantified using a randomised controlled trial and multilevel statistical modelling. To our knowledge, this is the first study that has used such techniques to evaluate the effectiveness of different knowledge-dissemination interventions for adult learning in developing countries. Five different combinations of knowledge-dissemination method were compared: 'diagrammatic handout' ('HO'), 'village meeting' ('VM'), 'village meeting and video' ('VM + V), 'village meeting and diagrammatic handout' ('VM + HO') and 'village meeting, video and diagrammatic handout' ('VM + V + HO'). Smallholder dairy farmers were exposed to only one of these interventions, and the effectiveness of each was compared to a control ('C') group, who received no intervention. The mastitis knowledge of each farmer (n = 256) was evaluated by questionnaire both pre- and post-dissemination. Generalised linear mixed models were used to evaluate the effectiveness of the different interventions. The outcome variable considered was the probability of volunteering correct responses to mastitis questions post-dissemination, with 'village' and 'farmer' considered as random effects in the model. Results showed that all five interventions, 'HO' (odds ratio (OR) = 3.50, 95% confidence intervals (CI) = 3.10, 3.96), 'VM + V + HO' (OR = 3.34, 95% CI = 2.94, 3.78), 'VM + HO, (OR=3.28, 95% CI=2.90, 3.71), WM+V (OR=3.22, 95% CI=2.84, 3.64) and 'VM' (OR = 2.61, 95% CI = 2.31, 2.95), were significantly (p < 0.0001) more effective at disseminating mastitis knowledge than no intervention. In addition, the 'VM' method was less effective at disseminating mastitis knowledge than other interventions. Combinations of methods showed no advantage over the diagrammatic handout alone. Other explanatory variables with significant positive associations on mastitis knowledge included education to secondary school level or higher, and having previously learned about mastitis by reading pamphlets or attendance at an animal-health course. (c) 2005 Elsevier B.V. All rights reserved.

Alternatives to linear analysis of energy balance data from lactating dairy cows

The current energy requirements system used in the United Kingdom for lactating dairy cows utilizes key parameters such as metabolizable energy intake (MEI) at maintenance (MEm), the efficiency of utilization of MEI for 1) maintenance, 2) milk production (k(l)), 3) growth (k(g)), and the efficiency of utilization of body stores for milk production (k(t)). Traditionally, these have been determined using linear regression methods to analyze energy balance data from calorimetry experiments. Many studies have highlighted a number of concerns over current energy feeding systems particularly in relation to these key parameters, and the linear models used for analyzing. Therefore, a database containing 652 dairy cow observations was assembled from calorimetry studies in the United Kingdom. Five functions for analyzing energy balance data were considered: straight line, two diminishing returns functions, (the Mitscherlich and the rectangular hyperbola), and two sigmoidal functions (the logistic and the Gompertz). Meta-analysis of the data was conducted to estimate k(g) and k(t). Values of 0.83 to 0.86 and 0.66 to 0.69 were obtained for k(g) and k(t) using all the functions (with standard errors of 0.028 and 0.027), respectively, which were considerably different from previous reports of 0.60 to 0.75 for k(g) and 0.82 to 0.84 for k(t). Using the estimated values of k(g) and k(t), the data were corrected to allow for body tissue changes. Based on the definition of k(l) as the derivative of the ratio of milk energy derived from MEI to MEI directed towards milk production, MEm and k(l) were determined. Meta-analysis of the pooled data showed that the average k(l) ranged from 0.50 to 0.58 and MEm ranged between 0.34 and 0.64 MJ/kg of BW0.75 per day. Although the constrained Mitscherlich fitted the data as good as the straight line, more observations at high energy intakes (above 2.4 MJ/kg of BW0.75 per day) are required to determine conclusively whether milk energy is related to MEI linearly or not.

Describing long-term trends in precipitation using generalized additive models

With the current concern over climate change, descriptions of how rainfall patterns are changing over time can be useful. Observations of daily rainfall data over the last few decades provide information on these trends. Generalized linear models are typically used to model patterns in the occurrence and intensity of rainfall. These models describe rainfall patterns for an average year but are more limited when describing long-term trends, particularly when these are potentially non-linear. Generalized additive models (GAMS) provide a framework for modelling non-linear relationships by fitting smooth functions to the data. This paper describes how GAMS can extend the flexibility of models to describe seasonal patterns and long-term trends in the occurrence and intensity of daily rainfall using data from Mauritius from 1962 to 2001. Smoothed estimates from the models provide useful graphical descriptions of changing rainfall patterns over the last 40 years at this location. GAMS are particularly helpful when exploring non-linear relationships in the data. Care is needed to ensure the choice of smooth functions is appropriate for the data and modelling objectives. (c) 2008 Elsevier B.V. All rights reserved.