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.

Graphical tracking systems revisited: a practical approach to computer scheduling in horticulture

Graphical tracking is a technique for crop scheduling where the actual plant state is plotted against an ideal target curve which encapsulates all crop and environmental characteristics. Management decisions are made on the basis of the position of the actual crop against the ideal position. Due to the simplicity of the approach it is possible for graphical tracks to be developed on site without the requirement for controlled experimentation. Growth models and graphical tracks are discussed, and an implementation of the Richards curve for graphical tracking described. In many cases, the more intuitively desirable growth models perform sub-optimally due to problems with the specification of starting conditions, environmental factors outside the scope of the original model and the introduction of new cultivars. Accurate specification for a biological model requires detailed and usually costly study, and as such is not adaptable to a changing cultivar range and changing cultivation techniques. Fitting of a new graphical track for a new cultivar can be conducted on site and improved over subsequent seasons. Graphical tracking emphasises the current position relative to the objective, and as such does not require the time consuming or system specific input of an environmental history, although it does require detailed crop measurement. The approach is flexible and could be applied to a variety of specification metrics, with digital imaging providing a route for added value. For decision making regarding crop manipulation from the observed current state, there is a role for simple predictive modelling over the short term to indicate the short term consequences of crop manipulation.

Case study part 2: probabilistic modelling of long-term effects of pesticides on individual breeding success in birds and mammals

Abstract: Long-term exposure of skylarks to a fictitious insecticide and of wood mice to a fictitious fungicide were modelled probabilistically in a Monte Carlo simulation. Within the same simulation the consequences of exposure to pesticides on reproductive success were modelled using the toxicity-exposure-linking rules developed by R.S. Bennet et al. (2005) and the interspecies extrapolation factors suggested by R. Luttik et al.(2005). We built models to reflect a range of scenarios and as a result were able to show how exposure to pesticide might alter the number of individuals engaged in any given phase of the breeding cycle at any given time and predict the numbers of new adults at the season’s end.

Potential Predictability and AMIP Implications of Midlatitude Climate Variability in Two General Circulation Models

Ensembles of extended Atmospheric Model Intercomparison Project (AMIP) runs from the general circulation models of the National Centers for Environmental Prediction (formerly the National Meteorological Center) and the Max-Planck Institute (Hamburg, Germany) are used to estimate the potential predictability (PP) of an index of the Pacific–North America (PNA) mode of climate change. The PP of this pattern in “perfect” prediction experiments is 20%–25% of the index’s variance. The models, particularly that from MPI, capture virtually all of this variance in their hindcasts of the winter PNA for the period 1970–93. The high levels of internally generated model noise in the PNA simulations reconfirm the need for an ensemble averaging approach to climate prediction. This means that the forecasts ought to be expressed in a probabilistic manner. It is shown that the models’ skills are higher by about 50% during strong SST events in the tropical Pacific, so the probabilistic forecasts need to be conditional on the tropical SST. Taken together with earlier studies, the present results suggest that the original set of AMIP integrations (single 10-yr runs) is not adequate to reliably test the participating models’ simulations of interannual climate variability in the midlatitudes.

The ModFOLD4 server for the quality assessment of 3D protein models

Once you have generated a 3D model of a protein, how do you know whether it bears any resemblance to the actual structure? To determine the usefulness of 3D models of proteins, they must be assessed in terms of their quality by methods that predict their similarity to the native structure. The ModFOLD4 server is the latest version of our leading independent server for the estimation of both the global and local (per-residue) quality of 3D protein models. The server produces both machine readable and graphical output, providing users with intuitive visual reports on the quality of predicted protein tertiary structures. The ModFOLD4 server is freely available to all at: http://www.reading.ac.uk/bioinf/ModFOLD/.

Wind gust estimation for Mid-European winter storms: towards a probabilistic view

Three wind gust estimation (WGE) methods implemented in the numerical weather prediction (NWP) model COSMO-CLM are evaluated with respect to their forecast quality using skill scores. Two methods estimate gusts locally from mean wind speed and the turbulence state of the atmosphere, while the third one considers the mixing-down of high momentum within the planetary boundary layer (WGE Brasseur). One hundred and fifty-eight windstorms from the last four decades are simulated and results are compared with gust observations at 37 stations in Germany. Skill scores reveal that the local WGE methods show an overall better behaviour, whilst WGE Brasseur performs less well except for mountain regions. The here introduced WGE turbulent kinetic energy (TKE) permits a probabilistic interpretation using statistical characteristics of gusts at observational sites for an assessment of uncertainty. The WGE TKE formulation has the advantage of a ‘native’ interpretation of wind gusts as result of local appearance of TKE. The inclusion of a probabilistic WGE TKE approach in NWP models has, thus, several advantages over other methods, as it has the potential for an estimation of uncertainties of gusts at observational sites.

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.

Can dynamically downscaled windstorm footprints be improved by observations through a probabilistic approach?

Windstorms are a main feature of the European climate and exert strong socioeconomic impacts. Large effort has been made in developing and enhancing models to simulate the intensification of windstorms, resulting footprints, and associated impacts. Simulated wind or gust speeds usually differ from observations, as regional climate models have biases and cannot capture all local effects. An approach to adjust regional climate model (RCM) simulations of wind and wind gust toward observations is introduced. For this purpose, 100 windstorms are selected and observations of 173 (111) test sites of the German Weather Service are considered for wind (gust) speed. Theoretical Weibull distributions are fitted to observed and simulated wind and gust speeds, and the distribution parameters of the observations are interpolated onto the RCM computational grid. A probability mapping approach is applied to relate the distributions and to correct the modeled footprints. The results are not only achieved for single test sites but for an area-wide regular grid. The approach is validated using root-mean-square errors on event and site basis, documenting that the method is generally able to adjust the RCM output toward observations. For gust speeds, an improvement on 88 of 100 events and at about 64% of the test sites is reached. For wind, 99 of 100 improved events and ~84% improved sites can be obtained. This gives confidence on the potential of the introduced approach for many applications, in particular those considering wind data.

Probabilistic parameterisation of the surface mass balance--elevation feedback in regional climate model simulations of the Greenland ice sheet

We present a new parameterisation that relates surface mass balance (SMB: the sum of surface accumulation and surface ablation) to changes in surface elevation of the Greenland ice sheet (GrIS) for the MAR (Modèle Atmosphérique Régional: Fettweis, 2007) regional climate model. The motivation is to dynamically adjust SMB as the GrIS evolves, allowing us to force ice sheet models with SMB simulated by MAR while incorporating the SMB–elevation feedback, without the substantial technical challenges of coupling ice sheet and climate models. This also allows us to assess the effect of elevation feedback uncertainty on the GrIS contribution to sea level, using multiple global climate and ice sheet models, without the need for additional, expensive MAR simulations. We estimate this relationship separately below and above the equilibrium line altitude (ELA, separating negative and positive SMB) and for regions north and south of 77� N, from a set of MAR simulations in which we alter the ice sheet surface elevation. These give four “SMB lapse rates”, gradients that relate SMB changes to elevation changes. We assess uncertainties within a Bayesian framework, estimating probability distributions for each gradient from which we present best estimates and credibility intervals (CI) that bound 95% of the probability. Below the ELA our gradient estimates are mostly positive, because SMB usually increases with elevation: 0.56 (95% CI: −0.22 to 1.33) kgm−3 a−1 for the north, and 1.91 (1.03 to 2.61) kgm−3 a−1 for the south. Above the ELA, the gradients are much smaller in magnitude: 0.09 (−0.03 to 0.23) kgm−3 a−1 in the north, and 0.07 (−0.07 to 0.59) kgm−3 a−1 in the south, because SMB can either increase or decrease in response to increased elevation. Our statistically founded approach allows us to make probabilistic assessments for the effect of elevation feedback uncertainty on sea level projections (Edwards et al., 2014).

An evaluation of decadal probability forecasts from state-of-the-art climate models

While state-of-the-art models of Earth's climate system have improved tremendously over the last 20 years, nontrivial structural flaws still hinder their ability to forecast the decadal dynamics of the Earth system realistically. Contrasting the skill of these models not only with each other but also with empirical models can reveal the space and time scales on which simulation models exploit their physical basis effectively and quantify their ability to add information to operational forecasts. The skill of decadal probabilistic hindcasts for annual global-mean and regional-mean temperatures from the EU Ensemble-Based Predictions of Climate Changes and Their Impacts (ENSEMBLES) project is contrasted with several empirical models. Both the ENSEMBLES models and a “dynamic climatology” empirical model show probabilistic skill above that of a static climatology for global-mean temperature. The dynamic climatology model, however, often outperforms the ENSEMBLES models. The fact that empirical models display skill similar to that of today's state-of-the-art simulation models suggests that empirical forecasts can improve decadal forecasts for climate services, just as in weather, medium-range, and seasonal forecasting. It is suggested that the direct comparison of simulation models with empirical models becomes a regular component of large model forecast evaluations. Doing so would clarify the extent to which state-of-the-art simulation models provide information beyond that available from simpler empirical models and clarify current limitations in using simulation forecasting for decision support. Ultimately, the skill of simulation models based on physical principles is expected to surpass that of empirical models in a changing climate; their direct comparison provides information on progress toward that goal, which is not available in model–model intercomparisons.

Probabilistic skill in ensemble seasonal forecasts

Simulation models are widely employed to make probability forecasts of future conditions on seasonal to annual lead times. Added value in such forecasts is reflected in the information they add, either to purely empirical statistical models or to simpler simulation models. An evaluation of seasonal probability forecasts from the Development of a European Multimodel Ensemble system for seasonal to inTERannual prediction (DEMETER) and ENSEMBLES multi-model ensemble experiments is presented. Two particular regions are considered: Nino3.4 in the Pacific and the Main Development Region in the Atlantic; these regions were chosen before any spatial distribution of skill was examined. The ENSEMBLES models are found to have skill against the climatological distribution on seasonal time-scales. For models in ENSEMBLES that have a clearly defined predecessor model in DEMETER, the improvement from DEMETER to ENSEMBLES is discussed. Due to the long lead times of the forecasts and the evolution of observation technology, the forecast-outcome archive for seasonal forecast evaluation is small; arguably, evaluation data for seasonal forecasting will always be precious. Issues of information contamination from in-sample evaluation are discussed and impacts (both positive and negative) of variations in cross-validation protocol are demonstrated. Other difficulties due to the small forecast-outcome archive are identified. The claim that the multi-model ensemble provides a ‘better’ probability forecast than the best single model is examined and challenged. Significant forecast information beyond the climatological distribution is also demonstrated in a persistence probability forecast. The ENSEMBLES probability forecasts add significantly more information to empirical probability forecasts on seasonal time-scales than on decadal scales. Current operational forecasts might be enhanced by melding information from both simulation models and empirical models. Simulation models based on physical principles are sometimes expected, in principle, to outperform empirical models; direct comparison of their forecast skill provides information on progress toward that goal.

Towards improving the framework for probabilistic forecast evaluation

The evaluation of forecast performance plays a central role both in the interpretation and use of forecast systems and in their development. Different evaluation measures (scores) are available, often quantifying different characteristics of forecast performance. The properties of several proper scores for probabilistic forecast evaluation are contrasted and then used to interpret decadal probability hindcasts of global mean temperature. The Continuous Ranked Probability Score (CRPS), Proper Linear (PL) score, and IJ Good’s logarithmic score (also referred to as Ignorance) are compared; although information from all three may be useful, the logarithmic score has an immediate interpretation and is not insensitive to forecast busts. Neither CRPS nor PL is local; this is shown to produce counter intuitive evaluations by CRPS. Benchmark forecasts from empirical models like Dynamic Climatology place the scores in context. Comparing scores for forecast systems based on physical models (in this case HadCM3, from the CMIP5 decadal archive) against such benchmarks is more informative than internal comparison systems based on similar physical simulation models with each other. It is shown that a forecast system based on HadCM3 out performs Dynamic Climatology in decadal global mean temperature hindcasts; Dynamic Climatology previously outperformed a forecast system based upon HadGEM2 and reasons for these results are suggested. Forecasts of aggregate data (5-year means of global mean temperature) are, of course, narrower than forecasts of annual averages due to the suppression of variance; while the average “distance” between the forecasts and a target may be expected to decrease, little if any discernible improvement in probabilistic skill is achieved.

Probabilistic wind power forecasts with an inverse power curve transformation and censored regression

Forecasting wind power is an important part of a successful integration of wind power into the power grid. Forecasts with lead times longer than 6 h are generally made by using statistical methods to post-process forecasts from numerical weather prediction systems. Two major problems that complicate this approach are the non-linear relationship between wind speed and power production and the limited range of power production between zero and nominal power of the turbine. In practice, these problems are often tackled by using non-linear non-parametric regression models. However, such an approach ignores valuable and readily available information: the power curve of the turbine's manufacturer. Much of the non-linearity can be directly accounted for by transforming the observed power production into wind speed via the inverse power curve so that simpler linear regression models can be used. Furthermore, the fact that the transformed power production has a limited range can be taken care of by employing censored regression models. In this study, we evaluate quantile forecasts from a range of methods: (i) using parametric and non-parametric models, (ii) with and without the proposed inverse power curve transformation and (iii) with and without censoring. The results show that with our inverse (power-to-wind) transformation, simpler linear regression models with censoring perform equally or better than non-linear models with or without the frequently used wind-to-power transformation.

A global empirical system for probabilistic seasonal climate prediction

Preparing for episodes with risks of anomalous weather a month to a year ahead is an important challenge for governments, non-governmental organisations, and private companies and is dependent on the availability of reliable forecasts. The majority of operational seasonal forecasts are made using process-based dynamical models, which are complex, computationally challenging and prone to biases. Empirical forecast approaches built on statistical models to represent physical processes offer an alternative to dynamical systems and can provide either a benchmark for comparison or independent supplementary forecasts. Here, we present a simple empirical system based on multiple linear regression for producing probabilistic forecasts of seasonal surface air temperature and precipitation across the globe. The global CO2-equivalent concentration is taken as the primary predictor; subsequent predictors, including large-scale modes of variability in the climate system and local-scale information, are selected on the basis of their physical relationship with the predictand. The focus given to the climate change signal as a source of skill and the probabilistic nature of the forecasts produced constitute a novel approach to global empirical prediction. Hindcasts for the period 1961–2013 are validated against observations using deterministic (correlation of seasonal means) and probabilistic (continuous rank probability skill scores) metrics. Good skill is found in many regions, particularly for surface air temperature and most notably in much of Europe during the spring and summer seasons. For precipitation, skill is generally limited to regions with known El Niño–Southern Oscillation (ENSO) teleconnections. The system is used in a quasi-operational framework to generate empirical seasonal forecasts on a monthly basis.

Data Assimilation and Inverse Methods in Terms of a Probabilistic Formulation

The weak-constraint inverse for nonlinear dynamical models is discussed and derived in terms of a probabilistic formulation. The well-known result that for Gaussian error statistics the minimum of the weak-constraint inverse is equal to the maximum-likelihood estimate is rederived. Then several methods based on ensemble statistics that can be used to find the smoother (as opposed to the filter) solution are introduced and compared to traditional methods. A strong point of the new methods is that they avoid the integration of adjoint equations, which is a complex task for real oceanographic or atmospheric applications. they also avoid iterative searches in a Hilbert space, and error estimates can be obtained without much additional computational effort. the feasibility of the new methods is illustrated in a two-layer quasigeostrophic model.