Adjoint methods in data assimilation for estimating model error

Data assimilation aims to incorporate measured observations into a dynamical system model in order to produce accurate estimates of all the current (and future) state variables of the system. The optimal estimates minimize a variational principle and can be found using adjoint methods. The model equations are treated as strong constraints on the problem. In reality, the model does not represent the system behaviour exactly and errors arise due to lack of resolution and inaccuracies in physical parameters, boundary conditions and forcing terms. A technique for estimating systematic and time-correlated errors as part of the variational assimilation procedure is described here. The modified method determines a correction term that compensates for model error and leads to improved predictions of the system states. The technique is illustrated in two test cases. Applications to the 1-D nonlinear shallow water equations demonstrate the effectiveness of the new procedure.

Long-distance dispersal and its influence on adaptation to host resistance in a heterogeneous landscape

Small propagules like pollen or fungal spores may be dispersed by the wind over distances of hundreds or thousands of kilometres,even though the median dispersal may be only a few metres. Such long-distance dispersal is a stochastic event which may be exceptionally important in shaping a population. It has been found repeatedly in field studies that subpopulations of wind-dispersed fungal pathogens virulent on cultivars with newly introduced, effective resistance genes are dominated by one or very few genotypes. The role of propagule dispersal distributions with distinct behaviour at long distances in generating this characteristic population structure was studied by computer simulation of dispersal of clonal organisms in a heterogeneous environment with fields of unselective and selective hosts. Power-law distributions generated founder events in which new, virulent genotypes rapidly colonized fields of resistant crop varieties and subsequently dominated the pathogen population on both selective and unselective varieties, in agreement with data on rust and powdery mildew fungi. An exponential dispersal function, with extremely rare dispersal over long distances, resulted in slower colonization of resistant varieties by virulent pathogens or even no colonization if the distance between susceptible source and resistant target fields was sufficiently large. The founder events resulting from long-distance dispersal were highly stochastic and exact quantitative prediction of genotype frequencies will therefore always be difficult.

Reading comprehension in autism spectrum disorders: The role of oral language and social functioning

Reading comprehension is an area of difficulty for many individuals with autism spectrum disorders (ASD). According to the Simple View of Reading, word recognition and oral language are both important determinants of reading comprehension ability. We provide a novel test of this model in 100 adolescents with ASD of varying intellectual ability. Further, we explore whether reading comprehension is additionally influenced by individual differences in social behaviour and social cognition in ASD. Adolescents with ASD aged 14-16 years completed assessments indexing word recognition, oral language, reading comprehension, social behaviour and social cognition. Regression analyses show that both word recognition and oral language explain unique variance in reading comprehension. Further, measures of social behaviour and social cognition predict reading comprehension after controlling for the variance explained by word recognition and oral language. This indicates that word recognition, oral language and social impairments may constrain reading comprehension in ASD.

Sensitivity and out-of-sample error in continuous time data assimilation

Data assimilation refers to the problem of finding trajectories of a prescribed dynamical model in such a way that the output of the model (usually some function of the model states) follows a given time series of observations. Typically though, these two requirements cannot both be met at the same time–tracking the observations is not possible without the trajectory deviating from the proposed model equations, while adherence to the model requires deviations from the observations. Thus, data assimilation faces a trade-off. In this contribution, the sensitivity of the data assimilation with respect to perturbations in the observations is identified as the parameter which controls the trade-off. A relation between the sensitivity and the out-of-sample error is established, which allows the latter to be calculated under operational conditions. A minimum out-of-sample error is proposed as a criterion to set an appropriate sensitivity and to settle the discussed trade-off. Two approaches to data assimilation are considered, namely variational data assimilation and Newtonian nudging, also known as synchronization. Numerical examples demonstrate the feasibility of the approach.

Synoptic scale disturbances of the Indian Summer Monsoon as simulated in a high resolution climate model

Hamburg atmospheric general circulation model ECHAM3 at T106 resolution (1.125' lat.Aon.) has considerable skill in reproducing the observed seasonal reversal of mean sea level pressure, the location of the summer heat low as well as the position of the monsoon trough over the Indian subcontinent. The present-day climate and its seasonal cycle are realistically simulated by the model over this region. The model simulates the structure, intensity, frequency, movement and lifetime of monsoon depressions remarkably well. The number of monsoon depressions/storms simulated by the model in a year ranged from 5 to 12 with an average frequency of 8.4 yr-', not significantly different from the observed climatology. The model also simulates the interannual variability in the formation of depressions over the north Bay of Bengal during the summer monsoon season. In the warmer atmosphere under doubled CO2 conditions, the number of monsoon depressions/cyclonic storms forming in Indian seas in a year ranged from 5 to 11 with an average frequency of 7.6 yr-', not significantly different from those inferred in the control run of the model. However, under doubled CO2 conditions, fewer depressions formed in the month of June. Neither the lowest central pressure nor the maximum wind speed changes appreciably in monsoon depressions identified under simulated enhanced greenhouse conditions. The analysis suggests there will be no significant changes in the number and intensity of monsoon depressions in a warmer atmosphere.

Predicting outcomes following cognitive behavior therapy in child anxiety disorders: the influence of genetic, demographic and clinical information

Background. Within a therapeutic gene by environment (GxE) framework, we recently demonstrated that variation in the Serotonin Transporter Promoter Polymorphism; 5HTTLPR and marker rs6330 in Nerve Growth Factor gene; NGF is associated with poorer outcomes following cognitive behaviour therapy (CBT) for child anxiety disorders. The aim of this study was to explore one potential means of extending the translational reach of G×E data in a way that may be clinically informative. We describe a ‘risk-index’ approach combining genetic, demographic and clinical data and test its ability to predict diagnostic outcome following CBT in anxious children. Method. DNA and clinical data were collected from 384 children with a primary anxiety disorder undergoing CBT. We tested our risk model in five cross-validation training sets. Results. In predicting treatment outcome, six variables had a minimum mean beta value of 0.5: 5HTTLPR, NGF rs6330, gender, primary anxiety severity, comorbid mood disorder and comorbid externalising disorder. A risk index (range 0-8) constructed from these variables had moderate predictive ability (AUC = .62-.69) in this study. Children scoring high on this index (5-8) were approximately three times as likely to retain their primary anxiety disorder at follow-up as compared to those children scoring 2 or less. Conclusion. Significant genetic, demographic and clinical predictors of outcome following CBT for anxiety-disordered children were identified. Combining these predictors within a risk-index could be used to identify which children are less likely to be diagnosis free following CBT alone or thus require longer or enhanced treatment. The ‘risk-index’ approach represents one means of harnessing the translational potential of G×E data.

Correlations of long-lived chemical species in a middle atmosphere general circulation model

Correlations between various chemical species simulated by the Canadian Middle Atmosphere Model, a general circulation model with fully interactive chemistry, are considered in order to investigate the general conditions under which compact correlations can be expected to form. At the same time, the analysis serves to validate the model. The results are compared to previous work on this subject, both from theoretical studies and from atmospheric measurements made from space and from aircraft. The results highlight the importance of having a data set with good spatial coverage when working with correlations and provide a background against which the compactness of correlations obtained from atmospheric measurements can be confirmed. It is shown that for long-lived species, distinct correlations are found in the model in the tropics, the extratropics, and the Antarctic winter vortex. Under these conditions, sparse sampling such as arises from occultation instruments is nevertheless suitable to define a chemical correlation within each region even from a single day of measurements, provided a sufficient range of mixing ratio values is sampled. In practice, this means a large vertical extent, though the requirements are less stringent at more poleward latitudes.

Comparison of polar ozone loss rates simulated by one-dimensional and three-dimensional models with Match observations in recent Antarctic and Arctic winters

Simulations of ozone loss rates using a three-dimensional chemical transport model and a box model during recent Antarctic and Arctic winters are compared with experimental loss rates. The study focused on the Antarctic winter 2003, during which the first Antarctic Match campaign was organized, and on Arctic winters 1999/2000, 2002/2003. The maximum ozone loss rates retrieved by the Match technique for the winters and levels studied reached 6 ppbv/sunlit hour and both types of simulations could generally reproduce the observations at 2-sigma error bar level. In some cases, for example, for the Arctic winter 2002/2003 at 475 K level, an excellent agreement within 1-sigma standard deviation level was obtained. An overestimation was also found with the box model simulation at some isentropic levels for the Antarctic winter and the Arctic winter 1999/2000, indicating an overestimation of chlorine activation in the model. Loss rates in the Antarctic show signs of saturation in September, which have to be considered in the comparison. Sensitivity tests were performed with the box model in order to assess the impact of kinetic parameters of the ClO-Cl2O2 catalytic cycle and total bromine content on the ozone loss rate. These tests resulted in a maximum change in ozone loss rates of 1.2 ppbv/sunlit hour, generally in high solar zenith angle conditions. In some cases, a better agreement was achieved with fastest photolysis of Cl2O2 and additional source of total inorganic bromine but at the expense of overestimation of smaller ozone loss rates derived later in the winter.

The ocean's gravitational potential energy budget in a coupled climate model

This study examines, in a unified fashion, the budgets of ocean gravitational potential energy (GPE) and available gravitational potential energy (AGPE) in the control simulation of the coupled atmosphere–ocean general circulation model HadCM3. Only AGPE can be converted into kinetic energy by adiabatic processes. Diapycnal mixing supplies GPE, but not AGPE, whereas the reverse is true of the combined effect of surface buoyancy forcing and convection. Mixing and buoyancy forcing, thus, play complementary roles in sustaining the large scale circulation. However, the largest globally integrated source of GPE is resolved advection (+0.57 TW) and the largest sink is through parameterized eddy transports (-0.82 TW). The effect of these adiabatic processes on AGPE is identical to their effect on GPE, except for perturbations to both budgets due to numerical leakage exacerbated by non-linearities in the equation of state.

Improving the evaluation of hydrological multi-model forecast performance in the Upper Danube Catchment

Medium range flood forecasting activities, driven by various meteorological forecasts ranging from high resolution deterministic forecasts to low spatial resolution ensemble prediction systems, share a major challenge in the appropriateness and design of performance measures. In this paper possible limitations of some traditional hydrological and meteorological prediction quality and verification measures are identified. Some simple modifications are applied in order to circumvent the problem of the autocorrelation dominating river discharge time-series and in order to create a benchmark model enabling the decision makers to evaluate the forecast quality and the model quality. Although the performance period is quite short the advantage of a simple cost-loss function as a measure of forecast quality can be demonstrated.

Travelling waves in a model of species migration

A model of species migration is presented which takes the form of a reaction-diffusion system. We consider special limits of this model in which we demonstrate the existence of travelling wave solutions. These solutions can be used to describe the migration of cells, bacteria, and some organisms. © 2000 Elsevier Science Ltd. All rights reserved.

Relationship between condensed tannin structures and their ability to precipitate feed proteins in the rumen

Abstract BACKGROUND Tannins can bind to and precipitate protein by forming insoluble complexes resistant to fermentation and with a positive effect on protein utilisation by ruminants. Three protein types, Rubisco, rapeseed protein and bovine serum albumin (a single high-molecular weight protein), were used to test the effects of increasing concentrations of structurally different condensed tannins on protein solubility/precipitation. RESULTS Protein type (PT) influenced solubility after addition of condensed tannins (P < 0.001) in the order: Rubisco < rapeseed < BSA (P < 0.05). The type of condensed tannin (CT) affected protein solubility (P = 0.001) with a CT × PT interaction (P = 0.001). Mean degree of polymerisation, proportions of cis- versus trans-flavanol subunits or prodelphinidins versus procyanidins among CTs could not explain precipitation capacities. Increasing tannin concentration decreased protein solubility (P < 0.001) with a PT × CT concentration interaction. The proportion of low-molecular weight rapeseed proteins remaining in solution increased with CT concentration but not with Rubisco. CONCLUSIONS Results of this study suggest that PT and CT type are both of importance for protein precipitation but that the CT structures investigated did not allow identification of parameters that contribute most to precipitation. It is possible that the three-dimensional structures of tannins and proteins may be more important factors in tannin–protein interactions. © 2013 Society of Chemical Industry