Dynamic integrated system optimization and parameter estimation for discrete time optimal control of nonlinear systems

An algorithm for solving nonlinear discrete time optimal control problems with model-reality differences is presented. The technique uses Dynamic Integrated System Optimization and Parameter Estimation (DISOPE), which achieves the correct optimal solution in spite of deficiencies in the mathematical model employed in the optimization procedure. A version of the algorithm with a linear-quadratic model-based problem, implemented in the C+ + programming language, is developed and applied to illustrative simulation examples. An analysis of the optimality and convergence properties of the algorithm is also presented.

Model predictive control using dynamic integrated system optimisation and parameter estimation (DISOPE)

DISOPE is a technique for solving optimal control problems where there are differences in structure and parameter values between reality and the model employed in the computations. The model reality differences can also allow for deliberate simplification of model characteristics and performance indices in order to facilitate the solution of the optimal control problem. The technique was developed originally in continuous time and later extended to discrete time. The main property of the procedure is that by iterating on appropriately modified model based problems the correct optimal solution is achieved in spite of the model-reality differences. Algorithms have been developed in both continuous and discrete time for a general nonlinear optimal control problem with terminal weighting, bounded controls and terminal constraints. The aim of this paper is to show how the DISOPE technique can aid receding horizon optimal control computation in nonlinear model predictive control.

A comparative analysis of projected impacts of climate change on river runoff from global and catchment-scale hydrological models

We present a comparative analysis of projected impacts of climate change on river runoff from two types of distributed hydrological model, a global hydrological model (GHM) and catchment-scale hydrological models (CHM). Analyses are conducted for six catchments that are global in coverage and feature strong contrasts in spatial scale as well as climatic and development conditions. These include the Liard (Canada), Mekong (SE Asia), Okavango (SW Africa), Rio Grande (Brazil), Xiangu (China) and Harper's Brook (UK). A single GHM (Mac-PDM.09) is applied to all catchments whilst different CHMs are applied for each catchment. The CHMs typically simulate water resources impacts based on a more explicit representation of catchment water resources than that available from the GHM, and the CHMs include river routing. Simulations of average annual runoff, mean monthly runoff and high (Q5) and low (Q95) monthly runoff under baseline (1961-1990) and climate change scenarios are presented. We compare the simulated runoff response of each hydrological model to (1) prescribed increases in global mean temperature from the HadCM3 climate model and (2)a prescribed increase in global-mean temperature of 2oC for seven GCMs to explore response to climate model and structural uncertainty. We find that differences in projected changes of mean annual runoff between the two types of hydrological model can be substantial for a given GCM, and they are generally larger for indicators of high and low flow. However, they are relatively small in comparison to the range of projections across the seven GCMs. Hence, for the six catchments and seven GCMs we considered, climate model structural uncertainty is greater than the uncertainty associated with the type of hydrological model applied. Moreover, shifts in the seasonal cycle of runoff with climate change are presented similarly by both hydrological models, although for some catchments the monthly timing of high and low flows differs.This implies that for studies that seek to quantify and assess the role of climate model uncertainty on catchment-scale runoff, it may be equally as feasible to apply a GHM as it is to apply a CHM, especially when climate modelling uncertainty across the range of available GCMs is as large as it currently is. Whilst the GHM is able to represent the broad climate change signal that is represented by the CHMs, we find, however, that for some catchments there are differences between GHMs and CHMs in mean annual runoff due to differences in potential evaporation estimation methods, in the representation of the seasonality of runoff, and in the magnitude of changes in extreme monthly runoff, all of which have implications for future water management issues.

Production of pH-responsive microparticles by spray drying: investigation of experimental parameter effects on morphological and release properties

During spray drying, emphasis is placed on process optimisation to generate favourable particle morphological and flow properties. The effect of the initial feed solution composition on the drug release from the prepared microparticles is rarely considered. We investigated the effects of solvent composition, feed solution concentration and drug-loading on sodium salicylate, hydrocortisone and triamcinolone release from spray dried Eudragit L100 microparticles. Eudragit L100 is a pH-responsive polymer whose dissolution threshold is pH 6 so dissolution testing of the prepared microparticles at pH 5 and 1.2 illustrated non-polymer controlled burst release. Increasing the water content of the initial ethanolic feed solution significantly reduced hydrocortisone burst release at pH 5, as did reducing the feed solution concentration. These findings caution that changes in feed solution concentration or solvent composition not only affect particles’ morphological characteristics but can also negatively alter their drug release properties. This work also illustrate that drug-free microparticles can have different morphological properties to drug-loaded microparticles. Therefore, process optimisation needs to be carried out using drug-loaded systems. Depending on the physicochemical properties of the encapsulated API, drug-loading can affect the polymer solubility in the initial feed solution with consequent impact on microparticles morphological and release properties.

Hillslope scale surface runoff, sediment, and nutrient losses associated with tramline wheelings

Research on arable sandy loam and silty clay loam soils on 4° slopes in England has shown that tramlines (i.e. the unseeded wheeling areas used to facilitate spraying operations in cereal crops) can represent the most important pathway for phosphorus and sediment loss from moderately sloping fields. Detailed monitoring over the October–March period in winters 2005–2006 and 2006–2007 included event-based sampling of surface runoff, suspended and particulate sediment, and dissolved and particulate phosphorus from hillslope segments (each ∼300–800 m2) established in a randomized block design with four replicates of each treatment at each of two sites on lighter and heavier soils. Experimental treatments assessed losses from the cropped area without tramlines, and from the uncropped tramline area, and were compared to losses from tramlines which had been disrupted once in the autumn with a shallow tine. On the lighter soil, the effects of removal or shallow incorporation of straw residues was also determined. Research on both sandy and silty clay loam soils across two winters showed that tramline wheelings represented the dominant pathway for surface runoff and transport of sediment, phosphorus and nitrogen from cereal crops on moderate slopes. Results indicated 5·5–15·8% of rainfall lost as runoff, and losses of 0·8–2·9 kg TP ha−1 and 0·3–4·8 t ha−1 sediment in tramline treatments, compared to only 0·2–1·7% rainfall lost as runoff, and losses of 0·0–0·2 kg TP ha−1 and 0·003–0·3 t ha−1 sediment from treatments without tramlines or those where tramlines had been disrupted. The novel shallow disruption of tramline wheelings using a tine once following the autumn spray operation consistently and dramatically reduced (p < 0·001) surface runoff and loads of sediment, total nitrogen and total phosphorus to levels similar to those measured in cropped areas between tramlines. Results suggest that options for managing tramline wheelings warrant further refinement and evaluation with a view to incorporating them into spatially-targeted farm-level management planning using national or catchment-based agri-environment policy instruments aimed at reducing diffuse pollution from land to surface water systems. Copyright © 2010 John Wiley & Sons, Ltd.

Data assimilation for state and parameter estimation: application to morphodynamic modelling

Data assimilation is predominantly used for state estimation; combining observational data with model predictions to produce an updated model state that most accurately approximates the true system state whilst keeping the model parameters fixed. This updated model state is then used to initiate the next model forecast. Even with perfect initial data, inaccurate model parameters will lead to the growth of prediction errors. To generate reliable forecasts we need good estimates of both the current system state and the model parameters. This paper presents research into data assimilation methods for morphodynamic model state and parameter estimation. First, we focus on state estimation and describe implementation of a three dimensional variational(3D-Var) data assimilation scheme in a simple 2D morphodynamic model of Morecambe Bay, UK. The assimilation of observations of bathymetry derived from SAR satellite imagery and a ship-borne survey is shown to significantly improve the predictive capability of the model over a 2 year run. Here, the model parameters are set by manual calibration; this is laborious and is found to produce different parameter values depending on the type and coverage of the validation dataset. The second part of this paper considers the problem of model parameter estimation in more detail. We explain how, by employing the technique of state augmentation, it is possible to use data assimilation to estimate uncertain model parameters concurrently with the model state. This approach removes inefficiencies associated with manual calibration and enables more effective use of observational data. We outline the development of a novel hybrid sequential 3D-Var data assimilation algorithm for joint state-parameter estimation and demonstrate its efficacy using an idealised 1D sediment transport model. The results of this study are extremely positive and suggest that there is great potential for the use of data assimilation-based state-parameter estimation in coastal morphodynamic modelling.

Ensemble forecasts of a flood-producing storm: comparison of the influence of model-state perturbations and parameter modifications

High-resolution ensemble simulations (Δx = 1 km) are performed with the Met Office Unified Model for the Boscastle (Cornwall, UK) flash-flooding event of 16 August 2004. Forecast uncertainties arising from imperfections in the forecast model are analysed by comparing the simulation results produced by two types of perturbation strategy. Motivated by the meteorology of the event, one type of perturbation alters relevant physics choices or parameter settings in the model's parametrization schemes. The other type of perturbation is designed to account for representativity error in the boundary-layer parametrization. It makes direct changes to the model state and provides a lower bound against which to judge the spread produced by other uncertainties. The Boscastle has genuine skill at scales of approximately 60 km and an ensemble spread which can be estimated to within ∼ 10% with only eight members. Differences between the model-state perturbation and physics modification strategies are discussed, the former being more important for triggering and the latter for subsequent cell development, including the average internal structure of convective cells. Despite such differences, the spread in rainfall evaluated at skilful scales is shown to be only weakly sensitive to the perturbation strategy. This suggests that relatively simple strategies for treating model uncertainty may be sufficient for practical, convective-scale ensemble forecasting.

European plant phenology and climate as seen in a 20-year AVHRR land-surface parameter dataset

Vegetation distribution and state have been measured since 1981 by the AVHRR (Advanced Very High Resolution Radiometer) instrument through satellite remote sensing. In this study a correction method is applied to the Pathfinder NDVI (Normalized Difference Vegetation Index) data to create a continuous European vegetation phenology dataset of a 10-day temporal and 0.1° spatial resolution; additionally, land surface parameters for use in biosphere–atmosphere modelling are derived. The analysis of time-series from this dataset reveals, for the years 1982–2001, strong seasonal and interannual variability in European land surface vegetation state. Phenological metrics indicate a late and short growing season for the years 1985–1987, in addition to early and prolonged activity in the years 1989, 1990, 1994 and 1995. These variations are in close agreement with findings from phenological measurements at the surface; spring phenology is also shown to correlate particularly well with anomalies in winter temperature and winter North Atlantic Oscillation (NAO) index. Nevertheless, phenological metrics, which display considerable regional differences, could only be determined for vegetation with a seasonal behaviour. Trends in the phenological phases reveal a general shift to earlier (−0.54 days year−1) and prolonged (0.96 days year−1) growing periods which are statistically significant, especially for central Europe.

Bayesian parameter estimation for latent Markov random fields and social networks

Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the calculation of an intractable normalising constant. This problem has received much attention, but very little of this has focussed on the important practical case where the data consists of noisy or incomplete observations of the underlying hidden structure. This paper specifically addresses this problem, comparing two alternative methodologies. In the first of these approaches particle Markov chain Monte Carlo (Andrieu et al., 2010) is used to efficiently explore the parameter space, combined with the exchange algorithm (Murray et al., 2006) for avoiding the calculation of the intractable normalising constant (a proof showing that this combination targets the correct distribution in found in a supplementary appendix online). This approach is compared with approximate Bayesian computation (Pritchard et al., 1999). Applications to estimating the parameters of Ising models and exponential random graphs from noisy data are presented. Each algorithm used in the paper targets an approximation to the true posterior due to the use of MCMC to simulate from the latent graphical model, in lieu of being able to do this exactly in general. The supplementary appendix also describes the nature of the resulting approximation.

The importance of friction in mountain wave drag amplification by Scorer parameter resonance

A mechanism for amplification of mountain waves, and their associated drag, by parametric resonance is investigated using linear theory and numerical simulations. This mechanism, which is active when the Scorer parameter oscillates with height, was recently classified by previous authors as intrinsically nonlinear. Here it is shown that, if friction is included in the simplest possible form as a Rayleigh damping, and the solution to the Taylor-Goldstein equation is expanded in a power series of the amplitude of the Scorer parameter oscillation, linear theory can replicate the resonant amplification produced by numerical simulations with some accuracy. The drag is significantly altered by resonance in the vicinity of n/l_0 = 2, where l_0 is the unperturbed value of the Scorer parameter and n is the wave number of its oscillation. Depending on the phase of this oscillation, the drag may be substantially amplified or attenuated relative to its non-resonant value, displaying either single maxima or minima, or double extrema near n/l_0 = 2. Both non-hydrostatic effects and friction tend to reduce the magnitude of the drag extrema. However, in exactly inviscid conditions, the single drag maximum and minimum are suppressed. As in the atmosphere friction is often small but non-zero outside the boundary layer, modelling of the drag amplification mechanism addressed here should be quite sensitive to the type of turbulence closure employed in numerical models, or to computational dissipation in nominally inviscid simulations.

Input type and parameter resetting: is naturalistic input necessary?

It has been argued that extended exposure to naturalistic input provides L2 learners with more of an opportunity to converge of target morphosyntactic competence as compared to classroom-only environments, given that the former provide more positive evidence of less salient linguistic properties than the latter (e.g., Isabelli 2004). Implicitly, the claim is that such exposure is needed to fully reset parameters. However, such a position conflicts with the notion of parameterization (cf. Rothman and Iverson 2007). In light of two types of competing generative theories of adult L2 acquisition – the No Impairment Hypothesis (e.g., Duffield and White 1999) and so-called Failed Features approaches (e.g., Beck 1998; Franceschina 2001; Hawkins and Chan 1997), we investigate the verifiability of such a claim. Thirty intermediate L2 Spanish learners were tested in regards to properties of the Null-Subject Parameter before and after study-abroad. The data suggest that (i) parameter resetting is possible and (ii) exposure to naturalistic input is not privileged.

Complex dynamics in simple systems with periodic parameter oscillations

We study systems with periodically oscillating parameters that can give way to complex periodic or nonperiodic orbits. Performing the long time limit, we can define ergodic averages such as Lyapunov exponents, where a negative maximal Lyapunov exponent corresponds to a stable periodic orbit. By this, extremely complicated periodic orbits composed of contracting and expanding phases appear in a natural way. Employing the technique of ϵ-uncertain points, we find that values of the control parameters supporting such periodic motion are densely embedded in a set of values for which the motion is chaotic. When a tiny amount of noise is coupled to the system, dynamics with positive and with negative nontrivial Lyapunov exponents are indistinguishable. We discuss two physical systems, an oscillatory flow inside a duct and a dripping faucet with variable water supply, where such a mechanism seems to be responsible for a complicated alternation of laminar and turbulent phases.

Multi-site evaluation of an urban land-surface model: intra-urban heterogeneity, seasonality and parameter complexity requirements

An extensive off-line evaluation of the Noah/Single Layer Urban Canopy Model (Noah/SLUCM) urban land-surface model is presented using data from 15 sites to assess (1) the ability of the scheme to reproduce the surface energy balance observed in a range of urban environments, including seasonal changes, and (2) the impact of increasing complexity of input parameter information. Model performance is found to be most dependent on representation of vegetated surface area cover; refinement of other parameter values leads to smaller improvements. Model biases in net all-wave radiation and trade-offs between turbulent heat fluxes are highlighted using an optimization algorithm. Here we use the Urban Zones to characterize Energy partitioning (UZE) as the basis to assign default SLUCM parameter values. A methodology (FRAISE) to assign sites (or areas) to one of these categories based on surface characteristics is evaluated. Using three urban sites from the Basel Urban Boundary Layer Experiment (BUBBLE) dataset, an independent evaluation of the model performance with the parameter values representative of each class is performed. The scheme copes well with both seasonal changes in the surface characteristics and intra-urban heterogeneities in energy flux partitioning, with RMSE performance comparable to similar state-of-the-art models for all fluxes, sites and seasons. The potential of the methodology for high-resolution atmospheric modelling application using the Weather Research and Forecasting (WRF) model is highlighted. This analysis supports the recommendations that (1) three classes are appropriate to characterize the urban environment, and (2) that the parameter values identified should be adopted as default values in WRF.