Inverting recurrent neural networks for internal model control of nonlinear systems

In this paper, we show how a set of recently derived theoretical results for recurrent neural networks can be applied to the production of an internal model control system for a nonlinear plant. The results include determination of the relative order of a recurrent neural network and invertibility of such a network. A closed loop controller is produced without the need to retrain the neural network plant model. Stability of the closed-loop controller is also demonstrated.

Internal model control of nonlinear systems through the inversion of recurrent neural networks

Recurrent neural networks can be used for both the identification and control of nonlinear systems. This paper takes a previously derived set of theoretical results about recurrent neural networks and applies them to the task of providing internal model control for a nonlinear plant. Using the theoretical results, we show how an inverse controller can be produced from a neural network model of the plant, without the need to train an additional network to perform the inverse control.

Inverse model control using recurrent networks

This paper illustrates how internal model control of nonlinear processes can be achieved by recurrent neural networks, e.g. fully connected Hopfield networks. It is shown that using results developed by Kambhampati et al. (1995), that once a recurrent network model of a nonlinear system has been produced, a controller can be produced which consists of the network comprising the inverse of the model and a filter. Thus, the network providing control for the nonlinear system does not require any training after it has been trained to model the nonlinear system. Stability and other issues of importance for nonlinear control systems are also discussed.

Evaluation of water and energy budgets in regional climate models applied over Europe

This study presents a model intercomparison of four regional climate models (RCMs) and one variable resolution atmospheric general circulation model (AGCM) applied over Europe with special focus on the hydrological cycle and the surface energy budget. The models simulated the 15 years from 1979 to 1993 by using quasi-observed boundary conditions derived from ECMWF re-analyses (ERA). The model intercomparison focuses on two large atchments representing two different climate conditions covering two areas of major research interest within Europe. The first is the Danube catchment which represents a continental climate dominated by advection from the surrounding land areas. It is used to analyse the common model error of a too dry and too warm simulation of the summertime climate of southeastern Europe. This summer warming and drying problem is seen in many RCMs, and to a less extent in GCMs. The second area is the Baltic Sea catchment which represents maritime climate dominated by advection from the ocean and from the Baltic Sea. This catchment is a research area of many studies within Europe and also covered by the BALTEX program. The observed data used are monthly mean surface air temperature, precipitation and river discharge. For all models, these are used to estimate mean monthly biases of all components of the hydrological cycle over land. In addition, the mean monthly deviations of the surface energy fluxes from ERA data are computed. Atmospheric moisture fluxes from ERA are compared with those of one model to provide an independent estimate of the convergence bias derived from the observed data. These help to add weight to some of the inferred estimates and explain some of the discrepancies between them. An evaluation of these biases and deviations suggests possible sources of error in each of the models. For the Danube catchment, systematic errors in the dynamics cause the prominent summer drying problem for three of the RCMs, while for the fourth RCM this is related to deficiencies in the land surface parametrization. The AGCM does not show this drying problem. For the Baltic Sea catchment, all models similarily overestimate the precipitation throughout the year except during the summer. This model deficit is probably caused by the internal model parametrizations, such as the large-scale condensation and the convection schemes.

Evaluation of water and energy budgets in regional climate models applied over Europe

Abstract This study presents a model intercomparison of four regional climate models (RCMs) and one variable resolution atmospheric general circulation model (AGCM) applied over Europe with special focus on the hydrological cycle and the surface energy budget. The models simulated the 15 years from 1979 to 1993 by using quasi-observed boundary conditions derived from ECMWF re-analyses (ERA). The model intercomparison focuses on two large atchments representing two different climate conditions covering two areas of major research interest within Europe. The first is the Danube catchment which represents a continental climate dominated by advection from the surrounding land areas. It is used to analyse the common model error of a too dry and too warm simulation of the summertime climate of southeastern Europe. This summer warming and drying problem is seen in many RCMs, and to a less extent in GCMs. The second area is the Baltic Sea catchment which represents maritime climate dominated by advection from the ocean and from the Baltic Sea. This catchment is a research area of many studies within Europe and also covered by the BALTEX program. The observed data used are monthly mean surface air temperature, precipitation and river discharge. For all models, these are used to estimate mean monthly biases of all components of the hydrological cycle over land. In addition, the mean monthly deviations of the surface energy fluxes from ERA data are computed. Atmospheric moisture fluxes from ERA are compared with those of one model to provide an independent estimate of the convergence bias derived from the observed data. These help to add weight to some of the inferred estimates and explain some of the discrepancies between them. An evaluation of these biases and deviations suggests possible sources of error in each of the models. For the Danube catchment, systematic errors in the dynamics cause the prominent summer drying problem for three of the RCMs, while for the fourth RCM this is related to deficiencies in the land surface parametrization. The AGCM does not show this drying problem. For the Baltic Sea catchment, all models similarily overestimate the precipitation throughout the year except during the summer. This model deficit is probably caused by the internal model parametrizations, such as the large-scale condensation and the convection schemes.

The synergies between goal sketching and enterprise architecture

This paper introduces a pragmatic and practical method for requirements modeling. The method is built using the concepts of our goal sketching technique together with techniques from an enterprise architecture modeling language. Our claim is that our method will help project managers who want to establish early control of their projects and will also give managers confidence in the scope of their project. In particular we propose the inclusion of assumptions as first class entities in the ArchiMate enterprise architecture modeling language and an extension of the ArchiMate Motivation Model principle to allow radical as well as normative analyses. We demonstrate the usefulness of this method using a simple university library system as an example.

Ice internal friction: Standard theoretical perspectives on friction codified, adapted for the unusual rheology of ice, and unified

Sea ice contains flaws including frictional contacts. We aim to describe quantitatively the mechanics of those contacts, providing local physics for geophysical models. With a focus on the internal friction of ice, we review standard micro-mechanical models of friction. The solid's deformation under normal load may be ductile or elastic. The shear failure of the contact may be by ductile flow, brittle fracture, or melting and hydrodynamic lubrication. Combinations of these give a total of six rheological models. When the material under study is ice, several of the rheological parameters in the standard models are not constant, but depend on the temperature of the bulk, on the normal stress under which samples are pressed together, or on the sliding velocity and acceleration. This has the effect of making the shear stress required for sliding dependent on sliding velocity, acceleration, and temperature. In some cases, it also perturbs the exponent in the normal-stress dependence of that shear stress away from the value that applies to most materials. We unify the models by a principle of maximum displacement for normal deformation, and of minimum stress for shear failure, reducing the controversy over the mechanism of internal friction in ice to the choice of values of four parameters in a single model. The four parameters represent, for a typical asperity contact, the sliding distance required to expel melt-water, the sliding distance required to break contact, the normal strain in the asperity, and the thickness of any ductile shear zone.

A mechanism of internal decadal atlantic ocean variability in a high-resolution coupled climate model

The North Atlantic Ocean subpolar gyre (NA SPG) is an important region for initialising decadal climate forecasts. Climate model simulations and palaeo climate reconstructions have indicated that this region could also exhibit large, internally generated variability on decadal timescales. Understanding these modes of variability, their consistency across models, and the conditions in which they exist, is clearly important for improving the skill of decadal predictions — particularly when these predictions are made with the same underlying climate models. Here we describe and analyse a mode of internal variability in the NA SPG in a state-of-the-art, high resolution, coupled climate model. This mode has a period of 17 years and explains 15–30% of the annual variance in related ocean indices. It arises due to the advection of heat content anomalies around the NA SPG. Anomalous circulation drives the variability in the southern half of the NA SPG, whilst mean circulation and anomalous temperatures are important in the northern half. A negative feedback between Labrador Sea temperatures/densities and those in the North Atlantic Current is identified, which allows for the phase reversal. The atmosphere is found to act as a positive feedback on to this mode via the North Atlantic Oscillation which itself exhibits a spectral peak at 17 years. Decadal ocean density changes associated with this mode are driven by variations in temperature, rather than salinity — a point which models often disagree on and which we suggest may affect the veracity of the underlying assumptions of anomaly-assimilating decadal prediction methodologies.

The effect of doubled CO2 and model basic state biases on the monsoon-ENSO system. I: Mean response and interannual variability

The impact of doubled CO2 concentration on the Asian summer monsoon is studied using a coupled ocean-atmosphere model. Both the mean seasonal precipitation and interannual monsoon variability are found to increase in the future climate scenario presented. Systematic biases in current climate simulations of the coupled system prevent accurate representation of the monsoon-ENSO teleconnection, of prime importance for seasonal prediction and for determining monsoon interannual variability. By applying seasonally varying heat flux adjustments to the tropical Pacific and Indian Ocean surface in the future climate simulation, some assessment can be made of the impact of systematic model biases on future climate predictions. In simulations where the flux adjustments are implemented, the response to climate change is magnified, with the suggestion that systematic biases may be masking the true impact of increased greenhouse gas forcing. The teleconnection between ENSO and the Asian summer monsoon remains robust in the future climate, although the Indo-Pacific takes on more of a biennial character for long periods of the flux-adjusted simulation. Assessing the teleconnection across interdecadal timescales shows wide variations in its amplitude, despite the absence of external forcing. This suggests that recent changes in the observed record cannot be distinguished from internal variations and as such are not necessarily related to climate change.

QUAGMIRE v1.3: a quasi-geostrophic model for investigating rotating fluids experiments

QUAGMIRE is a quasi-geostrophic numerical model for performing fast, high-resolution simulations of multi-layer rotating annulus laboratory experiments on a desktop personal computer. The model uses a hybrid finite-difference/spectral approach to numerically integrate the coupled nonlinear partial differential equations of motion in cylindrical geometry in each layer. Version 1.3 implements the special case of two fluid layers of equal resting depths. The flow is forced either by a differentially rotating lid, or by relaxation to specified streamfunction or potential vorticity fields, or both. Dissipation is achieved through Ekman layer pumping and suction at the horizontal boundaries, including the internal interface. The effects of weak interfacial tension are included, as well as the linear topographic beta-effect and the quadratic centripetal beta-effect. Stochastic forcing may optionally be activated, to represent approximately the effects of random unresolved features. A leapfrog time stepping scheme is used, with a Robert filter. Flows simulated by the model agree well with those observed in the corresponding laboratory experiments.

A semi-quantitative approach to deriving a model structure for the uptake of organic chemicals by vegetation

An expert elicitation exercise was undertaken to determine those components and processes that are most important for modeling plant uptake of organic chemicals. The state of our knowledge of these processes was also assessed. This semi-quantitative analysis allowed the construction of an idealized model with seven compartments; soil bulk, soil water, roots, stem, leaves, fruit, and air. Three main areas were identified further research: 1) the uptake of organic chemicals by fruit; 2) the internal transfer of organic chemicals between plant structures (e.g., stem and leaves); and 3) the transfer via the soil-air-plant pathway. Until new data becomes available to quantify these processes, it is proposed that an equilibrium partitioning approach is used between plant components other than fruit or that models consist of both an edible and inedible compartment.

The Phosphorus Indicators Tool: a simple model of diffuse P loss from agricultural land to water

The Phosphorus Indicators Tool provides a catchment-scale estimation of diffuse phosphorus (P) loss from agricultural land to surface waters using the most appropriate indicators of P loss. The Tool provides a framework that may be applied across the UK to estimate P loss, which is sensitive not only to land use and management but also to environmental factors such as climate, soil type and topography. The model complexity incorporated in the P Indicators Tool has been adapted to the level of detail in the available data and the need to reflect the impact of changes in agriculture. Currently, the Tool runs on an annual timestep and at a 1 km(2) grid scale. We demonstrate that the P Indicators Tool works in principle and that its modular structure provides a means of accounting for P loss from one layer to the next, and ultimately to receiving waters. Trial runs of the Tool suggest that modelled P delivery to water approximates measured water quality records. The transparency of the structure of the P Indicators Tool means that identification of poorly performing coefficients is possible, and further refinements of the Tool can be made to ensure it is better calibrated and subsequently validated against empirical data, as it becomes available.

An adaptive finite element water column model using the Mellor-Yamada level 2.5 turbulence closure scheme

A one-dimensional water column model using the Mellor and Yamada level 2.5 parameterization of vertical turbulent fluxes is presented. The model equations are discretized with a mixed finite element scheme. Details of the finite element discrete equations are given and adaptive mesh refinement strategies are presented. The refinement criterion is an "a posteriori" error estimator based on stratification, shear and distance to surface. The model performances are assessed by studying the stress driven penetration of a turbulent layer into a stratified fluid. This example illustrates the ability of the presented model to follow some internal structures of the flow and paves the way for truly generalized vertical coordinates. (c) 2005 Elsevier Ltd. All rights reserved.

Anthropogenic warming of the oceans: Observations and model results

Observations show the oceans have warmed over the past 40 yr. with appreciable regional variation and more warming at the surface than at depth. Comparing the observations with results from two coupled ocean-atmosphere climate models [the Parallel Climate Model version 1 (PCM) and the Hadley Centre Coupled Climate Model version 3 (HadCM3)] that include anthropogenic forcing shows remarkable agreement between the observed and model-estimated warming. In this comparison the models were sampled at the same locations as gridded yearly observed data. In the top 100 m of the water column the warming is well separated from natural variability, including both variability arising from internal instabilities of the coupled ocean-atmosphere climate system and that arising from volcanism and solar fluctuations. Between 125 and 200 m the agreement is not significant, but then increases again below this level, and remains significant down to 600 m. Analysis of PCM's heat budget indicates that the warming is driven by an increase in net surface heat flux that reaches 0.7 W m(-2) by the 1990s; the downward longwave flux increases bv 3.7 W m(-2). which is not fully compensated by an increase in the upward longwave flux of 2.2 W m(-2). Latent and net solar heat fluxes each decrease by about 0.6 W m(-2). The changes in the individual longwave components are distinguishable from the preindustrial mean by the 1920s, but due to cancellation of components. changes in the net surface heat flux do not become well separated from zero until the 1960s. Changes in advection can also play an important role in local ocean warming due to anthropogenic forcing, depending, on the location. The observed sampling of ocean temperature is highly variable in space and time. but sufficient to detect the anthropogenic warming signal in all basins, at least in the surface layers, bv the 1980s.