Conditioning and preconditioning of the variational data assimilation problem

Numerical weather prediction (NWP) centres use numerical models of the atmospheric flow to forecast future weather states from an estimate of the current state. Variational data assimilation (VAR) is used commonly to determine an optimal state estimate that miminizes the errors between observations of the dynamical system and model predictions of the flow. The rate of convergence of the VAR scheme and the sensitivity of the solution to errors in the data are dependent on the condition number of the Hessian of the variational least-squares objective function. The traditional formulation of VAR is ill-conditioned and hence leads to slow convergence and an inaccurate solution. In practice, operational NWP centres precondition the system via a control variable transform to reduce the condition number of the Hessian. In this paper we investigate the conditioning of VAR for a single, periodic, spatially-distributed state variable. We present theoretical bounds on the condition number of the original and preconditioned Hessians and hence demonstrate the improvement produced by the preconditioning. We also investigate theoretically the effect of observation position and error variance on the preconditioned system and show that the problem becomes more ill-conditioned with increasingly dense and accurate observations. Finally, we confirm the theoretical results in an operational setting by giving experimental results from the Met Office variational system.

Adaptive recursive control of a soil testing load frame

Recursive Learning Control (RLC) has the potential to significantly reduce the tracking error in many repetitive trajectory applications. This paper presents an application of RLC to a soil testing load frame where non-adaptive techniques struggle with the highly nonlinear nature of soil. The main purpose of the controller is to apply a sinusoidal force reference trajectory on a soil sample with a high degree of accuracy and repeatability. The controller uses a feedforward control structure, recursive least squares adaptation algorithm and RLC to compensate for periodic errors. Tracking error is reduced and stability is maintained across various soil sample responses.

Modelling and inverting complex-valued Wiener systems

We develop a complex-valued (CV) B-spline neural network approach for efficient identification and inversion of CV Wiener systems. The CV nonlinear static function in the Wiener system is represented using the tensor product of two univariate B-spline neural networks. With the aid of a least squares parameter initialisation, the Gauss-Newton algorithm effectively estimates the model parameters that include the CV linear dynamic model coefficients and B-spline neural network weights. The identification algorithm naturally incorporates the efficient De Boor algorithm with both the B-spline curve and first order derivative recursions. An accurate inverse of the CV Wiener system is then obtained, in which the inverse of the CV nonlinear static function of the Wiener system is calculated efficiently using the Gaussian-Newton algorithm based on the estimated B-spline neural network model, with the aid of the De Boor recursions. The effectiveness of our approach for identification and inversion of CV Wiener systems is demonstrated using the application of digital predistorter design for high power amplifiers with memory

Does increased hydrochemical model complexity decrease robustness?

The aim of this study was, within a sensitivity analysis framework, to determine if additional model complexity gives a better capability to model the hydrology and nitrogen dynamics of a small Mediterranean forested catchment or if the additional parameters cause over-fitting. Three nitrogen-models of varying hydrological complexity were considered. For each model, general sensitivity analysis (GSA) and Generalized Likelihood Uncertainty Estimation (GLUE) were applied, each based on 100,000 Monte Carlo simulations. The results highlighted the most complex structure as the most appropriate, providing the best representation of the non-linear patterns observed in the flow and streamwater nitrate concentrations between 1999 and 2002. Its 5% and 95% GLUE bounds, obtained considering a multi-objective approach, provide the narrowest band for streamwater nitrogen, which suggests increased model robustness, though all models exhibit periods of inconsistent good and poor fits between simulated outcomes and observed data. The results confirm the importance of the riparian zone in controlling the short-term (daily) streamwater nitrogen dynamics in this catchment but not the overall flux of nitrogen from the catchment. It was also shown that as the complexity of a hydrological model increases over-parameterisation occurs, but the converse is true for a water quality model where additional process representation leads to additional acceptable model simulations. Water quality data help constrain the hydrological representation in process-based models. Increased complexity was justifiable for modelling river-system hydrochemistry. Increased complexity was justifiable for modelling river-system hydrochemistry.

The gender gap in real estate sales: negotiation skill or agent selection?

This study examines differences in net selling price for residential real estate across male and female agents. A sample of 2,020 home sales transactions from Fulton County, Georgia are analyzed in a two-stage least squares, geospatial autoregressive corrected, semi-log hedonic model to test for gender and gender selection effects. Although agent gender seems to play a role in naïve models, its role becomes inconclusive as variables controlling for possible price and time on market expectations of the buyers and sellers are introduced to the models. Clear differences in real estate sales prices, time on market, and agent incomes across genders are unlikely due to differences in negotiation performance between genders or the mix of genders in a two-agent negotiation. The evidence suggests an interesting alternative to agent performance: that buyers and sellers with different reservation price and time on market expectations, such as those selling foreclosure homes, tend to select agents along gender lines.

Accurate analysis of noble gas concentrations in small water samples and its application to fluid inclusions in stalagmites

The concentrations of dissolved noble gases in water are widely used as a climate proxy to determine noble gas temperatures (NGTs); i.e., the temperature of the water when gas exchange last occurred. In this paper we make a step forward to apply this principle to fluid inclusions in stalagmites in order to reconstruct the cave temperature prevailing at the time when the inclusion was formed. We present an analytical protocol that allows us accurately to determine noble gas concentrations and isotope ratios in stalagmites, and which includes a precise manometrical determination of the mass of water liberated from fluid inclusions. Most important for NGT determination is to reduce the amount of noble gases liberated from air inclusions, as they mask the temperature-dependent noble gas signal from the water inclusions. We demonstrate that offline pre-crushing in air to subsequently extract noble gases and water from the samples by heating is appropriate to separate gases released from air and water inclusions. Although a large fraction of recent samples analysed by this technique yields NGTs close to present-day cave temperatures, the interpretation of measured noble gas concentrations in terms of NGTs is not yet feasible using the available least squares fitting models. This is because the noble gas concentrations in stalagmites are not only composed of the two components air and air saturated water (ASW), which these models are able to account for. The observed enrichments in heavy noble gases are interpreted as being due to adsorption during sample preparation in air, whereas the excess in He and Ne is interpreted as an additional noble gas component that is bound in voids in the crystallographic structure of the calcite crystals. As a consequence of our study's findings, NGTs will have to be determined in the future using the concentrations of Ar, Kr and Xe only. This needs to be achieved by further optimizing the sample preparation to minimize atmospheric contamination and to further reduce the amount of noble gases released from air inclusions.

A critical review of methodologies for measuring rental depreciation applied to UK commercial real estate

Real estate depreciation continues to be a critical issue for investors and the appraisal profession in the UK in the 1990s. Depreciation-sensitive cash flow models have been developed, but there is a real need to develop further empirical methodologies to determine rental depreciation rates for input into these models. Although building quality has been found to be an important explanatory variable in depreciation it is very difficult to incorporate it into such models or to analyse it retrospectively. It is essential to examine previous depreciation research from real estate and economics in the USA and UK to understand the issues in constructing a valid and pragmatic way of calculating rental depreciation. Distinguishing between 'depreciation' and 'obsolescence' is important, and the pattern of depreciation in any study can be influenced by such factors as the type (longitudinal or crosssectional) and timing of the study, and the market state. Longitudinal studies can analyse change more directly than cross-sectional studies. Any methodology for calculating rental depreciation rate should be formulated in the context of such issues as 'censored sample bias', 'lemons' and 'filtering', which have been highlighted in key US literature from the field of economic depreciation. Property depreciation studies in the UK have tended to overlook this literature, however. Although data limitations and constraints reduce the ability of empirical property depreciation work in the UK to consider these issues fully, 'averaging' techniques and ordinary least squares (OLS) regression can both provide a consistent way of calculating rental depreciation rates within a 'cohort' framework.

Differentiated effects of formal and informal institutional distance between countries 2 on the environmental performance of multinational enterprises

This research examines the influence of environmental institutional distance between home and host countries on the standardization of environmental performance among multinational enterprises using ordinary least-squares (OLS) regression techniques and a sample of 128 multinationals from high-polluting industries. The paper examines the environmental institutional distance of countries using the concepts of formal and informal institutional distances. The results show that whereas a high formal environmental distance between home and host countries leads multinational enterprises to achieve a different level of environmental performance according to each country's legal requirements, a high informal environmental distance encourages these firms to unify their environmental performance independently of the countries in which their units are based. The study also discusses the implications for academia, managers, and policy makers.

Numerical conformal mapping and mesh generation for polygonal and multiply-connected regions

Details are given of a boundary-fitted mesh generation method for use in modelling free surface flow and water quality. A numerical method has been developed for generating conformal meshes for curvilinear polygonal and multiply-connected regions. The method is based on the Cauchy-Riemann conditions for the analytic function and is able to map a curvilinear polygonal region directly onto a regular polygonal region, with horizontal and vertical sides. A set of equations have been derived for determining the lengths of these sides and the least-squares method has been used in solving the equations. Several numerical examples are presented to illustrate the method.

Impact of geographical region on urinary metabolomic and plasma fatty acid profiles in subjects with the metabolic syndrome across Europe: the LIPGENE study

The application of metabolomics in multi-centre studies is increasing. The aim of the present study was to assess the effects of geographical location on the metabolic profiles of individuals with the metabolic syndrome. Blood and urine samples were collected from 219 adults from seven European centres participating in the LIPGENE project (Diet, genomics and the metabolic syndrome: an integrated nutrition, agro-food, social and economic analysis). Nutrient intakes, BMI, waist:hip ratio, blood pressure, and plasma glucose, insulin and blood lipid levels were assessed. Plasma fatty acid levels and urine were assessed using a metabolomic technique. The separation of three European geographical groups (NW, northwest; NE, northeast; SW, southwest) was identified using partial least-squares discriminant analysis models for urine (R 2 X: 0•33, Q 2: 0•39) and plasma fatty acid (R 2 X: 0•32, Q 2: 0•60) data. The NW group was characterised by higher levels of urinary hippurate and N-methylnicotinate. The NE group was characterised by higher levels of urinary creatine and citrate and plasma EPA (20 : 5 n-3). The SW group was characterised by higher levels of urinary trimethylamine oxide and lower levels of plasma EPA. The indicators of metabolic health appeared to be consistent across the groups. The SW group had higher intakes of total fat and MUFA compared with both the NW and NE groups (P≤ 0•001). The NE group had higher intakes of fibre and n-3 and n-6 fatty acids compared with both the NW and SW groups (all P< 0•001). It is likely that differences in dietary intakes contributed to the separation of the three groups. Evaluation of geographical factors including diet should be considered in the interpretation of metabolomic data from multi-centre studies.

Bicorrelations and cross-bicorrelations as non-linearity tests and tools for exchange rate forecasting

This paper proposes and implements a new methodology for forecasting time series, based on bicorrelations and cross-bicorrelations. It is shown that the forecasting technique arises as a natural extension of, and as a complement to, existing univariate and multivariate non-linearity tests. The formulations are essentially modified autoregressive or vector autoregressive models respectively, which can be estimated using ordinary least squares. The techniques are applied to a set of high-frequency exchange rate returns, and their out-of-sample forecasting performance is compared to that of other time series models

Single-carrier frequency domain equalisation for hammerstein communication systems using complex-valued neural networks

Single-carrier (SC) block transmission with frequency-domain equalisation (FDE) offers a viable transmission technology for combating the adverse effects of long dispersive channels encountered in high-rate broadband wireless communication systems. However, for high bandwidthefficiency and high power-efficiency systems, the channel can generally be modelled by the Hammerstein system that includes the nonlinear distortion effects of the high power amplifier (HPA) at transmitter. For such nonlinear Hammerstein channels, the standard SC-FDE scheme no longer works. This paper advocates a complex-valued (CV) B-spline neural network based nonlinear SC-FDE scheme for Hammerstein channels. Specifically, We model the nonlinear HPA, which represents the CV static nonlinearity of the Hammerstein channel, by a CV B-spline neural network, and we develop two efficient alternating least squares schemes for estimating the parameters of the Hammerstein channel, including both the channel impulse response coefficients and the parameters of the CV B-spline model. We also use another CV B-spline neural network to model the inversion of the nonlinear HPA, and the parameters of this inverting B-spline model can easily be estimated using the standard least squares algorithm based on the pseudo training data obtained as a natural byproduct of the Hammerstein channel identification. Equalisation of the SC Hammerstein channel can then be accomplished by the usual one-tap linear equalisation in frequency domain as well as the inverse B-spline neural network model obtained in time domain. Extensive simulation results are included to demonstrate the effectiveness of our nonlinear SC-FDE scheme for Hammerstein channels.

Variational data assimilation for very large environmental problems

Variational data assimilation is commonly used in environmental forecasting to estimate the current state of the system from a model forecast and observational data. The assimilation problem can be written simply in the form of a nonlinear least squares optimization problem. However the practical solution of the problem in large systems requires many careful choices to be made in the implementation. In this article we present the theory of variational data assimilation and then discuss in detail how it is implemented in practice. Current solutions and open questions are discussed.

Calibration of structure in a distributed forecasting model for a semiarid flash flood: dynamic surface storage and channel roughness

Flash floods pose a significant danger for life and property. Unfortunately, in arid and semiarid environment the runoff generation shows a complex non-linear behavior with a strong spatial and temporal non-uniformity. As a result, the predictions made by physically-based simulations in semiarid areas are subject to great uncertainty, and a failure in the predictive behavior of existing models is common. Thus better descriptions of physical processes at the watershed scale need to be incorporated into the hydrological model structures. For example, terrain relief has been systematically considered static in flood modelling at the watershed scale. Here, we show that the integrated effect of small distributed relief variations originated through concurrent hydrological processes within a storm event was significant on the watershed scale hydrograph. We model these observations by introducing dynamic formulations of two relief-related parameters at diverse scales: maximum depression storage, and roughness coefficient in channels. In the final (a posteriori) model structure these parameters are allowed to be both time-constant or time-varying. The case under study is a convective storm in a semiarid Mediterranean watershed with ephemeral channels and high agricultural pressures (the Rambla del Albujón watershed; 556 km 2 ), which showed a complex multi-peak response. First, to obtain quasi-sensible simulations in the (a priori) model with time-constant relief-related parameters, a spatially distributed parameterization was strictly required. Second, a generalized likelihood uncertainty estimation (GLUE) inference applied to the improved model structure, and conditioned to observed nested hydrographs, showed that accounting for dynamic relief-related parameters led to improved simulations. The discussion is finally broadened by considering the use of the calibrated model both to analyze the sensitivity of the watershed to storm motion and to attempt the flood forecasting of a stratiform event with highly different behavior.

The impact of social and relational contexts on innovation transfer in foreign subsidiaries

It is widely acknowledged that innovation is one of the pillars of multinational enterprises (MNEs) and that technological knowledge from different host locations is a key factor to the MNEs’ competitive advantages development. Concerning these assumptions, in this paper we aim to understand how the social and the relational contexts affect the conventional and reverse transfer of innovation from MNEs’ subsidiaries hosted in emerging markets. We analyzed the social context through the institutional profile (CIP) level and the relational context through trust and integration levels utilizing a survey sent to 172 foreign subsidiaries located in Brazil, as well as secondary data. Through an ordinary least squares regression (OLS) analysis we found that the relational context affects the conventional and reverse innovation transfer in subsidiaries hosted in emerging markets. We however did not find support for the social context effect.