Breakdown of hydrostatic balance at convective scales in the forecast errors in the Met Office Unified Model

For data assimilation in numerical weather prediction, the initial forecast-error covariance matrix Pf is required. For variational assimilation it is particularly important to prescribe an accurate initial matrix Pf, since Pf is either static (in the 3D-Var case) or constant at the beginning of each assimilation window (in the 4D-Var case). At large scales the atmospheric flow is well approximated by hydrostatic balance and this balance is strongly enforced in the initial matrix Pf used in operational variational assimilation systems such as that of the Met Office. However, at convective scales this balance does not necessarily hold any more. Here we examine the extent to which hydrostatic balance is valid in the vertical forecast-error covariances for high-resolution models in order to determine whether there is a need to relax this balance constraint in convective-scale data assimilation. We use the Met Office Global and Regional Ensemble Prediction System (MOGREPS) and a 1.5 km resolution version of the Unified Model for a case study characterized by the presence of convective activity. An ensemble of high-resolution forecasts valid up to three hours after the onset of convection is produced. We show that at 1.5 km resolution hydrostatic balance does not hold for forecast errors in regions of convection. This indicates that in the presence of convection hydrostatic balance should not be enforced in the covariance matrix used for variational data assimilation at this scale. The results show the need to investigate covariance models that may be better suited for convective-scale data assimilation. Finally, we give a measure of the balance present in the forecast perturbations as a function of the horizontal scale (from 3–90 km) using a set of diagnostics. Copyright © 2012 Royal Meteorological Society and British Crown Copyright, the Met Office

Robust inference in an heteroscedastic measurement error model

In this paper we deal with robust inference in heteroscedastic measurement error models Rather than the normal distribution we postulate a Student t distribution for the observed variables Maximum likelihood estimates are computed numerically Consistent estimation of the asymptotic covariance matrices of the maximum likelihood and generalized least squares estimators is also discussed Three test statistics are proposed for testing hypotheses of interest with the asymptotic chi-square distribution which guarantees correct asymptotic significance levels Results of simulations and an application to a real data set are also reported (C) 2009 The Korean Statistical Society Published by Elsevier B V All rights reserved

Invariant tests in an instrumental variables model with unknown data generating process

In this work we focus on tests for the parameter of an endogenous variable in a weakly identi ed instrumental variable regressionmodel. We propose a new unbiasedness restriction for weighted average power (WAP) tests introduced by Moreira and Moreira (2013). This new boundary condition is motivated by the score e ciency under strong identi cation. It allows reducing computational costs of WAP tests by replacing the strongly unbiased condition. This latter restriction imposes, under the null hypothesis, the test to be uncorrelated to a given statistic with dimension given by the number of instruments. The new proposed boundary condition only imposes the test to be uncorrelated to a linear combination of the statistic. WAP tests under both restrictions to perform similarly numerically. We apply the di erent tests discussed to an empirical example. Using data from Yogo (2004), we assess the e ect of weak instruments on the estimation of the elasticity of inter-temporal substitution of a CCAPM model.

Modifying the stochastic model to mitigate GPS systematic errors in relative positioning

The GPS observables are subject to several errors. Among them, the systematic ones have great impact, because they degrade the accuracy of the accomplished positioning. These errors are those related, mainly, to GPS satellites orbits, multipath and atmospheric effects. Lately, a method has been suggested to mitigate these errors: the semiparametric model and the penalised least squares technique (PLS). In this method, the errors are modeled as functions varying smoothly in time. It is like to change the stochastic model, in which the errors functions are incorporated, the results obtained are similar to those in which the functional model is changed. As a result, the ambiguities and the station coordinates are estimated with better reliability and accuracy than the conventional least square method (CLS). In general, the solution requires a shorter data interval, minimizing costs. The method performance was analyzed in two experiments, using data from single frequency receivers. The first one was accomplished with a short baseline, where the main error was the multipath. In the second experiment, a baseline of 102 km was used. In this case, the predominant errors were due to the ionosphere and troposphere refraction. In the first experiment, using 5 minutes of data collection, the largest coordinates discrepancies in relation to the ground truth reached 1.6 cm and 3.3 cm in h coordinate for PLS and the CLS, respectively, in the second one, also using 5 minutes of data, the discrepancies were 27 cm in h for the PLS and 175 cm in h for the CLS. In these tests, it was also possible to verify a considerable improvement in the ambiguities resolution using the PLS in relation to the CLS, with a reduced data collection time interval. © Springer-Verlag Berlin Heidelberg 2007.

Modeling approach based on experimental results for prediction of measurement errors in energy meters

This paper presents a general modeling approach to investigate and to predict measurement errors in active energy meters both induction and electronic types. The measurement error modeling is based on Generalized Additive Model (GAM), Ridge Regression method and experimental results of meter provided by a measurement system. The measurement system provides a database of 26 pairs of test waveforms captured in a real electrical distribution system, with different load characteristics (industrial, commercial, agricultural, and residential), covering different harmonic distortions, and balanced and unbalanced voltage conditions. In order to illustrate the proposed approach, the measurement error models are discussed and several results, which are derived from experimental tests, are presented in the form of three-dimensional graphs, and generalized as error equations. © 2009 IEEE.

Cholesky Residuals for Assessing Normal Errors in a Linear Model with Correlated Outcomes: Technical Report

Despite the widespread popularity of linear models for correlated outcomes (e.g. linear mixed models and time series models), distribution diagnostic methodology remains relatively underdeveloped in this context. In this paper we present an easy-to-implement approach that lends itself to graphical displays of model fit. Our approach involves multiplying the estimated margional residual vector by the Cholesky decomposition of the inverse of the estimated margional variance matrix. The resulting "rotated" residuals are used to construct an empirical cumulative distribution function and pointwise standard errors. The theoretical framework, including conditions and asymptotic properties, involves technical details that are motivated by Lange and Ryan (1989), Pierce (1982), and Randles (1982). Our method appears to work well in a variety of circumstances, including models having independent units of sampling (clustered data) and models for which all observations are correlated (e.g., a single time series). Our methods can produce satisfactory results even for models that do not satisfy all of the technical conditions stated in our theory.

Factors predictive of intravenous fluid administration errors in Australian surgical care wards

Background: Intravenous (IV) fluid administration is an integral component of clinical care. Errors in administration can cause detrimental patient outcomes and increase healthcare costs, although little is known about medication administration errors associated with continuous IV infusions. Objectives: ( 1) To ascertain the prevalence of medication administration errors for continuous IV infusions and identify the variables that caused them. ( 2) To quantify the probability of errors by fitting a logistic regression model to the data. Methods: A prospective study was conducted on three surgical wards at a teaching hospital in Australia. All study participants received continuous infusions of IV fluids. Parenteral nutrition and non-electrolyte containing intermittent drug infusions ( such as antibiotics) were excluded. Medication administration errors and contributing variables were documented using a direct observational approach. Results: Six hundred and eighty seven observations were made, with 124 (18.0%) having at least one medication administration error. The most common error observed was wrong administration rate. The median deviation from the prescribed rate was 247 ml/h (interquartile range 275 to + 33.8 ml/ h). Errors were more likely to occur if an IV infusion control device was not used and as the duration of the infusion increased. Conclusions: Administration errors involving continuous IV infusions occur frequently. They could be reduced by more common use of IV infusion control devices and regular checking of administration rates.

Artificial pumping errors in the Kool-Parker scaling model of soil moisture hysteresis

Hysteresis models that eliminate the artificial pumping errors associated with the Kool-Parker (KP) soil moisture hysteresis model, such as the Parker-Lenhard (PL) method, can be computationally demanding in unsaturated transport models since they need to retain the wetting-drying history of the system. The pumping errors in these models need to be eliminated for correct simulation of cyclical systems (e.g. transport above a tidally forced watertable, infiltration and redistribution under periodic irrigation) if the soils exhibit significant hysteresis. A modification is made here to the PL method that allows it to be more readily applied to numerical models by eliminating the need to store a large number of soil moisture reversal points. The modified-PL method largely eliminates any artificial pumping error and so essentially retains the accuracy of the original PL approach. The modified-PL method is implemented in HYDRUS-1D (version 2.0), which is then used to simulate cyclic capillary fringe dynamics to show the influence of removing artificial pumping errors and to demonstrate the ease of implementation. Artificial pumping errors are shown to be significant for the soils and system characteristics used here in numerical experiments of transport above a fluctuating watertable. (c) 2005 Elsevier B.V. All rights reserved.

Operator-induced errors in Hartmann-Shack wavefront sensing:model eye study

Purpose: To evaluate the effects of instrument realignment and angular misalignment during the clinical determination of wavefront aberrations by simulation in model eyes. Setting: Aston Academy of Life Sciences, Aston University, Birmingham, United Kingdom. Methods: Six model eyes were examined with wavefront-aberration-supported cornea ablation (WASCA) (Carl Zeiss Meditec) in 4 sessions of 10 measurements each: sessions 1 and 2, consecutive repeated measures without realignment; session 3, realignment of the instrument between readings; session 4, measurements without realignment but with the model eye shifted 6 degrees angularly. Intersession repeatability and the effects of realignment and misalignment were obtained by comparing the measurements in the various sessions for coma, spherical aberration, and higher-order aberrations (HOAs). Results: The mean differences between the 2 sessions without realignment of the instrument were 0.020 μm ± 0.076 (SD) for Z3 - 1(P = .551), 0.009 ± 0.139 μm for Z3 1(P = .877), 0.004 ± 0.037 μm for Z4 0 (P = .820), and 0.005 ± 0.01 μm for HO root mean square (RMS) (P = .301). Differences between the nonrealigned and realigned instruments were -0.017 ± 0.026 μm for Z3 - 1(P = .159), 0.009 ± 0.028 μm for Z3 1 (P = .475), 0.007 ± 0.014 μm for Z4 0(P = .296), and 0.002 ± 0.007 μm for HO RMS (P = 0.529; differences between centered and misaligned instruments were -0.355 ± 0.149 μm for Z3 - 1 (P = .002), 0.007 ± 0.034 μm for Z3 1(P = .620), -0.005 ± 0.081 μm for Z4 0(P = .885), and 0.012 ± 0.020 μm for HO RMS (P = .195). Realignment increased the standard deviation by a factor of 3 compared with the first session without realignment. Conclusions: Repeatability of the WASCA was excellent in all situations tested. Realignment substantially increased the variance of the measurements. Angular misalignment can result in significant errors, particularly in the determination of coma. These findings are important when assessing highly aberrated eyes during follow-up or before surgery. © 2007 ASCRS and ESCRS.

Using Bayesian methods for the estimation of uncertainty in complex statistical models

The research objectives of this thesis were to contribute to Bayesian statistical methodology by contributing to risk assessment statistical methodology, and to spatial and spatio-temporal methodology, by modelling error structures using complex hierarchical models. Specifically, I hoped to consider two applied areas, and use these applications as a springboard for developing new statistical methods as well as undertaking analyses which might give answers to particular applied questions. Thus, this thesis considers a series of models, firstly in the context of risk assessments for recycled water, and secondly in the context of water usage by crops. The research objective was to model error structures using hierarchical models in two problems, namely risk assessment analyses for wastewater, and secondly, in a four dimensional dataset, assessing differences between cropping systems over time and over three spatial dimensions. The aim was to use the simplicity and insight afforded by Bayesian networks to develop appropriate models for risk scenarios, and again to use Bayesian hierarchical models to explore the necessarily complex modelling of four dimensional agricultural data. The specific objectives of the research were to develop a method for the calculation of credible intervals for the point estimates of Bayesian networks; to develop a model structure to incorporate all the experimental uncertainty associated with various constants thereby allowing the calculation of more credible credible intervals for a risk assessment; to model a single day’s data from the agricultural dataset which satisfactorily captured the complexities of the data; to build a model for several days’ data, in order to consider how the full data might be modelled; and finally to build a model for the full four dimensional dataset and to consider the timevarying nature of the contrast of interest, having satisfactorily accounted for possible spatial and temporal autocorrelations. This work forms five papers, two of which have been published, with two submitted, and the final paper still in draft. The first two objectives were met by recasting the risk assessments as directed, acyclic graphs (DAGs). In the first case, we elicited uncertainty for the conditional probabilities needed by the Bayesian net, incorporated these into a corresponding DAG, and used Markov chain Monte Carlo (MCMC) to find credible intervals, for all the scenarios and outcomes of interest. In the second case, we incorporated the experimental data underlying the risk assessment constants into the DAG, and also treated some of that data as needing to be modelled as an ‘errors-invariables’ problem [Fuller, 1987]. This illustrated a simple method for the incorporation of experimental error into risk assessments. In considering one day of the three-dimensional agricultural data, it became clear that geostatistical models or conditional autoregressive (CAR) models over the three dimensions were not the best way to approach the data. Instead CAR models are used with neighbours only in the same depth layer. This gave flexibility to the model, allowing both the spatially structured and non-structured variances to differ at all depths. We call this model the CAR layered model. Given the experimental design, the fixed part of the model could have been modelled as a set of means by treatment and by depth, but doing so allows little insight into how the treatment effects vary with depth. Hence, a number of essentially non-parametric approaches were taken to see the effects of depth on treatment, with the model of choice incorporating an errors-in-variables approach for depth in addition to a non-parametric smooth. The statistical contribution here was the introduction of the CAR layered model, the applied contribution the analysis of moisture over depth and estimation of the contrast of interest together with its credible intervals. These models were fitted using WinBUGS [Lunn et al., 2000]. The work in the fifth paper deals with the fact that with large datasets, the use of WinBUGS becomes more problematic because of its highly correlated term by term updating. In this work, we introduce a Gibbs sampler with block updating for the CAR layered model. The Gibbs sampler was implemented by Chris Strickland using pyMCMC [Strickland, 2010]. This framework is then used to consider five days data, and we show that moisture in the soil for all the various treatments reaches levels particular to each treatment at a depth of 200 cm and thereafter stays constant, albeit with increasing variances with depth. In an analysis across three spatial dimensions and across time, there are many interactions of time and the spatial dimensions to be considered. Hence, we chose to use a daily model and to repeat the analysis at all time points, effectively creating an interaction model of time by the daily model. Such an approach allows great flexibility. However, this approach does not allow insight into the way in which the parameter of interest varies over time. Hence, a two-stage approach was also used, with estimates from the first-stage being analysed as a set of time series. We see this spatio-temporal interaction model as being a useful approach to data measured across three spatial dimensions and time, since it does not assume additivity of the random spatial or temporal effects.

Inherent errors in pollutant build-up estimation in considering urban land use as a lumped parameter

Stormwater quality modelling results is subject to uncertainty. The variability of input parameters is an important source of overall model error. An in-depth understanding of the variability associated with input parameters can provide knowledge on the uncertainty associated with these parameters and consequently assist in uncertainty analysis of stormwater quality models and the decision making based on modelling outcomes. This paper discusses the outcomes of a research study undertaken to analyse the variability related to pollutant build-up parameters in stormwater quality modelling. The study was based on the analysis of pollutant build-up samples collected from 12 road surfaces in residential, commercial and industrial land uses. It was found that build-up characteristics vary appreciably even within the same land use. Therefore, using land use as a lumped parameter would contribute significant uncertainties in stormwater quality modelling. Additionally, it was also found that the variability in pollutant build-up can also be significant depending on the pollutant type. This underlines the importance of taking into account specific land use characteristics and targeted pollutant species when undertaking uncertainty analysis of stormwater quality models or in interpreting the modelling outcomes.

Do Measurement Errors in GDP Announcements Cause Output Fluctuations?

This thesis studies empirically whether measurement errors in aggregate production statistics affect sentiment and future output. Initial announcements of aggregate production are subject to measurement error, because many of the data required to compile the statistics are produced with a lag. This measurement error can be gauged as the difference between the latest revised statistic and its initial announcement. Assuming aggregate production statistics help forecast future aggregate production, these measurement errors are expected to affect macroeconomic forecasts. Assuming agents’ macroeconomic forecasts affect their production choices, these measurement errors should affect future output through sentiment. This thesis is primarily empirical, so the theoretical basis, strategic complementarity, is discussed quite briefly. However, it is a model in which higher aggregate production increases each agent’s incentive to produce. In this circumstance a statistical announcement which suggests aggregate production is high would increase each agent’s incentive to produce, thus resulting in higher aggregate production. In this way the existence of strategic complementarity provides the theoretical basis for output fluctuations caused by measurement mistakes in aggregate production statistics. Previous empirical studies suggest that measurement errors in gross national product affect future aggregate production in the United States. Additionally it has been demonstrated that measurement errors in the Index of Leading Indicators affect forecasts by professional economists as well as future industrial production in the United States. This thesis aims to verify the applicability of these findings to other countries, as well as study the link between measurement errors in gross domestic product and sentiment. This thesis explores the relationship between measurement errors in gross domestic production and sentiment and future output. Professional forecasts and consumer sentiment in the United States and Finland, as well as producer sentiment in Finland, are used as the measures of sentiment. Using statistical techniques it is found that measurement errors in gross domestic product affect forecasts and producer sentiment. The effect on consumer sentiment is ambiguous. The relationship between measurement errors and future output is explored using data from Finland, United States, United Kingdom, New Zealand and Sweden. It is found that measurement errors have affected aggregate production or investment in Finland, United States, United Kingdom and Sweden. Specifically, it was found that overly optimistic statistics announcements are associated with higher output and vice versa.

Methods in general model localization

The aim of this study was to evaluate and test methods which could improve local estimates of a general model fitted to a large area. In the first three studies, the intention was to divide the study area into sub-areas that were as homogeneous as possible according to the residuals of the general model, and in the fourth study, the localization was based on the local neighbourhood. According to spatial autocorrelation (SA), points closer together in space are more likely to be similar than those that are farther apart. Local indicators of SA (LISAs) test the similarity of data clusters. A LISA was calculated for every observation in the dataset, and together with the spatial position and residual of the global model, the data were segmented using two different methods: classification and regression trees (CART) and the multiresolution segmentation algorithm (MS) of the eCognition software. The general model was then re-fitted (localized) to the formed sub-areas. In kriging, the SA is modelled with a variogram, and the spatial correlation is a function of the distance (and direction) between the observation and the point of calculation. A general trend is corrected with the residual information of the neighbourhood, whose size is controlled by the number of the nearest neighbours. Nearness is measured as Euclidian distance. With all methods, the root mean square errors (RMSEs) were lower, but with the methods that segmented the study area, the deviance in single localized RMSEs was wide. Therefore, an element capable of controlling the division or localization should be included in the segmentation-localization process. Kriging, on the other hand, provided stable estimates when the number of neighbours was sufficient (over 30), thus offering the best potential for further studies. Even CART could be combined with kriging or non-parametric methods, such as most similar neighbours (MSN).

Data assimilation using ensemble transform Kalman filter (ETKF) in ROMS model for Indian Ocean

Study of Oceans dynamics and forecast is crucial as it influences the regional climate and other marine activities. Forecasting oceanographic states like sea surface currents, Sea surface temperature (SST) and mixed layer depth at different time scales is extremely important for these activities. These forecasts are generated by various ocean general circulation models (OGCM). One such model is the Regional Ocean Modelling System (ROMS). Though ROMS can simulate several features of ocean, it cannot reproduce the thermocline of the ocean properly. Solution to this problem is to incorporates data assimilation (DA) in the model. DA system using Ensemble Transform Kalman Filter (ETKF) has been developed for ROMS model to improve the accuracy of the model forecast. To assimilate data temperature and salinity from ARGO data has been used as observation. Assimilated temperature and salinity without localization shows oscillations compared to the model run without assimilation for India Ocean. Same was also found for u and v-velocity fields. With localization we found that the state variables are diverging within the localization scale.