Global runoff routing with the hydrological component of the ECMWF NWP system

A global river routing scheme coupled to the ECMWF land surface model is implemented and tested within the framework of the Global Soil Wetness Project II, to evaluate the feasibility of modelling global river runoff at a daily time scale. The exercise is designed to provide benchmark river runoff predictions needed to verify the land surface model. Ten years of daily runoff produced by the HTESSEL land surface scheme is input into the TRIP2 river routing scheme in order to generate daily river runoff. These are then compared to river runoff observations from the Global Runoff Data Centre (GRDC) in order to evaluate the potential and the limitations. A notable source of inaccuracy is bias between observed and modelled discharges which is not primarily due to the modelling system but instead of to the forcing and quality of observations and seems uncorrelated to the river catchment size. A global sensitivity analysis and Generalised Likelihood Uncertainty Estimation (GLUE) uncertainty analysis are applied to the global routing model. The ground water delay parameter is identified as being the most sensitive calibration parameter. Significant uncertainties are found in results, and those due to parameterisation of the routing model are quantified. The difficulty involved in parameterising global river discharge models is discussed. Detailed river runoff simulations are shown for the river Danube, which match well observed river runoff in upstream river transects. Results show that although there are errors in runoff predictions, model results are encouraging and certainly indicative of useful runoff predictions, particularly for the purpose of verifying the land surface scheme hydrologicly. Potential of this modelling system on future applications such as river runoff forecasting and climate impact studies is highlighted. Copyright © 2009 Royal Meteorological Society.

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.

URANS calculations for smooth circular cylinder flow in a wide range of Reynolds Numbers: solution verification and validation

The flow around circular smooth fixed cylinder in a large range of Reynolds numbers is considered in this paper. In order to investigate this canonical case, we perform CFD calculations and apply verification & validation (V&V) procedures to draw conclusions regarding numerical error and, afterwards, assess the modeling errors and capabilities of this (U)RANS method to solve the problem. Eight Reynolds numbers between Re = 10 and Re 5 x 10(5) will be presented with, at least, four geometrically similar grids and five discretization in time for each case (when unsteady), together with strict control of iterative and round-off errors, allowing a consistent verification analysis with uncertainty estimation. Two-dimensional RANS, steady or unsteady, laminar or turbulent calculations are performed. The original 1994 k - omega SST turbulence model by Menter is used to model turbulence. The validation procedure is performed by comparing the numerical results with an extensive set of experimental results compiled from the literature. [DOI: 10.1115/1.4007571]

Parametrização e avaliação do modelo DSSAT/Canegro para variedades brasileiras de cana-de-açúcar

O objetivo deste trabalho foi parametrizar e avaliar o modelo DSSAT/Canegro para cinco variedades brasileiras de cana-de-açúcar. A parametrização foi realizada a partir do uso de dados biométricos e de crescimento das variedades CTC 4, CTC 7, CTC 20, RB 86-7515 e RB 83-5486, obtidos em cinco localidades brasileiras. Foi realizada análise de sensibilidade local para os principais parâmetros. A parametrização do modelo foi feita por meio da técnica de estimativa da incerteza de probabilidade generalizada ("generalized likelihood uncertainty estimation", Glue). Para a avaliação das predições, foram utilizados, como indicadores estatísticos, o coeficiente de determinação (R2), o índice D de Willmott e a raiz quadrada do erro-médio (RMSE). As variedades CTC apresentaram índice D entre 0,870 e 0,944, para índice de área foliar, altura de colmo, perfilhamento e teor de sacarose. A variedade RB 83-5486 apresentou resultados similares para teor de sacarose e massa de matéria fresca do colmo, enquanto a variedade RB 86-7515 apresentou valores entre 0,665 e 0,873, para as variáveis avaliadas.

The Importance of Scale for Spatial-confounding Bias and Precision of Spatial Regression Estimators

Increasingly, regression models are used when residuals are spatially correlated. Prominent examples include studies in environmental epidemiology to understand the chronic health effects of pollutants. I consider the effects of residual spatial structure on the bias and precision of regression coefficients, developing a simple framework in which to understand the key issues and derive informative analytic results. When the spatial residual is induced by an unmeasured confounder, regression models with spatial random effects and closely-related models such as kriging and penalized splines are biased, even when the residual variance components are known. Analytic and simulation results show how the bias depends on the spatial scales of the covariate and the residual; bias is reduced only when there is variation in the covariate at a scale smaller than the scale of the unmeasured confounding. I also discuss how the scales of the residual and the covariate affect efficiency and uncertainty estimation when the residuals can be considered independent of the covariate. In an application on the association between black carbon particulate matter air pollution and birth weight, controlling for large-scale spatial variation appears to reduce bias from unmeasured confounders, while increasing uncertainty in the estimated pollution effect.

A framework for benchmarking of homogenisation algorithm performance on the global scale

The International Surface Temperature Initiative (ISTI) is striving towards substantively improving our ability to robustly understand historical land surface air temperature change at all scales. A key recently completed first step has been collating all available records into a comprehensive open access, traceable and version-controlled databank. The crucial next step is to maximise the value of the collated data through a robust international framework of benchmarking and assessment for product intercomparison and uncertainty estimation. We focus on uncertainties arising from the presence of inhomogeneities in monthly mean land surface temperature data and the varied methodological choices made by various groups in building homogeneous temperature products. The central facet of the benchmarking process is the creation of global-scale synthetic analogues to the real-world database where both the "true" series and inhomogeneities are known (a luxury the real-world data do not afford us). Hence, algorithmic strengths and weaknesses can be meaningfully quantified and conditional inferences made about the real-world climate system. Here we discuss the necessary framework for developing an international homogenisation benchmarking system on the global scale for monthly mean temperatures. The value of this framework is critically dependent upon the number of groups taking part and so we strongly advocate involvement in the benchmarking exercise from as many data analyst groups as possible to make the best use of this substantial effort.

Evaluación y análisis de la trazabilidad metrológica en redes para la verificación y calibración de instrumental GNSS (Global Navigation Satellite System)

Los estudios realizados hasta el momento para la determinación de la calidad de medida del instrumental geodésico han estado dirigidos, fundamentalmente, a las medidas angulares y de distancias. Sin embargo, en los últimos años se ha impuesto la tendencia generalizada de utilizar equipos GNSS (Global Navigation Satellite System) en el campo de las aplicaciones geomáticas sin que se haya establecido una metodología que permita obtener la corrección de calibración y su incertidumbre para estos equipos. La finalidad de esta Tesis es establecer los requisitos que debe satisfacer una red para ser considerada Red Patrón con trazabilidad metrológica, así como la metodología para la verificación y calibración de instrumental GNSS en redes patrón. Para ello, se ha diseñado y elaborado un procedimiento técnico de calibración de equipos GNSS en el que se han definido las contribuciones a la incertidumbre de medida. El procedimiento, que se ha aplicado en diferentes redes para distintos equipos, ha permitido obtener la incertidumbre expandida de dichos equipos siguiendo las recomendaciones de la Guide to the Expression of Uncertainty in Measurement del Joint Committee for Guides in Metrology. Asimismo, se han determinado mediante técnicas de observación por satélite las coordenadas tridimensionales de las bases que conforman las redes consideradas en la investigación, y se han desarrollado simulaciones en función de diversos valores de las desviaciones típicas experimentales de los puntos fijos que se han utilizado en el ajuste mínimo cuadrático de los vectores o líneas base. Los resultados obtenidos han puesto de manifiesto la importancia que tiene el conocimiento de las desviaciones típicas experimentales en el cálculo de incertidumbres de las coordenadas tridimensionales de las bases. Basándose en estudios y observaciones de gran calidad técnica, llevados a cabo en estas redes con anterioridad, se ha realizado un exhaustivo análisis que ha permitido determinar las condiciones que debe satisfacer una red patrón. Además, se han diseñado procedimientos técnicos de calibración que permiten calcular la incertidumbre expandida de medida de los instrumentos geodésicos que proporcionan ángulos y distancias obtenidas por métodos electromagnéticos, ya que dichos instrumentos son los que van a permitir la diseminación de la trazabilidad metrológica a las redes patrón para la verificación y calibración de los equipos GNSS. De este modo, ha sido posible la determinación de las correcciones de calibración local de equipos GNSS de alta exactitud en las redes patrón. En esta Tesis se ha obtenido la incertidumbre de la corrección de calibración mediante dos metodologías diferentes; en la primera se ha aplicado la propagación de incertidumbres, mientras que en la segunda se ha aplicado el método de Monte Carlo de simulación de variables aleatorias. El análisis de los resultados obtenidos confirma la validez de ambas metodologías para la determinación de la incertidumbre de calibración de instrumental GNSS. ABSTRACT The studies carried out so far for the determination of the quality of measurement of geodetic instruments have been aimed, primarily, to measure angles and distances. However, in recent years it has been accepted to use GNSS (Global Navigation Satellite System) equipment in the field of Geomatic applications, for data capture, without establishing a methodology that allows obtaining the calibration correction and its uncertainty. The purpose of this Thesis is to establish the requirements that a network must meet to be considered a StandardNetwork with metrological traceability, as well as the methodology for the verification and calibration of GNSS instrumental in those standard networks. To do this, a technical calibration procedure has been designed, developed and defined for GNSS equipment determining the contributions to the uncertainty of measurement. The procedure, which has been applied in different networks for different equipment, has alloweddetermining the expanded uncertainty of such equipment following the recommendations of the Guide to the Expression of Uncertainty in Measurement of the Joint Committee for Guides in Metrology. In addition, the three-dimensional coordinates of the bases which constitute the networks considered in the investigationhave been determined by satellite-based techniques. There have been several developed simulations based on different values of experimental standard deviations of the fixed points that have been used in the least squares vectors or base lines calculations. The results have shown the importance that the knowledge of experimental standard deviations has in the calculation of uncertainties of the three-dimensional coordinates of the bases. Based on high technical quality studies and observations carried out in these networks previously, it has been possible to make an exhaustive analysis that has allowed determining the requirements that a standard network must meet. In addition, technical calibration procedures have been developed to allow the uncertainty estimation of measurement carried outby geodetic instruments that provide angles and distances obtained by electromagnetic methods. These instruments provide the metrological traceability to standard networks used for verification and calibration of GNSS equipment. As a result, it has been possible the estimation of local calibration corrections for high accuracy GNSS equipment in standardnetworks. In this Thesis, the uncertainty of calibration correction has been calculated using two different methodologies: the first one by applying the law of propagation of uncertainty, while the second has applied the propagation of distributions using the Monte Carlo method. The analysis of the obtained results confirms the validity of both methodologies for estimating the calibration uncertainty of GNSS equipment.

Caracterización de sistemas vibroacústicos mediante análisis estadístico de energía

Hoy día nadie discute la importancia de predecir el comportamiento vibroacústico de estructuras (edificios, vehículos aeronaves, satélites). También se ha hecho patente, con el tiempo, que el rango espectral en el que la respuesta es importante se ha desplazado hacia alta frecuencia en prácticamente todos los campos. Esto ha hecho que los métodos de análisis en este rango alto de frecuencias cobren importancia y actualidad. Uno de los métodos más extendidos para este fin es el basado en el Análisis Estadístico de la Energía, SEA. Es un método que ha mostrado proporcionar un buen equilibrio entre potencia de calculo, precisión y fiabilidad. En un SEA el sistema (estructura, cavidades o aire circundante) se modela mediante una matriz de coeficientes que dependen directamente de los factores de pérdidas de las distintas partes del sistema. Formalmente es un método de análisis muy cómodo e intuitivo de manejar cuya mayor dificultad es precisamente la determinación de esos factores de pérdidas. El catálogo de expresiones analíticas o numéricas para su determinación no es suficientemente amplio por lo que normalmente siempre se suele acabar necesitando hacer uso de herramientas experimentales, ya sea para su obtención o la comprobación de los valores utilizados. La determinación experimental tampoco está exenta de problemas, su obtención necesita de configuraciones experimentales grandes y complejas con requisitos que pueden llegar a ser muy exigentes y en las que además, se ven involucrados problemas numéricos relacionados con los valores de los propios factores de pérdidas, el valor relativo entre ellos y las características de las matrices que conforman. Este trabajo estudia la caracterización de sistemas vibroacústicos mediante el análisis estadístico de energía. Se centra en la determinación precisa de los valores de los factores de pérdidas. Dados los problemas que puede presentar un sistema experimental de estas características, en una primera parte se estudia la influencia de todas las magnitudes que intervienen en la determinación de los factores de pérdidas mediante un estudio de incertidumbres relativas, que, por medio de los coeficientes de sensibilidad normalizados, indicará la importancia de cada una de las magnitudes de entrada (esencialmente energías y potencias) en los resultados. De esta parte se obtiene una visión general sobre a qué mensurados se debe prestar más atención, y de qué problemas pueden ser los que más influyan en la falta de estabilidad (o incoherencia) de los resultados. Además, proporciona un modelo de incertidumbres válido para los casos estudiados y ha permitido evaluar el error cometido por algún método utilizado habitualmente para la caracterización de factores de pérdidas como la aproximación a 2 subsistemas En una segunda parte se hace uso de las conclusiones obtenidas en la primera, de forma que el trabajo se orienta en dos direcciones. Una dirigida a la determi nación suficientemente fiel de la potencia de entrada que permita simplificar en lo posible la configuración experimental. Otra basada en un análisis detallado de las propiedades de la matriz que caracteriza un SEA y que conduce a la propuesta de un método para su determinación robusta, basada en un filtrado de Montecarlo y que, además, muestra cómo los problemas numéricos de la matriz SEA pueden no ser tan insalvables como se apunta en la literatura. Por último, además, se plantea una solución al caso en el que no todos los subsistemas en los que se divide el sistema puedan ser excitados. El método propuesto aquí no permite obtener el conjunto completo de coeficientes necesarios para definir un sistema, pero el solo hecho de poder obtener conjuntos parciales ya es un avance importante y, sobre todo, abre la puerta al desarrollo de métodos que permitan relajar de forma importante las exigencias que la determinación experimental de matrices SEA tiene. ABSTRACT At present there is an agreement about the importance to predict the vibroacoustic response of structures (buildings, vehicles, aircrafts, satellites, etc.). In addition, there has become clear over the time that the frequency range over which the response is important has been shift to higher frequencies in almost all the engineering fields. As a consequence, the numerical methods for high frequency analysis have increase in importance. One the most widespread methods for this type of analysis is the one based on the Statistical Energy Analysis, SEA. This method has shown to provide a good balance among calculation power, accuracy and liability. Within a SEA, a system (structure, cavities, surrounding air) is modeled by a coefficients matrix that depends directly on the loss factors of the different parts of the system. Formally, SEA is a very handy and intuitive analysis method whose greatest handicap is precisely the determination of the loss factors. The existing set of analytical or numerical equations to obtain the loss factor values is not enough, so that usually it is necessary to use experimental techniques whether it is to its determination to to check the estimated values by another mean. The experimental determination presents drawbacks, as well. To obtain them great and complex experimental setups are needed including requirements that can be very demanding including numerical problems related to the values of the loss factors themselves, their relative value and the characteristics of the matrices they define. The present work studies the characterization of vibroacousti systems by this SEA method. It focuses on the accurate determination of the loss factors values. Given all the problems an experimental setup of these characteristics can show, the work is divided in two parts. In the first part, the influence of all the quantities involved on the determination of the loss factors is studied by a relative uncertainty estimation, which, by means of the normalised sensitivity coefficients, will provide an insight about the importance of every input quantities (energies and input powers, mainly) on the final result. Besides, this part, gives an uncertainty model that has allowed assessing the error of one of the methods more widely used to characterize the loss factors: the 2-subsystem approach. In the second part, use of the former conclusions is used. An equation for the input power into the subsystems is proposed. This equation allows simplifying the experimental setup without changing the liability of the test. A detailed study of the SEA matrix properties leads to propose a robust determination method of this SEA matrix by a Monte Carlo filtering. In turn, this new method shows how the numerical problems of the SEA matrix can be overcome Finally, a solution is proposed for the case where not all the subsystems are excited. The method proposed do not allows obtaining the whole set of coefficients of the SEA matrix, but the simple fact of getting partial sets of loss factors is a significant advance and, over all, it opens the door to the development of new methods that loosen the requirements that an experimental determination of a SEA matrix have.

Using apparent activation energy as a reactivity criterion for biomass pyrolysis

The reactivity of chemically isolated lignocellulosic blocks, namely, α-cellulose, holocellulose, and lignin, has been rationalized on the basis of the dependence of the effective activation energy (Eα) upon conversion (α) determined via the popular isoconversional kinetic analysis, Friedman’s method. First of all, a detailed procedure for the thermogravimetric data preparation, kinetic calculation, and uncertainty estimation was implemented. Resulting Eα dependencies obtained for the slow pyrolysis of the extractive-free Eucalyptus grandis isolated α-cellulose and holocellulose remained constant for 0.05 < α < 0.80 and equal to 173 ± 10, 208 ± 11, and 197 ± 118 kJ/mol, thus confirming the single-step nature of pyrolysis. On the other hand, large and significant variations in Eα with α from 174 ± 10 to 322 ± 11 kJ/mol in the region of 0.05 and 0.79 were obtained for the Klason lignin and reported for the first time. The non-monotonic nature of weight loss at low and high conversions had a direct consequence on the confidence levels of Eα. The new experimental and calculation guidelines applied led to more accurate estimates of Eα values than those reported earlier. The increasing Eα dependency trend confirms that lignin is converted into a thermally more stable carbonaceous material.

Multi-temporal monitoring of wetland water levels in the Florida Everglades using interferometric synthetic aperture radar (InSAR)

Interferometric synthetic aperture radar (InSAR) techniques can successfully detect phase variations related to the water level changes in wetlands and produce spatially detailed high-resolution maps of water level changes. Despite the vast details, the usefulness of the wetland InSAR observations is rather limited, because hydrologists and water resources managers need information on absolute water level values and not on relative water level changes. We present an InSAR technique called Small Temporal Baseline Subset (STBAS) for monitoring absolute water level time series using radar interferograms acquired successively over wetlands. The method uses stage (water level) observation for calibrating the relative InSAR observations and tying them to the stage's vertical datum. We tested the STBAS technique with two-year long Radarsat-1 data acquired during 2006–2008 over the Water Conservation Area 1 (WCA1) in the Everglades wetlands, south Florida (USA). The InSAR-derived water level data were calibrated using 13 stage stations located in the study area to generate 28 successive high spatial resolution maps (50 m pixel resolution) of absolute water levels. We evaluate the quality of the STBAS technique using a root mean square error (RMSE) criterion of the difference between InSAR observations and stage measurements. The average RMSE is 6.6 cm, which provides an uncertainty estimation of the STBAS technique to monitor absolute water levels. About half of the uncertainties are attributed to the accuracy of the InSAR technique to detect relative water levels. The other half reflects uncertainties derived from tying the relative levels to the stage stations' datum.

Applying Least Absolute Shrinkage Selection Operator and Akaike Information Criterion Analysis to Find the Best Multiple Linear Regression Models between Climate Indices and Components of Cow’s Milk

This study focuses on multiple linear regression models relating six climate indices (temperature humidity THI, environmental stress ESI, equivalent temperature index ETI, heat load HLI, modified HLI (HLI new), and respiratory rate predictor RRP) with three main components of cow’s milk (yield, fat, and protein) for cows in Iran. The least absolute shrinkage selection operator (LASSO) and the Akaike information criterion (AIC) techniques are applied to select the best model for milk predictands with the smallest number of climate predictors. Uncertainty estimation is employed by applying bootstrapping through resampling. Cross validation is used to avoid over-fitting. Climatic parameters are calculated from the NASA-MERRA global atmospheric reanalysis. Milk data for the months from April to September, 2002 to 2010 are used. The best linear regression models are found in spring between milk yield as the predictand and THI, ESI, ETI, HLI, and RRP as predictors with p-value < 0.001 and R2 (0.50, 0.49) respectively. In summer, milk yield with independent variables of THI, ETI, and ESI show the highest relation (p-value < 0.001) with R2 (0.69). For fat and protein the results are only marginal. This method is suggested for the impact studies of climate variability/change on agriculture and food science fields when short-time series or data with large uncertainty are available.

The Effect of Climate Variability on Main Components of Cow Milk in Iran

The main purpose of this study is to assess the relationship between six bioclimatic indices for cattle (temperature humidity (THI), environmental stress (ESI), equivalent temperature (ESI), heat load (HLI), modified heat load (HLInew) and respiratory rate predictor(RRP)) and fundamental milk components (fat, protein, and milk yield) considering uncertainty. The climate parameters used to calculate the climate indices were taken from the NASA-Modern Era Retrospective-Analysis for Research and Applications (NASA-MERRA) reanalysis from 2002 to 2010. Cow milk data were considered for the same period from April to September when cows use natural pasture, with possibility for cows to choose to stay in the barn or to graze on the pasture in the pasturing system. The study is based on a linear regression analysis using correlations as a summarizing diagnostic. Bootstrapping is used to represent uncertainty estimation through resampling in the confidence intervals. To find the relationships between climate indices (THI, ETI, HLI, HLInew, ESI and RRP) and main components of cow milk (fat, protein and yield), multiple liner regression is applied. The least absolute shrinkage selection operator (LASSO) and the Akaike information criterion (AIC) techniques are applied to select the best model for milk predictands with the smallest number of climate predictors. Cross validation is used to avoid over-fitting. Based on results of investigation the effect of heat stress indices on milk compounds separately, we suggest the use of ESI and RRP in the summer and ESI in the spring. THI and HLInew are suggested for fat content and HLInew also is suggested for protein content in the spring season. The best linear models are found in spring between milk yield as predictands and THI, ESI,HLI, ETI and RRP as predictors with p-value < 0.001 and R2 0.50, 0.49. In summer, milk yield with independent variables of THI, ETI and ESI show the highest relation (p-value < 0.001) with R2 (0.69). For fat and protein the results are only marginal. It is strongly suggested that new and significant indices are needed to control critical heat stress conditions that consider more predictors of the effect of climate variability on animal products, such as sunshine duration, quality of pasture, the number of days of stress (NDS), the color of skin with attention to large black spots, and categorical predictors such as breed, welfare facility, and management system. This methodology is suggested for studies investigating the impacts of climate variability/change on food quality/security, animal science and agriculture using short term data considering uncertainty or data collection is expensive, difficult, or data with gaps.

Metrological characterization of sensors and instrumentation for distribution grid monitoring and electrical asset diagnostics

The Smart Grid needs a large amount of information to be operated and day by day new information is required to improve the operation performance. It is also fundamental that the available information is reliable and accurate. Therefore, the role of metrology is crucial, especially if applied to the distribution grid monitoring and the electrical assets diagnostics. This dissertation aims at better understanding the sensors and the instrumentation employed by the power system operators in the above-mentioned applications and studying new solutions. Concerning the research on the measurement applied to the electrical asset diagnostics: an innovative drone-based measurement system is proposed for monitoring medium voltage surge arresters. This system is described, and its metrological characterization is presented. On the other hand, the research regarding the measurements applied to the grid monitoring consists of three parts. The first part concerns the metrological characterization of the electronic energy meters’ operation under off-nominal power conditions. Original test procedures have been designed for both frequency and harmonic distortion as influence quantities, aiming at defining realistic scenarios. The second part deals with medium voltage inductive current transformers. An in-depth investigation on their accuracy behavior in presence of harmonic distortion is carried out by applying realistic current waveforms. The accuracy has been evaluated by means of the composite error index and its approximated version. Based on the same test setup, a closed-form expression for the measured current total harmonic distortion uncertainty estimation has been experimentally validated. The metrological characterization of a virtual phasor measurement unit is the subject of the third and last part: first, a calibrator has been designed and the uncertainty associated with its steady-state reference phasor has been evaluated; then this calibrator acted as a reference, and it has been used to characterize the phasor measurement unit implemented within a real-time simulator.

Uncertainty in the estimation of potential evapotranspiration under climate change.

21st century climate change is projected to result in an intensification of the global hydrological cycle, but there is substantial uncertainty in how this will impact freshwater availability. A relatively overlooked aspect of this uncertainty pertains to how different methods of estimating potential evapotranspiration (PET) respond to changing climate. Here we investigate the global response of six different PET methods to a 2 °C rise in global mean temperature. All methods suggest an increase in PET associated with a warming climate. However, differences in PET climate change signal of over 100% are found between methods. Analysis of a precipitation/PET aridity index and regional water surplus indicates that for certain regions and GCMs, choice of PET method can actually determine the direction of projections of future water resources. As such, method dependence of the PET climate change signal is an important source of uncertainty in projections of future freshwater availability.

Estimation of Parameters in Random Effect Models with Incidence Matrix Uncertainty

Random effect models have been widely applied in many fields of research. However, models with uncertain design matrices for random effects have been little investigated before. In some applications with such problems, an expectation method has been used for simplicity. This method does not include the extra information of uncertainty in the design matrix is not included. The closed solution for this problem is generally difficult to attain. We therefore propose an two-step algorithm for estimating the parameters, especially the variance components in the model. The implementation is based on Monte Carlo approximation and a Newton-Raphson-based EM algorithm. As an example, a simulated genetics dataset was analyzed. The results showed that the proportion of the total variance explained by the random effects was accurately estimated, which was highly underestimated by the expectation method. By introducing heuristic search and optimization methods, the algorithm can possibly be developed to infer the 'model-based' best design matrix and the corresponding best estimates.