Henrik Madsen

Automatic calibration of a conceptual rainfall-runoff model using multiple objectives

Formulation of an automatic calibration strategy for the MIKE 11/NAM rainfall–runoff model is outlined. The calibration scheme includes optimisation of multiple objectives that measure different aspects of the hydrograph: (1) overall water balance, (2) overall shape of the hydrograph, (3) peak flows, and (4) low flows. An automatic optimisation procedure based on the shuffled complex evolution algorithm is introduced for solving the multi-objective calibration problem. A test example is presented that illustrates the principles and implications of using multiple objectives in model calibration. Significant trade-offs between the different objectives are observed in this case and no single unique set of parameter values is able to optimise all objectives simultaneously. Instead, the solution to the calibration problem is given as a set of Pareto optimal solutions, which from a multi-objective viewpoint are equivalent. A large variability is observed in the Pareto optimal parameter sets, resulting in a large range of “equally good” simulated hydrographs. From the set of Pareto optimal solutions, one can draw a single solution according to priorities of the different objectives for the specific model application being considered. A balanced aggregated objective function is proposed, which provides a compromise solution that puts equal weights to the different objectives.

Preoperative Staging of Lung Cancer with Combined PET–CT

BACKGROUND Fast and accurate staging is essential for choosing treatment for non-small-cell lung cancer (NSCLC). The purpose of this randomized study was to evaluate the clinical effect of combined positron-emission tomography and computed tomography (PET-CT) on preoperative staging of NSCLC. METHODS We randomly assigned patients who were referred for preoperative staging of NSCLC to either conventional staging plus PET-CT or conventional staging alone. Patients were followed until death or for at least 12 months. The primary end point was the number of futile thoracotomies, defined as any one of the following: a thoracotomy with the finding of pathologically confirmed mediastinal lymph-node involvement (stage IIIA [N2]), stage IIIB or stage IV disease, or a benign lung lesion; an exploratory thoracotomy; or a thoracotomy in a patient who had recurrent disease or death from any cause within 1 year after randomization. RESULTS From January 2002 through February 2007, we randomly assigned 98 patients to the PET-CT group and 91 to the conventional-staging group. Mediastinoscopy was performed in 94% of the patients. After PET-CT, 38 patients were classified as having inoperable NSCLC, and after conventional staging, 18 patients were classified thus. Sixty patients in the PET-CT group and 73 in the conventional-staging group underwent thoracotomy (P=0.004). Among these thoracotomies, 21 in the PET-CT group and 38 in the conventional-staging group were futile (P=0.05). The number of justified thoracotomies and survival were similar in the two groups. CONCLUSIONS The use of PET-CT for preoperative staging of NSCLC reduced both the total number of thoracotomies and the number of futile thoracotomies but did not affect overall mortality. (ClinicalTrials.gov number, NCT00867412.)

Parameter estimation in distributed hydrological catchment modelling using automatic calibration with multiple objectives

A consistent framework for parameter estimation in distributed hydrological catchment modelling using automatic calibration is formulated. The framework focuses on the different steps in the estimation process from model parameterisation and selection of calibration parameters, formulation of calibration criteria, and choice of optimisation algorithm. The calibration problem is formulated in a general multi-objective context in which different objective functions that measure individual process descriptions can be optimised simultaneously. Within this framework it is possible to tailor the model calibration to the specific objectives of the model application being considered. A test example is presented that illustrates the use of the calibration framework for parameter estimation in the MIKE SHE integrated and distributed hydrological modelling system. A significant trade-off between the performance of the groundwater level simulations and the catchment runoff is observed in this case, defining a Pareto front with a very sharp structure. The Pareto optimum solution corresponding to a proposed balanced aggregated objective function is seen to provide a proper balance between the two objectives. Compared to a manual expert calibration, the balanced Pareto optimum solution provides generally better simulation of the runoff, whereas virtually similar performance is obtained for the groundwater level simulations.

Parameter estimation in stochastic grey-box models

An efficient and flexible parameter estimation scheme for grey-box models in the sense of discretely, partially observed Ito stochastic differential equations with measurement noise is presented along with a corresponding software implementation. The estimation scheme is based on the extended Kalman filter and features maximum likelihood as well as maximum a posteriori estimation on multiple independent data sets, including irregularly sampled data sets and data sets with occasional outliers and missing observations. The software implementation is compared to an existing software tool and proves to have better performance both in terms of quality of estimates for nonlinear systems with significant diffusion and in terms of reproducibility. In particular, the new tool provides more accurate and more consistent estimates of the parameters of the diffusion term.

Standardizing the Performance Evaluation of Short-Term Wind Power Prediction Models

Short-term wind power prediction is a primary requirement for efficient large-scale integration of wind generation in power systems and electricity markets. The choice of an appropriate prediction model among the numerous available models is not trivial, and has to be based on an objective evaluation of model performance. This paper proposes a standardized protocol for the evaluation of short-term windpower prediction systems. A number of reference prediction models are also described, and their use for performance comparison is analysed. The use of the protocol is demonstrated, using results from both on-shore and offshore wind farms. The work was developed in the frame of the Anemos project (EU R&D project) where the protocol has been used to evaluate more than 10 prediction systems.

Comparison of different automated strategies for calibration of rainfall-runoff models

Three different automated methods for calibration of rainfall-runoff models are presented and compared. The methods represent various calibration strategies that utilise multiple objectives and allow user intervention on different levels and different stages in the calibration process. The methods have been applied for calibration of a test catchment and compared on validation data with respect to overall performance measures in terms of water balance error and general hydrograph shape, and simulation of high and low flow events. The results illustrate the problem of non-uniqueness in model calibration since none of the methods are superior with respect to all performance measures considered. In general, the different methods put emphasis on different response modes of the hydrograph. Calibration based on the use of generic search routines in combination with user-specified calibration priorities is seen to compare favourably with an expert system that is designed for the specific model being considered and requires user intervention during the entire calibration process.

Power Fluctuations From Large Wind Farms

This paper deals with power fluctuations from wind farms. The time range in focus is between one minute and up to a couple of hours. In this time range, substantial power fluctuations have been observed during unstable weather conditions. A wind power fluctuation model is described, and measured time series from the first large offshore wind farm, Horns Rev in Denmark, are compared to simulated time series. The comparison between measured and simulated time series focuses on the ramping characteristics of the wind farm at different power levels and on the need for system generation reserves due to the fluctuations. The comparison shows a reasonable agreement between simulations and measurements, although there is still room for improvement of the simulation model.

On the definition and modelling of streamflow drought duration and deficit volume

Abstract The threshold level approach is used to define drought characteristics, i.e. drought duration and deficit volume from time series of daily streamflow. Three different procedures for pooling dependent droughts are compared: a method based on an inter-event time and volume criterion (IC), a moving average procedure (MA), and a method based on the sequent peak algorithm (SPA). The extreme values of drought duration and deficit volume are analysed using both an annual maximum series (AMS) and a partial duration series (PDS) approach. Two Danish catchments with very different flow regimes were used in the study. The IC and MA methods provided virtually the same sample statistics of the AMS of drought duration and deficit volume for all thresholds considered. The results of the SPA method differed significantly from the other two methods for high thresholds due to the presence of multi-year droughts. For analysis of seasonal droughts the SPA method is restricted to low thresholds. The occurrence of a l...

Estimation of continuous-time models for the heat dynamics of a building

Abstract This paper describes a method for estimation of continuous-time models for the heat dynamics of buildings based on discrete-time building performance data. The parameters in the continuous-time model are estimated by the maximum likelihood method where a Kalman filter is used in calculating the likelihood function. The modeling procedure is illustrated by using measurements from an experiment where the heat input from electrical heaters is controlled by a pseudorandom binary signal. For the considered building a rather simple model containing two time constants is found adequate. Owing to the continuous-time formulation the parameters of the model are directly physically interpretable. The performance of the model for both forecasting and simulation is illustrated.

Prediction in partial duration series with generalized pareto‐distributed exceedances

As a generalization of the common assumption of exponential distribution of the exceedances in partial duration series the generalized Pareto distribution has been adopted. Estimators for the parameters are presented using estimation by both method of moments and probability-weighted moments. The corresponding estimators for the T-year event are given and approximate expressions for bias and variance of the estimators are derived in both cases. Using the mean square error of the T-year event estimator as a performance index it is shown that the method of moments is preferable to the probability-weighted moments. Maintaining the generalized Pareto distribution as the parent exceedance distribution the T-year event is estimated assuming the exceedances to be exponentially distributed. For moderately long-tailed exceedance distributions and small to moderate sample sizes it is found, by comparing mean square errors of the T-year event estimators, that the exponential distribution is preferable to the correct generalized Pareto distribution despite the introduced model error and despite a possible rejection of the exponential hypothesis by a test of significance. For moderately short-tailed exceedance distributions (with physically justified upper limit) the correct exceedance distribution should be applied despite a possible acceptance of the exponential assumption by a test of significance.