Semi-lumped Model Research Articles

Trade-offs between parameter constraints and model realism: a case study

Tightly constraint parameter ranges are seen as an important goal in constructing hydrological models, a difficult task in complex models. However, many studies show that complex models are often good at capturing the behaviour of a river. Therefore, this study explores the trade-offs between tightly constrained parameters and the ability to predict hydrological signatures, that capture the behaviour of a river. To accomplish this we built five models of differing complexity, ranging from a simple lumped model to a semi-lumped model with eight spatial subdivisions. All models are built within the same modelling framework, use the same data, and are calibrated with the same algorithm. We also consider two different methods for the potential evapotranspiration. We found that that there is a clear trade-off along the axis of complexity. While the more simple models can constrain their parameters quite well, they fail to get the hydrological signatures right. It is the other way around for the more complex models. The method of evapotranspiration only influences the parameters directly related to it. This study highlights that it is important to focus not only on parametric uncertainty. Tightly constrained parameters can be misguiding as they give credibility to oversimplified model structures.

Miniaturized overlapped LC phase delay line

A novel miniaturized ultra-wide bandwidth (DC–35 GHz) LC phase delay line (PDL) based on overlapped meander inductors and air-bridge capacitors is proposed and fabricated. Two 45º and 90º PDLs were designed using a semi-lumped model, and the parameters were calculated and optimized based on transmission line theory and 3D simulations. The lengths of the 45º and 90º delay lines are 110 μm and 286 μm, respectively, which represent respective length reductions of 50% and 75% when compared with the corresponding conventional transmission lines. Over the entire operating band, the phase error is less than 0.6º for the 45º PDL and 2.5º for the 90º PDL. The return loss (S11) for both PDLs is better than 15.5 dB, while the insertion loss (S21) is less than 0.62 dB for both devices. Measured results show perfect consistency with the simulation results for these PDLs, and demonstrate the validity of the corresponding model.

Integrating point glacier mass balance observations into hydrologic model identification

Abstract. The hydrology of high mountainous catchments is often predicted with conceptual precipitation-discharge models that simulate the snow accumulation and ablation behavior of a very complex environment using as only input temperature and precipitation. It is hereby often assumed that some glacier-wide annual balance estimates, in addition to observed discharge, are sufficient to reliably calibrate such a model. Based on observed data from Rhonegletscher (Switzerland), we show in this paper that information on the seasonal mass balance is a pre-requisite for model calibration. And we present a simple, but promising methodology to include point mass balance observations into a systematic calibration process. The application of this methodology to the Rhonegletscher catchment illustrates that even small samples of point observations do contain extractable information for model calibration. The reproduction of these observed seasonal mass balance data requires, however, a model structure modification, in particular seasonal lapse rates and a separate snow accumulation and rainfall correction factor. This paper shows that a simple conceptual model can be a valuable tool to project the behavior of a glacier catchment but only if there is enough seasonal information to constrain the parameters that directly affect the water mass balance. The presented multi-signal model identification framework and the simple method to calibrate a semi-lumped model on point observations has potential for application in other modeling contexts.

Comparison of conceptual model performance using different representations of spatial variability

The objective in this study is to explore a solution to the question whether model input data having higher spatial resolution and higher model resolution, as most people assume, lead to better model performance within a given modelling objective. An attempt was made to modify the conceptual rainfall-runoff model HBV to incorporate a spatially distributed structure. Additionally, three more model structures based on the HBV model concept were designed: lumped, semi-lumped and semi-distributed. An automatic calibration procedure based on simulated annealing optimization algorithm was followed for maximizing an objective function composed of Nash-Sutcliffe coefficients of several temporal aggregation steps. The predictive performance from each model was then assessed and compared with other model structures with respect to stream flow prediction at the catchment outlet. The spatial variation of the meteorological input was produced using external drift kriging method from available limited point measurements. The models were applied to a mesoscale catchment located in central Europe. The simulated hydrographs obtained using different model structures were analyzed through comparison of their Nash-Sutcliffe coefficients and other goodness-of-fit indices. For the present study, semi-distributed and semi-lumped model structures outperformed the distributed and fully-lumped model structures. A possible explanation why the distributed model did not perform better than the simpler model structures is the use of limited available spatial information. The models use interpolated precipitation and temperature as input, which probably cannot reflect the true spatial variability. Another possible explanation is that only discharge at the catchment outlet was predicted; which is the purpose for which lumped and semi-distributed models were actually designed.

Design and modeling of 4-bit slow-wave MEMS phase shifters

A true-time-delay multibit microelectromechanical systems (MEMS) phase-shifter topology based on impedance-matched slow-wave coplanar-waveguide sections on a 500-mum-thick quartz substrate is presented. A semilumped model for the unit cell is derived and its equivalent-circuit parameters are extracted from measurement and electromagnetic simulation data. This unit cell model can be cascaded to accurately predict N-section phase-shifter performance. Experimental data for a 4.6-mm-long 4-bit device shows a maximum phase error of 5.5deg and S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sub> less than -21 dB from 1 to 50 GHz with worst case S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">21</sub> less than -1.2 dB. In a second design, the slow-wave phase shifter was additionally loaded with MEMS capacitors to result in a phase shift of 257deg/dB at 50 GHz, while keeping S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sub> below -19 dB (with S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">21</sub> <-1.9 dB). The beams are actuated using high-resistance SiCr bias lines with typical actuation voltage around 30-45 V

Dynamic modelling and network simulation of n-heptane catalytic cracking: influence of kinetic parameters

A new predictive semi-lumped model developed for the cracking of paraffins has been applied to n-heptane. The model is based on a complex network reaction scheme including the ensemble of reactions taking place during the catalytic cracking of paraffins. The reaction scheme is detailed to the carbon atom number level and a large number of reactions are taken into account, ranging from cracking, hydride transfer and chain growth, which eventually leads to coking. It is considered that all the species present can participate in all of the above reactions, creating a complex network where all the species interact with all the others by means of the three sets of reactions included. Since the reaction network involves 1125 reactions, written in terms of elementary steps, an important problem to be solved hereby is to assign values to the corresponding reaction rate constants. For most of the elementary reactions considered experimental data is not directly available in the literature so, for their kinetic rate constants quite simple arbitrary equations were used to estimate them for each set of reactant/products considered. Each kinetic expression was parameterised with three parameters in order to describe the dependence of the corresponding kinetic rate constant on the number of carbon atoms of the adsorbed and gas phase species involved. The estimation of the nine rate constant parameters is discussed, as well as their influence on the evolution with time on stream of the profiles of global gas phase and predicted surface species distributions, coke content, catalytic activities and deactivation curves. The model is applied to the cracking of n-heptane and validated using experimental data. It can be shown that, despite the assumptions that were considered in this approach, very meaningful results are obtained. The model computes the product distributions at the exit of the reactor as well as the global distribution of surface adsorbed species, the coke content at the surface and the global activities, can be predicted as a function of time on stream.