Model structure and uncertainty for stochastic non-point source modelling applications

The uncertainty associated with a rainfall-runoff and non-point source loading (NPS) model can be attributed to both the parameterization and model structure. An interesting implication of the areal nature of NPS models is the direct relationship between model structure (i.e. sub-watershed size) and sample size for the parameterization of spatial data. The approach of this research is to find structural limitations in scale for the use of the conceptual NPS model, then examine the scales at which suitable stochastic depictions of key parameter sets can be generated. The overlapping regions are optimal (and possibly the only suitable regions) for conducting meaningful stochastic analysis with a given NPS model. Previous work has sought to find optimal scales for deterministic analysis (where, in fact, calibration can be adjusted to compensate for sub-optimal scale selection); however, analysis of stochastic suitability and uncertainty associated with both the conceptual model and the parameter set, as presented here, is novel; as is the strategy of delineating a watershed based on the uncertainty distribution. The results of this paper demonstrate a narrow range of acceptable model structure for stochastic analysis in the chosen NPS model. In the case examined, the uncertainties associated with parameterization and parameter sensitivity are shown to be outweighed in significance by those resulting from structural and conceptual decisions. © 2011 Copyright IAHS Press.

Coupling model uncertainty for coupled rainfall/runoff and surface water quality models in river problems

Coupled hydrology and water quality models are an important tool today, used in the understanding and management of surface water and watershed areas. Such problems are generally subject to substantial uncertainty in parameters, process understanding, and data. Component models, drawing on different data, concepts, and structures, are affected differently by each of these uncertain elements. This paper proposes a framework wherein the response of component models to their respective uncertain elements can be quantified and assessed, using a hydrological model and water quality model as two exemplars. The resulting assessments can be used to identify model coupling strategies that permit more appropriate use and calibration of individual models, and a better overall coupled model response. One key finding was that an approximate balance of water quality and hydrological model responses can be obtained using both the QUAL2E and Mike11 water quality models. The balance point, however, does not support a particularly narrow surface response (or stringent calibration criteria) with respect to the water quality calibration data, at least in the case examined here. Additionally, it is clear from the results presented that the structural source of uncertainty is at least as significant as parameter-based uncertainties in areal models. © 2012 John Wiley & Sons, Ltd.

Two-port calibration of test fixtures with different test ports

The open-short-load (OSL) method is very simple and widely used for one-port test fixture calibration. In this paper, this method is extended, for the first time, to the two-port calibration of test fixtures with different test ports. The problem of phase uncertainty arising in this application has been solved. The comparison between our results and those obtained with the SOLT method shows that the method established is accurate for practical applications. (C) 2002 Wiley Periodicals, Inc.

Phase uncertainty in calibrating microwave test fixtures

The problem of phase uncertainty arising in calibration of the test fixtures is investigated in this paper, It is shown that the problem exists no matter what kinds of calibration standards are used. It is also found that there is no need to determine the individual S-parameters of the test fixtures. In order to eliminate the problem of phase uncertainty, three different precise (known) reflection standards or one known reflection standard plus one known transmission standard should be used to calibrate symmetrical test fixtures. For the asymmetrical cases, three known standards, including at least one transmission standard, should be used. The thru-open-match (TOM) and thru-short-match (TSM) techniques are the simplest methods, and they have no bandwidth limitation. When the standards are imprecise (unknown), it is recommended to use any suitable technique, such as the thru-reflect-line, line-reflect-line, thru-short-delay, thru-open-delay,line-reflect-match, line-reflect-reflect-match, or multiline methods, to accurately determine the values of the required calibration terms and, in addition, to use the TOM or TSM method with the same imprecise standards to resolve the phase uncertainty.

Two-port calibration of test fixtures with OSL method.

The open-short-load (OSL) method is very simple and widely used, for one-port test fixture calibration. In this paper, this method. is extended to the two-port calibration of test fixtures for the first time. The problem of phase uncertainty arising in this application has been solved. The comparison between our results and those obtained with the short-open-load-thru (SOLT) method shows that the method established is accurate enough for practical applications.

Marine04 marine radiocarbon age calibration, 0-26 cal kyr BP

New radiocarbon calibration curves, IntCal04 and Marine04, have been constructed and internationally ratified to replace the terrestrial and marine components of IntCal98. The new calibration data sets extend an additional 2000 yr, from 0–26 cal kyr BP (Before Present, 0 cal BP = AD 1950), and provide much higher resolution, greater precision, and more detailed structure than IntCal98. For the Marine04 curve, dendrochronologically-dated tree-ring samples, converted with a box diffusion model to marine mixed-layer ages, cover the period from 0–10.5 cal kyr BP. Beyond 10.5 cal kyr BP, high-resolution marine data become available from foraminifera in varved sediments and U/Th-dated corals. The marine records are corrected with site-specific 14C reservoir age information to provide a single global marine mixed-layer calibration from 10.5–26.0 cal kyr BP. A substantial enhancement relative to IntCal98 is the introduction of a random walk model, which takes into account the uncertainty in both the calendar age and the 14C age to calculate the underlying calibration curve (Buck and Blackwell, this issue). The marine data sets and calibration curve for marine samples from the surface mixed layer (Marine04) are discussed here. The tree-ring data sets, sources of uncertainty, and regional offsets are presented in detail in a companion paper by Reimer et al. (this issue).

IntCal04 terrestrial radiocarbon age calibration, 0-26 cal kyr BP

A new calibration curve for the conversion of radiocarbon ages to calibrated (cal) ages has been constructed and internationally ratified to replace IntCal98, which extended from 0-24 cal kyr BP (Before Present, 0 cal BP = AD 1950). The new calibration data set for terrestrial samples extends from 0-26 cal kyr BP, but with much higher resolution beyond 11.4 cal kyr BP than IntCal98. Dendrochronologically-dated tree-ring samples cover the period from 0-12.4 cal kyr BP. Beyond the end of the tree rings, data from marine records (corals and foraminifera) are converted to the atmospheric equivalent with a site-specific marine reservoir correction to provide terrestrial calibration from 12.4-26.0 cal kyr BP. A substantial enhancement relative to IntCal98 is the introduction of a coherent statistical approach based on a random walk model, which takes into account the uncertainty in both the calendar age and the (super 14) C age to calculate the underlying calibration curve (Buck and Blackwell, this issue). The tree-ring data sets, sources of uncertainty, and regional offsets are discussed here. The marine data sets and calibration curve for marine samples from the surface mixed layer (Marine04) are discussed in brief, but details are presented in Hughen et al. (this issue a). We do not make a recommendation for calibration beyond 26 cal kyr BP at this time; however, potential calibration data sets are compared in another paper (van der Plicht et al., this issue).

High precision C-14 dating of Holocene peat deposits: A comparison of Bayesian calibration and wiggle-matching approaches

The chronologies of five northern European ombrotrophic peat bogs subjected to a large ANIS C-14 dating effort (32-44 dates/site) are presented here. The results of Bayesian calibration (BCal) of dates with a prior assumption of chronological ordering were compared with a Bayesian wiggle-match approach (Bpeat) which assumes constant linear accumulation over sections of the peat profile. Interpolation of BCal age estimates of dense sequences of C-14 dates showed variable patterns of peat accumulation with time, with changes in accumulation occurring at intervals ranging from 20 to 50 cm. Within these intervals, peat accumulation appeared to be relatively linear. Close analysis suggests that some of the inferred variations in accumulation rate were related to the plant macrofossil composition of the peat. The wiggle-matched age-depth models had relatively high chronological uncertainty within intervals of closely spaced 14 C dates, suggesting that the premise of constant linear accumulation over large sections of the peat profile is unrealistic. Age models based on the assumption of linear accumulation over large parts of a peat core (and therefore only effective over millennial timescales), are not compatible with studies examining environmental change during the Holocene, where variability often occurs at decadal to centennial time-scales. Ideally, future wiggle-match age models should be constrained, with boundaries between sections based on the plant macrofossil composition of the peat and physical-chemical parameters such as the degree of decomposition. Strategies for the selection of material for dating should be designed so that there should be enough C-14 dates to accurately reconstruct the peat accumulation rate of each homogeneous stratigraphic unit. (c) 2006 Elsevier Ltd. All rights reserved.

IntCal09 and Marine09 radiocarbon age calibration curves, 0 - 50,000 years cal BP

The IntCal04 and Marine04 radiocarbon calibration curves have been updated from 12 cal kBP (cal kBP is here defined as thousands of calibrated years before AD 1950), and extended to 50 cal kBP, utilizing newly available data sets that meet the IntCal Working Group criteria for pristine corals and other carbonates and for quantification of uncertainty in both the ¹⁴C and calendar timescales as established in 2002. No change was made to the curves from 0-12 cal kBP. The curves were constructed using a Markov chain Monte Carlo (MCMC) implementation of the random walk model used for IntCal04 and Marine04. The new curves were ratified at the 20th International Radiocarbon Conference in June 2009 and are available in the Supplemental Material at www.radiocarbon.org.

Extended Radiocarbon Calibration in the Anglo-Saxon Period, AD395-485 and AD735-805

Radiocarbon dating has been used infrequently as a chronological tool for research in Anglo-Saxon archaeology. Primarily, this is because the uncertainty of calibrated dates provides little advantage over traditional archaeological dating in this period. Recent advances in Bayesian methodology in conjunction with high-precision 14C dating have, however, created the possibility of both testing and refining the established Anglo-Saxon chronologies based on typology of artifacts. The calibration process within such a confined age range, however, relies heavily on the structural accuracy of the calibration curve. We have previously reported decadal measurements on a section of the Irish oak chronology for the period AD 495–725 (McCormac et al. 2004). In this paper, we present decadal measurements for the periods AD 395–485 and AD 735–805,which extends the original calibration set.

Selection and Treatment of Data for Radiocarbon Calibration: An Update to the International Calibration (IntCal) Criteria

High-quality data from appropriate archives are needed for the continuing improvement of radiocarbon calibration curves. We discuss here the basic assumptions behind 14C dating that necessitate calibration and the relative strengths and weaknesses of archives from which calibration data are obtained. We also highlight the procedures, problems and uncertainties involved in determining atmospheric and surface ocean 14C/12C in these archives, including a discussion of the various methods used to derive an independent absolute timescale and uncertainty. The types of data required for the current IntCal database and calibration curve model are tabulated with examples.

Reducing Parametric Uncertainty in Limit Cycle Oscillations

The assimilation of discrete higher fidelity data points with model predictions can be used to achieve a reduction in the uncertainty of the model input parameters which generate accurate predictions. The problem investigated here involves the prediction of limit-cycle oscillations using a High-Dimensional Harmonic Balance method (HDHB). The efficiency of the HDHB method is exploited to enable calibration of structural input parameters using a Bayesian inference technique. Markov-chain Monte Carlo is employed to sample the posterior distributions. Parameter estimation is carried out on both a pitch/plunge aerofoil and Goland wing configuration. In both cases significant refinement was achieved in the distribution of possible structural parameters allowing better predictions of their
true deterministic values.

Does uncertainty cause inertia in decision making? An experimental study of the role of regret aversion and indecisiveness

Previous research has shown that often there is clear inertia in individual decision making---that is, a tendency for decision makers to choose a status quo option. I conduct a laboratory experiment to investigate two potential determinants of inertia in uncertain environments: (i) regret aversion and (ii) ambiguity-driven indecisiveness. I use a between-subjects design with varying conditions to identify the effects of these two mechanisms on choice behavior. In each condition, participants choose between two simple real gambles, one of which is the status quo option. I find that inertia is quite large and that both mechanisms are equally important.

Calibration of uncertain flood inundation models using remotely sensed water levels

A traditional method of validating the performance of a flood model when remotely sensed data of the flood extent are available is to compare the predicted flood extent to that observed. The performance measure employed often uses areal pattern-matching to assess the degree to which the two extents overlap. Recently, remote sensing of flood extents using synthetic aperture radar (SAR) and airborne scanning laser altimetry (LIDAR) has made more straightforward the synoptic measurement of water surface elevations along flood waterlines, and this has emphasised the possibility of using alternative performance measures based on height. This paper considers the advantages that can accrue from using a performance measure based on waterline elevations rather than one based on areal patterns of wet and dry pixels. The two measures were compared for their ability to estimate flood inundation uncertainty maps from a set of model runs carried out to span the acceptable model parameter range in a GLUE-based analysis. A 1 in 5-year flood on the Thames in 1992 was used as a test event. As is typical for UK floods, only a single SAR image of observed flood extent was available for model calibration and validation. A simple implementation of a two-dimensional flood model (LISFLOOD-FP) was used to generate model flood extents for comparison with that observed. The performance measure based on height differences of corresponding points along the observed and modelled waterlines was found to be significantly more sensitive to the channel friction parameter than the measure based on areal patterns of flood extent. The former was able to restrict the parameter range of acceptable model runs and hence reduce the number of runs necessary to generate an inundation uncertainty map. A result of this was that there was less uncertainty in the final flood risk map. The uncertainty analysis included the effects of uncertainties in the observed flood extent as well as in model parameters. The height-based measure was found to be more sensitive when increased heighting accuracy was achieved by requiring that observed waterline heights varied slowly along the reach. The technique allows for the decomposition of the reach into sections, with different effective channel friction parameters used in different sections, which in this case resulted in lower r.m.s. height differences between observed and modelled waterlines than those achieved by runs using a single friction parameter for the whole reach. However, a validation of the modelled inundation uncertainty using the calibration event showed a significant difference between the uncertainty map and the observed flood extent. While this was true for both measures, the difference was especially significant for the height-based one. This is likely to be due to the conceptually simple flood inundation model and the coarse application resolution employed in this case. The increased sensitivity of the height-based measure may lead to an increased onus being placed on the model developer in the production of a valid model

Parameter sensitivity and predictive uncertainty in a new water quality model, Q(2)

A new dynamic model of water quality, Q(2), has recently been developed, capable of simulating large branched river systems. This paper describes the application of a generalized sensitivity analysis (GSA) to Q(2) for single reaches of the River Thames in southern England. Focusing on the simulation of dissolved oxygen (DO) (since this may be regarded as a proxy for the overall health of a river); the GSA is used to identify key parameters controlling model behavior and provide a probabilistic procedure for model calibration. It is shown that, in the River Thames at least, it is more important to obtain high quality forcing functions than to obtain improved parameter estimates once approximate values have been estimated. Furthermore, there is a need to ensure reasonable simulation of a range of water quality determinands, since a focus only on DO increases predictive uncertainty in the DO simulations. The Q(2) model has been applied here to the River Thames, but it has a broad utility for evaluating other systems in Europe and around the world.