Individual Parameter Perturbation Research Articles

Anisotropic Born scattering for the qP scalar wavefield using a low-rank symbol approximation

We have developed a procedure to derive low-rank evolution operators in the mixed space-wavenumber domain for modeling the qP Born-scattered wavefield at perturbations of an anisotropic medium under the pseudoacoustic approximation. To approximate the full wavefield, this scattered field is then added to the reference wavefield obtained with the corresponding low-rank evolution operator in the background medium. Being built upon a Hamiltonian formulation using the dispersion relation for qP-waves, this procedure avoids pseudo-S-wave artifacts and provides a unified approach for linearizing anisotropic pseudoacoustic evolution operators. Therefore, it is immediately applicable to any arbitrary class of anisotropy. As an additional asset, the scattering operators explicitly contain the sensitivity kernels of the Born-scattered wavefield with respect to the anisotropic medium parameters. This enables direct access to important information such as its offset dependence or directional characteristics as a function of the individual parameter perturbations. For our numerical tests, we specify the operators for a mildly anisotropic tilted transversely isotropic (TTI) medium. We validate our implementation in a simple model with weak contrasts and simulate reflection data in the BP TTI model to indicate that the procedure works in a more realistic scenario. The Born-scattering results indicate that our procedure is applicable to strongly heterogeneous anisotropic media. Moreover, we use the analytical capabilities of the kernels by means of sensitivity tests to demonstrate that using two different medium parameterizations leads to different results. The mathematical formulation of the method is such that it allows for an immediate application to least-squares migration in pseudoacoustic anisotropic media.

The effect of perturbing body segment parameters on calculated joint moments and muscle forces during gait

This study examined the effect of body segment parameter (BSP) perturbations on joint moments calculated using an inverse dynamics procedure and muscle forces calculated using computed muscle control (CMC) during gait. BSP (i.e. segment mass, center of mass location (com) and inertia tensor) of the left thigh, shank and foot of a scaled musculoskeletal model were perturbed. These perturbations started from their nominal value and were adjusted to ±40% in steps of 10%, for both individual as well as combined perturbations in BSP. For all perturbations, an inverse dynamics procedure calculated the ankle, knee and hip moments based on an identical inverse kinematics solution. Furthermore, the effect of applying a residual reduction algorithm (RRA) was investigated. Muscle excitations and resulting muscle forces were calculated using CMC. The results show only a limited effect of an individual parameter perturbation on the calculated moments, where the largest effect is found when perturbing the shank com (MScom,shank, the ratio of absolute difference in torque and relative parameter perturbation, is maximally −7.81Nm for hip flexion moment). The additional influence of perturbing two parameters simultaneously is small (MSmass+com,thigh is maximally 15.2Nm for hip flexion moment). RRA made small changes to the model to increase the dynamic consistency of the simulation (after RRA MScom,shank is maximally 5.01Nm). CMC results show large differences in muscle forces when BSP are perturbed. These result from the underlying forward integration of the dynamic equations.

A sensitivity study of radiative fluxes at the top of atmosphere to cloud-microphysics and aerosol parameters in the community atmosphere model CAM5

Abstract. In this study, we investigated the sensitivity of net radiative fluxes (FNET) at the top of atmosphere (TOA) to 16 selected uncertain parameters mainly related to the cloud microphysics and aerosol schemes in the Community Atmosphere Model version 5 (CAM5). We adopted a quasi-Monte Carlo (QMC) sampling approach to effectively explore the high-dimensional parameter space. The output response variables (e.g., FNET) are simulated using CAM5 for each parameter set, and then evaluated using the generalized linear model analysis. In response to the perturbations of these 16 parameters, the CAM5-simulated global annual mean FNET ranges from −9.8 to 3.5 W m−2 compared to 1.9 W m−2 with the default parameter values. Variance-based sensitivity analysis is conducted to show the relative contributions of individual parameter perturbations to the global FNET variance. The results indicate that the changes in the global mean FNET are dominated by changes in net cloud forcing (CF) within the parameter ranges being investigated. The threshold size parameter related to auto-conversion of cloud ice to snow is identified as one of the most influential parameters for FNET in CAM5 simulations. The strong heterogeneous geographic distribution of FNET variance shows that parameters have a clear localized effect over regions where they are acting. However, some parameters also have non-local impacts on FNET variance. Although external factors, such as perturbations of anthropogenic and natural emissions, largely affect FNET variance at the regional scale, their impact is weaker than that of model internal parameters in terms of simulating global mean FNET. The interactions among the 16 selected parameters contribute a relatively small portion to the total FNET variance over most regions of the globe. This study helps us better understand the parameter uncertainties in the CAM5 model, and thus provides information for further calibrating uncertain model parameters with the largest sensitivity.

Sensitivity-Indices-Based Risk Assessment of Large-Scale Solar PV Investment Projects

Large-scale solar photovoltaic (PV) generation is now a viable, economically feasible and clean energy supply option. Incentive schemes, such as the Feed-in-Tariff (FIT) in Ontario, have attracted large-scale investments in solar PV generation. In a previous work, the authors presented an investor-oriented planning model for optimum selection of solar PV investment decisions. In this paper, a method for determining the sensitivity indices, based on the application of duality theory on the Karush–Kuhn–Tucker (KKT) optimality conditions, pertaining to the solar PV investment model is presented. The sensitivity of the investors' profit to various parameters, for a case study in Ontario, Canada are presented and discussed and these are found to be very close to those obtained using the Monte Carlo simulation and finite-difference (individual parameter perturbation) based approaches. Furthermore, a novel relationship is proposed between the sensitivity indices and the investor's profit for a given confidence level to evaluate the risk for an investor in solar PV projects.

Stratospheric water vapour and high climate sensitivity in a version of the HadSM3 climate model

Abstract. It has been shown previously that one member of the Met Office Hadley Centre single-parameter perturbed physics ensemble – the so-called "low entrainment parameter" member – has a much higher climate sensitivity than other individual parameter perturbations. Here we show that the concentration of stratospheric water vapour in this member is over three times higher than observations, and, more importantly for climate sensitivity, increases significantly when climate warms. The large surface temperature response of this ensemble member is more consistent with stratospheric humidity change, rather than upper tropospheric clouds as has been previously suggested. The direct relationship between the bias in the control state (elevated stratospheric humidity) and the cause of the high climate sensitivity (a further increase in stratospheric humidity) lends further doubt as to the realism of this particular integration. This, together with other evidence, lowers the likelihood that the climate system's physical sensitivity is significantly higher than the likely upper range quoted in the Intergovernmental Panel on Climate Change's Fourth Assessment Report.

Reconstructing migrations of individual cod (Gadus morhuaL.) in the Baltic Sea by using electronic data storage tags

AbstractA new methodology is presented to reconstruct migration pathways of individual fish inhabiting ecosystems with moderate‐to‐strong gradients in temperature or salinity. The method uses measurements of ambient pressure, temperature and salinity obtained from electronic data storage tags attached to individual fish and is particularly applicable in areas with negligible tides. We demonstrate the method with Baltic cod. Hydrographic fields obtained from hydrodynamic modelling were used as a geolocation database to identify daily positions of Baltic cod by comparison with the environmental data collected by the tags. Using randomly distributed individual parameter perturbations in the range of the instrument precision of the tag we simulated a cod migrating through the Baltic Sea. The distance between the prescribed and geolocated positions of this artificial cod was on average 2.9 ± 4.7 (SD) km. Subsequently, the method was used to reconstruct migration routes of 10 real cod tagged in the Bornholm Basin of the Baltic Sea in early spring 2003. Differences were compared between the tag data and the geolocation database. The uncertainty in geolocation at recapture day was on average 75 ± 23 (SD) km, as shown by comparison between geolocated position and recapture position.

Modelling feeding, growth, and habitat selection in larval Atlantic cod (Gadus morhua): observations and model predictions in a macrocosm environment

Individual-based models (IBMs) integrate behavioural, physiological, and developmental features and differences among individuals. Building on previous process-based models, we developed an IBM of larval Atlantic cod (Gadus morhua) that included foraging, size-, temperature-, and food-limited growth, and environmental factors such as prey-field, turbulence, and light. Direct comparison between larval fish IBMs and experimental studies is lacking. Using data from a macrocosm study on growth and feeding of larval cod, we forced the model with observed temperature and prey-field and compared model predictions with observed distribution, diet, size-at-age, and specific growth rates. We explored implications of habitat selection rules on predicted growth rates. We analyze the sensitivity of model predictions by the Latin Hypercube Sampling method and individual parameter perturbation. Food limitation prevented larvae from growing at their physiological maximum, especially in the period 5–17 days post hatch (DPH). Active habitat selection had the potential to enhance larval growth rates. The model predicted temperature-limited growth rates for first-feeding larvae (5–20 DPH) when prey density is >5 nauplii·L–1. After age 20 DPH, maximum modelled growth required a diet of copepodites. Simulated growth rates were close to observed values except for the period just after the start of exogenous feeding when prey density was low.

Development and application of a bioenergetics model for juvenile walleye Pollock

A bioenergetics model was parameterized for age‐0 walleye pollock, Theragra chalcogramma, based on a synthesis of literature data. The sensitivity of the new parameters was tested by individual parameter perturbation (IPP) analysis. The model was applied to estimate individual and total cohort food consumption of age‐0 pollock in two areas of high pollock density in the Gulf of Alaska during the summer of 1990. Total cohort consumption was compared with zooplankton biomass and production estimates for the same areas and times of the year. The model was also used to examine the bioenergetic implications of age‐0 pollock diel vertical migration through a thermal gradient. During a 1‐month bioenergetics simulation, individual daily consumption decreased from 16·0 to 6·0% of wet body weight. Daily ration estimates corresponded well with independent field estimates of daily ration for the same areas and time of the year. Comparison of total cohort consumption with prey availability (production and biomass) indicated minimal potential for food limitation. Bioenergetic optimization of growth can be a potential benefit of diel vertical migration to age‐0 pollock, however more information on prey density and distribution is needed to test this hypothesis thoroughly.

Development and application of a bioenergetics model for juvenile walleye pollock

A bioenergetics model was parameterized for age-0 walleye pollock, Theragra chalcogramma, based on a synthesis of literature data. The sensitivity of the new parameters was tested by individual parameter perturbation (IPP) analysis. The model was applied to estimate individual and total cohort food consumption of age-0 pollock in two areas of high pollock density in the Gulf of Alaska during the summer of 1990. Total cohort consumption was compared with zooplankton biomass and production estimates for the same areas and times of the year. The model was also used to examine the bioenergetic implications of age-0 pollock diel vertical migration through a thermal gradient. During a 1-month bioenergetics simulation, individual daily consumption decreased from 16·0 to 6·0% of wet body weight. Daily ration estimates corresponded well with independent field estimates of daily ration for the same areas and time of the year. Comparison of total cohort consumption with prey availability (production and biomass) indicated minimal potential for food limitation. Bioenergetic optimization of growth can be a potential benefit of diel vertical migration to age-0 pollock, however more information on prey density and distribution is needed to test this hypothesis thoroughly.

Food Dispersion and Foraging Energetics: A Mechanistic Synthesis for Field Studies of Avian Benthivores

Much effort has focused on modeling and measuring the energy costs of free existence and the foraging strategies of animals. However, few studies have quantitatively linked these approaches to the patch structure of foods in the field. We developed an individual—based model that relates field measurements of the dispersion of benthic foods to search costs and foraging profitability of diving ducks. On Lake Mattamuskeet, North Carolina, Canvasback ducks (Aythya valisineria) eat only the belowground winter buds of the submerged plant Vallisneria americana. We measured and modeled the patch structure of winter buds at the level of potential foraging "loci," defined as contiguous circles 1 m in diameter. In the field and in the model, Canvasbacks make repeated vertical dives in such loci, foraging in the sediments by touch, before surface—swimming to another locus. We quantified first—order patchiness by fitting a negative binomial distribution to core samples taken at 50—m intervals along transects, to yield the frequencies of loci with different bud densities. Second—order patchiness was measured by taking cores at 1—m increments radiating from each sampling point, and regressing bud density at each sampling point on densities at these increments. No significant correlations were found, indicating that Canvasbacks could not predict food densities based on densities in nearby foraging loci. For the model, we generated food grids from the negative binomial distributions of core samples. Energy costs of diving were calculated by applying aerobic efficiencies (mechanical power output $\div$ aerobic power input) to biomechanical models. Unlike respirometry alone, this method accounts for effects on dive costs of varying water depth and dive duration. We used measurements of Canvasback intake rates at different bud densities to calculate profitability (energy intake minus expenditure) for each dive. Multivariate uncertainty analyses (Latin hypercube) indicated that profitability for Canvasbacks foraging on Vallisneria buds is determined mainly by food—item size and locomotor costs of descent. Bud metabolizable energy, water temperature, bud dispersion, and search and handling time coefficients of the functional response for intake rate have relatively minor influence. Individual—parameter perturbations indicated that to maintain the same foraging benefits, the total area of Vallisneria habitat would have to increase by 1.4—fold if dry mass per bud decreased from 0.10 to 0.03 g, and by 2.1—fold if water depth increased from 0.5 to 2 m. Our method allows study of interactions between patch structure and foraging energetics without detailed spatial mapping of foods, which is not feasible at appropriate scales for highly mobile benthivores. The model yields estimates of energy balance, contaminant intake, and amount and quality of foraging habitat required to sustain diving duck populations under varying environmental conditions. More accurate prediction of giving—up times and giving—up food densities will require better understanding of the time scale over which ducks balance their energy budgets.