Random Measurement Uncertainty Research Articles

A detectable change in the air-sea CO2 flux estimate from sailboat measurements

The sailboat Seaexplorer collected underway sea surface partial pressure of CO2 (pCO2) data for 129 days (2018–2021), including an Antarctic circumnavigation. By comparing ensembles of data-driven air-sea CO2 fluxes computed with and without sailboat data and applying a detection algorithm, we show that these sailboat observations significantly increase the regional carbon uptake in the North Atlantic and decrease it in the Southern Ocean. While compensating changes in both basins limit the global effect, the Southern Ocean–particularly frontal regions (40°S–60°S) during summertime—exhibited the largest air-sea CO2 flux changes, averaging 20% of the regional mean. Assessing the sensitivity of the air-sea CO2 flux to measurement uncertainty, the results stay robust within the expected random measurement uncertainty (± 5 μatm) but remain undetectable with a measurement offset of 5 µatm. We thus conclude that sailboats fill essential measurement gaps in remote ocean regions.

Data quality control considerations in multivariate environmental monitoring: experience of the French coastal network SOMLIT

IntroductionWhile crucial to ensuring the production of accurate and high-quality data—and to avoid erroneous conclusions—data quality control (QC) in environmental monitoring datasets is still poorly documented.MethodsWith a focus on annual inter-laboratory comparison (ILC) exercises performed in the context of the French coastal monitoring SOMLIT network, we share here a pragmatic approach to QC, which allows the calculation of systematic and random errors, measurement uncertainty, and individual performance. After an overview of the different QC actions applied to fulfill requirements for quality and competence, we report equipment, accommodation, design of the ILC exercises, and statistical methodology specially adapted to small environmental networks (<20 laboratories) and multivariate datasets. Finally, the expanded uncertainty of measurement for 20 environmental variables routinely measured by SOMLIT from discrete sampling—including Essential Ocean Variables—is provided.Results, Discussion, ConclusionThe examination of the temporal variations (2001–2021) in the repeatability, reproducibility, and trueness of the SOMLIT network over time confirms the essential role of ILC exercises as a tool for the continuous improvement of data quality in environmental monitoring datasets.

The measurement of mean wind, variances, and covariances from an instrumented mobile car in a rural environment

Abstract. On 20 and 22 August 2019, a small tripod was outfitted with a sonic anemometer and placed in a highway shoulder to compare with measurements made on an instrumented car as it traveled past the tripod. The rural measurement site in this investigation was selected so that the instrumented car traveled past many upwind surface obstructions and experienced the occasional passing vehicle. To obtain an accurate mean wind speed and mean wind direction on a moving car, it is necessary to correct for flow distortion and remove the vehicle speed from the measured velocity component parallel to vehicle motion (for straight-line motion). In this study, the velocity variances and turbulent fluxes measured by the car are calculated using two approaches: (1) eddy covariance and (2) wavelet analysis. The results show that wavelet analysis can better resolve low frequency contributions, and this leads to a reduction in the horizontal velocity variances measured on the car, giving a better estimate for some measurement averages when compared to the tripod. A wavelet-based approach to remove the effects of sporadic passing traffic is developed and applied to a measurement period during which a heavy-duty truck passes in the opposite highway lane; removing the times with traffic in this measurement period gives a reduction of approximately 10 % in the turbulent kinetic energy. The vertical velocity variance and vertical turbulent heat flux measured on the car are biased low compared to the tripod. This low bias may be related to a mismatch in the flux footprint of the car versus the tripod or perhaps to rapid flow distortion at the measurement location on the car. When random measurement uncertainty is considered, the vertical momentum flux is found to be consistent with the tripod in the 95 % confidence interval and statistically different than 0 for most measurement periods.

Towards subpercentage uncertainty proton stopping-power mapping via dual-energy CT: Direct experimental validation and uncertainty analysis of a statistical iterative image reconstruction method.

To assess the potential of a joint dual-energy computerized tomography (CT) reconstruction process (statistical image reconstruction method built on a basis vector model (JSIR-BVM)) implemented on a 16-slice commercial CT scanner to measure high spatial resolution stopping-power ratio (SPR) maps with uncertainties of less than 1%. JSIR-BVM was used to reconstruct images of effective electron density and mean excitation energy from dual-energy CT (DECT) sinograms for 10 high-purity samples of known density and atomic composition inserted into head and body phantoms. The measured DECT data consisted of 90 and 140 kVp axial sinograms serially acquired on a Philips Brilliance Big Bore CT scanner without beam-hardening corrections. The corresponding SPRs were subsequently measured directly via ion chamber measurements on a MEVION S250 superconducting synchrocyclotron and evaluated theoretically from the known sample compositions and densities. Deviations of JSIR-BVM SPR values from their theoretically calculated and directly measured ground-truth values were evaluated for our JSIR-BVM method and our implementation of the Hünemohr-Saito (H-S) DECT image-domain decomposition technique for SPR imaging. A thorough uncertainty analysis was then performed for five different scenarios (comparison of JSIR-BVM stopping-power ratio/stopping power (SPR/SP) to International Commission on Radiation Measurements and Units benchmarks; comparison of JSIR-BVM SPR to measured benchmarks; and uncertainties in JSIR-BVM SPR/SP maps for patients of unknown composition) per the Joint Committee for Guides in Metrology and the Guide to Expression of Uncertainty in Measurement, including the impact of uncertainties in measured photon spectra, sample composition and density, photon cross section and I-value models, and random measurement uncertainty. Estimated SPR uncertainty for three main tissue groups in patients of unknown composition and the weighted proportion of each tissue type for three proton treatment sites were then used to derive a composite range uncertainty for our method. Mean JSIR-BVM SPR estimates deviated by less than 1% from their theoretical and directly measured ground-truth values for most inserts and phantom geometries except for high-density Delrin and Teflon samples with SPR error relative to proton measurements of 1.1% and -1.0% (head phantom) and 1.1% and -1.1% (body phantom). The overall root-mean-square (RMS) deviations over all samples were 0.39% and 0.52% (head phantom) and 0.43% and 0.57% (body phantom) relative to theoretical and directly measured ground-truth SPRs, respectively. The corresponding RMS (maximum) errors for the image-domain decomposition method were 2.68% and 2.73% (4.68% and 4.99%) for the head phantom and 0.71% and 0.87% (1.37% and 1.66%) for the body phantom. Compared to H-S SPR maps, JSIR-BVM yielded 30% sharper and twofold sharper images for soft tissues and bone-like surrogates, respectively, while reducing noise by factors of 6 and 3, respectively. The uncertainty (coverage factor k=1) of the DECT-to-benchmark values comparison ranged from 0.5% to 1.5% and is dominated by scanning-beam photon-spectra uncertainties. An analysis of the SPR uncertainty for patients of unknown composition showed a JSIR-BVM uncertainty of 0.65%, 1.21%, and 0.77% for soft-, lung-, and bony-tissue groups which led to a composite range uncertainty of 0.6-0.9%. Observed JSIR-BVM SPR estimation errors were all less than 50% of the estimated k=1 total uncertainty of our benchmarking experiment, demonstrating that JSIR-BVM high spatial resolution, low-noise SPR mapping is feasible and is robust to variations in the geometry of the scanned object. In contrast, the much larger H-S SPR estimation errors are dominated by imaging noise and residual beam-hardening artifacts. While the uncertainties characteristic of our current JSIR-BVM implementation can be as large as 1.5%, achieving<1% total uncertainty is feasible by improving the accuracy of scanner-specific scatter-profile and photon-spectrum estimates. With its robustness to beam-hardening artifact, image noise, and variations in phantom size and geometry, JSIR-BVM has the potential to achieve high spatial-resolution SPR mapping with subpercentage accuracy and estimated uncertainty in the clinical setting.

Adaptive Control and Estimation of the Condition of a Small Unmanned Aircraft Using a Kalman Filter

The article was motivated by the design of adaptive control algorithms for the control of a a fixed wing unmanned aerial vehicle (UAV). An adaptive system is a system that, with its structure or parameters, adapts to changes in the behavior of the object and based on the knowledge of variable properties, maintains the quality of its regulatory transition. The knowledge gained on this small UAV can be applied to larger aircraft. The creation of the proposed adaptive control into the UAV consisted of the creation of a simulation model of the aircraft based on known physical laws, the properties of the aircraft and a mathematical description. An adaptive PID controller for stabilization with changing coefficients based on the airspeed of the aircraft was designed and simulated. A validated control of the mathematical model of an unmanned aircraft was designed and simulated using the methods of estimation and identification of the UAV model parameter based on measured data from flight tests. Identifying dynamic parameters is a challenging task due to several factors, such as random vibration noise, interference, and sensor measurement uncertainty. The designed adaptive UAV control provides very promising results in improving the controllability of the aircraft while reducing the effect of speed changes on the stability and controllability of the system compared to the conventional PID controller. The comparison was performed on three selected types of PID controllers. The first type had fixed coefficients for the entire range of speeds calculated using the Control toolbox in MatLab. The second type also had constant coefficients over the entire range of speeds calculated using the Naslin method. The third adaptive type of PID controller had variable coefficients based on approximate polynomials dependent on the change in flight speed. The reason for the comparison was to show an increase in margin of stability using the method of variable coefficients of the PID controller based on the change of flight speeds. The obtained results show that the proposed adaptive control algorithm is robust enough to control the movement of the aircraft in the longitudinal plane and due to the introduced process and measurement errors, while the used Kalman filter effectively eliminates these errors.

Improved gap filling approach and uncertainty estimation for eddy covariance N2O fluxes

Agricultural nitrous oxide (N2O) emissions comprise a majority of the global source of this powerful greenhouse gas. Mitigation approaches for reducing emissions are difficult to evaluate at appropriate field scales because of the substantial effort and expense associated with relatively new technology allowing eddy covariance measurements of N2O fluxes (FN2O). Here we present a new approach for gap filling eddy covariance FN2O and estimating annual uncertainties for a temperate grazed grassland. We tested the potential of using one flux tower to evaluate emissions mitigation options in one paddock relative to an adjacent, unchanged paddock by partitioning data by source footprint contribution. Because of the complexity of spatiotemporal controls on FN2O, we generated a large set of environmental variables and features as input for machine learning algorithms. Inputs were transformed using partial least squares (PLS) decomposition, isolating features with the greatest influence on FN2O. PLS scores were fed to both a neural network (NN) and a locally-weighted k-nearest neighbours (kNN) regression. While the NN and kNN preformed similarly well, kNN regression accounted for the largest proportion of variance (52-72%) and resulted in the lowest bias for each of the three source footprint areas (full footprint and two separated adjacent paddocks, P53 and P54). Annual uncertainty estimates included random measurement uncertainty, accuracy and precision of the gap filling approach, and uncertainty associated with choice of threshold for atmospheric turbulence filtering and footprint contributions. Total N2O emissions for the full footprint, P53, and P54 were 7.4 ±0.35, 7.7 ±0.80, and 6.4 ±0.63 kg N2O-N ha−1, respectively in Year 1, and 6.9 ±0.33, 7.3 ±0.63, and 6.7 ±0.63 kg N2O-N ha−1, respectively in Year 2. These 95% confidence intervals on the annual FN2O suggest that we could detect differences of 10-15% between paddocks at this site when testing mitigation options.

A practical handling of measurement uncertainties in frequency based substructuring

A proper acquisition of FRFs is a prerequisite for a successful implementation of experimental substructuring techniques in the frequency domain. In this context, the study of uncertainty associated with measurements is of particular interest due to the precision standards required by industrial practice. This paper aims to provide a practical and reliable methodology for the quantification and propagation of the random measurement uncertainty in Frequency Based Substructuring applications. Extending previous studies, the framework presents a covariance-based approach for quantifying the complex-valued random uncertainty on measured FRFs and analytical methods for propagating it through interface modeling and substructures coupling approaches. The assumptions underlying the correct application of the method are investigated. An optimal number of impacts for an appropriate Gaussianity of the FRF distribution is computed based on empirical data. Experimental testing reveals encouraging results in the validation of the small error approximation. Considerable correlation effects between FRFs are found, although their impact on the coupled FRFs uncertainty seems to be limited. The methodology is applied to an experimental example.

Experimental design and measurement uncertainty in ligand binding studies by affinity capillary electrophoresis.

In all life sciences ligand binding assays (LBAs) play a crucial role. Unfortunately these are very error prone. One part of this uncertainty results from the unavoidable random measurement uncertainty, another part can be attributed to the experimental design. To investigate the latter, uncertainty propagation was evaluated as a function of the given experimental design. A design space including the normalized maximum response range (nMRR), the data point position (DPP), the data point range (DPR) and the number of data points (NoDP) was defined. Based on ten measured ms ACE source data sets 20 specific parameter sets were selected by Design of Experiments. Monte Carlo simulations using 100 000 repeats for every parameter set were employed. The resulting measurement uncertainty propagation factors (measurement uncertainty multiplier: MUM) were used to describe the whole design space by polynomial regression. The resulting 5-dimensional response surface was investigated to evaluate the design parameter's influence and to find the minimal uncertainty propagation. It could be shown, that the nMRR is of highest importance, followed by DPP and DPR. Interestingly, the NoDP is less relevant. However, the interactions of the four parameters need to be carefully considered during design optimization. Using at least five data points which cover over 40% of the upper part of the binding hyperbola (DPP > 0.57) the MUM will be minimized (MUM approximately 1.5) when the nMRR is appropriate. It is possible to reduce the measurement uncertainty propagation more than one order of magnitude.

Bunch-by-bunch longitudinal phase monitor at SSRF

Beam signals captured from a button-type pickup contain multidimensional information including the bunch charge, transverse position, bunch length, and longitudinal phase. A bunch phase monitor, which retrieves longitudinal phase information from a pickup signal at a bunch-by-bunch rate, has been developed at the Shanghai Synchrotron Radiation Facility. This paper introduces the basic principles, system setup, data processing method, and preliminary experimental results of this system. The systematic measurement error introduced by the limited system bandwidth, bunch length, and bunch charge variation was studied using simulation data. The random measurement uncertainty was evaluated using experimental beam data. The experimental result shows that the longitudinal phase resolution of this system is better than 1.0 ps. The first application, measuring the relationship between the longitudinal phase and bunch charge to determine the energy loss factor, was implemented, and the preliminary result is also discussed.

Statistical analysis of the gamma evaluation acceptance criteria: A simulation study of 2D dose distributions under error free conditions

PurposeTo investigate the statistical distribution of the gamma value under error-free conditions, in order to study the relation between the gamma evaluation failure rate and statistically significant deviations in the general situation. MethodsThe 2D absorbed dose distribution for 30 clinical head-and-neck IMRT fields were calculated in a QC phantom. For the same fields, dose measurements were simulated by assuming that the calculated value represented the expectation value, and by adding a random spatial uncertainty of 1–9 mm (1SD) and a random dose uncertainty of 1%–3% (1SD). The simulated measurements were then compared to the calculated dose using the gamma evaluation, and the distribution of the failure rate (i.e. the probability of gamma values above unity) was analysed. ResultsFor a wide range of the random measurement uncertainty, a distinct peak in the failure rate distribution was observed. The presence of higher failure rates was associated with large values of the second order derivative of the dose distribution. For spatial uncertainties larger than or equal to the resolution of the dose matrix, and for reasonable dose uncertainties, the median value of the failure rate distribution was fairly constant. ConclusionsSimulations showed, in the general case, that the probability of having a gamma value above unity under error-free conditions was not spatially uniform. We believe that this shortcoming may be partly responsible for the limited ability of the gamma evaluation method to detect errors in clinically relevant situations.

Variability in quartz OSL signals caused by measurement uncertainties: Problems and solutions

Abstract We simulated the variability in measured quartz optically stimulated luminescence (OSL) signals and dose response curves (DRCs) caused by measurement uncertainties, including counting statistics and instrumental irreproducibility. We find that these measurement errors can give rise to large variations in the observed luminescence signal and contribute to among-aliquot or among-grain scatter in DRCs and equivalent dose (De) values. Different measurement systems (i.e., luminescence readers) may have different counting statistics properties and, hence, may exhibit differing extents of variation in the observed OSL signal, even for the same sample. Our simulation shows that the random measurement uncertainties may result in some grains or aliquots being ‘saturated’ (that is, the measured natural signal is consistent with, or lies above, the saturation level of the measured DRC) and that the rejection of these ‘saturated’ grains may result in a truncated De distribution, with De underestimation for samples with natural doses close to saturation (e.g., twice the characteristic saturation dose, D0). We propose a new method to deal with this underestimation problem, in which standardised growth curves (SGCs) are established and the weighted-mean natural signal (Ln/Tn) from all measured grains is projected on to the corresponding SGCs to determine De. Our simulation results show that this method can produce reliable De estimates up to 5D0, which is far beyond the conventional limit of ∼2D0 using the standard SAR procedure.

Metrology of ground-based satellite validation: co-location mismatch and smoothing issues of total ozone comparisons

Abstract. Comparisons with ground-based correlative measurements constitute a key component in the validation of satellite data on atmospheric composition. The error budget of these comparisons contains not only the measurement errors but also several terms related to differences in sampling and smoothing of the inhomogeneous and variable atmospheric field. A versatile system for Observing System Simulation Experiments (OSSEs), named OSSSMOSE, is used here to quantify these terms. Based on the application of pragmatic observation operators onto high-resolution atmospheric fields, it allows a simulation of each individual measurement, and consequently, also of the differences to be expected from spatial and temporal field variations between both measurements making up a comparison pair. As a topical case study, the system is used to evaluate the error budget of total ozone column (TOC) comparisons between GOME-type direct fitting (GODFITv3) satellite retrievals from GOME/ERS2, SCIAMACHY/Envisat, and GOME-2/MetOp-A, and ground-based direct-sun and zenith–sky reference measurements such as those from Dobsons, Brewers, and zenith-scattered light (ZSL-)DOAS instruments, respectively. In particular, the focus is placed on the GODFITv3 reprocessed GOME-2A data record vs. the ground-based instruments contributing to the Network for the Detection of Atmospheric Composition Change (NDACC). The simulations are found to reproduce the actual measurements almost to within the measurement uncertainties, confirming that the OSSE approach and its technical implementation are appropriate. This work reveals that many features of the comparison spread and median difference can be understood as due to metrological differences, even when using strict co-location criteria. In particular, sampling difference errors exceed measurement uncertainties regularly at most mid- and high-latitude stations, with values up to 10 % and more in extreme cases. Smoothing difference errors only play a role in the comparisons with ZSL-DOAS instruments at high latitudes, especially in the presence of a polar vortex due to the strong TOC gradient it induces. At tropical latitudes, where TOC variability is lower, both types of errors remain below about 1 % and consequently do not contribute significantly to the comparison error budget. The detailed analysis of the comparison results, including the metrological errors, suggests that the published random measurement uncertainties for GODFITv3 reprocessed satellite data are potentially overestimated, and adjustments are proposed here. This successful application of the OSSSMOSE system to close for the first time the error budget of TOC comparisons, bodes well for potential future applications, which are briefly touched upon.

Adiabatic release measurements in aluminum between 400 and 1200 GPa: Characterization of aluminum as a shock standard in the multimegabar regime

Aluminum has been used prolifically as an impedance matching standard in the multimegabar regime (1 Mbar = 100 GPa), particularly in nuclear driven, early laser driven, and early magnetically driven flyer plate experiments. The accuracy of these impedance matching measurements depends upon the knowledge of both the Hugoniot and release or reshock response of aluminum. Here, we present the results of several adiabatic release measurements of aluminum from $\ensuremath{\sim}400\text{--}1200$ GPa states along the principal Hugoniot using full density polymethylpentene (commonly known as TPX), and both $\ensuremath{\sim}190$ and $\ensuremath{\sim}110$ mg/cc silica aerogel standards. These data were analyzed within the framework of a simple, analytical model that was motivated by a first-principles molecular dynamics investigation into the release response of aluminum, as well as by a survey of the release response determined from several tabular equations of state for aluminum. Combined, this theoretical and experimental study provides a method to perform impedance matching calculations without the need to appeal to any tabular equation of state for aluminum. As an analytical model, this method allows for propagation of all uncertainty, including the random measurement uncertainties and the systematic uncertainties of the Hugoniot and release response of aluminum. This work establishes aluminum for use as a high-precision standard for impedance matching in the multimegabar regime.

An uncertainty analysis of mean flow velocity measurements used to quantify emissions from stationary sources

Point velocity measurements conducted by traversing a Pitot tube across the cross section of a flow conduit continue to be the standard practice for evaluating the accuracy of continuous flow-monitoring devices. Such velocity traverses were conducted in the exhaust duct of a reduced-scale analog of a stationary source, and mean flow velocity was computed using several common integration techniques. Sources of random and systematic measurement uncertainty were identified and applied in the uncertainty analysis. When applicable, the minimum requirements of the standard test methods were used to estimate measurement uncertainty due to random sources. Estimates of the systematic measurement uncertainty due to discretized measurements of the asymmetric flow field were determined by simulating point velocity traverse measurements in a flow distribution generated using computational fluid dynamics. For the evaluated flow system, estimates of relative expanded uncertainty for the mean flow velocity ranged from ±1.4% to ±9.3% and depended on the number of measurement locations and the method of integration.Implications:Accurate flow measurements in smokestacks are critical for quantifying the levels of greenhouse gas emissions from fossil-fuel-burning power plants, the largest emitters of carbon dioxide. A systematic uncertainty analysis is necessary to evaluate the accuracy of these measurements. This study demonstrates such an analysis and its application to identify specific measurement components and procedures needing focused attention to improve the accuracy of mean flow velocity measurements in smokestacks.

Prospects for in vivo estimation of photon linear attenuation coefficients using postprocessing dual‐energy CT imaging on a commercial scanner: Comparison of analytic and polyenergetic statistical reconstruction algorithms

Accurate patient-specific photon cross-section information is needed to support more accurate model-based dose calculation for low energy photon-emitting modalities in medicine such as brachytherapy and kilovoltage x-ray imaging procedures. A postprocessing dual-energy CT (pDECT) technique for noninvasive in vivo estimation of photon linear attenuation coefficients has been experimentally implemented on a commercial CT scanner and its accuracy assessed in idealized phantom geometries. Eight test materials of known composition and density were used to compare pDECT-estimated linear attenuation coefficients to NIST reference values over an energy range from 10 keV to 1 MeV. As statistical image reconstruction (SIR) has been shown to reconstruct images with less random and systematic error than conventional filtered backprojection (FBP), the pDECT technique was implemented with both an in-house polyenergetic SIR algorithm, alternating minimization (AM), as well as a conventional FBP reconstruction algorithm. Improvement from increased spectral separation was also investigated by filtering the high-energy beam with an additional 0.5 mm of tin. The law of propagated uncertainty was employed to assess the sensitivity of the pDECT process to errors in reconstructed images. Mean pDECT-estimated linear attenuation coefficients for the eight test materials agreed within 1% of NIST reference values for energies from 1 MeV down to 30 keV, with mean errors rising to between 3% and 6% at 10 keV, indicating that the method is unbiased when measurement and calibration phantom geometries are matched. Reconstruction with FBP and AM algorithms conferred similar mean pDECT accuracy. However, single-voxel pDECT estimates reconstructed on a 1 × 1 × 3 mm(3) grid are shown to be highly sensitive to reconstructed image uncertainty; in some cases pDECT attenuation coefficient estimates exhibited standard deviations on the order of 20% around the mean. Reconstruction with the statistical AM algorithm led to standard deviations roughly 40% to 60% less than FBP reconstruction. Additional tin filtration of the high energy beam exhibits similar pDECT estimation accuracy as the unfiltered beam, even when scanning with only 25% of the dose. Using the law of propagated uncertainty, low Z materials are found to be more sensitive to image reconstruction errors than high Z materials. Furthermore, it is estimated that reconstructed CT image uncertainty must be limited to less than 0.25% to achieve a target linear-attenuation coefficient estimation uncertainty of 3% at 28 keV. That pDECT supports mean linear attenuation coefficient measurement accuracies of 1% of reference values for energies greater than 30 keV is encouraging. However, the sensitivity of the pDECT measurements to noise and systematic errors in reconstructed CT images warrants further investigation in more complex phantom geometries. The investigated statistical reconstruction algorithm, AM, reduced random measurement uncertainty relative to FBP owing to improved noise performance. These early results also support efforts to increase DE spectral separation, which can further reduce the pDECT sensitivity to measurement uncertainty.

Adiabatic release measurements inα-quartz between 300 and 1200 GPa: Characterization ofα-quartz as a shock standard in the multimegabar regime

$\ensuremath{\alpha}$-quartz has been used prolifically in recent years as an impedance matching standard in the multimegabar regime (1 Mbar $=$ 100 GPa). This is due to the fact that above $\ensuremath{\sim}$90--100 GPa along the principal Hugoniot $\ensuremath{\alpha}$-quartz becomes reflective, and thus shock velocities can be measured to high precision using velocity interferometry. This property allows for high-precision measurements, however, the accuracy of impedance matching measurements depends upon the knowledge of both the Hugoniot and the release or reshock response of $\ensuremath{\alpha}$-quartz. Here, we present the results of several adiabatic release measurements of $\ensuremath{\alpha}$-quartz from $\ensuremath{\sim}$300--1200 GPa states along the principal Hugoniot using full density polymethylpentene (commonly known as TPX), and both $\ensuremath{\sim}$190 and $\ensuremath{\sim}$110 mg/cc silica aerogel standards. These data were analyzed within the framework of a simple, analytical model that was motivated by a first-principles molecular dynamics investigation into the release response of $\ensuremath{\alpha}$-quartz. Combined, this theoretical and experimental study provides a method to perform impedance matching calculations without the need to appeal to any tabular equation of state for $\ensuremath{\alpha}$-quartz. As an analytical model, this method allows for propagation of all uncertainty, including the random measurement uncertainties and the systematic uncertainties of the Hugoniot and release response of $\ensuremath{\alpha}$-quartz. This work establishes $\ensuremath{\alpha}$-quartz for use as a high-precision standard for impedance matching in the multimegabar regime. We also note that the experimentally validated model framework should prove to be useful in the development of wide range equations of state for silica, a major constituent in the Earth's crust and mantle. Such models are crucial for accurate simulations of high-velocity giant impacts that are thought to be prevalent in the final stages of terrestrial planet formation.

Energy and surface moisture seasonally limit evaporation and sublimation from snow-free alpine tundra

This study highlights the importance of landscape position and resultant snow accumulation to the hydrologic balance of snow-free alpine tundra, and suggests that modeling studies must account for seasonally dissimilar partitioning of the energy balance in order to accurately predict evaporation and/or sublimation. The eddy covariance method was used to measure the surface energy balance above high-elevation (3502m above sea level) alpine tundra at Niwot Ridge, CO, over 3 years from 2007 to 2009. During the winter the site was characterized by wind scour, with little snow accumulation. Two co-located towers afforded the opportunity to constrain the influence of complex mountain topography on measurement uncertainty, and overall errors were comparable to other FLUXNET sites. Random measurement uncertainty for the turbulent fluxes was approximately 10% of midday summertime values. The 0.5-h mean energy balance closure was 81% over the entire measurement period, and improved to 91% during the summer when the magnitude of the turbulent fluxes was larger. In spite of 955mm mean annual precipitation, the 24-h mean evaporative fraction was 0.39, typical of dry grassland or rangeland ecosystems. These low values were attributed to rapid, efficient removal of snow by prevailing windy conditions throughout the winter. During the summer when rainfall provided moisture, evaporation was principally limited by available energy. Overall, an average of 39% of annual precipitation was evaporated or sublimated back to the atmosphere. We conclude that the annual distribution of precipitation is an essential control on evaporation and sublimation from this ecosystem.

Leaf area index uncertainty estimates for model–data fusion applications

Estimates of data uncertainties are required to integrate different observational data streams as model constraints using model–data fusion. We describe an approach with which random and systematic uncertainties in optical measurements of leaf area index [LAI] can be quantified. We use data from a measurement campaign at the spruce-dominated Howland Forest AmeriFlux site for illustrative purposes. We made measurements along two transects (one in a mature stand, one in a recently harvested shelterwood) before sunset on successive days using both the Li-Cor LAI-2000 plant canopy analyzer and digital hemispherical photography (DHP). The random measurement uncertainty (1 σ) at a given point for a single measurement is about 5% for LAI-2000 and 10% for DHP. These uncertainties are small compared to potential systematic biases due to instrument calibration errors and data processing decisions, which are estimated to be 10–20% for each instrument. Sampling uncertainty (due to the spatial variability along each transect where we conducted our measurements) is an additional, but again relatively small, uncertainty. Assumptions about clumping parameters, for which standard literature values are typically used, remain large sources of uncertainty. This analysis can also be used to develop strategies to reduce measurement uncertainties.

Estimating uncertainties in individual eddy covariance flux measurements: A comparison of methods and a proposed new method

We present a review of four methods that are currently and formerly used to estimate random flux measurement uncertainties in eddy covariance instrument systems, examining their theoretical basis. In our review, we illustrate a few of the strengths and weaknesses of each, paying particular attention to the explicit and implicit assumptions made. We then evaluate the practicality, ease of use, and relative performance for the methods reviewed. We also describe a new method of random flux uncertainty estimation that is designed to only be sensitive to random instrument noise, and compare its predictions with other methods on both real and synthetic data. We conclude that our new method is a good complement to the others examined. We also suggest that when our proposed technique is used with one or more of the other methods, new information is obtained about how contributions to the total uncertainty are distributed among their various causes.

Improving apparent diffusion coefficient estimates and elucidating tumor heterogeneity using Bayesian adaptive smoothing

The spatial distribution of apparent diffusion coefficient (ADC) estimates in tumors is typically heterogeneous, although this observed variability is composed of both true regional differences and random measurement uncertainty. In this study, an adaptive Bayesian adaptive smoothing (BAS) model for estimating ADC values is developed and applied to data acquired in two murine tumor models in vivo. BAS models have previously been shown to reduce parameter uncertainty through the use of a Markov random field. Here, diffusion data acquired with four averages was used as an empirical gold standard for evaluating the BAS model. ADC estimates using BAS displayed a significantly closer accordance with the gold standard data and, following analysis of uncertainty estimates, appeared to even outperform the gold standard. These observations were also reflected in simulations. These results have strong implications for clinical studies, as it suggests that the BAS postprocessing technique can be used to improve ADC estimates without the need to compromise on spatial resolution or signal-to-noise or for the adaptation of acquisition hardware. A novel measure of tumor ADC heterogeneity was also defined, which identified differences between tumors derived from different cell lines, which were reflected in histological variations within the tissue microenvironment.