Comment on os-2021-113

<strong class="journal-contentHeaderColor">Abstract.</strong> In sequential estimation methods often used in oceanic and general climate calculations of the state and of forecasts, observations act mathematically and statistically as forcings. For purposes of calculating changes in important functions of state variables such as total mass and energy, or volumetric current transports, results are sensitive to mis-representation of a large variety of parameters, including initial conditions, prior uncertainty covariances, and systematic and random errors in observations. Here toy models of a mass-spring oscillator and of a barotropic Rossby-wave equation are used to demonstrate many of the issues. Results from Kalman-filter estimates, and those from finite interval smoothing are analyzed. In the filter (and prediction) problem, entry of data leads to violation of conservation and other invariant rules. A finite interval smoothing method restores the conservation rules, but uncertainties in all such estimation results remain. Convincing trend and other time-dependent determinations in "reanalysis" -like estimates require a full understanding of both models and observations.

Abstract. In sequential estimation methods often used in oceanic and general climate calculations of the state and of forecasts, observations act mathematically and statistically as source or sink terms in conservation equations for heat, salt, mass, and momentum. These artificial terms obscure the inference of the system's variability or secular changes. Furthermore, for the purposes of calculating changes in important functions of state variables such as total mass and energy or volumetric current transports, results of both filter and smoother-based estimates are sensitive to misrepresentation of a large variety of parameters, including initial conditions, prior uncertainty covariances, and systematic and random errors in observations. Here, toy models of a coupled mass–spring oscillator system and of a barotropic Rossby wave system are used to demonstrate many of the issues that arise from such misrepresentations. Results from Kalman filter estimates and those from finite interval smoothing are analyzed. In the filter (and prediction) problem, entry of data leads to violation of conservation and other invariant rules. A finite interval smoothing method restores the conservation rules, but uncertainties in all such estimation results remain. Convincing trend and other time-dependent determinations in “reanalysis-like” estimates require a full understanding of models, observations, and underlying error structures. Application of smoother-type methods that are designed for optimal reconstruction purposes alleviate some of the issues.

Precise Point Positioning (PPP) is an increasingly recognized precisely the GPS/GNSS positioning technique. In order to improve the accuracy of PPP, the error sources in PPP measurements should be reduced as much as possible and the ambiguities should be correctly resolved. The correct ambiguity resolution requires a careful control of residual errors that are normally categorized into random and systematic errors. To understand effects from two categorized errors on the PPP ambiguity resolution, those two GPS datasets are simulated by generating in locations in South Korea (denoted as SUWN) and Hong Kong (PolyU). Both simulation cases are studied for each dataset; the first case is that all the satellites are affected by systematic and random errors, and the second case is that only a few satellites are affected. In the first case with random errors only, when the magnitude of random errors is increased, L1 ambiguities have a much higher chance to be incorrectly fixed. However, the size of ambiguity error is not exactly proportional to the magnitude of random error. Satellite geometry has more impacts on the L1 ambiguity resolution than the magnitude of random errors. In the first case when all the satellites have both random and systematic errors, the accuracy of fixed ambiguities is considerably affected by the systematic error. A pseudorange systematic error of 5 cm is the much more detrimental to ambiguity resolutions than carrier phase systematic error of 2 mm. In the 2 nd case when only a portion of satellites have systematic and random errors, the L1 ambiguity resolution in PPP can be still corrected. The number of allowable satellites varies from stations to stations, depending on the geometry of satellites. Through extensive simulation tests under different schemes, this paper sheds light on how the PPP ambiguity resolution (more precisely L1 ambiguity resolution) is affected by the characteristics of the residual errors in PPP observations. The numerical examples recall the PPP data analysts that how accurate the error correction models must achieve in order to get all the ambiguities resolved correctly.

A perfect model Monte Carlo experiment was conducted to explore the characteristics of analysis error in a quasigeostrophic model. An ensemble of cycled analyses was created, with each member of the ensemble receiving different observations and starting from different forecast states. Observations were created by adding random error (consistent with observational error statistics) to vertical profiles extracted from truth run data. Assimilation of new observations was performed every 12 h using a three-dimensional variational analysis scheme. Three observation densities were examined, a low-density network (one observation ; every 202 grid points), a moderate-density network (one observation ; every 102 grid points), and a high-density network (; every 52 grid points). Error characteristics were diagnosed primarily from a subset of 16 analysis times taken every 10 days from a long time series, with the first sample taken after a 50-day spinup. The goal of this paper is to understand the spatial, temporal, and some dynamical characteristics of analysis errors. Results suggest a nonlinear relationship between observational data density and analysis error; there was a much greater reduction in error from the low- to moderate-density networks than from moderate to high density. Errors in the analysis reflected both structured errors created by the chaotic dynamics as well as random observational errors. The correction of the background toward the observations reduced the error but also randomized the prior dynamical structure of the errors, though there was a dependence of error structure on observational data density. Generally, the more observations, the more homogeneous the errors were in time and space and the less the analysis errors projected onto the leading backward Lyapunov vectors. Analyses provided more information at higher wavenumbers as data density increased. Errors were largest in the upper troposphere and smallest in the mid- to lower troposphere. Relatively small ensembles were effective in capturing a large percentage of the analysis-error variance, though more members were needed to capture a specified fraction of the variance as observation density increased.

The estimation of thermal diffusivity using a flash experiment is studied. The sequential estimation method is presented and compared to the original flash method as well as two other methods that account for heat loss. The potential accuracy of the four methods is tested with a numerical simulation. The thermal diffusivity of a stainless steel sample is estimated from experimental data. The estimates given by the different methods are compared and analyzed. The sequential estimation method is shown to be less sensitive to random measurement errors and to provide more information regarding the accuracy of the estimated parameters.

The readings comprising the measurement of fiber diameter on two tops by the projection micro scope were perturbed by moving one-quarter of the readings in each histogram element to the element next below and one-quarter to the element next above, thus simulating random error of observation. It is shown that the resulting increase in between-fiber variance may be neglected. It is further shown that, in the CSIRO Fiber Fineness Distribution Analyser, which is in effect an automatic projection- microscope method, the variance observed between mean diameters is greater than can be accounted for by the observed between-fiber variance, which in turn is greater than can be accounted for by random error of observation, thus implying a source of systematic error in the measurement of between- fiber variance.

The noise scale factor (NSF) is useful in calculating the random errors of lidar signals. A new method is proposed for estimating the NSF of lidar systems. Instead of measuring the solar background in the traditional method that demands special experiments or additional devices, the new method utilizes the molecular backscattered signal fragments of routinely observed lidar profiles to extract the light intensities and shot noises. Based on a 355 nm lidar system, experiments with the two methods have been carried out. The NSF calculated with the new method is 0.6473, very close to the value resulted from the traditional method, which is 0.6496. The experiments indicate that the new method is feasible and accurate. An example of calculating the random errors and signal to noise ratios (SNR) of lidar signals by using NSF is presented. Compared with the results calculated from multiple lidar profiles, the method using NSF eliminates the influence of aerosols and clouds.

This brief presents a sequential fusion estimation method for maneuvering target tracking in asynchronous wireless sensor networks. The modeling error caused by asynchronous sampling and communication uncertainties is considered and compensated for by introducing a time-varying fading factor into the unscented Kalman filter (UKF). A square root form of the unscented strong tracking filter (SR-USTF) based on QR decomposition is proposed to improve the stability and performance of the USTF. Moreover, a hybrid sequential fusion estimation method is presented to estimate the state of the target, and the proposed sequential fusion estimation method combines the superiorities of both the SR-USTF and the conventional UKF, and is able to deal with communication uncertainties such as time delay and packet loss in a unified framework. Both simulations and experiments of an E-puck robot tracking example are provided to demonstrate the effectiveness and superiorities of the proposed sequential fusion estimation method.

A common question in movement studies is how the results should be interpreted with respect to systematic and random errors. In this study, simulations are made in order to see how a rigid body's orientation in space (i.e. helical angle between two orientations) is affected by (1) a systematic error added to a single marker (2) a combination of this systematic error and Gaussian white noise. The orientation was estimated after adding a systematic error to one marker within the rigid body. This procedure was repeated with Gaussian noise added to each marker. In conclusion, results show that the systematic error's effect on estimated orientation depends on number of markers in the rigid body and also on which direction the systematic error is added. The systematic error has no effect if the error is added along the radial axis (i.e. the line connecting centre of mass and the affected marker).

Measured surface-atmosphere fluxes of energy (sensible heat, H, and latent heat, LE) and CO 2 ( FCO 2) represent the “true” flux plus or minus potential random and systematic measurement errors. Here, we use data from seven sites in the AmeriFlux network, including five forested sites (two of which include “tall tower” instrumentation), one grassland site, and one agricultural site, to conduct a cross-site analysis of random flux error. Quantification of this uncertainty is a prerequisite to model-data synthesis (data assimilation) and for defining confidence intervals on annual sums of net ecosystem exchange or making statistically valid comparisons between measurements and model predictions. We differenced paired observations (separated by exactly 24 h, under similar environmental conditions) to infer the characteristics of the random error in measured fluxes. Random flux error more closely follows a double-exponential (Laplace), rather than a normal (Gaussian), distribution, and increase as a linear function of the magnitude of the flux for all three scalar fluxes. Across sites, variation in the random error follows consistent and robust patterns in relation to environmental variables. For example, seasonal differences in the random error for H are small, in contrast to both LE and FCO 2, for which the random errors are roughly three-fold larger at the peak of the growing season compared to the dormant season. Random errors also generally scale with R n ( H and LE) and PPFD ( FCO 2). For FCO 2 (but not H or LE), the random error decreases with increasing wind speed. Data from two sites suggest that FCO 2 random error may be slightly smaller when a closed-path, rather than open-path, gas analyzer is used.

Purpose: To investigate dosimetric effect of the random and systematic errors of MLC leaf positions on the IMRT plans for patients with head and neck cancer. Method and Materials: For six clinical IMRT plans, random errors (from −2 to 2 mm) and systematic errors (±0.5 mm and ±1 mm) MLC positioning errors were introduced into the each segment for these plans, simulating the mechanical uncertainties and potential miscalibration of the MLC. The altered MLC segments for each plan were imported to a commercial treatment planning system to evaluate dosimetric changes of the plan. The altered plans were compared to the original plans, based on DVHs and defined endpoint doses. Results: With the up‐to‐2 mm random errors in MLC positions, the dose changes to the 95% of the tumor volumes were (−1.247± 1.153)%. For serial structures, the dose changes to the 0.1 cc of the brainstem and spinal cord were (0.230±0.794)% and (−0.340±1.254)%, respectively. The dose changes to the 50% of the parotids varied from patient to patient, from 0.536% to 11.333%, (1.641±4.274)% and (4.910±5.322)% overall. With systematic errors in MLC positions up to 1 mm, the dose changes to the 95% of the tumor volumes were (−0.078±1.048)%. The dose changes to the 0.1 cc of the brainstem and spinal cord for all patients except one were (0.591±1.058)%. The dose changes to the 50% of the parotids overall were (7.782±3.111)%, beyond 5% limit. Conclusion: The dosimetric changes introduced by the random errors for each leaf within 2mm were not significant compared to the original plans. The systematic error up to 1mm for each leaf did not significantly changed the target dose and the maximum doses to the serial structures while the doses changes to the parotid could be significant. Conflict of Interest: This project is partly funded by SIEMENS.

Evaluation of errors in the determination of gas chromatographic retention parameters and derivative quantities

Over the past decade, the relation between the Balmer-line luminosity of HII galaxies and the velocity width of the emission lines, the relation, has been painstakingly calibrated as a cosmological distance indicator with seemingly spectacular results: the Hubble constant and the energy density of dark energy obtained using the indicator agree remarkably well with the values from canonical indicators. Since most of the luminosity of these young compact starburst galaxies is emitted by a few narrow emission lines, they can be observed with good precision up to redshifts of $z with JWST, making the indicator a potentially unique cosmological probe. However, the precision of the method remains too low to effectively constrain the relevant cosmological parameters, notably the equation of state of dark energy. The scatter of the relation is significantly larger than the random observational errors, so we do not have a good handle on the systematics of the method. In a previous paper, we posited that since the ionizing radiation of these young galaxies fades rapidly over timescales of only a few million years, age differences could be the main underlying cause of the scatter. In this paper, we explore several different ways of explaining the scatter of the correlation, but without success. We show that the majority of HII galaxies are powered by multiple starbursts of slightly different ages, and therefore that the equivalent widths are not reliable chronometers to correct the luminosities for evolution. Thus, it is not likely that the accuracy of the distance indicator can be improved in the near future. Since we do not fully understand either the systematics or the underlying physics of the relation, using large samples of distant HII galaxies may or may not improve the accuracy of the method.

Users of climate records frequently require data at geographical locations where no direct measurements of climatological variables are collected. Climatological conditions at the areas or points of interest have to be estimated by interpolating observations from neighbouring stations. An objective of assessing spatial representativeness of a network of observing stations is to outline the areas for which the network is capable of providing sufficiently accurate climatological information, i.e., where interpolation errors do not exceed a value acceptable to the user. Two statistical methods: Gandin's point‐to‐point optimal interpolation and Kagan's pointto‐area interpolation were applied to monthly, seasonal and annual total precipitation records gathered by a long‐term, high quality, nationwide network of Canadian climate stations. Due to substantial differences in seasonal climate conditions in the Arctic versus the rest of the country, the national network had to be split into two subsets: north and south of 60°N latitude. Both interpolation techniques use a spatial correlation function to compute interpolation errors. The correlation function of departures or ratios from the “first guess” field of long‐term averages can be considered homogeneous and isotropic over a wide range of distances. Exponential functions are especially suitable to model correlation of precipitation. Alone, they can supply an abundance of information about the nature of precipitation, random observational errors and microclimatic uncertainties. The widely scattered northern stations showed poor spatial correlation and consequently unacceptably large interpolation errors in all cases except summer. The conclusion was that at present the climate network does not provide adequate climatological information north of 60° latitude. The southern stations exhibited fairly good spatial correlation, which allowed computation of the longest acceptable interstation distances that satisfy various interpolation error criteria. The results were tabulated to serve as a reference. In Gandin's case, the areas where the interpolation error does not exceed 65% of a local standard deviation were delineated for all months and seasons using so‐called circles of representativeness. This example revealed vast regions without adequate precipitation gauge coverage, especially in summer and winter. Kagan's method, which is concerned with area averages, produced less demanding results. Intuitively, a less dense network is required for area‐average estimates than for point value estimates. At the same time though, acceptable areal relative errors should be set at lower values. Assuming an arbitrary 10% relative error in the areal estimate, the southern half of the country is adequately represented by the network except for some relatively small sections around Hudson Bay.

Thermodilution cardiac output using a pulmonary artery catheter is the reference method against which all new methods of cardiac output measurement are judged. However, thermodilution lacks precision and has a quoted precision error of ± 20%. There is uncertainty about its true precision and this causes difficulty when validating new cardiac output technology. Our aim in this investigation was to determine the current precision error of thermodilution measurements. A test rig through which water circulated at different constant rates with ports to insert catheters into a flow chamber was assembled. Flow rate was measured by an externally placed transonic flowprobe and meter. The meter was calibrated by timed filling of a cylinder. Arrow and Edwards 7Fr thermodilution catheters, connected to a Siemens SC9000 cardiac output monitor, were tested. Thermodilution readings were made by injecting 5 mL of ice-cold water. Precision error was divided into random and systematic components, which were determined separately. Between-readings (random) variability was determined for each catheter by taking sets of 10 readings at different flow rates. Coefficient of variation (CV) was calculated for each set and averaged. Between-catheter systems (systematic) variability was derived by plotting calibration lines for sets of catheters. Slopes were used to estimate the systematic component. Performances of 3 cardiac output monitors were compared: Siemens SC9000, Siemens Sirecust 1261, and Philips MP50. Five Arrow and 5 Edwards catheters were tested using the Siemens SC9000 monitor. Flow rates between 0.7 and 7.0 L/min were studied. The CV (random error) for Arrow was 5.4% and for Edwards was 4.8%. The random precision error was ± 10.0% (95% confidence limits). CV (systematic error) was 5.8% and 6.0%, respectively. The systematic precision error was ± 11.6%. The total precision error of a single thermodilution reading was ± 15.3% and ± 13.0% for triplicate readings. Precision error increased by 45% when using the Sirecust monitor and 100% when using the Philips monitor. In vitro testing of pulmonary artery catheters enabled us to measure both the random and systematic error components of thermodilution cardiac output measurement, and thus calculate the precision error. Using the Siemens monitor, we established a precision error of ± 15.3% for single and ± 13.0% for triplicate reading, which was similar to the previous estimate of ± 20%. However, this precision error was significantly worsened by using the Sirecust and Philips monitors. Clinicians should recognize that the precision error of thermodilution cardiac output is dependent on the selection of catheter and monitor model.