Comparison of two measurement devices for obtaining horizontal force-velocity profile variables during sprint running

This study established the magnitude of systematic bias and random error of horizontal force-velocity (F-v) profile variables obtained from a 1080 Sprint compared to that obtained from a Stalker ATS II radar device. Twenty high-school athletes from an American football training group completed a 30 m sprint while the two devices simultaneously measured velocity-time data. The velocity-time data were modelled by an exponential equation fitting process and then used to calculate individual F-v profiles and related variables (theoretical maximum velocity, theoretical maximum horizontal force, slope of the linear F-v profile, peak power, time constant tau, and horizontal maximal velocity). The devices were compared by determining the systematic bias and the 95% limits of agreement (random error) for all variables, both of which were expressed as percentages of the mean radar value. All bias values were within 6.32%, with the 1080 Sprint reporting higher values for tau, horizontal maximal velocity, and theoretical maximum velocity. Random error was lowest for velocity-based variables but exceeded 7% for all others, with slope of the F-v profile being greatest at ±12.3%. These results provide practitioners with the information necessary to determine if the agreement between the devices and the magnitude of random error is acceptable within the context of their specific application.

Error Analysis and Modeling of GPM Dual-Frequency Precipitation Radar Near-surface Rainfall Product

The error characterization of rainfall products of spaceborne radar is essential for better applications of radar data, such as multi-source precipitation data fusion and hydrological modeling. In this study, we analyzed the error of the near-surface rainfall product of the dual-frequency precipitation radar (DPR) on the Global Precipitation Measurement Mission (GPM) and modeled it based on ground C-band dual-polarization radar (CDP) data with optimization rainfall retrieval. The comparison results show that the near-surface rainfall data were overestimated by light rain and slightly underestimated by heavy rain. The error of near-surface rainfall of the DPR was modeled as an additive model according to the comparison results. The systematic error of near-surface rainfall was in the form of a quadratic polynomial, while the systematic error of stratiform precipitation was smaller than that of convective precipitation. The random error was modeled as a Gaussian distribution centered at −1−0 mm h−1. The standard deviation of the Gaussian distribution of convective precipitation was 1.71 mm h−1 and the standard deviation of stratiform precipitation was 1.18 mm h−1, which is smaller than that of convective precipitation. In view of the precipitation retrieval algorithm of DPR, the error causes were analyzed from the reflectivity factor (Z) and the drop size distribution (DSD) parameters (Dm, Nw). The high accuracy of the reflectivity factor measurement results in a small systematic error. Importantly, the negative bias of Nw was very obvious when the rain type was convective precipitation, resulting in a large random error.

Ridge Estimation's Effectiveness for Multiple Linear Regression with Multicollinearity: An Investigation Using Monte-Carlo Simulations

The goal of this research is to compare multiple linear regression coefficient estimations with multicollinearity. In order to quantify the effectiveness of estimations by the mean of average mean square error, the ordinary least squares technique (OLS), modified ridge regression method (MRR), and generalized Liu-Kejian method (LKM) are compared (AMSE). For this study, the simulation scenarios are 3 and 5 independent variables with zero mean normally distributed random error of variance 1, 5, and 10, three correlation coefficient levels; i.e., low (0.2), medium (0.5), and high (0.8) are determined for independent variables, and all combinations are performed with sample sizes 15, 55, and 95 by Monte Carlo simulation technique for 1,000 times in total. As the sample size rose, the AMSE decreased. The MRR and LKM both outperformed the LSM. At random error of variance 10, the MRR is the most suitable for all circumstances.

The effect of noise on the predictive limit of QSAR models

A key challenge in the field of Quantitative Structure Activity Relationships (QSAR) is how to effectively treat experimental error in the training and evaluation of computational models. It is often assumed in the field of QSAR that models cannot produce predictions which are more accurate than their training data. Additionally, it is implicitly assumed, by necessity, that data points in test sets or validation sets do not contain error, and that each data point is a population mean. This work proposes the hypothesis that QSAR models can make predictions which are more accurate than their training data and that the error-free test set assumption leads to a significant misevaluation of model performance. This work used 8 datasets with six different common QSAR endpoints, because different endpoints should have different amounts of experimental error associated with varying complexity of the measurements. Up to 15 levels of simulated Gaussian distributed random error was added to the datasets, and models were built on the error laden datasets using five different algorithms. The models were trained on the error laden data, evaluated on error-laden test sets, and evaluated on error-free test sets. The results show that for each level of added error, the RMSE for evaluation on the error free test sets was always better. The results support the hypothesis that, at least under the conditions of Gaussian distributed random error, QSAR models can make predictions which are more accurate than their training data, and that the evaluation of models on error laden test and validation sets may give a flawed measure of model performance. These results have implications for how QSAR models are evaluated, especially for disciplines where experimental error is very large, such as in computational toxicology. Graphical Abstract

Validation of Aeolus Level 2B wind products using wind profilers, ground-based Doppler wind lidars, and radiosondes in Japan

The first space-based Doppler wind lidar (DWL) on board the Aeolus satellite was launched by the European Space Agency (ESA) on 22 August 2018 to obtain global profiles of horizontal line-of-sight (HLOS) wind speed. In this study, the Raleigh-clear and Mie-cloudy winds for periods of baseline 2B02 (from 1 October to 18 December 2018) and 2B10 (from 28 June to 31 December 2019 and from 20 April to 8 October 2020) were validated using 33 wind profilers (WPRs) installed all over Japan, two ground-based coherent Doppler wind lidars (CDWLs), and 18 GPS radiosondes (GPS-RSs). In particular, vertical and seasonal analyses were performed and discussed using WPR data. During the baseline 2B02 period, a positive bias was found to be in the ranges of 0.5 to 1.7 m s−1 for Rayleigh-clear winds and 1.6 to 2.4 m s−1 for Mie-cloudy winds using the three independent reference instruments. The statistical comparisons for the baseline 2B10 period showed smaller biases, −0.8 to 0.5 m s−1 for the Rayleigh-clear and −0.7 to 0.2 m s−1 for the Mie-cloudy winds. The vertical analysis using WPR data showed that the systematic error was slightly positive in all altitude ranges up to 11 km during the baseline 2B02 period. During the baseline 2B10 period, the systematic errors of Rayleigh-clear and Mie-cloudy winds were improved in all altitude ranges up to 11 km as compared with the baseline 2B02. Immediately after the launch of Aeolus, both Rayleigh-clear and Mie-cloudy biases were small. Within the baseline 2B02, the Rayleigh-clear and Mie-cloudy biases showed a positive trend. For the baseline 2B10, the Rayleigh-clear wind bias was generally negative for all months except August 2020, and Mie-cloudy wind bias gradually fluctuated. Both Rayleigh-clear and Mie-cloudy biases did not show a marked seasonal trend and approached zero towards September 2020. The dependence of the Rayleigh-clear wind bias on the scattering ratio was investigated, showing that there was no significant bias dependence on the scattering ratio during the baseline 2B02 and 2B10 periods. Without the estimated representativeness error associated with the comparisons using WPR observations, the Aeolus random error was determined to be 6.7 (5.1) and 6.4 (4.8) m s−1 for Rayleigh-clear (Mie-cloudy) winds during the baseline 2B02 and 2B10 periods, respectively. The main reason for the large Aeolus random errors is the lower laser energy compared to the anticipated 80 mJ. Additionally, the large representativeness error of the WPRs is probably related to the larger Aeolus random error. Using the CDWLs, the Aeolus random error estimates were in the range of 4.5 to 5.3 (2.9 to 3.2) and 4.8 to 5.2 (3.3 to 3.4) m s−1 for Rayleigh-clear (Mie-cloudy) winds during the baseline 2B02 and 2B10 periods, respectively. By taking the GPS-RS representativeness error into account, the Aeolus random error was determined to be 4.0 (3.2) and 3.0 (2.9) m s−1 for Rayleigh-clear (Mie-cloudy) winds during the baseline 2B02 and 2B10 periods, respectively.

Growth of random errors in temperature forecasts by numerical method using centred time-differences

The growth of initial random errors in temperature forecasts by numerical method using centred time-differenced is investigated. Horizontal advection in one dimension is considered. Assuming that there is no correlation between the initial random errors as the different grid points and neglecting any correlation that may develop in the col1rse of computation, the random errors grow much more rapidly in this method than in forward time differencing. In both methods, correlations develop between the random errors at different grid points in the course of computation. When these are taken in to account, the growth of random errors is further enhanced in the forward differences. In the centred time-differences method, these correlations keep the random error almost at the initial level.

Equalities between the BLUEs and BLUPs under the partitioned linear fixed model and the corresponding mixed model

In this article we consider the partitioned fixed linear model F : y = X1β1 + X2β2 + ε" and the corresponding mixed model M : y =X1β1+X2u+ ε, where ε is a random error vector and u is a random effect vector. In 2006, Isotalo, M¨ols, and Puntanen found conditions under which an arbitrary representation of the best linear unbiased estimator (BLUE) of an estimable parametric function of β1 in the fixed model F remains BLUE in the mixed model M . In this paper we extend the results concerning further equalities arising from models F and M.

The Application of Mixed Smoothing Spline and Fourier Series Model in Nonparametric Regression

In daily life, mixed data patterns are often found, namely, those that change at a certain sub-interval or that follow a repeating pattern in a certain trend. To handle this kind of data, a mixed estimator of a Smoothing Spline and a Fourier Series has been developed. This paper describes a simulation study of the estimator in nonparametric regression and its implementation in the case of poor households. The minimum Generalized Cross Validation (GCV) was used in order to select the best model. The simulation study used generation data with a Uniform distribution and a random error with a symmetrical Normal distribution. The result of the simulation study shows that the larger the sample size n, the better the mixed estimator as a model of nonparametric regression for all variances. The smaller the variance, the better the model for all combinations of samples n. Very poor households are characterized predominantly in their consumption of carbohydrates compared to that of fat and protein. The results of this study suggest that the distribution of assistance to poor households is not the same, because in certain groups there are poor households that consume higher carbohydrates, and some households may consume higher fats.