Measurements of diapycnal diffusivities in stratified fluids

2001 ◽  
Vol 442 ◽  
pp. 267-291 ◽  
Author(s):  
MICHAEL E. BARRY ◽  
GREGORY N. IVEY ◽  
KRAIG B. WINTERS ◽  
JÖRG IMBERGER
Keyword(s):  
Root Mean Square ◽  
Buoyancy Frequency ◽  
Data Sets ◽  
Laboratory System ◽  
Mean Square ◽  
Wide Range ◽  
Vertical Grid ◽  
Order Of Magnitude ◽  
Set Up ◽  
Rate Of Dissipation

Linearly stratified salt solutions of different Prandtl number were subjected to turbulent stirring by a horizontally oscillating vertical grid in a closed laboratory system. The experimental set-up allowed the independent direct measurement of a root mean square turbulent lengthscale Lt, turbulent diffusivity for mass Kρ, rate of dissipation of turbulent kinetic energy ε, buoyancy frequency N and viscosity v, as time and volume averaged quantities. The behaviour of both Lt and Kρ was characterized over a wide range of the turbulence intensity measure, ε/vN2, and two regimes were identified.In the more energetic of these regimes (Regime E, where 300 < ε/vN2 < 105), Lt was found to be a function of v, κ and N, whilst Kρ was a function of v, κ and (ε/vN2)1/3. From these expressions for Lt and Kρ, a scaling relation for the root mean square turbulent velocity scale Ut was derived, and this relationship showed good agreement with direct measurements from other data sets.In the weaker turbulence regime (Regime W, where 10 < ε/vN2 < 300) Kρ was a function of v, κ and ε/vN2.For 10 < ε/vN2 < 1000, our directly measured diffusivities, Kρ, are approximately a factor of 2 different to the diffusivity predicted by the model of Osborn (1980). For ε/vN2 > 1000, our measured diffusivities diverge from the model prediction. For example, at ε/vN2 ≈ 104 there is at least an order of magnitude difference between the measured and predicted diffusivities.

Coherence Length in a Two-Dimensional Anisotropic Model of Superconductivity

1998 ◽  
Vol 12 (32) ◽  
pp. 3475-3483 ◽  
Author(s):  
L. Bujkiewicz ◽  
L. Jacak
Keyword(s):  
Coherence Length ◽  
Order Parameter ◽  
Cooper Pair ◽  
Mean Square ◽  
Two Dimensional ◽  
Anisotropic Model ◽  
Wide Range ◽  
Order Of Magnitude ◽  
Range Of Values

The coherence length as a mean-square radius of a Cooper pair is calculated for various forms of the anisotropic order parameter. A wide range of values of this quantity is obtained and the smallest values are of the order of magnitude of a few lattice spacings.

scholarly journals HEPPA III intercomparison experiment on electron precipitation impacts:  Estimated ionization rates during a geomagnetic active period in April 2010

2021 ◽  
Author(s):  
Hilde Nesse Tyssøy ◽  
Miriam Sinnhuber ◽  
Timo Asikainen ◽  
Stefan Bender ◽  
Mark A. Clilverd ◽  
...  
Keyword(s):  
Climate Models ◽  
Climate Model ◽  
Ionization Rate ◽  
Data Sets ◽  
Active Period ◽  
Medium Energy ◽  
Model Driven ◽  
Wide Range ◽  
Order Of Magnitude ◽  
Ionization Rates

&lt;p&gt;Precipitating auroral and radiation belt electrons are considered an important part of the natural forcing of the climate system.&amp;#160; Recent studies suggest that this forcing is underestimated in current chemistry-climate models. The HEPPA III intercomparison experiment is a collective effort to address this point. Here, eight different estimates of medium energy electron (MEE) (&gt;30 keV) ionization rates are assessed during a geomagnetic active period in April 2010.&amp;#160; The objective is to understand the potential uncertainty related to the MEE energy input. The ionization rates are all based on the Medium Energy Proton and Electron Detector (MEPED) on board the NOAA/POES and EUMETSAT/MetOp spacecraft series. However, different data handling, ionization rate calculations, and background atmospheres result in a wide range of mesospheric electron ionization rates. Although the eight data sets agree well in terms of the temporal variability, they differ by about an order of magnitude in ionization rate strength both during geomagnetic quiet and disturbed periods. The largest spread is found in the aftermath of the geomagnetic activity.&amp;#160; Furthermore, governed by different energy limits, the atmospheric penetration depth varies, and some differences related to latitudinal coverage are also evident. The mesospheric NO densities simulated with the Whole Atmospheric Community Climate Model driven by highest and lowest ionization rates differ by more than a factor of eight. In a follow-up study, the atmospheric responses are simulated in four chemistry-climate models and compared to satellite observations, considering both the model structure and the ionization forcing.&lt;/p&gt;

scholarly journals CHEMOMETRIC ASSISTED QUANTITATIVE DETERMINATION OF VITEXIN IN ETHANOLIC EXTRACT OF BINAHONG (ANREDERA CORDIFOLIA (TEN.) STEENIS) LEAVES

2020 ◽  
pp. 69-75
Author(s):  
OCTAVIANUS BUDI SANTOSA ◽  
MICHAEL RAHARJA GANI ◽  
SRI HARTATI YULIANI
Keyword(s):  
Root Mean Square Error ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Cross Validation ◽  
Multivariate Calibration ◽  
Data Sets ◽  
Calibration Data ◽  
Mean Square ◽  
Calibration Models ◽  
Pcr Method

Objective: The objective of this study was to develop a UV spectroscopy method in combination with multivariate analysis for determining vitexin in binahong (Anredera cordifolia (Ten.) Steenis) leaves extract. Methods: The partial least square (PLS) regression and the principal component regression (PCR) was performed in this study to evaluate several statistical performances such as coefficient of determination (R2), root mean square error of calibration (RMSEC), root mean square error of cross-validation (RMSECV), root mean square error of prediction (RMSEP) and relative error of prediction (REP). Cross-validation in this study was performed using leave one out technique. Results: The R2 values of calibration data sets resulted from PLS ​​and PCR method were 0.9675 and 0.9648, respectively. The low values of RMSEC and RMSECV both for PLS ​​and PCR method indicated the minimum error of the calibration models. The R2 values of validation data sets resulted from PLS ​​and PCR method were 0.9778 and 0.9820, respectively. The low values of RMSEP both for PLS ​​and PCR method indicated the minimum error of prediction generated from the calibration data sets. Multivariate calibration techniques were applied to determine the content of vitexin in binahong leaves extract. Predicted values from the multivariate calibration models were compared to the actual values determined from a validated HPLC method. It was found that PLS models resulted in the lowest REP values compared to the PCR models. Conclusion: The chemometrics technique can be applied as an alternative method for determining vitexin levels in the ethanol solution of binahong leaves extract.

scholarly journals The application of data mining techniques for the regionalisation of hydrological variables

2002 ◽  
Vol 6 (4) ◽  
pp. 685-694 ◽  
Author(s):  
M. J. Hall ◽  
A. W. Minns ◽  
A. K. M. Ashrafuzzaman
Keyword(s):  
Data Mining ◽  
Neural Networks ◽  
Artificial Neural Networks ◽  
Root Mean Square ◽  
Data Sets ◽  
Mean Square ◽  
Data Set ◽  
South West ◽  
Catchment Areas ◽  
Hydrological Variables

Abstract. Flood quantile estimation for ungauged catchment areas continues to be a routine problem faced by the practising Engineering Hydrologist, yet the hydrometric networks in many countries are reducing rather than expanding. The result is an increasing reliance on methods for regionalising hydrological variables. Among the most widely applied techniques is the Method of Residuals, an iterative method of classifying catchment areas by their geographical proximity based upon the application of Multiple Linear Regression Analysis (MLRA). Alternative classification techniques, such as cluster analysis, have also been applied but not on a routine basis. However, hydrological regionalisation can also be regarded as a problem in data mining — a search for useful knowledge and models embedded within large data sets. In particular, Artificial Neural Networks (ANNs) can be applied both to classify catchments according to their geomorphological and climatic characteristics and to relate flow quantiles to those characteristics. This approach has been applied to three data sets from the south-west of England and Wales; to England, Wales and Scotland (EWS); and to the islands of Java and Sumatra in Indonesia. The results demonstrated that hydrologically plausible clusters can be obtained under contrasting conditions of climate. The four classes of catchment found in the EWS data set were found to be compatible with the three classes identified in the earlier study of a smaller data set from south-west England and Wales. Relationships for the parameters of the at-site distribution of annual floods can be developed that are superior to those based upon MLRA in terms of root mean square errors of validation data sets. Indeed, the results from Java and Sumatra demonstrate a clear advantage in reduced root mean square error of the dependent flow variable through recognising the presence of three classes of catchment. Wider evaluation of this methodology is recommended. Keywords: regionalisation, floods, catchment characteristics, data mining, artificial neural networks

Assessment of Pareto Calibration, Stability, and Wavelength Selection

2003 ◽  
Vol 57 (3) ◽  
pp. 309-316 ◽  
Author(s):  
Kelly J. Anderson ◽  
John H. Kalivas
Keyword(s):  
Root Mean Square Error ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Principal Component Regression ◽  
Principal Component ◽  
Data Sets ◽  
Mean Square ◽  
Wavelength Selection ◽  
Pareto Model ◽  
Improve Analysis

Recent work has shown that ridge regression (RR) is Pareto to partial least squares (PLS) and principal component regression (PCR) when the variance indicator Euclidian norm of the regression coefficients, ‖p̂‖, is plotted against the bias indicator root mean square error of calibration (RMSEC). Simplex optimization demonstrates that RR is Pareto for several other spectral data sets when ‖p̂‖ is used with RMSEC and the root mean square error of evaluation (RMSEE) as optimization criteria. From this investigation, it was observed that while RR is Pareto optimal, PLS and PCR harmonious models are near equivalent to harmonious RR models. Additionally, it was found that RR is Pareto robust, i.e., models formed at one temperature were then used to predict samples at another temperature. Wavelength selection is commonly performed to improve analysis results such that bias indicators RMSEC, RMSEE, root mean square error of validation, or root mean square error of cross-validation decrease using a subset of wavelengths. Just as critical to an analysis of selected wavelengths is an assessment of variance. Using wavelengths deemed optimal in a previous study, this paper reports on the variance/bias tradeoff. An approach that forms the Pareto model with a Pareto wavelength subset is suggested.

On the inference of the state of turbulence and mixing efficiency in stably stratified flows

2019 ◽  
Vol 867 ◽  
pp. 323-333 ◽  
Author(s):  
Amrapalli Garanaik ◽  
Subhas K. Venayagamoorthy
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Stratified Flows ◽  
Dynamic State ◽  
Mixing Efficiency ◽  
Buoyancy Frequency ◽  
Length Scale ◽  
Stratified Turbulence ◽  
Wide Range ◽  
Rate Of Dissipation

Scaling arguments are presented to quantify the widely used diapycnal (irreversible) mixing coefficient $\unicode[STIX]{x1D6E4}=\unicode[STIX]{x1D716}_{PE}/\unicode[STIX]{x1D716}$ in stratified flows as a function of the turbulent Froude number $Fr=\unicode[STIX]{x1D716}/Nk$. Here, $N$ is the buoyancy frequency, $k$ is the turbulent kinetic energy, $\unicode[STIX]{x1D716}$ is the rate of dissipation of turbulent kinetic energy and $\unicode[STIX]{x1D716}_{PE}$ is the rate of dissipation of turbulent potential energy. We show that for $Fr\gg 1$, $\unicode[STIX]{x1D6E4}\propto Fr^{-2}$, for $Fr\sim \mathit{O}(1)$, $\unicode[STIX]{x1D6E4}\propto Fr^{-1}$ and for $Fr\ll 1$, $\unicode[STIX]{x1D6E4}\propto Fr^{0}$. These scaling results are tested using high-resolution direct numerical simulation (DNS) data from three different studies and are found to hold reasonably well across a wide range of $Fr$ that encompasses weakly stratified to strongly stratified flow conditions. Given that the $Fr$ cannot be readily computed from direct field measurements, we propose a practical approach that can be used to infer the $Fr$ from readily measurable quantities in the field. Scaling analyses show that $Fr\propto (L_{T}/L_{O})^{-2}$ for $L_{T}/L_{O}>O(1)$, $Fr\propto (L_{T}/L_{O})^{-1}$ for $L_{T}/L_{O}\sim O(1)$, and $Fr\propto (L_{T}/L_{O})^{-2/3}$ for $L_{T}/L_{O}<O(1)$, where $L_{T}$ is the Thorpe length scale and $L_{O}$ is the Ozmidov length scale. These formulations are also tested with DNS data to highlight their validity. These novel findings could prove to be a significant breakthrough not only in providing a unifying (and practically useful) parameterization for the mixing efficiency in stably stratified turbulence but also for inferring the dynamic state of turbulence in geophysical flows.

scholarly journals The Mimas-Tethys and Enceladus-Dione systems

1996 ◽  
Vol 172 ◽  
pp. 143-144 ◽  
Author(s):  
A. Vienne ◽  
L. Duriez ◽  
S. Champenois
Keyword(s):  
Root Mean Square ◽  
Data Sets ◽  
Mean Square

We have recently built a coherent theory of the motion of the satellites Mimas, Enceladus, Tethys, Dione, Rhea, Titan and Iapetus. The final form of the “Théorie Analytique des Satellites de Saturne” (TASS1.6) is presented in Vienne & Duriez (1995). The internal precision of TASS is a few kilometers over three years and some tens kilometers over one century. The root-mean-square residuals of the adjustment of TASS over one century of Earth based observations reach 0″.12 for the best data sets, until 0″.015 for the few mutual phenomenas of 1981.

scholarly journals Minimum Local Emissivity Variance Retrieval of Cloud Altitude and Effective Spectral Emissivity—Simulation and Initial Verification

2004 ◽  
Vol 43 (5) ◽  
pp. 795-809 ◽  
Author(s):  
Hung-Lung Huang ◽  
William L. Smith ◽  
Jun Li ◽  
Paolo Antonelli ◽  
Xiangqian Wu ◽  
...  
Keyword(s):  
Root Mean Square ◽  
Spectral Resolution ◽  
Single Layer ◽  
Spectral Emissivity ◽  
Pressure Level ◽  
High Spectral Resolution ◽  
Mean Square ◽  
Atmospheric Conditions ◽  
Wide Range ◽  
Mean Square Errors

Abstract This paper describes the theory and application of the minimum local emissivity variance (MLEV) technique for simultaneous retrieval of cloud pressure level and effective spectral emissivity from high-spectral-resolution radiances, for the case of single-layer clouds. This technique, which has become feasible only with the recent development of high-spectral-resolution satellite and airborne instruments, is shown to provide reliable cloud spectral emissivity and pressure level under a wide range of atmospheric conditions. The MLEV algorithm uses a physical approach in which the local variances of spectral cloud emissivity are calculated for a number of assumed or first-guess cloud pressure levels. The optimal solution for the single-layer cloud emissivity spectrum is that having the “minimum local emissivity variance” among the retrieved emissivity spectra associated with different first-guess cloud pressure levels. This is due to the fact that the absorption, reflection, and scattering processes of clouds exhibit relatively limited localized spectral emissivity structure in the infrared 10–15-μm longwave region. In this simulation study it is shown that the MLEV cloud pressure root-mean-square errors for a single level with effective cloud emissivity greater than 0.1 are ∼30, ∼10, and ∼50 hPa, for high (200– 300 hPa), middle (500 hPa), and low (850 hPa) clouds, respectively. The associated cloud emissivity root-mean-square errors in the 900 cm−1 spectral channel are less than 0.05, 0.04, and 0.25 for high, middle, and low clouds, respectively.

scholarly journals Numerical Quantification of Controllability in the Null Space for Redundant Manipulators

2021 ◽  
Vol 11 (13) ◽  
pp. 6190
Author(s):  
Seonwoo Kim ◽  
Seongseop Yun ◽  
Dongjun Shin
Keyword(s):  
Root Mean Square ◽  
Null Space ◽  
Robotic Manipulators ◽  
Robotic Arm ◽  
Redundant Manipulators ◽  
Mean Square ◽  
Wide Range ◽  
Sinusoidal Input ◽  
Space Projection ◽  
Rms Error

Redundant motion, which is possible when robotic manipulators are over-actuated, can be used to control robot arms for a wide range of tasks. One of the best known methods for controlling redundancy is the null space projection, which assigns a priority while executing desired tasks. However, when the manipulator is projected into null space, its motion would be limited, since the motion is only permitted in the direction that does not interfere with the primary task. In this study, we have analyzed the null space projector matrix to derive the appropriate direction of the redundant motion by quantifying the allowed motion in each direction. As a result, we have found an ellipsoidal boundary, in which the redundant motion is permitted to move. We have named this ellipsoidal boundary as ’null space quality’ in directions. The proposed null space quality shows similar aspects with that of the robot manipulability, but it reveals a decisively different value when the manipulator operates within the null space. The experimental results showed that the robotic manipulator tracked the sinusoidal input trajectory with reduced root mean square (RMS) error by 33.84%. Furthermore, we have demonstrated the obstacle avoidance of a robotic arm utilizing the null space projector while considering the null space quality.

Evaluation of the APSIM-Wheat model in terms of different cultivars, management regimes and environmental conditions

2012 ◽  
Vol 92 (5) ◽  
pp. 937-949 ◽  
Author(s):  
Yi Zhang ◽  
Liping Feng ◽  
Enli Wang ◽  
Jing Wang ◽  
Baoguo Li
Keyword(s):  
Root Mean Square ◽  
Environmental Conditions ◽  
Field Experiments ◽  
Growth And Yield ◽  
Planting Density ◽  
Mean Square ◽  
Sowing Dates ◽  
Wide Range ◽  
Management Regimes ◽  
Mean Square Errors

Zhang, Y., Feng, L., Wang, E., Wang, J. and Li, B. 2012. Evaluation of the APSIM-Wheat model in terms of different cultivars, management regimes and environmental conditions. Can. J. Plant Sci. 92: 937–949. Wheat is one of the most important crops in the world, and wheat models have been widely used to study yield responses to changes in management and climate. However, less information is available on how a wheat model performs in simulation of wheat response to changes in varieties, sowing dates and planting densities across space. This study presents an evaluation of the APSIM-Wheat model using data from field experiments consisting of three sowing dates, two and three crop varieties and three planting densities in a split-split plot design at three ecological sites from 2008 to 2010 in the North China Plain. The results show that the APSIM-Wheat model could capture a large part of the variation in phenology, biomass and yield for the same variety across sites. However, errors of simulation in phenology and yield were increased with delay in sowing date, with the average absolute root mean square errors of 2 d, 3 d, and 3–4 d in phenology, and the normalized root mean square error (RMSEn) of 7–12%, 11–16%, 16–22% in yield at early, medium, and late sowing dates, respectively. Simulation of yield achieved poor results with decreased planting density, with average RMSEn of 9–12%, 11–12%, and 16–19% at high, medium, and low density, respectively. Additionally, the simulation behaved in a complex manner, and the errors varied greatly with different combinations of sowing dates and planting densities. These alerted us that the model should be used cautiously to simulate growth and yield over a wide range of sowing dates and planting densities. Improved modeling of the responses of wheat growth to extreme temperatures during winter and spring periods, and to varying planting densities is needed for better future prediction. Other areas of model improvements are also discussed.

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