Mean Temperature Error Research Articles

Generation and Validation of CFD-Based ROMs for Real-Time Temperature Control in the Main Control Room of Nuclear Power Plants

This study develops and validates a Reduced Order Model (ROM) integrated with Digital Twin technology for real-time temperature control in the Main Control Room (MCR) of a nuclear power plant. Utilizing Computational Fluid Dynamics (CFD) simulations, we obtained detailed three-dimensional thermal flow distributions under various operating conditions. A ROM was generated using machine learning techniques based on 94 CFD cases, achieving a mean temperature error of 0.35%. The ROM was further validated against two excluded CFD cases, demonstrating high correlation coefficients (R > 0.84) and low error metrics, confirming its accuracy and reliability. Integrating the ROM with the Heating, Ventilating, and Air Conditioning (HVAC) system, we conducted a two-month simulation, showing effective maintenance of MCR temperature within predefined criteria through adaptive HVAC control. This integration significantly enhances operational efficiency and safety by enabling real-time monitoring and control while reducing computational costs and time associated with full-scale CFD analyses. Despite promising results, the study acknowledges limitations related to ROM’s dependency on training data quality and the need for more comprehensive validation under diverse and unforeseen conditions. Future research will focus on expanding the ROM’s applicability, incorporating advanced machine learning methods, and conducting pilot tests in actual nuclear plant environments to further optimize the Digital Twin-based control system.

Estimating temperatures with low-cost infrared cameras using physically-constrained deep neural networks.

Low-cost thermal cameras are inaccurate (usually ±3∘ C) and have space-variant nonuniformity across their detectors. Both inaccuracy and nonuniformity are dependent on the ambient temperature of the camera. The goal of this work was to estimate temperatures with low-cost infrared cameras, and rectify the nonuniformity. A nonuniformity simulator that accounts for the ambient temperature was developed. An end-to-end neural network that incorporates both the physical model of the camera and the ambient camera temperature was introduced. The neural network was trained with the simulated nonuniformity data to estimate the object's temperature and correct the nonuniformity, using only a single image and the ambient temperature measured by the camera itself. The proposed method significantly reduced the mean temperature error compared to previous state-of-the-art methods, with a gap of 0.29∘ C when compared to the closest previous approaches. In addition, constraining the physical model of the camera with the network lowered the error by an additional 0.1∘ C. The mean temperature error over an extensive validation dataset was 0.37∘ C. The method was verified on real data in the field and produced equivalent results.

Design of a hemispherical shell shaped natural ventilation temperature observation instrument.

Atmospheric temperature is fundamental information for various industries, such as production, life, and scientific research. The temperature error induced by the solar rays can reach 1 °C or even higher. A hemispherical shell-shaped atmospheric temperature measuring instrument that can reduce heat pollution and increase air velocity was designed. First, the instrument was optimized using computational fluid dynamics (CFD) software packages. Then, the CFD software packages were employed to quantify the temperature errors of the instrument with varying situations. A neural network model was employed to develop a temperature error correction model that can be targeted for multi-variable changes. This model provides accurate correction data when the influencing factors change continuously. Finally, field experiments were performed. The experimental data analysis indicates that the mean temperature error and the maximum error of the instrument before correction are 0.08 and 0.25 °C, respectively. The root mean square error, the mean absolute error, and the correlation coefficient between measured temperature errors from experiments and corrected temperature errors from the correction model are 0.099, 0.016, and 0.952 °C, respectively. By utilizing a temperature error correction model, the measuring error of the instrument can be minimized to a range between -0.05 and 0.04 °C. Consequently, the instrument is anticipated to enhance temperature measurement accuracy to ∼0.1 °C.

Comparative analysis of versatile temperature-controlled systems using fuzzy logic controllers

Abstract This article presents a comparison of versatile temperature-controlled systems utilizing fuzzy logic (FL) controller, highlighting their unique functionalities and verifying objectives. The meditate focuses on the following four primary systems: a temperature-controlled fan system, a temperature-controlled warmer system, a cool-controlled warmer system, and a cool-controlled fan system. The primary quill function of each system, control objectives, identify stimulant and output variables, response characteristics, normal applications, system complexity, vitality efficiency, and situation suitability are examined. The temperature-controlled fan system primarily cools by regulation airflow, achieving a mean temperature error of −0.0319°C. The temperature-controlled heater system heats the environment, with a mean temperature error of 1.4696°C. The cool-controlled heater system of rules prevents overheating by modulating heat output and maintains a stable environment, while the cool-controlled fan system of rules maintains a tankful undefined by increasing airflow. Differences in system complexity with fan systems managing humidness and warmer systems focused on a temperature increase are noted. The wallpaper provides a comprehensive overview, making it clear how each system of rules is the best right for particular conditions and applications.

Monitoring Thermal Exchange of Hot Water Mass via Underwater Acoustic Tomography with Inversion and Optimization Method

Thermal exchange of underwater water mass caused by marine heat wave is a hot point of research recently. In particular, because the water temperature observation along hot water mass transportation is hard work. Acoustic tomography is an advanced method to measure water temperature variations via sound signal transmission with multi-station network sensing. The 5 kHz frequency acoustic tomography used for observing water temperature variations caused by ocean heat waves is interesting work. In this paper, the numerical simulation of hot water mass is completed first, then floatation and diffusion of hot water mass in a simulation are monitored by acoustic tomography. A new inversion optimization method is proposed to obtain hot water mass transportation variations at two-dimensional temperature vertical profile. The proposed inversion method adds a regularized mode matrix and the optimization method adds the model correlation matrix to improve the results quality. The accuracy of inversion optimization results is compared and discussed, where the mean temperature error is less than 0.4 °C. Sensing water temperature variation of marine heat waves is verified via acoustic signal transmission and improved inversion optimization method. The water dynamical process observation is an application of acoustic tomography, which can be further used observe underwater environmental characteristics.

U-Net for temperature estimation from simulated infrared images in tokamaks

Surface temperature measurement is critical for the safety and proper operation of nuclear fusion reactors such as tokamaks, which operate at high temperature [100–3600 °C] in the presence of complex and unknown surface reflectance properties, causing a reflected flux that disturbs measurement interpretations. This paper describes a numerical approach based on machine learning techniques to estimate the surface temperature of in-vessel components from infrared images, despite the presence of reflections and the unknown emissivity of materials. Our contributions are two-fold: for the first time in the infrared domain, we generate a huge dataset of simulated images thanks to a novel GPU implementation of a Monte Carlo infrared ray tracer. This implementation offers the great advantage of enabling the generation of a very large amount of synthetic images for different plasma scenarios. Hence the second contribution of this paper: we propose an infrared inverse lighting model, based on a Convolutional Neural Network (CNN) trained with the images generated by our ray tracer. The proposed approach is applied on a numerical prototype of W Environment Steady state Tokamak (WEST), including complex simulated thermal scenes. Using synthetic test data, and without providing the surface optical properties, the mean temperature error predicted by the CNN on ITER-like wide angle view of WEST is evaluated to 9% with standard plasma scenarios and 22% in case of exotic thermal scenes.

Bistatic Radar Tomography of Shear Margins: Simulated Temperature and Basal Material Inversions

A significant portion of the sea level contributions of Antarctica and Greenland comes from ice streams, but the physical processes controlling ice stream width are poorly understood, especially when topographic controls are absent. Recent modeling studies have indicated that ice stream width may be controlled by elevated temperatures inside ice stream shear margins. While radio echo sounders can provide measurements of englacial water storage and subglacial conditions, existing radar-sounding techniques cannot measure temperature profiles at the scale required to test this hypothesis. We propose using a wide-angle radar survey and tomographic inversion to resolve temperature profiles, gradients, and anomalies at the scale required to study the thermophysical controls on shear margins. Recent work produced a bistatic radar system capable of obtaining the long offsets required for well-constrained inversions; however, shear-margin-specific temperature inversion techniques have not been developed for this system. In this article, we develop Newton’s method and alternating direction method of multipliers’ inversions for estimating temperature distribution and basal material across ice stream shear margins. We evaluate the performance of these inversion techniques on simulated bistatic radar-sounding data. Our results suggest that bistatic radar tomography experiments should be able to produce temperature maps on 50 m <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times50$ </tex-math></inline-formula> m grids with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.83~^{\circ} \text{C}~\pm ~0.084~^{\circ} \text{C}$ </tex-math></inline-formula> mean temperature error, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3.58~^{\circ} \text{C}~\pm ~0.20~^{\circ} \text{C}$ </tex-math></inline-formula> maximum temperature error, and an error in relative basal permittivity of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.63~\pm ~0.08$ </tex-math></inline-formula> for a 4-km transect.

Comparison of Ventilated and Unventilated Air Temperature Measurements in Inland Dronning Maud Land on the East Antarctic Plateau

Abstract Surface temperature measurements with naturally ventilated (NV) sensors over the Antarctic Plateau are largely subject to systematic errors caused by solar radiative heating. Here we examined the radiative heating error in Dronning Maud Land on the East Antarctic Plateau using both the newly installed automatic weather stations (AWSs) at NDF and Relay Station and the existing AWSs at Relay Station and Dome Fuji. Two types of NV shields were used in these AWSs: a multiplate radiation shield and a simple cylinder-shaped shield. In austral summer, the temperature bias between the force-ventilated (FV) sensor and the NV sensor never reached zero because of continuous sunlight. The hourly mean temperature errors reached up to 8°C at noon on a sunny day with weak wind conditions. The errors increased linearly with increasing reflected shortwave radiation and decreased nonlinearly with increasing wind speed. These features were observed in both the multiplate and the cylinder-shaped shields. The magnitude of the errors of the multiplate shield was much larger than that of the cylinder-shaped shield. To quantify the radiative errors, we applied an existing correction model based on the regression approach and successfully reduced the errors by more than 70% after the correction. This indicates that we can use the corrected temperature data instead of quality controlled data, which removed warm bias during weak winds in inland Dronning Maud Land.

Anatomical Phase Extraction (APE) Method: A Novel Method to Correct Detrimental Effects of Tissue-Inhomogeneity in Referenceless MR Thermometry-Preliminary Ex Vivo Investigation.

Purpose We present a novel background tissue phase removing method, called anatomical phase extraction (APE), and to investigate the accuracy of temperature estimation and capability of reducing background artifacts compared with the conventional referenceless methods. Methods Susceptibility variance was acquired by subtracting pretreatment baseline images taken at different locations (nine pretreatment baselines are acquired and called φ1 to φ9). The susceptibility phase data φS was obtained using the Wiener deconvolution algorithm. The background phase data φT was isolated by subtracting φS from the whole phase data. Finally, φT was subtracted from the whole phase data before applying the referenceless method. As a proof of concept, the proposed APE method was performed on ex vivo pork tenderloin and compared with other two referenceless temperature estimation approaches, including reweighted ℓ1 referenceless (RW- ℓ1) and ℓ2 referenceless methods. The proposed APE method was performed with four different baselines combination, namely, (φ1, φ5, φ2, φ4), (φ3, φ5, φ2, φ6), (φ7, φ5, φ8, φ4), and (φ9, φ5, φ8, φ6), and called APE experiment 1 to 4, respectively. The multibaseline method was used as a standard reference. The mean absolute error (MAE) and two-sample t-test analysis in temperature estimation of three regions of interest (ROI) between the multibaseline method and the other three methods, i.e., APE, RW- ℓ1, and ℓ2, were calculated and compared. Results Our results show that the mean temperature errors of the APE method-experiment 1, APE method-experiment 2, APE method-experiment 3, APE method-experiment 4, and RW- ℓ1 and ℓ2 referenceless method are 1.02°C, 1.04°C, 1.00°C, 1.00°C, 4.75°C, and 13.65°C, respectively. The MAEs of the RW- ℓ1 and ℓ2 referenceless methods were higher than that of APE method. The APE method showed no significant difference (p > 0.05), compared with the multibaseline method. Conclusion The present work demonstrates the use of the APE method on referenceless MR thermometry to improve the accuracy of temperature estimation during MRI guided high-intensity focused ultrasound for ablation treatment.

A quasi-transient coupling approach to the modeling of conjugate heat transfer in the autoclave

Structural aerospace composite parts are generally cured in an autoclave. To achieve a homogeneous curing, computational fluid dynamics simulations have been increasingly used in thermal optimization. However, a transient computational fluid dynamics simulation of autoclave processing is resource intensive. This article outlines the concept of a quasi-transient coupling strategy to deal with the conjugate heat transfer problem inside an autoclave. In this approach, a computational fluid dynamics model is coupled with a finite element method (FEM) model through incorporating an empirical-based analytic equation, which describes the dependence of the heat transfer coefficient on pressure and temperature, into the computational fluid dynamics computations. This approach bridges the temporal disparities between the fluid and the solid, thus minimizing the global computing time. To validate this method, two simulation cases have been studied. In both cases, two different coupling computations are compared, namely a full-transient simulation as the reference computation and the introduced quasi-transient simulation. First, the quasi-transient coupling approach is implemented by performing the transient heat transfer analysis on a flat plate. The results indicate that this approach can predict accurate transient temperature fields, and the computational effort is reduced by up to 87%. Subsequently, this method is used in a real autoclave and validated by known experimental data. The simulation results are in good agreement with the experimental results, with a mean temperature error lower than 1.9°C. This indicates the capability and efficiency of this approach in solving a conjugate heat transfer problem for autoclave processing.

Influences of blood flow parameters on temperature distribution during liver tumor microwave ablation.

Highlights: (1) A 3D simulation model of MWA (microwave ablation) based on the temperature-dependent characteristic parameters and blood flow parameters was established to realize the visual simulation of temperature distribution and coagulation zone. The internal forced convection condition was used to accurately characterize the large vessel. (2) The ex vivo MWA experimental platform was built to verify the accuracy of the simulation model. A peristaltic pump was employed for operatively controlling blood circulation and a medical soft plastic tube was introduced for appropriately simulating a blood vessel. (3) The influences of blood flow parameters of large vessels on temperature distribution and coagulation zone were systematically analyzed in order to provide reference and guidance for MWA clinicians. Purpose: Clinical MWA of liver tumor is significantly limited by the accurate prediction of vascular cooling effects. To provide reference and guidance for clinical MWA of liver tumor, the three-dimensional effects of different blood flow parameters of large vessels on MWA temperature distribution were systematically evaluated. Materials and methods: Firstly, the MWA three-dimensional finite element simulation model with blood flow parameters was established. Secondly, to verify the effectiveness of the model, MWA was performed ex vivo in porcine liver for 360 s and the temperature was measured by thermocouples. A medical soft plastic tube was placed parallel to the MWA antenna to simulate a natural liver vessel. Finally, based on this model, the influences of different vessel diameters and vessel-antenna spacings on MWA temperature distribution were analyzed. Results: Sixteen ablations were performed to verify the accuracy of the simulation model. The mean temperature errors between measured data and simulation results at six measurement points were 3.87 ℃. In the first 10 seconds of MWA, the vessel cooling effect on temperature distribution was negligible. When the vessel-antenna spacing was 5 mm and the vessel diameter varied from 3 mm to 6 mm, the temperature at the measured point near the vessel decreased by 2.11 ℃ at 360 s. When the vessel diameter was 6 mm and the vessel-antenna spacing varied from 5 mm to 7 mm, the temperature at the measured point near the vessel reduced by 14.91 ℃ at 360 s. In addition, blood diameter had little influence on the temperature distribution near the heating point. The volume of coagulation zone will not be obviously affected once the vessel lies outside the predicted coagulation zone. Conclusions: The MWA simulation model with blood flow parameters is established. Vessel-antenna spacing is the primary factor affecting the temperature distribution. A vessel with larger diameter can have a more significant effect on the temperature distribution. The large vessel will take away and block part of conduction heat, so the coagulation zone will not be formed on the lateral side of the vessel.

A Lumped Parameter Thermal Model for Single-Sided AFPM Machines With Experimental Validation

Axial flux permanent magnet (AFPM) machines are promising for hybrid electric vehicles (HEVs) due to the compactness, high torque density, and high efficiency. However, poor thermal characterization leads to an oversizing of these machines, which ultimately compromises overall system efficiency. In this article, the transient thermal behavior of all the components in the single-sided AFPM machine is characterized in an accurate but computationally efficient lumped parameter thermal model (LPTM). For the first time, contact measurements on the rotor have been used in AFPM machines to demonstrate the ability of the model to predict all component temperatures within 4 °C for steady state. The mean temperature error over a load step transient was less than 5 °C with a maximum error of less than 13.5 °C that was for the winding. The model has a running time of approximately 1000 times faster than real time on a desktop machine and is suitable for integration into system simulation tools and predictive control strategies to avoid oversizing of the motor and improve the usage of the electric machine in dynamic duty cycles.

MULTISCALE SEAMLESS-DOMAIN METHOD FOR NONPERIODIC FIELDS: NONLINEAR HEAT CONDUCTION ANALYSIS

A multiscale numerical solver called the seamless-domain method (SDM) is used in linear heat conduction analysis of nonperiodic simulated fields. The practical feasibility of the SDM has been verified for use with periodic fields but has not previously been verified for use with nonperiodic fields. In this paper, we illustrate the mathematical framework of the SDM and the associated error factors in detail. We then analyze a homogeneous temperature field using the SDM, the standard finite difference method, and the conventional domain decomposition method (DDM) to compare the convergence properties of these methods. In addition, to compare their computational accuracies and time requirements, we also simulated a nonperiodic temperature field with a nonuniform thermal conductivity distribution using the three methods. The accuracy of the SDM is very high and is approximately equivalent to that of the DDM. The mean temperature error is less than 0.02% of the maximum temperature in the simulated field. The total central processing unit (CPU) times required for the analyses using the most efficient SDM model and the DDM model represent 13% and 17% of that of the finite difference model, respectively.

Computational fluid dynamics analysis and experimental study of a low measurement error temperature sensor used in climate observation.

To improve the air temperature observation accuracy, a low measurement error temperature sensor is proposed. A computational fluid dynamics (CFD) method is implemented to obtain temperature errors under various environmental conditions. Then, a temperature error correction equation is obtained by fitting the CFD results using a genetic algorithm method. The low measurement error temperature sensor, a naturally ventilated radiation shield, a thermometer screen, and an aspirated temperature measurement platform are characterized in the same environment to conduct the intercomparison. The aspirated platform served as an air temperature reference. The mean temperature errors of the naturally ventilated radiation shield and the thermometer screen are 0.74 °C and 0.37 °C, respectively. In contrast, the mean temperature error of the low measurement error temperature sensor is 0.11 °C. The mean absolute error and the root mean square error between the corrected results and the measured results are 0.008 °C and 0.01 °C, respectively. The correction equation allows the temperature error of the low measurement error temperature sensor to be reduced by approximately 93.8%. The low measurement error temperature sensor proposed in this research may be helpful to provide a relatively accurate air temperature result.

A temperature error correction method for a naturally ventilated radiation shield

Due to solar radiation exposure, air flowing inside a naturally ventilated radiation shield may produce a measurement error of 0.8°C or higher. To improve the air temperature observation accuracy, a temperature error correction method is proposed. The correction method is based on a Computational Fluid Dynamics (CFD) method and a Genetic Algorithm (GA) method. The CFD method is implemented to analyze and calculate the temperature errors of a naturally ventilated radiation shield under various environmental conditions. Then, a temperature error correction equation is obtained by fitting the CFD results using the GA method. To verify the performance of the correction equation, the naturally ventilated radiation shield and an aspirated temperature measurement platform are characterized in the same environment to conduct the intercomparison. The aspirated temperature measurement platform serves as an air temperature reference. The mean temperature error given by measurements is 0.36°C, and the mean temperature error given by correction equation is 0.34°C. This correction equation allows the temperature error to be reduced by approximately 95%. The mean absolute error (MAE) and the root mean square error (RMSE) between the temperature errors given by the correction equation and the temperature errors given by the measurements are 0.07°C and 0.08°C, respectively.

An Evaluation of HIRS Near-Surface Air Temperature Product in the Arctic with SHEBA Data

AbstractThe accuracy of cloud-screened 2-m air temperatures derived from the intersatellite-calibrated brightness temperatures based on the High Resolution Infrared Radiation Sounder (HIRS) measurements on board the National Oceanic and Atmospheric Administration (NOAA) Polar-Orbiting Operational Environmental Satellite (POES) series is evaluated by comparing HIRS air temperatures to 1-yr quality-controlled measurements collected during the Surface Heat Budget of the Arctic Ocean (SHEBA) project (October 1997–September 1998). The mean error between collocated HIRS and SHEBA 2-m air temperature is found to be on the order of 1°C, with a slight sensitivity to spatial and temporal radii for collocation. The HIRS temperatures capture well the temporal variability of SHEBA temperatures, with cross-correlation coefficients higher than 0.93, all significant at the 99.9% confidence level. More than 87% of SHEBA temperature variance can be explained by linear regression of collocated HIRS temperatures. The analysis found a strong dependency of mean temperature errors on cloud conditions observed during SHEBA, indicating that availability of an accurate cloud mask in the region is essential to further improve the quality of HIRS near-surface air temperature products. This evaluation establishes a baseline of accuracy of HIRS temperature retrievals, providing users with information on uncertainty sources and estimates. It is a first step toward development of a new long-term 2-m air temperature product in the Arctic that utilizes intersatellite-calibrated remote sensing data from the HIRS instrument.

Accelerated model-based proton resonance frequency shift temperature mapping using echo-based GRAPPA reconstruction

PurposeTo develop an acceleration method for MR temperature estimation using model-based proton resonance frequency (PRF) shift method. Materials and MethodsImages of 16 different echo times (TE) were acquired in one RF excitation using a multi-echo gradient-recalled echo (GRE) sequence. Fully sampled k-space data were retrospectively under-sampled at a net reduction factor between two and three using the proposed under-sampling strategy. K-spaces of three different TEs were combined together to perform the proposed reconstruction method called Echo-based GRAPPA. Ex vivo goose liver cooling experiment and in vivo breast imaging experiment were performed to investigate the accuracy of Echo-based GRAPPA. Conventional GRAPPA reconstruction was implemented for comparison using the same sampling pattern. ResultsThe goose liver imaging experiment shows that the reconstruction-induced temperature RMSE of a selected region of interest (ROI) is less than 1.4°C for Echo-based GRAPPA at a net reduction factor of 2.3. The breast imaging experiment shows that the mean temperature error of water–fat mixed ROIs is 2.3°C at a net reduction factor of 2.7. Conventional GRAPPA shows larger temperature RMSE than Echo-based GRAPPA. ConclusionThe proposed method can accelerate the MR temperature estimation using model-based PRF at a net reduction factor between two and three with a reconstruction-induced temperature error less than 3°C in water–fat mixed ROIs.

Verification of surface minimum, mean, and maximum temperature forecasts in Calabria for summer 2008

Abstract. Since 2005, one-hour temperature forecasts for the Calabria region (southern Italy), modelled by the Regional Atmospheric Modeling System (RAMS), have been issued by CRATI/ISAC-CNR (Consortium for Research and Application of Innovative Technologies/Institute for Atmospheric and Climate Sciences of the National Research Council) and are available online at http://meteo.crati.it/previsioni.html (every six hours). Beginning in June 2008, the horizontal resolution was enhanced to 2.5 km. In the present paper, forecast skill and accuracy are evaluated out to four days for the 2008 summer season (from 6 June to 30 September, 112 runs). For this purpose, gridded high horizontal resolution forecasts of minimum, mean, and maximum temperatures are evaluated against gridded analyses at the same horizontal resolution (2.5 km). Gridded analysis is based on Optimal Interpolation (OI) and uses the RAMS first-day temperature forecast as the background field. Observations from 87 thermometers are used in the analysis system. The analysis error is introduced to quantify the effect of using the RAMS first-day forecast as the background field in the OI analyses and to define the forecast error unambiguously, while spatial interpolation (SI) analysis is considered to quantify the statistics' sensitivity to the verifying analysis and to show the quality of the OI analyses for different background fields. Two case studies, the first one with a low (less than the 10th percentile) root mean square error (RMSE) in the OI analysis, the second with the largest RMSE of the whole period in the OI analysis, are discussed to show the forecast performance under two different conditions. Cumulative statistics are used to quantify forecast errors out to four days. Results show that maximum temperature has the largest RMSE, while minimum and mean temperature errors are similar. For the period considered, the OI analysis RMSEs for minimum, mean, and maximum temperatures vary from 1.8, 1.6, and 2.0 °C, respectively, for the first-day forecast, to 2.0, 1.9, and 2.6 °C, respectively, for the fourth-day forecast. Cumulative statistics are computed using both SI and OI analysis as reference. Although SI statistics likely overestimate the forecast error because they ignore the observational error, the study shows that the difference between OI and SI statistics is less than the analysis error. The forecast skill is compared with that of the persistence forecast. The Anomaly Correlation Coefficient (ACC) shows that the model forecast is useful for all days and parameters considered here, and it is able to capture day-to-day weather variability. The model forecast issued for the fourth day is still better than the first-day forecast of a 24-h persistence forecast, at least for mean and maximum temperature. The impact of using the RAMS first-day forecast as the background field in the OI analysis is quantified by comparing statistics computed with OI and SI analyses. Minimum temperature is more sensitive to the change in the analysis dataset as a consequence of its larger representative error.

Analysis of slit function errors in single-shot coherent anti-Stokes Raman spectroscopy (CARS) in practical combustors

The temperature determined by a single-shot coherent anti-Stokes Raman spectroscopy (CARS) system is directly related to the half width at half maximum of the instrument slit function. Therefore, an accurate knowledge of the instrument slit function is necessary to determine temperature with CARS. However, in turbulent systems, the input slits of the spectrometer may be removed in order to guarantee signal throughput and establish the necessary dynamic range. In this case, the physical input slits of the spectrometer are replaced with apparent slits created by focussing the input beams near the entrance plane of the spectrometer. The slit function will then depend on the physical relationship among all of the optical components, the probe volume, and the dispersive performance of the spectrometer and detector, as well as the optical path through density and temperature gradients which may not be invariant in a turbulent system. The presence of high temperatures and turbulence levels can effect the size of the CARS signal origin and the optical path, and as a result, the slit function is not invariant. Ignoring these changes can result in large root mean square temperatures (decreased precision) as well as mean temperature errors. The variability of the slit width can be accounted for on a shot-to-shot basis by using a two parameter (HWHM of the slit function and temperature) fitting routine. For temperatures greater than 1200 K there is convergence on a best curve implying both a temperature and a slit width. This method can be used alone or in concert with various weighting schemes to improve the precision. There are two major advantages gained by allowing the slit function to vary in a CARS system: (a) it allows an increase in the precision; (b) it allows temperatures to be calculated without the assumption that the slit function does not change with temperature or turbulence or position within the flame. In fact, it allows the temperature to be determined with almost no previous knowledge of the slit function except the general shape. These two advantages combine to significantly simplify the study of turbulent combusting systems with CARS and to improve the precision, both point-to-point and shot-to-shot, of CARS.