Temperature Probability Distribution Research Articles

Establishing a practical method to accurately determine and manage wellbore thermal behavior in high-temperature drilling

As deeper reservoirs are pursued around the globe, the oil and gas industry has shown a keen interest in high-temperature operations, despite the significant drilling problems such operations pose. In order to formulate guidelines to manage wellbore temperatures accurately and maintain drilling safety, it is crucial to develop a method to quantitatively identify the effects of various parameters, both controllable and uncontrollable, on circulating fluid temperature through sound statistical methods with field validations. In this paper, the transient heat transfer mechanisms of each region of wellbore and formation were investigated. Based on the first law of thermodynamics, a set of transient heat transfer models were developed and solved using the fully implicit finite difference method. The change in the thermal behavior of the wellbore and formation was analyzed to ascertain the range of change in the sensitivity parameters. Using the Monte Carlo simulation technique, the input parameters were treated as uniform, and triangular distributions were applied to estimate the probability distribution of the bottom-hole temperature. The contributing factors of the bottom-hole temperature were ranked based on their level of influences as fluid heat capacity, formation thermal conductivity, inlet temperature, flow rate, and fluid density. The research findings from this study provides a quantitative evaluation of each parameter’s relative significance to circulating fluids temperatures during oil and gas wells or geothermal well drilling operations and therefore provides practical guidance in managing downhole temperatures by identifying the most effective and controllable operation parameters.

Impacts of 1.5 °C and 2 °C global warming on winter snow depth in Central Asia

Snow depth plays an essential role in the water and energy balance of the land surface. It is of special importance in arid and semi-arid regions of Central Asia. Owing to the limited availability of field observations, the spatial and temporal variations of snow depth are still poorly known. Using the Japanese 55-year (JRA-55) and the ERA-Interim reanalysis snow depth products, we considered four global climate models (GCMs) applied in the Inter-Sectoral Impact Model Intercomparison Project (ISI-MIP), examining how they represent snow depth in Central Asia during the period 1986–2005 in terms of spatial and temporal characteristics. We also investigated changes of winter (January–March) snow depth in Central Asia, at 1.5 °C and 2 °C global warming levels. Finally, the joint probabilistic behavior of winter temperature and precipitation at 1.5 °C and 2 °C global warming are investigated using the kernel density estimator (KDE). The result shows that the snow depth climatology of Central Asia is generally well simulated in both spatial pattern and temporal (inter-annual and inter-seasonal) pattern. All models approximately simulate the winter maximum and the summer minimum values of snow depth but tend to overestimate the amplitude during October–December. Only the trend in HadGEM2-ES matches fairly well to the JRA-55 reanalysis snow depth. When comparing the projections of spatial distribution of winter snow depth, distinctive spatial pattern is noted at both 1.5 °C and 2 °C global warming levels, when the snow depth is shown to increase in northeastern and to decrease in midwestern regions of Central Asia. According to the joint probability distributions of precipitation and temperature, Central Asia will tend to experience a warmer and wetter winter at both 1.5 °C and 2 °C global warming levels, which can be associated with an increase in snow depth in the northeastern regions.

The Effect of Human Error on the Temperature Monitoring and Control of Freeze Drying Processes by Means of Thermocouples.

Monitoring product temperature is mandatory in a freeze-drying process, in particular in the process development stage, as final product quality may be jeopardized when its temperature trespasses a threshold value, that is a characteristic of each product being freeze-dried. To this purpose thermocouples are usually inserted in some of the vials of the batch to track product dynamics. The position of the thermocouple inside the vials strongly affects the reading of the temperature evolution during the freeze-drying process and, thus, it is necessary to place them in the right position, in such a way that correct information about product temperature is obtained. In this work, at first, the probability of the operational error resulting into a wrong positioning of the thermocouple inside the vial has been estimated experimentally. Then, the effect of this error has been assessed in terms of risk of exceeding the limit temperature in the primary drying step. Both 4R and 10R vials have been considered, and the investigation evidenced that the probability of incorrect thermocouples placement can reach 30% for 10R vials, and about 32% for 4R vials. These probability values increase, respectively, to 47 and 39% when the trays containing the vials are shifted to their final position. Then, through IR thermal imaging it has been possible to evaluate the temperature gradients in a vial, pointing out that the temperature difference between the product at the center of the vial, where the thermocouple is supposed to be, and that of the wall, that is quite often measured by the thermocouples, can be about 1°C. Therefore, associated to each thermocouple reading there is a probability distribution of product temperature. These figures can be used to assess the risk of exceeding the limit temperature in a freeze-drying process and, thus, to quantify suitable safety margins when evaluating thermocouple readings to take into account the operational errors, given a risk tolerability criteria.

Particle scale modeling of heat transfer in granular flows in a double screw reactor

Heat transfer in granular flows plays an important role in particulate material processing such as food production, pharmaceuticals and biorenewable energy production. Better understanding of the thermodynamics in granular flows is essential for equipment design and product quality control. In this research, a particle-scale heat transfer model was developed within the frame of traditional Discrete Element Method (DEM), which considers both conductive heat transfer and radiative heat transfer among particles. A particle-wall heat transfer model was also proposed for resolving particle-wall conductive and radiative heat transfer. The developed thermal DEM model was validated by modeling heat transfer in packed beds and comparing simulation predictions with experimental measurements. The thermal DEM model was successfully applied to the simulation of heat transfer in binary component granular flows in a double screw reactor designed for biomass fast pyrolysis to gain better understanding of the heat transfer in the system. The existence of both spatial and temporal temperature oscillations is observed in the double screw reactor. The effects of the operating conditions on the average temperature profile, biomass particle temperature probability distribution, heat flux and heat transfer coefficient are analyzed. Results indicate that the particle-fluid-particle conductive heat transfer pathways are the dominant contributors to the total heat flux, which accounts for approximately 70%–80% in the total heat flux. Radiative heat transfer contributes 14%–26% to the total heat flux and the conductive heat transfer through contact surface takes only 1%–5% in the total heat flux. The total heat transfer coefficient in the double screw reactor is also reported, which varies from 70 to 110 W/(m2 ⋅K) depending on the operating conditions.

Model for calorimetric measurements in an open quantum system

We investigate the experimental setup proposed in [New J. Phys., 15, 115006 (2013)] for calorimetric measurements of thermodynamic indicators in an open quantum system. As theoretical model we consider a periodically driven qubit coupled with a large yet finite electron reservoir, the calorimeter. The calorimeter is initially at equilibrium with an infinite phonon bath. As time elapses, the temperature of the calorimeter varies in consequence of energy exchanges with the qubit and the phonon bath. We show how under weak coupling assumptions, the evolution of the qubit-calorimeter system can be described by a generalized quantum jump process including as dynamical variable the temperature of the calorimeter. We study the jump process by numeric and analytic methods. Asymptotically with the duration of the drive, the qubit-calorimeter attains a steady state. In this same limit, we use multiscale perturbation theory to derive a Fokker--Planck equation governing the calorimeter temperature distribution. We inquire the properties of the temperature probability distribution close and at the steady state. In particular, we predict the behavior of measurable statistical indicators versus the qubit-calorimeter coupling constant.

Weak Cooling of Cold Extremes Versus Continued Warming of Hot Extremes in China During the Recent Global Surface Warming Hiatus

AbstractUsing daily maximum temperature (Tmax), minimum temperature (Tmin), and mean temperature data of 437 weather stations in China, we compared variations of the mean with extreme ends of probability distribution of temperatures in China from 1960 to 2015. Our analysis confirmed that annual mean Tmax and Tmin experienced warming hiatus in China after 1998. The warming hiatus is also reflected by the weak cooling of cold extremes across China, but hot extremes continue the significant warming trend nationally and in climate regions of East China, Southwest China, and the Tibetan Plateau. During 1999–2015, the hot day frequency (Tx90, based on base period 1961–1990) and averaged Tmax above the 90th percentile of each year (Txp90) increased significantly by 3.70 d/decade and 0.20°C/decade nationally. But there were significant cooling trends of cold extremes in East China and Southeast China from 1999 to 2015. During the warming hiatus period, the obvious decline in warm season precipitation contributed to the ongoing warming of hot extremes in East China and Southwest China. Both the decrease of warming season solar irradiance and increase of warm season precipitation facilitated the weak cooling trends of hot extremes in Northeast China and North China Plain. Although mean temperature experienced warming hiatus after 1998, the continued warming of hot extremes and reverse from warming to weak cooling of cold extremes imply an increase of temperature variability in China simultaneously.

Energy Consumption Scheduling of HVAC Considering Weather Forecast Error Through the Distributionally Robust Approach

In this paper, the distributionally robust optimization approach (DROA) is proposed to schedule the energy consumption of the heating, ventilation and air conditioning (HVAC) system with consideration of the weather forecast error. The maximum interval of the outdoor temperature is partitioned into subintervals, and the proposed DROA constructs the ambiguity set of the probability distribution of the outdoor temperature based on the probabilistic information of these subintervals of historical weather data. The actual energy consumption will be adjusted according to the forecast error and the scheduled consumption in real time. The energy consumption scheduling of HVAC through the proposed DROA is formulated as a nonlinear problem with distributionally robust chance constraints. These constraints are reformulated to be linear and then the problem is solved via linear programming. Compared with the method that takes into account the weather forecast error based on the mean and the variance of historical data, simulation results demonstrate that the proposed DROA effectively reduces the electricity cost with less computation time, and the electricity cost is reduced compared with the traditional robust method.

Humidity build-up in electronic enclosures exposed to different geographical locations by RC modelling and reliability prediction

Electronic devices are exposed to a wide range of climatic conditions. This study shows a reliability prediction of electronic devices exposed to different climates (from arid to humid and cold to hot regions). Temperature and humidity probability distribution functions have been calculated to indicate the change of climate exposure along year. While temperature and relative humidity (RH) are important factors in terms of water diffusion and electronic reliability, the internal climatic condition of 25 °C and 60% RH is widely used as threshold for electronic safety. Acceleration factors according to this steady state (25 °C and 60% RH) have been calculated for the different climates, and the protection offered by the enclosures has been estimated under different casing materials and resistor-capacitor (RC) simulation. This method offers a way to predict the average value of failure rate for electronic devices based on climate information and enclosure material.

Heat wave probability in the changing climate of the Southwest US

Analyses of observed non-Gaussian daily minimum and maximum temperature probability distribution functions (PDFs) in the Southwest US highlight the importance of variance and warm tail length in determining future heat wave probability. Even if no PDF shape change occurs with climate change, locations with shorter warm tails and/or smaller variance will see a greater increase in heat wave probability, defined as exceedances above the historical 95th percentile threshold, than will long tailed/larger variance distributions. Projections from ten downscaled CMIP5 models show important geospatial differences in the amount of warming expected for a location. However, changes in heat wave probability do not directly follow changes in background warming. Projected changes in heat wave probability are largely explained by a rigid shift of the daily temperature distribution. In some locations where there is more warming, future heat wave probability is buffered somewhat by longer warm tails. In other parts of the Southwest where there is less warming, heat wave probability is relatively enhanced because of shorter tailed PDFs. Effects of PDF shape changes are generally small by comparison to those from a rigid shift, and fall within the range of uncertainty among models in the amount of warming expected by the end of the century.

Quantitative risk assessment of the effects of drought on extreme temperature in eastern China

AbstractHot extremes may lead to disastrous impacts on human health and agricultural production. Previous studies have revealed the feedback between drought and hot extremes in large regions of eastern China, while quantifying the impact of antecedent drought on hot extremes has been limited. This study aims at quantitatively assessing the risk of extreme temperature conditioned on the antecedent drought condition represented by Standardized Precipitation Index (SPI) during summer time in eastern China. A copula‐based model is proposed to construct the joint probability distribution of extreme temperature and drought based on 6 month SPI (SPI6). Accordingly, the conditional probability distribution is employed to quantify impacts of antecedent dry (and wet) conditions on the exceedance probability of extreme temperature. Results show that the likelihood of extreme temperature exceeding high quantiles is higher given antecedent dry conditions than that given antecedent wet conditions in large regions from southwestern to northeastern China. Specifically, the conditional probability difference of temperature exceeding 80th percentile given SPI6 lower than or equal to −0.5 and SPI6 higher than 0.5 is around 0.2–0.3. The case study of the 2006 summer hot extremes and drought in Sichuan and Chongqing region shows that the conditional return period of extreme temperature conditioned on antecedent drought is around 5–50 years shorter than univariate return period. These results quantify the impact of antecedent drought on subsequent extreme temperature and highlight the important role of antecedent drought in intensifying hot extremes in these regions.

Giant dipole resonance and shape transitions in hot and rotating Mo88

The giant dipole resonance (GDR) observables are calculated within the thermal shape fluctuation model by considering the probability distributions of different angular momentum ($I$) and temperature ($T$) values estimated recently in the deexcitation process of the compound nucleus $^{88}\mathrm{Mo}$. These results are found to be very similar to the results obtained with the average $T$ (${T}_{\mathrm{ave}}$) and average $I$ (${I}_{\mathrm{ave}}$) corresponding to those distributions. The shape transitions in $^{88}\mathrm{Mo}$ at different $T$ and $I$ are also studied through the free energy surfaces calculated within the microscopic-macroscopic approach. The deformation of $^{88}\mathrm{Mo}$ is found to increase considerably with $T$ and $I$, leading to the Jacobi shape transition at $I\ensuremath{\sim}50\phantom{\rule{0.28em}{0ex}}\ensuremath{\hbar}$. The combined effect of increasing deformation, larger fluctuations at higher $T$, and larger Coriolis splitting of GDR components at higher $I$, leads to a rapid increase in the GDR width.

Contribution of urbanization to the increase of extreme heat events in an urban agglomeration in east China

AbstractThe urban agglomeration of Yangtze River Delta (YRD) is emblematic of China's rapid urbanization during the past decades. Based on homogenized daily maximum and minimum temperature data, the contributions of urbanization to trends of summer extreme temperature indices (ETIs) in YRD are evaluated. Dynamically classifying the observational stations into urban and rural, this study presents unexplored changes in temperature extremes during the past four decades in YRD and quantifies the amplification of the positive trends in ETIs by the urban heat island effect. Overall, urbanization contributes to more than one third of the increase of intensity of extreme heat events in the region, which is comparable to the contribution of greenhouse gases. Compared to rural stations, more notable shifts to the right in the probability distribution of temperature and ETIs are found in urban stations. The rapid urbanization in YRD has resulted in large increases in the risk of heat extremes.

Distribution and trend in the thermal growing season in China during 1961–2015

Based on daily mean temperature at 1863 meteorological stations in China, the trend in the thermal growing season was investigated and time-evolving probability distributions of temperature were examined. Results showed that during 1961–2015, the growing season was extended at rates of 1.5–5.0 days decade−1 in Northeast China, North China, Northwest China, and western and central parts of Southwest China. This change was ascribed to an earlier start of the growing season at rates of 1.5–3.0 days decade−1 in North China, the northern and western parts of Northeast China, and the northeastern part of Northwest China, and a later end at rates of 0.5–2.5 days decade−1 in Northwest China, the western and northern parts of Southwest China, and the northwest of North China. The earlier start of the growing season was in accordance with the rapid warming of lower portions of the spring temperature distribution in Northeast China, North China, and Northwest China. The later end of the growing season corresponded to rapid warming in the lower percentiles of autumn temperature distribution in Northwest China. The growing season is more sensitive to warming of lower percentiles of temperature distribution than other portions.

Temperature trends and prediction skill in NMME seasonal forecasts

The North American Multi-Model Ensemble (NMME) provides hindcasts and real-time predictions for monthly mean climate fields at lead times of up to a year. These global climate model outputs can be useful in constructing improved seasonal forecasts. Here, several simple methods are developed and evaluated for forecasting monthly temperatures up to a year in advance based on either unweighted or weighted NMME outputs, and compared to previously developed statistical forecast methods that use only time series of past observations. It is found that the NMME-based methods produce forecast temperature probability distributions that are appropriately shifted toward the warm end of past experience and also show skill at representing interannual variability. NMME-based methods clearly outperformed purely statistical methods for forecasting temperatures over ocean, though over land this improvement is less clear over the evaluation period tested. The NMME seasonal forecasts may be particularly useful for giving early warning of heat waves, given their societal significance and higher conditional skill under those conditions.

Evolution of mean, variance and extremes in 21st century temperatures

Warming of the climate system can result in very large corresponding changes in the occurrence of climate extremes. Temperature extremes may occur due to a shift in the whole distribution, where there is an increase in the entire temperature probability distribution, or to changes in the shape of the distribution, such as an increase in variability causing a widening of the distribution. Understanding the precise characteristics of changes in temperature distributions in response to background warming is an important aspect of fully understanding changes in heat extremes and their associated impacts on human and ecosystem health. This study investigates projected 21st century changes in the characteristics of mean, maximum and minimum temperature on daily- and annual- timescales for various regions (Australia, Asia, Europe and North America) using data from seven models participating in the Coupled Model Intercomparison Phase 5 (CMIP5). Using the RCP8.5 experiment we show that an increase in mean temperature throughout the 21st century is a consistent feature of all models for each region. Changes in the variance of simulated temperatures are equivocal, with the sign and magnitude of variance changes in the 21st century varying in different models and regions. A quantile regression analysis demonstrates differences in upper and lower quantile slopes, relative to the mean, including a consistent skew in daily temperatures towards hot extremes. These potentially complex characteristics of temperature changes should not be overlooked, as temperature extremes are potentially more sensitive to changes in the variance and higher order moments than in the mean. Furthermore, a wider range of extreme temperature behaviour may have important consequences for various stakeholders, due to impacts on public health, agriculture and ecological systems.

Quantifying the attribution of model bias in simulating summer hot days in China with IAP AGCM 4.1

AbstractUsing IAP AGCM simulation results for the period 1961–2005, summer hot days in China were calculated and then compared with observations. Generally, the spatial pattern of hot days is reasonably reproduced, with more hot days found in northern China, the Yangtze and Huaihe River basin, the Chuan-Yu region, and southern Xinjiang. However, the model tends to overestimate the number of hot days in the above-mentioned regions, particularly in the Yangtze and Huaihe River basin where the simulated summer-mean hot days is 13 days more than observed when averaged over the whole region, and the maximum overestimation of hot days can reach 23 days in the region. Analysis of the probability distribution of daily maximum temperature (Tmax) suggests that the warm bias in the model-simulated Tmax contributes largely to the overestimation of hot days in the model. Furthermore, the discrepancy in the simulated variance of the Tmax distribution also plays a non-negligible role in the overestimation of hot days. I...

5 kHz thermometry in a swirl-stabilized gas turbine model combustor using chirped probe pulse femtosecond CARS. Part 2. Analysis of swirl flame dynamics

We have performed a detailed analysis of the temperature field in a turbulent swirl flame operating with a self-excited thermo-acoustic instability. The temperature field was measured using 5 kHz chirped-probe-pulse (CPP) femtosecond (fs) coherent anti-Stokes Raman scattering (CARS). The measurements are described in detail in the part 1 companion article. In this paper, part 2, a detailed analysis of the time-resolved temperature measurements and simultaneous pressure measurements is performed to provide insight into the dynamics and structure of the swirl-stabilized flame. This work is the first to capture the dynamics of the flame, flow, and coupled flow-flame processes using high-fidelity, spatially- and temporally-resolved thermometry in a flame of practical relevance. The time-averaged contour plot of the temperature field indicates that the flame is very flat and stabilizes approximately 10 mm downstream of the burner face. In this region, there are very significant temperature fluctuations indicating a very high level of unsteadiness. The temperature probability distribution functions (PDFs) are clearly bimodal in this region near the injector face. A Fourier analysis of the temperature time series revealed multiple coherent oscillatory modes. The strongest oscillation was found to be coherent and in-phase with an acoustic resonance at 314 Hz, as expected from the Rayleigh criteria for the unstable flame. An analysis of the phase-conditioned average temperature fields clearly shows an axial pumping of low-temperature reactants, which are consumed after a convective delay and result in a spike in the global heat-release rate. Continued analysis also revealed a 438 Hz oscillation that was found to correspond with the dynamics of convective transport by a helical precessing vortex core (PVC). The structure of the PVC, and its interaction with the flame, were studied based on the presence of this characteristic frequency in the power spectral densities computed throughout the flow. The precision and time-resolution of the CPP fsCARS measurements was also sufficient to enable computation of the integral time-scales as well as the PDFs of the temporal temperature gradients. A sample of state space trajectories were used to provide insight into the nature of coupling between the narrowband acoustic resonance and the broadband spectrum of turbulent flame processes.

GRADIENT-DIFFUSION CLOSURE AND THE EJECTION-SWEEP CYCLE IN CONVECTIVE BOUNDARY LAYERS

The inadequacy of conventional gradient-diffusion closure in modeling turbulent heat flux within the convective atmospheric boundary-layer is often alleviated by accounting for nonlocal transport. Such nonlocal effects are a manifestation of the inherent asymmetry in vertical transport in the convective boundary layer, which is in turn associated with third-order moments (skewness and fluxes of fluxes). In this work, the role of these third-order moments in second-order turbulence closure of the sensible heat flux is examined with the goal of reconciling the models to various closure assumptions. Surface layer similarity theory and mixed-layer parametrizations are used here, complemented by LES results when needed. The turbulent heat flux with various closure assumptions of the flux transport term is solved, including both local and nonlocal approaches. We connect to ejection-sweep cycles in the flow field using the GramCharlier cumulant expansion of the joint probability distribution of vertical velocity and potential temperature. In this nonlocal closure, the transport asymmetry models that include the vertical velocity skewness as a correction term to H originate from ejection-sweep events. Vertical inhomogeneity results in a modified-skewness correction to the nonlocal contribution to the heat flux associated with the relative intensity of ejections and sweeps.

Markov Chain Monte Carlo inversion of temperature and salinity structure of an internal solitary wave packet from marine seismic data

AbstractMarine seismic reflection technique is used to observe the strong ocean dynamic process of nonlinear internal solitary waves (ISWs or solitons) in the near‐surface water. Analysis of ISWs is problematical because of their transient nature and limitations of classical physical oceanography methods. This work explores a Markov Chain Monte Carlo (MCMC) approach to recover the temperature and salinity of ISW field using the seismic reflectivity data and in situ hydrographic data. The MCMC approach is designed to directly sample the posterior probability distributions of temperature and salinity which are the solutions of the system under investigation. The principle improvement is the capability of incorporating uncertainties in observations and prior models which then provide quantified uncertainties in the output model parameters. We tested the MCMC approach on two acoustic reflectivity data sets one synthesized from a CTD cast and the other derived from multichannel seismic reflections. This method finds the solutions faithfully within the significantly narrowed confidence intervals from the provided priors. Combined with a low frequency initial model interpreted from seismic horizons of ISWs, the MCMC method is used to compute the finescale temperature, salinity, acoustic velocity, and density of ISW field. The statistically derived results are equivalent to the conventional linearized inversion method. However, the former provides us the quantified uncertainties of the temperature and salinity along the whole section whilst the latter does not. These results are the first time ISWs have been mapped with sufficient detail for further analysis of their dynamic properties.

Projections of high resolution climate changes for South Korea using multiple-regional climate models based on four RCP scenarios. Part 1: surface air temperature

We projected surface air temperature changes over South Korea during the mid (2026-2050) and late (2076-2100) 21st century against the current climate (1981-2005) using the simulation results from five regional climate models (RCMs) driven by Hadley Centre Global Environmental Model, version 2, coupled with the Atmosphere- Ocean (HadGEM2-AO), and two ensemble methods (equal weighted averaging, weighted averaging based on Taylor’s skill score) under four Representative Concentration Pathways (RCP) scenarios. In general, the five RCM ensembles captured the spatial and seasonal variations, and probability distribution of temperature over South Korea reasonably compared to observation. They particularly showed a good performance in simulating annual temperature range compared to HadGEM2-AO. In future simulation, the temperature over South Korea will increase significantly for all scenarios and seasons. Stronger warming trends are projected in the late 21st century than in the mid-21st century, in particular under RCP8.5. The five RCM ensembles projected that temperature changes for the mid/late 21st century relative to the current climate are +1.54°C/+1.92°C for RCP2.6, +1.68°C/+2.91°C for RCP4.5, +1.17°C/+3.11°C for RCP6.0, and +1.75°C/+4.73°C for RCP8.5. Compared to the temperature projection of HadGEM2-AO, the five RCM ensembles projected smaller increases in temperature for all RCP scenarios and seasons. The inter-RCM spread is proportional to the simulation period (i.e., larger in the late-21st than mid-21st century) and significantly greater (about four times) in winter than summer for all RCP scenarios. Therefore, the modeled predictions of temperature increases during the late 21st century, particularly for winter temperatures, should be used with caution.