Stochastic modelling of stratospheric temperature

2021 ◽  
Author(s):  
Mari Eggen ◽  
Kristina Rognlien Dahl ◽  
Sven Peter Näsholm ◽  
Steffen Mæland
Keyword(s):  
Stochastic Model ◽  
Large Scale ◽  
Weather Forecasting ◽  
Stochastic Modelling ◽  
Temperature Data ◽  
Analysis Model ◽  
Stratospheric Temperature ◽  
Stochastic Characterization ◽  
Stratospheric Dynamics ◽  
Volatility Function

<p>A stochastic model for daily-spatial mean stratospheric temperature over a given area is suggested. The model is a sum of a deterministic seasonality function and a Lévy driven vectorial Ornstein-Uhlenbeck process, which is a mean-reverting stochastic process. More specifically, the model is an order 4 continuous-time autoregressive (CAR(4)) process, derived from data analysis suggesting an order 4 autoregressive (AR(4)) process to model the deseasonalized stochastic temperature data empirically. In this analysis, temperature data as represented in ECMWF re-analysis model products are considered. The residuals of the AR(4) process turn out to be normal inverse Gaussian distributed random variables scaled with a time dependent volatility function. In general, it is possible to show that the discrete time AR(p) process is closely related to CAR(p) processes, its continuous counterpart. An equivalent effort is made in deriving a dual stochastic model for stratospheric temperature, in the sense that the year is divided into summer and winter seasons. However, this seems to further complicate the modelling, rather than obtaining a simplified analytic framework. A stochastic characterization of the stratospheric temperature representation in model products, such as the model proposed in this paper, can be used in geophysical analyses to improve our understanding of stratospheric dynamics. In particular, such characterizations of stratospheric temperature may be a step towards greater insight in modelling and prediction of large-scale middle atmospheric events like sudden stratospheric warmings. Through stratosphere-troposphere coupling, this is important in the work towards an extended predictability of long-term tropospheric weather forecasting.</p>

scholarly journals Stochastic Modeling of Stratospheric Temperature

2022 ◽  
Author(s):  
Mari Dahl Eggen ◽  
Kristina Rognlien Dahl ◽  
Sven Peter Näsholm ◽  
Steffen Mæland
Keyword(s):  
Continuous Time ◽  
Autoregressive Model ◽  
Large Scale ◽  
Temperature Model ◽  
Weather Forecasts ◽  
Stratospheric Temperature ◽  
Proposed Model ◽  
Stratospheric Dynamics ◽  
Volatility Function ◽  
Industry Sectors

AbstractThis study suggests a stochastic model for time series of daily zonal (circumpolar) mean stratospheric temperature at a given pressure level. It can be seen as an extension of previous studies which have developed stochastic models for surface temperatures. The proposed model is a combination of a deterministic seasonality function and a Lévy-driven multidimensional Ornstein–Uhlenbeck process, which is a mean-reverting stochastic process. More specifically, the deseasonalized temperature model is an order 4 continuous-time autoregressive model, meaning that the stratospheric temperature is modeled to be directly dependent on the temperature over four preceding days, while the model’s longer-range memory stems from its recursive nature. This study is based on temperature data from the European Centre for Medium-Range Weather Forecasts ERA-Interim reanalysis model product. The residuals of the autoregressive model are well represented by normal inverse Gaussian-distributed random variables scaled with a time-dependent volatility function. A monthly variability in speed of mean reversion of stratospheric temperature is found, hence suggesting a generalization of the fourth-order continuous-time autoregressive model. A stochastic stratospheric temperature model, as proposed in this paper, can be used in geophysical analyses to improve the understanding of stratospheric dynamics. In particular, such characterizations of stratospheric temperature may be a step towards greater insight in modeling and prediction of large-scale middle atmospheric events, such as sudden stratospheric warming. Through stratosphere–troposphere coupling, the stratosphere is hence a source of extended tropospheric predictability at weekly to monthly timescales, which is of great importance in several societal and industry sectors.

Incorporating concepts from physical theory into stochastic modelling of urban runoff pollution

1998 ◽  
Vol 37 (1) ◽  
pp. 179-185
Author(s):  
Morten Grum
Keyword(s):  
Stochastic Model ◽  
Continuous Time ◽  
Measurement Errors ◽  
Physical Theory ◽  
Oxygen Demand ◽  
Stochastic Modelling ◽  
Urban Runoff ◽  
Primary Input ◽  
Deterministic Modelling ◽  
Runoff Pollution

On evaluating the present or future state of integrated urban water systems, sewer drainage models, with rainfall as primary input, are often used to calculate the expected return periods of given detrimental acute pollution events and the uncertainty thereof. The model studied in the present paper incorporates notions of physical theory in a stochastic model of water level and particulate chemical oxygen demand (COD) at the overflow point of a Dutch combined sewer system. A stochastic model based on physical mechanisms has been formulated in continuous time. The extended Kalman filter has been used in conjunction with a maximum likelihood criteria and a non-linear state space formulation to decompose the error term into system noise terms and measurement errors. The bias generally obtained in deterministic modelling, by invariably and often inappropriately assuming all error to result from measurement inaccuracies, is thus avoided. Continuous time stochastic modelling incorporating physical, chemical and biological theory presents a possible modelling alternative. These preliminary results suggest that further work is needed in order to fully appreciate the method's potential and limitations in the field of urban runoff pollution modelling.

Stochastic Modelling of Particle Segregation in a Horizontal Drum Mixer

1992 ◽  
Vol 57 (10) ◽  
pp. 2100-2112 ◽  
Author(s):  
Vladimír Kudrna ◽  
Pavel Hasal ◽  
Andrzej Rochowiecki
Keyword(s):  
Differential Equation ◽  
Diffusion Coefficient ◽  
Stochastic Model ◽  
Diffusion Process ◽  
Stochastic Modelling ◽  
Solid Particles ◽  
Kolmogorov Equation ◽  
Particle Segregation ◽  
Drum Mixer ◽  
Horizontal Drum

A process of segregation of two distinct fractions of solid particles in a rotating horizontal drum mixer was described by stochastic model assuming the segregation to be a diffusion process with varying diffusion coefficient. The model is based on description of motion of particles inside the mixer by means of a stochastic differential equation. Results of stochastic modelling were compared to the solution of the corresponding Kolmogorov equation and to results of earlier carried out experiments.

scholarly journals Comparative Analysis of the Life-Cycle Cost of Robot Substitution: A Case of Automobile Welding Production in China

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 226
Author(s):  
Xuyang Zhao ◽  
Cisheng Wu ◽  
Duanyong Liu
Keyword(s):  
Life Cycle ◽  
Systems Engineering ◽  
Life Cycle Cost ◽  
Manufacturing Systems ◽  
Large Scale ◽  
Cost Allocation ◽  
Industrial Robot ◽  
Case Analysis ◽  
Industrial Robots ◽  
Analysis Model

Within the context of the large-scale application of industrial robots, methods of analyzing the life-cycle cost (LCC) of industrial robot production have shown considerable developments, but there remains a lack of methods that allow for the examination of robot substitution. Taking inspiration from the symmetry philosophy in manufacturing systems engineering, this article further establishes a comparative LCC analysis model to compare the LCC of the industrial robot production with traditional production at the same time. This model introduces intangible costs (covering idle loss, efficiency loss and defect loss) to supplement the actual costs and comprehensively uses various methods for cost allocation and variable estimation to conduct total cost and the cost efficiency analysis, together with hierarchical decomposition and dynamic comparison. To demonstrate the model, an investigation of a Chinese automobile manufacturer is provided to compare the LCC of welding robot production with that of manual welding production; methods of case analysis and simulation are combined, and a thorough comparison is done with related existing works to show the validity of this framework. In accordance with this study, a simple template is developed to support the decision-making analysis of the application and cost management of industrial robots. In addition, the case analysis and simulations can provide references for enterprises in emerging markets in relation to robot substitution.

scholarly journals Hemispherical variance anomaly and reionization optical depth

2020 ◽  
Vol 499 (3) ◽  
pp. 3563-3570
Author(s):  
Márcio O’Dwyer ◽  
Craig J Copi ◽  
Johanna M Nagy ◽  
C Barth Netterfield ◽  
John Ruhl ◽  
...  
Keyword(s):  
Optical Depth ◽  
Large Scale ◽  
Cold Dark Matter ◽  
Signal To Noise Ratio ◽  
Cosmological Parameters ◽  
Temperature Data ◽  
Microwave Background ◽  
Parameter Uncertainties ◽  
Polarization Data ◽  
Best Fitting

ABSTRACT Cosmic microwave background (CMB) full-sky temperature data show a hemispherical asymmetry in power nearly aligned with the Ecliptic, with the Northern hemisphere displaying an anomalously low variance, while the Southern hemisphere appears consistent with expectations from the best-fitting theory, Lambda Cold Dark Matter (ΛCDM). The low signal-to-noise ratio in current polarization data prevents a similar comparison. Polarization realizations constrained by temperature data show that in ΛCDM the lack of variance is not expected to be present in polarization data. Therefore, a natural way of testing whether the temperature result is a fluke is to measure the variance of CMB polarization components. In anticipation of future CMB experiments that will allow for high-precision large-scale polarization measurements, we study how the variance of polarization depends on ΛCDM-parameter uncertainties by forecasting polarization maps with Planck’s Markov chain Monte Carlo chains. We show that polarization variance is sensitive to present uncertainties in cosmological parameters, mainly due to current poor constraints on the reionization optical depth τ, which drives variance at low multipoles. We demonstrate how the improvement in the τ measurement seen between Planck’s two latest data releases results in a tighter constraint on polarization variance expectations. Finally, we consider even smaller uncertainties on τ and how more precise measurements of τ can drive the expectation for polarization variance in a hemisphere close to that of the cosmic-variance-limited distribution.

scholarly journals A Scale-Selective Data Assimilation Approach to Improving Tropical Cyclone Track and Intensity Forecasts in a Limited-Area Model: A Case Study of Hurricane Felix (2007)

2012 ◽  
Vol 27 (1) ◽  
pp. 124-140 ◽  
Author(s):  
Bin Liu ◽  
Lian Xie
Keyword(s):  
Data Assimilation ◽  
Large Scale ◽  
Dynamical Downscaling ◽  
Weather Forecasting ◽  
Forecast Error ◽  
Regional Model ◽  
Small Scale ◽  
Limited Area ◽  
Track Forecast ◽  
Global Models

Abstract Accurately forecasting a tropical cyclone’s (TC) track and intensity remains one of the top priorities in weather forecasting. A dynamical downscaling approach based on the scale-selective data assimilation (SSDA) method is applied to demonstrate its effectiveness in TC track and intensity forecasting. The SSDA approach retains the merits of global models in representing large-scale environmental flows and regional models in describing small-scale characteristics. The regional model is driven from the model domain interior by assimilating large-scale flows from global models, as well as from the model lateral boundaries by the conventional sponge zone relaxation. By using Hurricane Felix (2007) as a demonstration case, it is shown that, by assimilating large-scale flows from the Global Forecast System (GFS) forecasts into the regional model, the SSDA experiments perform better than both the original GFS forecasts and the control experiments, in which the regional model is only driven by lateral boundary conditions. The overall mean track forecast error for the SSDA experiments is reduced by over 40% relative to the control experiments, and by about 30% relative to the GFS forecasts, respectively. In terms of TC intensity, benefiting from higher grid resolution that better represents regional and small-scale processes, both the control and SSDA runs outperform the GFS forecasts. The SSDA runs show approximately 14% less overall mean intensity forecast error than do the control runs. It should be noted that, for the Felix case, the advantage of SSDA becomes more evident for forecasts with a lead time longer than 48 h.

An applied mathematics perspective on stochastic modelling for climate

2008 ◽  
Vol 366 (1875) ◽  
pp. 2427-2453 ◽  
Author(s):  
Andrew J Majda ◽  
Christian Franzke ◽  
Boualem Khouider
Keyword(s):  
Stochastic Model ◽  
General Circulation ◽  
Applied Mathematics ◽  
Low Frequency ◽  
Lattice Models ◽  
Stochastic Modelling ◽  
General Circulation Models ◽  
Teleconnection Patterns ◽  
Slowing Down ◽  
Low Dimensional

Systematic strategies from applied mathematics for stochastic modelling in climate are reviewed here. One of the topics discussed is the stochastic modelling of mid-latitude low-frequency variability through a few teleconnection patterns, including the central role and physical mechanisms responsible for multiplicative noise. A new low-dimensional stochastic model is developed here, which mimics key features of atmospheric general circulation models, to test the fidelity of stochastic mode reduction procedures. The second topic discussed here is the systematic design of stochastic lattice models to capture irregular and highly intermittent features that are not resolved by a deterministic parametrization. A recent applied mathematics design principle for stochastic column modelling with intermittency is illustrated in an idealized setting for deep tropical convection; the practical effect of this stochastic model in both slowing down convectively coupled waves and increasing their fluctuations is presented here.

scholarly journals Stochastic modelling and diffusion modes for proper orthogonal decomposition models and small-scale flow analysis

2017 ◽  
Vol 826 ◽  
pp. 888-917 ◽  
Author(s):  
Valentin Resseguier ◽  
Etienne Mémin ◽  
Dominique Heitz ◽  
Bertrand Chapron
Keyword(s):  
Fluid Flow ◽  
Velocity Component ◽  
Large Scale ◽  
Stochastic Modelling ◽  
Wake Flow ◽  
Small Scale ◽  
Cylinder Wake ◽  
Diffusion Term ◽  
Advection Term ◽  
Dimensional Models

We present here a new stochastic modelling approach in the constitution of fluid flow reduced-order models. This framework introduces a spatially inhomogeneous random field to represent the unresolved small-scale velocity component. Such a decomposition of the velocity in terms of a smooth large-scale velocity component and a rough, highly oscillating component gives rise, without any supplementary assumption, to a large-scale flow dynamics that includes a modified advection term together with an inhomogeneous diffusion term. Both of those terms, related respectively to turbophoresis and mixing effects, depend on the variance of the unresolved small-scale velocity component. They bring an explicit subgrid term to the reduced system which enables us to take into account the action of the truncated modes. Besides, a decomposition of the variance tensor in terms of diffusion modes provides a meaningful statistical representation of the stationary or non-stationary structuration of the small-scale velocity and of its action on the resolved modes. This supplies a useful tool for turbulent fluid flow data analysis. We apply this methodology to circular cylinder wake flow at Reynolds numbers $Re=100$ and $Re=3900$. The finite-dimensional models of the wake flows reveal the energy and the anisotropy distributions of the small-scale diffusion modes. These distributions identify critical regions where corrective advection effects, as well as structured energy dissipation effects, take place. In providing rigorously derived subgrid terms, the proposed approach yields accurate and robust temporal reconstruction of the low-dimensional models.

scholarly journals A Two-Season Impact Study of Radiative Forced Tropospheric Response to Stratospheric Initial Conditions Inferred From Satellite Radiance Assimilation

Climate ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 114
Author(s):  
Min Shao ◽  
Yansong Bao ◽  
George P. Petropoulos ◽  
Hongfang Zhang
Keyword(s):  
Weather Forecasting ◽  
Initial Conditions ◽  
Stratospheric Ozone ◽  
Wrf Model ◽  
Lower Troposphere ◽  
Short Wave ◽  
Advanced Technology ◽  
Short Term ◽  
Radiative Processes ◽  
Stratospheric Temperature

This study investigated the impacts of stratospheric temperatures and their variations on tropospheric short-term weather forecasting using the Advanced Research Weather Research and Forecasting (WRF-ARW) system with real satellite data assimilation. Satellite-borne microwave stratospheric temperature measurements up to 1 mb, from the Advanced Microwave Sounding Unit-A (AMSU-A), the Advanced Technology Microwave Sounder (ATMS), and the Special Sensor microwave Imager/Sounder (SSMI/S), were assimilated into the WRF model over the continental U.S. during winter and summer 2015 using the community Gridpoint Statistical Interpolation (GSI) system. Adjusted stratospheric temperature related to upper stratospheric ozone absorption of short-wave (SW) radiation further lead to vibration in downward SW radiation in winter predictions and overall reduced with a maximum of 5.5% reduction of downward SW radiation in summer predictions. Stratospheric signals in winter need 48- to 72-h to propagate to the lower troposphere while near-instant tropospheric response to the stratospheric initial conditions are observed in summer predictions. A schematic plot illustrated the physical processes of the coupled stratosphere and troposphere related to radiative processes. Our results suggest that the inclusion of the entire stratosphere and better representation of the upper stratosphere are important in regional NWP systems in short-term forecasts.

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