Covariate-based stochastic parameterization of baroclinic ocean eddies

We present a study of the distribution of ozone in the lowermost stratosphere with the goal of characterizing the observed variability. The air in the lowermost stratosphere is divided into two population groups based on Ertel's potential vorticity at 300 hPa. High (low) potential vorticity at 300 hPa indicates that the tropopause is low (high), and the identification of these two groups is made to account for the dynamic variability. Conditional probability distribution functions are used to define the statistics of the ozone distribution from both observations and a three‐dimensional model simulation using winds from the Goddard Earth Observing System Data Assimilation System for transport. Ozone data sets include ozonesonde observations from northern midlatitude stations (1991–1996) and midlatitude observations made by the Halogen Occultation Experiment (HALOE) on the Upper Atmosphere Research Satellite (UARS) (1994–1998). The conditional probability distribution functions are calculated at a series of potential temperature surfaces spanning the domain from the midlatitude tropopause to surfaces higher than the mean tropical tropopause (∼380 K). The probability distribution functions are similar for the two data sources, despite differences in horizontal and vertical resolution and spatial and temporal sampling. Comparisons with the model demonstrate that the model maintains a mix of air in the lowermost stratosphere similar to the observations. The model also simulates a realistic annual cycle. Results show that during summer, much of the observed variability is explained by the height of the tropopause. During the winter and spring, when the tropopause fluctuations are larger, less of the variability is explained by tropopause height. This suggests that more mixing occurs during these seasons. During all seasons, there is a transition zone near the tropopause that contains air characteristic of both the troposphere and the stratosphere. The relevance of the results to the assessment of the environmental impact of aircraft effluence is also discussed.

Conditional statistical properties of the complex systems having long-duration memory

Operational forest fire danger rating systems rely on the recent evolution of meteorological variables to estimate dead fuel condition. Further combining the latter with meteorological and environmental variables, they predict fire occurrence and spread. In this study we retrieved live fuel condition from MODIS multispectral measurements in the near infrared and shortwave infrared. Next, we combined these retrievals with an extensive dataset on actual forest fires in Campania (13,595 km2), Italy, to determine how live fuel condition affects the probability distribution functions of fire characteristics. Accordingly, the specific objective of this study was to develop and evaluate a new approach to estimate the probability distribution functions of fire burned area, duration and rate of spread as a function of the Perpendicular Moisture Index (PMI), whose value decreases with decreasing live fuel moisture content (LFMC). To this purpose, available fire data was intersected with MODIS 8-day composited reflectance data so to associate each fire event with the corresponding pre-fire PMI observation. Fires were then grouped in ten decile bins of PMI, and the conditional probability distribution functions of burned area, fire duration and rate of spread were determined in each bin. Distributions of burned area and rate of spread vary across PMI decile bins, while no significant difference was observed for fire duration. Further testing this result with a likelihood ratio test confirmed that PMI is a covariate of burned area and rate of spread, but not of fire duration. We defined an extreme event as a fire whose burned area (respectively rate of spread) exceeds the 95th percentile of the frequency distribution of all observed fire events. The probability distribution functions in the ten decile bins of PMI were combined to obtain a conditional probability distribution function, which was then used to predict the probability of extreme fires, as defined. It was found that the probability of extreme events steadily increases with decreasing PMI. Overall, at the end of the dry season the probability of extreme events is about the double than at the beginning. These results may be used to produce frequently (e.g. daily) updated maps of the probability of extreme events given a PMI map retrieved from e.g. MODIS reflectance data.

A lattice Boltzmann (LB) model with overall second-order accuracy is applied to the 1.5-layer shallow water equation for a wind-driven double-gyre ocean circulation. By introducing the second-order integral approximation for the collision operator, the model becomes fully explicit. In this case, any iterative technique is not needed. The Coriolis force and other external forces are included in the model with second-order accuracy, which is consistent with the discretized accuracy of the LB equation. The numerical results show correct physics of the ocean circulation driven by the double-gyre wind stress with different Reynolds numbers and different spatial resolutions. An intrinsic low-frequency variability of the shallow water model is also found. The wind-driven ocean circulation exhibits subannual and interannual oscillations, which are comparable to those of models in which the conventional numerical methods are used.

Pseudo-measurements are artificially generated estimates derived from historical data to represent power system variables that are not directly measured in real-time. In active distribution networks (ADNs), where the limited sensor coverage and high uncertainty from distributed energy resources (DERs) exist, pseudo-measurements are essential for ensuring the system observability. This paper presents a deep learning model for the pseudo-measurement generation in active distribution networks. The model uses a Quantized SoftMax Network (QSN) to estimate conditional probability distribution functions (CPDFs) without assuming any predefined statistical model. To capture spatial and temporal patterns, the QSN is combined with convolutional neural networks (CNNs), gated recurrent units (GRUs), and an attention mechanism. The proposed model is tested on the IEEE 123-bus system using real residential load and renewable generation data. Results show that the proposed model provides more accurate and reliable pseudo-measurements compared to existing conditional kernel density estimator (CKDE) and deep mixture density network (DMDN)-based models.

Copula based post-processing for improving the NMME precipitation forecasts

On the anti-causal path of the path probability method by Kikuchi

The effect of sawteeth on plasma performance and transport in the plasma of tokamak is an important problem in the fusion field. Sawtooth oscillations can trigger off heat and turbulence pulses that propagate into the edge plasma, and thus enhancing the edge shear flow and inducing a transition from low confinement mode to high confinement mode. The influences of turbulence spreading and symmetry breaking on edge shear flow with sawtooth crashes are observed in the J-TEXT tokamak. The edge plasma turbulence and shear flow are measured using a fast reciprocating electrostatic probe array. The experimental data are analyzed using some methods such as conditional average and probability distribution function. After sawtooth crashes, the heat and turbulence pulses in the core propagate to the edge, with the turbulence pulse being faster than the heat pulse. The attached figures (a)–(e) show the core electron temperature, and the edge electron temperature, turbulence intensity, turbulence drive and spreading rates, Reynolds stress and its gradient, and shearing rates, respectively. After sawtooth crashes, the edge electron temperature increases and the edge turbulence is enhanced, with turbulence preceding temperature. The enhanced edge turbulence is mainly composed of two parts: the turbulence driven by local gradient and the turbulence spreading from core to edge. The development of the estimated turbulence spreading rate is prior to that of the turbulence driving rate. The increase in the turbulence intensity can cause the turbulent Reynold stress and its gradient to increase, thereby enhancing shear flows and radial electric fields. Turbulence spreading leads the edge Reynolds stresses to develop and the shear flow to be faster than edge electron temperature. The Reynolds stress arises from the symmetry breaking of the turbulence wave number spectrum. After sawtooth collapses, the joint probability density function of radial wave number and poloidal wave number of turbulence intensity becomes highly skewed and anisotropic, exhibiting strong asymmetry, which can be seen in attached figures (f) and (g). The development of turbulence spreading flux at the edge is also prior to the particle flux driven by turbulence, indicating that turbulent energy transport is not simply accompanied by turbulent particle transport. These results show that the turbulence spreading and symmetry breaking can enhance turbulent Reynolds stress, thereby driving shear flows, after sawtooth has crashed.

Using the two-point Edgeworth series up to second order in the linear rms density fluctuation we construct the weakly non-linear conditional probability distribution function for the density field around an overdense region. This requires calculating the two-point analogues of the skewness parameter S3. We test the dependence of the two-point skewness on distance from the peak for scale-free power spectra and Gaussian smoothing. The statistical features of such a conditional distribution are given as the values obtained within linear theory corrected by the terms that arise as a result of weakly non-linear evolution. The expected density around the peak is found to be always below the linear prediction while its dispersion is always larger than in the linear case. For large enough overdensities the weakly non-linear corrections can be more significant than the peak constraint introduced by Bardeen et al. We apply these results to the spherical model of collapse as developed by Hoffman & Shaham and find that in general the effect of weakly non-linear interactions is to decrease the scale from which a peak gathers mass and therefore also the mass itself. In the case of an open universe this results in steepening of the final profile of the virialized proto-object.

This paper studies the effects of time-dependent, mesoscale turbulence on the wind-driven ocean circulation in a closed basin with variable topography. Numerical simulations of a single-layer fluid with finite topography at the sloping boundaries are performed. The flow is forced by a suitable combination of a steady, basin-scale wind that generates the classical western-intensified anticyclonic gyre, plus a shorter, time-dependent forcing that injects energy at a narrow range of scales. Two contrasting situations are considered. First, in the absence of the large-scale forcing, the turbulence generates a cyclonic flow that follows the geostrophic contours around the basin. Second, the resulting mean circulation is studied when the large and small-scale forcing terms are considered together. In particular, it is discussed that the alteration of the anticyclonic gyre may be due to the turbulent-induced cyclonic circulation.

Consider the sample X1, X2, ..., XN of N independent and identically distributed (iid) random variables with common cumulative distribution function (cdf)F, and let Fu be their conditional excess distribution function F. We define the ordered sample by . Pickands (1975), Balkema and de Haan (1974) posed that for a large class of underlying distribution functions F , and large u ,Fu is well approximated by the Generalized Pareto Distribution.The mixed method is a method for determining thresholds. This method consists in minimizing the variance of a convex combination of other thresholds.The objective of the mixed method is to determine by which probability distribution one can approach this conditional distribution. In this article, we propose a theorem which specifies the conditional distribution of excesses when the deterministic threshold tends to the end point.

A random variable Y 1 is said to be smaller than Y 2 in the increasing concave stochastic order if for all increasing concave functions for which the expected values exist, and smaller than Y 2 in the increasing convex order if for all increasing convex ψ. This article develops nonparametric estimators for the conditional cumulative distribution functions of a response variable Y given a covariate X, solely under the assumption that the conditional distributions are increasing in x in the increasing concave or increasing convex order. Uniform consistency and rates of convergence are established both for the K-sample case and for continuously distributed X.

Wind-driven ocean circulation—Part 2. Numerical solutions of the non-linear problem

The vertically averaged equations of motion for the barotropic model of wind-driven ocean circulation on the β-plane are discussed. An attempt is made to evaluate the two non-dimensional parameters, viz., the Rossby number, R , and the (bottom) frictional parameter, ?, by comparing observed scales with those derived from simple boundary layer arguments. It is found that ? and R are (upper) bounded for the model if one imposes the scale of the Gulf Stream as the smallest significant scale of the ocean. Maximum values for the bottom-friction coefficient and for the ratio of wind-stress to depth of the model are determined. The general problem of analyzing the equations by approximate (numerical) techniques is discussed and a proposal is made to carry out the analysis by working with limited representations and correspondingly exaggerated values of the parameters. Finally a comparison is made of the error involved in treating Stommel's steady, linear, frictional model by two approximate methods, a limited Fourier representation and a finite-difference scheme. The latter is found to describe the solution of the linear model with considerably less distortion than the former. Flans to treat the fully non-linear, time-dependent system are described. DOI: 10.1111/j.2153-3490.1965.tb00196.x

The Use of Conditional Probability Functions in Range Data Analysis and Simulation