Stochastic Cloud Model Research Articles

A Novel Stochastic Cloud Model for Statistical Characterization of Wind Turbine Output

To overcome the problems of wind power forecast for the current deterministic wind power turbine output model cannot accurately describe the statistical characterization of wind turbine output, this article proposes a novel wind power stochastic cloud model. There are three steps to build this model. Firstly, it is necessary to analyze the power data and to filter out the disturbed data by utilizing the improved Bin method and data fitting. Secondly, it is available to obtain respectively two groups of the expectation, entropy and hyper entropy of the waist and upper data of stochastic cloud model by the known and unknown membership of backward cloud generators. Finally, the wind-speed data can be transformed into a stochastic cloud model, which is composed of X condition cloud generator and the positive cloud generator component. In short, the comparative data of the wind power cloud droplets and the measured data of wind power show that the line correlation coefficient of the wind power frequency of the proposed model reaches to 0.8868, which could simulate the statistical characterization of wind turbine output effectively.

The cloud model based stochastic multi-criteria decision making technology for river health assessment under multiple uncertainties

The river health assessment (RHA) usually concerns multiple criteria including streamflow, ecology, physical structure, water quality and social service functions and evaluation standards formulated by managers as well as groups with different interests. Conventional multi-criteria decision making (MCDM) models are used to comprehensively evaluate river condition through multiple criteria under deterministic environment. In fact, uncertainties are always existed in these criteria data since they are correlated with hydrology and water resources system. In this work, we proposed a stochastic cloud model based MCDM framework for solving RHA considering multiple uncertainties in criteria performance values (PVs) and criteria weights (CWs). The cloud model is allied to describe uncertainty of PVs using numerous drops following normal distribution generated by forward drop generator (FDG). The minimum deviation principle based aggregated CWs are utilized to efficiently quantify uncertainty in CWs and reduce conflict between multiple CWs sources. A novel stochastic multi-criteria acceptability analysis (SMAA) is developed coupling with grey correlation analysis (GCA) and TOPSIS. The risk information for river evaluation caused by multiple uncertainties are described using quantified decision error risk (QDER) and rank uncertainty degree (RUD). The proposed methodology is verified practicability by applying it to river health evaluation in Taihu basin. The numerical simulations are conducted to demonstrate superiority and efficiency of novel SMAA in comparison with conventional SMAA and deterministic MCDM models based on GCA and TOPSIS. The robustness analysis is implemented to disclose its computation stability and reliability as well as effects of cloud parameters on final MCDM results. The results of novel SMAA show that it provides river managers with comprehensive river health and risk analysis information, assisting them to make highly reliable assessment and adopt effective measures harnessing rivers.

Coastal Tropical Convection in a Stochastic Modeling Framework

AbstractRecent research has suggested that the overall dependence of convection near coasts on large‐scale atmospheric conditions is weaker than over the open ocean or inland areas. This is due to the fact that in coastal regions convection is often supported by meso‐scale land‐sea interactions and the topography of coastal areas. As these effects are not resolved and not included in standard cumulus parametrization schemes, coastal convection is among the most poorly simulated phenomena in global models. To outline a possible parametrization framework for coastal convection we develop an idealized modeling approach and test its ability to capture the main characteristics of coastal convection. The new approach first develops a decision algorithm, or trigger function, for the existence of coastal convection. The function is then applied in a stochastic cloud model to increase the occurrence probability of deep convection when land‐sea interactions are diagnosed to be important. The results suggest that the combination of the trigger function with a stochastic model is able to capture the occurrence of deep convection in atmospheric conditions often found for coastal convection. When coastal effects are deemed to be present the spatial and temporal organization of clouds that has been documented form observations is well captured by the model. The presented modeling approach has therefore potential to improve the representation of clouds and convection in global numerical weather forecasting and climate models.

A stochastic cloud model for cloud and ozone retrievals from UV measurements

The new generation of satellite instruments provides measurements in and around the Oxygen A-band on a global basis and with a relatively high spatial resolution. These data are commonly used for the determination of cloud properties. A stochastic model and radiative transfer model, previously developed by the authors, is used as the forward model component in retrievals of cloud parameters and ozone total and partial columns. The cloud retrieval algorithm combines local and global optimization routines, and yields a retrieval accuracy of about 1% and a fast computational time. Retrieved parameters are the cloud optical thickness and the cloud-top height. It was found that the use of the independent pixel approximation instead of the stochastic cloud model leads to large errors in the retrieved cloud parameters, as well as, in the retrieved ozone height resolved partial columns. The latter can be reduced by using the stochastic cloud model to compute the optimal value of the regularization parameter in the framework of Tikhonov regularization.

Testing particle filters on simple convective‐scale models Part l: A stochastic cloud model

Convective‐scale applications require data assimilation methods that can cope with nonlinear dynamics and the stochastic nature of convection. For this application, the particle filter is a promising data assimilation method because it estimates the probability density function (PDF) of the atmospheric state and not only its first two moments. However, in order to represent PDFs with a small number of particles, the particle filter is usually combined with another data assimilation technique. In this article we investigate a hybrid algorithm, the nudging proposal particle filter, which combines the sequential importance resampling particle filter with nudging.Analytic and experimental results on an idealized, nonlinear, one‐dimensional model are used to show that there exists a combination of the two methods such that the nudging proposal particle filter outperforms both of its components. In this article, a stochastic cloud model, represented through a birth–death process, serves as a first test model for the filter. The transition probability density can be calculated exactly for this model, thus providing insight into its contribution to the selection of particles during resampling. The functioning mechanism of the nudging proposal particle filter in its simplest form is investigated and the impact of the model parameters on the filter's behaviour highlighted.

A simple model for the cloud adjacency effect and the apparent bluing of aerosols near clouds

In determining aerosol‐cloud interactions, the properties of aerosols must be characterized in the vicinity of clouds. Numerous studies based on satellite observations have reported that aerosol optical depths increase with increasing cloud cover. Part of the increase comes from the humidification and consequent growth of aerosol particles in the moist cloud environment, but part comes from 3‐D cloud‐radiative transfer effects on the retrieved aerosol properties. Often, discerning whether the observed increases in aerosol optical depths are artifacts or real proves difficult. The paper only addresses the cloud‐clear sky radiative transfer interaction part. It provides a simple model that quantifies the enhanced illumination of cloud‐free columns in the vicinity of clouds that are used in the aerosol retrievals. This model is based on the assumption that the enhancement in the cloud‐free column radiance comes from enhanced Rayleigh scattering that results from the presence of the nearby clouds. This assumption leads to a larger increase of AOT for shorter wavelengths, or to a “bluing” of aerosols near clouds. The assumption that contribution from molecular scattering dominates over aerosol scattering and surface reflection is justified for the case of shorter wavelengths, dark surfaces, and an aerosol layer below the cloud tops. The enhancement in Rayleigh scattering is estimated using a stochastic cloud model to obtain the radiative flux reflected by broken clouds and comparing this flux with that obtained with the molecules in the atmosphere causing extinction, but no scattering.

What does reflection from cloud sides tell us about vertical distribution of cloud droplet sizes?

Abstract. Cloud development, the onset of precipitation and the effect of aerosol on clouds depend on the structure of the cloud profiles of droplet size and phase. Aircraft measurements of cloud profiles are limited in their temporal and spatial extent. Satellites were used to observe cloud tops not cloud profiles with vertical profiles of precipitation-sized droplets anticipated from CloudSat. The recently proposed CLAIM-3D satellite mission (cloud aerosol interaction mission in 3-D) suggests to measure profiles of cloud microphysical properties by retrieving them from the solar and infrared radiation reflected or emitted from cloud sides. Inversion of measurements from the cloud sides requires rigorous understanding of the 3-dimentional (3-D) properties of clouds. Here we discuss the reflected sunlight from the cloud sides and top at two wavelengths: one nonabsorbing to solar radiation (0.67 μm) and one with liquid water efficient absorption of solar radiation (2.1 μm). In contrast to the plane-parallel approximation, a conventional approach to all current operational retrievals, 3-D radiative transfer is used for interpreting the observed reflectances. General properties of the radiation reflected from the sides of an isolated cloud are discussed. As a proof of concept, the paper shows a few examples of radiation reflected from cloud fields generated by a simple stochastic cloud model with the prescribed vertically resolved microphysics. To retrieve the information about droplet sizes, we propose to use the probability density function of the droplet size distribution and its first two moments instead of the assumption about fixed values of the droplet effective radius. The retrieval algorithm is based on the Bayesian theorem that combines prior information about cloud structure and microphysics with radiative transfer calculations.

A 3D stochastic cloud model for investigating the radiative properties of inhomogeneous cirrus clouds

AbstractThe three‐dimensional structure of clouds is known to be important for determining their radiative effects, but it is difficult to obtain this structure directly from observations. In this paper a stochastic model is described that is capable of simulating the structural properties unique to cirrus: fallstreak geometry and shear‐induced mixing. We first present an analysis of time–height cloud radar sections from southern England to extract the cirrus parameters of interest. It is found that horizontal power spectra of the logarithm of ice‐water content (estimated from radar reflectivity factor and temperature) typically exhibit a spectral slope of around −5/3 near cloud top that decreases with depth into the cloud, to values as low as −3.5 in some cases. This decrease can be explained by wind shear coupled with a spread of particle fall speeds leading to a homogenization that acts preferentially at smaller scales. The power spectra exhibit a distinct scale break, becoming flat at scales larger than around 50 km (the ‘outer scale’). The orientation of the fallstreaks may be predicted from the profile of mean wind and mean ice fall speed. We then describe the stochastic model, which takes as input profiles of the mean and fractional standard deviation of ice‐water content, spectral slope, outer scale and wind speed. It first generates an isotropic 3‐D fractal field by performing an inverse 3‐D Fourier transform on a matrix of simulated Fourier coefficients with amplitudes consistent with the observed 1‐D spectra. Random phases for the coefficients allow multiple realizations of a cloud with the same statistical properties to be generated. Then horizontal slices from the domain are manipulated in turn to simulate horizontal displacement and changes to the spectra with height. Finally the field is scaled to produce the observed mean and fractional standard deviation of ice‐water content. Vertical 2‐D slices extracted from the domain are very similar in appearance to cloud radar observations. Radiative‐transfer calculations using the independent column approximation are used to show that the different fallstreak orientation resulting from different wind shears can change mean top‐of‐atmosphere radiative fluxes by in excess of 45 W m−2 in the short‐wave and 15 W m−2 in the long‐wave. The effect of wind shear to induce horizontal mixing causes an additional but smaller radiative effect. We also investigate the biases that would be expected from the assumptions made in the radiation schemes of general‐circulation models (GCMs). It is found that there is some compensation between the errors arising from the assumptions of horizontal homogeneity and maximum‐random overlap; if a GCM were to improve the overlap assumption but still assume clouds to be horizontally homogeneous then the total error in cloud radiative effect would be likely to increase. Copyright © 2005 Royal Meteorological Society.

Modeling of rapid variability in the spectral line profiles of Wolf-Rayet stars

Profiles of variable emission lines in the spectra of Wolf-Rayet stars are calculated using a stochastic cloud model for the inhomogeneous atmospheres of early-type stars. The model assumes that most of the line flux is formed in cold, dense condensations (clouds) that move through a rarified inter-cloud medium whose density monotonically decreases outwards. The formation of clouds is taken to be stochastic. Wavelet analysis is used to estimate the parameters of cloud ensembles. The model can reproduce the general pattern of line-profile variability observed in the spectra of Wolf-Rayet stars.

Simulation study of the effects of model uncertainty in variational assimilation of radar data on rainfall forecasting

Recent developments in data assimilation techniques make use of cloud models initialized with radar data an attractive alternative for real-time quantitative precipitation forecasting (QPF). Before such approaches are used operationally, there are a number of aspects that need to be addressed to understand better the benefits and drawbacks of the practical applications of cloud models in QPF. One aspect is the effect of various sources of uncertainty on the forecasting performance. Data assimilation formulations based on variational techniques allow accounting for uncertainty in observations but have no efficient mechanism of accounting for uncertainty in the model on which they are based. To investigate the issue, a simulation-based Monte Carlo methodology, suitable for the analysis of complex nonlinear models, is used. A one-dimensional stochastic-dynamic cloud model, derived by considering stochastic terms in a physically based cloud model is used to simulate rainfall and radar reflectivity data. A deterministic version of the model is then initialized by a variational assimilation technique and used for forecasting. The differences between the forecasts and actual realizations of the stochastic cloud model are statistically analyzed to assess the effect of cloud model uncertainty on forecasting. In this paper this methodology is also used to study additional effects of other types of uncertainty, such as those in radar observations and in the description of rain drop size distribution, for a more complete understanding of the impact of uncertainties on rainfall forecasting. Based on the scenarios investigated in the paper, conclusions and recommendations concerning the use of complex cloud models in real-world applications are made.

Ionization structure of the atmospheres and line profiles in the spectra of Wolf-Rayet stars

The ionization structure of the atmospheres of Wolf-Rayet (WR) and WC stars is studied. The stellar atmospheres were assumed to consist of helium, hydrogen, and carbon. Profiles of the C III l 5696 line are calculated, both for a spherically symmetric atmosphere with a density that decreases monotonically outward and for an atmosphere containing a dense condensation (inhomogeneity). The dependence of line profiles on the parameters of the inhomogeneity is investigated. It is shown that profiles of the C III λ 5696 line calculated assuming no inhomogeneities in the atmosphere are too weak, whereas assuming the existence of inhomogeneities enables one to reconcile the observed and calculated profiles. An equation is obtained relating the mass of an inhomogeneity to the flux in the detail of the total profile of the CIII λ 5696 line formed by that inhomogeneity. This equation is used to construct a stochastic cloud model of the atmosphere of a WR star, consisting of a large number of inhomogeneities in a homogeneous, spherically symmetric stellar wind. In the proposed model, the formation of inhomogeneities was treated as a random process. It is shown that in this model it is possible both to obtain an average line profile corresponding to the observed one and to reproduce the amplitude and overall pattern of variability of profiles in the spectra of Wolf-Rayet stars.