Fog Model Research Articles

Fog Prediction for Road Traffic Safety in a Coastal Desert Region: Improvement of Nowcasting Skills by the Machine-Learning Approach

A new model for nowcasting fog events in the coastal desert area of Dubai is presented, based on a machine-learning algorithm—decision-tree induction. In the investigated region high frequency observations from automatic weather stations were utilized as a database for the analysis of useful patterns. The induced decision trees yield for the first six forecasting hours increased prediction skill when compared to the coupled Weather Research and Forecasting (WRF) model and the PAFOG fog model (Bartok et al., Boundary-Layer Meteorol 145:485–506, 2012). The decision tree results were further improved by integrating the output of the coupled numerical fog forecasting models in the training database of the decision tree. With this treatment, the statistical quality measures, i.e. the probability of detection, the false alarm ratio, and the Gilbert’s skill score, achieved values of 0.88, 0.19, and 0.69, respectively. From these results we conclude that the best fog forecast in the Dubai region is obtained by applying for the first six forecast hours the newly-developed machine-learning algorithm, while for forecast times exceeding 6 h the coupled numerical models are the best choice.

Comparison of NRZ, RZ-OOK Modulation Formats for FSO Communications under Fog Weather Condition

In this paper, the performance of an FSO wireless communications system is theoretically analyzed, using NRZ, RZ-OOK modulation formats and a Si PIN photodiodes receiver over fog weather conditions. Based on different fog models for optical beam propagation horizontally at 850 nm1550nm on an FSO, the visibility of weather and power of the transmitter under fog weather are analyzed. The characteristics of bit error rate BER for NRZ and RZ-OOK optical modulation formats are studied under different fog models. Simulation results indicate that the performance of 1550nmis more suited for an FSO communication system. On the other hand, we discuss the suitability of fog models under these modulation formats.

Numerical Modeling of Ice Fog in Interior Alaska Using the Weather Research and Forecasting Model

An ice microphysics parameterization scheme has been modified to better describe and understand ice fog formation. The modeling effort is based on observations in the Sub-Arctic Region of Interior Alaska, where ice fog occurs frequently during the cold season due to abundant water vapor sources and strong inversions existing near the surface at extremely low air temperatures. The microphysical characteristics of ice fog are different from those of other ice clouds, implying that the microphysical processes of ice should be changed in order to generate ice fog particles. Ice fog microphysical characteristics were derived with the NCAR Video Ice Particle Sampler during strong ice fog cases in the vicinity of Fairbanks, Alaska, in January and February 2012. To improve the prediction of ice fog in the Weather Research and Forecasting model, observational data were used to change particle size distribution properties and gravitational settling rates, as well as to implement a homogeneous freezing process. The newly implemented homogeneous freezing process compliments the existing heterogeneous freezing scheme and generates a higher number concentration of ice crystals than the original Thompson scheme. The size distribution of ice crystals is changed into a Gamma distribution with the shape factor of 2.0, using the observed size distribution. Furthermore, gravitational settling rates are reduced for the ice crystals since the crystals in ice fog do not precipitate in a similar manner when compared to the ice crystals of cirrus clouds. The slow terminal velocity plays a role in increasing the time scale for the ice crystals to settle to the surface. Sensitivity tests contribute to understanding the effects of water vapor emissions as an anthropogenic source on the formation of ice fog.

Performance Analysis of Ultraviolet Communication System in Fog Environment

Based on the analysis of ultraviolet single scattering channel model, the attenuation model of fog and its impact on signal attenuation is investigated. Under foggy environment, the study on the performance of ultraviolet communications is carried, simulation results show that the fog will not only make ultraviolet communication system BER performance deterioration, but also make information transmission rate substantially lowered. In addition, to guarantee a certain system performance indicators, the average transmitted optical power will have higher requirements.

A model-based approach to adjust microwave observations for operational applications: results of a campaign at Munich Airport in winter 2011/2012

Abstract. In the frame of the project "LuFo iPort VIS" which focuses on the implementation of a site-specific visibility forecast, a field campaign was organised to offer detailed information to a numerical fog model. As part of additional observing activities, a 22-channel microwave radiometer profiler (MWRP) was operating at the Munich Airport site in Germany from October 2011 to February 2012 in order to provide vertical temperature and humidity profiles as well as cloud liquid water information. Independently from the model-related aims of the campaign, the MWRP observations were used to study their capabilities to work in operational meteorological networks. Over the past decade a growing quantity of MWRP has been introduced and a user community (MWRnet) was established to encourage activities directed at the set up of an operational network. On that account, the comparability of observations from different network sites plays a fundamental role for any applications in climatology and numerical weather forecast. In practice, however, systematic temperature and humidity differences (bias) between MWRP retrievals and co-located radiosonde profiles were observed and reported by several authors. This bias can be caused by instrumental offsets and by the absorption model used in the retrieval algorithms as well as by applying a non-representative training data set. At the Lindenberg observatory, besides a neural network provided by the manufacturer, a measurement-based regression method was developed to reduce the bias. These regression operators are calculated on the basis of coincident radiosonde observations and MWRP brightness temperature (TB) measurements. However, MWRP applications in a network require comparable results at just any site, even if no radiosondes are available. The motivation of this work is directed to a verification of the suitability of the operational local forecast model COSMO-EU of the Deutscher Wetterdienst (DWD) for the calculation of model-based regression operators in order to provide unbiased vertical profiles during the campaign at Munich Airport. The results of this algorithm and the retrievals of a neural network, specially developed for the site, are compared with radiosondes from Oberschleißheim located about 10 km apart from the MWRP site. Outstanding deviations for the lowest levels between 50 and 100 m are discussed. Analogously to the airport experiment, a model-based regression operator was calculated for Lindenberg and compared with both radiosondes and operational results of observation-based methods. The bias of the retrievals could be considerably reduced and the accuracy, which has been assessed for the airport site, is quite similar to those of the operational radiometer site at Lindenberg above 1 km height. Additional investigations are made to determine the length of the training period necessary for generating best estimates. Thereby three months have proven to be adequate. The results of the study show that on the basis of numerical weather prediction (NWP) model data, available everywhere at any time, the model-based regression method is capable of providing comparable results at a multitude of sites. Furthermore, the approach offers auspicious conditions for automation and continuous updating.

Modeling of Fog and Smoke Attenuation in Free Space Optical Communications Link Under Controlled Laboratory Conditions

This paper theoretically and experimentally investigate the spectrum attenuation of free space optical (FSO) communication systems operating at visible and near infrared (NIR) wavelengths $(0.6 \mu{\rm m} under fog and smoke in a controlled laboratory condition. Fog and smoke are generated and controlled homogeneously along a dedicated atmospheric chamber of length 5.5 m. A new wavelength dependent empirical model is proposed to predict the fog and smoke attenuation operating at visible and NIR wavelengths. Comparison of the new proposed model with the measured continuous attenuation spectrum from visible—NIR in the fog and smoke channels shows a close relationship than the semi-empirical Kim and Kruse fog models. The experimental results also show the selection for the possible appropriate wavelengths from visible—NIR for FSO links to achieve the maximum link span in dense fog conditions.

Peculiar velocity decomposition, redshift space distortion, and velocity reconstruction in redshift surveys: The methodology

Massive spectroscopic surveys will measure the redshift space distortion (RSD) induced by galaxy peculiar velocity to unprecedented accuracy and open a new era of precision RSD cosmology. We develop a new method to improve the RSD modeling and to carry out robust reconstruction of the 3D large scale peculiar velocity through galaxy redshift surveys, in light of RSD. (1) We propose a mathematically unique and physically motivated decomposition of peculiar velocity into three eigencomponents: an irrotational component completely correlated with the underlying density field (${\mathbf{v}}_{\ensuremath{\delta}}$), an irrotational component uncorrelated with the density field (${\mathbf{v}}_{S}$), and a rotational (curl) component (${\mathbf{v}}_{B}$). The three components have different origins, different scale dependences, and different impacts on RSD. (2) This decomposition has the potential to simplify and improve the RSD modeling. (i) ${\mathbf{v}}_{B}$ damps the redshift space clustering. (ii) ${\mathbf{v}}_{S}$ causes both damping and enhancement to the redshift space power spectrum ${P}^{s}(k,u)$. Nevertheless, the leading order contribution to the enhancement has a ${u}^{4}$ directional dependence, distinctively different from the Kaiser formula. Here, $u\ensuremath{\equiv}{k}_{z}/k$, $k$ is the amplitude of the wave vector, and ${k}_{z}$ is the component along the line of sight. (iii) ${\mathbf{v}}_{\ensuremath{\delta}}$ is of the greatest importance for the RSD cosmology. We find that the induced redshift clustering shows a number of important deviations from the usual Kaiser formula. Even in the limit of ${\mathbf{v}}_{S}\ensuremath{\rightarrow}0$ and ${\mathbf{v}}_{B}\ensuremath{\rightarrow}0$, the leading order contribution $\ensuremath{\propto}(1+f\stackrel{\texttildelow{}}{W}(k){u}^{2}{)}^{2}$. It differs from the Kaiser formula by a window function $\stackrel{\texttildelow{}}{W}(k)$. Nonlinear evolution generically drives $\stackrel{\texttildelow{}}{W}(k)\ensuremath{\le}1$. We hence identify a significant systematical error causing underestimation of the structure growth parameter $f$ by as much as $O(10%)$ even at a relatively large scale $k=0.1h/\mathrm{Mpc}$. (iv) The velocity decomposition reveals the three origins of the ``finger-of-God'' (FOG) effect and suggests how to simplify and improve the modeling of FOG by treating the three components separately. (v) We derive a new formula for the redshift space power spectrum. Under the velocity decomposition scheme, all high order Gaussian corrections and non-Gaussian corrections of order ${\ensuremath{\delta}}^{3}$ can be taken into account without introducing extra model uncertainties. Here $\ensuremath{\delta}$ is the nonlinear overdensity. (3) The velocity decomposition clarifies issues in peculiar velocity reconstruction through 3D galaxy distribution. We discuss two possible ways to carry out the 3D ${\mathbf{v}}_{\ensuremath{\delta}}$ reconstruction. Both use the otherwise troublesome RSD in velocity reconstruction as a valuable source of information. Both have the advantage of rendering the reconstruction of a stochastic 3D field into the reconstruction of a deterministic window function ${W}^{s}(k,u)$ of limited degrees of freedom. Both can automatically and significantly alleviate the galaxy bias problem and, in the limit of a deterministic galaxy bias, completely overcome it. Part 1 of this series of works lays out the methodology. Companion papers Y. Zheng et al. (in preparation). will extensively evaluate its performance against N-body simulations.

Fog Prediction for Road Traffic Safety in a Coastal Desert Region

Modern weather prediction models use relatively high grid resolutions as well as sophisticated parametrization schemes for microphysical and other subgrid-scale atmospheric processes. Nonetheless, with these models it remains a difficult task to perform successful numerical fog forecasts since many factors controlling a particular fog event are not yet sufficiently simulated. Here we describe our efforts to create a mechanism that produces successful predictions of fog in the territory located on the north coast of the Arabian Peninsula. Our approach consists in the coupling of the one-dimensional PAFOG fog model with the three-dimensional WRF 3.0 (Weather Research and Forecast) modelling system. The proposed method allows us to construct an efficient operative road traffic warning system for the occurrence of fog in the investigated region. In total 84 historical situations were studied during the period 2008–2009. Moreover, results of operative day-by-day fog forecasting during January and February 2010 are presented. For the investigated arid and hot climate region the land-sea breeze circulation seems to be the major factor affecting the diurnal variations of the meteorological conditions, frequently resulting in the formation of fog.

Fog and Dew Observations and Modeling: Introduction

Fog and Dew Observations and Modeling: Introduction

Further results on fog modeling for terrestrial free-space optical links

Recent measurement campaigns in Prague, Czech Republic have recorded the specific attenuation caused by fog in terrestrial free-space optical (FSO) links along with visibility, liquid water content (LWC), and integrated particle surface area for operational wavelengths of 1550 and 830 nm. Data recorded during 5 months of measurements has been analyzed in an attempt to validate and improve the empirical models for LWC and visibility-based attenuation and the probability density function (PDF) estimation of the received signal strength (RSS). The results strongly suggest that further attempts in refinement of the empirical modeling for visibility-based attenuation or LWC-based attenuation shall move towards the establishment of a global data bank of fog attenuation measurements in different climatic regions. This data bank can then help develop generic models which could lead to better system design of future terrestrial FSO links. The PDF estimation of RSS puts forth the Kumaraswamy distribution as the best fit for settled continental fog conditions.

Integration of Local Observations into the One Dimensional Fog Model PAFOG

The numerical prediction of fog requires a very high vertical resolution of the atmosphere. Owing to a prohibitive computational effort of high resolution three dimensional models, operational fog forecast is usually done by means of one dimensional fog models. An important condition for a successful fog forecast with one dimensional models consists of the proper integration of observational data into the numerical simulations. The goal of the present study is to introduce new methods for the consideration of these data in the one dimensional radiation fog model PAFOG. First, it will be shown how PAFOG may be initialized with observed visibilities. Second, a nudging scheme will be presented for the inclusion of measured temperature and humidity profiles in the PAFOG simulations. The new features of PAFOG have been tested by comparing the model results with observations of the German Meteorological Service. A case study will be presented that reveals the importance of including local observations in the model calculations. Numerical results obtained with the modified PAFOG model show a distinct improvement of fog forecasts regarding the times of fog formation, dissipation as well as the vertical extent of the investigated fog events. However, model results also reveal that a further improvement of PAFOG might be possible if several empirical model parameters are optimized. This tuning can only be realized by comprehensive comparisons of model simulations with corresponding fog observations.

A Fuzzy Logic Fog Forecasting Model for Perth Airport

Perth Airport is a major airport along the southwest coast of Australia. Even though, on average, fog only occurs about twelve times a year, the lack of suitable alternate aerodromes nearby for diversion makes fog forecasts for Perth Airport very important to long-haul international flights. Fog is most likely to form in the cool season between April and October. This study developed an objective fuzzy logic fog forecasting model for Perth Airport for the cool season. The fuzzy logic fog model was based on outputs from a high-resolution operational NWP model called LAPS125 that ran twice daily at 00 and 12 UTC, but fuzzy logic was employed to deal with the inaccuracy of NWP prediction and uncertainties associated with relationships between fog predictors and fog occurrence. The outcome of the fuzzy logic fog model is in one of the four categories from low to high fog risk as FM0, FM5, FM15 or FM30, intended to map to approximate fog probability of 0, 5, 15 and 30%, respectively. The model was found useful in its 5 year performance in the cool seasons between 2004 and 2008 and required little recalibration if mist was treated as if it were also a fog event in the skill evaluation. To generate an operational fog forecast for Perth Airport, the outcome of the fuzzy logic fog model was averaged with the outcomes of two other fog forecasting methods using a simple consensus approach. Fog forecast so generated is known as the operational consensus forecast. Skill assessment using frequency distribution diagram, Hansen and Kuiper skill score, and Relative Operating Characteristic curve showed that the operational consensus forecast outperformed all three individual methods. Out of the three methods, the fuzzy logic fog model ranked second. It performed better than the other objective method called GASM but worse than the subjective method which relied on forecaster’s subjective assessment. The skills of the fuzzy logic fog model can be further improved with the tuning of fuzzy functions. In addition, similar models can be customised for other airports. The study also suggested the use of the simple consensus approach to enhance forecasting skills for other stations or weather phenomena if there were two or more independent forecasting methods available.

Fog Simulations Based on Multi-Model System: A Feasibility Study

Accurate forecasts of fog and visibility are very important to air and high way traffic, and are still a big challenge. A 1D fog model (PAFOG) is coupled to MM5 by obtaining the initial and boundary conditions (IC/BC) and some other necessary input parameters from MM5. Thus, PAFOG can be run for any area of interest. On the other hand, MM5 itself can be used to simulate fog events over a large domain. This paper presents evaluations of the fog predictability of these two systems for December of 2006 and December of 2007, with nine regional fog events observed in a field experiment, as well as over a large domain in eastern China. Among the simulations of the nine fog events by the two systems, two cases were investigated in detail. Daily results of ground level meteorology were validated against the routine observations at the CMA observational network. Daily fog occurrences for the two study periods was validated in Nanjing. General performance of the two models for the nine fog cases are presented by comparing with routine and field observational data. The results of MM5 and PAFOG for two typical fog cases are verified in detail against field observations. The verifications demonstrated that all methods tended to overestimate fog occurrence, especially for near-fog cases. In terms of TS/ETS, the LWC-only threshold with MM5 showed the best performance, while PAFOG showed the worst. MM5 performed better for advection–radiation fog than for radiation fog, and PAFOG could be an alternative tool for forecasting radiation fogs. PAFOG did show advantages over MM5 on the fog dissipation time. The performance of PAFOG highly depended on the quality of MM5 output. The sensitive runs of PAFOG with different IC/BC showed the capability of using MM5 output to run the 1D model and the high sensitivity of PAFOG on cloud cover. Future works should intensify the study of how to improve the quality of input data (e.g. cloud cover, advection, large scale subsidence) for the 1D model, particularly how to eliminate near-fog case in fog forecasting.

Regeneration patterns and persistence of the fog‐dependent Fray Jorge forest in semiarid Chile during the past two centuries

AbstractThe persistence of rainforest patches at Fray Jorge National Park (FJNP) in semiarid Chile (30°40′S), a region receiving approximately 147 mm of annual rainfall, has been a source of concern among forest managers. These forests are likely dependent on water inputs from oceanic fog and their persistence seems uncertain in the face of climate change. Here, we assessed tree radial growth and establishment during the last two centuries and their relation to trends in climate and canopy disturbance. Such evaluation is critical to understanding the dynamics of these semiarid ecosystems in response to climate change. We analyzed forest structure of six forest patches (0.2–22 ha) in FJNP based on sampling within 0.1 ha permanent plots. For the main canopy species, the endemic Aextoxicon punctatum (Aextoxicaceae), we used tree‐ring analysis to assess establishment periods, tree ages, growing trends and their relation to El Niño Southern Oscillation (ENSO), rainfall, and disturbance. The population dynamics of A. punctatum can be described by a continuous regeneration mode. Regeneration of A. punctatum was sensitive to different canopy structures. Growth release patterns suggest the absence of large scale human impact. Radial growth and establishment of A. punctatum were weakly correlated with rainfall and ENSO. If water limits forests patch persistence, patches are likely dependent on the combination of fog and rain water inputs. Forest patches have regenerated continuously for at least 250 years, despite large fluctuations in rainfall driven by ENSO and a regional decline in rainfall during the last century. Because of the positive influence on fog interception, forest structure should be preserved under any future climate scenario. Future research in FJNP should prioritize quantifying the long‐term trends of fog water deposition on forests patches. Fog modeling is crucial for understanding the interplay among physical drivers of water inputs under climate change.

Evaluation method for radiative heat transfer in polydisperse water droplets

Simplifications of the model for nongray radiative heat transfer analysis in participating media comprised of polydisperse water droplets are presented. Databases of the radiative properties for a water droplet over a wide range of wavelengths and diameters are constructed using rigorous Mie theory. The accuracy of the radiative properties obtained from the database interpolation is validated by comparing them with those obtained from the Mie calculations. The radiative properties of polydisperse water droplets are compared with those of monodisperse water droplets with equivalent mean diameters. Nongray radiative heat transfer in the anisotropic scattering fog layer, including direct and diffuse solar irradiations and infrared sky flux, is analyzed using REM 2. The radiative heat fluxes within the fog layer containing polydisperse water droplets are compared with those in the layer containing monodisperse water droplets. Through numerical simulation of the radiative heat transfer, polydisperse water droplets can be approximated by using the Sauter diameter, a technique that can be useful in several research fields, such as engineering and atmospheric science. Although this approximation is valid in the case of pure radiative transfer problems, the Sauter diameter is reconfirmed to be the appropriate diameter for approximating problems in radiative heat transfer, although volume–length mean diameter shows better accordance in some cases. The CPU time for nongray radiative heat transfer analysis with a fog model is evaluated. It is proved that the CPU time is decreased by using the databases and the approximation method for polydisperse particulate media.

Fog and Boundary Layer Clouds: Introduction

This special issue of the Journal of Pure and Applied Geophysics contains 15 papers related to fog, visibility, and low clouds that focus on microphysical and conventional surface observations, satellite detection techniques, modeling aspects, and climatological and statistical methods for fog forecasting. The results presented in this special issue come from research efforts in North America and Europe, mainly from the Canadian Fog Remote Sensing And Modeling (FRAM) and European COST-722 fog/visibility related projects. COST (http://www. cost.esf.org/) is an intergovernmental European framework for international cooperation between nationally funded research activities. COST creates scientific networks and enables scientists to collaborate in a wide spectrum of activities in research and technology. COST activities are administered by the COST Office.

Implementation of a Single-Column Model for Fog and Low Cloud Forecasting at Central-Spanish Airports

Operations at Central-Spanish airports are often, especially in winter, affected by visibility reduction. The Instituto Nacional de Meteorologia (INM), the Spanish Weather Service, has developed a single-column model (SCM) in order to improve short-term forecasts of fog, visibility and low-clouds. The SCM, called H1D, is a one-dimensional version of the HIRLAM limited-area model. It is operationally run for three airports in the region: Madrid-Barajas, Almagro and Albacete-Los Llanos. Since SCMs cannot deal with horizontal heterogeneity, the terms that depend on the horizontal structure of the atmosphere are estimated from the outputs of the three-dimensional (3-D) model and introduced into the SCM as external forcings. The systematic analysis of the meteorological situations has evidenced the existence of a close relationship between fog formation and the presence of drainage winds in the region. Since the 3-D model docs not have the necessary resolution to correctly simulate the main features of the drainage flow caused by the complex topography in the proximity of Madrid-Barajas, it cannot provide the SCM with the correct forcings. This problem has been partially overcome through the introduction of a module that, under certain conditions, substitutes the values computed from the 3-D model outputs by others that are based on a conceptual model of the phenomenon and have been empirically derived from climatological knowledge. This module improves the H1D verification scores for the basic meteorological variables—wind, temperature and humidity—and reduces the false alarm rate in fog forecast.

A New Visibility Parameterization for Warm-Fog Applications in Numerical Weather Prediction Models

Abstract The objective of this work is to suggest a new warm-fog visibility parameterization scheme for numerical weather prediction (NWP) models. In situ observations collected during the Radiation and Aerosol Cloud Experiment, representing boundary layer low-level clouds, were used to develop a parameterization scheme between visibility and a combined parameter as a function of both droplet number concentration Nd and liquid water content (LWC). The current NWP models usually use relationships between extinction coefficient and LWC. A newly developed parameterization scheme for visibility, Vis = f (LWC, Nd), is applied to the NOAA Nonhydrostatic Mesoscale Model. In this model, the microphysics of fog was adapted from the 1D Parameterized Fog (PAFOG) model and then was used in the lower 1.5 km of the atmosphere. Simulations for testing the new parameterization scheme are performed in a 50-km innermost-nested simulation domain using a horizontal grid spacing of 1 km centered on Zurich Unique Airport in Switzerland. The simulations over a 10-h time period showed that visibility differences between old and new parameterization schemes can be more than 50%. It is concluded that accurate visibility estimates require skillful LWC as well as Nd estimates from forecasts. Therefore, the current models can significantly over-/underestimate Vis (with more than 50% uncertainty) depending on environmental conditions. Inclusion of Nd as a prognostic (or parameterized) variable in parameterizations would significantly improve the operational forecast models.

Calculated and measured values of liquid water content in clean and polluted environments

The relationship between liquid water content (LWC) and visibility (VIS) in a fog was examined by a field measurement of LWC values at a clean location of the meteorological observatory Sodankyla (Finland) and in a polluted region at the meteorological observatory Milesovka (Czech Republic). Furthermore, the use of a simple regression fog model to determine LWC from VIS is examined by comparing well-known relationships with the measurement results.

A practical analytic single scattering model for real time rendering

We consider real-time rendering of scenes in participating media, capturing the effects of light scattering in fog, mist and haze. While a number of sophisticated approaches based on Monte Carlo and finite element simulation have been developed, those methods do not work at interactive rates. The most common real-time methods are essentially simple variants of the OpenGL fog model. While easy to use and specify, that model excludes many important qualitative effects like glows around light sources, the impact of volumetric scattering on the appearance of surfaces such as the diffusing of glossy highlights, and the appearance under complex lighting such as environment maps. In this paper, we present an alternative physically based approach that captures these effects while maintaining real time performance and the ease-of-use of the OpenGL fog model. Our method is based on an explicit analytic integration of the single scattering light transport equations for an isotropic point light source in a homogeneous participating medium. We can implement the model in modern programmable graphics hardware using a few small numerical lookup tables stored as texture maps. Our model can also be easily adapted to generate the appearances of materials with arbitrary BRDFs, environment map lighting, and precomputed radiance transfer methods, in the presence of participating media. Hence, our techniques can be widely used in real-time rendering.