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Mikhail D. Alexandrov and Alexander Marshak

Abstract

In the fourth part of our “Cellular Statistical Models of Broken Cloud Fields” series we use the binary Markov processes framework for quantitative investigation of the effects of low resolution of idealized satellite observations on the statistics of the retrieved cloud masks. We assume that the cloud fields are Markovian and are characterized by the “actual” cloud fraction (CF) and scale length. We use two different models of observations: a simple discrete-point sampling and a more realistic “pixel” protocol. The latter is characterized by a state attribution function (SAF), which has the meaning of the probability that the pixel with a certain CF is declared cloudy in the observed cloud mask. The stochasticity of the SAF means that the cloud–clear attribution is not ideal and can be affected by external or unknown factors. We show that the observed cloud masks can be accurately described as Markov chains of pixels and use the master matrix formalism (introduced in Part III of the series) for analytical computation of their parameters: the “observed” CF and scale length. This procedure allows us to establish a quantitative relationship (which is pixel-size dependent) between the actual and the observed cloud-field statistics. The feasibility of restoring the former from the latter is considered. The adequacy of our analytical approach to idealized observations is evaluated using numerical simulations. Comparison of the observed parameters of the simulated datasets with their theoretical expectations showed an agreement within 0.005 for the CF, while for the scale length it is within 1% in the sampling case and within 4% in the pixel case.

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Mikhail D. Alexandrov and Alexander Marshak

Abstract

In the third part of the “Cellular Statistical Models of Broken Cloud Fields” series the cloud statistics formalism developed in the first two parts is interpreted in terms of the theory of Markov processes. The master matrix introduced in this study is a unifying generalization of both the cloud fraction probability distribution function (PDF) and the Markovian transition probability matrix. To illustrate the new concept, the master matrix is used for computation of the moments of the cloud fraction PDF—in particular, the variance—which until now has not been analytically derived in the framework of the authors’ previous work. This paper also serves as a bridge to the proposed future studies of the effects of sampling and averaging on satellite-based cloud masks.

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Mikhail D. Alexandrov, Alexander Marshak, and Andrew S. Ackerman

Abstract

A new analytical statistical model describing the structure of broken cloud fields is presented. It depends on two parameters (cell size and occupancy probability) and provides chord distributions of clouds and gaps between them by length, as well as the cloud fraction distribution. This approach is based on the assumption that the structure of a cloud field is determined by a semiregular grid of cells (an abstraction of the atmospheric convective cells), which are filled with cloud with some probability. First, a simple discrete model is introduced, where clouds and gaps can occupy an integer number of cells, and then a continuous analog is developed, allowing for arbitrary cloud and gap sizes. The influence of a finite sample size on the retrieved statistics is also described.

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Mikhail D. Alexandrov, Andrew S. Ackerman, and Alexander Marshak

Abstract

Cellular statistical models are designed to provide a simple two-parameter characterization of the structure of broken cloud fields described through distributions of cloud fraction and of chord lengths for clouds and clear gaps. In these analytical models cloud fields are assumed to occur on a semiregular grid of cells (which can be vaguely interpreted as atmospheric convective cells). In a simple, discrete cell model, cell size is fixed and each cell can either be completely filled with cloud with some probability or remain empty. Extending the discrete model to a continuous case provides more realism by allowing arbitrary cloud and gap sizes. Here the continuous cellular model is tested by comparing its statistics with those from large-eddy simulations (LES) of marine boundary layer clouds based on case studies from three trade-cumulus field projects. The statistics largely agree with some differences in small sizes approaching the LES model grid spacing. Exponential chord-length distributions follow from the assumption that the probability of any cell being cloudy is constant, appropriate for a given meteorological state (narrow sampling). Relaxing that assumption, and instead allowing this probability to have its own distribution, leads to a power-law distribution of chord lengths, appropriate to a broader sample of meteorological states (diverse sampling).

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Mikhail D. Alexandrov, Andrew A. Lacis, Barbara E. Carlson, and Brian Cairns

Abstract

Measurements from ground-based sun photometer networks can be used both to provide ground-truth validation of satellite aerosol retrievals and to produce a land-based aerosol climatology that is complementary to satellite retrievals that are currently performed mostly over ocean. The multifilter rotating shadowband radiometer (MFRSR) has become a popular network instrument in recent years. Several networks operate about a hundred instruments providing good geographical coverage of the United States. In addition, international use of the MFRSR has continued to increase, allowing MFRSR measurements to significantly contribute to aerosol climatologies.

This study investigates the feasibility of creating a ground-based aerosol climatology using MFRSR measurements. Additionally, this analysis allows for testing of the performance of the retrieval algorithm under a variety of conditions. The retrieval algorithm is used for processing MFRSR data from clear and partially cloudy days to simultaneously retrieve daily time series of column mean aerosol particle size, aerosol optical depth, NO2, and ozone column amounts together with the instrument's calibration constants directly from the MFRSR measurements for a variety of sites covering a range of atmospheric and surface conditions. This analysis provides a description of seasonal changes in aerosol parameters and in column amounts of ozone and NO2 as a function of geographical location. In addition, the relationship between NO2 column amount and aerosol optical depth as a potential indicator of tropospheric pollution is investigated. Application of this analysis method to the measurements from growing numbers of MFRSRs will allow for expansion on this developing climatology.

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Mikhail D. Alexandrov, Alexander Marshak, Brian Cairns, Andrew A. Lacis, and Barbara E. Carlson

Abstract

Statistical scale-by-scale analysis, for the first time, has been applied to the aerosol optical thickness (AOT) retrieved from the Multi-Filter Rotating Shadowband Radiometer (MFRSR) network. The MFRSR data were collected in September 2000 from the dense local network operated by the U.S. Department of Energy Atmospheric Radiation Measurement program, located in Oklahoma and Kansas. These data have 20-s temporal resolution. The instrument sites form an irregular grid with the mean distance between neighboring sites about 80 km. It is found that temporal variability of AOT can be separated into two well-established scale-invariant regimes: 1) microscale (0.5–15 km), where fluctuations are governed by 3D turbulence, and 2) intermediate scale (15–100 km), characterized by a transition toward large-scale 2D turbulence. The spatial scaling of AOT was determined by the comparison of retrievals between different instrument sites (distance range 30–400 km). The authors investigate how simultaneous determination of AOT scaling in space and time can provide means to examine the validity of Taylor's frozen turbulence hypothesis. The temporal evolution of AOT scaling exponents during the month appeared to be well correlated with changes in aerosol vertical distribution, while their spatial variability reflects the concavity/convexity of the site topography. Explanations based on dynamical processes in atmospheric convective boundary layer are suggested.

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Mikhail D. Alexandrov, Igor V. Geogdzhayev, Kostas Tsigaridis, Alexander Marshak, Robert Levy, and Brian Cairns

Abstract

A novel model for the variability in aerosol optical thickness (AOT) is presented. This model is based on the consideration of AOT fields as realizations of a stochastic process that is the exponent of an underlying Gaussian process with a specific autocorrelation function. In this approach, AOT fields have lognormal PDFs and structure functions with the correct asymptotic behavior at large scales. The latter is an advantage compared with fractal (scale invariant) approaches. The simple analytical form of the structure function in the proposed model facilitates its use for the parameterization of AOT statistics derived from remote sensing data. The new approach is illustrated using a 1-yr-long global MODIS AOT dataset (over ocean) with 10-km resolution. It was used to compute AOT statistics for sample cells forming a grid with 5° spacing. The observed shapes of the structure functions indicated that, in a large number of cases, the AOT variability is split into two regimes that exhibit different patterns of behavior: small-scale stationary processes and trends reflecting variations at larger scales. The small-scale patterns are suggested to be generated by local aerosols within the marine boundary layer, while the large-scale trends are indicative of elevated aerosols transported from remote continental sources. This assumption is evaluated by comparison of the geographical distributions of these patterns derived from MODIS data with those obtained from the GISS GCM. This study shows considerable potential to enhance comparisons between remote sensing datasets and climate models beyond regional mean AOTs.

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Mikhail D. Alexandrov, Andrew A. Lacis, Barbara E. Carlson, and Brian Cairns

Abstract

A retrieval algorithm for processing multifilter rotating shadowband radiometer (MFRSR) data from clear and partially cloudy days is described and validated. This method, while complementary to the Langley approach, uses consistency between the direct normal and diffuse horizontal measurements combined with a regression technique to simultaneously retrieve daily time series of column mean aerosol particle size, aerosol optical depth, NO2, and ozone amounts along with the instrument's calibration constants. Comparison with the traditional Langley calibration method demonstrates two advantages of the approach described here: greater calibration stability and a decreased sensitivity of retrievals to calibration errors.

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