Junge Power Law Research Articles

Simultaneous determination of aerosol optical depth and exponent of the Junge power law from MODIS shortwave infrared bands over Qinghai Lake.

The water-leaving radiances for shortwave infrared (SWIR) channels can be negligible, and these channels also contain information on aerosol particle size. Therefore, the satellite-based data of SWIR channels can be used to estimate aerosol particle size over inland waters [Appl. Opt.39, 887 (2000)APOPAI0003-693510.1364/AO.39.000887]. Supposing the actual atmospheric aerosol size distribution is based on the Junge power law, in this paper an iterative algorithm is used to simultaneously determine the aerosol optical depth (AOD) and the exponent of the Junge power law from Aqua MODIS L1B reflectance data of channels 1.64μm and 2.13μm over Qinghai Lake. Whether using the constant or variable aerosol complex refractive index (ACRI), the retrieved exponent of the Junge power law is always larger than the product value. Supposing the product values are accurate, for the constant ACRI, there are 68.91% and 25.48% pixels of acceptable retrieval AOD and the exponent of the Junge power-law value, respectively. Likewise, there are 71.63% and 43.75% pixels for variable ACRI. Compared with the retrieval error under constant ACRI, there are 58.65% and 98.72% pixels, with a smaller AOD and Junge power-law index retrieval error under variable ACRIs, respectively. In addition, the precision of the AOD retrieved with variable ACRI is improved when the AOD product is less than 0.17. However, under the current environment with frequent aerosol particle pollution, the same ACRI for the ten wavelengths can achieve results with equivalent accuracy compared with variable ACRI.

Variability of apparent and inherent optical properties of sediment-laden waters in large river basins - lessons from in situ measurements and bio-optical modeling.

We investigated the relationships between inherent and apparent optical properties (IOP and AOP, respectively) and suspended sediment concentrations (SSC) in the main Amazonian river waters. In situ measurements of SSC, remote sensing reflectance (Rrs), the diffuse light attenuation coefficient (Kd) and the total and non-algal particle (NAP) absorption coefficients (aTOT and aNAP, respectively) were conducted during three sampling trips along different streams of the Amazon River catchment (104 stations). The size distribution and chemical characteristics of the suspended sediment were also determined for 85 stations. We show that the particle size distribution (PSD) in the river water is best described by a segmented Junge power law distribution with a smaller slope value for the smallest particles (J1 = 2.4) and a larger slope value (J2 = 4.1) for the largest particles (> 10 µm). A strong relationship was found between AOPs and IOPs and SSC when the entire data set was considered. However, for the Madeira River, the primary Amazon River tributary in terms of suspended sediment discharge, a significant dispersion was detected for the Rrs - SSC relationship but not for the Kd - SSC relationship. This dispersion has been shown by a previous study, using MODIS data, to display a seasonal pattern, which we investigated in this study using Mie modeling calibrated with suspended sediment characteristics. In the Madeira River, suspended sediment had a finer distribution size and a different mineralogy (e.g., a greater smectite content and a lower kaolinite content) during the rising water stage. Spectral variations of the imaginary part n'(λ) of the refraction index also showed significant differences during the rising water stage. In contrast, other streams of the Amazon basin had very stable properties with respect to granulometry and mineralogy. Model simulations made possible to reproduce both field and satellite observations, showing that the Rrs hysteresis observed in the Madeira River in the near infrared was mainly due to n'(λ) seasonal variations, leading to a decrease of absorption during the rising water stage. Kd was shown to remain stable because of its strong dependency on scattering processes. The model was used to further understand how suspended sediment size distribution and refraction index drive the IOPs in large rivers: n'(λ) variations were shown to control primarily the reflectance variability; Rrs(850) presented limited variations as a function of PSD in the range typical of large rivers (J1 < 3) although it remained sensitive to particle mineralogical composition; Rrs(670) showed the opposite behavior with a higher sensitivity to PSD variation for coarser PSD. Finally, we demonstrate that the use of the Rrs ratio between the red and infrared channels allowed a reduction of the Rrs sensitivity in all cases, by an average of 50% with respect to changes in the mineral composition or size distribution of suspended sediment. In particular, the Rrs ratio varied by less than 5% for PSD representative of surface river waters.

Spatial heterogeneity in spectral variability of aerosol optical depth and its implications to aerosol radiative forcing in the Tropical Indian Ocean and in the Indian Ocean Sector of Southern Ocean

The aerosol optical depths (AODs) in the wavelength range 380–875nm and black carbon (BC) mass concentrations were estimated over the tropical Indian Ocean and in the Indian Ocean sector of Southern Ocean, between 14°N and 53°S, during December 2011–February 2012, onboard the Ocean Research Vessel (ORV) Sagar Nidhi. The data were analysed to understand the spectral variability, micro-physical characteristics of aerosols and the associated radiative forcing. Concurrent MODIS-derived chlorophyll a (Chl-a) and sea-surface temperature (SST) provided ancillary data used to understand the variability of biomass in association with fronts and the possible role of phytoplankton as a source of aerosols. AODs and their spectral dependencies were distinctly different north and south of the Inter-Tropical Convergence Zone (ITCZ). North of 11°S (the northern limit of ITCZ), the spectral distribution of AOD followed Ängstrom turbidity formule (Junge power law function), while it deviated from such a distribution south of 16°S (southern boundary of ITCZ). At the southern limit of the ITCZ and beyond, the spectral variation of AOD showed a peak around 440nm, the amplitude of which was highest at ~43°S, the axis of the subtropical front (STF) with the highest Chl-a concentration (0.35µgl−1) in the region. To understand the role of Chl-a in increasing AOD at 440nm, AOD at this wavelength was estimated using Optical properties of Aerosols and Clouds (OPAC) model. The anomalies between the measured and model-estimated (difference between the measured and estimated AOD values at 440nm) AOD440 were correlated with Chl-a concentrations. A very high and significant association with coefficient of determination (R2=0.80) indicates the contribution of Chl-a as a source of aerosols in this part of the ocean. On the basis of the measured aerosol properties, the study area was divided into three zones; Zone 1 comprising of the area between 10°N and 11°S; Zone 2 from 16°S to 53°S; and Zone 3 from 52°S to 24°S during the return leg. BC mass concentration was in the range 520ngm−3 to 2535ngm−3 in Zone 1, while it was extremely low in the other zones (ranging from 49.3 to 264.4ngm−3 in Zone 2 and from 61.6ngm−3 to 303.3ngm−3 in Zone 3). The atmospheric direct-short wave radiative forcing (DRSF), estimated using a radiative transfer model (Santa Barbara DISORT Atmospheric Radiative Transfer – SBDART), was in the range 4.72–27.62wm−2 north of 16°S, and 4.80–6.25wm−2 south of 16°S.

利用MODIS数据同时反演中国近海海域气溶胶光学厚度和Junge谱指数

Based on the reflectance data of the fifteenth and sixteenth channels in near-infrared bands and spatial geometrical angles of the moderate resolution imaging spectro-radiometer,aphysical iterative algorithm was proposed,using the Junge power-law size distribution to approximate the actual atmospheric aerosol model.The algorithm was used for simultaneous determination of the aerosol optical thickness and the exponent of the Jung power law.The results show that the aerosol optical thickness over most of the studied ocean is in the range of 0.02~0.17,the exponent of the Jung power law is in the range of 2.8~3.8,and both the aerosol optical thickness and exponent of the Jung power law have the trend of descending from coast to open sea.Therefore,the reasonable spatial distributions of the exponent of the Junge power law and aerosol optical thickness were obtained.Comparing the retrieval results with the moderate resolution imaging spectro-radiometer product and aerosol robotic network measurements,the retrieval algorithm whose results are more approach aerosd robotic network data than moderate resolution imaging spectro-radiometer product,is more accurate than moderate resolution imaging spectro-radiometer algorithm.Therefore,the retrieval method which is applied for the studied region is feasible and reliable.

利用MODIS数据同时反演中国近海海域气溶胶光学厚度和Junge谱指数

Based on the reflectance data of the fifteenth and sixteenth channels in near-infrared bands and spatial geometrical angles of the moderate resolution imaging spectro-radiometer,aphysical iterative algorithm was proposed,using the Junge power-law size distribution to approximate the actual atmospheric aerosol model.The algorithm was used for simultaneous determination of the aerosol optical thickness and the exponent of the Jung power law.The results show that the aerosol optical thickness over most of the studied ocean is in the range of 0.02~0.17,the exponent of the Jung power law is in the range of 2.8~3.8,and both the aerosol optical thickness and exponent of the Jung power law have the trend of descending from coast to open sea.Therefore,the reasonable spatial distributions of the exponent of the Junge power law and aerosol optical thickness were obtained.Comparing the retrieval results with the moderate resolution imaging spectro-radiometer product and aerosol robotic network measurements,the retrieval algorithm whose results are more approach aerosd robotic network data than moderate resolution imaging spectro-radiometer product,is more accurate than moderate resolution imaging spectro-radiometer algorithm.Therefore,the retrieval method which is applied for the studied region is feasible and reliable.

Simultaneous determination of aerosol optical thickness and exponent of Junge power law from satellite measurements of two near-infrared bands over the ocean

An iterative algorithm is presented in this study for simultaneous determination of both the aerosol optical thickness and the exponent of the Junge power law from the total reflectance data of two satellite-based, near-infrared bands over the ocean. The atmospheric aerosol model is assumed as the Junge power-law size distribution in retrieval of the data. Numerical simulations show that relative errors in retrieval of the aerosol optical thickness and the exponent of the Junge power law are less than 5% when the actual atmospheric aerosol follows the Junge power-law size distribution. For other aerosol size distributions, relative errors of the aerosol optical thickness are less than approximately 10%. The proposed method is applied to a case study of the data of two near-infrared channels of the Sea-Viewing Wide Field-of-View Sensor (SeaWiFS) over the East China Sea area. The results show that reasonable spatial distribution of the exponent of the Junge law and the aerosol optical thickness may be obtained on a pixel-by-pixel basis through use of the proposed retrieval algorithm.

An algorithm for determination of aerosol opticalthickness from AVHRR imagery over oceans

The uncertainty in aerosol size distributions is a main source of errors in aerosol optical thickness determined from satellite measurements. To reduce the errors resulting from the uncertainty in aerosol size distributions, we have performed sensitivity analyses. It is found the errors resulting from the uncertainty in aerosol size distribution can be considerably reduced by using the Junge power law to approximate the aerosol size distribution in an actual atmosphere, if the exponent value is determined at the same time. An iterative algorithm is then developed for the simultaneous determination of aerosol optical thickness and the exponent of the Junge power law over ocean areas from the upwelling radiances measured in AVHRR visible and near infrared channels. A number of numerical experiments are carried out to investigate the validity of the Junge power law approximation by assuming the aerosol size distributions in an actual atmosphere are bimodal with different mode parameters, and by using the actual aerosol size distributions determined at several places by Kaufman et al. (1994). The results show that the errors in determined aerosol optical thickness resulting from the Junge power law approach are significantly reduced. The iterative algorithm is investigated further by comparing the aerosol optical thickness deduced from satellite measurement with that observed by a sun photometer.

Size distribution of aerosol particles: comparison between agricultural and industrial areas in Egypt

Mie theory has been used in this work to obtain a theoretical calculation of the size distribution of aerosol particles by using tabulated mean of the Angstrom wavelength exponent α o. Comparison was done between an industrial polluted area (Helwan, which is a neighbor to Cairo city), and an agricultural relatively unpolluted area (Mansoura, about 140 km from Cairo). The results show that the size distribution obeys the Junge power law. The size of particles in the polluted area is larger than that in the unpolluted area.

Atmospheric correction of ocean color imagery: use of the Junge power-law aerosol size distribution with variable refractive index to handle aerosol absorption

When strongly absorbing aerosols are present in the atmosphere, the usual two-step procedure of processing ocean color data-(1) atmospheric correction to provide the water-leaving reflectance (rho(w)), followed by (2) relating rho(w) to the water constituents-fails and simultaneous estimation of the ocean and aerosol optical properties is necessary. We explore the efficacy of using a simple model of the aerosol-a Junge power-law size distribution consisting of homogeneous spheres with arbitrary refractive index-in a nonlinear optimization procedure for estimating the relevant oceanic and atmospheric parameters for case 1 waters. Using simulated test data generated from more realistic aerosol size distributions (sums of log-normally distributed components with different compositions), we show that the ocean's pigment concentration (C) can be retrieved with good accuracy in the presence of weakly or strongly absorbing aerosols. However, because of significant differences in the scattering phase functions for the test and power-law distributions, large error is possible in the estimate of the aerosol optical thickness. The positive result for C suggests that the detailed shape of the aerosol-scattering phase function is not relevant to the atmospheric correction of ocean color sensors. The relevant parameters are the aerosol single-scattering albedo and the spectral variation of the aerosol optical depth. We argue that the assumption of aerosol sphericity should not restrict the validity of the algorithm and suggest an avenue for including colored aerosols, e.g., wind-blown dust, in the procedure. A significant advantage of the new approach is that realistic multicomponent aerosol models are not required for the retrieval of C.

Studies of the number concentration and size distribution of the suspended dust particles in the atmosphere of Qena/Egypt

Studies of particle number concentration, size, shape and distribution of the dust particles suspended in the atmosphere of Qena (upper Egypt) have been conducted. The results show that the concentration of these particles decreases with increasing size according to the Junge power law size distribution: n(dp) = C/ln10 (dp)−(α+1. The values of the exponent α range from 1.3 to 2. The largest number of particles have sizes less than 2 μm with irregular shape. The effect of some weather conditions on the total number of particles was considered. The total number of particles and effective mean diameters were calculated.

Evaluation of a new aerosol model with a Brownian diffusion technique

Measurements in Alaska in sub-polar night conditions have indicated that the size distribution of atmospheric aerosols varies significantly and systematically depending upon the type of air mass. Atmospheric aerosol particles are small and numerous in warm Pacific marine air mass systems and large and sparse in cold, Arctic-derived air mass systems. In a previous paper this was hypothesized to be associated with the progressive loss of the smallest particles by attachment to cloud droplets under the driving influence of thermal Brownian motion. A theory involving two parameters, r (mean particle radius), and n 0 (aerosol number concentration) was developed to describe the process. In the previous paper, the relationship r ∞ n 0 ν where ν is the Junge power law exponent (ν ≌ 3) was derived and has recently been confirmed to acceptable accuracy with the use of a simple experiment which employed diffusive separation. The diffusion experiment has also allowed us to estimate that the fraction of time, φ, that the aerosol-laden polar air masses coexist in the presence of cloud is ≌0.01 < φ < 0.1. The submicron aerosol particles in Arctic-derived air masses flowing into central Alaska are deduced to have residence times on the order of ∼10 days.

On the Form of Stationary Size Distributions Established by Coagulation and Sedimentation

Abstract In stationary solutions of the equations for nucleation, coagulation and sedimentation, the concentration of large particles falls off more strongly than any power of particle size. The tails of stationary size distributions established by these processes are thus of Marshall-Palmer (exponential), rather than Junge (power law), type.

Calculated Distribution Characteristics for a Reinforced Coagulating Aerosol at Steady State

Abstract The steady-state number balance for a reinforced coagulating aerosol, with particle removal at some selected size, was solved as a continuous function of particle volume. Using a variety of log-normal feed distributions, it was demonstrated that a power law relationship will result between particle concentration n(v) and volume v, regardless of feed distribution shape. The standard deviation σ of the feed distribution was varied from 1.21 to 20.09. The slopes of the calculated distributions varied with σ. For values of σ 8.0 the slope approached −1.0. Calculated distribution slopes for σ < 2 were similar to those of atmospheric distributions reported for stable meteorological conditions. The time to reach steady state was estimated and found not to be unreasonable compared to meteorological time scales. The results suggest that the Junge power law relationship observed in many atmospheric size distributions may be explained principa...

Size distribution of atmospheric particles

The size distribution of atmospheric particles cannot be represented by the Junge power law, as a coherent function, because this law is independent of the larger particles. The shape of the atmospheric distribution is governed by the sources of aerosol. A method of fitting the distributions by number and volume of particles with lognormal components is described. As an illustration the experimentally measured distributions of Los Angeles smog are fitted with seven components.