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Computational physics — This article is about computational science applied in physics. epub, mobi, pdf, html, pdb, lit, doc, rtf, txt); Computational Liquid Crystal Photonics. Fundamentals, Modelling and Applications, Salah Obayya, Optical.

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Algorithms considering various other factors have also been proposed to retrieve soil moisture content from passive microwave remote sensed data. Jackson Jackson, developed a so-called single channel algorithm SCA , in which the brightness temperature of the 6. In this algorithm, ancillary data such as air temperature, land cover, Normalized Difference Vegetation Index NDVI , surface roughness, and soil texture and porosity are needed.

Using their algorithm, the surface temperature, the vegetation opacity and the soil moisture are estimated simultaneously. The algorithm proposed by Paloscia Paloscia et al. After more than 20 years effort, good results were obtained and several global and continental scale soil moisture datasets e.

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Njoku et al. But both the quality and application region of these algorithms can be further improved. For example, Shibata et al.

To solve such problem, the forward model, viz. In this study, we present a new soil moisture retrieval algorithm developed at the University of Tokyo. This algorithm is based on a modified radiative transfer model Lu et al. The optimal values of forward model parameters are estimated using in situ observation data and lower frequency brightness temperature data. And with those optimized parameters, we run the forward model to generate a lookup table, which relates the variables of interest, such as soil moisture content, soil physical temperature, vegetation water content and atmosphere optical thickness, to the brightness temperature or some indexes calculated from brightness temperature data.

Finally, soil moisture content is estimated by linearly interpolating the brightness temperature or index into the inversed lookup table. The paper is organized as follows. In Section 3 we describe the structure of our algorithm. Section 6 contains some concluding remarks. Our algorithm is based on a look up table, which is a database of brightness temperature simulated by a radiative transfer model for various possible conditions. The quality of retrieved soil moisture, therefore, is heavily dependent on the performance of the radiative transfer model. So, the main task of our algorithm development was to develop a physically-based soil moisture retrieval algorithm, which is able to estimate soil moisture content from low frequency passive microwave remote sensing data and to overcome the misrepresent problems occurred in dry areas.

For the land surface remote sensing by spaceborne microwave radiometers, the radiative transfer process from land to space can be divided into as four stages as follows:. At the same time, parts of the upward radiation from vegetations join our target radiation. After transmitting from vegetation layer, the radiation continues its way, traversing the cloud and precipitation layers, affected by the absorptive atmosphere gases, scattered by precipitation drops, incorporating the emission from surroundings, finally detected by the sensors boarded on satellites.

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The story of radiative transfer is so complicate that make it necessary to simplify the process to make it computable. The downward radiation from vegetation and rainfall, which is reflected by the soil surface, therefore, is neglected. Moreover, for the lower frequencies region of microwave, the atmosphere is transparent. Finally, after neglecting all the downward radiation and parts of upward radiation from surroundings, the radiative transfer model is written as:.

For the frequencies less than 18GHz, equation 1 can be even simplified by omitting the precipitation layer, as:. Microwave can penetrate into soil media, especially for dry cases, in which the penetration depth of C-band is about several centimeters.

Satellite Soil Moisture Retrieval

The soil moisture observed by microwave remote sensing, therefore, is inside a soil media with a volume of several centimeters depth. The radiative transfer process inside a soil media includes various effects, such as moisture and temperature profile effects and the volume scattering effects of dry soil particles. To simulate these effects, the dielectric constant model should be addressed at first.

In the view of microwave, soil is a multi-phase mixture, with a dielectric constant decided by moisture content, bulk density, soil textural composition, soil temperature and salinity. In our algorithm, the dielectric constant of soil is calculated using Dobson model Dobson et al. The heterogeneity inside soil media causes the so-called profile effects. The profile effects can be accounted for by using the simple zero-order noncoherent model proposed by Schmugge and Choudhury or by more complicate first-order noncoherent model given by Burke et al.

The volume scattering effects inside soil media are not included in both models. In order to include the volume scattering effects, a more complicate model was adopted in our algorithm. We assumed that the soil has a multi-layer structure and is composed of many plane-parallel and azimuthally symmetric soil slabs with spherical scattering particles. The 4-stream fast model proposed by Liu Liu, solves 5 by using the discrete ordinate method and assuming that no cross-polarization exist. With considering the facts that the soil particles are densely compacted, the multi-scattering effects of soil particles should be accounted for.

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And then the radiance of each soil slab was calculated by the 4-stream fast model. Finally, the apparent emission of soil media, T bs in equation 1 and 2 , was obtained. The roughness of the interface divides the reflected wave into two parts, one is reflected in the specular direction and another is scattered in all directions. Generally, the specular component is often referred to as the coherent scattering component.

And the scattered component is known as the diffuse or noncoherent component, which consists of power scattered in all directions but with a smaller magnitude than that of the coherent component. Qualitatively, surface roughness increases the apparent emissivity of natural surfaces, which is caused by increased scattering due to the increase in surface area of the emitting surfaces. In general, the surface roughness effects are simulated by two ways: semi-empirical models and fully physical-based models.

The semi-empirical models are simply and do not cost too much computation efforts. The parameters used in semi-empirical models are often derived from field observations. Depending on the parameters involved, there are three different semi-empirical models: Q-H model Choudhury et al.

AIEM is a physically-based model with only two parameters: standard deviation of the height variations s or rms height and surface correlation length. As a result, the parameters of DMRT-AIEM, such as the rms height, correlation length and soil particle size, have clear physical meanings and their values can be obtained either from field measurement or theoretical calculation. The existence of canopy layers complicates the electromagnetic radiation which is originally emitted solely by soil layers.

The vegetation may absorb or scatter the radiation, but it will also emit its own radiation. The vegetation opacity in turn is strongly affected by the vegetation columnar water content W c. It is a function of plant geometry, and consequently varies according to plant species and associations. Experimental data for this parameter are limited, and values for selected crops have been found to vary from 0. By searching the data base or look up table with the satellite observation as the input, soil moisture and other related variables of interest can be estimated quickly.

Such high searching speed is the main reason why we adopt the look up table method for soil moisture retrieval. The implementation of our algorithm consists of three steps: 1 fixing the parameters used in the forward model; 2 generating a look up table by running forward model; and 3 retrieving soil moisture by searching the look up table. As in other physically-based algorithms, such as that developed by Njoku et al. This advantage derives from the strength of the forward radiative transfer model. Before running the forward RTM to generate look up table, the parameters should be confirmed at first.

For the region where in-situ soil moisture and temperature observation are available and when such observation are also representative, we can use a best-fitting way to optimize parameters. In order to simplify the calculation, low frequencies simulation and observation were used. These parameters are optimized by minimizing the cost function:.

For most remote regions, in-situ representative observation is not available.

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A more general parameter optimization method is proposed by Yang et al. In this method, long term around 2 months meteorological field was used to drive a land surface model Simple Biosphere model, SiB2 to generate time series of soil moisture and temperature data set. Since the land surface parameter set soil texture, porosity, particle size, roughness, etc.

By minimizing the difference between simulated TB and that of satellite observation, the best parameter set can be obtained. The optimized parameters by LDAS-UT, therefore, are depended on models and also influenced by the quality of forcing data. The detail of this method can be found from Yang et al. After Step 1, the optimal parameter values are then stored in the forward RTM. We then run the forward model by inputting all possible values of variables used in Equation 1 , such as soil moisture content, soil temperature, vegetation water content and atmosphere optical thickness.

A family of brightness temperatures is then generated. Based on this brightness temperature database, we select brightness temperatures of special frequencies and polarization to compile a lookup table or to calculate some indices to compile a lookup table. For example, in order to partly remove the influences of physical temperature, the ratio of TB at different frequencies and polarizations can be used.

For instant, we can compile a look up table by using the index of soil wetness ISW Koike et al. The lookup table generated in Step 2 is reversed to give a relationship which maps the brightness temperature or indices obtained from satellite remote sensing data to the variables of interest such as soil moisture, soil temperature and vegetation water content. Finally, we estimate soil moisture content by linear interpolation of the brightness temperature or indices into the inverted lookup table. In this area, meteorological and land hydrological factors are measured with very densely installed instruments.

Figure 1 illustrates the distribution of observation sites in this area.