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Electrical Engineering Assignment on Radar Images Derived Soil for Mapping

Question

Task

Prepare a detailed electrical engineering assignment on “Radar image derived soil”. The main aim is to find the mapping between the soil moisture and the radar image features. This will enable us to do the soil moisture estimation through analyzing radar images, using matlab and big data.

Answer

Abstract
It is discussed in this electrical engineering assignment that the distribution of soil moisture for a potential and reliable mapping is very critical and this can be done using the Remote Satellite Sensing. For the satellite remote sensing it was analyzed by use of radar images using the MatLab and Bigdata. To perform this test, we need a big data that is typically complex due to its inherent characteristics of the soil. In the analysis we are also going to have a look at the various land surface parameters that provides retrieval processes. The parameters that affected our results includes soil characteristics, vegetation density and land cover. We are going to use impact variables when analyzing images derived on the set conditions. In this study we are going to use neural networks and MatLab algorithm codes in the analysis using soil moisture content. We are going to factor in the Normalized Difference Vegetation Index (NDVI) that we got it from the infrared and visible measurement.

Radar Images Derived Soil for Mapping between Soil Moisture and Radar Image Feature

Introduction
The Complex nature of the soil moisture, the backscatter and the non-parametric techniques such as the MatLab Algorithms makes it empirical in ascertaining any statistical relationship (Jacobs, Myers & Whitfield, 2003). This relationship that is created is actually the presence of soil moisture on the surface that is covered with vegetation. Instead of using the classical modeling technique such as hydrological and meteorological applications you can go for the non-parametric methods. In remote sensing the first step will be considering the tools that are used image classifications and pattern recognition done in MatLab. Using this non-parametric technique, we will exploit any statistical relationships that exists between the hydrologic inputs and the outputs. This is an important process that is made through data fusion. This is done through multiple sensors and data sources through alternative techniques such as fuzzy logic that was done through MatLab Algorithms. When using the non-parametric methods, no assumptions that is made for the data fitness.

Objectives
This paper evaluates the multiple regression and MatLab algorithm techniques. These techniques were applied for the retrieval on the spatial soil moisture. From this we are going to set the following objectives;

  • To generate a multivariate model through the regression analysis technique on the soil moisture retrieval technique.
  • To make a comparative analysis on the retrieved soil moisture technique.
  • To make an evaluation of the NDVI effect based on the soil moisture retrieval.

Literature Review
A lot of studies have been conducted on the techniques of measuring the soil moisture content. A lot of research has been done based on these two techniques, point measurement and remote sensing. The remote sensing technique was first introduced with the Integral Equation Model and the Modified Integral Equation Model (Engman & Chauhan, 1995). This technique is proposed for both the spatial and temporal variation for profiles of the soil moisture. An example of the Point Measurement of soil moisture profile is the thermogravimetric Method and Neutron Scattering technique (Paige & Keefer, 2008). Neutron scattering technique is a technique where the soil moisture content will be determined indirectly. The high energy neutrons will be emitted into the source through a radioactive source which will in turn slow down the elastic collisions (HOWARD, 1987). Thermogravimetric method is where moisture will be measured using a drying oven at 105C. The remote sensing technique used algorithm-based techniques that we are going to discuss below.

Ebrahim Babayan et al. (2013) estimated the soil moisture content using the ASAR images. In addition to that he also validated the data using the humidifier. From the research he concluded that GM mode of ASAR is considered as the number one option in the analysis of the semi-arid and undercoats conditions during the estimation of the soil moisture content.

Foson Balik et al. (2008), designed a dual soil moisture model that was used in the measurement of the soil moisture and surface temperature. The model was also critical in determining and estimation of the soil measure based on the depth of the surface. He also used the following models to measure the soil moisture content PALSAR, ASAR, and RADARSTAT. After which he made comparison on the on the different polarization of the three sensors. The results obtained from his experiment was almost similar to that of Izmir from Turkey. In the estimation of the soil moisture content, Saloni et al. (2008), made a comparison of the accuracy of the ASAR images, PALSAR and RADASAT-1. From the comparison he discovered that they all had a coefficient of soil to be R2=0.77, 082, and 0.89 respectively.

In other studies Baghdadi et al (2012) made an estimation of the soil moisture content in a vegetation-free conditions using the TERRASAR-X test data. Kulas et al. (2016), discovered that there are some improvements in the detection of soil moisture in the ranges of 5 to 19%. This was done using the ASCAT which is an active radar and the SMOS which is a passive radar.

Consistent with Algeo et al (2018), with its antenna already rotating at full speed, NASA's SMAP satellite has generated its first global maps of soil moisture, which at extreme latitudes also detects whether or not they are frozen. The Soil Moisture Active Passive (SMAP) spacecraft will help scientists understand the links between the cycles of water, energy and carbon on Earth.It reduces uncertainty in weather and climate forecasting, and it will improve our ability to monitor and predict natural disasters, such as floods and droughts.The radar data obtained from the test has been processed to generate data products with a spatial resolution of approximately 30 kilometers. The radar system operates at 1.2 gigahertz, works by transmitting microwave impulses to Earth and receiving and measuring the intensity of signals that bounce off Earth.

According to Bousbih et al, (2019), various pilot projects have shown that soil moisture can be estimated by remote sensing. Three techniques were evaluated with some success: thermal inertia, passive microwave systems, and synthetic aperture radar (SAR). The advantages and limitations of each technique have been summarized. Most Canadian studies in the field of soil moisture have focused on SAR. They have shown that several parameters, such as angle of incidence, roughness, polarization and frequency, can affect the accuracy of soil moisture estimates. A database collected during the SIR-C / X-SAR Altona experiment in Manitoba was used in this study to assess the impact of angle of incidence on soil moisture estimates. The angle of incidence was the most significant factor to explain the temporal variations of the signal. Its effect on the signal was linear in October. The correlation between soil moisture and signal was greatest with surface moisture (02.5cm) during the wet period (April) but not significant during the dry period (October). A statistical model using humidity and angle of incidenceshowed that an increase of 1 of the angles could lead to a decrease of 0.25dB of the signal in the C-HH band and of 0.30dB in the L-HH band. Such a variation generated a variation of 2% (C-HH) and 5% (L-HH) in the estimates of soil moisture. Keywords: Radar, remote detection, soil moisture, and microwave(Bousbih et al, 2019).

In their study, Poggio, and Gimona, (2017, pp.1094-1110) states the development of biological crusts on bare soils of fallows and plateaus plays a predominant role from an ecological point of view. The physical characteristics and the microbiotic activity of these crusts make it possible to enrich or even stabilize the soil. In-depth study of this crust appears necessary and its monitoring on a regional scale would be facilitated by the use of satellite imagery.

The study is part of the BioCrust project on the vulnerability of microbiotic crusts and soil degradation in the Sahelian zone. Optical imagery provides land cover maps while radar imagery helps track soil moisture. One of the objectives of the BioCrust project is to study the possibility of mapping areas where the presence of biological crusts is important. The soil moisture, which seems to be correlated with the presence of crust, will make it possible to establish relationships between radar signal and humidity, then between humidity and crust. Changes in soil moisture during the seasons will also be taken into account (Brandt et al, 2020).

Study strives to obtain reliable soil moisture maps, in order to subsequently enrich the possibilities for mapping the biological crust in the Sahel. The study relates to two sites in Niger of 100 km² each on which land surveys were carried out simultaneously with the acquisition of the TerraSAR-X radar images. Multi-date data allow an estimate of soil moisture according to the type of season. The mapping of the humidity of the bare soils on the two Nigerien sites and on the various dates shows estimated humidity with an accuracy of around 2.34% in the best cases. However, the link between humidity and the presence of crust remains to be established. These results will contribute to the establishment of a tool for monitoring soil degradation and the vulnerability of microbiotic crusts to climate change and changes in land use (?ekertekin et al 2018, 178-188).

Consistent with Wu et al. (2019), the work essentially focused on the evaluation of the ability to obtain data from the reflection of the electromagnetic wave on the soil surface to determine possible correlations between variations in signal amplitude and the moisture content present in the most superficial layer.An 800 MHz antenna was attached to the GPR. Two profiles were made in two different climatic periods and, simultaneously, measurements of the moisture content were performed using the TethaProbe ML2x humidity sensor, in order to compare the amplitude values ??with the rates humidity measured by the sensor. The results point to the existence of a correlation between the amplitude values ??and the soil moisture.

Blarel et al, (2018) employs a methodological review of indirect techniques of pedological mapping, GIS and remote sensing within digital soil mapping, spectroradiometry and Georadar (GPR), compared to landscape analysis. Research has shown that digital soil mapping (MDS) has been an efficient tool since the beginning of the year 2000, associated with other methods such as remote sensing and laboratory analysis, MDS has provided the world with maps that represent the reality of soils well. But direct techniques are still usual and efficient, and can be associated with indirect methods, so that local mapping information can be dispersed regionally. The search for low-cost, efficient and practical techniques has led researchers to seek techniques such as Georadar to check the depth of the soil, without the need to destroy profiles by opening trenches, as well as using radar images that provide a high spatial resolution product, regardless of the platform's altitude, and which has helped to extract various landscape information directly linked to pedogenesis. Spectroradiometry is a methodology that works with the measurement of radiant electromagnetic energy, and allows for quick associations between targets and spectral curves, allowing the creation of global libraries of these curves. Radiometry in turn has been widely used in systems that operate in the microwave frequency range, ranging from 1mm to 1m in length, and allow you to locate objects.

The research of Klotzsche, et al (2018)aimed to integrate the GPR method (Ground Penetrating Radar) with the refraction seismic, aiming at mapping the NA and estimating the moisture content in an area of ??hydrogeological studies on the USP campus, as well as analyzing the accuracy of the measurement of the two methods. Geophysical, granulometric tests, moisture content, saturation degree, monitoring of NA and monitoring of rainfall indexes were carried out in three periods with seasonal variations over a year called the rainy period, intermediate period and dry period.

The mapping of NA with GPR was done with multi-offset geometry, with the central frequency antennas 50 MHz, 100 MHz and 200 MHz, with the antennas of 100 MHz and 200 MHz being the ones that characterized the NA, reflecting its seasonal variation and maintaining the prof. NA January

The use of refractive seismic generated greater errors and ambiguities in the inversion of the data. In this study, the refractive seismic was not sensitive to seasonal variations and, although the results were close to direct observations, they did not allow mapping the NA fluctuation between the different periods. The estimation of the volumetric moisture content by GPR was obtained with two different methodologies that used the direct wave in the soil. Antennas of 50 MHz, 100 MHz and 200 MHz were used in the different periods. There was a variation in humidity between the periods, with the moisture content of January> April> September (Mahdavi et al, 2018).

According to Mahdavi et al, (2018),the study considered the climatic seasonality, the association of survey data with records collected by the use of the Ground Penetrating Radar (GPR) revealed the behaviour of the water table and the record of salt wedge penetration into the subsurface in this estuarine area. The water table identification was very simple, showing a transition from an unsaturated zone to a well-defined saturated zone. The GPR profiles indicate that a solid horizontal reflector, dipping into the ground, records the depth of the top of the water table. In the post-beach area, the top of the water table is placed around 1 meter deep in the rainy season, becoming deeper in the intertidal zone.

Consistent with Ghorbanian et al, (2020), the top surface of the layer undergoes deepening during the dry season (November), varying from 1.9 metres in the supramarine zone to 2 metres in the intertidal zone. The soil moisture and, above all, the presence of salt in the beach sediments had a significant effect on the reflection signals, changing the dielectric constant of the sediments and thereby generating signal attenuation zones, causing the subsurface salt wedge to be traced during the dry season (Mahdavi et al, 2018). A geophysical research, however, is advised using other approaches, while finding better results from a hydrogeological point of view, establishing signal attenuation zones, allowing the subsurface salt wedge to be mapped during the dry season.

Methodology

Satellite Data
In this research that was used was both from the field data and the satellite data. From the field data we observed the soil type and measured its moisture content. The field measurement was mandatory cause the comparison was done with the moisture obtained on the radar images. This was done on the result to create the relationship between the data from the field and the data from the satellite. To employ the images, we considered two satellites that is the LANDSAT-8 and the SENTINEL-1. The SENTINEL-1 satellite was very important in deleting the vegetation backscatter from the radar images(Houser et al., 1998). This was very important in processing the soil moisture measurement. In addition to that the NDVI index was also calculated so as to measure and formulate the Leaf Area Index (LAI) equation.

Algorithm
In this context, the soil moisture is represented by the water amounting the top layer in the soil surface. We also have the spatial variations of the soil moisture that will be analyzed through the hydrological modelling processes(Li & Islam, 1999). The model was created using algorithmic codes in MatLab. The MatLab Algorithm code had the functions of the basic range-Doppler algorithm that had a focus on the single-look complex (SLC). The big data image that was used was a SAR RAW data. The inputs in the code include;

  • Raw: this is the big data that exists in a complex format i.e., with range along lines.
  • Vr is the sensor velocity (m/s)
  • F0: SAR Central frequency (Hz)
  • PRF: Pulse repetition frequency
  • Fs: range sampling frequency

Output was the single-look-complex image is a double format.

This was the algorithm that was used;

%% RAW data conditioning

display 'RAW data conditioning'

% Subtract raw mean value

raw = raw - mean(mean(raw));

%% Range compression

display 'Range compression'

chirp_rg = chirp_comp(chirp_rg_BW,chirp_rg_T,fs);   % Reference range chirp

 

% Compress each range line

data_rg_compr = zeros(size(raw));                       

% Initialize matrix

for k=1:size(raw,1)

     aux = compress(chirp_rg,raw(k,:),rg_fft_size);      % Correlation

     data_rg_compr(k,:) = aux(1:size(data_rg_compr,2));  % Save result for line k

end

 

%% Doppler centroid estimation

display 'Doppler centroid estimation'

% Change to range-Doppler domain in power

data_doppler = abs(fftshift(fft(data_rg_compr),1)).^2;

% Filter some noise

data_doppler = filter2(ones(101,3)/303,data_doppler,'same');

% Search for each column peak power (position of centroid)

[~,doppler_idx] = max(data_doppler);

% Map found indexes into frequencies

doppler_frec_idx = linspace(-PRF/2,PRF/2,size(data_rg_compr,1));

doppler_centroid_v = doppler_frec_idx(doppler_idx(near_rg_offset+1:end));

 

% Polynomial fit of Doppler centroid

warning off

doppler_centroid_coef = polyfit(near_rg_offset+1:size(data_rg_compr,2),doppler_centroid_v,doppler_pol_deg);

warning on

% Handler to evaluate Doppler centroid [Hz] as function of range pixel numb

doppler_centroid = @(p)(polyval(doppler_centroid_coef,p));

%% Range cell migration correction

display 'RCMC'

% Define Doppler frequencies vector

fdopp = linspace (-PRF/2, PRF/2, size(data_rg_compr,1));

% Range/Doppler domain

data_rg_compr_fft = fftshift(fft(data_rg_compr),1);

% Original slant range spacing vector

R1 = slant_range(1:size(data_rg_compr,2));

 

for k=1:size(data_rg_compr,1)

% New slant range spacing vector, compensates range migration for every

% doppler frequency fdopp(k)

     R2 = R1 + R1*(lambda*fdopp(k)).^2/(8*Vr^2);

 

% Interpolate to compensate migration

     data_rg_compr_fft(k,:) = interp1(R1,data_rg_compr_fft(k,:),R2,'cubic',NaN);

end

 

% Back to Range-Azimuth domain

data_rg_compr_rcmc = ifft(ifftshift(data_rg_compr_fft,1));

size(data_rg_compr_rcmc) 

%% Azimuth compression

display 'Azimuth compression'

 

% Doppler BW to process

chirp_az_BW = 2/lambda*Vr*beam_width_az*pi/180;

% Compress each column in azimuth

slc = zeros(size(data_rg_compr_rcmc));   % initialize matrix

for k=near_rg_offset+1:size(data_rg_compr_rcmc,2)

% Evaluate Doppler centroid

DC = doppler_centroid(k);

 

% Azimuth chirp duration: azimuth footprint length [m] / Vr

chirp_az_T = slant_range(k)*(beam_width_az*pi/180)/Vr;

 

% generate azimuth chirp and conjugate (down-chirp)

chirp_az = chirp_comp(chirp_az_BW,chirp_az_T,PRF,DC)';  

% Compress and save result

aux = compress(chirp_az,data_rg_compr_rcmc(:,k),az_fft_size);

slc(:,k) = aux(1:size(slc,1));

end

 

display 'END'

end

 

function [y,t] = chirp_comp( BW, T, fs, CA, phi)

% [y,t] = chirp_comp( BW , T, fs , CA , phi )

%

% Generates baseband (complex) up-chirp vector.

%

% Inputs:

%    BW: bandwidth [Hz]

%    T: duration [s]

%    fs: sampling frequency [Hz]

%    CA: carrier [Hz] (optional)

%    phi: initial phase [rad] (optional)

% Outputs:

%    y: sampled complex up-chirp vector

%    t: time vector used to sample the chirp

%

% Example:

%    [y,t] = chirp_comp( 40e6 , 10e-6 , 50e6);

%    specgram(y,[],50e6,hanning(70),65)

%

%    Author: Mario Azcueta

 

if ~exist('CA','var')

     CA = 0;

end

if ~exist('phi','var')

     phi = 0;

end

if nargin<3

error('Error. Not enough input arguments.')

end

if BW/2+CA>fs

display('Warning. Aliasing will be produced since BW/2+CA < fs');

end

b = -BW/2 + CA;

a = (BW/2 + CA - b)/(2*T);

t = 0:1/fs:T;

y = exp(1i*2*pi*(a*t.^2+b*t+phi/(2*pi)));

end

Results
The State Geographic Database (STATSGO) provided a platform where data was acquired from the 1 km grid. Using the bi-linear interpolations the data was resampled to 800 m. This was done to match the ESTAR resolution (Geomatica Software). Using the Landsat TM image, we were able to obtain the NDVI values that was calculated from the 30m resolution. We obtained the Vegetation Optical Depth (VOD) functional for the crop type. This VOD Function is meant to cover the water content in the vegetation cover and theb parameters of the vegetation. We developed the NDVI based algorithms on MatLab to determine the vegetation water content.

For the backscatter data we used the Synthetic Aperture Radar (SAR) that was obtained from the RADARSAT-1 satellite image analysis. The satellite has a C-band channel, this provides an effective channel of the beam that might be shallower compared to that less than 5 cm. this is meant for the wet soil and it can also penetrate more than 5 cm for the dry soil. This will create the two images that was taken from the SCANSAR narrow mode. The two images include RADARSAT-1

Once the Algorithm was run, we found the following results;

electrical-engineering-assignment

electrical-engineering-assignment-1

Discussion
There are two methods that were used in this analysis the Multiple regression technique and the fuzzy logic methods(Govind et al., 2009). We had the following combinations as our inputs;

  • Soil characteristics
  • Backscatter
  • NDVI

The above was discussed in this section and the soil moisture content was derived based on the ESTER for 500 pixels from the study. The testing for the models were done for both area A and B and this was done using the backscatter images. The independent pixelswere used in the training models for validation purposes. The soil moisture data was used for predication purposes using the multi-regression structures and fuzzy logic. After that, we'll have two separate data sets. Measurements of field soil moisture and the derived soil moisture, as seen in figure 1. In contrast to area A, lower RMSE was found for area A. This is as seen in Figure 2 by using the overestimated Fuzzy Logic in the soil moisture content. At lower values, higher soil moisture values were underestimated.

The neural models for the NDVI are very critical in the reduction of the RMSE error by about 9.5% using the fuzzy logic model. From the analysis the fuzzy logic models the RMSE of the soil that is predicted. From the analysis the structure of the vegetation includes; canopy height, vegetation water content, the density and geometry. Unavailability of measurements on similar parameters over large areas makes NDVI to be used directly in the calculations(Cao & Woodward, 1998). NDVI provides an impact on the addition of the information on the retrieval of soil moisture(Moran, Peters-Lidard, Watts & McElroy, 2004).

In the paper we observed other additional soil characteristics search as the percentage of sand in the paper which is critical in improving the soil moisture retrieval. This additional soil characteristics played a critical role in the reduction of the RMSE error by 13% using the fuzzy logic model. This is attributed to the facts such as variability in the class covers in the pixels that also generate additional errors. This occurs when there is the conversion of the soil moisture point measurements in the spatial maps. The other observations that were made in the paper also included the heterogeneity on the surface of the soil moisture fields. The other factor was also the heterogeneity of the surface land cover.

For Fuzzy Logic the algorithms that was used was used on a MatLab is

%% RAW data conditioning

display 'RAW data conditioning'

% Subtract raw mean value

raw = raw - mean(mean(raw));

%% Range compression

display 'Range compression'

 

chirp_rg = chirp_comp(chirp_rg_BW,chirp_rg_T,fs);   % Reference range chirp

 

% Compress each range line

data_rg_compr = zeros(size(raw));   % Initialize matrix

for k=1:size(raw,1)

     aux = compress(chirp_rg,raw(k,:),rg_fft_size);      % Correlation

     data_rg_compr(k,:) = aux(1:size(data_rg_compr,2));  % Save result for line k

end

 

%% Doppler centroid estimation

display 'Doppler centroid estimation'

 

% Change to range-Doppler domain in power

data_doppler = abs(fftshift(fft(data_rg_compr),1)).^2;

 

% Filter some noise

data_doppler = filter2(ones(101,3)/303,data_doppler,'same');

 

% Search for each column peak power (position of centroid)

[~,doppler_idx] = max(data_doppler);

 

% Map found indexes into frequencies

doppler_frec_idx = linspace(-PRF/2,PRF/2,size(data_rg_compr,1));

doppler_centroid_v = doppler_frec_idx(doppler_idx(near_rg_offset+1:end));

 

% Polynomial fit of Doppler centroid

warning off

doppler_centroid_coef = polyfit(near_rg_offset+1:size(data_rg_compr,2),doppler_centroid_v,doppler_pol_deg);

warning on

 

% Handler to evaluate Doppler centroid [Hz] as function of range pixel numb

doppler_centroid = @(p)(polyval(doppler_centroid_coef,p));

 

%% Range cell migration correction

display 'RCMC'

 

% Define Doppler frequencies vector

fdopp = linspace(-PRF/2,PRF/2,size(data_rg_compr,1));

% Range/Doppler domain

data_rg_compr_fft = fftshift(fft(data_rg_compr),1);

 

% Original slant range spacing vector

R1 = slant_range(1:size(data_rg_compr,2));

 

for k=1:size(data_rg_compr,1)

% New slant range spacing vector, compensates range migration for every

% doppler frequency fdopp(k)

     R2 = R1 + R1*(lambda*fdopp(k)).^2/(8*Vr^2); 

% Interpolate to compensate migration

    data_rg_compr_fft(k,:) = interp1(R1,data_rg_compr_fft(k,:),R2,'cubic',NaN);

end

 

% Back to Range-Azimuth domain

data_rg_compr_rcmc = ifft(ifftshift(data_rg_compr_fft,1));

 

size(data_rg_compr_rcmc) 

%% Azimuth compression

display 'Azimuth compression'

 

% Doppler BW to process

chirp_az_BW = 2/lambda*Vr*beam_width_az*pi/180;

 

% Compress each column in azimuth

slc = zeros(size(data_rg_compr_rcmc));   % initialize matrix

for k=near_rg_offset+1:size(data_rg_compr_rcmc,2)

 

% Evaluate Doppler centroid

     DC = doppler_centroid(k);

 

% Azimuth chirp duration: azimuth footprint length [m] / Vr

     chirp_az_T = slant_range(k)*(beam_width_az*pi/180)/Vr;

 

% generate azimuth chirp and conjugate (down-chirp)

     chirp_az = chirp_comp(chirp_az_BW,chirp_az_T,PRF,DC)';

 

% Compress and save result

     aux = compress(chirp_az,data_rg_compr_rcmc(:,k),az_fft_size);

     slc(:,k) = aux(1:size(slc,1));

end

display 'END'

end

 

function [y,t] = chirp_comp( BW, T, fs, CA, phi)

% [y,t] = chirp_comp( BW , T, fs , CA , phi )

%

% Generates baseband (complex) up-chirp vector.

%

% Inputs:

%    BW: bandwidth [Hz]

%    T: duration [s]

%    fs: sampling frequency [Hz]

%    CA: carrier [Hz] (optional)

%    phi: initial phase [rad] (optional)

% Outputs:

%    y: sampled complex up-chirp vector

%    t: time vector used to sample the chirp

%

% Example:

%    [y,t] = chirp_comp( 40e6 , 10e-6 , 50e6);

%    specgram(y,[],50e6,hanning(70),65)

%

%    Author: Mario Azcueta

 

if ~exist('CA','var')

     CA = 0;

end

if ~exist('phi','var')

     phi = 0;

end

if nargin<3

error('Error. Not enough input arguments.')

end

if BW/2+CA>fs

display('Warning. Aliasing will be produced since BW/2+CA < fs');

end

 

b = -BW/2 + CA;

a = (BW/2 + CA - b)/(2*T);

 

t = 0:1/fs:T;

y = exp(1i*2*pi*(a*t.^2+b*t+phi/(2*pi)));

end

From the discussion above, it’s very clear that the non-parametric statistical models facilitateusing simplified parametric relationships, real procedures. The models provide a deeper view of the effect of the factors in the process of recovery. Throughout the mentioned retrieval processes and techniques, there was no exact formulation. The variables are not affected by hydrological processes, climate change and weather prediction (Kirstetter et al., 2014). The fuzzy logic model that we used has its own limitations since it doesn’t provide the relationship between the variables. Hence, they are considered as black box. Despite that, the non-parametric methods such as fuzzy logic is the best in soil retrieval under vegetative cover.

The estimate of soil moisture using images radar proved to be physically and mathematically feasible. The use of monopolarized images required the insertion of estimated or measured values of roughness. In this case, the accuracy of the estimate of humidity was considered moderate. The accuracy of the roughness data introduced revealed a strong influence on theresults. This technique cannot be recommended yet for an operational mapping of the humidity of the soil or as a method of controllingirrigation.The general analysis of the results indicates that the technique soil moisture estimation from images of synthetic aperture radar was shown to be physically and mathematically feasible.

Fuzzy cognitive map consists of a directed graph with several nodes that represent the causal concepts that arise from the topic at hand and of directed arcs connected to the nodes that represent the causal relationships between them. However, it presented a moderate precision which is not yet recommended for operational usein soil moisture mapping.Regarding the study and evaluation of the use of GPR (Ground Penetrating Radar) to determine the humidity profile in unsaturated tropical soils, the results obtained so far indicate that it is technically feasible to estimate the moisture profile with GPR under the conditions of field. The GPR proved to be a promising method for monitoring the amount of water on natural slopes and embankments located in areas at risk of landslides. A good correlation was obtained between the values ??of the average dielectric constants obtained with the GPR and the moisture content determined in the laboratory with the gravimetric technique.

Conclusion
From the MatLab algorithms its very clear that Fuzzy Logic has better capabilities in estimating soil moisture through soil retrieval technique. This technique is very fast and more reliable since it provides high levels of accuracy. There are various factors that we have seen that affects soil retrieval technique and this includes soil texture and vegetation parameters. The significance of this parameters was automatically weighted. These parameters were derived from the correlation coefficient and the RMSE. There is still more discussion that needs to be held and further studies to be conducted on the same. There was a validation results that we obtained indicates the fuzzy logic that has MatLab codes. One area that needs to be handled is the Green Leaf Area Index, and the Fractional Green Vegetation Cover.

To strengthen the study of soil-landscape relationship in mountain areas a digital soil mapping approach based on the theory of fuzzy sets was applied. Initially, soil properties were estimated with the regression kriging method (RK), combining soil data and ancillary information derived from a digital elevation model (DEM) and satellite images. Subsequently, the grouping of soil properties was performed on raster format by means of Fuzzy c-Mean algorithm (FCM), whose final product resulted in a variation model of fuzzy soil classes to semi-detailed level. The validation of the model presented an overall accuracy of 88% and Kappa index of 84%, which shows the usefulness of fuzzy clustering in the evaluation of soil-landscape relationships and correlation with soil taxonomic categories.

The very dynamics of events and the number of variables that make up the system under study add additional complexity to the situation was analyzed. The problem is of a methodological nature and in order to respond to it, the combined use of a cognitive map with fuzzy logic techniques is proposed since they provide elements that allow translating verbal expressions and ambiguous sayings into specific numerical values. A specific case of application to the economy is analyzed, although the proposed methodology can be easily extended to other areas related to decision-making and political and production strategies.An inductive method was used to obtain the soil fertility classes, and a soil class model was obtained based on the integration of the variables. The reliability of the individual maps of each soil variable was made by cross validation.To corroborate the predictive capacity of the variables, an analysis of variance was applied, and multivariate statistics were used to assess the final model.

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