The analysis performed in this research is performed in ArcGIS 10.8, MATLAB, and SPSS software. To evaluate and compare the accuracy of each index, we used cubic spline interpolation, Pearson correlation coefficient, explanation coefficient (R2), Root Mean Square Error (RMSE), Mean Absolute Deviation (MAD), and Standard Mean Error (MSE). Finally, the correlation equation of each index with its actual values is measured. In this study, wheat and alfalfa crops are assessed in different areas. Figure 2shows the pixels corresponded with one of the agricultural areas. Furthermore, the selected pixels are from a large number of pixels for evaluation and analysis. We have also elected a few pixels to represent non-agricultural areas. For example, pixels 5, 6, 7, 25, and 30 are non-agricultural areas. We also evaluated the alfalfa crop to increase the accuracy and efficiency of the research. Pixels 24, 26, 28, and 29 are for the alfalfa crop. Usually, the alfalfa is harvested at regular periods.
7.1. Plant height assessment
In this research, plant height is evaluated during different stages of growth. Plant height is calculated based on Eq. 12. Table 5 shows the cloud status, surface albedo, NDVI, SAVI, NSAVI, LAI, NLAI, Zom, and Zom_new for wheat at pixel 16. The cultivation date of the crop is 21/10/2020. Therefore, the algorithm for calculating the plant height and other parameters performs from the next period of receiving images (i.e. 16 days later). The last row of Table 2 is the height of the plant (cm) during different stages of growth. As can be seen from Table 5, Pixel 16 is overcast on 22/11/2020, 24/12/2020, and 1/5/2021. Cloud values are determined based on the CDI index moreover are updated by the CFI index to calculate their actual values. Appendix A shows the steps for modifying and updating the parameters according to the cloud days. Table 6 also shows the final values (or updates) for cloud days in Appendix A. the pixel values are updated based on the cubic spline interpolation.
As shown from Table 6, the end condition of the algorithm is when the NLAI < 7 or the current NSAVI is lower than the previous period. In farm studies, the observed plant height for pixel 16 was between 85 and 93 cm on 30/3/2021 (the last stage of crop growth), which is close to the results obtained in this research (i.e. 88.42436 cm). Furthermore, we observed the height of the crop 19 to 24 cm in pixel 16 on 14/3/2021, which is close to our results in this research (i.e. 21 cm). According to the performed analysis, the end of the crop growth period is when NLAI > = 7. To prove this claim, we use hypothesis testing. In other words, we present the following hypothesis and confirm it using hypothesis testing.
Table 3
Surface
|
Albedo
|
Source
|
Surface
|
Albedo
|
Source
|
Absolute black body
|
0
|
(Riihelä, Manninen, Laine, Andersson, & Kaspar, 2013)
|
Grass or pasture
|
0.15–0.25
|
(Lee, 1978; Rosenberg, Blad, & Verma, 1983; Taylor, Thomas, Truhlar, & Whelpdale, 1996)
|
Soils, dark, wet to light, dry
|
0.05–0.5
|
(Oke, 2002)
|
Corn fields
|
0.15–0.22
|
(Lee, 1978; Rosenberg et al., 1983; Taylor et al., 1996)
|
Dry sandy soils
|
0.25–0.45
|
(Rosenberg et al., 1983)
|
Rice fields
|
0.17–0.22
|
(Lee, 1978; Rosenberg et al., 1983; Taylor et al., 1996)
|
Sand, wet
|
0.09
|
(Oke, 2002; Riihelä et al., 2013; Rosenberg et al., 1983; VAN WIJK, 1964)
|
Coniferous forest
|
0.10–0.15
|
(Lee, 1978; Rosenberg et al., 1983; Taylor et al., 1996)
|
Sand, dry
|
0.18
|
(Oke, 2002; Riihelä et al., 2013; Rosenberg et al., 1983; VAN WIJK, 1964)
|
Deciduous forest
|
0.15–0.20
|
(Lee, 1978; Rosenberg et al., 1983; Taylor et al., 1996)
|
Dark clay, wet
|
0.02–0.08
|
(Oke, 2002; Riihelä et al., 2013; Rosenberg et al., 1983; VAN WIJK, 1964)
|
Water
|
0.025–0.35
|
(Lee, 1978; Rosenberg et al., 1983; Taylor et al., 1996)
|
Dark clay, dry
|
0.16
|
(Oke, 2002; Riihelä et al., 2013; Rosenberg et al., 1983; VAN WIJK, 1964)
|
Fresh deep snow
|
0.9
|
(Lee, 1978; Rosenberg et al., 1983; Taylor et al., 1996)
|
Fields, bare
|
0.12–0.25
|
(Oke, 2002; Riihelä et al., 2013; Rosenberg et al., 1983; VAN WIJK, 1964)
|
Dry silt loam soil (before cultivation)
|
0.23–0.28
|
(Lee, 1978; Rosenberg et al., 1983; Taylor et al., 1996)
|
Grass, green
|
0.16–0.27
|
(Oke, 2002; Riihelä et al., 2013; Rosenberg et al., 1983; VAN WIJK, 1964)
|
Dry silt loam soil (after cultivation)
|
0.15–0.18
|
(Lee, 1978; Rosenberg et al., 1983; Taylor et al., 1996)
|
Fresh snow
|
0.8–0.85
|
(Lee, 1978; Robinson, 2009; Rosenburg, Blad, & Verma, 1974; Taylor et al., 1996)
|
Dry clay loam soil
|
0.18–0.22
|
(Lee, 1978; Rosenberg et al., 1983; Taylor et al., 1996)
|
Old snow and ice
|
0.3–0.7
|
(Lee, 1978; Rosenberg et al., 1983; Taylor et al., 1996)
|
Wet clay loam soil
|
0.11–0.13
|
(Lee, 1978; Rosenberg et al., 1983; Taylor et al., 1996)
|
Black soil
|
0.08–0.14
|
(Lee, 1978; Rosenberg et al., 1983; Taylor et al., 1996)
|
Wet ploughed fields
|
0.05–0.14
|
(Lee, 1978; Rosenberg et al., 1983; Taylor et al., 1996)
|
Clay
|
0.16–0.23
|
(Lee, 1978; Rosenberg et al., 1983; Taylor et al., 1996)
|
Dry salt cover
|
0.5
|
(Lee, 1978; Rosenberg et al., 1983; Taylor et al., 1996)
|
White-yellow sand
|
0.34–0.40
|
(Lee, 1978; Rosenberg et al., 1983; Taylor et al., 1996)
|
Absolute white surfaces
|
1
|
(Lee, 1978; Rosenberg et al., 1983; Taylor et al., 1996)
|
Gray-white sand
|
0.18-23
|
(Lee, 1978; Rosenberg et al., 1983; Taylor et al., 1996)
|
Alfalfa
|
0.25–0.31
|
(Lee, 1978; Rosenberg et al., 1983; Taylor et al., 1996)
|
Table 4
Surface emissivity and albedo values for soil texture
Albedo(α)
|
Emissivity(ε)
|
Soil type
|
α>=0.15 and α<=0.18
|
ε <=0.28 [28–30]
|
Silt loam
|
α>=0.23
|
ε <=0.28 [28–30]
|
Silt loam
|
α>=0.15
|
ε <=0.35 [28–30]
|
Clay
|
α>=0.02 and α < 0.08
|
ε = 0.97 [28–30]
|
Clay
|
α = 0.16
|
ε = 0.95 [28–30]
|
Clay
|
α = 0.12 or α = 0.14
|
-
|
Clay
|
α>=0.18
|
ε <=0.21 [28–30]
|
Sand
|
α = 0.09
|
ε = 0.98 [28–30]
|
Sand
|
α = 0.18
|
ε = 0.95 [28–30]
|
Sand
|
α = 0.19 or α = 0.09
|
-
|
Sand
|
α = 0.16 or α = 0.18
|
-
|
Loamy sand
|
α = 0.13 α = 0.1
|
-
|
Loam
|
α = 0.15 or α = 0.17
|
-
|
Sandy loam
|
α = 0.11
|
-
|
Silt clay loam
|
Table 5
Cloud status, Albedo, NDVI, SAVI, NSAVI, LAI, NLAI, Zom, and Zom−new in pixel 16
Pixel 16
|
21/10/2020
|
6/11/2020
|
22/11/2020
|
8/12/2020
|
24/12/2020
|
9/1/2021
|
25/1/2021
|
Cloud status
|
Sunny
|
Sunny
|
Overcast
|
Sunny
|
Overcast
|
Sunny
|
Sunny
|
Albedo
|
0.102547
|
0.119428
|
0.127351
|
0.059780
|
0.391589
|
0.070059
|
0.066931
|
NDVI
|
0.082330
|
0.057918
|
0.039461
|
0.090315
|
0.042559
|
0.097660
|
0.102393
|
SAVI
|
0.123493
|
0.086875
|
0.059191
|
0.135469
|
0.063838
|
0.146486
|
0.153586
|
NSAVI
|
0.165028
|
0.116015
|
0.078997
|
0.180907
|
0.085294
|
0.195663
|
0.205171
|
LAI
|
0.044651
|
-0.024178
|
-0.073495
|
0.068131
|
-0.065371
|
0.090183
|
0.104633
|
NLAI
|
0.128323
|
0.030241
|
-0.038438
|
0.162078
|
-0.027056
|
0.194401
|
0.215742
|
Zom
|
0.000804
|
-0.000435
|
-0.001323
|
0.001226
|
-0.001177
|
0.001623
|
0.001883
|
Zom_new
|
0.002310
|
0.000544
|
-0.000692
|
0.002917
|
-0.000487
|
0.003499
|
0.003883
|
Pixel 16
|
10/2/2021
|
26/2/2021
|
14/3/2021
|
30/3/2021
|
15/4/2021
|
1/5/2021
|
17/5/2021
|
Cloud status
|
Sunny
|
Sunny
|
Sunny
|
Sunny
|
Sunny
|
Overcast
|
Sunny
|
Albedo
|
0.050937
|
0.193367
|
0.060623
|
0.066288
|
0.062319
|
0.291793
|
0.076985
|
NDVI
|
0.081549
|
0.096981
|
0.180234
|
0.265875
|
0.341465
|
0.036723
|
0.244286
|
SAVI
|
0.122320
|
0.145470
|
0.270345
|
0.398805
|
0.512189
|
0.055084
|
0.366424
|
NSAVI
|
0.163327
|
0.194660
|
0.361758
|
0.534694
|
0.687585
|
0.073615
|
0.491598
|
LAI
|
0.042378
|
0.088131
|
0.374383
|
0.775967
|
1.318022
|
-0.08062
|
0.660096
|
NLAI
|
0.124771
|
0.192173
|
0.644363
|
1.466728
|
6.042331
|
-0.04807
|
1.197614
|
Zom
|
0.000763
|
0.001586
|
0.006739
|
0.013967
|
0.023724
|
-0.00145
|
0.011882
|
Zom_new
|
0.002246
|
0.003459
|
0.011599
|
0.026401
|
0.108762
|
-0.00086
|
0.021557
|
Table 6
The modified values of Table 5 based on the algorithm presented in Appendix A
Pixel 16
|
21/10/2020
|
6/11/2020
|
22/11/2020
|
8/12/2020
|
24/12/2020
|
9/1/2021
|
25/1/2021
|
Cloud status
|
Sunny
|
Sunny
|
Overcast
|
Sunny
|
Overcast
|
Sunny
|
Sunny
|
NSAVI
|
0. 116015
|
0.148461
|
0.180907
|
0.265559
|
0.350211
|
0.434862
|
0.519512
|
NLAI
|
0.030241
|
0.09616
|
0.162078
|
0.227997
|
0.293915
|
0.359834
|
0.425752
|
Zom_new
|
0.000544
|
0.001731
|
0.002917
|
0.004104
|
0.00529
|
0.006477
|
0.007664
|
Plant Height
|
0.442551
|
1.407212
|
2.371873
|
3.336534
|
4.301195
|
5.265856
|
6.230517
|
Pixel 16
|
10/2/2021
|
26/2/2021
|
14/3/2021
|
30/3/2021
|
15/4/2021
|
1/5/2021
|
17/5/2021
|
Cloud status
|
Sunny
|
Sunny
|
Sunny
|
Sunny
|
Sunny
|
Overcast
|
Sunny
|
NSAVI
|
0.604162
|
0.688812
|
0.773461
|
0.858109
|
Stop
|
-
|
-
|
NLAI
|
0.491671
|
0.644363
|
1.466728
|
6.042331
|
18.0908
|
-
|
-
|
Zom_new
|
0.00885
|
0.011599
|
0.026401
|
0.108762
|
Stop
|
-
|
-
|
Plant Heitgh
|
7.195178
|
9.429702
|
21.46431
|
88.42436
|
Stop
|
-
|
-
|
Lemma 1
The end of the crop growth is when NLAI > = 7. In other words, the maximum crop height is when the NLAI is < 7.
Proof
According to the hypothesis testing, the hypothesis is in H1, and its contradiction is in H0. So, we can determine the accuracy of Lemma 1 at the significant level α (error).
$$\left\{\begin{array}{c}{H}_{0}: \mu \ge 7 Null hypothesis \\ {H}_{1}: \mu <7 Opposite hypothesis \left(claim\right) \end{array}\right. \left(21\right)$$
In a population with the normal \(\stackrel{-}{X}\)-distribution, there are z-distribution or t-distribution, which are defined as follows:
1) If n ≤ 30, then the distribution is the Student’s t-distribution, and the test statistic is defined as follows:
$$t=\frac{\stackrel{-}{X}-{\mu }_{0}}{{S}_{\overline{X}}} \left(22\right)$$
$${S}_{\overline{X}}=\frac{T}{\sqrt{n}}$$
23
2) If n > 30, then the distribution is the Z-distribution, and the test statistic is defined as follows:
$$z=\frac{\stackrel{-}{X}-{\mu }_{0}}{{S}_{\overline{X}}} \left(24\right)$$
Where µ0 is the statistical symbol of the hypothesis (i.e. µ0 = 7), \({S}_{\overline{X}}\) is the standard deviation, T is the average, and n is the number of samples. In this research, n is the number of days observed by the satellite. After specifying the values defined above, the critical values (the boundaries of H0 and H1) are determined based on α, as shown in Fig. 3 and Appendixes B and C. As shown in Table 2, n is less than 30 (n = 18). Therefore, the test is the Student’s t-distribution. According to Fig. 3, the claim is in the H1 area. So, we use the left-tailed test (Fig. 3, Part 2). After determining the H1 and n values, we must specify the critical values or boundaries H0 and H1 based on α, as shown in Appendixes B and C.
To prove the hypothesis test, we examine the equations 21 to 24 based on Table 6:
$$degrre of freedom(d.f)=n-1=10$$
$$\stackrel{-}{X}=0.931006$$
$${s}_{\stackrel{-}{X}}=0.524569$$
If the test statistic is in the H0 area, the H0 hypothesis is accepted. Otherwise, the assumption H0 is rejected. According to Appendix B, the critical value at the error level 0.0005 is \({t}_{\text{0.0005,10}}=-4.587\), which is placed before the value − 11.57 (in the H1 area). So, the hypothesis µ < 7 is confirmed with an error level of 0.0005%. Therefore, the final period of crop growth is when µ < 7. On the other hand, according to the FAO-56 paper, the maximum height of wheat is 1 m (h = 1m). So, according to equations 9 and 10:
$${Z}_{om}=0.123*h=0.123*1=0.123m$$
$${Z}_{om}=0.018*NLAI=0.018*7=0.126m$$
\({Z}_{om}\) =126m is the maximum value Zom because the NLAI value never becomes 7. Therefore, the value of Zom will be less than 0.126 m (i.e. Zom<0.126m). Hence, the value obtained for Zom in this study is very close to the suggested value in the FAO-56 paper (i.e. 0.123m). Figure 4 shows the height of the crop during different growth stages in pixel 16.
Table 7 represents the plant height for other pixels in the study area. The values of Table 6 are according to the algorithm presented in Appendix A. For some pixels, such as Pixel 3, the maximum NLAI value was less than 7, but NSAVI was lower than in previous periods. For this reason, in this pixel, the algorithm is stopped when NSAVI is lower than the previous periods. As mentioned in previous sections, pixels 5, 6, 7, 25, and 30 represent non-agricultural areas. Therefore, they have not listed in Table 7. For example, after running the proposed algorithm, the height of pixel 7 was 7.78 cm. In the local review was discovered that in this pixel, weeds resulting from the excess water of agricultural land have grown. Pixels 26 to 29 and pixel 24 correspond to the alfalfa crop. Because alfalfa is usually harvested at periodic intervals, the height of the crop is lower than that of wheat in Table 7. Figure 5 shows the length of the alfalfa crop in different periods (6/11/2020 to 5/17/2021). As can be seen from Fig. 5, the height of the crop increases or decreases periodically. It is due to the crop harvest at periodic times.
In addition, Fig. 5 shows the growth period of the alfalfa in spring and summer is longer than in winter and autumn.
Table 7
Plant height in agricultural field (30 selected pixels)
|
Pixel 1
|
Pixel 2
|
Pixel 3
|
Pixel 4
|
Pixel 5
|
Pixel 6
|
Pixel 7
|
Pixel 8
|
Plant Height
|
62.44683
|
95.9588
|
15.66455
|
71.57664
|
-
|
-
|
-
|
26.55421
|
|
Pixel 9
|
Pixel 10
|
Pixel 11
|
Pixel 12
|
Pixel 13
|
Pixel 14
|
Pixel 15
|
Pixel 16
|
Plant Height
|
84.57621
|
69.37449
|
53
|
37
|
71.28399
|
93.93727
|
44.39287
|
88.42436
|
|
Pixel 17
|
Pixel 18
|
Pixel 19
|
Pixel 20
|
Pixel 21
|
Pixel 22
|
Pixel 23
|
Pixel 24
|
Plant Height
|
35.65393
|
15.72616
|
44.84101
|
15.00217
|
59.37066
|
84.17111
|
58.99047
|
12.5146
|
|
Pixel 25
|
Pixel 26
|
Pixel 27
|
Pixel 28
|
Pixel 29
|
Pixel 30
|
|
|
Plant Height
|
-
|
11.47016
|
12.34447
|
12.14943
|
7.135624
|
-
|
|
|
Figure 6 represents the plant height during different growth stages. Furthermore, Fig. 7 illustrates the plant height in the final growth stage. As it is clear, in some areas the plant height is taller than in others because there are factors such as land slope, soil moisture, and soil texture type. Figure 8 shows the slope of the land in the study area. We used the digital elevation model (DEM) to calculate the slope of the land. As shown in Figs. 7 and 8, plant growth is higher in areas with low slopes because of the proper water absorption, excellent materials, and minerals. The spaces between soil particles are called porosity. The porosity provides the required water and air for the plant. If the empty spaces in the soil are small, the plant cannot grow well. In general, 50% of suitable soil is porosity, and the other 50% is solid. The solid part of the soil contains minerals and organic matter. In section 5, we determine the type of soil texture using the albedo and emissivity. Figures 9 and 10 show the volumetric structure of suitable soil with four soil components and the soil texture in the study area. As shown in Fig. 9, water intake in sandy soils is lower than in clay and mixed soils. Therefore, the plant grows is better in clay soils or soils with more clay than in other areas. According to Figs. 7 and 10, it is clear that plant growth in the clay area is better than in other areas. On the other hand, Sandy areas have grown less than other areas.
Another major factor in plant growth is soil moisture. In this study, we have used three indicators Soil Moisture (SM), Normalized Difference Temperature Index (NDTI), and Perpendicular Soil Moisture Index (PSMI), which are defined as follows:
$${PSMI}_{i}=\frac{{D}_{i}}{(1+{NDVI}_{i})} \left(25\right)$$
$$SM=\frac{{\gamma }_{6}}{{\gamma }_{7}} \left(26\right)$$
$$NDTI=\frac{{\gamma }_{6}-{\gamma }_{7}}{{\gamma }_{6}+{\gamma }_{7}} \left(27\right)$$
where
\({\gamma }_{6}\) and \({\gamma }_{7}\): Bands 6 and 7 of the Landsat 8,
\({D}_{i}\) : The vertical distance,
\({NDVI}_{i}\) : Vegetation index of each pixel.
The vertical distance is defined as follows:
$${D}_{i}=\frac{({TIR}_{i.norm}+{NDVI}_{i})}{\sqrt{2}} \left(28\right)$$
\({TIR}_{i.norm}\) is the normalized temperature and is defined as follows:
$${TIR}_{i.norm}=\frac{{TIR}_{i}-{TIR}_{min}}{{TIR}_{max}-{TIR}_{min}} \left(29\right)$$
\({TIR}_{i}, {TIR}_{min}\) , and \({TIR}_{max}\) are the correspondent pixel temperature, minimum, and maximum area temperature, respectively.
PSMI is used to measure surface moisture using two indices of temperature and vegetation. The low value of the PSMI leads to high soil moisture(B. Li, Ti, Zhao, & Yan, 2016; Z. Li & Tan, 2013). NDVI can separate agricultural areas from bare soil(Gao et al., 2013; Wang, 2000). On the other hand, Li et al.(Z. Li & Tan, 2013) consider this index for measuring soil surface moisture. They proved that as long as the soil volumetric moisture is less than 50%, the shortwave infrared band can better show soil moisture than red and near-infrared bands. They also proved that Landsat short-band infrared bands provide better information on soil surface moisture in arid and desert areas. Therefore, NDTI uses two shortwave infrared data (bands 6 and 7). Soil moisture (SM) of the shortwave infrared is another index studied in this study. This index consists of a simple fraction of the spectral reflection values of bands 6 and 7. At different amounts of soil moisture, two important drops are observed in the absorption of the electromagnetic spectrum. The drops are in the
range of 1.4 to 1.6µm and 1.9 to 2.1µm in the soil spectrum(Fabre, Briottet, & Lesaignoux, 2015). These two spectral ranges correspond to the bands 6 and 7 in Landsat 8. Therefore, we can calculate the soil moisture by these two bands. Figure 11 shows the values of the three indices during the plant growth period in the study area.
Figure 11 shows the SM and NDTI are low in areas with high PSMI and vice versa. In other words, in fields that PSMI is high or the SM and NDTI are low, soil moisture is low. Therefore, the plant height is better in clay areas by comparing Figs. 11, 7, and 10.
7.2. Detection of cloud pixels
We used CDI, CMI, and CFI to detect and eliminate cloudy pixels. From Table 4 it is clear that on 22/11/2020, 24/12/2020, and 1/5/2021, the study area has cloud cover (overcast). Figures 12, 13, 14, and 15 show the cloud cover on these dates. As it clear, the three indices significantly reduce cloud effects.
As mentioned earlier, pixels with the CDI between the minimum (CDImin) and average (CDImean) have selected as cloud pixels. CDImin and CDImean are visible in the properties/symbology section of ArcGIS software. The values have shown in Fig. 16 on 21/10/2020 (cloudless) and 1/5/2021 (overcast). Tables 8 and 9 show the CDI values on 21/10/2020 and 1/5/2021. As Fig. 16 shows, the CDImin and CDImean values are − 10.71 and − 8.73 on 1/5/2021. Furthermore, these two values are − 9.75 and − 8.86 on 21/10/2020. Figure 16 and Tables 8, 9 show the CDI value of all pixels is between CDImin and CDImean on 1/5/2021. On the other hand, the CDI values are outside the range of CDImin and CDImean on 21/10/2020. We can separate the overcast from cloudless using the CDI index. Figures 14 and 17 show the cloud cover and CDI performance in overcast and cloudless on 1/5/2021, respectively. As shown in Fig. 17, thin clouds have removed by this index. From Fig. 17, it is clear that there are three areas including overcast, partly cloudy, and cloudless. Tables 10, 11, and 12 show some
pixels in overcast, partly cloudy, and sunny, respectively. As shown in Fig. 16, the CDI is between − 8.73 and − 10.71 in overcast pixels. Table 10 illustrates the CDI index. As shown in Table 10, the CDI values are between − 8.73 and − 10.71.
From Table 11, it is clear that some pixels are between − 8.73 and − 10.71, and some are outside this range. On the other hand, the cloud impacts are negligible outside this range, and the values observed by Landsat 8 are close to the original values. Therefore, there is no need to delete or modify these areas. Table 12 shows all pixels that are outside of the range in the sunny field. In other words, Table 12indicates that the area is perfectly cloudless. In this study, we used cubic spline interpolation to modify cloud pixels (see Appendix 1). The total values for the overcast and partly cloudy areas have listed in Appendices D and E.
Table 8
CDI
|
Pixel 1
|
Pixel 2
|
Pixel 3
|
Pixel 4
|
Pixel 5
|
Pixel 6
|
Pixel 1
|
-8.34372
|
-8.09981
|
-8.11845
|
-8.391
|
-8.50872
|
-8.47154
|
Pixel 2
|
-8.34608
|
-8.32719
|
-8.45913
|
-8.43185
|
-8.44638
|
-8.31778
|
Pixel 3
|
-8.46102
|
-8.37378
|
-8.39657
|
-8.38519
|
-8.39037
|
-8.3654
|
Pixel 4
|
-8.40091
|
-8.42686
|
-8.40353
|
-8.40955
|
-8.42599
|
-8.36081
|
Pixel 5
|
-8.43731
|
-8.41394
|
-8.41966
|
-8.42284
|
-8.46918
|
-8.35763
|
Table 9
CDI
|
Pixel 1
|
Pixel 2
|
Pixel 3
|
Pixel 4
|
Pixel 5
|
Pixel 6
|
Pixel 1
|
-9.20094
|
-9.1274
|
-9.22131
|
-9.32931
|
-9.38488
|
-9.32433
|
Pixel 2
|
-9.08562
|
-9.20861
|
-9.38263
|
-9.52685
|
-9.60019
|
-9.40083
|
Pixel 3
|
-9.43486
|
-9.4822
|
-9.57821
|
-9.65114
|
-9.65962
|
-9.44145
|
Pixel 4
|
-9.62104
|
-9.67555
|
-9.66935
|
-9.7264
|
-9.68469
|
-9.5698
|
Pixel 5
|
-9.73253
|
-9.7585
|
-9.73008
|
-9.72573
|
-9.73791
|
-9.71482
|
Table 10
The CDI values for the overcast area in Fig. 17
-10.1499
|
-10.0776
|
-10.0556
|
-10.0557
|
-10.0298
|
-10.104
|
-10.15
|
-10.0864
|
-10.1162
|
-10.0901
|
-10.1083
|
-10.1025
|
-10.0583
|
-10.1083
|
-10.19
|
-10.1556
|
-10.1062
|
-10.1401
|
-10.1543
|
-10.1683
|
-10.1477
|
-10.1421
|
-10.1446
|
-10.1464
|
-10.1944
|
-10.2045
|
-10.2306
|
-10.2272
|
-10.1886
|
-10.1121
|
-10.1414
|
-10.101
|
-10.056
|
-10.1872
|
-10.2238
|
-10.1934
|
-10.1348
|
-10.1132
|
-10.1156
|
-10.0606
|
-10.0387
|
-10.0784
|
-10.1519
|
-10.1423
|
-10.0896
|
-10.0738
|
-10.0819
|
-10.0396
|
-9.99215
|
-9.94524
|
-10.0516
|
-10.1179
|
-10.136
|
-10.1024
|
-10.0712
|
-10.0145
|
-9.92738
|
-9.85839
|
-9.91515
|
-10.0327
|
-10.0667
|
-10.0156
|
-10.0522
|
-10.0277
|
Table 11
The CDI values for partly cloudy area in Fig. 17
-8.84953
|
-9.05979
|
-9.13364
|
-9.17697
|
-9.13909
|
-9.00994
|
-8.9245
|
-8.66631
|
-8.89867
|
-9.05646
|
-9.19931
|
-9.23919
|
-9.28833
|
-9.1164
|
-8.92191
|
-8.81394
|
-9.04441
|
-9.15237
|
-9.20858
|
-9.17145
|
-9.13305
|
-9.13475
|
-9.13107
|
-9.08042
|
-9.18
|
-9.30886
|
-9.32503
|
-9.25104
|
-9.1421
|
-9.1459
|
-9.30924
|
-9.23608
|
-9.16872
|
-9.24931
|
-9.33733
|
-9.38123
|
-9.24838
|
-9.02138
|
-9.15905
|
-9.20389
|
-9.14385
|
-9.32334
|
-9.40623
|
-9.33587
|
-9.14812
|
-9.16874
|
-9.1952
|
-9.26947
|
-9.17051
|
-9.14423
|
-9.34912
|
-9.30971
|
-9.14882
|
-9.09463
|
-9.23362
|
-9.38139
|
-9.18686
|
-9.16861
|
-9.35189
|
-9.38375
|
-9.39361
|
-9.44192
|
-9.46602
|
-9.50561
|
Table 12
CDI values for sunny area in Fig. 17
-8.51861
|
-8.45626
|
-8.4243
|
-8.45099
|
-8.26541
|
-8.31165
|
-8.36047
|
-8.34649
|
-8.42337
|
-8.43059
|
-8.44234
|
-8.33801
|
-8.18358
|
-8.25333
|
-8.30907
|
-8.27623
|
-8.41397
|
-8.41964
|
-8.39484
|
-8.29485
|
-8.21143
|
-8.31313
|
-8.22618
|
-8.2306
|
-8.3633
|
-8.31657
|
-8.24258
|
-8.22643
|
-8.21805
|
-8.17409
|
-8.14222
|
-8.22331
|
-8.38578
|
-8.34742
|
-8.31517
|
-8.29498
|
-8.37873
|
-8.38488
|
-8.46156
|
-8.44335
|
-8.3639
|
-8.36195
|
-8.37675
|
-8.40182
|
-8.39779
|
-8.32151
|
-8.34174
|
-8.41515
|
-8.37296
|
-8.35516
|
-8.3222
|
-8.41309
|
-8.37656
|
-8.21092
|
-8.22165
|
-8.67952
|
-8.39886
|
-8.40217
|
-8.38883
|
-8.46299
|
-8.43722
|
-8.36396
|
-8.44328
|
-8.52996
|
7.3. Improving the FAO-56 paper for calculating evapotranspiration
The method presented in the FAO-56 paper calculates the reference evapotranspiration of the grass and alfalfa crops. It is based on the plant height, surface albedo, surface resistance, etc. The parameters estimate evapotranspiration and water requirements of the plant under standard conditions and water stress. Different areas have different climatic conditions (e.g. soil type, soil surface moisture, desert and mountainous regions, aerodynamic conditions, vegetation, surface resistance, leaf stomata, etc.). Therefore, the FAO-56 paper is not proper in many areas. Identifying standard states and the water stress of plants is a challenge because diagnosing the conditions requires field inspection, and field inspection is very time-consuming and costly. Furthermore, the early, development, mid-season, and late stages of plant growth are also determined based on vegetation. It is a vital issue in the FAO-56 paper. In the FAO 56 paper, the early stage of plant growth (Kc-ini) is from the time of crop cultivation to 10% cover. The development stage is from 10% coverage to full coverage. If LAI is 3, then vegetation is full. Calculating the LAI in the FAO-56 paper is a big challenge because the LAI is maximum when shading the crop canopy is almost complete, and the plant can grow without interfering with adjacent leaves. The presented equations in the FAO-56 paper are not accurate enough to calculate the LAI because they are based on several different climates and do not perform well in many environments. Also, plant coefficients in the FAO-56 paper are calculated based on plant cultivation days that have various conditions and the number of plant cultivation days. Therefore, the indices presented in this study can better estimate the early, development, mid-season, and final stages of crop growth. For example, the number of cultivation days of the plant is applied to calculate plant coefficients during growth stages (i.e. Lini, Ldev, Lmid, and Llate). The growth stages of the plant are in terms of days and are calculated from the date of cultivation. Therefore, the length of growth stages under normal conditions is presented and changed based on climate, cultivation conditions, and plant variety in different regions. Hence, using local information or remote sensing is recommended.
The main factor in the growth rate of the plant is determining plant coefficients and evapotranspiration. We can determine the growth stages using plant height. In this study, we provided criteria to detect the land slope, growth rate or plant height, and soil moisture. The criteria can be less costly than the FAO-56 paper for determining standard conditions and water stress. In addition, we can predict the future states of plant growth with sufficient accuracy in several stages of plant growth. For example, we can determine the plant coefficients in conditions without water stress or with water stress by identifying the height of the crop, the amount of vegetation, the type of soil texture, surface albedo, soil moisture, and land slope. In this research, appropriate criteria are provided for determining the plant coefficients. In addition, by knowing criteria such as land slope, soil texture, and soil surface moisture, it is possible to identify water stress conditions in the plant and use them to calculate single and dual crop evapotranspiration. The following equation is applied to calculate the plant coefficient [17]:
$${K}_{cb}={K}_{cb}(table17\_FAO56)+\left[0.04\right({u}_{2}-2)-0.004({RH}_{min}-45\left)\right]{\frac{h}{3}}^{0.3} \left(30\right)$$
Where
\({K}_{cb}\) : crop coefficient (dimensionless),
\({K}_{cb}(table17\_FAO56)\) : basal crop coefficient or original \({K}_{cb}\) (dimensionless),
\({u}_{2}\) : the mean value for daily wind speed at 2 m height over grass or alfalfa during the mid or late season growth stage(m/s),
\(h\) : plant height,
\({RH}_{min}\) : the average value for daily minimum relative humidity during the mid- or late-season growth stage (%).
The original \({K}_{cb}\) for wheat in the early, mid, and late seasons is 0.5, 1.10, and 0.3, respectively [17]. If \({K}_{cb}\) is higher than 0.45, it must be corrected by relation 30. Otherwise, the value of \({K}_{cb}\) is equal to the original \({K}_{cb}\). The upper limit of the crop coefficient (\({K}_{c-max}\)) indicates the upper limit of plant evapotranspiration and is defined based on the basal crop coefficient as follows [17]:
\({K}_{c-max}=max\left\{\right(1.2+\left[0.04\right({u}_{2}-2)-0.004({RH}_{min}-45\left)\right]{\frac{h}{3}}^{0.3}),\) (\({K}_{cb}+0.05\))}s (31)
The fraction of vegetated soil is indicated by \({f}_{c}\). In other words, \({f}_{c}\) is the average fraction of soil covered by vegetation, and (1-\({f}_{c}\)) is the approximate fraction of soil surface that is exposed. \({f}_{c}\) is calculated from the following equation:
$${f}_{c}=\left({\frac{-{K}_{c-min}}{{K}_{c-max}-{K}_{c-min}})}^{(1+0.5h)} \right(32)$$
\({K}_{cb}\) is the minimum crop coefficient (dimensionless) for dry soil and is between 0.15 and 0.20. We have considered the first stage up to 10% growth of the plant. On the other hand, the maximum height of wheat is 1 meter [17]. So, the maximum plant height is 10 cm (0.1*100cm), or the NLAI index is less than 1 in the first stage. The development stage is when the NLAI is higher than 1 and less than 3. Finally, the final stage of plant growth is when the NLAI is higher than 3 and less than 7 (Lemma 1). To calculate evapotranspiration, we use the following equations:
$$ET=({k}_{s}{k}_{cb}+{k}_{e})*{ET}_{0} \left(33\right)$$
Where
\(ET\) : the reference evapotranspiration of the grass plant (mm/day),
\({k}_{s}\) : water stress coefficient (dimensionless),
\({K}_{cb}\) : basal plant coefficient(dimensionless) (relation 30),
\({k}_{e}\) : soil evaporation coefficient (dimensionless).
\(ET\) is calculated according to the Penman-Monteith equation in the FAO-56 paper. If \({k}_{s}\)<1 the plant has water stress and \({k}_{s}\)= 1 shows the plant has no water stress. \({k}_{s}\) and \({k}_{e}\) are calculated as follows:
$${k}_{e}=min\left({k}_{r}\right({K}_{c-max}-{K}_{cb}),{f}_{ew}*{K}_{c-max}) \left(34\right)$$
$${k}_{s}=\frac{TAW-{D}_{r}}{TAW-RAW} \left(35\right)$$
where
\({f}_{ew}\) : fraction of the soil that is both exposed and wetted (fraction of soil surface from which most evaporation occurs.) (dimensionless),
\({k}_{r}\) : evaporation reduction coefficient (dimensionless),
\({D}_{r}\) : root zone depletion (mm),
TAW: total available soil water in the root zone (mm).
RAW: the readily available soil water in the root zone (mm).
\({f}_{ew}\) and \({D}_{r}\) is defined as follows:
$${f}_{ew}=min(1-{f}_{c},{f}_{w}) \left(36\right)$$
$${D}_{r}={D}_{r-1}-P-R-I-C+ET+Dp \left(37\right)$$
where
\({f}_{w}:\) fraction of soil surface wetted by irrigation [0.01-1],
\({D}_{r-1}\) : water content in the root zone at the end of the previous day (mm),
\(P\) : precipitation on current day (mm),
\(R\) : runoff from the soil surface (mm),
\(I:\) irrigation depth on current day that infiltrates the soil (mm),
\(C:\) capillary rise from the groundwater table (mm),
ET: crop evapotranspiration (mm/day),
\(Dp\) : water loss out of the root zone by deep percolation (mm).
If the terrace and vegetation on the field are suitable, there is no runoff (R = 0). Also, assuming that the static surface distance from the root zone depletion is more than one meter, the capillary rise is zero (C = 0). Despite heavy irrigation or rainfall, the depletion is zero (\({D}_{r}\) = 0). Under these conditions, the deep percolation is calculated as follows:
$${DP}_{i}={p}_{i}-{RO}_{i}+{I}_{i}-{ET}_{ci}-{D}_{r-1} \left(38\right)$$
While the soil water is less than the field capacity, then the deep penetration of water into the soil is zero. \({f}_{w}\)can also be obtained in terms of irrigation depth in the whole field area and irrigation depth in wet soil fraction. \({f}_{w}\)is different in various irrigation methods. If the soil surface is more than 3 or 4 mm, the value of \({f}_{w}\)becomes 1. Table 13 shows the value of \({f}_{w}\)in different irrigation methods.
Readily available water (RAW) is the amount of water that is absorbed by the plant without water stress and is defined as ρ * TAW. In other words, RAW is readily available soil water in the root zone. TAW and ρ are the average fraction of total available water (TAW) and the soil water, respectively. ρ can be depleted from the root zone before water stress, and its value is between zero and one. In this study, we analyzed the field on 24/1/2020 because it rained 12 mm, and 11 days later the field was irrigated 40 mm by the Basin method. Figure 18 illustrates \({f}_{c}\), \({k}_{cb}\), and \({k}_{c-max}\) in pixel 4. As Fig. 18 represents at the beginning of the period the value of \({f}_{c}\)is somewhat high due to rainfall and gradually decreases until the beginning of the eleventh day. From the eleventh day, \({f}_{c}\) is increased due to irrigation, which is more than the first day. This is due to the amount of water in the soil, which is more on the eleventh day than on the first day. \({k}_{cb}\) and \({k}_{c-max}\) have also increased gradually at the beginning of the period until the eleventh day, and from the eleventh day onwards increase significantly due to irrigation. In another analysis, we considered a situation that the field was irrigated 45 mm and rained 12 mm on the sixth day. Figure 19 shows \({D}_{r}\)and RAW in whole agricultural pixels over 11 days.
Table 13
\({f}_{w}\) values based on irrigation type [17]
\({f}_{w}\)
|
Irrigation type
|
1.0
|
Precipitation
|
1.0
|
Sprinkler irrigation
|
1.0
|
Basin irrigation
|
1.0
|
Border irrigation
|
0.6 ... 1.0
|
Furrow irrigation (every furrow), narrow bed
|
0.4…0.6
|
Furrow irrigation (every furrow), wide bed
|
0.3…0.5
|
Furrow irrigation (alternated furrows)
|
0.3…0.4
|
Trickle irrigation
|
Figure 19 illustrates the irrigation is proper at the beginning of the period. Therefore, the and RAW also decrease significantly. Again, on the sixth days the and RAW also decrease due to rainfall (12 mm) but it is not as much as the first day because the rainfall is less than the irrigation of the first day. Figures 20 and 21 show the values of , , , and , respectively. As it is clear, the parameters also decrease during irrigation and rainfall. As can be seen from Figure 20, when the soil water becomes minimum on the last day, then is less than 1. So, the field needs re-irrigation.
Figure 21. \({k}_{cb}\),\({k}_{e}\) and \({k}_{cb}+{k}_{e}\)values with 45 mm irrigation on the first day and 12 mm of rainfall on the sixth day.
Figure 22 shows the reference evapotranspiration of the grass crop (\({ET}_{0}\)) and the evapotranspiration of the field under standard conditions (\({ET}_{c}\)) and water stress (\({ET}_{adj}\)). During this period, the field has been irrigated twice. The first irrigation has been performed two days before the start of the 10 days. Furthermore, the second irrigation has been performed on the sixth day. As Figs. 20 and 22 show, irrigation is performed on the sixth day because \({k}_{s}\) is less than 1. So, the rate of evapotranspiration is also reduced under water stress. As previously mentioned, in standard conditions \({k}_{s}\)= 1 and water stress \({k}_{s}\)<1.
7.4. Research validation
We have used the cubic spline interpolation, Pearson correlation coefficient, explanation coefficient (R2), root mean square error (RMSE), mean absolute deviation (MAD), and mean standard error (MSE) to evaluate and compare the accuracy of each index. Finally, the correlation of each index is calculated with its actual values. The equations are defined as follows:
$$RMSE=\sqrt{\frac{\sum _{i=1}^{n}{({A}_{t}-{F}_{t})}^{2}}{n}} \left(39\right)$$
$$MAD=\frac{\sum _{i=1}^{n}|{A}_{t}-{F}_{t}|}{n} \left(40\right)$$
$$MSE=\frac{\sum _{i=1}^{n}{({A}_{t}-{F}_{t})}^{2}}{n} \left(41\right)$$
where
n: number of samples (number of days viewed by Landsat 8 satellite),
\({A}_{t}\) : actual value observed by Landsat 8 satellite,
\({F}_{t}\) : predicted value observed by Landsat 8 satellite.
We calculate the LSAVI and CMI to determine the slope of the soil line. we use bands 4 and 5 to calculate the slope of the soil line. Figure 23 shows the regression equation of the slope of the soil line with determination and correlation coefficients. In Fig. 23, the high correlation and determination coefficients indicate high accuracy analyses.
Tables 14 and 15show the regression equations, determination and correlation coefficients, RMSE, MAD, and MSE for the pixels corresponding to the agricultural area, based on the two indices NSAVI and NLAI during the growth period. Non-agricultural pixels have not listed in the tables.
Table 14
Regression equation between NLAI index and plant height with correlation coefficient and the coefficient of determination, the MSE, RMSE, and MAD errors for agricultural pixels
|
Regression equation
(NLAI-Height)
|
Correlation
coefficient
|
Determination
coefficient
|
RMSE
|
MAD
|
MSE
|
Pixel 1
|
0.14634x + 4e-17
|
1
|
1
|
0.4374
|
0.298
|
0.1913
|
Pixel 2
|
0.14634x + 7e-17
|
1
|
1
|
2.1907
|
1.2896
|
4.799
|
Pixel 3
|
0.14634x + 2e-17
|
1
|
1
|
0.3531
|
0.2506
|
0.1247
|
Pixel 4
|
0.14634x − 2E-17
|
1
|
1
|
1.3609
|
0.7034
|
1.8522
|
Pixel 7
|
0.14634x − 2E-17
|
1
|
1
|
0.2738
|
0.2395
|
0.0750
|
Pixel 8
|
0.14634x + 6E-17
|
1
|
1
|
0.9184
|
0.7917
|
0.8435
|
Pixel 9
|
0.14634x
|
1
|
1
|
1.5842
|
0.9043
|
2.5098
|
Pixel 10
|
0.14634x + 6E-17
|
1
|
1
|
1.2862
|
0.7005
|
1.6544
|
Pixel 11
|
0.14634x
|
1
|
1
|
1.0864
|
0.6643
|
1.1803
|
Pixel 12
|
0.14634x − 2E-17
|
1
|
1
|
0.0140
|
0.0083
|
0.0001
|
Pixel 13
|
0.14634x
|
1
|
1
|
1.4273
|
0.9435
|
2.0731
|
Pixel 14
|
0.14634x
|
1
|
1
|
1.8228
|
1.1422
|
3.3226
|
Pixel 15
|
0.14634x
|
1
|
1
|
09290
|
0.6404
|
0.8631
|
Pixel 16
|
0.14634x
|
1
|
1
|
1.6239
|
0.7948
|
2.6369
|
Pixel 17
|
0.14634x
|
1
|
1
|
0.7479
|
0.4748
|
0.5621
|
Pixel 18
|
0.14634x − 2E-17
|
1
|
1
|
0.3787
|
0.2687
|
0.1434
|
Pixel 19
|
0.14634x
|
1
|
1
|
0.9217
|
0.6467
|
0.8495
|
Pixel 20
|
0.14634x
|
1
|
1
|
0.5536
|
0.4784
|
0.3065
|
Pixel 21
|
0.14634x
|
1
|
1
|
1.1471
|
0.6399
|
1.3157
|
Pixel 22
|
0.14634x
|
1
|
1
|
1.6327
|
0.9143
|
2.6657
|
Pixel 23
|
0.14634x − 2E-17
|
1
|
1
|
1.1542
|
0.7210
|
1.3322
|
Pixel 24
|
0.14634x
|
1
|
1
|
0.3929
|
0.3068
|
0.1543
|
Pixel 26
|
0.14634x − 4E-17
|
1
|
1
|
0.3980
|
0.3444
|
0.1584
|
Pixel 27
|
0.14634x − 5E-17
|
1
|
1
|
0.4550
|
0.3901
|
0.2070
|
Pixel 28
|
0.14634x − 2E-17
|
1
|
1
|
03365
|
0.2674
|
0.1132
|
Pixel 29
|
0.14634x − 3E-17
|
1
|
1
|
0.2337
|
0.1963
|
0.0546
|
According to Tables 14 and 15, it is clear that the height = 0.14634 * NLAI equation is more frequent. Therefore, the equation can be suggested to calculate the plant height based on the NLAI with a good approximation. We can use this equation to predict plant growth in later stages. Furthermore, the accuracy of this equation is better in the developmental and late stages than in the early stage. Therefore, the general equation based on NLAI is linear and is defined according to the following formula:
$$Plant Height=\alpha .NLAI+\beta \left(42\right)$$
where α and β are linear regression coefficients that are obtained up to the mid-season stage of plant growth. The equation is used to predict plant growth in later stages.
As stated in section 6.1, we use three indices SM, NDTI, and PSMI to measure soil moisture. The SM and NDTI are directly related to each other and inversely to the PSMI. To confirm the accuracy of the research results, we considered 22/11/2020, 26/2/2021, and 15/4/2021 because the dates are the beginning of the early, developmental, and final stages of plant growth, respectively. Tables 16, 17, and 18 show the values of hygrometry and the correlation and determination coefficients for 30 selected pixels in the agricultural field. In addition, Figs. 24, 25, and 26 show the values of the indices in the above periods. Tables 16, 17,18, and Figs. 25 and 26 show the NDTI and SM are directly related and inversely related to the PSMI. In other words, the correlation values and coefficient of explanation between NDTI and SM are high and in other states are low. Therefore, in pixels with high NDTI and low SM and PSMI, the soil moisture is high and vice versa. Figures 24, 25, and 26 also confirm this result.
Table 15
Regression equation between NLAI index and plant height with correlation coefficient and the coefficient of determination, the MSE, RMSE, and MAD errors for agricultural pixels
|
Regression equation
(NLAI-Height)
|
Correlation
coefficient
|
Determination
coefficient
|
RMSE
|
MAD
|
MSE
|
Pixel 1
|
0.14634x + 4e-17
|
1
|
1
|
0.4374
|
0.298
|
0.1913
|
Pixel 2
|
0.14634x + 7e-17
|
1
|
1
|
2.1907
|
1.2896
|
4.799
|
Pixel 3
|
0.14634x + 2e-17
|
1
|
1
|
0.3531
|
0.2506
|
0.1247
|
Pixel 4
|
0.14634x − 2E-17
|
1
|
1
|
1.3609
|
0.7034
|
1.8522
|
Pixel 7
|
0.14634x − 2E-17
|
1
|
1
|
0.2738
|
0.2395
|
0.0750
|
Pixel 8
|
0.14634x + 6E-17
|
1
|
1
|
0.9184
|
0.7917
|
0.8435
|
Pixel 9
|
0.14634x
|
1
|
1
|
1.5842
|
0.9043
|
2.5098
|
Pixel 10
|
0.14634x + 6E-17
|
1
|
1
|
1.2862
|
0.7005
|
1.6544
|
Pixel 11
|
0.14634x
|
1
|
1
|
1.0864
|
0.6643
|
1.1803
|
Pixel 12
|
0.14634x − 2E-17
|
1
|
1
|
0.0140
|
0.0083
|
0.0001
|
Pixel 13
|
0.14634x
|
1
|
1
|
1.4273
|
0.9435
|
2.0731
|
Pixel 14
|
0.14634x
|
1
|
1
|
1.8228
|
1.1422
|
3.3226
|
Pixel 15
|
0.14634x
|
1
|
1
|
09290
|
0.6404
|
0.8631
|
Pixel 16
|
0.14634x
|
1
|
1
|
1.6239
|
0.7948
|
2.6369
|
Pixel 17
|
0.14634x
|
1
|
1
|
0.7479
|
0.4748
|
0.5621
|
Pixel 18
|
0.14634x − 2E-17
|
1
|
1
|
0.3787
|
0.2687
|
0.1434
|
Pixel 19
|
0.14634x
|
1
|
1
|
0.9217
|
0.6467
|
0.8495
|
Pixel 20
|
0.14634x
|
1
|
1
|
0.5536
|
0.4784
|
0.3065
|
Pixel 21
|
0.14634x
|
1
|
1
|
1.1471
|
0.6399
|
1.3157
|
Pixel 22
|
0.14634x
|
1
|
1
|
1.6327
|
0.9143
|
2.6657
|
Pixel 23
|
0.14634x − 2E-17
|
1
|
1
|
1.1542
|
0.7210
|
1.3322
|
Pixel 24
|
0.14634x
|
1
|
1
|
0.3929
|
0.3068
|
0.1543
|
Pixel 26
|
0.14634x − 4E-17
|
1
|
1
|
0.3980
|
0.3444
|
0.1584
|
Pixel 27
|
0.14634x − 5E-17
|
1
|
1
|
0.4550
|
0.3901
|
0.2070
|
Pixel 28
|
0.14634x − 2E-17
|
1
|
1
|
03365
|
0.2674
|
0.1132
|
Pixel 29
|
0.14634x − 3E-17
|
1
|
1
|
0.2337
|
0.1963
|
0.0546
|
Table 16
|
Regression equation
(NSAVI-Height)
|
Correlation
coefficient
|
Determination
coefficient
|
RMSE
|
MAD
|
MSE
|
Pixel 1
|
0.3537x – 0.39031
|
0.9999
|
0.9999
|
0.7235
|
0.6489
|
0.5235
|
Pixel 2
|
0.29512x – 0.29956
|
1
|
1
|
1.1551
|
0.8992
|
1.3342
|
Pixel 3
|
0.44253x – 0.55999
|
0.98
|
0.9690
|
0.6867
|
0.6847
|
0.4715
|
Pixel 4
|
0.46825x – 0.061078
|
0.9999
|
0.9983
|
0.3505
|
0.2674
|
0.1228
|
Pixel 7
|
0.28912x – 0.29111
|
1
|
1
|
0.4670
|
0.4637
|
0.2181
|
Pixel 8
|
0.31428x – 0.032208
|
1
|
1
|
0.6948
|
0.6710
|
0.4828
|
Pixel 9
|
1.3923x0.025579
|
0.6666
|
0.88
|
1.0133
|
1.0059
|
1.0268
|
Pixel 10
|
0.75687x – 0.13951
|
0.9794
|
0.9593
|
0.2304
|
0.2229
|
0.0531
|
Pixel 11
|
1.251x0.024383
|
0.9029
|
0.9784
|
0.9100
|
0.8983
|
0.8282
|
Pixel 12
|
0.30502x – 0.026605
|
0.9959
|
0.992
|
0.3618
|
0.2681
|
0.1309
|
Pixel 13
|
0.60838x0.020132
|
0.7831
|
0.9356
|
0.2462
|
0.2028
|
0.0606
|
Pixel 14
|
0.59814x0.020077
|
0.7545
|
0.9257
|
0.2417
|
0.2038
|
0.0584
|
Pixel 15
|
0.74941x0.021806
|
0.8025
|
0.9376
|
0.3948
|
0.3652
|
0.1559
|
Pixel 16
|
1.4774x0.025704
|
0.8603
|
0.9650
|
1.1275
|
1.1182
|
1.2713
|
Pixel 17
|
1.1439x0.024185
|
0.9540
|
0.9693
|
0.8285
|
0.8172
|
0.6864
|
Pixel 18
|
0.42465x – 0.053129
|
0.9890
|
0.9783
|
0.1973
|
0.1875
|
0.0389
|
Pixel 19
|
0.15775x0.007399
|
0.6922
|
0.4701
|
0.4114
|
0.3435
|
0.1693
|
Pixel 20
|
0.29979x – 0.028928
|
0.9984
|
0.9968
|
0.2660
|
0.2203
|
0.0707
|
Pixel 21
|
1.2854x0.024959
|
0.9050
|
0.9714
|
0.9472
|
0.9358
|
0.8973
|
Pixel 22
|
1.2129x0.026111
|
0.9351
|
0.9353
|
0.8293
|
0.8040
|
0.6877
|
Pixel 23
|
1.3309x0.027425
|
0.7684
|
0.8903
|
0.9414
|
0.9306
|
0.8862
|
Pixel 24
|
0.38406x -0.0 46864
|
0.9807
|
0.9618
|
0.2182
|
0.2073
|
0.0476
|
Pixel 26
|
0.29139x – 0.029335
|
1
|
1
|
0.2580
|
0.2442
|
0.0666
|
Pixel 27
|
0.28365x – 0.26743
|
0.9980
|
0.9959
|
0.5139
|
0.5039
|
0.2641
|
Pixel 28
|
0.36173x – 0.042845
|
0.9732
|
0.9473
|
0.2082
|
0.1993
|
0.0433
|
Pixel 29
|
0.32224x – 0.034607
|
0.9906
|
0.9814
|
0.4606
|
0.4360
|
0.2122
|
Table 17
Correlation and determination coefficient for 30 pixels of agricultural field
22/11/2020
|
26/2/2021
|
15/4/2021
|
NDTI
|
SM
|
PSMI
|
NDTI
|
SM
|
PSMI
|
NDTI
|
SM
|
PSMI
|
0.03849
|
1.08
|
0.07514
|
0.03716
|
1.077
|
0.7071
|
0.0595
|
1.127
|
0.3613
|
0.03875
|
1.081
|
0.1272
|
0.03848
|
1.08
|
0.6422
|
0.05563
|
1.118
|
0.3655
|
0.03731
|
1.078
|
0.169
|
0.03329
|
1.069
|
0.4716
|
0.06756
|
1.145
|
0.2936
|
0.04049
|
1.084
|
0.2014
|
0.02841
|
1.058
|
0.301
|
0.06326
|
1.135
|
0.2569
|
0.04377
|
1.092
|
0.2067
|
0.03135
|
1.065
|
0.3416
|
0.04559
|
1.096
|
0.3092
|
0.04545
|
1.095
|
0.2046
|
0.03585
|
1.074
|
0.5483
|
0.04638
|
1.097
|
0.4325
|
0.03342
|
1.069
|
0.2129
|
0.03295
|
1.068
|
0.6839
|
0.06627
|
1.142
|
0.4306
|
0.03443
|
1.071
|
0.2346
|
0.03494
|
1.072
|
0.6715
|
0.09722
|
1.215
|
0.4247
|
0.03242
|
1.067
|
0.2502
|
0.04603
|
1.097
|
0.6158
|
0.0824
|
1.18
|
0.3168
|
0.03779
|
1.079
|
0.2723
|
0.05051
|
1.106
|
0.538
|
0.08709
|
1.191
|
0.2572
|
0.04282
|
1.089
|
0.2723
|
0.0458
|
1.096
|
0.54
|
0.09703
|
1.215
|
0.2488
|
0.04407
|
1.092
|
0.2714
|
0.04165
|
1.087
|
0.6203
|
0.07402
|
1.16
|
0.3813
|
0.02662
|
1.055
|
0.3923
|
0.0466
|
1.098
|
0.3396
|
0.1122
|
1.253
|
0.5245
|
0.03397
|
1.07
|
0.4015
|
0.0517
|
1.109
|
0.4481
|
0.1059
|
1.237
|
0.5537
|
0.03504
|
1.073
|
0.3976
|
0.05096
|
1.107
|
0.4951
|
0.1153
|
1.261
|
0.443
|
0.04051
|
1.084
|
0.3639
|
0.04746
|
1.1
|
0.545
|
0.1173
|
1.266
|
0.3448
|
0.04441
|
1.093
|
0.3264
|
0.04864
|
1.102
|
0.5917
|
0.1102
|
1.248
|
0.2973
|
0.04626
|
1.097
|
0.3248
|
0.04576
|
1.096
|
0.6774
|
0.08737
|
1.191
|
0.4
|
0.03709
|
1.077
|
0.6014
|
0.05391
|
1.114
|
0.142
|
0.1034
|
1.231
|
0.6124
|
0.03524
|
1.073
|
0.5972
|
0.04553
|
1.095
|
0.1852
|
0.08171
|
1.178
|
0.6845
|
0.04229
|
1.088
|
0.5755
|
0.04845
|
1.102
|
0.2362
|
0.1103
|
1.248
|
0.5948
|
0.04647
|
1.097
|
0.5123
|
0.05469
|
1.116
|
0.3044
|
0.1093
|
1.246
|
0.495
|
0.04862
|
1.102
|
0.4492
|
0.05647
|
1.12
|
0.449
|
0.0991
|
1.22
|
0.4388
|
0.04751
|
1.1
|
0.3766
|
0.05246
|
1.111
|
0.5841
|
0.08466
|
1.185
|
0.4938
|
0.04108
|
1.086
|
0.7069
|
0.03053
|
1.063
|
0.2383
|
0.0575
|
1.122
|
0.6042
|
0.04427
|
1.093
|
0.7071
|
0.02939
|
1.061
|
0.1948
|
0.05783
|
1.123
|
0.6933
|
0.04658
|
1.098
|
0.6825
|
0.04817
|
1.101
|
0.1685
|
0.07495
|
1.162
|
0.7071
|
0.04835
|
1.102
|
0.623
|
0.05089
|
1.107
|
0.2006
|
0.08403
|
1.183
|
0.6537
|
0.05085
|
1.107
|
0.5409
|
0.04604
|
1.097
|
0.3213
|
0.07464
|
1.161
|
0.6068
|
0.04574
|
1.096
|
0.4622
|
0.03924
|
1.082
|
0.4461
|
0.07066
|
1.152
|
0.5837
|
Table 18
Correlation and determination coefficient for 30 pixels of agricultural field
Date
|
22/11/2020
|
26/2/2021
|
15/4/2021
|
Index
|
NDTI
SM
|
NDTI
PSMI
|
SM
PSMI
|
NDTI
SM
|
NDTI
PSMI
|
SM
PSMI
|
NDTI
SM
|
NDTI
PSMI
|
SM
PSMI
|
Correlate
|
0.9999
|
0.2980
|
0.2994
|
0.9999
|
-0.0973
|
-0.100
|
0.9999
|
0.0337
|
0.0305
|
R2
|
1.0
|
0.0888
|
0.0897
|
1
|
0.0095
|
0.0101
|
1
|
0.0011
|
0.0009
|