**2. Materials and methods**

#### **2.1. Study area and data set**

**Figure 1** shows the location of the study area with the county divisions and the agrometeorological stations used in the semiarid region of the north of Minas Gerais state, Southeast Brazil. Water Productivity Modeling by Remote Sensing in the Semiarid Region of Minas Gerais State… http://dx.doi.org/10.5772/intechopen.72105 95

that other water users are competing with those from the agricultural sectors. The Jaíba irrigation scheme has a total area of 107,600 ha, being 65,800 ha irrigable, involving Jaíba and Matias Cardoso counties. The Gorotuba irrigation scheme has a total area of 11,280 ha, from which 4886 are irrigable, involving the counties of Janaúba, Nova Porteirinha, and Riacho dos Machados [1]. The irrigation schemes make the north of Minas an important agricultural growing region, because of the rapid development of the irrigation technologies. Under the actual climate and land-use change scenarios in the Brazilian semiarid region, the use of remote sensing from satellites, for quantifying the large-scale soil moisture and water productivity components in mixed agroecosystems, is strongly relevant. These knowledges provide valuable information for the water resource conservation practices without lowering the agricultural production. To meet this goal, there is the need for large scale quantifying both actual evapotranspiration

Actual evapotranspiration (ET) is critically important because of its relation with yield in all agroecosystems. On the one hand, it is the main water use for agriculture. On the other hand, increase in evapotranspiration rates results in less water availability for ecological and human uses in hydrological basins. The difficulties of acquiring large-scale water fluxes throughout field measurements in semiarid environments highlighted the use of remote sensing from

The Simple Algorithm for Evapotranspiration Retrieving (SAFER) model, for energy radiation and energy balance accounting, was developed and validated in the Brazilian semiarid region through simultaneous Landsat and field measurements, involving strong contrasting

Remote sensing from satellites is also an effective tool for large-scale biomass production estimations. The radiation use efficiency (RUE) model proposed by Monteith [6] has acceptable accuracy for this purpose, providing spatial and temporal information of vegetation locations

A third model, the Surface Resistance Algorithm (SUREAL), was elaborated to calculate the

for classifying mixed agroecosystems into irrigated crops (IC) and natural vegetation (NV) [8]. All the referred models are applied together with a net of agrometeorological stations in this chapter to retrieve large-scale water and vegetation indices, highlighting the combination of remote sensing algorithms as suitable tools for using together with weather data. The study aimed to apply these tools for subsidizing large-scale water productivity assessments in irrigated crops and natural vegetation under the semiarid conditions of Minas Gerais state, Southeast Brazil.

**Figure 1** shows the location of the study area with the county divisions and the agrometeorological stations used in the semiarid region of the north of Minas Gerais state, Southeast Brazil.

), a soil moisture index, with field and Landsat data [4, 5],

hydrological conditions and agroecosystem types during several years [4, 5].

(ET) and biomass production (BIO).

94 Arid Environments and Sustainability

and plant status [7].

surface resistance to water fluxes (r<sup>s</sup>

**2. Materials and methods**

**2.1. Study area and data set**

satellites, together with agrometeorological stations [2, 3].

**Figure 1.** Location of the study area and agrometeorological stations inside the counties under the semiarid conditions of the north of Minas Gerais state, Southeast Brazil.

The agrometeorological stations are Mocambinho (MC), Matias Cardoso (MC), Gameleiras (GA), Jaíba (JB), Varzelândia (VZ), Verdelândia (VD), Pai Pedro (PP), Nova Porteirinha (NP), São João da Ponte (SJP), Riacho dos Machado (RM), Bela Vista (BV), and Capitão Eneas (CE).

The predominant vegetation cover in the semiarid region of the northern Minas Gerais state, Southeast Brazil, is classified as "Cerrado," "Caatinga," and transitions [9], and the main hydrological basins are São Francisco and Jequitinhonha [10].

According to Lumbreras et al. [11], long-term rainfall is below 900 mm yr.−1, concentrated in the first and the last 3 months of the year. Thermal conditions are characterized by high air temperature (T<sup>a</sup> ), with averages of 24°C and maximums between 31 and 32°C, occurring from September to October, when the sun is around the zenith position in the region. The coldest period is from June to July, solstice period in the Southern hemisphere, when the minimums are from 14 to 17°C.

#### **2.2. Large-scale soil moisture and water productivity modeling**

The Landsat 8 images involved the orbit 218 and the points 70 and 71, which mosaics covered different hydrological conditions along the year 2015, represented by the Days of the Year (DOY) 019 (January 19), 163 (June 12), 259 (September 16) and 307 (November 03). **Figure 2** shows the steps for modeling the soil moisture indices and water productivity components throughout the Simple Algorithm for Evapotranspiration Retrieving (SAFER), Radiation Use Efficiency (RUE), and Surface Resistance Algorithm (SUREAL) models.

According to **Figure 2**, from the Digital Numbers (DN), the spectral radiances for each band (Lband) are calculated:

$$\mathbf{L}\_{\text{band}} = \mathbf{a}\mathbf{D}\mathbf{N} + \mathbf{b} \tag{1}$$

where a and b are regression coefficients given in the metadata file [12].

**Figure 2.** Flow chart for modeling soil moisture indices and water productivity components throughout application of the Simple Algorithm for Evapotranspiration Retrieving (SAFER), Radiation Use Efficiency (RUE), and Surface Resistance Algorithm (SUREAL) models to Landsat 8 images together with agrometeorological data.

The albedo at the top of the atmosphere for each band (αtband) of the satellite sensor was calculated as:

$$\alpha \text{ t}\_{\text{band}} = \frac{\text{L}\_{\text{band}} \pi d^2}{\text{Rt}\_{\text{band}} \cos \phi} \tag{2}$$

where K<sup>1</sup>

(T0

the surface:

(774.89 and 480.89) and K2

bands 10 and 11, respectively.

(1321.08 and 1201.14) the conversion coefficients for the

Water Productivity Modeling by Remote Sensing in the Semiarid Region of Minas Gerais State…

) and temperature

values [3].

(5)

97

and T<sup>0</sup>

http://dx.doi.org/10.5772/intechopen.72105

α0 NDVI)] (6)

<sup>s</sup>(R<sup>n</sup> <sup>−</sup> G) \_\_\_\_\_\_\_ <sup>s</sup> <sup>+</sup> <sup>γ</sup> ) (7)

) and the air tem-

The average Tband value from the two bands was considered as the brightness temperature (Tbright); however, conditional functions were used when one of the bands 10 or 11 presented

) surface instantaneous values, by regression equations determined from previous simultaneous Landsat and field measurements. Other regressions between the instantaneous and

The Normalized Difference Vegetation Index (NDVI) is a measure of the vegetation amount at

where αtnir and αtred represent the albedo at the top of the atmosphere over the ranges of wavelengths in the near infrared (subscript *nir*) and red (subscript *red*) regions of the solar

The satellite overpass (subscript *sat*) values for the ratio of actual evapotranspiration (ET) to

= exp[asf + bsf(

where asf and bsf are regression coefficients of 1.8 and −0.008, for the Brazilian semiarid conditions. Eq. 6 does not work for water bodies (i.e., NDVI <0). In these situations, the concept of equilibrium evapotranspiration (ETeq) is incorporated into the Simple Algorithm for Evapotranspiration Retrieving (SAFER) algorithm [13], applying conditional functions to negative NDVI values.

ET0 or 0.035(

Net radiation (Rn) can be described through the 24-h values of net shortwave radiation, with

R<sup>n</sup> = (1 − α0)R<sup>G</sup> − aLτ (8)

where aL is the regression coefficient of the relationship between net long wave radiation and

is the net radiation, G is the ground heat flux, and γ is the psychrometric constant.

) were modeled as [5]:

<sup>T</sup> \_\_\_\_\_\_\_ <sup>0</sup>

αt(nir) + αt(red)

pixel value problems to retrieve only one band Plank's result for Tbright.

Both αt and Tbright were corrected atmospherically for acquiring the albedo (α0

daily values were also applied to upscale the satellite overpass to the 24-h α0

spectrum, which for Landsat 8 satellite are the bands 5 and 4, respectively.

Then, the large-scale actual evapotranspiration (ET) values are obtained as:

\_\_\_ ET ET0)sat

where s is the inclination of the curve relating the saturation vapor pressure (e<sup>s</sup>

\_\_\_ ET ET0)sat

NDVI <sup>=</sup> <sup>α</sup>t(nir) <sup>−</sup> <sup>α</sup><sup>t</sup> \_\_\_\_\_\_\_\_\_(red)

the reference evapotranspiration (ET0

ET <sup>=</sup> (

a correction term for net longwave radiation [4]:

atmospheric transmissivity (τ) on a daily scale.

), R<sup>n</sup>

perature (T<sup>a</sup>

(

where Lband is in W m−2 sr−1 μm−1, d is the relative earth-sun distance, Rtband is the mean solar irradiance at the top of the atmosphere for each band (W m−2 μm−1), and ϕ is the solar zenith angle [3].

Following Teixeira et al. [3], the broadband albedo at the top of the atmosphere (αt) was calculated as the total sum of the different narrow-band αtband values according to the weights for each band (w<sup>b</sup> ).

$$\mathbf{a}\mathbf{t} = \sum \mathbf{w}\_{\text{band}} \mathbf{a}\mathbf{t}\_{\text{band}} \tag{3}$$

where the wband values were computed as the ratio of the amount of the incoming shortwave radiation from the sun at the top of the atmosphere in a particular band and the sum for all the bands.

The spectral radiances from the thermal bands 10 (L10) and 11 (L11) were used to calculate the radiometric temperatures (Tband) applying the Plank's law:

$$\mathbf{T}\_{\text{band}} = \frac{\mathbf{K}\_2}{\ln\left(\frac{\mathbf{K}\_1}{\mathbf{L}\_{\text{trad}} \bullet 1}\right)} \,\tag{4}$$

where K<sup>1</sup> (774.89 and 480.89) and K2 (1321.08 and 1201.14) the conversion coefficients for the bands 10 and 11, respectively.

The average Tband value from the two bands was considered as the brightness temperature (Tbright); however, conditional functions were used when one of the bands 10 or 11 presented pixel value problems to retrieve only one band Plank's result for Tbright.

Both αt and Tbright were corrected atmospherically for acquiring the albedo (α0 ) and temperature (T0 ) surface instantaneous values, by regression equations determined from previous simultaneous Landsat and field measurements. Other regressions between the instantaneous and daily values were also applied to upscale the satellite overpass to the 24-h α0 and T<sup>0</sup> values [3].

The Normalized Difference Vegetation Index (NDVI) is a measure of the vegetation amount at the surface:

$$\text{NIDVI} = \frac{\text{at}\_{\text{(in)}} - \text{at}\_{\text{(out)}}}{\text{at}\_{\text{(in)}} + \text{at}\_{\text{(out)}}} \tag{5}$$

where αtnir and αtred represent the albedo at the top of the atmosphere over the ranges of wavelengths in the near infrared (subscript *nir*) and red (subscript *red*) regions of the solar spectrum, which for Landsat 8 satellite are the bands 5 and 4, respectively.

The satellite overpass (subscript *sat*) values for the ratio of actual evapotranspiration (ET) to the reference evapotranspiration (ET0 ) were modeled as [5]:

The albedo at the top of the atmosphere for each band (αtband) of the satellite sensor was cal-

**Figure 2.** Flow chart for modeling soil moisture indices and water productivity components throughout application of the Simple Algorithm for Evapotranspiration Retrieving (SAFER), Radiation Use Efficiency (RUE), and Surface

Resistance Algorithm (SUREAL) models to Landsat 8 images together with agrometeorological data.

where Lband is in W m−2 sr−1 μm−1, d is the relative earth-sun distance, Rtband is the mean solar irradiance at the top of the atmosphere for each band (W m−2 μm−1), and ϕ is the solar zenith

Following Teixeira et al. [3], the broadband albedo at the top of the atmosphere (αt) was calculated as the total sum of the different narrow-band αtband values according to the weights

where the wband values were computed as the ratio of the amount of the incoming shortwave radiation from the sun at the top of the atmosphere in a particular band and the sum for all the bands.

The spectral radiances from the thermal bands 10 (L10) and 11 (L11) were used to calculate the

ln( \_\_\_\_\_\_ <sup>K</sup><sup>1</sup> <sup>L</sup>band <sup>+</sup> <sup>1</sup>)

\_\_\_\_\_\_\_\_

Rtband cos<sup>ϕ</sup> (2)

band (3)

, (4)

<sup>α</sup> tband <sup>=</sup> <sup>L</sup>band <sup>π</sup>d<sup>2</sup>

t = ∑wband αt

radiometric temperatures (Tband) applying the Plank's law:

Tband <sup>=</sup> \_\_\_\_\_\_\_\_\_ <sup>K</sup><sup>2</sup>

culated as:

96 Arid Environments and Sustainability

angle [3].

for each band (w<sup>b</sup>

).

$$\left(\frac{\text{ET}}{\text{ET}\_0}\right)\_{\text{sat}} = \exp\left[\mathbf{a}\_{st} + \mathbf{b}\_{st} \left(\frac{\text{T}\_0}{a\_0 \text{NDVI}}\right)\right] \tag{6}$$

where asf and bsf are regression coefficients of 1.8 and −0.008, for the Brazilian semiarid conditions.

Eq. 6 does not work for water bodies (i.e., NDVI <0). In these situations, the concept of equilibrium evapotranspiration (ETeq) is incorporated into the Simple Algorithm for Evapotranspiration Retrieving (SAFER) algorithm [13], applying conditional functions to negative NDVI values. Then, the large-scale actual evapotranspiration (ET) values are obtained as:

$$\text{ET} = \left(\frac{\text{ET}}{\text{ET}\_0}\right)\_{\text{sat}} \text{ET}\_0 \text{or } 0.035 \left(\frac{\text{s} (\text{R}\_n - \text{G})}{\text{s} + \text{\textdegree } \text{\textdegree}}\right) \tag{7}$$

where s is the inclination of the curve relating the saturation vapor pressure (e<sup>s</sup> ) and the air temperature (T<sup>a</sup> ), R<sup>n</sup> is the net radiation, G is the ground heat flux, and γ is the psychrometric constant.

Net radiation (Rn) can be described through the 24-h values of net shortwave radiation, with a correction term for net longwave radiation [4]:

$$\mathbf{R\_{n}} = (1 - \alpha\_{\mathrm{o}})\mathbf{R\_{c}} - \mathbf{a\_{L}}\tau \tag{8}$$

where aL is the regression coefficient of the relationship between net long wave radiation and atmospheric transmissivity (τ) on a daily scale.

For ground heat flux (G), the equation derived by Teixeira [5] was used:

$$\frac{\mathbf{G}}{\mathcal{R}\_{\mathbf{n}}} = \mathbf{a}\_{\mathbf{c}} \exp(\mathbf{b}\_{\mathbf{c}} \mathbf{a}\_{\mathbf{c}}) \tag{9}$$

where aG and bG (3.98; −25.47) are the regression coefficients.

A soil moisture index (ET<sup>r</sup> ) is considered by recalculating the ratio of the actual (ET) to reference (ET0 ) evapotranspiration on a daily scale:

$$\text{ET}\_{r} = \frac{\text{ET}}{\text{ET}\_{0}} \tag{10}$$

For biomass production (BIO) calculations, the radiation use efficiency (RUE) model was used, introducing the soil moisture effects through the daily ratio of actual to reference evapotranspiration (ET<sup>r</sup> ):

$$\text{BIO} = \text{g}\_{\text{max}} \text{ET PAR}\_{\text{abs}} 0.864 \tag{11}$$

where εmax is the maximum radiation efficiency use, PARabs is the absorbed photosynthetically active radiation, and 0.864 is a unit conversion factor.

The absorbed photosynthetically active radiation (PARabs) was estimated as function of the Normalized Difference Vegetation Index (NDVI) and the incident photosynthetically active radiation (PARinc), which in turn is considered a fraction of the global solar radiation (RG):

$$\text{PAR}\_{\text{abs}} = \left(\mathbf{a}\_{\text{tr}} \,\text{NDVI} + \mathbf{b}\_{\text{tr}}\right) \text{PAR}\_{\text{inc}} \tag{12}$$

Because of the semiarid characteristics of the study region and the proximity of the equator,

**Figure 3.** Climatic water balance components in the semiarid region of the northern Minas Gerais state, involving the fortnight periods from 2014 to 2015, before, during, and after the image acquisitions: precipitation (P) and reference

Water Productivity Modeling by Remote Sensing in the Semiarid Region of Minas Gerais State…

http://dx.doi.org/10.5772/intechopen.72105

99

concentrations were at the start and at the end of the years, in agreement with Lumbreras et al. [11]. The driest period, with precipitation (P) fortnight values below 5 mm, was from Day of the Year (DOY) 160 to 289 in 2015, lower than 10% of the reference evapotranspiration

were at the end of 2015, when the fortnight values were higher than 80 mm. Under these situations, the sun was around its zenith position with the sky presenting low cloud cover. Under

start and at the end of year, all agroecosystems, irrigated crops (IC) and natural vegetation (NV) were in favor for large actual evapotranspiration (ET) and biomass production (BIO) rates.

**Figure 4** shows the spatial distribution for the actual to reference evapotranspiration ratio (ET<sup>r</sup>

and its daily average values, involving different hydrological conditions and agroecosystems along the year 2015, in the semiarid region of the north of Minas Gerais state, Southeast Brazil.

the conditions of high both precipitation (P) and reference evapotranspiration (ET0

). However, one can see other natural water scarcity events, one at the start of January and from Day of the Year (DOY) 064 to 097, even inside the normal rainy season conditions

). Rainfall

), during the

)

) values, the largest atmospheric demands

precipitation (P) was much more variable than reference evapotranspiration (ET0

(ET0

of the region.

evapotranspiration (ET0

).

Regarding the reference evapotranspiration (ET0

**3.2. Large-scale soil moisture indices**

where the coefficients afr and bfr were considered 1.257 and −0.161 [14].

As another index, the surface resistance to the water fluxes (r<sup>s</sup> ) was used to picture the soil moisture conditions, but also for classifying the vegetation, into irrigated crops (IC) and natural vegetation (NV), throughout the surface resistance algorithm (SUREAL) model [5]:

$$\mathbf{r}\_s = \exp\left[\mathbf{a}\_r \left(\frac{\mathbf{T}\_0}{\alpha\_0}\right) (\mathbf{1} - \mathbf{N} \mathbf{D} \mathbf{V} \mathbf{I}) + \mathbf{b}\_r\right] \tag{13}$$

where ar and br are the regression coefficients of 0.04 and 2.72 for the Brazilian semiarid conditions.

#### **3. Results and discussion**

#### **3.1. Large-scale weather conditions**

**Figure 3** presents the tendencies of the fortnight mean pixel values for precipitation (P) and reference evapotranspiration (ET0 ) resulted from the weather interpolation process in the study area, including the periods before, during, and after the satellite image acquisitions. Weather conditions during these periods will affect the image process results.

Water Productivity Modeling by Remote Sensing in the Semiarid Region of Minas Gerais State… http://dx.doi.org/10.5772/intechopen.72105 99

**Figure 3.** Climatic water balance components in the semiarid region of the northern Minas Gerais state, involving the fortnight periods from 2014 to 2015, before, during, and after the image acquisitions: precipitation (P) and reference evapotranspiration (ET0 ).

Because of the semiarid characteristics of the study region and the proximity of the equator, precipitation (P) was much more variable than reference evapotranspiration (ET0 ). Rainfall concentrations were at the start and at the end of the years, in agreement with Lumbreras et al. [11]. The driest period, with precipitation (P) fortnight values below 5 mm, was from Day of the Year (DOY) 160 to 289 in 2015, lower than 10% of the reference evapotranspiration (ET0 ). However, one can see other natural water scarcity events, one at the start of January and from Day of the Year (DOY) 064 to 097, even inside the normal rainy season conditions of the region.

Regarding the reference evapotranspiration (ET0 ) values, the largest atmospheric demands were at the end of 2015, when the fortnight values were higher than 80 mm. Under these situations, the sun was around its zenith position with the sky presenting low cloud cover. Under the conditions of high both precipitation (P) and reference evapotranspiration (ET0 ), during the start and at the end of year, all agroecosystems, irrigated crops (IC) and natural vegetation (NV) were in favor for large actual evapotranspiration (ET) and biomass production (BIO) rates.

#### **3.2. Large-scale soil moisture indices**

For ground heat flux (G), the equation derived by Teixeira [5] was used:

where aG and bG (3.98; −25.47) are the regression coefficients.

) evapotranspiration on a daily scale:

ET<sup>r</sup> <sup>=</sup> \_\_\_ ET

active radiation, and 0.864 is a unit conversion factor.

Rn

= aG exp(bGα0) (9)

(10)

) was used to picture the soil

α0)(1 <sup>−</sup> NDVI) <sup>+</sup> br] (13)

) resulted from the weather interpolation process in the

) is considered by recalculating the ratio of the actual (ET) to refer-

ET0

For biomass production (BIO) calculations, the radiation use efficiency (RUE) model was used, introducing the soil moisture effects through the daily ratio of actual to reference evapo-

BIO = εmax ET<sup>r</sup> PARabs 0.864 (11)

where εmax is the maximum radiation efficiency use, PARabs is the absorbed photosynthetically

The absorbed photosynthetically active radiation (PARabs) was estimated as function of the Normalized Difference Vegetation Index (NDVI) and the incident photosynthetically active radiation (PARinc), which in turn is considered a fraction of the global solar radiation (RG):

PARabs = (afr NDVI + bfr)PARinc (12)

moisture conditions, but also for classifying the vegetation, into irrigated crops (IC) and natural vegetation (NV), throughout the surface resistance algorithm (SUREAL) model [5]:

**Figure 3** presents the tendencies of the fortnight mean pixel values for precipitation (P) and

study area, including the periods before, during, and after the satellite image acquisitions.

Weather conditions during these periods will affect the image process results.

are the regression coefficients of 0.04 and 2.72 for the Brazilian semiarid conditions.

T\_\_0

where the coefficients afr and bfr were considered 1.257 and −0.161 [14].

As another index, the surface resistance to the water fluxes (r<sup>s</sup>

rs = exp[ar(

\_\_G

):

A soil moisture index (ET<sup>r</sup>

98 Arid Environments and Sustainability

ence (ET0

where ar

and br

**3. Results and discussion**

**3.1. Large-scale weather conditions**

reference evapotranspiration (ET0

transpiration (ET<sup>r</sup>

**Figure 4** shows the spatial distribution for the actual to reference evapotranspiration ratio (ET<sup>r</sup> ) and its daily average values, involving different hydrological conditions and agroecosystems along the year 2015, in the semiarid region of the north of Minas Gerais state, Southeast Brazil.

In well-irrigated crops, the actual to reference evapotranspiration ratio (ET<sup>r</sup>

range from 0.47 to 0.92 in a non-irrigated pasture site in Florida, USA [18].

ferent spatial scales [15]. On the other hand, in natural vegetation, this ratio characterizes the

In a temperate desert steppe of the Inner Mongolia, China*,* the seasonal actual to reference

similar to several situations of the current study. However, Lu et al. [16], in the same Chinese region, found this ratio higher than 1.00 for six different ecosystems, while it was inside a

tions in a reed marsh in the Northeast China were attributed to air temperature, air humidity, and the available energy [19]. In the Brazilian semiarid conditions, previous rainy seasons were the most significant reason for the highest values of this ratio, increasing the soil moisture in the subsequent periods. However, the values of this soil moisture index in natural ecosystems also depend on the stomatal regulation and plant adaptation to water scarcity

date to picture the soil moisture conditions and to classify the agroecosystems into irrigated crops (IC) and natural vegetation (NV). As lower are its values, higher is the root zone moisture [3].

average daily values, involving different hydrological conditions and agroecosystems along

along the year 2015, confirming the sensibility of the Surface Resistance Algorithm (SUREAL) model for detecting differences in soil moisture conditions among agroecosystems under semiarid conditions. As in the case of the actual to reference evapotranspiration ratio (ET<sup>r</sup>

the spatial soil moisture differences are also strongly noticed comparing the representative images for the rainy period (DOY 019–January 19) against that for the driest conditions (DOY

the soil moisture differences stronger than the actual to reference evapotranspiration ratio

was taken for the vegetation classification. In this image, pixel values below 800 s m−1 and the Normalized Difference Vegetation Index (NDVI) above or equal to 0.30 were considered irrigated crops (IC), while those with values between 1000 and 10,000 s m−1 and the Normalized Difference Vegetation Index (NDVI) below 0.30 were considered natural vegetation (NV). The high end of this last range was included to filter rocks and buildings [3]. The lowest values of

) when analyzing the images of DOY 259 (September 19) and 307 (November 03) from

**Figure 5** shows the spatial distribution for the surface resistance to water fluxes (r<sup>s</sup>

the year 2015, in semiarid region of the north of Minas Gerais state, Southeast Brazil.

307–November 03). However, it is clear that the surface resistance to water fluxes (r<sup>s</sup>

while the highest ones are related to water stress in all agroecosystems.

The spatial and temporal variations of the surface resistance to water fluxes (r<sup>s</sup>

The most important variables for the actual to reference evapotranspiration ratio (ET<sup>r</sup>

this case the crop coefficient (K<sup>c</sup>

evapotranspiration ratio (ET<sup>r</sup>

conditions [20].

(ET<sup>r</sup>

**Figures 4** and **5**.

Then, the surface resistance to water fluxes (r<sup>s</sup>

the surface resistance to water fluxes (r<sup>s</sup>

degree of the water stress in the plant root zones [16].

In this chapter, the surface resistance to the water fluxes (r<sup>s</sup>

) values, called in

101

http://dx.doi.org/10.5772/intechopen.72105

) varia-

) and its

),

) detects

) are also clear

) is considered for both, being a candi-

) image during the driest conditions of DOY 259

) in vegetation indicate good soil moisture conditions,

), may be used for estimating the water requirements at dif-

Water Productivity Modeling by Remote Sensing in the Semiarid Region of Minas Gerais State…

) ranged from mean daily values of 0.16 to maximum of 0.75 [17],

**Figure 4.** Spatial distribution of the daily values for the ratio of actual evapotranspiration – ET to the reference evapotranspiration – ET0 (ET<sup>r</sup> ), involving different hydrological conditions and agroecosystems along the year 2015, in the north of Minas Gerais state, Southeast Brazil. DOY is the Day of the Year, and the over bars mean averages showed together with the standard deviation (SD).

The spatial and temporal variations, the actual (ET) to reference evapotranspiration (ET0 ) ratio (ET<sup>r</sup> ), along the year 2015 are evident, confirming the sensibility of the Simple Algorithm for Evapotranspiration Retrieving (SAFER) model to picture the soil moisture involving different hydrological conditions and agroecosystems. The spatial variations of this ratio are much strongly noticed when comparing the images representative of the rainy period (DOY 027, January 29) when some well irrigated areas presented values above 1.00, against that for the driest one of DOY 307 (November 03), when some pixels reach to 0.00 values in natural species (**Figures 3** and **4**). The highest values for Jaíba, Nova Porteirinha, and Riacho dos Machados counties during the climatically driest periods (**Figures 1** and **4**) may be attributed to largest concentrations of irrigated areas.

In well-irrigated crops, the actual to reference evapotranspiration ratio (ET<sup>r</sup> ) values, called in this case the crop coefficient (K<sup>c</sup> ), may be used for estimating the water requirements at different spatial scales [15]. On the other hand, in natural vegetation, this ratio characterizes the degree of the water stress in the plant root zones [16].

In a temperate desert steppe of the Inner Mongolia, China*,* the seasonal actual to reference evapotranspiration ratio (ET<sup>r</sup> ) ranged from mean daily values of 0.16 to maximum of 0.75 [17], similar to several situations of the current study. However, Lu et al. [16], in the same Chinese region, found this ratio higher than 1.00 for six different ecosystems, while it was inside a range from 0.47 to 0.92 in a non-irrigated pasture site in Florida, USA [18].

The most important variables for the actual to reference evapotranspiration ratio (ET<sup>r</sup> ) variations in a reed marsh in the Northeast China were attributed to air temperature, air humidity, and the available energy [19]. In the Brazilian semiarid conditions, previous rainy seasons were the most significant reason for the highest values of this ratio, increasing the soil moisture in the subsequent periods. However, the values of this soil moisture index in natural ecosystems also depend on the stomatal regulation and plant adaptation to water scarcity conditions [20].

In this chapter, the surface resistance to the water fluxes (r<sup>s</sup> ) is considered for both, being a candidate to picture the soil moisture conditions and to classify the agroecosystems into irrigated crops (IC) and natural vegetation (NV). As lower are its values, higher is the root zone moisture [3].

**Figure 5** shows the spatial distribution for the surface resistance to water fluxes (r<sup>s</sup> ) and its average daily values, involving different hydrological conditions and agroecosystems along the year 2015, in semiarid region of the north of Minas Gerais state, Southeast Brazil.

The spatial and temporal variations of the surface resistance to water fluxes (r<sup>s</sup> ) are also clear along the year 2015, confirming the sensibility of the Surface Resistance Algorithm (SUREAL) model for detecting differences in soil moisture conditions among agroecosystems under semiarid conditions. As in the case of the actual to reference evapotranspiration ratio (ET<sup>r</sup> ), the spatial soil moisture differences are also strongly noticed comparing the representative images for the rainy period (DOY 019–January 19) against that for the driest conditions (DOY 307–November 03). However, it is clear that the surface resistance to water fluxes (r<sup>s</sup> ) detects the soil moisture differences stronger than the actual to reference evapotranspiration ratio (ET<sup>r</sup> ) when analyzing the images of DOY 259 (September 19) and 307 (November 03) from **Figures 4** and **5**.

The spatial and temporal variations, the actual (ET) to reference evapotranspiration (ET0

**Figure 4.** Spatial distribution of the daily values for the ratio of actual evapotranspiration – ET to the reference

north of Minas Gerais state, Southeast Brazil. DOY is the Day of the Year, and the over bars mean averages showed together

for Evapotranspiration Retrieving (SAFER) model to picture the soil moisture involving different hydrological conditions and agroecosystems. The spatial variations of this ratio are much strongly noticed when comparing the images representative of the rainy period (DOY 027, January 29) when some well irrigated areas presented values above 1.00, against that for the driest one of DOY 307 (November 03), when some pixels reach to 0.00 values in natural species (**Figures 3** and **4**). The highest values for Jaíba, Nova Porteirinha, and Riacho dos Machados counties during the climatically driest periods (**Figures 1** and **4**) may be attributed

), along the year 2015 are evident, confirming the sensibility of the Simple Algorithm

), involving different hydrological conditions and agroecosystems along the year 2015, in the

ratio (ET<sup>r</sup>

evapotranspiration – ET0

with the standard deviation (SD).

100 Arid Environments and Sustainability

to largest concentrations of irrigated areas.

(ET<sup>r</sup>

)

Then, the surface resistance to water fluxes (r<sup>s</sup> ) image during the driest conditions of DOY 259 was taken for the vegetation classification. In this image, pixel values below 800 s m−1 and the Normalized Difference Vegetation Index (NDVI) above or equal to 0.30 were considered irrigated crops (IC), while those with values between 1000 and 10,000 s m−1 and the Normalized Difference Vegetation Index (NDVI) below 0.30 were considered natural vegetation (NV). The high end of this last range was included to filter rocks and buildings [3]. The lowest values of the surface resistance to water fluxes (r<sup>s</sup> ) in vegetation indicate good soil moisture conditions, while the highest ones are related to water stress in all agroecosystems.

**Figure 5.** Spatial distribution for the surface resistance to water fluxes (r<sup>s</sup> ), under different hydrological conditions and agroecosystems along the year 2015, in the north of Minas Gerais state, Southeast Brazil. DOY is the Day of the Year, and the over bars means averages showed together with standard deviation (SD).

rainy period, when the accumulated precipitation (P) favored the natural species, while besides

**Figure 6.** Spatial distribution and the daily average values for the water productivity parameters, under different hydrological conditions along the year 2015, in the north of Minas Gerais state, Southeast Brazil. (a) Actual evapotranspiration (ET) and (b) biomass production (BIO). DOY is the Day of the Year and the over bars means averages

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The lowest actual evapotranspiration (ET) and standard deviation (SD) values for irrigated crops (IC) were soon after the rainy period, conditions represented by the image of DOY 163 (June 12). For biomass production (BIO), they were during the climatically driest conditions, represented by the image of DOY 259 (September 16), however with the lowest spatial variations in November (DOY 307). Considering the natural vegetation ecosystem (NV), the highest both actual evapotranspiration (ET) and biomass production (BIO) values occurred during the rainy period, represented by the image of DOY 019 (January 19), while the lowest ones were during the climatically driest period (DOY 259, September 16), because of the low soil moisture conditions promoting short vegetative development of natural species. Under these last conditions, the native plants are in dormancy stage, closing stomata what limit both transpiration and photosynthesis, and in general, crops are regularly daily irrigated, increasing the water productivity parameters.

The average pixel values for actual evapotranspiration (ET) and biomass production (BIO), in irrigated crops (IC), ranged respectively from 2.5 ± 1.3 to 4.1 ± 1.6 mm d−1 and from 78 ± 62 to 132 ± 64 kg ha−1 d−1. The corresponding ranges for natural vegetation (NV) were 0.1 ± 0.2 to 1.9 ± 1.3 mm d−1 and de 1 ± 1 to 44 ± 42 kg ha−1 d−1. Leivas et al. [2] reported maximum actual evapotranspiration (ET) values of 3.5 ± 1.0 mm d−1 in the Jaíba irrigation scheme. In the Petrolina/Juazeiro agricultural growing region, under the semiarid conditions of the São

the rainfall water supply, irrigated crops were beneficed with supplementary irrigation.

for irrigated crops (IC) and natural vegetation (NV) showed together with standard deviations (SD).

#### **3.3. Large-scale water productivity parameters**

**Figure 6** shows the spatial distribution and the average daily values for actual evapotranspiration (ET) and biomass production (BIO) for irrigated crops (IC) and natural vegetations (NV), under different hydrological conditions along the year 2015, in the north of Minas Gerais state, Southeast Brazil.

The spatial and temporal variations for actual evapotranspiration (ET) (**Figure 6a**) and biomass production (BIO) (**Figure 6b**) are both strong. This is noticed mainly when comparing the wettest conditions (represented by the image of DOY 019—January 19) with the driest ones (represented by the image of DOY 259—September 16), where the pixels with the high values represent irrigated crops (IC). The largest rates for both water productivity parameters occurred during the Water Productivity Modeling by Remote Sensing in the Semiarid Region of Minas Gerais State… http://dx.doi.org/10.5772/intechopen.72105 103

**Figure 6.** Spatial distribution and the daily average values for the water productivity parameters, under different hydrological conditions along the year 2015, in the north of Minas Gerais state, Southeast Brazil. (a) Actual evapotranspiration (ET) and (b) biomass production (BIO). DOY is the Day of the Year and the over bars means averages for irrigated crops (IC) and natural vegetation (NV) showed together with standard deviations (SD).

rainy period, when the accumulated precipitation (P) favored the natural species, while besides the rainfall water supply, irrigated crops were beneficed with supplementary irrigation.

The lowest actual evapotranspiration (ET) and standard deviation (SD) values for irrigated crops (IC) were soon after the rainy period, conditions represented by the image of DOY 163 (June 12). For biomass production (BIO), they were during the climatically driest conditions, represented by the image of DOY 259 (September 16), however with the lowest spatial variations in November (DOY 307). Considering the natural vegetation ecosystem (NV), the highest both actual evapotranspiration (ET) and biomass production (BIO) values occurred during the rainy period, represented by the image of DOY 019 (January 19), while the lowest ones were during the climatically driest period (DOY 259, September 16), because of the low soil moisture conditions promoting short vegetative development of natural species. Under these last conditions, the native plants are in dormancy stage, closing stomata what limit both transpiration and photosynthesis, and in general, crops are regularly daily irrigated, increasing the water productivity parameters.

**3.3. Large-scale water productivity parameters**

**Figure 5.** Spatial distribution for the surface resistance to water fluxes (r<sup>s</sup>

the over bars means averages showed together with standard deviation (SD).

Southeast Brazil.

102 Arid Environments and Sustainability

**Figure 6** shows the spatial distribution and the average daily values for actual evapotranspiration (ET) and biomass production (BIO) for irrigated crops (IC) and natural vegetations (NV), under different hydrological conditions along the year 2015, in the north of Minas Gerais state,

agroecosystems along the year 2015, in the north of Minas Gerais state, Southeast Brazil. DOY is the Day of the Year, and

), under different hydrological conditions and

The spatial and temporal variations for actual evapotranspiration (ET) (**Figure 6a**) and biomass production (BIO) (**Figure 6b**) are both strong. This is noticed mainly when comparing the wettest conditions (represented by the image of DOY 019—January 19) with the driest ones (represented by the image of DOY 259—September 16), where the pixels with the high values represent irrigated crops (IC). The largest rates for both water productivity parameters occurred during the The average pixel values for actual evapotranspiration (ET) and biomass production (BIO), in irrigated crops (IC), ranged respectively from 2.5 ± 1.3 to 4.1 ± 1.6 mm d−1 and from 78 ± 62 to 132 ± 64 kg ha−1 d−1. The corresponding ranges for natural vegetation (NV) were 0.1 ± 0.2 to 1.9 ± 1.3 mm d−1 and de 1 ± 1 to 44 ± 42 kg ha−1 d−1. Leivas et al. [2] reported maximum actual evapotranspiration (ET) values of 3.5 ± 1.0 mm d−1 in the Jaíba irrigation scheme. In the Petrolina/Juazeiro agricultural growing region, under the semiarid conditions of the São Francisco river basin, Teixeira et al. [7] found maximum values of biomass production (BIO) of 100 and 46 kg ha−1 d−1 in irrigated crops (IC) and natural vegetation (NV) agroecosystems, respectively. These differences, regarding the results in this chapter, may be related, in part, to the lower spatial resolution of the MODIS images used in the previous studies, in comparison with that for the Landsat 8 in the current research.

While along the year, the values for actual evapotranspiration (ET) and biomass production (BIO) were progressively declining, reaching close to zero in November (DOY 307) in the natural vegetation (NV) ecosystem, in irrigated crops (IC), they were always above 2.5 mm d−1 and 78 kg ha d−1, respectively. In an annual scale, the incremental rates resulting from the replacement of natural species by irrigated crops were 2.7 mm d−1 and 83 kg ha d−1.

The largest both actual evapotranspiration (ET) and biomass production (BIO) were for the Jaíba and Matias Cardoso counties (**Figures 1** and **6**), because of the irrigation water availability in the Jaíba irrigation scheme, from the São Francisco river. Highlights in the region are also for Nova Porteirinha and Janaúba counties, inside the Gorotuba irrigation scheme, but in this last case, the dam Bico da Pedra is the water source. These irrigation schemes concentrate mainly irrigated fruit cops and sugar cane. The Riacho dos Machados county also presents some areas with high actual evapotranspiration (ET) and biomass production (BIO), being these large values probably related to cattle and family farms, with the main water sources from the Vacaria River and the Samambaia Stream.

**Figure 7** shows the spatial distribution and the average daily values for the water productivity based on evapotranspiration (WP) for irrigated crops (IC) and natural vegetation (NV), under different hydrological conditions along the year 2015, in the north of Minas Gerais state, Southeast Brazil.

In the case of the water productivity based on evapotranspiration (WP), considered as the ratio of biomass production (BIO) to actual evapotranspiration (ET), the largest values and spatial variations for irrigated crops (IC) were in June (representative image of DOY 163), period of optimum crop root-zone moisture conditions, happening soon after the rainy period. On the other hand, inside the rainy period (conditions represented by the image of DOY 019), happened the highest values for the natural vegetation (NV) ecosystem. The large spatial variations indicated different soil moisture and vegetation conditions in natural species and heterogeneity on crop stages in irrigated crops. More uniformity on the values of water productivity based on evapotranspiration (WP) was for the natural vegetation (NV) ecosystem, evidenced by the lower standard deviations when compared to the irrigated crops (IC) agroecosystem.

**4. Conclusions**

showed together with the standard deviation (SD).

The coupled use of Landsat 8 images and a net of agrometeorological stations allowed the largescale quantification of the water productivity parameters, under different hydrological conditions and agroecosystems during the year 2015 in the north of Minas Gerais state, Southeast Brazil. The analyses may subsidize a better understanding of the soil moisture, actual evapotranspiration (ET) and biomass production (BIO) dynamics, important water policy issues under the actual climate and land-use change conditions in the Brazilian semiarid region.

**Figure 7.** Spatial distribution of the daily values for the water productivity based on evapotranspiration (WP), under different hydrological conditions along the year 2015, in the north of Minas Gerais state, Southeast Brazil. DOY is the Day of the Year and the over bars means averages in irrigated crops (IC) and natural vegetation (NV) agroecosystems,

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105

Vegetated surfaces were classified into irrigated crops (IC) and natural vegetation (NV), highlighting the rainy period as the one with the highest actual evapotranspiration (ET) and biomass production (BIO) rates for both irrigated crops (IC) and natural vegetation (NV) agroecosystems.

The seasonal values of the water productivity based on evapotranspiration (WP) for the irrigated crops (IC) agroecosystem ranged from 2.2 ± 0.8 to 3.3 ± 0.9 kg m−3. The corresponding range for the natural vegetation (NV) ecosystem was from 0.6 ± 0.3 to 1.8 ± 0.8 kg m−3. These values when multiplied by the harvest index (HI) give the crop water productivity (CWP). Reported harvest index (HI) values were around 0.60 and 0.80 for vineyards and mango orchard under the semiarid conditions of Northeast Brazil, retrieving crop water productivity (CWP) values of 2.8 and 3.4 kg m−3 [21]. The maximum values for water productivity based on evapotranspiration (WP) in the current study when multiplied by these harvest indexes (HI) are lower, being the probable reason the water allocation restriction for irrigation schemes during the drought events in the year 2015.

Water Productivity Modeling by Remote Sensing in the Semiarid Region of Minas Gerais State… http://dx.doi.org/10.5772/intechopen.72105 105

**Figure 7.** Spatial distribution of the daily values for the water productivity based on evapotranspiration (WP), under different hydrological conditions along the year 2015, in the north of Minas Gerais state, Southeast Brazil. DOY is the Day of the Year and the over bars means averages in irrigated crops (IC) and natural vegetation (NV) agroecosystems, showed together with the standard deviation (SD).

### **4. Conclusions**

Francisco river basin, Teixeira et al. [7] found maximum values of biomass production (BIO) of 100 and 46 kg ha−1 d−1 in irrigated crops (IC) and natural vegetation (NV) agroecosystems, respectively. These differences, regarding the results in this chapter, may be related, in part, to the lower spatial resolution of the MODIS images used in the previous studies, in comparison

While along the year, the values for actual evapotranspiration (ET) and biomass production (BIO) were progressively declining, reaching close to zero in November (DOY 307) in the natural vegetation (NV) ecosystem, in irrigated crops (IC), they were always above 2.5 mm d−1 and 78 kg ha d−1, respectively. In an annual scale, the incremental rates resulting from the replace-

The largest both actual evapotranspiration (ET) and biomass production (BIO) were for the Jaíba and Matias Cardoso counties (**Figures 1** and **6**), because of the irrigation water availability in the Jaíba irrigation scheme, from the São Francisco river. Highlights in the region are also for Nova Porteirinha and Janaúba counties, inside the Gorotuba irrigation scheme, but in this last case, the dam Bico da Pedra is the water source. These irrigation schemes concentrate mainly irrigated fruit cops and sugar cane. The Riacho dos Machados county also presents some areas with high actual evapotranspiration (ET) and biomass production (BIO), being these large values probably related to cattle and family farms, with the main water sources

**Figure 7** shows the spatial distribution and the average daily values for the water productivity based on evapotranspiration (WP) for irrigated crops (IC) and natural vegetation (NV), under different hydrological conditions along the year 2015, in the north of Minas Gerais state,

In the case of the water productivity based on evapotranspiration (WP), considered as the ratio of biomass production (BIO) to actual evapotranspiration (ET), the largest values and spatial variations for irrigated crops (IC) were in June (representative image of DOY 163), period of optimum crop root-zone moisture conditions, happening soon after the rainy period. On the other hand, inside the rainy period (conditions represented by the image of DOY 019), happened the highest values for the natural vegetation (NV) ecosystem. The large spatial variations indicated different soil moisture and vegetation conditions in natural species and heterogeneity on crop stages in irrigated crops. More uniformity on the values of water productivity based on evapotranspiration (WP) was for the natural vegetation (NV) ecosystem, evidenced by the

lower standard deviations when compared to the irrigated crops (IC) agroecosystem.

The seasonal values of the water productivity based on evapotranspiration (WP) for the irrigated crops (IC) agroecosystem ranged from 2.2 ± 0.8 to 3.3 ± 0.9 kg m−3. The corresponding range for the natural vegetation (NV) ecosystem was from 0.6 ± 0.3 to 1.8 ± 0.8 kg m−3. These values when multiplied by the harvest index (HI) give the crop water productivity (CWP). Reported harvest index (HI) values were around 0.60 and 0.80 for vineyards and mango orchard under the semiarid conditions of Northeast Brazil, retrieving crop water productivity (CWP) values of 2.8 and 3.4 kg m−3 [21]. The maximum values for water productivity based on evapotranspiration (WP) in the current study when multiplied by these harvest indexes (HI) are lower, being the probable reason the water allocation restriction for irrigation schemes

ment of natural species by irrigated crops were 2.7 mm d−1 and 83 kg ha d−1.

with that for the Landsat 8 in the current research.

104 Arid Environments and Sustainability

from the Vacaria River and the Samambaia Stream.

during the drought events in the year 2015.

Southeast Brazil.

The coupled use of Landsat 8 images and a net of agrometeorological stations allowed the largescale quantification of the water productivity parameters, under different hydrological conditions and agroecosystems during the year 2015 in the north of Minas Gerais state, Southeast Brazil. The analyses may subsidize a better understanding of the soil moisture, actual evapotranspiration (ET) and biomass production (BIO) dynamics, important water policy issues under the actual climate and land-use change conditions in the Brazilian semiarid region.

Vegetated surfaces were classified into irrigated crops (IC) and natural vegetation (NV), highlighting the rainy period as the one with the highest actual evapotranspiration (ET) and biomass production (BIO) rates for both irrigated crops (IC) and natural vegetation (NV) agroecosystems. However, the largest water productivity based on evapotranspiration (WP) values, considered as the ratio of biomass production (BIO) to actual evapotranspiration (ET), was during the rainy period for the natural species, while for the irrigated crops they were soon after this period.

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The remote sensing model algorithms applied here demonstrated enough accuracy to be implemented in rational water resource policies in the Brazilian semiarid region experiencing climate and land use changes, once having available spatially distributed agrometeorological data. From the sensibility of the models to detect soil moisture conditions, the results revealed confidence for later applications of monitoring water and vegetation indices, quantifying the effects of water scarcity along the years.
