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

This chapter aimed to demonstrate the potential of monitoring water and vegetation parameters by combining weather and satellite measurements in mixed agroecosystems in the semiarid region of the northern Minas Gerais state, Southeast Brazil. Soil moisture indices and water productivity components were quantified with Landsat 8 images under different hydrological conditions along the year 2015. The surface resistance to the water fluxes (r s ) performed better than the ratio of actual to the reference evapotranspiration (ET r ) to detect soil moisture conditions. The mean pixel values for actual evapotranspira- tion (ET), biomass production (BIO), and water productivity based on evapotranspiration (WP), for irrigated crops (IC), ranged respectively from 2.5 ± 1.3 to 4.1 ± 1.6 mm d −1 ; 78 ± 62 to 132 ± 64 kg ha −1 d −1 ; and from 2.2 ± 0.8 to 3.3 ± 0.9 kg m −3 . The corresponding ranges for natural vegetation (NV) were 0.1 ± 0.2 to 1.9 ± 1.3 mm d −1 ; 1 ± 1 to 44 ± 42 kg ha −1 d −1 , and 0.6 ± 0.3 to 1.8 ± 0.8 kg m −3 . The incremental values, resulting from the replacement of natural species by agricultural crops, were respectively 2.7 mm d −1 and 83 kg ha d −1 . However, this replacement increased water productivity based on evapotranspiration (WP) by 264% during the studied year, what should be considered in land use and climate change studies in the Brazilian semiarid region.


Introduction
In the semiarid region of the northern Minas Gerais state, Southeast Brazil, the availability of water resources for irrigation is responsible for the rural economy growth. The main commercial crops are fruits and sugar cane; however, one of the main consequences of this development is 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 (ET) and biomass production (BIO).
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 satellites, together with agrometeorological stations [2,3].
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 hydrological conditions and agroecosystem types during several years [4,5].
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 and plant status [7].
A third model, the Surface Resistance Algorithm (SUREAL), was elaborated to calculate the surface resistance to water fluxes (r s ), a soil moisture index, with field and Landsat data [4,5], 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. 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].

Study area and data set
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 a ), 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.  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. Figure 2, from the Digital Numbers (DN), the spectral radiances for each band (L band ) are calculated:

According to
where a and b are regression coefficients given in the metadata file [12]. The albedo at the top of the atmosphere for each band (αt band ) of the satellite sensor was calculated as: where L band is in W m −2 sr −1 μm −1 , d is the relative earth-sun distance, Rt band 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 αt band values according to the weights for each band (w b ).
where the w band 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 (L 10 ) and 11 (L 11 ) were used to calculate the radiometric temperatures (T band ) applying the Plank's law: where K 1 (774.89 and 480.89) and K 2 (1321.08 and 1201.14) the conversion coefficients for the bands 10 and 11, respectively.
The average T band value from the two bands was considered as the brightness temperature (T bright ); 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 T bright .
Both αt and T bright were corrected atmospherically for acquiring the albedo (α 0 ) and temperature (T 0 ) 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 α 0 and T 0 values [3].
The Normalized Difference Vegetation Index (NDVI) is a measure of the vegetation amount at the surface: where αt nir and αt red 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 (ET 0 ) were modeled as [5]: where a sf and b sf 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 (ET eq ) 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: where s is the inclination of the curve relating the saturation vapor pressure (e s ) and the air temperature (T a ), R n is the net radiation, G is the ground heat flux, and γ is the psychrometric constant.
Net radiation (R n ) can be described through the 24-h values of net shortwave radiation, with a correction term for net longwave radiation [4]: where a L 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: where a G and b G (3.98; −25.47) are the regression coefficients.
A soil moisture index (ET r ) is considered by recalculating the ratio of the actual (ET) to reference (ET 0 ) evapotranspiration on a daily scale: 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 r ): where ε max is the maximum radiation efficiency use, PAR abs is the absorbed photosynthetically active radiation, and 0.864 is a unit conversion factor.
The absorbed photosynthetically active radiation (PAR abs ) was estimated as function of the Normalized Difference Vegetation Index (NDVI) and the incident photosynthetically active radiation (PAR inc ), which in turn is considered a fraction of the global solar radiation (R G ): where the coefficients a fr and b fr were considered 1.257 and −0.161 [14].
As another index, the surface resistance to the water fluxes (r s ) 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]: where a r and b r are the regression coefficients of 0.04 and 2.72 for the Brazilian semiarid conditions. Figure 3 presents the tendencies of the fortnight mean pixel values for precipitation (P) and reference evapotranspiration (ET 0 ) resulted from the weather interpolation process in the study area, including the periods before, during, and after the satellite image acquisitions.

Large-scale weather conditions
Weather conditions during these periods will affect the image process results.
Because of the semiarid characteristics of the study region and the proximity of the equator, precipitation (P) was much more variable than reference evapotranspiration (ET 0 ). 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 (ET 0 ). 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 (ET 0 ) 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 (ET 0 ), 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. Figure 4 shows the spatial distribution for the actual to reference evapotranspiration ratio (ET r ) 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 spatial and temporal variations, the actual (ET) to reference evapotranspiration (ET 0 ) ratio (ET r ), 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 r ) values, called in this case the crop coefficient (K c ), 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].

Large-scale soil moisture indices
In a temperate desert steppe of the Inner Mongolia, China, the seasonal actual to reference evapotranspiration ratio (ET r ) 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 r ) 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 s ) 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]. The spatial and temporal variations of the surface resistance to water fluxes (r s ) 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 r ), 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 s ) detects the soil moisture differences stronger than the actual to reference evapotranspiration ratio (ET r ) when analyzing the images of DOY 259 (September 19) and 307 (November 03) from Figures 4 and 5.
Then, the surface resistance to water fluxes (r s ) 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 s ) in vegetation indicate good soil moisture conditions, while the highest ones are related to water stress in all agroecosystems. 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 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.

Large-scale water productivity parameters
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.  [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.

Conclusions
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.
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.