\documentclass[10pt]{article}

\usepackage{fullpage}
\usepackage{setspace}
\usepackage{parskip}
\usepackage{titlesec}
\usepackage[section]{placeins}
\usepackage{xcolor}
\usepackage{breakcites}
\usepackage{lineno}
\usepackage{hyphenat}





\PassOptionsToPackage{hyphens}{url}
\usepackage[colorlinks = true,
            linkcolor = blue,
            urlcolor  = blue,
            citecolor = blue,
            anchorcolor = blue]{hyperref}
\usepackage{etoolbox}
\makeatletter
\patchcmd\@combinedblfloats{\box\@outputbox}{\unvbox\@outputbox}{}{%
  \errmessage{\noexpand\@combinedblfloats could not be patched}%
}%
\makeatother


\usepackage{natbib}




\renewenvironment{abstract}
  {{\bfseries\noindent{\abstractname}\par\nobreak}\footnotesize}
  {\bigskip}

\titlespacing{\section}{0pt}{*3}{*1}
\titlespacing{\subsection}{0pt}{*2}{*0.5}
\titlespacing{\subsubsection}{0pt}{*1.5}{0pt}


\usepackage{authblk}


\usepackage{graphicx}
\usepackage[space]{grffile}
\usepackage{latexsym}
\usepackage{textcomp}
\usepackage{longtable}
\usepackage{tabulary}
\usepackage{booktabs,array,multirow}
\usepackage{amsfonts,amsmath,amssymb}
\providecommand\citet{\cite}
\providecommand\citep{\cite}
\providecommand\citealt{\cite}
% You can conditionalize code for latexml or normal latex using this.
\newif\iflatexml\latexmlfalse
\providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}%

\AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}}

\usepackage[utf8]{inputenc}
\usepackage[ngerman,greek,english]{babel}



\usepackage{float}








\begin{document}

\title{Dynamics and temporal trend of evapotranspiration in semiarid native
forests in Brazil and Spain using remote sensing}



\author[1]{Juliana Alcântara Costa}%
\author[2]{Joaquín Navarro-Hevia}%
\author[1]{Carlos Alexandre Costa}%
\author[1]{José de Araújo}%
\affil[1]{Federal University of Ceara}%
\affil[2]{University of Valladolid - La Yutera Campus}%


\vspace{-1em}



  
  \date{June 13, 2024}


\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup





\selectlanguage{english}
\begin{abstract}
Evapotranspiration (ET) plays an important role in integrated water
resource planning, development and management. This process is
particularly relevant in semiarid regions. The aim of the present study
is to compare the actual spatial and temporal evapotranspiration (ETa)
patterns and temporal trends in two semiarid forests, one in Brazil
(Aiuaba) and the other in Spain (Valladolid). We used the Surface Energy
Balance Algorithm for Land (SEBAL) to assess the effect of climatic
variation in both areas. In the Brazilian semiarid forest, Caatinga is
the main vegetation, while it is stone pine in Spain. For this purpose,
69 Landsat-5 and 42 Landsat-8 images (1995 -- 2019) were used. The
Mann-Kendall test was applied to assess the occurrence of trends in
precipitation, temperature and potential evapotranspiration data; and
the Temporal Stability Index (TSI) to know which areas have greater
seasonal ETa. The annual amplitude of the potential evapotranspiration
(ET0) is the same in both areas, however, the Caatinga values are
higher. In the Caatinga forest, when ET0 presents its highest values
throughout the year, ETa presents the lowest, and vice versa. In the
Pinares forest, ETa follows the ET0 dynamics during the year, and the
difference between ET0 and ETa is maximum during the summer. The
Caatinga forest showed a greater spatial variation of ETa than the
Pinares forest as well as a greater extension with lower temporal
stability of ETa than the Pinares forest. Both the Caatinga forest and
the Pinares forest showed significant annual trends of increase for ET0
and ETa: 3.5 mm and 2.2 mm, and 7.0 mm and 3.9 mm, respectively.%
\end{abstract}%



\sloppy


\textbf{1. Introduction}

The continuous increase in water demand is subject of concern (Cosgrove
\& Loucks, 2015; Boretti \& Rosa, 2019) and demands efficient management
systems, particularly in semiarid regions (Sun et al., 2019), which
account for 15\% of the global land area and feed 14\% of the global
population. Besides, semiarid ecosystems are very fragile and sensitive
to climate change (Safriel \& Adeel, 2005).

The Brazilian semiarid zone is characterized by an extremely negative
atmospheric water balance (annual precipitation of 549 mm against
potential evaporation of 2,500 mm) and a considerable spatial and
temporal variability in water supply. This area presents only two annual
seasons: dry and rainy (de Ara\selectlanguage{ngerman}újo \& Piedra, 2009; de Figueiredo, de
Araújo, Medeiros, \& Costa, 2016; Pinheiro, Metselaar, Lier, \& Araújo,
2016). These features contrast with other semiarid areas, such as the
Spanish Northern Plateau, where precipitation distribution is relatively
uniform throughout the year and presents well-defined seasons (Calama et
al., 2019). These differences may lead to a distinct spatial and
temporal behaviour of the actual evapotranspiration
(ET\textsubscript{a}) in those semiarid areas.

Evapotranspiration (ET) is one of the most challenging components of the
water balance equation to be measured (Castelli et al., 2018). It can be
quantified using lysimeters or aerodynamic methods (e.g., Bowen ratio
and Eddy Covariance), but such methods only represent the specific area
around the experimental setup. The spatial variation of
evapotranspiration on a large scale can be better captured by models
based on remote sensing (Jaafar \& Ahmad, 2020). The high spatial
resolution and long registration period of a USGS Landsat permits to
assess a spatiotemporal ET series of vegetated and non-vegetated
surfaces (Chen \& Liu, 2020; Jaafar \& Ahmad, 2020).

Thermal-energy balance models that use remote sensing, such as SEBAL
(Surface Energy Balance Algorithm for Land), have been successfully
applied to assess ET\textsubscript{a} at field scale in many areas of
the world. Teixeira, Bastiaanssen, Ahmad, and Bos (2009) applied SEBAL
to estimate evapotranspiration in irrigated agriculture and Caatinga
vegetation in the semiarid region of the São Francisco River basin,
north-eastern Brazil; Losgedaragh and Rahimzadegan (2018) used it to
compute evaporation from the freshwater bodies; the same authors (2018),
as well as Rahimzadegan and Janani (2019), applied SEBAL to agricultural
lands in a semiarid climate in Iran; Senkondo, Munishi, Tumbo, Nobert,
and Lyon (2019) used it in a sub-tropical region in Tanzania's Kilombero
Valley; whereas Gobbo et al. (2019) and Grosso et al. (2018) applied it
to assess ET at irrigated and non-irrigated maize fields in Italy.

In the years to come, a significant reduction of precipitation and a
temperature increase can be expected over global typical semiarid
regions as a result of climate change (Yang, Zhang, Hao, \& Yue, 2019).
This trend may influence both the atmospheric and vegetation water
demand, that is, the ET\textsubscript{a}. Therefore, it is crucial and
challenging to research for a better hydrological understanding of
water-balance changes that may occur in semiarid ecosystems, such as
Caatinga (Brazil) and Tierra de Pinares (Spain). The aim of this study
is, hence, to compare spatial and temporal patterns of actual
evapotranspiration, as well as to identify temporal evapotranspiration
trends in both semiarid forests: Caatinga (Brazil) and Tierra de Pinares
(Spain).

\textbf{2. Methods}

2.1 Study areas

The research took place in two forested semiarid areas (Figure 1). The
Caatinga experimental area is located inside the Aiuaba Ecological
Station (ESEC, 117 km²), a Federal preservation area located in the
Brazilian Northeast. This space has been fully preserved since 1978 and
monitored since 2003 by the Semiarid Hydro-Sedimentological Research
Group (http://www.hidrosed.ufc.br/index.php).

The Caatinga experimental area is part of the Jaguaribe River basin.
According to the Köppen classification, the local climate is Bsh (hot
semiarid) with potential annual evaporation of 2,500 mm, average annual
precipitation of 549 mm, and average annual temperature of 26 ºC
(Pinheiro et al., 2016). The rainy season is concentrated from January
to April. The predominant lithology is the crystalline complex of
metasedimentary formation. Soils in the region are generally shallow and
originated from a crystalline substrate. The predominant soil types are
Luvisols, Latosols, and Argisols (de Araújo \& Piedra, 2009; Farias,
Medeiros, Navarro-Hevia, \& de Araújo, 2019).

The Pinares forest (106 km\textsuperscript{2}) is located in Tierra de
Pinares, in the province of Valladolid, Spanish Northern Plateau. Local
vegetation there is formed mainly by stone pine (\emph{Pinus pinea} L),
but the maritime pine (\emph{Pinus pinaster} ) and holm oak
(\emph{Quercus ilex} ) can also be found (Bello, 2004). The soil is deep
and sedimentary, with a sandy texture (more than 90\% sand) and low
water-holding capacity (Calama et al., 2019). Pinares forest has a
continental Mediterranean climate which, according to the Köppen
classification, is Bsk (cold semiarid). The annual rainfall is 400 mm,
the annual mean temperature 11 °C (Moreno-Fernández, Montes,
Sánchez-González, Gordo, \& Cañellas, 2018) and the potential annual
evapotranspiration 1,100 mm (Vicente-Serrano et al., 2014). In the area,
the confluence of the rivers Pisuerga and Duero takes place.

2.2 Satellite Imagery and Meteorological data

Actual evapotranspiration was estimated for the two experimental areas
by using the imagery of Landsat 5 and Landsat 8. Landsat 5 captured
images from March 1984 to January 2012 on six 30-m visible bands and a
120-m thermal band. Landsat 8 was launched in February 2013 and is still
operating. Landsat 8 OLI images have eight 30-m bands, two 100-m thermal
bands and a 15-m panchromatic band. In this study, all the available
cloudless images between 1995 and 2019 were used (Figure 2): 37 images
of the Caatinga forest and 74 of the Pinares forest, totalling 111
images. The imaging time was 12:00 UTC (path 217 and row 65) for
Caatinga, and 11:00 UTC (path 202 and row 31) for Pinares.

The Caatinga forest usually is excessively cloudy during the rainy
season, so that practically no image was cloudless. During the rainy
months, were used images with up to 10\% cloud coverage, but the
specific areas covered by clouds were disregarded.

Shuttle Radar Topography Mission (SRTM) images were employed to generate
the Digital Elevation Model (DEM). Both Landsat and SRTM data were
provided by the United States Geological Survey (USGS)
(https://earthexplorer.usgs.gov/).

Daily and hourly field data of wind speed, temperature, relative
humidity, solar radiation, air pressure and precipitation were obtained
from the National Institute of Meteorology (INMET) and the Ceará
Foundation of Meteorology and Water Resources (FUNCEME) for the
Brazilian forest, and from the State Meteorological Agency (AEMET) for
the Spanish forest. Table 1 shows the stations and periods of available
data.

In the Caatinga forest, meteorological data were obtained from one of
the four stations close to the area, depending on data availability on
the analysis day (Figure 1): the BEA station is located inside the
experimental area and provided 27\% of the data; IBAMA, 8\%; Campos
Sales, 62\%; and Tauá, 3\%. In the case of the Pinares forest, data
concerning air temperature, wind speed and relative humidity were used
from the Villanubla station, which is located outside the city of
Valladolid and suffers less influence of urbanization effects. All other
data were provided by the Valladolid station, which is closest to the
area.

2.3 Surface Energy Balance Algorithm for Land (SEBAL) model

The SEBAL model, applied in this work for having been used with success
in many scientific research, calculates the components of the surface
energy balance (Liaqat \& Choi, 2015), so that the ET for each image
pixel can be estimated using Eq. 1 (Bastiaanssen, Menenti, Feddes, \&
Holtslag, 1998):\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\(\selectlanguage{greek}\text{λE}\selectlanguage{english}_{\text{inst}}=R_{N}-G-H\) & (1)\tabularnewline
\bottomrule
\end{longtable}

where \(\selectlanguage{greek}\text{λE}\selectlanguage{english}_{\text{inst}}\) is the latent heat flow at the time of imaging,
R\textsubscript{N} the net radiation on the surface, G the heat flow
from the soil and H is the heat flow sensitive to air. All units are W
m\textsuperscript{-2}. R\textsubscript{N} (Eq. 2) is a key
hydrometeorological parameter and considers both short- and longwave
radiation flows.\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\(R_{N}=\left(1-\alpha\right)R_{S\downarrow}+R_{L\downarrow}-R_{L\uparrow}-(1-\varepsilon_{S})R_{L\downarrow}\) & (2)\tabularnewline
\bottomrule
\end{longtable}

where \(\alpha\) is the surface albedo and \selectlanguage{greek}ε\selectlanguage{english}\textsubscript{S}
the surface emissivity, R\textsubscript{L|} and R\textsubscript{L|} are
the respective surface upward and downward longwave radiations (W
m\textsuperscript{-2}). R\textsubscript{S|} is the shortwave incoming
radiation (W m\textsuperscript{-2}) and primary energy source for ET.
The incoming shortwave radiation is obtained from Eq. 3:\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\(R_{S\downarrow}=G_{\text{SC}}\selectlanguage{greek}\text{\ cosθ\ dr\ }\selectlanguage{english}\tau_{\text{sw}}\) & (3)\tabularnewline
\bottomrule
\end{longtable}

where G\textsubscript{SC} is the solar constant (1367
Wm\textsuperscript{-2}), \selectlanguage{greek}θ \selectlanguage{english}the solar incidence angle, dr the inverse
squared relative distance between sun and earth, and
\selectlanguage{greek}τ\selectlanguage{english}\textsubscript{sw}the atmospheric transmissivity, which can be
calculated by the empirical Eq. 4.\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\(\tau_{\text{sw}}=0.75+0.00002z\) & (4)\tabularnewline
\bottomrule
\end{longtable}

where z is the height above mean sea level (m). The outgoing
longwave\(R_{L\uparrow}\) is obtained from Eq. 5:\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\(R_{L\uparrow}=\varepsilon_{0}\selectlanguage{greek}\text{\ σ}\selectlanguage{english}\text{\ T}_{s}^{4}\) & (5)\tabularnewline
\bottomrule
\end{longtable}

where \(\varepsilon_{0}\) is the (dimensionless) surface emissivity, \selectlanguage{greek}σ
\selectlanguage{english}the Stefan-Boltzmann constant
(5.67\selectlanguage{ngerman}×10\selectlanguage{english}\textsuperscript{-8}Wm\textsuperscript{-}2K\textsuperscript{-4})
and T\textsubscript{S} the surface temperature (K). Emissivity can be
calculated based on empirical equations of the Normalized Difference
Vegetation Index (NDVI) and the leaf area index (LAI). The leaf area
index (Eq. 6) is calculated by using an empirical equation of the Soil
Adjusted Vegetation Index (SAVI) (Allen, Tasumi, Trezza, Bastiaanssen,
\& Waters, 2002):\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\(LAI=-\frac{\ln\left(\frac{0.69-SAVI}{0.59}\right)}{0.91}\) & (6)\tabularnewline
\bottomrule
\end{longtable}

SAVI (Eq. 7) is meant to reduce soil effect on reflectance of surface in
arid areas and, thus, decreases soil moisture impacts on the index
results (Allen et al., 2002).\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\(SAVI=\frac{\left(R_{\text{IR}}-R_{R}\right)}{{(L+R}_{\text{IR}}+R_{R})}(1+L)\) & (7)\tabularnewline
\bottomrule
\end{longtable}

where \(R_{\text{IR}}\) and \(R_{R}\) are the reflectivity for
infrared and red bands, respectively. L is a parameter for SAVI and if
it is zero, SAVI becomes equal to NDVI. A value of 0.5 frequently
appears in the literature for L and was used in this work. Incoming
longwave radiation is calculated as in Eq. 8:\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\(R_{L\downarrow}=\varepsilon_{a}\selectlanguage{greek}\text{\ σ\ }\selectlanguage{english}T_{a}^{4}\) & (8)\tabularnewline
\bottomrule
\end{longtable}

where \selectlanguage{greek}ε\selectlanguage{english}\textsubscript{a} is the atmospheric emissivity, and
T\textsubscript{a} the near surface air temperature (K). Soil and water
heat flux G (Eq. 9) is the rate of heat storage in soil, plants and
water in heat transfer. It is not possible to calculate this factor by
remote sensing methods, but it can be determined relating
G/R\textsubscript{n}, NDVI, T\textsubscript{S} and albedo.\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\(\frac{G}{R_{n}}=\frac{T_{S}}{\alpha}(0.0038\alpha+0.0074\alpha^{2})(1-0.98\text{NDVI}^{4})\) & (9)\tabularnewline
\bottomrule
\end{longtable}

where the surface temperature (T\textsubscript{S}) is in \selectlanguage{ngerman}°C. The
sensible heat flux H (Eq. 10) is heat transferred to the air by
convection due to a temperature difference.\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\(H=\selectlanguage{greek}\frac{\rho\text{\ C}_{P}\text{\ ΔT}}\selectlanguage{english}{r_{\text{ah}}}\) & (10)\tabularnewline
\bottomrule
\end{longtable}

where \selectlanguage{greek}ρ \selectlanguage{english}is air density, C\textsubscript{P} the specific heat capacity of
air for which 1004 Jkg\textsuperscript{-1}k\textsuperscript{-1} was
used, \selectlanguage{greek}Δ\selectlanguage{english}T is the temperature difference from height Z\textsubscript{1} to
Z\textsubscript{2} (K), and r\textsubscript{ah} the aerodynamic
resistance to heat transport (s m\textsuperscript{-1}). Since there are
two unknown variables (\selectlanguage{greek}Δ\selectlanguage{english}T and r\textsubscript{ah}) in Eq. 10, acquiring
a sensible heat flux can be complex. This is why the SEBAL process
utilizes two ``anchor'' pixels, ``hot'' and ``cold'', to fix boundary
conditions for the energy balance. The selected ``cold'' pixel is a wet,
well-irrigated crop surface with full vegetation ground cover. The
surface and near-surface air temperatures are assumed to be similar at
this pixel. The selected ``hot'' pixel is a dry, bare agricultural field
with ET assumed to be zero (Allen et al., 2002). Afterwards, the
variables \selectlanguage{greek}Δ\selectlanguage{english}T and r\textsubscript{ah} are calculated in the first loop,
subsequently current values are implemented in the next loop as new
initial values, and variables are updated in every loop. This process
continues until the variables converge, which enables the algorithm to
assess the sensible heat flux (Losgedaragh \& Rahimzadegan, 2018).

The SEBAL model was applied in GRASS GIS 7.6, the Geographic Information
System called Geographic Resources Analysis Support System; a script
developed for each Landsat platform was used to facilitate the loop
procedure to obtain \selectlanguage{greek}Δ\selectlanguage{english}T, r\textsubscript{ah} and, consequently, H.

The instantaneous ET value (mm h\textsuperscript{-1}) at the time of
image acquisition and in an equivalent evaporation depth is computed as
in Eq.11:\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\(\text{ET}_{\text{inst}}=3600\selectlanguage{greek}\frac{\text{λE}_{\text{inst}}}\selectlanguage{english}{\lambda}\) & (11)\tabularnewline
\bottomrule
\end{longtable}

where 3600 is the time conversion from seconds to hours, and \selectlanguage{greek}λ \selectlanguage{english}the
latent vaporization heat or the heat absorbed when a kilogram of water
evaporates (J kg\textsuperscript{-1}). After this, the daily ET value
(mm day\textsuperscript{-1}) can be computed as in Eq. 12:\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\(\text{ET}_{\text{day}}=\frac{\text{ET}_{\text{inst}}}{\text{ET}_{r}}\text{ET}_{r_{\text{day}}}\) & (12)\tabularnewline
\bottomrule
\end{longtable}

where ETr is the reference ET at the time of the image. For natural
forest areas, ET\textsubscript{inst}/ET\textsubscript{r}, denominated
evapotranspiration faction (ET\textsubscript{frac}), is similar to the
product between crop coefficient (K\textsubscript{c}, dimensionless) and
water stress coefficient (K\textsubscript{s}, dimensionless).
\(\text{ET}_{r_{\text{day}}}\) is the cumulative 24-hour ET\textsubscript{r} for the
day of the image. Both ET\textsubscript{r} and \(\text{ET}_{r_{\text{day}}}\) were
obtained with the program REF-ET 4.1 (Allen, 2016) (mm
h\textsuperscript{-1}) by using the Penman-Monteith FAO equation
(PM-FAO: Allen, Pereira, Raes, \& Smith, 1998). The actual annual
evapotranspiration to be used in trend analyses was derived from
ET\textsubscript{frac} data.

2.4 Validation and climate change trend analysis

In order to evaluate the performance of SEBAL, its
ET\textsubscript{a}results were compared with those calculated by Eq.
13.\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
ET\textsubscript{a} =
ET\textsubscript{0}.K\textsubscript{c}.K\textsubscript{s} &
(13)\tabularnewline
\bottomrule
\end{longtable}

Three statistical metrics were used: the determination coefficient
(R\textsuperscript{2}, Eq.14), Nash--Sutcliffe efficiency coefficient
(NSE, Eq.15), and Pearson's correlation coefficient (r, Eq.16).\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\(R^{2}=\frac{\left[\sum_{i=1}^{n}{(\text{ETa}_{Sebal,i}-{\overset{\overline{}}{\text{ETa}}}_{\text{Sebal}})(\text{ETa}_{i}-\overset{\overline{}}{\text{ETa}})}\right]^{2}}{\sum_{i=1}^{n}{{(\text{ETa}_{Sebal,i}-{\overset{\overline{}}{\text{ETa}}}_{\text{Sebal}})}^{2}\sum_{i=1}^{n}{(\text{ETa}_{i}-\overset{\overline{}}{\text{ETa}})}^{2}}}\) & (14)\tabularnewline
\midrule
\endhead
\(NSE=1-\frac{{\sum_{i=1}^{n}(\text{ETa}_{i}-\text{ETa}_{Sebal,i})}^{2}}{{\sum_{i=1}^{n}{(\text{ETa}_{i}}-\ {\overset{\overline{}}{\text{ET}}a}_{i})}^{2}}\) & (15)\tabularnewline
\(r=\frac{\sum_{i=1}^{n}{(\text{ETa}_{Sebal,i}-{\overset{\overline{}}{\text{ETa}}}_{\text{Sebal}})(\text{ETa}_{i}-\overset{\overline{}}{\text{ETa}})}}{\sqrt{\sum_{i=1}^{n}{{(\text{ETa}_{Sebal,i}-{\overset{\overline{}}{\text{ETa}}}_{\text{Sebal}})}^{2}\sum_{i=1}^{n}{(\text{ETa}_{i}-\overset{\overline{}}{\text{ETa}})}^{2}}}}\) & (16)\tabularnewline
\bottomrule
\end{longtable}

where \(\text{ETa}_{Sebal,i}\) is the SEBAL actual evapotranspiration for each
day and \(\text{ETa}_{i}\) the actual evapotranspiration obtained by Eq.
13. For both semiarid zones the ET\textsubscript{0} was determined by
using Penman-Monteith FAO equation (Allen et al., 1998). In the Pinares
forest, we used the seasonal value of the ratio
ET\textsubscript{a}/ET\textsubscript{0} obtained by Liu et al. (2017)
for pines (Table 2). In the Caatinga forest (Table 2),
ET\textsubscript{a}/ET\textsubscript{0} was calculated from
the\emph{on-site} water balance (Teixeira, 2018).

The trend analysis was performed using Mann-Kendall method (Mann, 1945;
Kendall, 1975): it is a nonparametric test to identify a trend in a
series. The null hypothesis H\textsubscript{0} for this test means that
there is no trend in the series, whereas the three alternative
hypotheses are a negative, non-null, or positive trend. A significance
level of p = 0.05 was applied in this study. The Mann-Kendall test was
employed with weather variables (rainfall, maximum and minimum
temperature) and with the actual and potential evapotranspiration.

2.6 Temporal Stability Index

The Temporal Stability Index (TSI) was calculated as in Penna et al.
(2013) and in Zhao et al. (2010) for each season (autumn, winter, spring
and summer) in the Pinares forest. For the Caatinga forest, we
calculated TSI for the rainy season and for the dry season, since the
four seasons cannot be differentiated there. Eqs. 16, 17, and 18 were
used to assess the TSI:\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\(\delta_{\text{ij}}=\frac{(\text{ETa}_{\text{ij}}-\ {\overset{\overline{}}{\text{ETa}}}_{j})}{{\overset{\overline{}}{\text{ETa}}}_{j}}\) & (16)\tabularnewline
\midrule
\endhead
\(\sigma_{\text{ij}}=\sqrt{\frac{{(\text{ETa}_{\text{ij}}-\ {\overset{\overline{}}{\text{ETa}}}_{j})}^{2}}{np-1}}\) & (17)\tabularnewline
\(\text{TSI}=\sqrt{{\delta_{\text{ij}}}^{2}+\sigma_{\text{ij}}{\delta_{\text{ij}}}^{2}}\) & (18)\tabularnewline
\bottomrule
\end{longtable}

where \(\text{ETa}_{\text{ij}}\) is the actual evapotranspiration value at
position i at time j, \({\overset{\overline{}}{\text{ETa}}}_{j}\) the average actual
evapotranspiration of all positions in space at time
j,\(\sigma\) the standard deviation and np the number of pixels.
Low TSI values indicate zones with high temporal stability of
ET\textsubscript{a}, while high TSI values indicate zones of low
stability over time.

\textbf{3 Results and discussion}

3.1 Time series analysis of evapotranspiration

Figure 3 shows the daily time series of potential and actual
evapotranspiration, as well as precipitation. It can be seen that the
annual amplitude of ET\textsubscript{0} in the two areas is very
similar: they range from 2 to 10 mm day\textsuperscript{-1} in the
Caatinga forest and from 0 to 8 mm day\textsuperscript{-1} in the
Pinares forest. In the Caatinga forest, however, value dispersion is
higher, since the area does not have a well-defined distinction between
four seasons. We also observe that ET\textsubscript{a} is much closer to
ET\textsubscript{0} in the Pinares forest, especially in the winter,
when the atmospheric water demand is lower. In summer (July-September),
the soil is dryer due to the combination of high potential
evapotranspiration and low precipitation (Calama et al., 2019), which
diminishes soil moisture and, consequently, actual evapotranspiration.

During the dry season in the Caatinga forest, actual evapotranspiration
is generally much lower (low ET\textsubscript{a}) than the potential one
(Figure 3a). In that period, the potential evapotranspiration is high
due to a high air temperature and low air moisture, which raise the
vegetative water demand. Simultaneously, water availability for the
plants is limited due to a continuous absence of precipitation for
several months (Medeiros \& de Ara\selectlanguage{ngerman}újo, 2014), so that soil moisture is
extremely low (in the Caatinga forest, moisture is below wilting point
during more than six months annually: Costa, Lopes, Pinheiro, Araújo, \&
Gomes Filho, 2013). The combination of high atmospheric-water demand and
low soil-water availability causes the plants to actually
evapotranspirate considerably less than the potential value. During the
rainy season, in contrast, soil moisture increases and potential
evapotranspiration decreases, leading to high ET\textsubscript{a} values
compared to potential ET (Figure 3b).

Due to the presence of clouds it was not possible to obtain images
during the rainiest months of the year (February, March and April in the
Caatinga forest and December in Pinares). According to Jaafar and Ahmad
(2020), some limitation exists when cloudy days are frequent: estimated
ET\textsubscript{a} may be higher than the actual values during winter
and early spring, considering that the cloudless images are not
representative of that period, and in images of cloudy days,
evapotranspiration is below the period average. This is true for the
Brazilian semiarid during the rainy season, when cloudiness prevails,
and it explains why the curve generated in Figure 4a is incomplete.
Despite data gaps, however, one can observe the annual behaviour of
ET\textsubscript{frac} in both areas and its value can be used for
prospective estimates of ET\textsubscript{a}. According to Teixeira et
al. (2009), the value of ET\textsubscript{frac} during a Caatinga dry
season is around 0.20. Yet, for the present study the maximum
ET\textsubscript{frac} value could not be identified, considering that
no useful images were available during the months with the highest
precipitation rates. In accordance with the authors \emph{op cit.} , the
ET\textsubscript{frac} may surpass 0.90 during wet season in a Caatinga
vegetation. This value was admitted for the months of February, March
and April for the complete construction of Figure 4c.

With regards to the Pinares forest (Figure 4b), a large dispersion of
ET\textsubscript{frac} data in late autumn and winter can be perceived;
it may be related to the high daily ranges of wind speed (standard
deviation = 1.9 m s\textsuperscript{-1}) and precipitation (standard
deviation = 3.9 mm) during that period. The gradient of water potential
in the soil-plant-atmosphere complex causes soil water to be carried
through the plant and transpired through the leaves. When the
precipitation rate is low and there is not enough soil moisture present,
the water potential gradient is reduced and does not favour
transpiration. Wind also influences the evapotranspiration process, as
it carries moist air over the surface of leaves, soil and water bodies,
renewing the air and keeping it prone to receive more steam. Thus, the
daily variation of these factors influences the increase and decrease of
ET\textsubscript{a} and explains the behaviour of Kc.Ks in the Pinares
forest.

The box-plot graph of the daily actual evapotranspiration in Figure 5 is
divided into colours corresponding to the seasons for the two study
areas. As in the Brazilian semiarid zone the four typical seasons are
not well-defined like in the Pinares forest, only rainy (first semester)
and dry seasons (second semester) are distinguished. The individual
box-plots correspond to the ET\textsubscript{a} data of each of the
pixels of the images that represent the two studied sites. There is a
greater amplitude in the Caatinga forest ET\textsubscript{a} data
(Figure 5a) than in the Pinares forest (Figure 5b).

The Caatinga forest is an area of natural vegetation and, hence,
characterized by a wider range of species and a higher irregularity in
the distribution of vegetation density, if compared to the Pinares
forest. It may also be highlighted that there are pixels of reservoir
water or rivers and pixels of exposed soil from roads and badlands in
both areas; these pixels influence the respective maximum and minimum
ET\textsubscript{a} peaks. Many pixels in the Caatinga area show an
ET\textsubscript{0} equal or close to zero in almost all the images. In
some cases, such as on 10/Sep/1998, 1/Jul//2007, 18/Aug/2007,
9/Jul/2016, 10/Aug/2016 the median was zero; note that the first and
last of these three years (1998 and 2016) were very dry (see Figure 3a).
In the Pinares forest the medians are higher in summer and spring.
Autumn and winter have the lowest atmospheric demands of the year and,
as a consequence, they present the lowest medians.

As there is no agricultural production around the study areas during
some time spans of the year, such as the dry season at Caatinga forest
and winter at the Pinares forest, it was difficult to choose a cold
pixel for the execution of SEBAL; that being so, a pixel within a water
body was selected. This circumstance makes it a somewhat inconvenient
method to be used in natural areas. Still, the ET\textsubscript{a} data
obtained using SEBAL adjust well to the ET\textsubscript{a} data
assessed by Penman-Monteith times Kc and Ks (Figure 6ab). Teixeira et
al. (2009) also found a good correlation (R\textsuperscript{2} = 0.87)
between the daily ET\textsubscript{a} data by SEBAL and field data from
a mixed agricultural and natural ecosystem in a Brazilian semiarid
region.

In both forests, the correlation between NDVI and ET\textsubscript{a}was
greater in areas of less dense vegetation (Figure 7). As the most
vegetated areas have a more constant NDVI throughout the year, the
annual variations of ET\textsubscript{a} are more dependent on
meteorological factors (related to the atmospheric demand for humidity)
than on vegetation. Areas of less dense vegetation, on the other hand,
show greater variation in NDVI according to the season. In the case of
the Caatinga forest, NDVI is highly influenced by the variation of soil
moisture between the rainy and dry months, and in the Pinares vegetation
the NDVI varies depending on the four seasons of the year. It is also
possible to observe greater NDVI ET\textsubscript{a} correlations in the
Caatinga than in Pinares. This is due to the strong deciduousness that
exists in Caatinga vegetation in the dry months, causing the NDVI to
vary more throughout the year.

3.3 Temporal Stability Index (TSI) of actual ET

In Figure 8 it may be noticed that the zones of lower and higher TSI are
always the same in both areas; what changes from season to season is the
intensity. The areas with the highest TSI are the ones that respond
strongest to differences in soil moisture. In the Caatinga forest, these
are the highest regions with denser vegetation and, consequently, a huge
capacity to expand leaf mass and increase evapotranspiration when soil
moisture is higher after precipitation. High TSI values can also be
observed in areas of exposed soil at the edges of the study area. There
herbaceous vegetation grows during the rainy season, disappears during
the dry season and leaves the soil bare. According to Tasumi (2019), in
bare soils ET overestimations are more frequent that underestimations,
since there the ET\textsubscript{a} in dry seasons should be near zero.
The overestimated amount is not negligible when compared to annual
precipitation.

The same observations in relation to exposed soil areas can be made in
the Pinares forest, especially during winter and spring. There, however,
unlike in the Caatinga forest, the areas with the highest TSI have
sparse vegetation, as they produce a more substantial herbaceous layer
under proper environmental conditions.

The Caatinga forest presents a greater extension with lower temporal
stability than the Pinares forest (Figure 8). This is due to the greater
variety of species in the Caatinga with different transpiration
strategies and growth stages throughout the year, as well as to the fact
that vegetation density throughout the area demonstrates a greater
variation.

3.4 Trends in evapotranspiration (ET)

Evapotranspiration is a very complex process and influenced by many
factors as precipitation, temperature, radiation, wind speed (Yang et
al., 2019), type and stage of vegetation. That is why it is important to
identify eventual existing trends in variables that influence
ET\textsubscript{a} trend interpretations (Jaafar \& Ahmad, 2020). In
order to investigate the reasons for ET\textsubscript{a} changes, three
basic factors that control ET were calculated for the study period
(Figure 9 and Table 3): ET\textsubscript{0} and temperature (that
indicate the atmospheric demand); as well as precipitation, which is an
indicator of water availability for evapotranspiration. According to
Yang et al. (2019), surface moisture, which is affected by
precipitation, is the basic material for the ET\textsubscript{a} process
and also the main limiting factor in arid and semiarid regions.

When no monthly value of ET\textsubscript{frac} produced by SEBAL was
available, values from literature were used to calculate the
ET\textsubscript{a}. In the Caatinga area, maximum temperature, annual
Penman-Monteith ET\textsubscript{0} and annual
ET\textsubscript{a}present a discernible positive trend over the period
1963--2017. Annual maximum air temperature increased at 0.027 °C per
year (which means in arithmetic progression 1.5 °C over 55 years). There
are no trends for annual rainfall (583 mm yr\textsuperscript{-1}) or
minimum temperature (20 °C) in the Caatinga. The ET\textsubscript{0}
displays a mean value of 5.5 mm d\selectlanguage{english}\textsuperscript{-1} (total of 1990 mm
yr\selectlanguage{english}\textsuperscript{-1}), a minimum of 1298 mm (during the year of 1999,
Figure 9a), a maximum of 2466 mm (in the drought and hot year of 2016,
Figure 9ab) and an increase of 3.5 mm yr\selectlanguage{english}\textsuperscript{-1}, which
means that it rose by 192.5 mm during the entire period.
ET\textsubscript{a} showed a comparable significant positive trend with
an annual mean of 877 mm yr\textsuperscript{-1}, a variation that is
similar to ET\textsubscript{0} throughout the period (Figure 9c) and an
annual increase of 2.2 mm (121 mm over the investigated time span).

The Pinares forest trends are similar to those observed in the Caatinga.
Precipitation has a non-significant negative trend, while all the other
analysed variables showed a significant positive temporal trend. The
maximum temperature (17.5 degC) showed a trend of 0.023 degC per year, which
supports the results of del Rio, Fraile, Herrero, and Penas (2007) who
worked with a historical series (1961--1997) for the Castile and Leon
region and assessed a trend of 0.02 degC yr\textsuperscript{-1}. The
minimum temperature (5 degC) of the Pinares forest showed a trend of 0.014
degC per year; again, the authors \emph{op. cit.} computed a very similar
result for the same variable: a temporal trend of 0.01 degC
yr\textsuperscript{-1} for the minimum temperature in Castile and Leon.
ET\textsubscript{0} showed a trend of 7.0 mm yr\textsuperscript{-1} (191
mm for all the period), higher than the trend of 10 mm
decade\textsuperscript{-1} found by Vicente-Serrano et al. (2014). The
mentioned authors used a larger time series for their study (1961-2011).
They found a more linear ET\textsubscript{0} pattern until 1990, after
that period, coinciding with the years of our historical series,
ET\textsubscript{a} had a greater annual increase. That means that we
find a greater tendency for an annual increase in ET\textsubscript{a}due
to the size of the historical series studied (1992-2018). In the series
established for the present study, the minimum ET\textsubscript{0} was
897 mm (during the wet year of 1997, the rainiest in the series, Figure
9d), and the maximum value was 1278 mm in 2017 (the year with the
highest maximum temperature, Figure 9e). Likewise, the
ET\textsubscript{a} (average 513.4 mm yr\textsuperscript{-1}) presented
an increasing trend of 3.9 mm yr\textsuperscript{-1} (106 mm for the
period), so that the ET\textsubscript{a} variation was also similar to
ET\textsubscript{0}throughout the period (Figure 9f).

In both study areas, the annual ET\textsubscript{a} was assessed to be
superior to annual precipitation. The Pinares pine stone forest benefits
from the moisture of the water table of the Pisuerga, Duero, Cega and
Adaja rivers. In the Caatinga forest, the explanation may stem from the
fact that part of a reservoir, named Begue, is within this area and it
receives input from a larger area (932 km\textsuperscript{2}). Thus, the
reservoir evaporation and the maintenance of a higher humidity in the
surrounding soil could justify an annual ET\textsubscript{a} greater
than precipitation in the area.

It is interesting to observe that annual ET\textsubscript{0} and
ET\textsubscript{a} in Caatinga Forest (10deg South latitude) are almost
twice than in Pinares forest (40deg North latitude). This is an
interesting result that must be studied in other semiarid environments
with different latitudes.

\textbf{4 Conclusions}

The results of the present study have the potential to be used in
hydrological modelling and for a better understanding of
evapotranspiration patterns in both investigated areas. They reveal that
the annual amplitude of ET\textsubscript{0} is very similar in both
semiarid regions under study, even if values are higher in the Caatinga
forest. They, moreover, demonstrate that actual evapotranspiration
(ET\textsubscript{a}) is low in the Caatinga forest when
ET\textsubscript{0} presents its highest values throughout the year, and
vice versa, due to the annual distribution of precipitation. In the
Pinares forest, on the other hand, ET\textsubscript{a} follows the
ET\textsubscript{0} up and down dynamics during the year, though with a
lesser degree during summer.

ET\textsubscript{a} in denser vegetation areas is more dependent on
meteorological factors (related to atmospheric demand for humidity) than
on vegetation. This behaviour is common to both forests. The irregular
distribution of vegetation density, the presence of reservoir water or
rivers and pixels of exposed soil from roads and badlands influenced the
values of maximum and minimum ET\textsubscript{a}. The Caatinga forest
showed a greater spatial variation of ET\textsubscript{a} than the
Pinares forest. The zones of a lower and higher Temporal Stability Index
(TSI) of ET\textsubscript{a} are always the same in both areas
throughout the year, what changes from season to season is the
intensity. The areas with the highest TSI are those that respond most to
differences in soil moisture. In the Caatinga forest these are the
highest areas of denser vegetation with their huge capacity to expand
leaf mass and increase evapotranspiration, when soil moisture rises
after precipitation. The Caatinga forest presents a greater extension
with lower temporal stability than the Pinares forest.

It is important to mention that semiarid forests may have their water
balance greatly affected by climate changes, due to temporal trends that
could also be observed in the present work: in the Caatinga forest,
potential evapotranspiration (ET\textsubscript{0}) shows a trend to
annually increase by 3.5 mm. Likewise, ET\textsubscript{a} demonstrated
a significant positive annual trend of 2.2 mm. The Pinares forest also
presents positive annual trends for ET\textsubscript{0} and
ET\textsubscript{a}: 7.0 mm and 3.9 mm, respectively. Finally, we found
out that annual ET\textsubscript{0} and ET\textsubscript{a} in Caatinga
were almost twice than in Pinares forest, which could be related with
the latitude of these regions.

\textbf{Acknowledgments}

The authors acknowledge the funding from the Programa Institucional de
Internacionalizacao (CAPES/PrInt) for the scholarship granted to the
first author, and the support of the University of Valladolid and the
Federal University of Ceara. We also thank the meteorological agencies
AEMET, INMET and FUCEME for the data provided for the present work.

\textbf{References}

Allen R., Tasumi M., Trezza R., Bastiaanssen W., \& Waters R. (2002).
SEBAL, Surface Energy Balance Algorithms for Land. Idaho Implementation.
Advanced Training and Users Manual.

Allen R. G. (2016). REF-ET: Reference evapotranspiration calculator.

Allen R. G., Pereira L. S., Raes D., \& Smith M. (1998). Crop
Evapotranspiration: guidelines for computing crop water requirements.
FAO Irrigation and drainage paper 56. Food and Agriculture Organization,
Rome.

de Araujo J. C., \& Piedra J. I. G. (2009). Comparative hydrology:
analysis of a semiarid and a humid tropical watershed.\emph{Hydrological
Processes} , 23(8), 1169--1178. DOI: 10.1002/hyp.7232

Bastiaanssen W. G. M., Menenti M., Feddes R. A., \& Holtslag A. A. M.
(1998). A remote sensing surface energy balance algorithm for land
(SEBAL): 1. Formulation. \emph{Journal of Hydrology} , 212--213(1--4),
198--212. DOI: 10.1016/S0022-1694(98)00253-4

Bello J. A. L. (2004). El Pinar de Antequera (Valladolid, Espana): flora
vascular de interes. \emph{Botanica Complutensis} , 28, 67--70.

Boretti A., \& Rosa L. (2019). Reassessing the projections of the World
Water Development Report. \emph{npj Clean Water} , 15, 1--6. DOI:
10.1038/s41545-019-0039-9

Calama R., Conde M., De-Dios-Garcia J., Madrigal G., Vazquez-Pique J.,
Gordo F. J., \& Pardos M. (2019). Linking climate, annual growth and
competition in a Mediterranean forest: Pinus pinea in the Spanish
Northern Plateau. \emph{Agricultural and Forest Meteorology journal} ,
264, 309--321. DOI: 10.1016/j.agrformet.2018.10.017

Castelli M., Anderson M. C., Yang Y., Wohlfahrt G., Bertoldi G.,
Niedrist G., Hammerle A., Zhao P., Zebisch M., \& Notarnicola C. (2018).
Two-source energy balance modeling of evapotranspiration in Alpine
grasslands. \emph{Remote Sensing of Environment} , 209, 327--342. DOI:
10.1016/j.rse.2018.02.062

Chen J. M., \& Liu J. (2020). Evolution of evapotranspiration models
using thermal and shortwave remote sensing data. \emph{Remote Sensing of
Environment} , 237, 1--20. DOI: 10.1016/j.rse.2019.111594

Cosgrove W. J., \& Loucks D. P. (2015). Water management: Current and
future challenges and research directions. \emph{Water Resources
Research} , 51(6), 4823--4839. DOI: 10.1002/2014WR016869

Costa C. A. G., Lopes J. W. B., Pinheiro E. A. R., Araujo J. C. de., \&
Gomes Filho R. R. (2013). Spatial behaviour of soil moisture in the root
zone of the Caatinga Comportamento espacial da umidade do solo na zona
das raizes do Bioma Caatinga. \emph{Revista Ciencia Agronomica} , 44(4),
685--694. DOI: 10.1590/S1806-66902013000400004

Farias T. R. L., Medeiros P. H. A., Navarro-Hevia J., \& de Araujo J. C.
(2019). Unpaved rural roads as source areas of sediment in a watershed
of the Brazilian semi-arid region. \emph{International Journal of
Sediment Research} , 34(5), 475--485. DOI: 10.1016/j.ijsrc.2019.03.002

de Figueiredo J. V., de Araujo J. C., Medeiros P. H. A., \& Costa A. C.
(2016). Runoff initiation in a preserved semiarid Caatinga small
watershed, Northeastern Brazil. \emph{Hydrological Processes} , 30(13),
2390--2400. DOI: 10.1002/hyp.10801

Gobbo S., Lo Prest S., Martello M., Lorenza P., Antonio B., \& Morari F.
(2019). Integrating SEBAL with in-Field Crop Water Status Measurement
for Precision Irrigation Applications---A Case Study. \emph{Remote
Sensing} , 11, 1--18. DOI: 10.3390/rs11172069

Grosso C., Manoli G., Martello M., Chemin Y., Pons D., Teatini P.,
Piccoli I., \& Morari F. (2018). Mapping Maize Evapotranspiration at
Field Scale Using SEBAL: A Comparison with the FAO Method and Soil-Plant
Model Simulations. \emph{Remote Sensing} , 10, 1--17. DOI:
10.3390/rs10091452

Jaafar H. H., \& Ahmad F. A. (2020). Time series trends of Landsat-based
ET using automated calibration in METRIC and SEBAL: The Bekaa Valley,
Lebanon. \emph{Remote Sensing of Environment} , 238, 1--17. DOI:
10.1016/j.rse.2018.12.033

Kendall M. G. (1975). \emph{Rank Correlation Measures} . Charles
Griffin: London.

Liaqat U. W., \& Choi M. (2015). Surface energy fluxes in the Northeast
Asia ecosystem: SEBS and METRIC models using Landsat satellite
images.\emph{Agricultural and Forest Meteorology} , 214--215, 60--79.
DOI: 10.1016/j.agrformet.2015.08.245

Liu C., Sun G., Mcnulty S. G., Noormets A., \& Fang Y. (2017).
Environmental controls on seasonal ecosystem evapotranspiration/
potential evapotranspiration ratio as determined by the global eddy flux
measurements. \emph{Hydrology and Earth System Sciences} , 21, 311--322.
DOI: 10.5194/hess-21-311-2017

Losgedaragh S. Z., \& Rahimzadegan M. (2018). Evaluation of SEBS, SEBAL,
and METRIC models in estimation of the evaporation from the freshwater
lakes (Case study: Amirkabir dam, Iran). \emph{Journal of Hydrology} ,
561, 523--531. DOI: 10.1016/J.JHYDROL.2018.04.025

Mann H. B. (1945). Nonparametric tests against trend.\emph{Econometrica}
, 13, 245--259.

Medeiros P. H. A., \& de Araujo J. C. (2014). Temporal variability of
rainfall in a semiarid environment in Brazil and its effect on sediment
transport processes. \emph{Journal of Soils and Sediments} , 14(7),
1216--1223. DOI: 10.1007/s11368-013-0809-9

Moreno-Fernandez D., Montes F., Sanchez-Gonzalez M., Gordo F. J., \&
Canellas I. (2018). Regeneration dynamics of mixed stands of Pinus
pinaster Ait. and Pinus pinea L. in Central Spain. \emph{Eur J Forest
Res} , 137, 17--27. DOI: 10.1007/s10342-017-1086-8

Penna D., Brocca L., Borga M., \& Dalla Fontana G. (2013). Soil moisture
temporal stability at different depths on two alpine hillslopes during
wet and dry periods. \emph{Journal of Hydrology} , 477, 55--71. DOI:
10.1016/j.jhydrol.2012.10.052

Pinheiro E. A. R., Metselaar K., Lier Q. de J. van., \& Araujo J. C. de.
(2016). Importance of soil-water to the Caatinga biome,
Brazil.\emph{Ecohydrology} , 9(7), 1313--1327. DOI: 10.1002/eco.1728

Rahimzadegan M., \& Janani A. S. (2019). Estimating evapotranspiration
of pistachio crop based on SEBAL algorithm using Landsat 8 satellite
imagery. \emph{Agricultural Water Management} , 217, 383--390. DOI:
10.1016/j.agwat.2019.03.018

del Rio S., Fraile R., Herrero L., \& Penas A. (2007). Analysis of
recent trends in mean maximum and minimum temperatures in a region of
the NW of Spain (Castilla y Leon). \emph{Theoretical and Applied
Climatology} , 90(1--2), 1--12. DOI: 10.1007/s00704-006-0278-9

Safriel U., \& Adeel Z. (2005). Dryland Systems. In \selectlanguage{english}\emph{Ecosystems and
Human Well-being, Current State and Trends} , Hassan R., Scholes R., Ash
N. (eds). Island Press: Washington; 625--658.

Senkondo W., Munishi S. E., Tumbo M., Nobert J., \& Lyon S. W. (2019).
Comparing remotely-sensed surface energy balance evapotranspiration
estimates in heterogeneous and data-limited regions: A case study of
Tanzania's Kilombero Valley. \emph{Remote Sensing} , 11, 1--33. DOI:
10.3390/rs11111289

Sun H., Yang Y., Wu R., Gui D., Xue J., Liu Y., \& Yan D. (2019).
Improving estimation of cropland evapotranspiration by the Bayesian
model averaging method with surface energy balance
models.\emph{Atmosphere} , 10, 1--19. DOI: 10.3390/atmos10040188

Tasumi M. (2019). Estimating evapotranspiration using METRIC model and
Landsat data for better understandings of regional hydrology in the
western Urmia Lake Basin. \emph{Agricultural Water Management} , 226,
1--11. DOI: 10.1016/j.agwat.2019.105805

Teixeira A. H. de C., Bastiaanssen W. G. M., Ahmad M. D., \& Bos M. G.
(2009). Reviewing SEBAL input parameters for assessing
evapotranspiration and water productivity for the Low-Middle Sa o
Francisco River basin, Brazil Part A: Calibration and
validation.\emph{Agricultural and Forest Meteorology} , 149, 462--476.
DOI: 10.1016/j.agrformet.2008.09.016

Teixeira L. M. N. (2018). Evapotranspiracao em vegetacao natural do
bioma Caatinga obtida por balanco hidrico no solo e por sensoreamento
remoto.Federal University of Ceara, Fortaleza, CE.

Vicente-Serrano S. M., Azorin-Molina C., Sanchez-Lorenzo A., Revuelto
J., Lopez-Moreno J. I., Gonzalez-Hidalgo J. C., Moran-Tejeda E., \&
Espejo F. (2014). Reference evapotranspiration variability and trends in
Spain, 1961-2011. \emph{Global and Planetary Change} , 121, 26--40. DOI:
10.1016/j.gloplacha.2014.06.005

Yang Z., Zhang Q., Hao X., \& Yue P. (2019). Changes in
evapotranspiration over global semiarid regions 1984--2013.\emph{Journal
of Geophysical Research: Atmospheres} , 124, 1--18. DOI:
10.1029/2018JD029533

Zhao Y., Peth S., Wang X. Y., Lin H., \& Horn R. (2010). Controls of
surface soil moisture spatial patterns and their temporal stability in a
semi-arid steppe. \emph{Hydrological Processes} , 24(18), 2507--2519.
DOI: 10.1002/hyp.7665

Table 1. Synthesis of meteorological data obtained for the Caatinga
forest and the Pinares forest.

Table 2. Ratio ET\textsubscript{a}/ET\textsubscript{0} (which equals
K\textsubscript{c}.K\textsubscript{s}, Eq. 13) for the Caatinga
(Teixeira, 2018) and Pinares (Liu et al., 2017) semiarid forests.

Table 3. Trend analysis of weather variables and potential and actual
evapotranspiration (ET\textsubscript{0} and ET\textsubscript{a},
respectively). S indicates the trend (negative or positive), Sen's Slope
represents the annual increase/decrease of the variable and p-value is
the trend significance. *There is a significant positive temporal trend
at the 5\% level.

Figure 1. Geographical location of the study areas and meteorological
stations: Caatinga forest in north-eastern of Brazil and Tierra de
Pinares forest in Valladolid (Castile and Leon), Spain.

Figure 2. Satellite data of the period from 1995 to 2019, used for the
assessment of actual evapotranspiration in the Caatinga forest and the
Pinares forest.

Figure 3. Time series of daily rainfall and actual (ET\textsubscript{a})
and potential evapotranspiration (ET\textsubscript{0}) for (a) the
Caatinga forest and (b) the Pinares forest. Daily values are
interpolated from the satellite overpass time.

Figure 4. Monthly fraction of evapotranspiration
(ET\textsubscript{frac}= K\textsubscript{c}.K\textsubscript{s}) for both
forests (a) Caatinga and (b) Pinares obtained by
ET\textsubscript{a\_SEBAL}/ET\textsubscript{0\_PM} for each scene of
Landsat used and (c) for each month by ET\textsubscript{frac} average.

Figure 5. Box-plot of daily actual evapotranspiration
(ET\textsubscript{a}) for the two forests (a) Caatinga (N \selectlanguage{english}[?] 146,799
pixels) and (b) Pinares (N \selectlanguage{english}[?] 168,956 pixels), elaborated for each of 111
Landsat overpasses and computed by using the Surface Energy Balance
Algorithm for Land (SEBAL) model. The colours represent the different
seasons of the year.

Figure 6. Validation of daily actual evapotranspiration
(ET\textsubscript{a}) for the two forests: (a) Caatinga and (b) Pinares,
using ET\textsubscript{0} calculated with the Penman-Monteith FAO-56
equation and K\textsubscript{c}.K\textsubscript{s}. The statistical
parameters are determination coefficient (R\textsuperscript{2}),
Nash--Sutcliffe coefficient (NSE), and Pearson's correlation coefficient
(r).

Figure 7. Pearson's correlation (r) between Normalized Difference
Vegetation Index (NDVI) and actual evapotranspiration
(ET\textsubscript{a}) for each pixel of Caatiga forest (a) and Pinares
forest (b) images.

Figure 8. Temporal Stability Index (TSI) of ET\textsubscript{a} for the
(a) rainy season and (b) dry season of the Caatinga forest, and for the
four seasons (c) spring, (d) summer, (e) autumn and (f) winter of the
Pinares forest.

Figure 9. Yearly data of the variables used for trend analysis ((a, d)
rainfall; (b, e) maximum and minimum temperature; and (c, f) potential
and actual evapotranspiration, ET\textsubscript{0} and
ET\textsubscript{a}, respectively) for (a, b, c) Caatinga forest and (d,
e, f) Pinares forest. Yearly ET\textsubscript{a} was calculated by
multiplying monthly
ET\textsubscript{frac}(K\textsubscript{c}.K\textsubscript{s}) and daily
Penman-Monteith ET\textsubscript{0}.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-1/Figure-1}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-2/Figure-2}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-3/Figure-3}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-4/Figure-4}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-5a/Figure-5a}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-5b/Figure-5b}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-6/Figure-6}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-7/Figure-7}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-8/Figure-8}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-9/Figure-9}

\end{center}
\end{figure}

\textbf{Hosted file}

\verb`tables.docx`  available at \url{https://authorea.com/users/353387/articles/477307-dynamics-and-temporal-trend-of-evapotranspiration-in-semiarid-native-forests-in-brazil-and-spain-using-remote-sensing}

\selectlanguage{english}
\FloatBarrier
\end{document}

