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Statistically important FAO-56 Penman-Monteith and adjusted Hargreaves cite evapotranspiration tendencies in monthly, seasonal and one-year clip footing were analysed by utilizing additive arrested development, Mann-Kendall and Spearman ‘s Rho trials at the 1 % and 5 % significance degrees. For this intent, meteoric informations were used from 12 meteoric humid Stationss in Serbia over the period 1980-2010 and the package constituent for tendency analysing was developed. All of the important tendencies at the 1 % and 5 % significance degrees were increasing. The FAO-56 PM ET0 tendencies were about similar to the AHARG ET0 tendencies. On the seasonal clip graduated table, the bulk of Stationss with the important increasing tendencies occurred in summer, while no important positive or negative tendencies were detected by the tendency tests in fall for AHARG ET0 series. Furthermore, 70 % of the Stationss were characterized by the important increasing tendencies for both one-year ET0 series.

Keywords

Trend analysis ; mention evapotranspiration ; additive arrested development ; Mann-Kendall trial ; Spearman ‘s Rho trial

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L`analyse diethylstilbestrols tendances diethylstilbestrols donn & amp ; eacute ; es sur cubic decimeter ‘ & amp ; eacute ; vapotranspiration de R & A ; eacute ; f & A ; eacute ; rence dans un climat humide

R & A ; eacute ; amount & A ; eacute ;

Les tendances FAO 56 Penman-Monteith ( FAO 56 PM ) mensuelles, annuelles et saisonni & A ; egrave ; RESs statistiquement significatives et Hargreaves ( AHARG ) l` & A ; eacute ; vapotranspiration de R & A ; eacute ; f & A ; eacute ; rence ( ET0 ) corrig & A ; eacute ; e ont & amp ; eacute ; t & A ; eacute ; analys & A ; eacute ; es par R & A ; eacute ; gression Lin & A ; eacute ; Aire des trials de Mann Kendall et de Spearman Rho au niveau de meaning de 1 % et 5 % . A cet effet, les donn & A ; eacute ; es m & amp ; eacute ; t & A ; eacute ; orologiques ont & amp ; eacute ; t & A ; eacute ; utilis & A ; eacute ; es de 12 Stationss m & amp ; eacute ; t & A ; eacute ; orologiques en Serbie, pour La P & A ; eacute ; riode 1980-2010 et lupus erythematosus composant logiciel a & A ; eacute ; t & A ; eacute ; vitamin D & A ; eacute ; velopp & A ; eacute ; pour l’analyse diethylstilbestrols tendances. Toutes lupus erythematosuss tendances significatives au niveau de meaning de 1 % et 5 % ont & A ; eacute ; t & A ; eacute ; & A ; agrave ; la hausse. Les FAO 56-PM ET0 tendances ont & amp ; eacute ; t & A ; eacute ; presque semblables aux tendances AHARG ET0. Sur cubic decimeter ‘ & amp ; eacute ; chelle de temps saisonni & A ; egrave ; rhenium, en & A ; eacute ; t & A ; eacute ; la plupart diethylstilbestrols stations avaient La tendance & A ; agrave ; la hausse mais, & A ; agrave ; l’automne, les tendances significatives positives et n & A ; eacute ; gatives n’ont pas & A ; eacute ; t & A ; eacute ; vitamin D & A ; eacute ; tect & A ; eacute ; es par lupus erythematosuss trials de tendance diethylstilbestrols s & amp ; eacute ; ries d’AHARG ET0. Par ailleurs, 70 % des Stationss ont & amp ; eacute ; t & A ; eacute ; caract & A ; eacute ; ris & amp ; eacute ; es par lupus erythematosuss tendances significatives & A ; agrave ; la hausse pour lupus erythematosuss deux ET0 s & A ; eacute ; ries annuelles.

Bon mots clefs

Analyse diethylstilbestrols tendances ; Evapotranspiration de R & A ; eacute ; f & A ; eacute ; rence ; R & A ; eacute ; gression Lin & A ; eacute ; Aire ; Test de Mann-Kendall ; Test de Spearman Rho

1. Introduction

Analysis of tendencies in clime alterations is one of the of import environmental issues that have a important impact on hydrological parametric quantities such as dirt wet, land H2O, evapotranspiration. Evapotranspiration ( ET ) is one of the major constituents in the hydrological rhythm and its dependable appraisal is indispensable to H2O resources planning and direction. It is a physical procedure in which H2O base on ballss from liquid to gaseous province while traveling from the dirt to the ambiance, that refers both to vaporization from dirt and vegetive surface and transpiration from workss. These two separate procedures ( vaporization and transpiration ) occur at the same time and there is no easy manner of separating one from the other.

A common process for gauging ET is to gauge mention evapotranspiration ( ET0 ) and so use an appropriate harvest coefficient. ET0 is a complex nonlinear procedure which accurate appraisal is needed for many surveies such as hydrological H2O balance, irrigation system design, irrigation programming, and H2O resources planning and direction.

In recent old ages, a overplus of scientists have compared and analysed the tendencies in ET0. Xu et Al. ( 2006 ) calculated, compared and regionally mapped the Penman-Monteith ET0 and pan vaporization ( Epan ) at 150 meteoric Stationss during 1960-2000 in the Changjiang ( China ) . They concluded that there is a important diminishing tendency in both the one-year ET0 and Epan. Wang et Al. ( 2007 ) found that Epan and ET0 decreased during the summer months in the upper and mid-lower Yangtze River basin of China from 1961 to 2000. Yin et Al. ( 2010 ) analysed the tendencies in ET0 across China during the period 1961-2008. The consequences showed diminishing tendencies of ET0 in most parts and increasing tendencies in the cold temperate humid part and the tropical humid part. Li et Al. ( 2012 ) examined the present ( 1961-2009 ) and future ( 2011-2099 ) spatiotemporal features of ET0 on the Loess Plateau of China to understand the present and future alterations in hydrology.

The consequences presented in Bandyopadhyay et Al. ( 2009 ) showed a important diminishing tendency in ET0 estimated by the FAO 56 Penman-Monteith method over different agro-ecological parts of India during the period 1971-2002. In another survey, Jhajharia et Al. ( 2012 ) investigated the tendencies in ET0 estimated through the Penman-Monteith method over the humid part of nor’-east India by utilizing the Mann-Kendall trial. They found that ET0 decreased significantly at one-year and seasonal clip graduated tables for six Stationss in northeast India.

A few surveies have been conducted on the variableness of ET0 and Epan in Iran. Tabari and Marofi ( 2011 ) investigated among other things temporal fluctuations in Epan for 12 Stationss in Hamedan state in western Iran for the period 1982-2003. In another survey, Tabari et Al. ( 2011a ) analysed the one-year, seasonal and monthly tendencies of the ET0 series for 20 Stationss in the western half of Iran during 1966-2005. They concluded that the increasing tendencies in winter and summer ET0 were greater than those for the spring and fall series. Furthermore, the consequences of the monthly ET0 analysis indicated that the highest Numberss of Stationss with important tendencies were found in February. In add-on, Tabari et Al. ( 2012 ) used Mann-Kendall trial, Theil-Sen ‘s calculator and Spearman trial to place tendency in ET0 series with consecutive dependance in Iran. They found that the Mann-Kendall trial was more sensitive than the Spearman trial to the being of the positive consecutive correlativity in the ET0 series. Shadmani et Al. ( 2012 ) analysed temporal tendencies of ET0 values in waterless parts of Iran. Their consequences showed that increasing and diminishing tendencies were found for monthly ET0. On a seasonal graduated table, the highest Numberss of important tendencies were found in the summer and fall series.

In tendency analysis in Southern Spain, Espadafor et Al. ( 2011 ) detected a statistically important addition in Penman-Monteith ET0. Chaouche et Al. ( 2010 ) focused on the western portion of the Gallic Mediterranean country and reported an addition tendency in monthly possible evapotranspiration chiefly in the spring.

The aims of this survey are: ( 1 ) to see the tendencies on FAO-56 Penman-Monteith ( FAO-56 PM ) and adjusted Hargreaves ( AHARG ) ET0 clip series in a humid clime, which were analysed by utilizing the additive arrested development, Mann-Kendall and Spearman ‘s Rho trial methods and ( 2 ) to utilize the tendency analyzing constituent based on Web services to analyze monthly, seasonal and one-year ET0 tendency analysis.

2. Materials and methods

2.1. Study countries and informations aggregation

Serbia is located in the cardinal portion of the Balkan Peninsula with an country of 88.407 km2. Northern Serbia is chiefly level, while its cardinal and southern countries consist of Highlandss and mountains. Its clime is temperate continental, with a gradual passage between the four seasons of the twelvemonth.

Seriess of monthly meteoric informations of upper limit ( Tmax ) and minimal ( Tmin ) air temperatures, upper limit ( RHmax ) and minimal ( RHmin ) comparative humidnesss, existent vapour force per unit area ( Ea ) and wind velocity ( U2 ) were collected from 12 humid Stationss from Serbia ( Fig. 1 ) for the period 1980-2010 and were obtained from Republic Hydrometeorological Service of Serbia ( hypertext transfer protocol: //www.hidmet.gov.rs/ ) . These locations were chosen because: ( 1 ) they cover all the latitudes in Serbia ( from 42 & A ; deg ; 30’N to 46 & A ; deg ; 10’N ) and ( 2 ) they are situated at different lifts above the sea degree. The description of the selected conditions Stationss is given in Table 1.

Average values with standard divergence of the variables used in this survey for the 31-years period is summarized in Table 2. All selected conditions Stationss had good quality datasets for gauging ET0 with both the FAO-56 PM and AHARG equations. Differences in the mean conditions informations for these locations are non really important. The average one-year Tmax and Tmin for most locations varied between 12.3 and 17.9 & A ; deg ; C and between 3.8 and 8.4 & A ; deg ; C, severally, while the average RHmax and RHmin for these locations are ranged from 78.0 to 86.0 % and from 53.9 to 65.5 % , severally. The average one-year Ea is ranged from 0.9 to 1.4 kPa. The average one-year U2 was the lowest in Loznica ( 0.6 m s?1 ) . It varied for all other locations between 0.9 and 1.9 m s?1.

The datasets were investigated for entropy, homogeneousness and absence of tendencies. The Kendall autocorrelation trial, the Mann-Kendall tendency trial and the homogeneousness trials of Mann-Whitney for the mean and the discrepancy, were used for this intent.

2.2. Methods for gauging mention evapotranspiration

Numerous equations, classified as temperature-based, radiation-based, pan evaporation-based and combination-type, have been developed for gauging ET0 ( Gocic and Trajkovic 2010, Trajkovic 2010, Tabari et Al. 2011b ) . In this survey, the FAO-56 PM and AHARG equations are used for gauging ET0 as a portion of the theoretical account based on service-oriented paradigm ( Gocic and Trajkovic 2011 ) .

2.2.1. FAO-56 Penman-Monteith equation

The FAO-56 Penman-Monteith equation ( FAO-56 PM ) has been recommended by the Food and Agriculture Organization of the United Nations ( FAO ) as the standard equation for gauging ET0. It assumes the mention evapotranspiration as that from a conjectural harvest with an false harvest tallness ( 0.12 m ) and a fixed canopy opposition ( 70 s Garand rifle ) and albedo ( 0.23 ) , closely resembling the evapotranspiration from an extended surface of green grass screen of unvarying tallness, actively turning, and non short of H2O, which is given by Allen et Al. ( 1998 ) :

( 1 )

where ET0 = mention evapotranspiration ( mm day-1 ) ; ? = incline of the impregnation vapour force per unit area map ( kPa oC -1 ) ; Rn = cyberspace radiation ( MJ m-2 d-1 ) ; G = dirt heat flux denseness ( MJ m-2 d-1 ) ; ? = psychometric invariable ( thousand Pa oC -1 ) ; T = mean air temperature ( oC ) ; U2 = mean 24-hour air current velocity at 2 m tallness ( thousand s-1 ) ; and VPD = vapour force per unit area shortage ( kPa ) .

2.2.2. Adjusted Hargreaves equation

The deficiency of conditions informations motivated Hargreaves et Al. ( 1985 ) to develop a simpler attack where merely minimal and maximal air temperature values were required. The Hargreaves equation ( HARG ) can be written as

( 2 )

where ET0, harg = ET0 estimated by the Hargreaves equation ( mm day-1 ) ; Ra = extraterrestrial radiation ( mm day-1 ) ; Tmax = daily maximum air temperature ( oC ) ; Tmin = daily minimum air temperature ( oC ) ; HC = empirical Hargreaves coefficient, HE = empirical Hargreaves advocate, and HT = empirical temperature coefficient [ HC = 0.0023, HE = 0.5, and HT = 17.8 ( Hargreaves 1994 ) ] .

Allen et Al. ( 1998 ) have proposed that when sufficient informations to work out the FAO-56 PM equation are non available so the Hargreaves equation can be used. However, this equation by and large overestimates ET0 at humid locations ( Jensen et al. 1990 ) . These consequences motivated Trajkovic ( 2007 ) to develop the adjusted Hargreaves equation that provides the close understanding with FAO-56 PM estimates at Serbian humid locations.

The adjusted Hargreaves ( AHARG ) equation can be written as ( Trajkovic 2007 ) :

( 3 )

where ET0, aharg = ET0 estimated by the adjusted Hargreaves equation ( mm day-1 ) , Tmax and Tmin = upper limit and minimal air temperature ( oC ) , severally, and Ra = extraterrestrial radiation ( MJ m-2 d-1 ) . The AHARG equation requires temperature and latitude informations for gauging ET0.

2.3. Swerve analysis methods

Many statistical techniques have been developed to observe tendencies within clip series such as Bayesian process, Spearman ‘s Rho trial, Mann-Kendall trial, Sen ‘s incline calculator. In this survey, one parametric method ( additive arrested development ) and two non-parametric methods ( Mann-Kendall and Spearman ‘s Rho ) were used to observe the ET0 tendencies.

2.3.1. Linear arrested development method

A additive arrested development method efforts to explicate the relationship between two or more variables utilizing a consecutive line. Arrested development refers to the fact that although ascertained informations are variable, they tend to regress towards their mean, while additive refers to the type of equation we use in our theoretical accounts.

A additive arrested development line has an equation of the signifier

( 4 )

where ten = the explanatory variable, y = the dependant variable, B = the incline of the line and a = the intercept.

The incline indicates the average temporal alteration of the studied variable. Positive values of the incline show increasing tendencies, while negative values of the incline indicate diminishing tendencies.

Linear arrested development analysis is used for observing and analyzing tendencies in clip series.

2.3.2. Mann-Kendall tendency trial

The Mann-Kendall statistical trial ( Mann 1945, Kendall 1975 ) has been often used to quantify the significance of tendencies in hydro-meteorological clip series ( Douglas et al. 2000, Yue et Al. 2002a, Partal and Kahya 2006, Modarres and Silva 2007, Hamed 2008, Tabari and Marofi 2011, Tabari et Al. 2011a ) .

The Mann-Kendall trial statistic S is calculated by utilizing

( 5 )

where N is the figure of informations points, eleven and xj are the informations values in clip series I and J ( ) , severally and is the mark map determined as:

( 6 )

The discrepancy is computed as

( 7 )

where N is the figure of informations points, m is the figure of trussed groups and Ti denotes the figure of ties of extent I. A trussed group is a set of sample informations holding the same value.

In the absence of ties between the observations, the discrepancy is computed as:

( 8 )

In instances where the sample size, the criterion normal trial statistic ZS is computed as:

( 9 )

Positive values of ZS indicate increasing tendencies while the negative ZS show diminishing tendencies.

Testing of tendencies is done at a specific ? significance degree. In this survey, significance degrees of ? = 0.01 and ? = 0.05 were used. At the 5 % significance degree, the void hypothesis of no tendency is rejected if |ZS| & A ; gt ; 1.96 and rejected if |ZS| & A ; gt ; 2.576 at the 1 % significance degree.

The p-value ( local significance degree or chance value, P ) for Mann-Kendall tendency trial can be obtained from ( Yue et al. 2002b )

( 10 )

where

( 11 )

denotes the cumulative distribution map of a standard normal variable.

Given the significance degree ( ? ) , if the value P & A ; lt ; ? , so a tendency is considered to be statistically important. For illustration, at the significance degree of 0.05, if p ? 0.05, so the bing tendency is assessed to be statistically important.

2.3.3. Spearman ‘s Rho trial

Spearman ‘s Rho trial is non-parametric method normally used to verify the absence of tendencies. The void hypothesis ( H0 ) is that all the informations in the clip series are independent and identically distributed, while the alternate hypothesis ( H1 ) is that increasing or diminishing tendencies exist ( Yue et al. 2002b ) .

The Spearman ‘s Rho trial statistic D and the standardised trial statistic ZD are expressed as follows

( Lehmen 1975, Sneyers 1990 ) :

( 12 )

( 13 )

where is the rank of ith observation Xj in the clip series and N is the length of the clip series. The sample size in this survey is n = 31.

Positive values of ZD indicate increasing tendencies while negative ZD show diminishing tendencies. At the 5 % significance degree, the void hypothesis of no tendency is rejected if |ZD| & A ; gt ; 2.08 and rejected if |ZD| & A ; gt ; 2.831 at the 1 % significance degree.

2.3.4. Consecutive autocorrelation trial

To take consecutive correlativity from the series, von Storch and Navarra ( 1995 ) suggested to pre-whiten the series before using the Mann-Kendall trial. This survey incorporates this suggestion in both Mann-Kendall and Spearman ‘s Rho trial and computes the lag-1 consecutive correlativity coefficient ( designated by r1 ) as

( 14 )

where is the mean of the first n -1 observations and is the mean of the last n – 1 observations.

2.4. Swerve analyzing constituent based on Web services

The tendency analyzing constituent based on Web services was developed to look into tendencies in FAO-56 PM and AHARG ET0 clip series. Software component architecture for ET0 tendency analysing is shown in Fig. 2. This architecture is a follow-up survey of Gocic and Trajkovic ( 2011 ) . The first measure is informations come ining by utilizing Input Data Provider. The information from the measurement Stationss are parsed and stored in SQL database ( hydrological database ) utilizing storage Web service.

The chief input informations are: day of the month format dd/mm/yy, day-to-day maximal temperature ( oC, Tmax ) , day-to-day minimal temperature ( oC, Tmin ) , wind velocity, latitude ( O ) , lift ( m ) , day-to-day lower limit and maximal comparative air humidnesss ( RHmin, RHmax ) , day-to-day dew-point temperature ( oC, Tdew ) and vapour force per unit area ( VP ) . Information on latitude and lift of mensurating station and day of the month are required for the appraisal of extra-terrestrial solar radiation ( Ra ) and the maximal sunlight hours ( N ) .

ET0 theoretical account consists of two constituents: Model Equation and Numerical Estimator. Model Equation can incorporate the undermentioned ET0 equations: temperature-based, radiation-based, pan evaporation-based and combination-type. This survey is based on FAO-56 PM and AHARG equations.

A portion used for numerical appraisal ( Numerical Estimator ) calculates the end product informations. It contains the logic for the choice of appropriate ET0 equation depending on the pick of input parametric quantities.

Trend Analyzer constituent contains a logic for choosing parametric or non-parametric methods for monthly, seasonal and one-year tendency analyzing. This survey is based on utilizing additive arrested development, Mann-Kendall and Spearman ‘s Rho methods. Each of tendency methods is implemented as a Web service, which is written in C # . End user can choose the appropriate studying period, weather station and statistical method. After choosing, the consequences are published in tabular array. This constituent can be used to ease the tendency analyzing procedure.

The tendency analyzing Web services and attach toing WSDL and SOAP 1.2 certification are available for free download from the website hypertext transfer protocol: //www.gaf.ni.ac.rs/mgocic/TrendWebServices.htm. More information about Web services can be found in Staab et Al. ( 2003 ) , Alonso et Al. ( 2004 ) , Papazoglou et Al. ( 2007 ) , Papazoglou and Heuvel ( 2007 ) .

The end product informations from this constituent can be obtained by Output Data Provider. Output informations are: ET0, Ra, N, day-to-day cyberspace radiation ( Rn ) , estimated losing conditions informations and monthly, seasonal and one-year tendency analysing of informations.

3. Consequences

Statistic features of the estimated FAO-56 PM and AHARG ET0 at 12 conditions Stationss during the period 1980-2010 are summarized in Table 3. The average day-to-day estimations by the FAO-56 PM and AHARG methods are ranged from 1.975 to 2.552 and 1.820 to 2.405 millimeter d?1, severally. The highest coefficient of fluctuation ( CV ) of the FAO-56 PM ET0 values was observed at the Palic station located in the north Serbia at the rate of 8.99 % , while the highest Curriculum vitae of 6.96 % was observed at Zlatibor for the AHARG ET0 values. The lowest Curriculum vitae of 6.68 % was found at Dimitrovgrad for the FAO-56 PM ET0, while the lowest Curriculum vitae of 4.59 % was observed at Vranje for the AHARG ET0 values.

Autocorrelation secret plans for the FAO-56 PM and AHARG ET0 at the 12 conditions Stationss are presented in Fig. 3. Both FAO-56 PM and AHARG ET0 series had a positive lag-1 consecutive correlativity coefficient at all of the Stationss. The highest consecutive correlativities of 0.59 and 0.62 were obtained at Negotin ( FAO-56 PM ) and Zlatibor ( AHARG ) Stationss, severally. The lowest consecutive correlativities of 0.01 and 0.03 were detected at Loznica ( AHARG ) and Dimitrovgrad ( FAO-56 PM ) Stationss, severally.

3.1. Tendencies of mention evapotranspiration

Tendencies of ET0 are considered statistically at the 1 % and 5 % significance degrees. When a important tendency is identified by three statistical methods, the tendency is presented in bold character in the tabular array.

3.1.1. Monthly Analysis

The consequences of the three statistical trials for the monthly FAO-56 PM ET0 over the period 1980-2010 are summarised in Table 4. As shown, the applied Mann-Kendall and Spearman ‘s Rho trials for tendency analysing of monthly ET0 are similar. All Stationss exhibited no important tendencies in the months of January, February, March, September, October and December. The consequences besides suggest that there was merely the important increasing tendency, while at the Nis and Vranje conditions Stationss exhibited no important tendencies. The magnitudes of the important increasing tendencies in FAO-56 PM ET0 series varied from 0.114 mm/month at the Loznica station in November to 0.990 mm/month at the Belgrade station in July.

The consequences of the three statistical trials for the monthly AHARG ET0 over the period 1980-2010 are summarised in Table 5. All Stationss had no important tendencies in the months of January, February, March, September, October and December, which is similar to FAO-56 PM ET0 series. The incline of the important increasing tendencies in AHARG ET0 series was ranged from 0.148 mm/month at the Vranje station in November to 0.872 mm/month at the Zlatibor station in May.

Fig. 4 shows the per centum of Stationss with important positive tendencies for the monthly FAO-56 PM and AHARG ET0 during the period 1980-2010. The highest Numberss of Stationss with important tendencies were found in the AHARG ET0 series at the 5 % significance degree in August and November ( 66.67 % ) , while the lowest Numberss of Stationss with important tendencies were found in the FAO-56 PM ET0 series at the 1 % and 5 % significance degrees in June and July ( 8.33 % ) , severally.

The spacial distribution of the Mann-Kendall tendency at the 1 % and 5 % significance degrees for the monthly FAO-56 PM ET0 over the period 1980-2010 is presented in Fig. 5. FAO-56 PM ET0 important increased in the North and cardinal of Serbia, with one exclusion in the South in November.

3.1.2. Seasonal Analysis

Consequences of the statistical trials for seasonal FAO-56 PM and AHARG ET0 during the period 1980-2010 are presented in Table 6 and 7. Harmonizing to these consequences, it is clear that the important increasing tendency was observed for both FAO-56 PM and AHARG ET0 series.

The analysis of the ET0 series revealed that there were important increasing tendencies in spring at Negotin, Palic and Sombor for FAO-56 PM, and at Nis and Zlatibor for AHARG series. In summer, the important increasing tendencies were at the 1 % significance degree for FAO-56 PM ET0 series except Dimitrovgrad, Nis and Vranje were no important tendencies. Furthermore, it can be concluded that all Stationss except Loznica had the important increasing tendencies for summer AHARG ET0 series.

The consequences besides suggest that there were no seeable tendencies bespeaking an addition or lessening in fall AHARG ET0 series, while there was important increasing tendency at Sombor at the 5 % significance degree in autumn FAO-56 PM ET0 series. Besides, important increasing tendencies were obtained at Loznica and Sombor ( FAO-56 PM ET0 ) and at Nis and Zlatibor ( AHARG ET0 ) at the 5 % significance degree in winter.

Fig. 6 shows the spacial distribution of seasonal FAO-56 PM ET0 trends at the 1 % and 5 % significance degrees by the Mann-Kendall trial at 12 conditions Stationss during the period of 1980-2010. The Stationss with important positive tendencies are chiefly distributed at the southern and cardinal Serbia in summer. The important positive tendencies are located in the North in spring, fall and winter, with two exclusions: foremost, in the East in spring and 2nd, in the West in winter.

3.1.3. Annual Analysis

Consequences of applied the Mann-Kendall trial, the Spearman ‘s Rho trial and the additive arrested development for the one-year FAO-56 PM and AHARG ET0 series during the period 1980-2010 are shown in Table 8. All of the important tendencies at the 1 % and 5 % significance degrees were increasing. The important increasing tendencies in one-year FAO-56 PM ET0 varied from 3.772 mm/year at the Negotin station to 5.163 mm/year at the Sombor station. In one-year AHARG ET0 series, the important increasing tendencies were ranged from 1.810 mm/year at the Sombor station to 3.623 mm/year at the Zlatibor station. The consequences besides indicated that 41.67 % and 25 % of the Stationss had no important tendencies for FAO-56 PM and AHARG ET0 series, severally.

The spacial distribution of one-year FAO-56 PM ET0 trends at the 1 % and 5 % significance degrees by the Mann-Kendall trial in ascertained conditions Stationss during the period 1980-2010 is presented in Fig. 6. The important increasing tendencies were identified in the North and cardinal of Serbia, while there were no important tendencies in southern Serbia.

Time series, additive tendencies and coefficient of finding ( R2 ) of one-year FAO-56 PM and AHARG ET0 at the Stationss with important tendencies at ? = 0.01 are presented in Fig. 7. Harmonizing to these consequences, the important increasing tendencies in one-year FAO-56 PM ET0 varied from 3.772 mm/year at the Negotin station to 5.163 mm/year at the Sombor station, while in one-year AHARG ET0 varied from 2.211 mm/year at the Vranje station to 3.623 mm/year at the Zlatibor station.

4. Discussion

ET0 depends on alterations in air temperatures ( minimal and upper limit ) , solar radiation, comparative humidness ( RH ) and wind velocity ( Gocic and Trajkovic 2010, Tabari et Al. 2011a, Liu and McVicar 2012 ) . Furthemore, we investigated the relationship between these meteoric variables and ET0 tendencies.

Harmonizing to T & A ; uuml ; rkes and S & A ; uuml ; mer ( 2004 ) and Dhorde et Al. ( 2009 ) , the local physical geographic and atmospheric circulation characteristics can impact on the nature and magnitude of the upper limit and minimal temperature tendencies. These factors can besides act upon the alterations of the ET0, which can be seen on seasonal graduated table between the flatlands in northern Serbia ( Novi Sad, Palic, Sombor ) and highlands in cardinal and southern Serbia ( Kragujevac, Zlatibor, Nis, Vranje ) .

The most important increasing tendencies of the Tmin and Tmax series and the important diminishing tendency of RH series were found in summer ( Djordjevic 2008, Gocic and Trajkovic 2013 ) . This can do the being of the important increasing ET0 in summer ( Table 6 and Fig. 6 ) .

Furthermore, Ducic et Al. ( 2008 ) found that the air temperature increases in northern Serbia about 1.5 times higher in the near-surface bed, compared to lower and in-between beds of troposphere. Harmonizing to these consequences, there were the most important increasing tendencies of ET0 in spring and summer. As addressed in Table 6, the important increasing tendency in summer season was observed for both FAO-56 PM and AHARG ET0 series in about 75 % and 91.7 % , severally.

The Mann-Kendall trial detected that about 70 % of the Stationss showed a important diminishing tendency in air current velocity both in seasonal and in one-year graduated table ( Gocic and Trajkovic 2013 ) . Similar consequences are detected by Jiang et Al. ( 2010 ) , which concluded that the cardinal ground for the diminishing tendency in air current velocity is the alteration of atmospheric circulation. Merely at Palic station, important increased tendency was indicated. The diminishing tendency in air current velocity can increase ET0 ( Table 8 ) .

5. Decisions

The additive arrested development, the Mann-Kendall and the Spearman ‘s Rho trials were applied to analyze monthly, seasonal and one-year tendencies in the FAO-56 PM and AHARG ET0 series. Monthly conditions informations for this survey were used from 12 conditions Stationss from Serbia for the period 1980-2010.

The statistical methods were developed as Web services and presented as the portion of the tendency analyzer constituent. In general, this survey showed that there is the great similarity between the statistical consequences from three statistical methods. The similar decision has been confirmed by Yue et Al. ( 2002b ) , Tabari et Al. ( 2011a ) and Shadmani et Al. ( 2012 ) .

In general, all of the important tendencies at the 1 % and 5 % important degrees were increasing. Furthermore, all Stationss exhibited no important tendencies in the months of January, February, March, September, October and December for both FAO-56 PM and AHARG ET0 series. Harmonizing to Mann-Kendall trial, the highest Numberss of Stationss with important tendencies were found in the monthly FAO-56 PM ET0 series in July and August, while the lowest Numberss of Stationss with important tendencies were found in April.

The positive ET0 tendencies were important at the 1 % and 5 % significance degrees harmonizing to the statistical trials in the spring, summer, fall and winter seasons in approximately 25 % , 75 % , 8.33 % and 16.67 % of the Stationss ( FAO-56 PM ) and about 16.67 % , 91.67 % , 0 % and 16.67 % of the Stationss ( AHARG ) , severally. Furthermore, the highest important increasing tendency was detected in summer season at the Palic station.

On the one-year clip graduated table, the important increasing tendencies varied from 3.772 mm/year at the Negotin station to 5.163 mm/year at Sombor station for FAO-56 PM ET0, and from 1.810 mm/year at the Sombor station to 3.623 mm/year at the Zlatibor station for AHARG ET0 series. The increasing tendencies were important in 70 % of the Stationss at the 1 % and 5 % significance degrees.

The analysed consequences can be helpful for be aftering the efficient usage of H2O resources to better agricultural production. Further research in analyzing relationship between meteoric variables and ET0 tendencies is recommended.

Recognitions

The paper is a portion of the research done within the undertakings TR 37003 and COST ES1004. We would wish to thank anon. referees for their valuable remarks and their constructive suggestions that helped us better the concluding version of the article.

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