Climatological Hydric Balance and the Trends Analysis Climatic in the Region of Machado in Minas Gerais State , Brazil

Lately the planet’s climate has been constantly changing, caused mainly by global warming which has exposed a great deal of concern to the population over the years. In order to understand the possible impacts that such changes may have on the environment and society in general, the importance of the analysis of climate and hydrological events trends and their performance in a region is justified. The objective of the present work was to perform the climatic classification and to evaluate the behavior of the Climatological Hydric Balance—CHB, from the region of Machado state of Minas Gerais—MG, taking into account a historical series of 55 years of climatic season data of the National Institute of Meteorology—INMET; to verify the occurrence of climatic changes by the temporal trends of precipitation and the average temperature, using the Mann-Kendall and Pettitt method; and the influence of these possible climate changes on CHB behavior and on the region’s climate classification. Based on the results found it verified the increase in the water deficit between the months of June to September and a reduction in the water surplus from November to February. By means of the trend analysis, there was a positive trend of increase in the average temperature of 1.6 ̊C until the year 2100. The continuity and occurrence of these trends may have impacts on the economy, agriculture, the hydrological cycle, and consequently on the fauna, the flora and the population.


Introduction
The world's climate activity has been suffering severe changes, producing a raise in the number of environmental disasters and natural catastrophes, causing huge financial losses in many areas of the planet [1].The studies and frequent discussions about natural resources and climate changes happen due to its importance to the existence of life on the planet, and, mainly, for its exaggerated and uncontrolled use [2].
The damage to the society, to the economy and to the environment caused by climate changes is frequently showed by the press and, among the most relevant economic activities, Cecílio et al. [3] and Pereira et al. [4] point out that the agribusiness sector is more dependent on the climate conditions.It happens because the climate conditions affect all of the phases of the productive chain, since the preparation of the soil for the seeding until the harvest, the transportation, the preparation, the products' storage and their commercialization.
In order to have an adequate planning of the tillage, the climate conditions and the soil from the different agricultural regions have to be considered.Thus, the good establishment of a crop in the tillage depends mainly on the water availability, on the soil technical features, on the amount of heat and solar energy.When a shortfall or excess of these elements occurs, it will possibly reduce the tillage's productivity.
According to Marin et al. [2], The Climate Hydric Balance-CHB is an important tool to study the clime of a certain region.In this sense, the CHB, described by Thornthwaite and Mather (1955), is used to monitor the water storage's variation in soil-plant-atmosphere system.
The CHB can be calculated by the accounting of the natural supply of groundwater, rainfall (P) and atmospheric demand, through the potential evapotranspiration (ETP), and with a maximum level of storage or available water capacity, appropriate to the present study.The CHB provides estimative of water deficiency (DEF), water surplus (EXC), real evapotranspiration (ETR) and storage of groundwater (ARM).The CHB can be elaborated in a daily scale, in specific days, or monthly or annual scale [4] [5] [6].
The Knowledge of the CHB elements guides the agricultural planning and management.Besides, it supports the climate and agro ecological zoning; the definition of the most appropriate times for the main processes in the crop, such as soil preparation, seeding and planting, pulverization and harvest; the estimation of the crops productivity; irrigation design and management; management of hydric resources in river basins; the selection and sizing of techniques for the conservation of water and soils [3] [7].
According to the IPCC report [1], it is clear that the earth's temperature is increasing and the projections to the end of this century point to raises from 1.1˚C to 6.4˚C in the average air temperature, in many places around the earth, including Brazil.It could bring considerable losses to agriculture and livestock activities and a new agroclimatic aptitude configuration to the many agricultural crops around the world.

G. S. Rodrigues et al.
Studies aiming the detection of possible climate tendencies applied satisfactorily the Mann-Kendell method in climate variations.The World Meteorological Organization (OMM) suggests this test for tendency identification in time series [8] [9] [10].In order to find if there was sudden change in the average of the series we can use the Pettitt test [11].Two samples from the same time series that could be considered belonging to the same population were analyzed.
Salviano, Groppo e Pellegrino [8] analyses the time inclinations of the average temperature and precipitation in Brazil.They show that these tendencies are not significant regarding precipitation in a big part of the country.However, the average temperature showed a significant raising tendency in a big part of Brazil over the year.Queiroz [9] tried to evaluate this tendency in 46 historical series in the State of Minas Gerais using the Mann-Kendall test and other methodologies.He found an increasing tendency in many historical series.
In the same way, the study of the climate information daily collected is of great importance to study and predict the main severe hydric phenomena such as droughts, storms and hail rains.Those phenomena are essential to understand the climate changes and the possible impacts that they may cause in a certain area [1] [8] [9].
The objective of this work was to evaluate the behavior of BHC and to determine the existence of changes in the climate due to the temporal trends of precipitation and the average temperature in the Machado-MG region, investigating the influence of possible climatic changes on BHC behavior.

Description of Study Area
The studying area is represented by the city of Machado, located in the micro region of Alfenas in the south of the Minas Gerais state.It has a territorial area of approximately 586 km 2 and is located in the geographic coordinates of latitude 21˚40'30''S and longitude 45˚55'12''W.Its main economic activity is the agriculture exploitation and coffee is the main economic product and a massive generator of employment [12].

Climate Data
In order to use the statistic method determined for this research, a meteorological mean of 55 years of daily climate data was applied.The data is from to the climatological station of the INMET-National Institute of Meteorology located in Machado-MG.
The data obtained in INMET are related to the monthly and annual means of a historical series from 1961 to 2015, referring to temperature and precipitation.The organization and tabulation of the data were executed using an electronic speadsheet.

Methodology of Hydric Balance and Climate Classification
According to Marin et al. [2]  sectional hydric availability information, the calculation of water deficit (DEF), the water excess (EXC) and the removal and recharging of groundwater.
In order to elaborate and estimate the CHB by Thornhwaite and Mather method [13] the balance between the inputs and outputs of water in the soil-plant system is made taking into account the storage capacity of soil water (CAD).The storage capacity of soil water (CAD) represents the maximum water availability that a certain kind of soil can retain depending on their physical characteristics.
To elaborate the CHB of this research, we used a model of an electronic spreadsheet developed by Rolim, Sentelhas and Barbieri [14].When the CHB has only climatic purposes, the use of CAD in the soil being equivalent to 100 or 125 mm is recommended.
Firstly, monthly climatic potential evapotranspiration, in mm, was estimated through the Thornthwaite and Mather [13] method, in which the uncorrected monthly evapotranspiration potential was calculated (considering 12 hour days and a 30 days month).Then, it was multiplied by the correction factor, which is a dependent on the latitude and on the months of the year.

( )
ETP 16 10 ETP = potential evapotranspiration for a 30 days month with a 12 hour insolation (mm), t is the average temperature of the month (˚C) and a is the cubic function of I (that can be calculated by the formula) I is the annual calorific value.The value of I can be calculated by summing the 12 values of the monthly calorific indices (i), which can be calculated by the following formula: ( ) t' is the common monthly average temperature (˚C).
After estimating the evapotranspiration, the calculation of Thornthwaite and Mather [13] started.To do so, some calculation factors used in CHB are necessary: P-ETP: Calculates the difference between precipitation P and the estimated potential evapotranspiration (ETP) in order to collect positives and negative balances.In most areas, the most common is the occurrence of a rainy season followed by a drought.In the humid months P-ETP are positives, indicating excessive rainfall, while in the dry months P-ETP is negative, representing potential water loss.When the situation is the water recharge in the soil, that is, whenever the (PETP) ≥ 0, it has to be added to ARM (storage) of the previous period and through this new ARM, it is possible to calculate the new NAc (accumulated negative) by the following expression: When there is withdrawal of the water in the soil, that is, when the (P-ETP) < DOI: 10.4236/ajcc.2018.74034G. S. Rodrigues et al.
0, it has to be accumulated and through the (P-ETP) we calculate the ARM, using the following expression: First, we calculate the Nac by the equation: Then, we calculate the ARM: ALT-Storage Alteration ALT > 0 There was replacement ALT < 0 There was withdrawal of water from the soil ETR-Real Evapotranspiration If, If ( ) DEF-Hydric deficiency: refers to the amount that the soil-plant system did not evapotranspirate EXC-Water surplus: it is related to the water that the soil cannot retain or evapotranspirate If ARM CAD = , ( ) In order to do the climate classification by the Thornthwaite and Mather method [13], we use indices calculated based on the CHB.The hydric index (I n ), the arid index (I a ) and the humidity index (I u ), connected to the hydric availability, are defined from the annual values.The climate types (Table 1) were defined based on the humidity index (I u ), while the subtypes were defined by the arid index (Table 2).
( ) ( ) ( ) In order to classify the thermal factor (TE), the climate types are defined based on the annual potential evapotranspiration (annual ETP).The subtypes depend on the percentage relation between the potential evapotranspiration in the  summer and the annual potential evapotranspiration (Table 3).ETP was used because it depends directly on the temperature [13].

Methodology of Tendency Analysis-Mann-Kendall and Pettitt Test
The non-parametric tendency test of Mann-kendall-MK [15] [16], consists of comparing each value of the time series with the rest of the values, always in a sequential order, counting the number of the times that the rest of the terms are higher than the analyzed value.The method describes the tendency of a time data series.It is appropriated when the case could be assumed as monotonic, therefore, they do not present any seasonal cycle or another tendency in the data DOI: 10.4236/ajcc.2018.74034(OMM) to identify tendencies in time series [18].
In MK test, the S statistic is calculated by the summing of all counts, as follows: ( ) In which, ( ) The S statistic tends to normality for a large n, with mean and variance given by: In which n is the size of the time series.Therefore, the statistic test Z is given by: The considerable statistic tendency in the temporal series is measured by the Z value.This statistic is used to test the null hypothesis that the tendency does not exist.In Mann-Kendall test, a tendency is considered positive or negative, indicating a decrease or increase in the elements of the analyzed series, the case of Kandall's Tau is negative or positive.The statistical significance was analyzed by the p-value test.The null hypothesis is not reject if p value is more or equal a; if p is less than a, the null hypothesis is rejected [15] [16].
In addition to the MK test, I did the Pettitt non parametric statistic test in order to evaluate the occurrence of abrupt changes in the means of the historical series.According to Pettitt [11], this test indicates if two samples from the same temporal series can be considered belonging to the same population.
The Petit test verifies two samples, , , , t t T X X X + +  belonging to the same population, providing also information about the data homogeneity from the historical series analyzed.This statistic finds the point where an abrupt change in a temporal series occurred [11].
The U t,T statistic counts the times that a member of the first sample is higher than a member of the second sample.It can be written as: where: sgn(x) = 1 para x > 0; sgn(x) = 0 for x = 0; sgn(x) = −1 for x < 0.
The U t,T statistic is calculated for the 1 < t < T values and the K(t) statistic from Pettitt test is the maximum absolute value for U t,T .This statistic locates the changing point of a temporal series and its meaning.It can be described as: ( ) The abrupt changing point is the time (t) where there is the maximum k(t).We can calculate the critical K values by the equation: The significance level used was 5%.
The software extension XLSTAT 2014.5.03, for Microsoft Office Excel, was used in order to analyse and organize the data.

Climatological Hydric Balance and Climate Classification
From of the graphs of surplus and water deficit we can precisely establish the driest periods, the rainy seasons, the traffic conditions for supplies and machines,  , varying between 9 to 16 mm in August, the most critical period regarding hydric deficiency (Table 4).
According to Matielo et al. [19], these climate conditions are favorable to the development of the coffee-growing in the region of Machado.According to Monteiro et al. [20], the climate characteristics of the region also favor the cultivation of other species, such as corn, beans and vegetables in general The CHB shows a reduction in the hydric surplus for the specific a) Period Thus, the climate classification of the region of Machado is a humid mesothermic clime, with little hydric deficit (B 3 r 3 B′ a′ ).

Analysis of Climate Change Tendencies
Craparo et al. [22] and Assad et al. [23] approaches climate changes and global warming as the beginning of a new geological configuration in the seeding and coffee-growing (Coffea arabica) in Brazil, bringing possible economic losses.In a pessimistic scenario, about 33% of the current coffee-growing areas can became unable or of climate high risks.The MAPA [24] shows that events such as hydric stress caused by the droughts, rain excess, low or high temperatures can bring serious damages to the agricultural and livestock activities.

Precipitation
According to the climatic data from region of Machado-MG, there is only a significant reduction tendency in October, with a rate of 1.7 mm per year, which is significant for two tests (  of this variation, stating that this fact may be reflections of natural fluctuations and random behaviors inherent to the historical series itself.
However, Salviano, Groppo and Pellegrino [8], in investigating the temporal trends of precipitation and average temperature in Brazil, verified that precipitation did not present significant trends in more than 70% of the Brazilian territory in every month.

Temperature
We can observe throught the climate data in Table 6 that there is a tendency of a raise in 0.019˚C per year in January, confirmed by the two tests, considering that according to Pettitt test, the tendency tends to occur from the year of 1994 on.
To February, the tendency is a 0.016˚C raise per year, significative to for Mann-kendall and not significant for Pettitt.However, the test indicates that the tendency started in 1976.October presents an increasing tendency of 0.029˚C per year, significant for Mann-kendall and not significant for Pettitt.
However, the test indicates that the tendency started in 1982.November presents an increasing tendency of 0.0016˚C per year, significant for Mann-kendall and not significant for Petit, considering that the tendency started in 1977.And for the month of December there is a trend of increase of 0.019˚C per year, significant for both tests, and the trend occurs from 1985.
In accordance with to the IPCC report [1], it is clear that the planet's temperature is increasing, and projections until the end of this century point to increases between 1.1˚C to 6.4˚C in the average air temperature in many areas of the planet, including Brazil.It can bring enormous damages to the agricultural and livestock activities, besides a new configuration of the agro-climatic aptitude in many agricultural crops cultivated all around the world [26] [27] [28].
According to the National Supply Company-CONAB [29] the coffee harvest in South Minas must be around 10 million bags 5.09% less than the estimative published in June and 5% less than the last harvest.The last harvest was extremely damaged by the long drought and high temperatures and was of 10.8 million bags.
Avila et al. [30], when evaluating the trends of minimum and maximum tem-

3 s 2 → 3 w 2 →
humid 40 ≤ I u < 60 40 ≤I u < 60 B 1 → humid 20 ≤ I u < 40 20 ≤ I u < 40 C 2 → semi-humid 0 ≤ I u < 20 0 ≤ I u < 20 C 1 → dry semi-humid −20 ≤ I u < 0 −20 ≤ I u < 0 D → semi-arid −40 ≤ I u < −20 −40 ≤ I u < −20 E → arid −60 ≤ I u < −40 −60 ≤ I u < −40 Table 2. Climatic subtypes, according to Thornthwaite, based on the arid (I a ) and hydric (I h ) indexes.Humid climes (A, B, C2) Arid index (I a ) r → without or with a small hydric deficit 0 ≤ I a < 16.7 s → moderate hydric deficit in the summer 16.7 ≤ I a < 33.3 w → moderate hydric deficit in the winter 16.7 ≤ I a < 33.big hydric deficit in the summer I a ≥ 33.big hydric deficit in the winter I a ≥ 33.3 Dry climes (C1, D, E) Arid index (I a ) d → small or null water surplus 0 ≤ I h < 10 s → moderate water surplus in the summer 10 ≤ I h < 20 w → moderate water surplus in the winter 10 ≤ I h < 20 s 2 → big water surplus in the summer I h ≥ 33.3 w 2 → big water surplus in the winter I h ≥ 33.3 the best seasons for the development of vegetation and for the beginning of a recovery process from degraded areas through the hydric surplus and deficiency graphics.The CHB analysis shows that, in the region of Machado, the dry season, when the highest hydric deficits are observed, maintains close values for the dif-DOI: 10.4236/ajcc.2018.74034G. S. Rodrigues et al. ferent periods analyzed: a) Period (1961-1979), b) Period (1979-1998); c) Period (1998-2015); d) Period (

Figure 1 .
Figure 1.Extract of the Climatological water balance in the Machado-MG region.

Table 8 .Figure 2 .
Figure 2. Extract of the Climatologial Hydric Balance in the region of Machado-MG between 1961 and 2015.

Figure 3 .
Figure 3. Simulation of the Climatological Hydric Balance Extract in the region of Machado-MG in the period 1961-2015 by the climatic trends.
the CHB can be determined through the local or

Table 1 .
Climate types, according to Thornthwaite, based on the humidity index (I u ).

Table 3 .
Climatic types and subtypes according to Thornthwaite, basead on the thermal index.
[17].The MK method is the most appropriate to analyze climate changes in climatological series.It is suggest by the World Meteorological Organization

Table 4 .
Mean monthly values of the volume (mm) of water deficiency and water surplus in the different periods analyzed for the region of Machado-MG.

Table 5 .
Statistic results from the Precipitation data for the Mann-Kendall and Pettitt Test for the region of Machado-MG.

Table 6 .
Statistic results of the Temperature data for Mann-kendall and Pettitt tests for Machado-MG.
Mann-Kendall and not significant for Pettitt.However, this test indicates that the tendency tends to occur at the same time as in January.April presents an increasing tendency of 0.021˚C per year, significant for the two tests, happening from 1982 on.July presents an increasing tendency of 0.016˚C per year, significant DOI: 10.4236/ajcc.2018.74034