**2.1 Region of study and rainfall data**

We used monthly rainfall data for the period 1945–2019 from 6 localities (**Figure 1** and **Table 1**) in the southern of department La Paz (Province of Entre Rios, Argentina): Hasenkamp (HAS), Las Garzas (LGA), Alcaraz Norte (ALN), Bovril (BOV), Hernandarias (HER), El Solar (ELS). This data were collected with



#### **Table 1.**

*Meteorological station used and the period analyzed.*

conventional rain gauges, from the official records of Hydraulic Directorate (Direccion Hidraulica de Entre Rios, in spanish) and Cereal Bag (Bolsa de Cereales de Entre Rios, in spanish) of the Province of Entre Rios.

The data from the 6 locations was subjected to a process of quality control for possible errors. All data above the third quartile plus three times the interquartile range and located more than five standard deviations from the mean was treated as outliers. These outliers were then contrasted climatographically with readings from nearby stations. If the same reading was labeled as out of range for more than two seasons, the value was correct. Months classed as outliers and those without data were treated as gaps. Both types of gaps were filled but no missing data was completed if there were more than three gaps in one year.

Stations with missing data techniques linear regression were used. The filling of missing data by the linear regression technique consisted in using data from neighboring stations that presented coefficients of significant linear correlations with the station to be used in the study [34, 35],

$$P\_{\mathbf{x}} = a\_o + \sum\_{i=1}^{n} a\_i P\_i \tag{1}$$

where *ao* and *ai* are the coeffcients of adjustment of the linear model, obtained in the processing of correlation. In this case, stations that presented an R<sup>2</sup> greater than 0.90 were included. The two techniques are widely used to fill gaps in historical series and present low average deviations suitable for climatic studies on monthly and seasonal scales [36].

After the treatment of the time series, the monthly values of all rainfall stations were grouped into scales, according to the following definitions: a) autumn (March, April, and May), b) winter (June, July, and August), c) spring (September, October, and November), and d) summer (December, January, and February). For selecting the change point for a particular parameter, the method presented below has been used [37]: a) no change point or homogeneous (HG), series may be considered as homogeneous, if no or one test out of four tests rejects the null hypothesis at 5% significant level; b) doubtful series (DF), series may be considered as inhomogeneous and critically evaluated before further analysis if two out of four tests reject the null hypothesis at 5% significant level; and c) change point or inhomogeneous (CP) when series may has change point or be inhomogeneous in nature, if more than two tests reject the null hypothesis at 5% significant level.

#### **2.2 Homogeneity tests for change point detection**

Homogeneity testing is very crucial in climatological studies to represent the real variations in weather and climate. Inhomogeneity occurs in climate data due to several reasons including instrumentation error, changes in the adjacent areas of the instrument, and mishandling of the human. If the homogeneity is not tested prior to trend analysis, the results will indicate erroneous trends. In this study, the absolute homogeneity tests were performed on individual station records and calculating the ratio of observed series to the reference series. Four widely used statistical tests mentioned below were applied to the data to test for homogeneity. All the following four tests used in this study assume the null hypothesis of data being homogeneous. The change point detection is an important aspect to assess the period from where significant change has occurred in a time series. Pettitt's test, von Neumann ratio test, Buishand range test and standard normal homogeneity tests have been applied for change point detection in climatic series. The details of various change point tests applied in the study are presented here.

*Rainfall Trends in Humid Temperate Climate in South America: Possible Effects… DOI: http://dx.doi.org/10.5772/intechopen.99080*

#### *2.2.1 Pettitt's test*

The Pettitt's test for change detection, developed by [38], is a non-parametric test, which is useful for evaluating the occurrence of abrupt changes in climatic records [39, 40] because its sensitivity. According to Pettitt's test, if *x*1, *x*2, *x*3, … *xn* is a series of observed data which has a change point at *t* in such a way that *x*1, *x*<sup>2</sup> … , *xt* has a distribution function *F*1(*x*) which is different from the distribution function *F*2(*x*) of the second part of the series *xt*+1, *xt*+2, *xt*+3 … , *xn*. The non-parametric test statistics *Ut* for this test may be described as follows:

$$U\_t = \sum\_{i=1}^t \sum\_{j=t+1}^n \text{sign}\left(\mathbf{x}\_t - \mathbf{x}\_j\right) \tag{2}$$

$$\text{sign}(\mathbf{x}\_t - \mathbf{x}\_j) = \begin{bmatrix} \mathbf{1}, & \dot{\mathbf{f}}(\mathbf{x}\_i - \mathbf{x}\_j) > \mathbf{0} \\ \mathbf{0}, & \dot{\mathbf{f}}(\mathbf{x}\_i - \mathbf{x}\_j) = \mathbf{0} \\ -\mathbf{1}, & \dot{\mathbf{f}}(\mathbf{x}\_i - \mathbf{x}\_j) < \mathbf{0} \end{bmatrix} \tag{3}$$

The test statistic *K* and the associated confidence level (*ρ*) for the sample length (*n*) may be described as:

$$K = \text{Max} |U\_t|\tag{4}$$

$$\rho = \exp\left(\frac{-K}{n^2 + n^3}\right) \tag{5}$$

When *ρ* is smaller than the specific confidence level, the null hypothesis is rejected. The approximate significance probability (*p*) for a change-point is defined as given below:

$$p = \mathbb{1} - \rho \tag{6}$$

The test statistic *K* can also be compared with standard values at different confidence level for detection of change point in a series. The critical values of *K* at 1 and 5% confidence levels for different tests used in the analysis has been presented in **Table 2** [37].

#### *2.2.2 von Neumann ratio test*

The von Neumann ratio test has been described by [41, 42] and others. The test statistics for change point detection in a series of observations *x*1, *x*2, *x*<sup>3</sup> … *xn* can be described as:


**Table 2.**

*Critical values of test statistics for different change point detections tests.*

*The Nature, Causes, Effects and Mitigation of Climate Change on the Environment*

$$N = \frac{\sum\_{i=1}^{n-1} (\mathbf{x}\_i - \mathbf{x}\_{i-1})^2}{\sum\_{i=1}^{n-1} (\mathbf{x}\_i - \overline{\mathbf{x}})^2} \tag{7}$$

According to this test, if the sample or series is homogeneous, then the expected value *E*(*N*) = 2 under the null hypothesis with constant mean. When the sample has a break, then the value of *N* must be lower than 2, otherwise we can imply that the sample has rapid variation in the mean. The critical values of *N* at 1 and 5% confidence levels given in **Table 2** can be used for identification of non-homogeneous series with change point.

#### *2.2.3 Buishand's range test*

The adjusted partial sum (*Sk*), that is the cumulative deviation from mean for *k*th observation of a series *x*1, *x*2, *x*3. … *xk*. … *xn* with mean (*x*) can be computed using following equation:

$$S\_k = \sum\_{i=1}^k (\mathbf{x}\_i - \overline{\mathbf{x}}) \tag{8}$$

A series may be homogeneous without any change point if *Sk*� 0, because in random series, the deviation from mean will be distributed on both sides of the mean of the series. The significance of shift can be evaluated by computing rescales adjusted range (*R*) using the following equation:

$$R = \frac{\text{Max}(\text{S}\_k) - \text{Min}(\text{S}\_k)}{\overline{\underline{x}}} \tag{9}$$

The computed value of *R=*√*n* is compared with critical values given by [37, 41] and has been used for detection of possible change (**Table 2**).

#### *2.2.4 Standard normal homogeneity (SNH) test*

The test statistic (*Tk*) is used to compare the mean of first *n* observations with the mean of the remaining (*n-k*) observations with *n* data points [32].

$$T\_k = kZ\_1^2 + (n-k)Z\_2^2\tag{10}$$

*Z*1and *Z*<sup>2</sup> can be computed as:

$$Z\_1 = \frac{1}{k} \sum\_{i=1}^{k} \frac{(\mathbf{x}\_i - \overline{\mathbf{x}})}{\sigma \mathbf{x}} \tag{11}$$

$$Z\_2 = \frac{1}{n-k} \sum\_{i=k+1}^{k} \frac{(\mathbf{x}\_i - \overline{\mathbf{x}})}{\sigma \mathbf{x}} \tag{12}$$

where, *x* and *σx* are the mean and standard deviation of the series. The year *k* can be considered as change point and consist a break where the value of *Tk* attains the maximum value. To reject the null hypothesis, the test statistic should be greater than the critical value, which depends on the sample size (*n*) given in **Table 2**.

*Rainfall Trends in Humid Temperate Climate in South America: Possible Effects… DOI: http://dx.doi.org/10.5772/intechopen.99080*

#### **2.3 Test for trend analysis**

All the trend tests in this section assume the null hypothesis of no trend and the alternative hypothesis of monotonic increasing or decreasing trend existence. When the time series are serially independent, the Mann–Kendall test [43, 44] and Spearman's Rho test [45, 46] were applied to test for trends. The magnitude of the trend was estimated using Sen's slope method [47]. Always suggested to apply various statistical tests to analyze the trends in serially correlated data.

## *2.3.1 Mann-Kendall test*

The Mann–Kendall test is a nonparametric test for monotonic trend detection. It does not assume the data to be normally distributed and is flexible to outliers in the data. The test assumes a null hypothesis, *H*0, of no trend and alternate hypothesis, *Ha*, of increasing or decreasing monotonic trend. For a time series *Xi* ¼ *x*1, *x*2, … , *xn*, the Mann–Kendall test statistic *S* is calculated as

$$S = \sum\_{i=1}^{n-1} \sum\_{j=i+1}^{n} \text{sign}\left(\mathbf{x}\_{j} - \mathbf{x}\_{i}\right) \tag{13}$$

where *n* is the number of data points, *xi* and *x <sup>j</sup>* are the data values in timeseries *i* and *j* (*j* > *i*), respectively, and *sign x <sup>j</sup>* � *xi* � � is the sign function as

$$\text{sign}(\mathbf{x}\_i - \mathbf{x}\_f) = \begin{bmatrix} \mathbf{1}, & \dot{\mathbf{f}}\left(\mathbf{x}\_j - \mathbf{x}\_i\right) > \mathbf{0} \\ \mathbf{0}, & \dot{\mathbf{f}}\left(\mathbf{x}\_j - \mathbf{x}\_i\right) = \mathbf{0} \\ -\mathbf{1}, & \dot{\mathbf{f}}\left(\mathbf{x}\_j - \mathbf{x}\_i\right) < \mathbf{0} \end{bmatrix} \tag{14}$$

Statistics *S* is normally distributed with parameters *E*(*S*) and variance *V*(*S*) as given below:

$$E(\mathbb{S}) = \mathbf{0} \tag{15}$$

$$V(\mathbf{S}) = \frac{n(n-1)(2n+5) - \sum\_{k=1}^{m} t\_k(k)(k-1)(2k+5)}{18} \tag{16}$$

where *n* is the number of data points, *m* is the number of tied groups, and *tk* denotes the number of ties of extent *k*. Standardized test statistic *Z* is calculated using the formula below.

$$Z = \begin{cases} \frac{\mathcal{S} - \mathbf{1}}{\sqrt{var(\mathcal{S})}} & \text{if } \mathcal{S} > \mathbf{0} \\ 0 & \text{if } \mathcal{S} = \mathbf{0} \\ \frac{\mathcal{S} + \mathbf{1}}{\sqrt{var(\mathcal{S})}} & \text{if } \mathcal{S} < \mathbf{0} \end{cases} \tag{17}$$

To test for a monotonic trend at an α significance level, the alternate hypothesis of trend is accepted if the absolute value of standardized test statistic Z is greater than the *Z*<sup>1</sup>�*α=*<sup>2</sup> value obtained from the standard normal cumulative distribution Tables. A positive sign of the test statistic indicates an increasing trend and a negative sign indicates a decreasing trend.

#### *2.3.2 Spearman's rho test*

The Spearman's rho test is a non-parametric widely used for studying populations that take on a ranked order. If there is no trend and all observations are independent, then all rank orderings are equally likely. In this test, the difference between order and rank (*di*) for all observations *x*1, *x*2, *x*3, … *xn* can be used to compute and Spearman's ρ, variance *Var*ð Þ*ρ* and test statistic ð Þ *Z* using following equations. The null hypothesis is tested in this test considering the statistic is normally distributed.

$$\rho = 1 - \frac{6\sum d\_i^2}{n(n-1)}\tag{18}$$

$$\text{Var}(\rho) = \frac{1}{(n-1)}\tag{19}$$

$$Z = \frac{\rho}{\sqrt{Var(\rho)}}\tag{20}$$

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

**Tables 3**–**8** show the results of the statistical analyzes carried out to know the point of change in monthly, seasonal and annual rainfall in each locality. A marked variability was observed in the months that changed significantly between the localities, fundamentally from January to May, even though the proximity between them does not exceed 40 km. This means, a priori and in subjective terms, that the climatic changes reported worldwide have a direct influence on a microspatial scale, as well as on the temporal window. However, in the region there was no heterogeneity in the breaking point between the localities evaluated for the months of November and December during the study period analyzed.

In relation to the statistical tests used, it is possible to conclude that the Von Neumman's test is more robust when establishing the heterogeneity of the time series, while the Standard Normal Homogeneity test a priori would require less demand from the variability of the time series. to set a breaking point. Based on the results of the SNH Test, it is observed that the month of May presents marked heterogeneity in all localities, but the year that defines the point of change differs significantly. When comparing and analyzing all the tests for each period of time, only Las Garzas and Hernandarias present a significant, but doubtful point of change in the year that followed.

In seasonal analysis, summer is the season of the year that presented marked heterogeneity in the time series in all localities. The year of break point was different by location. However, El Solar and Hernandarias presented significant modifications in the heterogeneity of the time series with breaking points during the 1970s and 1980s, respectively. Both locations are adjacent to the Middle Paraná River, a situation that could be influenced by local atmospheric conditions [48]. There is even greater concern today about the future of rivers worldwide due to a multitude of stressors that impact running waters including climate change [49]. We draw on the growing literature related to climate change to illustrate potential impacts rivers may experience and management options for protecting riverine ecosystems and the goods and services they provide. Regional patterns in precipitation and temperature are predicted to change and these changes have the potential to alter natural flow regimes. One of the key ways in which climate change or other stressors affect river ecosystems is by causing changes in river flow. Rivers vary geographically


**Table 3.** *Results of change point analysis with all test used in Las Garzas location.*

*Rainfall Trends in Humid Temperate Climate in South America: Possible Effects… DOI: http://dx.doi.org/10.5772/intechopen.99080*

**169**


*The Nature, Causes, Effects and Mitigation of Climate Change on the Environment*

**Table 4.**

*Results*

 *of change point analysis with all test used in Alcaraz Norte location.*


*Rainfall Trends in Humid Temperate Climate in South America: Possible Effects… DOI: http://dx.doi.org/10.5772/intechopen.99080*

> **Table5.**

*Results of change point analysis with all test used in Bovril location.*

**171**


**Table 6.** *Results of change point analysis with all test used in Hasenkamp location.*


*Rainfall Trends in Humid Temperate Climate in South America: Possible Effects… DOI: http://dx.doi.org/10.5772/intechopen.99080*

> **Table 7.**

*Results of change point analysis with all test used in El solar location.*


**Table 8.** *Results of change point analysis with all test used in Hernandarias location.*

#### *Rainfall Trends in Humid Temperate Climate in South America: Possible Effects… DOI: http://dx.doi.org/10.5772/intechopen.99080*

with respect to their natural flow regime and this variation is critical to the ecological integrity and health of streams and rivers and thus a great deal has been written on the topic [50, 51]. The ecological consequences and the required management responses for any given river will depend not only on the direct impacts of increased temperature. Otherwise how extensively the magnitude, frequency, timing, and duration of runoff events change relative to the historical and recent flow regime for that river, and how adaptable the aquatic and riparian species are to different degrees of alteration.

The results resume depicting the homogeneity state of different series have been presented in **Table 9** (See Supplementary Appendix with results of Test's trend). The change point analysis on long-term series in all localities has indicated that a significant change point in the annual rainfall. The breaking point occurred in 1977 for the LGA, ALC and HER locations; year 1997 for BOV and HAS; and 1982 for the ELS locality. **Figure 2** shows the average annual precipitation of all the localities evaluated in each year for the region, as well as the historical annual during the period. On the other hand, since the breaking point occurred in 1977 for most of the localities, it was established that the average annual rainfall in the region prior to that date was 946 mm, while after the same 1150 mm, equivalent to 21.5% higher than the 1945–1977 average and 8.5% higher according to the historical average 1945–2019. In addition, an important piece of information results from the linear model that made it possible to establish that the region's average rainfall increased 4.9 mm per year from 1945 to 2019.

These results are consistent with those obtained in the north of the country where the rainfall change was concentrated in a step change during the 1970s [52]. In this region, half or more of the annual rainfall trend occurred in the months of El Niño phase, with less contribution from La Niña and the neutral phases. However, in the rest of subtropical Argentina and especially south of 30°S, increased precipitation occurred mostly during months of the neutral phase of El Niño/Southern Oscillation (ENSO), with only small trends during months of El Niño and La Niña phases [53]. Accordingly, most of the annual precipitation trends since 1960 in subtropical Argentina can be accounted for by two modes. The first mode, which is positively correlated with precipitation in northern Argentina and with ENSO indices, had a steep increase in precipitation at the end of the 1970s. The second mode, which has a maximum positive correlation with annual precipitation between 30 and 40°S, had a regular positive trend starting in the early 1960s and it is correlated with the southward displacement of the South Atlantic high [53, 54]. In addition, several researchers analyzed the changes in the isohyets, showing that the rainfall regime in Argentina is subject to a positive fluctuation in the 1950s and that it reached maximum values in the 1970s [55], data that coincide with this manuscript.

Average rainfall increased, favoring the expansion of agriculture [16, 22]. This conclusion is obtained primarily because the studies of the time have been hampered by the low significance shown by statistical tests when applied to climatic data, especially precipitation. In the study region mention that one of the factors of change in precipitation is agrarian transformation and claim that the technological innovation of the sector was accompanied by a process of change in the water regime [16]. Furthermore, confirm that the expansion of agricultural structure of Entre Rios, is favored by increased precipitation, generating crops of the marginal territory.

The behavior of historical series of monthly rainfall confirm that November and December, as and summer season, have significant change point in all localities. The annual rainfall in all localities showed a significant increase such as summer season (**Table 9**). November and December showed and significant rise in contrast to the rest of months.


**Table 9.**

*Results of change point detection analysis and trends of rainfall for all localities.*

**176**

*Rainfall Trends in Humid Temperate Climate in South America: Possible Effects… DOI: http://dx.doi.org/10.5772/intechopen.99080*

#### **Figure 2.**

*Variation in the average annual rainfall of all the localities of the analyzed region.*

In the last decade, a substantial change in the average climate conditions was observed in many regions of Argentina, particularly in the southern region of Mesopotamian Pampa that showed two abrupt shifts [20]. The first of these was positive, with annual average rainfall increasing from 1062.9 mm during the 1941–1999 sub-period to 1568.9 mm during a short sub-period between 2000 and 2003. The second abrupt change, which began in 2004, was negative, with average annual rainfall dropping to 1108.0 mm, only slightly higher than what it had been in the initial 1941–1999 sub-period (**Figure 3**).

Like the regional results, this study observed a sustained increase in monthly rainfall to the breaking point in the 1970s, but then the annual rate of increase was even higher. In South America [56], observed increasing trends in total annual precipitation values in Ecuador, Paraguay, Uruguay, northern Peru, southern Brazil, and northern and central Argentina. Qualitatively there was a change that indicated a significant increase in summer precipitation, and a decrease in the number of annual frosts, concentrating the winter season (July and August), assuming a "tropicalization of the region". Rainfall tropicalization can be understood as local and regional processes and impacts of climate change, which can be observed mainly by changes in the precipitation regime and the intensification of tropical climatic characteristics [57]. This process is not exclusive of Espinal Ecorregion. It has been observed in other contexts and scales in tropical and subtropical regions that show an important increase in precipitation during the rainy season in tropical regions [58, 59].

Climate change can also indirectly affect organisms by altering biotic interactions, which can have profound consequences for populations, community composition and ecosystem functions [60]. Other aspects of biodiversity management will be affected by global change and will need adapting, including wildlife exploitation, e.g. forestry [61], pest and invasive species control [62] or human and wildlife disease management [63]. Indirect effects may occur: (i) via generation of new biotic interactions, as range-shifted species appear for the first time in naive communities [64]; (ii) by removing existing interactions when species shift out of their existing range [65]; or (iii) by modulating key behavioral, physiological or other traits that mediate species interactions [66]. When climate-driven changes in biotic interactions involve keystone or foundation species, impacts can cascade through

**Figure 3.**

*Variation in the average annual rainfall in each locality of the analyzed region. Reference: Black dash line () show historical rainfall (1945–2019), black solid line (—) the average rainfall before and after the break point and gray dash line () show a linear model annual rainfall.*

the associated community [61]. In this region, studies that have not yet been published for the province of Entre Ríos are showing indications of changes in the productivity of natural grasslands in native forests. Recently reports show that change the growth cycle has change in this ecosystem [67, 68], and mainly attributed to changes in precipitation regimes. These observations are like yields changes of the main crops, were the frequency of extreme weather events constitutes a growing risk.
