(1. INTRODUCTION

Currently there are various climatic indices and statistical parameters that allow studying the behavior of rainfall, whether on a daily, monthly or annual level (^{López et al., 2019}). Within this set of indicators, those related to the estimation of climatic aggressiveness and precipitation concentration stand out; since, over the years, it has been shown that both the aggressiveness of the rains and their concentration have made it possible to adequately manage the planning of water resources in the face of possible extreme events that may be associated with climate change, especially in Amazon basins (^{Zubieta et al., 2019}).

This is why the importance of its study arises, since by having seasonal variability in rainfall, these can affect the continental water balance of almost all the countries in South America, whose area of influence mainly includes the Amazon River and its tributaries (Da Mota et al., 2020). Likewise, precipitation is a variable of vital importance for hydrological, climatic, water resource management as well as for evaluating the event of natural disasters (^{Arriola et al., 2023}). It is necessary to know their behavior and distribution throughout a hydrographic basin or in an urban area (^{Llano, 2018}), given that the impact that abnormal rains can cause in short periods of time, will trigger extreme flows and subsequently floods (^{Caicedo et al., 2024}), or in other cases, significant droughts generated by increased erosion (^{Ilbay-Yupa et al., 2019}).

The climatic aggressiveness estimated from the balance of monthly and annual precipitation establishes the erosive hydrological condition to which a geographic area or basin is exposed (^{Baecheler & Bravo, 2019}). Hence, this indicator has served as a reference to adequately estimate erosivity by incorporating it into the original R factor of the universal soil loss equation, the latter known by its acronym as USLE (^{Bezak et al., 2023}; ^{Chen et al., 2023}). Usually, arid areas or areas near the coast with low altitude tend to present high climatic aggressiveness, while areas with abundant vegetation and intermediate to high altitude show low aggressive conditions (Arriola et al., 2022).

In relation to the concentration of precipitation, this is determined by means of a numerical index that establishes whether the precipitation obeys a uniform, seasonal or irregular climatic pattern (^{Azioune et al., 2023}). Furthermore, the concentration can be estimated under different rainfall scenarios, whether daily, monthly or annual, depending on the orographic conditions of the study area (^{Llano, 2023}).

That is why both the concentration of precipitation and the climatic aggressiveness tend to show a significant correspondence with respect to latitude, longitude, altitude and mean precipitation (Arriola et al., 2022; ^{Valdés-Pineda et al., 2016}). However, these conditions noted above will depend on the amount of historical records and weather stations available in the evaluation area (^{Bessaklia et al., 2018}). Therefore, these indices are not recommended for studies with a limited number of stations and short-duration precipitation records (^{Lana et al., 2023}).

According to the reviewed literature on climate aggressiveness, the Fournier index (IF), the modified Fournier index (IFM), the modified Fournier-Maule index (IFMM), are the most used aggressiveness estimators for the study of erosion processes in hydrographic basins (^{Back et al., 2019}). Meanwhile, for concentration analysis, the precipitation concentration index (ICP) has been widely used to evaluate the behavior of rainfall in relation to altitude and other climatic variables (^{Olguín, 2019}); including changes that have occurred in the precipitation pattern due to climate change (^{Diodato et al., 2020}).

However, a large amount of precipitation data is required at a daily level and with extensive lengths of annual records, which often limits this type of applications for hydrological and climatic studies (^{García-Barrón et al., 2018}).

Throughout the world, there are various investigations directly related to these indices, as indicated by ^{Llano (2021}). Despite this, very few studies have focused on Amazonian areas, especially South America. Among the limited scientific contributions, notable work has been developed in Brazil, including studies on precipitation, its extreme pattern and the distribution of its seasonality and variability, which were analyzed by ^{Aguiar et al. (2019}), ^{Da Motta et al. (2020}), ^{De Moura et al. (2021}), ^{De Brito et al. (2022}) and ^{Costa et al. (2023}).

In Peru, only three studies related to climatic aggressiveness and precipitation concentration have been developed, the first addressed by Arriola et al. (2022); while the research by Zubiate et al. (2017) has evaluated only the concentration of precipitation in a Peruvian Amazon area. Subsequently, Zubiate et al. (2019) carried out the largest scale analysis for the entire Amazon basin that covered Bolivia, Brazil, Colombia, Ecuador, Peru and Venezuela, whose results have only been validated for the precipitation concentration at a daily level. Therefore, it is necessary to incorporate the evaluation of climatic aggressiveness, that allows us to know the vulnerability to which the Peruvian Amazon area is exposed, since it could affect the abundance, richness and diversity of its flora and fauna (^{Llampazo et al., 2023}).

The present study aimed to evaluate the climatic aggressiveness and concentration of precipitation in the Alto Huallaga Interbasin, applying three aggressiveness indices: IF, IFM, and IFMM, and one of precipitation concentration: ICP, which are estimated from the rainfall record of the climatic stations available in the Peruvian Amazon area. Then, this area of Peru is susceptible to heavy rains, major floods and thus the subsequent collapse of the local infrastructure of some provinces of the San Martin, Huanuco, Pasco and La Libertad Regions of Peru, which are located within the delimitation of this basin.

That is why, with the findings of this research, it will be possible to know how the aggressiveness and concentration of precipitation is distributed in the Alto Huallaga Interbasin, serving at the same time as an updated scientific basis for researchers interested in understanding the rainfall behavior of this basin of the Peruvian jungle.

2. MATERIALS AND METHODS

2.1 Study zone

The Alto Huallaga Interbasin has a geographical area of 30276 Km², it is located between the coordinates 76 ° 00 ´ to 77 ° 00 ´ west longitude and 7 º 00 ' to 11 º 00 ' south latitude (Figure 1). Likewise, the basin has an altitude that varies between 750 m. s. n. m. up to 5500 m. s. n. m. above sea level and it has a rugged relief, whose slope varies from 0.20 % to 12.00 %, highlighting in its orography the presence of various mountainous areas and valleys, which cause various ecosystems and extensive plant coverage to occur in this basin (^{Carrión, 2018}).

Figure 1 Location of the Alto Huallaga Interbasin, South America, Peru 

Politically, the Alto Huallaga Interbasin covers some provinces in the San Martin, Huanuco, Pasco and La Libertad Regions of Peru. Located in a strategic area of the central jungle, it allows the constant exchange of essential products and export such as coffee and cocoa.

Regarding the availability of its water resources, the Alto Huallaga Interbasin is part of the set of basins of the Huallaga River, since this river in the study area has a length close to 770 km, whose route goes from west to east. In relation to the rainfall pattern, these usually occur between the months of November to April, with maximum values between February and April, as shown in Figure 2 for some climatic stations of the Alto Huallaga Interbasin.

2.3 Climate aggressiveness and precipitation concentration

To determine the climatic aggressiveness and the concentration of precipitation, as well as their respective classifications, the equations presented in Table 2 were used.

Figure 2.  Box diagram of the mean rainfall of some climatic stations of the Alto Huallaga Interbasin: a) Cachicoto; b) Campanilla; c) Huariaca; d) Milpo; e) Ongon and f) Tingo Maria 

Table 1 Climatic stations considered in this study 

Table 2 Applied indices and their respective classifications 

Where P max j is the mean precipitation of the rainiest month of the year j, P is the mean annual precipitation, 𝑃 𝑖𝑗 is the monthly precipitation of the month i in the year j and 𝑃 𝑗 is the annual precipitation for the year j.

It should also be noted that among the indices shown in Table 2, IF, IFM and ICP were cited from Ilbay et al. (2019), while IFMM was cited from ^{Pizarro et al. (2008}). It should be added that all these indices are also cited and explained in the research of Arriola et al. (2022).

Subsequently, the correlations of these indices were established with respect to the altitudes and mean precipitations of the climatic stations of the Alto Huallaga Interbasin, a procedure suggested by Ilbay et al. (2019), ^{Fernandez et al. (2020}), ^{Amiri & Gocić (2021}), Arriola et al. (2022) and ^{Lana et al. (2023}), whose ranges of the correlation coefficient r and its variations (Table 3) were taken from ^{Herrera et al. (2017}).

Table 3 Correlation coefficient ranks and classification 

Then, the extreme values of the IFM, IFMM and ICP were estimated for different return periods, applying for this purpose six theoretical distributions (Table 4) with linear moments, as suggested by ^{Hosking (1990}), for a significance level of 5 % and with the Kolmogorov-Smirnov goodness-of-fit test, whose best-performing distributions and the values of the tabular delta and theoretical delta obtained for each index are shown in Table 5. The equations of the theoretical distributions shown in Table 4 were cited from the research by ^{Vargas et al. (2023}).

Table 4 Theoretical distributions used for extreme value analysis 

Additionally, a multiple linear regression model was developed to relate climatic aggressiveness and precipitation concentration to estimate the mean precipitation in the Alto Huallaga Interbasin, with the purpose of knowing whether or not there is a significant relationship between said variables.

3. RESULTS AND DISCUSSION

According to the results found in this research, it is deduced from Figure 3a, that there is a high correlation between mean precipitation and altitude (r = 0.85; R² = 0.72), and in relation to climatic aggressiveness with respect to altitude, the IF (Figure 3b) showed a moderate correlation (r = 0.53; R² = 0.28), while the IFM (Figure 3c) and the IFMM (Figure 3d) showed very high correlations with this variable, that is, they were r = 0.82 and r = 0.85, respectively. In the case of the ICP (Figure 3e), a moderate correlation was established in relation to altitude (r = 0.46; R² = 0.21).

Regarding of mean precipitation, the IFMM was the one with the best correlation (r = 0.99; R² = 0.98) in correspondence to this variable (Figure 3h).

Table 5 Theoretical distributions of best fit chosen for each climatic station and for each applied index according to Kolmogorov - Smirnov test 

Likewise, with the IFM (Figure 3g) a high correlation was also established (r = 0.94; R² = 0.88), while the IF (Figure 3f) was the opposite since its correlation was moderate (r = 0.53; R² = 0.28). Finally, the ICP (Figure 3i) showed a low correlation with the mean precipitation (r = 0.40; R² = 0.16).

The results of these indices are similar to the variations reported in studies from various countries, highlighting ^{Baecheler & Bravo (2019}) and Valdés et al. (2016) for Chile, ^{Gallardo et al. (2018}) for Cuba, ^{Back et al. (2019}) for Brazil, ^{Olguín (2019}) for Bolivia, ^{Ilbay-Yupa et al. (2019}) for Ecuador, ^{Fernandez et al. (2020}) for Portugal and Arriola et al. (2022) for Peru. Despite these results, other researches carried out by ^{Zubieta et al. (2017}), ^{Bessaklia et al. (2018}), ^{Huang et al. (2018}), ^{Amiri & Gocić (2021}) and ^{Azioune et al. (2023}), note that there are significant variations in the low to moderate correlations of the ICP with respect to altitude and mean precipitation.

However, as stated by ^{Zubieta et al. (2019}), the concentration of precipitation in different parts of the world is irregular and does not necessarily have a spatial dependence on altitude or the same precipitation. Furthermore, in what corresponds to the Amazon basins, the spatial distribution of this indicator is influenced by winds, temperature changes and extreme precipitation (Zubieta et al., 2017).

In relation to the Alto Huallaga Interbasin, similar results of the ranges obtained from the IFM are shown in the research by ^{Back et al. (2019}) and ^{Nunes et al. (2023}), since their monthly values ​​ranged between 10 and 70. Regarding the other indices, no other scientific contributions related to Amazonian areas were found to make the corresponding comparison.

From the above and from the research findings, it is inferred that the IFMM is the one with the best correlation with both altitude and mean precipitation, while in second place corresponds to the IFM, consequently, both indices are suitable for estimating the climatic aggressiveness of the Alto Huallaga Interbasin. That is why Figure 4 was developed, corresponding to the distribution of these indices, while Figure 5 indicates the analysis of extremes of the IFM, IFMM and ICP, for return periods of 5, 10 and 25 years.

Likewise, the importance of using the analysis of extreme value adjustment for the different climatic indicators is to know how these indicators are spatially distributed in the study area and that according to the distribution of best performance, the possible pattern or change that they may have for different return periods can be known.

It should be noted that both Figure 4 and Figure 5 were developed through the process known as inverse distance weighting (IDW) interpolation from the value of each index obtained at the respective climatic station. The IDW method is highly recommended for the spatial analysis of climatic variables in different areas and hydrographic basins, as suggested by ^{Wang et al. (2022}), ^{Arriola et al. (2023}), ^{Lee et al. (2024}) and ^{Kabolizadeh et al. (2024}).

This is why this IDW technique is the most appropriate, especially when you want to extrapolate ranges of climatic indices in geographical areas where not much data is available,

Figure 3 Correlations with respect to altitude and: a) Mean precipitation; b) IF; c) IFM; d) IFMM; e) ICP; and mean precipitation in relation to: f) IF; g) IFM; h) IFMM; i) ICP 

Figure 4 Spatial distribution of climatic aggressiveness and precipitation concentration for the Alto Huallaga Interbasin: a) IFM; b) IFMM; c) ICP 

Figure 5 Distribution of extreme values of climatic aggressiveness and precipitation concentration for the Alto Huallaga Interbasin for 5 years return periods: a) IFM; d) IFMM; g) ICP; 10 years: b) IFM; e) IFMM; h) ICP, and 25 years: c) IFM; f) IFMM; i) ICP 

being in this case study the estimation of the IFM, IFMM and the ICP for all the Alto Huallaga Interbasin.

Likewise, the spatial pattern of the IFM (Figure 4a), IFMM (Figure 4b) and the ICP (Figure 4c) is shown, whose classifications according to Table 2, corresponded predominantly to very low for the first two indices and moderately seasonal for ICP.

As indicated previously, Figure 5 shows the analysis of extremes for three return periods, by applying the theoretical distributions adjusted to linear moments, but unlike ^{Gallardo et al. (2018}) only used a distribution for the study of extremes of the IFM, which is not very significant for the estimation of maximum values.

Moreover, as can be seen in Table 5, of all the theoretical distributions applied to each index, the GEV (Generalized Extreme Value) and Pareto distribution stand out as those with the best fit for the study area. This is because generally both distributions are the ones that best fit climatic variables where it is necessary to analyze extreme values ​​for different return periods, being in this case the climatic aggressiveness index and the ICP.

On the other hand, as expected, the patterns of climatic aggressiveness present low values in the southern zone, while the highest ranges are located in the northwest part of the Alto Huallaga Interbasin (Figure 5). Quite the opposite happened with the ICP, as this occurs because the highest precipitation is recorded in the middle and high areas, since said area of the basin covers a greater territory of the Peruvian jungle and the elevations are lower.

4. CONCLUSIONS

Climatic aggressiveness was determined using three climatic indices, among which the IFMM stands out as the best estimator. According to the qualitative classification criterion, the Alto Huallaga Interbasin has a very low aggressiveness, and is therefore, not prone to phases of erosion or degradation.

Regarding the precipitation concentration evaluated through the ICP, they did not show good correlations, but they were in a moderate range, in that sense, it is inferred that the basin has a moderately seasonal behavior, which is a typical pattern of the Amazon basins of Peru.

Of the theoretical distributions applied to the three climate indices, both the GEV distribution and the Pareto distribution stood out with the best fit, which allowed estimating the IFM, IFMM and the ICP, for return periods of 5, 10 and 25 years, determining that the Alto Huallaga Interbasin would become moderately aggressive and the precipitation concentration would remain in an irregular condition.

A multiple linear regression equation was developed to associate climate aggressiveness and precipitation concentration, using the IFM, IFMM and the ICP indices, to estimate the mean precipitation, establishing very high correlations, which finally makes the application of these indices valid for the area evaluated and can be replicated for the study of other basins of the Peruvian Amazon.

Finally, it is recommended that water resource planners and authorities in the Alto Huallaga Interbasin prioritize vulnerable areas, particularly those located in the central and northwest regions, as they are the most affected by extreme events and floods.