3.1. Environmental Variables
The results obtained from the correlation between environmental variables in a GIS environment showed the maximum correlation for each variable related to itself, resulting in the value of 1. The only high correlations, above 0.7 [29], were between the average maximum precipitations. The correlations did not exceed 0.4 among the other variables, indicating acceptable correlation levels below 0.7. A model containing more than one mean maximum precipitation will include a high correlation between these variables, which, according to Kornejady, Ownegh, and Bahremand [29], should be avoided to minimize the complexity of the model. In any case, Maxent remains minimally affected by the correlation of variables, even with small samples [48].
Regarding the physical characteristics of the study area (Figure 4), the altitude, according to the digital elevation model of the Department of Lima, ranges from 0 to 6401 m. The variation from 0 to 1000 m is located in the coastal region of the department, with approximately 30% of the Department of Lima within this altitude range. Moving inland, the altitude of the department increases. However, a closer look at the department’s relief reveals the “quebradas”, which are micro basins where significant variations in altitude occur on a small scale and where superficial flows are formed. These are found along the coastal region and the valleys of the perennial rivers of the department. The slope is also steeper in these regions, becoming flatter at the bottoms of the valleys and in the coastal region, which can be called a floodplain. Throughout the department, the slope varies from 0° to 89.95°, with 21% of the areas having a slope up to 10° and 83% having a slope up to 50°. The aspect ratio in the Department of Lima varies from 0° to 360°, with visual orientation patterns in the “quebradas”. The TRI (terrain ruggedness index) varies from 0 to 454, being lower in the lower and flatter areas. This TRI ranges from level to moderately rough, with the index reaching levels of extreme ruggedness. The TWI (topographic wetness index) varies from 0 to 20.01, with the highest values in the lower areas and less steep portions of the terrain, thus indicating that these areas are the most suitable for water accumulation and possible flooding.
The Department of Lima has 38 geological classifications, which are grouped into 14 macro-classifications in Figure 5.
On the other hand, the Department of Lima has 40 hydrogeological categories. Similar to the geology, these categories were grouped into classifications to facilitate visualization. Regional geomorphology has 45 classifications. It should be noted that the department’s 38 geological classifications, 40 hydrogeological classifications, and 45 geomorphological classifications were used for modeling. There are only seven pedological classifications in the Department of Lima.
The caption in Figure 5 presents the correspondence between the code for each class and the class denomination as a whole.
Figure 6 illustrates that the Euclidean distance from urbanized areas varies from 0 to 35.7 km, and the perennial watercourses in the department vary from 0 to 25.6 km. Regarding ecosystems, the Peruvian Pacific Coastal Desert classifications are observed. These are characterized by a hyper-arid climate devoid of vegetation, consisting of sandy soils and rocky outcrops. In addition, the classes of Serranía Esteparia (mountain range steppe) and Puna stand out for their herbaceous vegetation.
Figure 7 shows that some meteorological stations experienced historical precipitation maximums of as little as 1 mm in June, July, and August. In contrast, there are regions in the department where, during these same months, the average maximums reached 308 mm. In any case, February has historically had the highest average maximums for the stations with the lowest average maximums (52 mm). For the stations with the highest average maximums, precipitation during February was much larger (974 mm). March, October, and December also have quite pronounced historical average maximums. These observations are validated by the data shown in Figure 8, which indicates the average values for the 36 rainfall stations analyzed. They highlight the comparison between the averages and the maximums, where the average levels represent a maximum of 44% of the maximum historical levels in March, reaching only 13% of the maximum levels historically recorded in the department during May.
Regarding the increase in precipitation levels in Peru, the El Niño phenomenon responsible for warming the Pacific waters stands out [62]. For example, in the cycles of 1982–1983, 1997–1998, and 2017, precipitation levels were extraordinary, exceeding 1000 mm over a three-month cycle, triggering huaicos and floods that led to considerable economic losses and even deaths [62].
Gonzales and Ingol [41] observed the particular formation of the 2017 Coastal El Niño that directly and powerfully struck Peru’s coastal region. The authors concluded that it was a succession of events. In their own words, the Pacific Decade Oscillation in its positive phase gave rise to coupled ocean–atmosphere processes generating the ENSO Modoki and La Niña Modoki, and the coastal ENSO was a sub-process of the La Niña Modoki, the lower part of 2017’s ENSO Modoki. The Modoki event represents a unique pattern of tripolar pressure at sea level [63]. Strong El Niño events result in higher levels of precipitation and areas affected by precipitation, which consequently increase the occurrence and recurrence of huaicos.
Events such as the 2017 Coastal El Niño are difficult to predict and prepare for. Including the data in the modeling allows for an evaluation of how the Coastal El Niño intensity influences the occurrence of the huaicos.
3.2. Modeling in Maxent
Table 2 shows the quality of information of the Maxent models. All models have adequate quality, both in the “Test AUC”, which must be greater than 0.7, and in the “10 percentile training presence test omission”, which should not exceed 0.2. The area under the curve ranges from 0 to 1, with 1 indicating the highest accuracy. The AUC ranges of 0.5–0.6, 0.6–0.7, 0.7–0.8, 0.8–0.9, and 0.9–1 classify the models as poor, average, good, very good, and excellent, respectively, according to Yesilnacar [64], with our models classified as very good.
The kappa coefficient represents five classes—k < 0.4, 0.4 < k < 0.55, 0.55 < k < 0.85, 0.85 < k < 0.99, respectively—with poor, average, good, excellent, and very excellent validation [65]. In the kappa test, the models generated with all variables performed excellently. However, the models generated were based only on the environmental variables described by INGEMMET as influential in the formation of huaicos, and the kappa index was almost maximum, classified as very excellent.
Figure 9 and Figure 10 present the results of the models, reclassified to represent the areas with a probability of huaico occurrence.
On average, 17% of the areas in the Department of Lima have a probability of huaico occurrence when considering the models using all the variables. July and August had the lowest probability of huaicos occurring, while June and September had the highest likelihood of huaicos occurring. However, these higher areas in June and September seem inconsistent with the average maximum precipitation of these months, which is lower than those with the highest precipitation.
When analyzing the models generated using the INGEMMET variables identified as drivers of huaico occurrence, the models’ quality was better, and the areas with a probability of huaico occurrence were higher. On average, 42% of the Department of Lima has a likelihood of occurrence of huaicos. Using variables that do not effectively contribute to the occurrence of huaicos made the models complex, causing the algorithm to search for nonexistent relations between the sample data and the environmental variables. This resulted in lower model quality than those using influential contributing variables.
Regarding the coincidence between the monthly models, Table 3 shows the coincidence matrix of the areas with a probability of occurrence for each model, taking the months horizontally as a reference. On average, there is a coincidence of 84% between the monthly models. The greater the correspondence between the models throughout the year, the greater the chance that even with precipitation variation, the areas with a probability of occurrence will be basically the same.
Regarding the variables that contribute the most to the models, Figure 11 shows that the distance from water courses is the factor that contributes most to the monthly models, followed by geomorphology, digital elevation model, distance from urbanized areas, slope, and geology.
In general, there is a predominance of the probability of occurrence of huaicos up to 5 km from watercourses. The distance from urbanized areas coincides with the distance from rivers, as they are located primarily in the bottoms of valleys, close to waterways. Thus, the occurrence of huaicos is associated mainly with a distance of up to 2.5 km from urbanized areas.
The geomorphology representing the probability of occurrence includes mountains in intrusive rocks, mountains in volcanic rocks, mountains in volcanic-sedimentary rocks, and alluvial–torrential slopes or foothills.
Mountains in intrusive rock correspond to outcrops of intrusive rocks, igneous rocks with high degrees of fracturing due to tectonic processes that, together with the steep slopes associated with this formation, increase rockfalls [54]. Mountains in volcanic rocks are outcrops of volcanic rocks with steep slopes susceptible to rockfalls and collapses, and that may present intense fracturing and weathering [66]. Mountains in volcanic–sedimentary rocks also have steep slopes associated with large landslides, huaicos, and rock avalanches [54]. The geomorphological classification of alluvial–torrential slope or foothill is characterized by the accumulation of material mobilized by previous huaicos, which locally modify the direction of river courses and are located at the mouths of streams toward the main rivers [55].
Regarding the relief, the areas where huaicos are likely to occur are in the valleys, which corroborates precisely with the shorter distances from water courses. Regarding slope, the occurrences are related to inclinations of up to 30 degrees, which in themselves represent extremely high slopes of approximately 65%.
However, it is important to note that the variable contributing the most also has the greatest distance from a normal distribution.
In the monthly models that consider only the variables specified by INGEMMET as relevant to the occurrence of huaicos, all months presented a similar distribution of contributions from environmental variables, with the most significant contribution from geomorphology in the classes described above. The second most important contributing factor is relief, which also follows the ranges described in the characterization of the results of the previous model. The other factors, geology, slope, and average monthly precipitation, have the least influence in the models and similar influences (Figure 12).
Unlike the models using all variables, in the model using only the variables considered influential in the occurrence of huaicos according to INGEMMET, all variables have a normal distribution, contributing to their better quality and representativeness.
Kornejady, Ownegh, and Bahremand [29] and Phillips [26] warn against interpreting the contributions of factors in models, since Maxent can find the best solution through different paths, which may result in various factor contributions. In other words, the contribution cannot be considered an indicator of the importance of the environmental variable. The jackknife test provides more significant information regarding the importance of variables. The test requires removing a factor from the modeling, using a variable alone, and using all variables [29]. The jackknife tests responded almost equally to the contributions of the variables in all the models. Thus, in this work, it is safe to regard the relations of the variable contributions as a measure of the importance of the variables in predicting the occurrence of huaicos.
Although identifying areas where huaicos occur does not correspond to identifying areas where landslides and floods occur, Rusk et al. [28] evaluated both hazards and adopted variables similar to those in this work. For landslides, factors related to relief and geomorphology had a high contribution. However, unlike this work, for Rusk et al. [28], precipitation contributed significantly to the model for both types of hazards: approximately 35% for floods and 25% for landslides. The results for landslides by Javidan et al. [27] point in the same direction, where relevant geomorphological factors, such as slope and altitude alone, did not interfere with the model.
Although the occurrence of huaicos does not directly depend on the distance from watercourses, there is a concentrated probability of huaico occurrence in the vicinity of rivers in the models that used all variables, unlike the results of Javidan et al. [28]. They found the distance from watercourses to be an essential predictive factor due to its importance in the speed and magnitude of flooding, given the high flow concentration in the drainage network, increasing the occurrence of floods near streams. However, the relation is comprehensible because some “quebradas” belong to perennial water course watersheds.
Chen et al. [30] also indicated a relationship between landslides and the proximity of watercourses and roads in more significant portions of the terrain. The authors also highlighted the distance from roads in their models, an anthropic factor that modifies the natural stability of the studied areas and threatens the infrastructure, significantly decreasing the quality of the model. Anthropic factors do not influence huaico occurrences. This is due to the fact that the formation of huaicos does not occur in inhabited areas. The areas where huaicos form are areas of steep slope, difficult access, few inputs, that is, of low general attractiveness for the spread of urbanization and crops. In short, they are areas with desert characteristics. Still, the impacts are intensified by the anthropic factors of urbanized areas and infrastructure. Since, the expansion of urbanization in the flatter areas corresponds precisely to the areas where the flows generated by the huaicos are directed by gravity.
Similar to the results of Javidan et al. [27], there is a lower incidence of huaicos in high-altitude locations. This finding was based on the results of the elevation response curves, which demonstrate that huaicos, like floods, occur in low-lying areas and plains. It should be noted that the runoff from the basins that form the huaicos converges typically into a single channel, where it can either reach an urbanized area or follow a floodplain to the ocean and then reach an urbanized area.
Javidan et al. [27] found that higher precipitation levels increase landslides (650–690 mm annually) and lower rainfall levels cause erosion. For huaicos, an increase in precipitation should result in a larger area with a probability of huaicos occurring. However, the rise in precipitation did not respond linearly in the models. In general, precipitation did not contribute significantly to this phenomenon. Therefore, the model constitution does not permit us to infer the levels of rainfall that trigger the huaicos.
Giráldez et al. [67] evaluated the extreme climate events of precipitation in metropolitan Lima from 1965 to 2013. The authors found that 16 mm of precipitation occurred in 1970, which was sufficiently strong to flood the streets, causing power failures, damaging the Jorge Chávez International Airport facilities, destroying about 2000 homes, and triggering landslides and rivers to overflow. Although there are no specific data on huaicos, their occurrence during this extreme event is almost certain. This could mean that almost all the precipitation data used in this work would be enough to trigger a huaico occurrence.
In contrast, Rusk et al. [28] point out that climate change can alter model responses to increase the potential for disasters. A further step in taking action to prevent and mitigate the impacts of disasters is identifying the social vulnerability of the affected populations.
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Geise Macedo dos Santos www.mdpi.com
