RESULTS
One of the predominant characteristics of the annual distribution of rainfall during the year is the bimodal regime for most of the Andean and the Caribbean region except for the Bajo Nechí region, part of the Sinú River basin and the eastern sectors slope of the Central Cordillera at the height of Samaná (Caldas); and the unimodal regime for most of the Orinoquia and the Colombian Amazon and the sectors mentioned above as exceptions in the Andean region (Arango; C., Dorado, Guzmán D, & Ruiz, 2000; Martínez & Salas, 2015; Poveda, 2004).

Annual cycle

Figure 4 shows the results for multi-year monthly average precipitation for the stations in the study area. This figure verifies the bimodal precipitation in each season, with two periods of intense rain and two periods of low precipitation, as previously identified for the Andean region of Colombia. The low rainy seasons correspond to the months of December to February (DJF), and June to August (JJA), while the periods of high precipitation range from March to May (MAM), and from September to November (SON). The second season of low precipitation is slightly drier than the first, with July being the month with the lowest precipitation for all rain stations. The second season of high rainfall is much more intense than the first (except in La Nubia), with November generally being the month with the highest rainfall. However, the stations of Yarumos, Emas and Chec-Uribe stations show higher rainfall in October. Regardless, the stations of La Nubia and Posgrados show very few differences between the monthly values ​​of each winter period: rainfall is very similar in the four periods. On the contrary, stations like Chec-Uribe, Hospital and Los Yarumos show great differences between each high rainy season (over 100 mm), followed by Alcázares, La Palma and Bosques.
Figure 4 . Multi-year monthly average rainfall for network stations for landslide risk management
Figure 5 shows that the stations with the highest annual and monthly rainfall are El Carmen and Yarumos, the former located to the west of the city where it tends to rain more, while the latter is located in the east where it rains a little less. As this station is located in a forest reserve, this behavior is considered atypical. These stations have a rainfall of ~1800-1900 mm, and then there is a group that oscillates in annual mean rainfall ~1500 mm such as Emas, Alcázares located to the west, Hospital to the center and Posgrados to the south-east which is also near a reserve forest. The stations with the lowest rainfall are La Nubia and Milán Planta Niza located to the east of the city. The differences in average annual precipitation between the two stations with the highest and lowest precipitation in the analyzed period reach close to 800 mm, which evidences the high variability in the city. Despite the small area studied, the spatial distribution shows significant variability in the monthly precipitation values due to its microclimates, already identified (Vélez-upegui et al., 2012).
Regarding rainfall behavior during the analyzed period, the years 2010-2011 and 2017 were much rainier than usual (in Yarumos, Hospital de Caldas, Emas, and El Bosque in 2016 as well) especially in November (all stations). This is compatible with what was identified by the Institute of Hydrology, Meteorology and Environmental Studies in Colombia (IDEAM), which indicated that during the months of May and June of 2010 conditions close to neutrality prevailed, but that there was a rapid change in July towards the cold phase (La Niña phenomenon), month after which the Oceanic Child Index (ONI) certified the occurrence of La Niña, which lasted until May 2011. Thus, this period became one of the rainiest in the Andean region of Colombia, practically eliminating the period of least rainfall in the middle of the year and the second rainy season being one of the strongest winters in Colombia, generating numerous events triggered by the rains (landslides and floods). The stations Alcázares, Chec-Uribe, Hospital de Caldas, La Palma and Los Yarumos stand out, where rainfall anomalies came to be moderately above normal for some or both years (140-170%), while they were slightly above normal (110-140%) in the rest of stations (Ministerio de medio ambiente, 2011).
Figure 5 . Annual monthly precipitation for network stations for landslide risk management in the period 2010-2018
Similarly, this figure also shows that 2015 (and 2016 in the case of some stations) was drier than normal (~50-70% of a normal year). The El Niño phenomenon of 2015, which has been one of the most intense, began in the February-March-April quarter, when the positive temperature anomalies were +0.5ºC. In March-April-May they rose to +0.7ºC; in April-May-June, at +0.9 ºC, and reached +1.0 ºC in the May-June-July quarter. The El Niño Phenomenon lasted until 2016 causing serious shortages, reaching critical point in January 2016 when 124 municipalities in Colombia had water shortages. Additionally, according to IDEAM, the flow of the Magdalena and Cauca rivers during this stage reached historic lows in a period of 15 years. In the case of Manizales, most of the stations had the driest December in 2015 with historical lows, followed by a January 2016 with also considerably low values. The Chec-Uribe and Emas stations were the exception, showing its lowest precipitation in February 2016. The influence of both phases of the ENSO (El Niño and La Niña) has already been previously identified and their impact on monthly variability is recognized as considerable in Colombian hydrology, an impact that even reaches diurnal and hourly scales (Poveda, 2004; Poveda et al., 2002).
When observing the behavior of precipitation taking into account the altitude (see Figure 6), a positive linear relationship between elevation and precipitation is seen. However, given the short range of amplitude in elevation, no relevant conclusions can be derived without looking at the spatial distribution in the events.
Figure 6. Relationship between annual precipitation and elevation during the period 2010-2018 for the city of Manizales

Day-night cycle

Figure 6 shows the multiannual hourly average precipitation results, which varies between 1 - 4.5 mm/h. A bimodal behavior of the diurnal rainfall is observed. The stations of Alcázares and Hospital have the highest hourly maximum precipitation values, while La Nubia and Posgrados show the lowest diurnal precipitation values.
The hours with the highest precipitation magnitudes are from 1:00 h to 4:00 h and in the afternoon from 13:00 h to 18:00 h. The maximum hourly rainfall occurs in the early hours of the day for all stations, peaking at 1:00 h and around 15:00 h in several stations. However, bimodal behavior is modified in the low rainfall months (DJF) where a multimodal behavior can occur in the maximum hourly rainfall, that is, several peaks throughout the day. This is how in the off-peak hours (8:00-12:00 h) during these months high hourly rainfall has occurred. On the contrary, in the months of high rainfall the bimodal behavior is observed in a very marked way, especially for the first winter season.
Figure 7 . Multiannual mean hourly rainfall for network stations for landslide risk management
Figure 8 shows the results of the relative frequency of multi-year hourly precipitation for the analyzed period, which varies between 2 and 20%. The stations with the highest relative frequencies are Posgrados (26.7), Emas (26.3), Hospital (25.2), Yarumos (25.2), La Nubia (25.2) and Bosques (24.0), stations located in the north and center of the city. The bimodal behavior observed in the hourly precipitation magnitudes of the previous Figure is observed more precisely in this one, with two periods of 6 hours of low relative frequencies and 6 hours of high ones. The most frequent hours are from 1:00 h to 4:00 h and from 13:00 h to 16:00 h, the latter strip being the one with the highest occurrence of rain events. The hours with least frequency are from 6:00 h to 11:00 h and from 18:00 h to 22:00 h, where the former is much less frequent in rain occurrence in most stations. The second peak of high frequencies is highly concentrated between 13:00 h - 16:00 h, while the second peak of higher precipitation magnitudes can occur until 19:00 h.
Figure 8 . Relative frequency of multi-year hourly precipitation for each month for network stations for management of landslide risk

Temporal distribution of rain events

A description of the events selected during the 2006-2014 period and used in this analysis is shown in Table 2, with an average of 16.1 events per month that are distributed 2.2% of the time –that is, 1,643 events on average per season. Figure 9 shows the events for the different durations discretized, where it can be seen that the most frequent duration of rainstorms in the city varies between 20 and 55 minutes. The figure also shows that the largest number of events occur for almost all durations in El Carmen and Observatorio Vulcanológico stations located to the west of the city.
Table 2. Description of the isolated events considered for the analysis during the period 2006-2014
Figure 9 . Distribution of the durations of the events considered in the period 2006-2014
Figure 10 shows the temporal distribution of the precipitation of the stations analyzed for the 90% percentile. The distribution analysis shows that the most unfavorable temporal distribution for the design storms would be the 90% percentile, while the mean value would be a value that underestimates extreme events. Therefore, neither the 50th percentile nor the average value are taken into account in the analysis. Analyzed stations have a similar temporal distribution (this not only for the 90% percentile but for all the percentiles) showing only differences in the magnitude of precipitation as previously observed. It can also be seen that in Aranjuez, La Palma and Emas the rainfall is slightly more intense at the beginning than for the other stations.
Figure 10. Temporal distribution of rain events in the city of Manizales using 2006-2014 records for the 90% percentile
One of the most used patterns in Colombia to obtain the temporal distribution of precipitation is Huff’s distribution (Huff, 1967; Huff & Angel, 1989; Huff & Vogel, 1976) and it is an interesting comparison to the results obtained in Manizales (see Figure 11). Figure 11 shows that the temporal distribution resembles an intermediate value between the first and second Huff quartiles, which is important since the second quartile had always been proposed for Colombia. However, for design purposes, the most unfavorable situation is always recommended to have a conservative design, so the proposal is suitable for design storms in Colombia. It is observed that ~ 58% of the precipitations occur in 30% after the rain has passed (Table 3).
Figure 11. Comparison between the quartiles proposed by Huff for rainfall of 90% probability and the 90% percentile of the Posgrados station
Finally, for the design of hydraulic infrastructures and for the hydrological design in the city of Manizales, the 90th percentile of the dimensionless curve that relates duration (t/T) and total rainfall (P/TPP) is then proposed as the temporal distribution of the design storm as shown in Figure 11. The behavior for the different stations in the city is very similar. In conclusion, a temporal distribution is available for the design of rainfall in Manizales according to the distribution shown in Table 3.
Table 3. Temporal distribution of rains to be used in design events for the city of Manizales