Received: March 6, 2016; Accepted: June 6, 2016

ABSTRACT
Páramo ecosystems are located on the upper parts of the tropical mountains, below the snow line areas or in isolated areas where no glacier ecosystems occur. These ecosystems are considered important for their biodiversity, but mainly because they are permanent source of water for populations located at the upper and middle parts of the Andes. Recent studies indicate that ecosystems located at high altitudes, are more vulnerable to climate change and to changes in land use, which threatens the ecosystem services derived from them. There are very few studies in these ecosystems, within which, studies on the hydrological functioning are even scarcer, which seems to be related to their position in the top of the mountains and difficulties associated with the access to them. This implies that there is a need to create tools that allow us to study these ecosystems, overcoming the current difficulties. Hydrological TOPMODEL is used to investigate the hydrological functioning of the páramo of Chingaza, through a case study in La Chucua basin. For this, we calibrate and validate the model using two data sets of climate and the hydrology of the basin (climate and discharge from 2008 and 2009, respectively). Through the calibration procedure we obtain a high efficiency value of 0.76 model (coefficient Nash - Sutcliffe), which adequately represents the hydrological behavior of the páramo. Simulations with better adjustment between measured and predicted values of discharge, have low values of surface infiltration excess runoff, indicating high water storage capacity on the soils. This agrees with the predominance of subsurface flow in studied ecosystem, given the special characteristics of soils. Results also show the large influence of factors represented in the model (topography and soils), on water basin response to rainfall events. This is significant evidence of exceptional hydrological behavior of the páramos, mainly related to the presence of soil with high organic matter content. These results imply that TOPMODEL is a robust tool, able to represent in a precise manner the hydrological functioning of the basin La Chucua, and consequently it is expected that TOPMODEL can also represent hydrological conditions of Chingaza páramo.

RESUMEN
Los páramos son ecosistemas localizados hacia las partes altas de las montañas, por debajo de las zonas de nieves perpetuas o en áreas aisladas, donde no hay glaciar. Estos ecosistemas son considerados importantes, tanto por su biodiversidad, como por ser fuente permanente de agua para poblaciones ubicadas hacia las partes medias y altas de las montañas andinas. Estudios recientes indican que ecosistemas localizados en altitudes altas, son más vulnerable al cambio climático y cambios en el uso del suelo, lo que pone en peligro los servicios ecosistémicos que se derivan desde estos. Son muy pocos los estudios realizados en estos ecosistemas, dentro de los cuales, estudios sobre su funcionamiento hidrológico son aún más escasos, lo que parece estar relacionado con las dificultades asociadas con el acceso a los mismos. Esto implica que existe una necesidad de generar herramientas que nos permitan estudiar estos ecosistemas, sobreponiéndose a las dificultades actuales. En este sentido en la presente investigación, se utilizó el modelo hidrológico TOPMODEL con el fin de investigar el funcionamiento hidrológico del páramo de Chingaza, a través de un estudio de caso en la cuenca La Chucua. Para esto se calibró y validó el modelo, mediante dos series de datos del clima y la hidrología de la cuenca (clima y caudales de los años 2008 y 2009, respectivamente), obteniéndose un valor alto de eficiencia del modelo de 0.76 (coeficiente Nash-Sutcliffe), el cual representa adecuadamente el comportamiento hidrológico del páramo. Las simulaciones de mayor ajuste presentaron bajos valores de escorrentía superficial por exceso de infiltración, lo que indica alta capacidad de almacenamiento de agua en el suelo, y coincide con la predominancia de la escorrentía subsuperficial, dadas las características especiales de los suelos allí presentes. Se comprobó la influencia que tienen los factores representados en el modelo (topografía y suelos), sobre la respuesta hídrica de la cuenca. Esto constituye evidencia significativa del comportamiento hídrico excepcional de los páramos, debido a sus suelos. Estos resultados implican que TOPMODEL es una herramienta robusta, capaz de representar de una manera precisa el funcionamiento hidrológico de la cuenca La Chucua, y por ende se espera que pueda representar igualmente las condiciones del páramo de Chingaza.

Water supply, mainly for human consumption, food production and hydropower generation, has become a worldwide priority in the economic and social level (Buytaert et al., 2011). The provision of this service in Andean region, is mainly attributed to the high mountain ecosystems, specifically to páramos and cloud forests (Tobón, 2009), considered strategic ecosystems, given the multiplicity of the environmental services offered, in which stand out the water storage in soil and water regulation (Buytaert and Beven, 2011). During the last decades, water demand has increased rapidly due to population growth to establish economic activities such as agriculture and mining, very recurrent in páramos (Buytaert and Breuer, 2013). Despite its importance, the knowledge of the actual ecohydrological functioning of these ecosystems is still poor, along with the effects of climate change on this functioning.

Data scarcity is quite common in the Andean mountains, due to the complexity of topography which hinders the instrumentation of the basins (Buytaert and De Bièvre, 2012). Accordingly, hydrological modelling becomes an important tool to investigate and understand the behavior of strategic ecosystems, even with data scarce and also to make predictions of climate changing conditions (Buytaert et al., 2006a; Almeida et al., 2013).

One possibility for modeling at basin scale is the hydrological model TOPMODEL (TOPography based hydrological MODEL) a semi-distributed model that represents a simplified version on the spatial variability of the hydrological response, in which topography is spatially considered (Beven et al., 1984). In this case, the information of the topographic index is integrated into the overall structure of the model, throughout the spatial distribution of moisture content of the water table (Güntner et al., 1999). The advantage of TOPMODEL is that it requires values of few variables and parameters, which are easily determined in the field, overcoming limitations associated to data acquisition and the restrictions on computers capacities to perform simulations (Beven et al., 1984). Recently, TOPMODEL has been used to study páramos at a basin scale, and also, to test different climate change scenarios, including changes in land uses (Franchini et al., 1996; Dietterick et al., 1999; Da Silva and Kobiyama, 2007a).

Despite the lack of hydrological and climatological data that is required to model the hydrological functioning of a páramo ecosystem, the hydrological model has been applied at a basin scale (Buytaert et al., 2009). The advantage of TOPMODEL is its simple structure contrary to other models with more rigid structure and greater difficulties for its programming. Additionally TOPMODEL is available in a free programming language access, with libraries that facilitate code domain (Buytaert et al., 2008).

Páramos are considered important ecosystems in the tropical montane, given their large contribution to water supply (Tobón, 2009; Hofstede, 1995; Buytaert et al., 2010), their biodiversity (Myers et al., 2000) and carbon storage, mainly in the soil. Despite this importance, they are among the most susceptible ecosystems in the tropics, both to land use and climate change (Foster 2001; IDEAM 2002). Moreover, páramos, among other tropical mountain ecosystems, are considered unique areas for detection and assessment of impacts related to climate change (Vuille et al., 2008), thus nowadays there is a growing interest to understand it ecohydrological behavior.

According to the lack of knowledge, the associated difficulties to generate field data for most páramos, and the needs for hydrological information regarding the effects of climate change, we propose a modelling approach to characterize the hydrology of Chingaza páramo at a basin scale, through the hydrological processes modelling using TOPMODEL.

Study area
The study area is the Chucua basin, located in the Natural National Park Chingaza (4°40'6.38''N to 4°41'00''N and 73°49'5.27''W to 73°50'19.5''W), La Calera, Cundinamarca, Colombia. The area of the Chucua basin is 2.59 2.59 km², tributary (Figure 1), of Blanco and Negro rivers basins located at its greatest extent in the Forest Reserve Protected Area of Chingaza Park. This basin provides the drinking water to Bogotá city and for electric power generation (Guavio Dam).

The area was formed from Devonian sedimentary rocks containing limestone, silt stone and sandstone, determining an abrupt topography with slopes higher than 30%, and altitude around 3800 m. Soils derived from volcanic ashes, with an effective depth down to 1.2 m, moderately well-drained and belong to the order of Inceptisols (USDA, 2014). They have very high organic matter content, up to 38% and high water storage capacity (90% in saturation conditions, a high porosity of 80% and a rate infiltration around 20 - 60 mm h^-1) (Tobón, 2009). Vegetation is dominated by dominated by giant rosettes of the genus Espeletia, and grasses as Calamagrostis, and small patches of upright sclerophyllous shrubs and puyas (Sklenár, 2000).

Hydrological modelling
TOPMODEL is a conceptual model in which the predominant factors determining the formation of runoff are represented by the topography of the basin and a negative exponential tend line, linking the transmissivity of the soil with the saturated zone belowground. This model is frequently described as a physically based model in the sense that its parameters can be measured directly in situ (Franchini et al., 1996). See more details regarding to model structure in Beven and Kirkby (1979). The model requires the following data input: digital elevation model, hydrometeorological data, cumulative delay function and parameters.

Data input for the model

Digital elevation model (DEM) was derived from the SRTM data (2000) -zone u03_n004w074 available at 1-arc second resolution (approximately 30 m at the equator), and projected to a local coordinate system Colombia-Bogotá-Zone. The contour of the basin was delineated using the program GRASS GIS version 6.4. For the generation of topographic index map by class brands, the DEM was exported to TOPMODEL by library spgrass6 of R as an array of type ASCII data, with altitude information and using a flow direction algorithm called D8, which allows generating raster files of direction and accumulation flows. Hydrological similarity units were generated from the pixels grouping into categories based on the index function (Campling et al., 2002).

Hydrometeorological data was gathered through field monitoring of climate and hydrological variables, distributed along the altitude range of the Chucua basin, between 2007 and 2010 within the framework of the research project "Ecohydrology of the páramos in Colombia III: Páramo Chingaza", led by researchers from Universidad Nacional de Colombia. The instruments were installed in a transect of the basin by type of coverage (forest, ecotone and páramos) and altitude gradient from 2500 to 3550 m, in order to consider the spatial and temporal variability of the monitored variables.

Precipitation was measured with six automatic rain gauges, located every 200 m in the altitude gradient (between 2800 and 3800 m). The average precipitation in the basin was estimated by the method of kriging. Climatic variables, as temperature, air humidity, solar radiation, wind speed and wind direction, were measured with two automatic weather stations located at an altitude of 3000 and 3600 m within the basin. Horizontal precipitation was measured at two sites (by the weather stations) and soil moisture, at different soil depths was measured through the TDR technique, in four sites, located at within the range altitude of 2800 and 3800 m.

Evapotranspiration was calculated from climatic variables, by the Penman-Monteith method (1965) previously applied by Tobón (1999) and was developed in Stella version 8.0 to this work.

The discharge was continuous measured by installing a limnigraph in a rectangular weir, located at the close of the basin, at an altitude of 3034 m. The measurements of the water column above the bed of the creek, and the canal area was measured, were used to calculate discharge amounts through the measured period.

Cumulative delay function of the basin represents the residence time on the drainage network that takes the generated surface and subsurface flow over time in each sub-basin to be driven to the output (Topmodel, 2011). To represent this function, a matrix type data distributed in two columns: one represents a cumulative fraction of the area of the basin, which is divided according to the morphological characteristics (Da Silva and Kobiyama, 2007a), and the other represents the cumulative distance measured on the main channel, from the output, to each specific area, in relation to the cumulative area of the drainage network in each fraction (Topmodel, 2011). In that way the basin is divided into three homogeneous areas (Table 1), which assumes that in hydrological terms, its functioning is different in the area of wetlands, near the outlet and in the remaining area.

The values of the model parameters were initially established from reported literature values (Buytaert and Beven, 2011) (Table 2), and then were adjusted the ranges by the method of calibration (by inputting the information into the model as a set of data in matrix array organized into a text file) (Topmodel, 2011).

The values were settled at appropriate intervals to the páramo, also considering field data taken in 2008.

Baseline simulation: calibration and validation
The baseline includes hydrological modelling of the basin by applying a water balance with TOPMODEL version 0.7.2-2 available in R library (Topmodel, 2011). The model was implemented for field data during the 2008-2009 period, with a time scale of 30 minutes. Data from 2008 was used for the calibration of the model, by verifying site conditions adjusted to the structure and model assumptions and the establishment of a set of initial parameters which adequately describes the hydrological behavior of the study basin. Data from 2009 was used for the validation of the calibrated model for the Chucua basin.

Calibration is the procedure for obtaining a set of optimal parameters and initial values, adjusted to the particular characteristics of each basin (Blasone et al., 2008). Calibration was started in a sensitivity analysis of the parameters, to establish an order for its calibration and thus restrict the valid ranges for the parameters and to increase the number of subsequent simulations with higher efficiency during application of GLUE procedure (Generalized Likelihood Uncertainty Estimation).

The most sensitive parameters were found by graphical analysis that allowed detecting for each parameter variation range, the efficiency values that were reached. In these graphs, if apparent homogeneity that does not reveal a maximum efficiency value for a given parameter is observed, it is considered that there is little sensitivity and low influence on runoff response.

The parameters lay down a set of acceptable values, through an appropriate physical interpretation of them (Blasone et al., 2008). The parameter values were presented graphically as uncertainties associated with the model (Beven and Freer, 2001). It was therefore found based on initial simulations and in field data taken in 2008, the valid range of each parameter used in the general model calibration, product of the initial setting parameters reported in the literature. Finally, a recalibration was performed, in which the ranges of the tightest parameters, according to the maximum and minimum values found for the sets of parameters, with the best efficiencies (Nash-Sutcliffe) were selected.

The evaluation of the efficiency of the model and the uncertainties associated with the hydrological forecasting, considers the equifinality principle (Beven, 2001), which states that there are different sets of parameters that have acceptable adjustments to the observed flows. In that sense, it was carried out an adaptation on the GLUE (Beven and Binley, 1992) to restrict the values of the parameters. That method rejects the hypothesis of the existence of a unique set of optimum parameters, and instead, uses a large sample sets associated parameters for the same behavior model indicated that can be used in later predictions. GLUE is a package that integrates with TOPMODEL to generate a complete routine of hydrological modelling (Topmodel, 2011).

As indicated below, the decision criteria used in this phase was a value of [E(θ)]≥0.65 on the sets of simulated parameters. This means that parameter sets with efficiencies above this value, were considered as behavioral parameters. The selection of the best simulations was also performed using a physical criterion: the value produced by infiltration excess overland flow (FEX). This criterion along with the components of the dominant hydrological processes to the ecosystem greatly facilitates the understanding of the páramos and contributes to note the definition of the line base of hydrological simulation. Given the computational limitations for simultaneous simulation and calculation of all components of the model for thousands of set of parameters, only five sets of parameters were selected, which showed relatively high efficiencies (>70%) and low FEX values.

As for validation, at this stage it is determined in what degree of accuracy the model reproduces or imitates independent information, using the values of the parameters found during calibration (Beven, 2001). For this purpose, we used field data from 2009, for which the efficiencies parameter [E(θ)] > 0.755 were used to validate the model performance. The ranges of values obtained for each parameter in the calibration step were adjusted again in subsequent simulations to ensure greater efficiencies. Therefore it was obtained a new set of parameters whose values and efficiency is coincident with the found in 2008. The method used to validate the information was useful to incorporate the best set of parameters found and their subsequent application in the validation phase.

Baseline simulation
Topographic index map of the basin is presented in Figure 3, indicating a correspondence between the highest values of the index and the drainage network; where areas with higher values (9 to 12) correspond to the level where the drainage network occurs. These differences between values are attributed to the quality of the DEM (Pan et al., 2004). Although this may influence the spatial distribution of saturation zones, it does not affect the prediction of flows. High values of the topographic index are related to contributing areas which generate discharge and return flows, associated with topographically convergent places or smooth slopes (Beven, 1997), and they are characterized by low transmissivity, thus the water table reaches the surface. These areas in the basin may generally correspond to narrow valleys and/or holes or circles originated in Pleistocene (Güntner et al., 1999), in which, the saturation condition causes a decrease in the amount of subsurface flow and leads to fully development saturated areas.

The average value of the index for the basin was 8.10, which is relatively high; however the distribution of these values by class-mark, showed that the category where most of the pixels were grouped on the map (17.7% of basin area), has a lower value (5.19). Values of the index between 3 and 6, are associated with areas of higher slopes (Campling et al., 2002), which are very common in Chingaza páramo.

Topography has a strong influence on the hydrological response of a basin, and this is represented in the model with the topographic index. Local depressions and flat areas where drainage accumulates frequently generate saturated conditions. At the same time, the high porosity and infiltration capacity of the soils in páramos, in combination with the typical low rainfall intensity, virtually eliminate infiltration excess overland flow (Buytaert et al., 2006b). As a result, the dominant process to generate surface runoff is saturation excess overland flow, which is expected not to occur in studied páramo. In that sense TOPMODEL provides a more complex representation of the basin according to the functioning of the páramo (Buytaert and Beven, 2011).

Sensitivity analysis
Initial simulations with iterations between 10000 and 50000 for 2008 data were made, in which no significant differences in values of E(θ) and FEX were found. Therefore a maximum of 10000 iterations was selected to optimize the capacity of the computer in the execution of calibration and validation processes. From the 10000 simulations for 2008, 3065 simulations obtained E(θ)≥0.65, which would be considered acceptable (Buytaert et al., 2008). The results of the sensitivity analysis (Figure 4) showed that the parameters of lower sensitivity are those who did not reveal any optimum value over the range of possible values. Thus, the sensitive analysis showed that the order at which the model is more sensitivity to changes in parameter values is: Sr0, k0, CD, qs0, Srmax, td. This coincides with the sensitivity analysis performed in a páramo in Ecuador (Buytaert et al., 2003), where lower sensitivity parameter was Srmax.

Moreover, soil parameters m, vr and LnTe, results to be the most sensitive ones, since they showed their maximum values in the respective ranges 0 - 0.005, 1500 - 2300 and 0.5 - 3, which supports the importance premise of these three parameters in the hydrological response of the basin (Campling et al., 2002). Ranges of these parameters were adjusted, due to the fact they present an incidence on the discharge magnitude and thus in the efficiency, by 31.4%, 8.9% and 2.7%, respectively.

Parameter m represents the hydraulic conductivity of the páramo soils. A very small value of this parameter indicates a slow movement of water in the soil, and soil water flow drops at soil moisture below saturation point (Buytaert et al., 2003). This parameter is related to subsurface flow control and the deficit of local storage, which is important in the case of water regulation of the páramos, because it is common to attribute to páramos soils high buffering capacity. This condition is positively correlated with the continuous base flow in páramo ecosystems (Buytaert and Beven, 2011). Therefore, this parameter has a significant effect on the calculation of the local storage deficit, contributing areas (distribution of surface and / or subsurface flow) and the shape of the curve in the hydrograph recession.

Low values of m (as in our case 0.00065, see Table 4, parameter set 3) indicate an effective minimum depth of the water table, associated to a high transmissivity under saturation conditions (2.02 m² h^-1), which indicates a dominance of subsurface runoff generation in the soil. Moreover, smaller values of parameter m implies higher values of rainfall infiltration, which in fact occurs in studied páramo, as in most undisturbed páramos (Tobón, 2009). This, in time, explains the negligible infiltration excess overland flow found in this study, as most of the water is stored in the soil.

Model calibration
From the sensitivity analysis, the tightest range of each parameter was used in the overall calibration of the model (Table 2). Further, during the process of recalibration, the values of model parameters were selected (Table 3), and maxima and minima corresponding to the parameter sets with the highest values of efficiencies (>0.755) obtained in the simulations performed from table 2 values.

For a better fit in the values of the parameters to the conditions of the studied páramo, it was necessary to sacrifice efficiency in estimating the set of parameters, ie, slightly higher values of FEX resulted in a better fit between the model predictions and field measurements. Accordingly, we select parameter set number 3 (Table 4), although it has a low value of FEX, but with the highest efficiency (0.7558). This set of parameters was used to calculate simulated discharge by TOPMODEL during 2008 (Figure 5).

Model validation ]]> From the processes of validation of the model results obtained from the calibrated parameters, the values of efficiency and FEX are shown in table 5, with the best five sets of parameters. The assembly which had the highest efficiency value in the validation stage was the set number 6 with a [E(θ)] value near 0.7618.

The overall efficiency of the model slightly increase during the validation process, which means that the model efficiently predicts the hydrological functioning of the Chucua basin, not only for 2008, but also for 2009, with calibrated values of parameters.

According to the results, it appears to be a direct relationship between the FEX and efficiency associated with the parameter sets, suggesting that a gain on the predictive power of the model means a better ability to adequately represent the behavior of the páramo; so by choosing the sets that result in greater efficiency, meaning the increase of the generating process by infiltration excess overland flow. Therefore, we select the set of parameters with one of the lowest values of FEX (Figure 6), which have physical meaning consistent with the observed hydrological functioning of studied páramo ecosystem.

The model efficiency (0.7579) was slightly higher than that obtained during the calibration process, however discharge results shows a slightly underestimation of the peaks and overestimation of minimum values.

The efficiencies found are close to the values obtained for a proven model in a páramo basin in Ecuador [E(θ)= 0.67] (Buytaert and Beven, 2011). However, it is possible that shorter periods of time could help ensure better simulations and adjustments, because to the extent that more data is added to model variability increases. Moreover, it is widely known that TOPMODEL has some problems to accurately represent low flows during droughts (Dietterick et al., 1999; Güntner et al., 1999; Gallart et al., 2007; Buytaert and Beven, 2011). For periods where precipitation exceeds evapotranspiration (as most of the time in this study), the wide range of parameters provide acceptable simulations for basin discharge, although base flow is less accurately simulated, as it happen in other sites (Gallart et al., 2007).

Finally we identified the dominant hydrological processes for the studied páramo ecosystem (Table 6), based on the selected set of parameters, during the calibration and validation phases (set 3). These results showed that in general terms, the dominant process that control the hydrological processes of the studied páramo is mainly controlled is the subsurface flow discharge (qs). This process is 1.7 times greater than the surface discharge process excess saturation (qo) which generates only 933 mm of water on average for 2008 and 2009, thus, this process can also be considered important for these ecosystems, which is control the saturated contributing areas.

Comparisons with previous findings in similar páramo ecosystems (Buytaert and Beven, 2011), show that there is a tendency in the order of parameter sets, for the sensitivity analysis, but also a similarity on the parameters that control the hydrological functioning of the páramo ecosystems. This implies that undisturbed páramos, similar to that studied here, may have identical behavior of water flows, when investigated with TOPMODEL.

TOPMODEL applied to the páramo ecosystem in The Chucua basin, adequately represents the relationship between rainfall and discharge, since the parameter sets obtained had a physical explanation and generated high efficiency predicting flows with high efficiency coefficients Nash - Sutcliffe (greater than 0.75). In addition, the values of model parameters remain relatively stable over time, and indicate that subsurface discharge is the dominant process in studied basin. This result provides comparative advantages for the simulation of hydrological processes in tropical montane ecosystems, specifically in those sites where with difficulties to measure hydrological variables.

Although TOPMODEL showed to be a reliable tool to simulate several flows by component, certain shortcomings persist. These modelling challenges associated with complexity related to the spatial variation of hydrological processes and the structure of the model, can be effectively addressed in future research of hydrology of páramos ecosystems, with more accurate predictions.

The authors are grateful to Department of Science, Technology and Innovation -COLCIENCIAS for its Young Researchers and Innovators Program, years 2008-2009 and 2009-2010 and also the International Potato Center -CIP / Consortium for Sustainable Development of the Andean Ecoregion -CONDESAN, for providing financial support for this work.

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