Water Resources Research

Calibration of a physically based, spatially distributed hydrological model in a glacierized basin: On the use of knowledge from glaciometeorological processes to constrain model parameters

Authors


Abstract

[1] In the Dry Andes of central Chile, summer water resources originate mostly from snowmelt and ice melt. We use the physically based, spatially distributed hydrological model TOPKAPI to study the exchange between glaciers and climate in the upper Aconcagua River Basin during the summer season and identify the model parameters that are robust and transferable and those that are more dependent on calibration. TOPKAPI has recently been adapted to incorporate an enhanced temperature index approach for snow and ice melting. We suggest a calibration procedure that allows calibration of parameters in three steps by separating parameters governing distinct processes. We evaluate the parameters' transferability in time and in space by applying the model at two spatial scales. TOPKAPI's ability to simulate the relevant processes is tested against meteorological, ablation, and glacier runoff data measured on Juncal Norte Glacier during two glacier ablation seasons. The model was applied successfully to the climatic setting of the Dry Andes once its parameters were recalibrated. We found a clear distinction between parameters that are stable in time and those that need recalibration. The parameters of the melt model are transferable from one season to the other, while the parameters governing the extrapolation of meteorological input data and the routing of glacier meltwater need recalibration from one season to the other. Sensitivity analysis revealed that the model is most sensitive to the temperature lapse rate governing the extrapolation of air temperature from point measurements to the glacier scale and to the melt parameter that multiplies the shortwave radiation balance.

1. Introduction

[2] Physically based hydrological models are more suitable for simulations of basin response to a changing climate than empirical or conceptual models which rely more heavily on parameters' calibration. They require, however, a large amount of input and validation data, which are necessary to guarantee that all relevant processes are reproduced correctly [Beven and Binley, 1992; Feyen et al., 2000; Finger et al., 2011; Pellicciotti et al., 2012]. A certain degree of parameterization is inescapable also for physically based models, given the complexity of the hydrological processes that need to be simulated, especially at high temporal and spatial resolution [Foglia et al., 2009]. Additional parameters originate from the extrapolation of the input meteorological variables from point measurements to the basin-wide scale. The more physically based a model, the higher the number of meteorological input data, such as wind speed, relative humidity and radiation components, that need to be extrapolated to each grid cell or modeled at the catchment scale. Most of the parameters of physically based models should have a physical meaning and as such should be measurable. In practice, however, observed data are only sufficient to limit important parameter values to ranges of possible values [Binley et al., 1991; Anderton et al., 2002; Foglia et al., 2009].

[3] The applicability of such models for predictive or management purposes depends on the quality of model parameters and model calibration [Bittelli et al., 2010]. The use of a single integrated response variable (in general streamflow) for calibration may result in more than one combination of parameters providing the best fit [Anderton et al., 2002; Brooks et al., 2007; Pellicciotti et al., 2012], which has been famously referred to in the literature as an equifinality problem [e.g., Beven, 2001, 2002; Wagener et al., 2003]. In addition, calibration against one single variable does not guarantee that the single internal processes are correctly reproduced and might result in the compensation of errors through different model components [Anderton et al., 2002; Pellicciotti et al., 2012]. Therefore, we use a multistep and multivariable calibration procedure [Bergstrom et al., 2002; Cao et al., 2006; Stahl et al., 2008; F. Pellicciotti et al., Modeling melt and runoff from Gornergletscher: A study of model robustness and transferability, submitted to Journal of Geophysical Research, 2012] in which attention is given to model internal consistency by calibrating different parameters against internal variables representative of the process the parameter controls. Because of the high uncertainty related to the determination of model parameters [Beven and Freer, 2001], the calibration method [e.g., Seibert and McDonnell, 2002] and sensitivity analysis, where the relative influence of the parameters on modeling results is assessed [e.g., Kunstmann et al., 2006], represent a key issue for all models of complex hydrologic systems. For melt models, transferability of model parameters has been rarely looked at, but a couple of recent studies have addressed this issue both at the point and distributed scale [Carenzo et al., 2009; MacDougall and Flowers, 2011].

[4] Glacierized basins offer a special case of basin response to changes in the climatic forcing, since glaciers and seasonal snowpack store water in winter in the form of snow and ice and release it in summer, thus altering substantially the form of the annual hydrograph in comparison with nonglacierized basins in the same climatic setting [Jansson et al., 2003]. Streamflow diurnal variability is also remarkably more pronounced (J. Helbing and F. Pellicciotti, Runoff variations and seasonal evolution at the snout of Juncal Norte glacier, dry Andes of central Chile, manuscript in preparation, 2012) since the main mechanism of runoff generation is the melt production at the snow or ice surface, which has a strong diurnal cycle mainly controlled by variations in the shortwave radiation energy [e.g., Lecce, 1993; Arnold et al., 2006; Pellicciotti et al., 2008]. Changes in glacier storing mechanisms and atmosphere feedback processes, earlier onset of the melt season [e.g., Pellicciotti et al., 2010a] and long-term changes in glaciers volume associated with climate variations will therefore affect the amount, timing and seasonality of water resources in the upper watersheds of mountainous regions [e.g., Cline, 1997; Barnett et al., 2005; Stahl et al., 2008; Nayak et al., 2010; Pellicciotti et al., 2010a; Immerzeel et al., 2010]. This is of particular relevance for arid regions of the world, where snow and glaciers rather than rainfall are the main source for public water supply, agriculture irrigation, hydropower and other uses [Li and Williams, 2008].

[5] The Dry Andes of central Chile are a typical arid or semiarid mountainous region that relies on ice melt and snowmelt fed rivers for the supply of water to downstream agricultural areas during the dry summer months. Melt seasons are characterized by very low relative humidity, high incoming solar radiation (which reaches one of the global maxima), rare overcast conditions, air temperatures always above zero up to 3200 m above seal level (asl), and absence of precipitation [Pellicciotti et al., 2008, 2010b]. The region's dependency on snowmelt and ice melt in the months from November to March makes it vulnerable to changes in the cryospheric components of the water balance [Rivera et al., 2002; Carrasco et al., 2005; Masiokas et al., 2006; Bown et al., 2008; Pellicciotti et al., 2007], which will likely result in changes in the hydrological regime of the river flowing from the western slopes of the Andes Cordillera. Indeed, observed and projected changes in the streamflow regimes of basins in the central Cordillera have attracted growing attention in the past decade among the scientific community and governmental institutions [Rubio-Álvarez and McPhee, 2010]. Combined with the increasing pressure on water resources and competition for water allocation due to rapid economic growth [Rosegrant et al., 2000; Cai et al., 2003], this makes a reliable and accurate estimation of water resources and their projected changes a crucial priority in the region. One of the few in-depth hydrological studies that has been conducted in this region is that of Rubio-Álvarez and McPhee [2010]. However, no previous studies have made use of spatially distributed, physically based hydrological models to investigate ongoing changes in the basin hydrological response and no study has explicitly considered glaciers contribution to total streamflow.

[6] In this work, we use the spatially distributed, physically based model TOPKAPI (Topographic Kinematic Wave Approximation and Integration) [Liu and Todini, 2002; Ciarapica and Todini, 2002] to simulate glacier melt and runoff in an upper watershed of the Aconcagua River Basin (Figure 1) and identify uncertainties in the simulations and model skills and limitations. We focus on the glacier ablation season (December until February) and make use of a unique, extensive data set of glaciometeorological observations collected during two ablation seasons on one of the glaciers in the watershed [Pellicciotti et al., 2008, 2010b; Helbing and Pellicciotti, manuscript in preparation, 2012]. We then extend simulations to the entire hydrological season and to a larger basin scale. We use a melt approach of intermediate complexity between a full energy balance and the simple degree-day approach. Energy balance models provide accurate simulations at the point scale, but require a large number of input data normally not available and their distributed application is difficult because spatial extrapolation of wind speed, radiation fluxes, relative humidity and other input data is complex and affected by large errors. The model used in this work, despite its enhanced physical basis, can be run with temperature and precipitation as only input data. This is of value in a region characterized by scarcity of data. The particular climatic context of the Dry Andes and availability of high-resolution glaciometeorological data offers a unique chance to examine the model's applicability to arid, snow-dominated conditions and test its parameter transferability and robustness.

Figure 1.

(top) Map of the Aconcagua River Basin with the position of the stations providing temperature and precipitation data and position within Chile (inset map). (bottom) Map of the Juncal River Basin showing the position of the automatic weather stations (AWS) on (AWS1 and AWS3) and outside (AWS2) the Juncal Norte Glacier. The outline of the Juncal Glacier Basin is also shown in black. The position of the runoff gauging station at its outlet corresponds to that of AWS2. Contour lines are based upon Shuttle Radar Topography Mission (SRTM) elevation data.

[7] Given the issues mentioned above, this study has four main specific aims: (1) assess the applicability of a relatively complex, spatially distributed and physically based model such as TOPKAPI for the simulation of glacier melt and runoff in a mountainous, glacierized basin of the Dry Andes of Chile, (2) identify model parameters suitable for the distinct conditions of the Dry Andes and assess their transferability and robustness in time (from one season to another) and in space (from a smaller to a larger catchment area), (3) establish a calibration procedure that guarantees not only that the model correctly reproduces runoff but also demonstrates internal consistency in the simulation of the most relevant processes such as correct distribution of snow cover and diurnal variation of snow and ice ablation, and (4) test the model sensitivity to the model parameters in order to identify those that need accurate determination and establish model uncertainty.

2. Study Site and Data

[8] This study is conducted on the Juncal River Basin, a subbasin of the Upper Aconcagua Basin (Figure 1), in the Dry Andes of central Chile (32°–36°S). The area of the Juncal River Basin is 241 km2 (of which 14% is glacierized) and it comprises the Juncal Norte Glacier subbasin (23.49 km2, 42% glacierized; Figure 1). The climate is marked by mild wet winters and dry summers. In summer, precipitation is close to zero, the humidity is low and the solar radiation very intense [Pellicciotti et al., 2008]. Water originates almost exclusively from snowmelt and ice melt during the summer months from November to March [Masiokas et al., 2006]. In years of extreme drought glaciers can contribute up to 67% of late summer runoff of the main river basins in central Chile [Peña and Nazarala, 1987]. The central Andes of Chile are not left unaffected by climate change: the majority of glaciers in central Chile have receded in recent decades, from a few meters up to 50 m per year [Bown et al., 2008]. The Juncal Norte Glacier, in particular, has retreated by a total of 0.35 km2 in the period 1999 to 2006 [Bown et al., 2008].

[9] The basin is mainly characterized by bare soils and rocks of volcanic origin. Scleorphyll vegetation covers the lower sections of the Juncal River Basin but is almost absent in the Juncal Glacier Basin. Valley soils along the riverbed consist of Holocene sediments comprising glaciofluvial deposits and debris flow deposits from the surrounding slopes.

[10] Hydrometeorological measurements in the study area are available from the Direccion General de Aguas (DGA) standard network. Additional data were provided by two extensive field campaigns conducted on the Juncal Norte Glacier during the ablation season 2005/2006 and 2008/2009 (see Pellicciotti et al. [2008, 2010b] for details).

2.1. Meteorological Variables

[11] Two different types of meteorological data are used in this study. The model is run using as input hourly temperature and precipitation records from the standard hydrometeorological network. The precipitation station closest to the basin is Riecillos (Figure 1), at an elevation of 1290m (Table 1), while the closest temperature station is at Portillo (Figure 1, 2880 m). Both stations are located outside of the basin. The second data set consists of data collected on Juncal Norte Glacier during the two field seasons 2005/2006 and 2008/2009, from December to February, by the ETH expedition [Pellicciotti et al., 2008, 2010b]. These data are used to check the model internal consistency and for model calibration and validation. Two automatic weather stations (AWSs) were installed in 2005/2006 and three in 2008/2009 on the glacier and in the proglacial valley (Figure 1 and Table 1). We use in this paper the same naming convention as Pellicciotti et al. [2008] for the AWSs.

Table 1. Characteristics and Location of the Stations Providing the Input Data Used to Run TOPKAPI (Portillo and Rieccillos) and Characteristics, Locations, and Period of Functioning of the Automatic Weather Stations (AWSs) Installed on and Close to Juncal Norte Glacier in the 2005/2006 and 2008/2009 Seasons
StationElevation (m asl)LatitudeLongitudeInput Data
Portillo288032°50′4.05″ S70°7′0.26″Wtemperature
Riecillos129032°56′1.82″S70°21′50.15″Wprecipitation
StationElevation (m asl)LatitudeLongitudeLocationPeriod of Functioning
AWS1312732°59′26.58″S70°6′31.27″Wlowest ablation area11 Dec 2005 to 12 Feb 2006, 7 Dec 2008 to 15 Feb 2009
AWS2281132°58′27.64″S70°6′40.81″Wproglacial valley18–23 Dec 2005, 9 Jan to 14 Feb 2006, 7 Dec 2008 to 15 Feb 2009
AWS3330532°59′55.96″S70°5′57.80″Wupper ablation area8 Dec 2008 to 6 Feb 2009

[12] Each AWS measured 5 min interval records of air temperature (°C), relative humidity (%), wind speed ( inline image) and direction (degrees), incoming and reflected shortwave radiation ( inline image) (see Pellicciotti et al. [2008], for details). The sensors were fixed to an arm suspended from a mast. All measurements were taken at a height of 2 m above the ground [Pellicciotti et al., 2008]. Measurements of air temperature were shielded and ventilated. The air temperature data from the glacier are used to evaluate temperature changes with elevation. Measured incoming and reflected shortwave radiation allow calculation of hourly and daily albedo, which is used to calibrate some of the melt parameters. Measured incoming shortwave radiation is also used to validate the computed incoming shortwave radiation at AWS1 and AWS3. Temperature regimes on and off the glacier are distinct, with lower air temperatures and lower diurnal variability on the glacier than in the proglacial valley (Figure 2) because of the combined effect of glacier wind and melting glacier surface [Pellicciotti et al., 2008; Petersen and Pellicciotti, 2011]. Air temperature never dropped below zero at any of the AWSs during the period of record [Pellicciotti et al., 2008]. Temperature gradients between all stations are listed in Table 2.

Figure 2.

Average temperature per hour of day measured at AWS1 and AWS2 (solid and dashed lines) and average temperature lapse rates per hour of day between AWS1 and AWS2 (dotted lines) for both ablation seasons. Averages are computed over the period of functioning of AWSs indicated in Table 1.

Table 2. Mean Temperature Lapse Rates Between the Different AWSs for Ablation Seasons 2005/2006 and 2008/2009 (for the Common Period 9 December to 28 January)
Station XStation YTemperature Gradient (°C m−1)
Season 2005/2006Season 2008/2009
PortilloAWS2−0.0170−0.0218
PortilloAWS1−0.0136−0.0138
PortilloAWS3−0.0111
AWS2AWS1−0.0148−0.0156
AWS2AWS3−0.0126
AWS1AWS3−0.0074

2.2. Streamflow

[13] A continuous record of 5 min runoff is available at the location of AWS2 for both summers 2005/2006 and 2008/2009, and was obtained through a combination of salt dilution experiments and radar water level measurements (Helbing and Pellicciotti, manuscript in preparation, 2012). The dilution experiments provide a very accurate record of discrete measurements which were used to reconstruct a rating curve from which the continuous, 5 min water level readings of a VEGA radar device were converted into runoff. The record is described and analyzed by Helbing and Pellicciotti (manuscript in preparation, 2012) and the reader is referred to that publication for details.

2.3. Snow Depth and Density and Snow Water Equivalent Initial Distribution

[14] Snow density was measured in snow pits at the beginning of each measurement period. At the location of AWS1 the mean value was 524 inline image in December 2005 [Pellicciotti et al., 2008] and 481 inline image in December 2008 [Pellicciotti et al., 2010b]. Available snow depth data measured at ablation stakes are restricted to the glacier tongue since the upper part of the glacier is difficult to access. Snow depth readings were converted into snow water equivalents (mm swe) through the observed density and were used to validate the initial conditions prior to the period of melt modeling.

2.4. Digital Elevation Model

[15] The most accurate and complete digital elevation model (DEM) for the region is the Shuttle Radar Topography Mission (SRTM) 100 m resolution DEM. The glacier outlines were obtained from a recent glacier inventory of the region [Bown et al., 2008]. A grid size of 100 × 100 m is therefore used for this work.

2.5. Energy Balance Simulations

[16] As part of the calibration data set, we also use hourly melt rates simulated by an energy balance model applied at the location of the two glacier AWSs. The energy balance model is described by Pellicciotti et al. [2008, 2010b]. The model includes calculation of the subsurface heat flux, i.e., the exchange of heat between the surface and subsurface layers [Pellicciotti et al., 2009] and is forced by hourly measurements of incoming shortwave radiation (W m−2), reflected shortwave radiation (W m−2), air temperature (°C), air vapor pressure (Pa) and wind speed (m s−1). When driven by accurate measurements of surface meteorological variables, such as those available at the location of AWSs, energy balance simulations provide the best estimate of high temporal ablation rates at a point on a glacier surface [Pellicciotti et al., 2012]. They also offer the advantage of a continuous record which is not affected by the inaccuracies associated with surface lowering at ablation stakes or ultrasonic depth gauges (UDG) which are typical at daily and hourly scales [Pellicciotti et al., 2005]. The energy balance model simulations have been validated against ablation measurements at the locations of this study [Pellicciotti et al., 2008, 2010b] and agreed very well with both UDG and stake measurements. The model will be referred to as EB2, according to the nomenclature used by Pellicciotti et al. [2008].

3. Methods

3.1. The Physically Based, Distributed Model TOPKAPI

[17] TOPKAPI is a spatially distributed rainfall-runoff model that has been extensively used for flood forecasting applications and more recently for water balance assessment in both low land large catchments [Liu et al., 2005; Foglia et al., 2009; De Waele et al., 2010] and mountainous basins [Finger et al., 2011]. The model simulates all relevant components of the water balance and transfers the rainfall-runoff processes into nonlinear reservoir equations which represent drainage of the soils, overland flow and channel flow. The relevant information about topology, surface roughness and soil characteristics is commonly obtained from digital elevation models, land use maps and soil maps. For this application, since soil and land use maps are available in Chile only for low lands, we use estimates of soil and land use parameters by considering the variability of the topography given by the DEM and satellite images.

[18] TOPKAPI has been extensively modified for application to mountainous basins. A snowmelt and ice melt and glacier runoff generation component has been added on the basis of work by Pellicciotti et al. [2005]. Melt is computed using an enhanced temperature index (ETI) model that incorporates the full shortwave radiation balance [Pellicciotti et al., 2005, 2008]

display math

where M is the melt rate (mm water equivalent per unit of time, mm we h−1), α is albedo, I is the incoming shortwave radiation (W m−2) and T is the air temperature (°C). Here α, I, and T are calculated for each cell i of the grid. TF (temperature factor) and SRF (shortwave radiation factor) are empirical factors that are assumed constant in time and space. TT is the threshold air temperature for melt onset.

[19] The ETI melt model is of intermediate complexity between a full energy balance model and a simple temperature index model (see Pellicciotti et al. [2005] for a definition of the two methods). The shortwave radiation balance is explicitly calculated as in an energy balance model, but all remaining energy fluxes are lumped together into a temperature-dependent term (equation (1)). Carenzo et al. [2009] demonstrated that the value of the two empirical factors TF and SRF reflect the partition of the energy fluxes at the glacier surface. The threshold temperature TT is also an empirical element of the model. We chose this model because surface energy balance models require knowledge of numerous meteorological and surface input data, such as wind speed, relative humidity, longwave radiative fluxes, and scaling lengths for aerodynamic roughness, temperature and humidity, which are commonly not available. In addition, when applied to the distributed scale, these values need to be extrapolated from point observation to the entire domain of the DEM, and this introduces additional uncertainty because of the complexity of their spatial variations and inadequate modeling techniques [Carenzo et al., 2010].

[20] Clear-sky incoming shortwave radiation is simulated with a nonparametric model on the basis of the work by Iqbal [1983] and is described by Pellicciotti et al. [2011]. We use the vectorial algebra approach proposed by Corripio [2003] to account for the interaction between the solar beam and terrain geometry (shading, sky view factor, multiple reflection between slopes and sky). The reduction of incoming solar radiation caused by clouds is taken into account by means of a cloud transmittance factor [Pellicciotti et al., 2011]. This approach has been widely used in both mesoscale atmospheric studies [Thornton and Running, 1999; Pfister et al., 2003; Fitzpatrick et al., 2004; Fitzpatrick and Warren, 2005] and recent distributed models of glacier melt [Klok and Oerlemans, 2002; Anslow et al., 2008; Carenzo et al., 2010]. The method is based on daily cloud transmittance factors derived from the range of diurnal variations of air temperature outside the glacier boundary layer and is described by Pellicciotti et al. [2011]. Snow albedo is computed using the parameterization by Brock et al. [2000] on the basis of a logarithmic decay of fresh snow albedo as a function of cumulated daily maximum positive air temperature ( inline image)

display math

where inline image is the snow albedo of cell i on the current day, inline image and inline image are empirical factors controlling the reset to the maximum albedo after snowfall and the decrease in albedo of inline image with increasing inline image, respectively. A space and time invariant value of ice albedo ( inline image) is attributed to all glacier cells that become snow free [Finger et al., 2011].

[21] Snowmelt for nonglacierized cells is treated as liquid precipitation and infiltrated or evaporated on the basis of the water balance of the cell. Meltwater from glacierized cells is routed into the closest ice-free cell using the linear reservoir approach, which has been commonly used for the transformation of surface meltwater into glacier discharge [e.g., Hannah and Gurnell, 2001; Jansson et al., 2003]. We distinguish two reservoirs for snow and ice, respectively. The linear reservoir model is a conceptual approach to represent the transformation of surface melt water into glacier runoff [Jansson et al., 2003] compared to more sophisticated physical descriptions of the glacier internal drainage system [Flowers, 2008]. Despite its simplicity, it represents the current state of the art to model the transformation of surface melt water into glacier runoff for the majority of glaciers for which a detailed description of the characteristics of the subglacial drainage system does not exist [Jansson et al., 2003].

[22] TOPKAPI uses the Makkink approach [Makkink, 1957] based on air temperature and incoming shortwave radiation to compute evapotranspiration.

[23] The model is applied at an hourly resolution in a two-step procedure to the Juncal Norte Glacier basin (23.49 km2, 42% glacierized) and the Juncal River Basin (241 km2, 14% glacierized). For the small basin, the model is run for the glacier ablation season for which data from the glaciometeorological experiments are available. For the larger basin, we run the model for the entire year.

3.2. Model Calibration

[24] We separate the model parameters into three subsets, in order to take into account their influence on different processes, following recent similar approaches by Huss et al. [2008], Stahl et al. [2008], and Huss et al. [2009]. We group parameters sets according to their importance for (1) the characterization of the late winter snowpack (loop 1 of Figure 3), (2) simulation of surface melt at the glacier and snow surface (loop 2), and (3) the lumped response of the catchment to the meteorological forcing and the transformation of surface meltwater into runoff (loop 3).

Figure 3.

Scheme of the calibration procedure used in this work to optimize TOPKAPI's parameters. The data sets used in each of the three calibration steps are indicated to the right. In parentheses it is reported whether the optimization is conducted at the point or distributed scale.

[25] Initially, we ran TOPKAPI with combinations of parameter values included in a range of possible values. The initial values of the parameters are taken from literature [Brock et al., 2000; Pellicciotti et al., 2005, 2008; Carenzo et al., 2009]. Eventually, the ranges of parameter values are narrowed and the model is run again for a number of different parameter sets with smaller increments between parameter values. If the increments between tested parameter values are reduced to 5% of the optimal parameter value and modeling results do not significantly improve, we proceed to the next loop.

[26] During the first loop the three precipitation distribution parameters are calibrated against snow depth measurements on the glacier tongue (see Table 3 for a description of model parameters). At least one annual cycle of winter snow accumulation is modeled until the best possible correspondence between observed snow conditions at the beginning of the ablation season and snow conditions modeled by TOPKAPI is obtained. The root-mean-square error (RMSE) statistical criterion is applied to compare modeled and observed snow depths. The snow maps of the Juncal Glacier area for the best model fit to observed snow depths serve as initial conditions for the following two calibration steps where the model is run for the ablation season only.

Table 3. Description of the TOPKAPI Parameters That Were Optimized During the Calibration Procedure Presented in Figure 3 and Parameters That Were Not Recalibrated But Considered in the Analysis of Model Sensitivity to Individual Parameters
 SymbolDescriptionUnit
Loop 1βMAXDetermines the redistribution of snow due to effect of slopes. All snow precipitated on slopes above a certain angle is accumulated at the bottom of the slope.tan(°)
 PgradPrecipitation lapse rate: gradient for the change of precipitation with elevation.percent per 100 m
 PTThreshold temperature to distinguish between solid (snow) and liquid (rain) precipitation.°C
Loop 2α1First parameter of equation (2), representing the albedo of fresh snow.
 α2Second parameter of equation (2), characterizing the decay of snow albedo with the accumulated daily maximum temperature ( inline image).
 TFTemperature factor in equation (1), parameterizing the temperature-dependent radiation components.mm d−1 °C−1
 SRFShortwave radiation factor in equation (1). The physically based value of SRF would correspond to the conversion of W m−2 to mm we h−1.m2 mm W−2 h−1
 TTThreshold temperature for melt onset. Melt does not occur below this value.°C
Loop 3TgradTemperature lapse rate for attributing temperatures to the grid cells according to their elevation.°C m−1
 TmodTemperature decrease over glacierized surface.°C
 KiceStorage coefficient of the glacier ice meltwater reservoir.h
 KsnowStorage coefficient of the glacier snow meltwater reservoir.h
Unrecalibrated ParametersαiceAlbedo of ice (glacier surface).
 c1First Makkink coefficient for evapotranspiration computation.
 sSoil depth.m
 θSSaturated soil moisture content: water content held in soil during saturated soil conditions.%
 KshHorizontal soil conductivity at saturation. Regulates the amount of water moving horizontally in the soil superficial layer.m s−1
 KsvVertical soil conductivity at saturation. Regulates the amount of water moving vertically in the soil superficial layer.m s−1

[27] During the second loop, the parameters of the melt model (equation (1) and Table 3) are calibrated against the changes in measured albedo, snow depths and hourly ablation rates at the AWSs provided by the energy balance model (EB2). Parameter ranges and increments are reduced until the RMSE and the difference of the modeled total sum of melt to the total sum of melt computed by EB2 are minimized. No extrapolation of meteorological input data is required for this step since the calibration is performed at the point scale and measured data from the AWSs are used as input. We are aware, however, that in this way the parameters obtained will be biased toward conditions typical of the glacier tongue.

[28] The parameters of the third parameter set calibrated in loop 3 (Table 3) have no direct influence on melt processes at the AWSs, therefore the agreement achieved in the second calibration step between in situ melt measurements and melt modeling results is maintained. The parameters are calibrated by optimizing the agreement between the measured and the modeled runoff (Q) at the outlet of the Juncal Norte Glacier catchment. The quality of fit is assessed using the Nash-Sutcliffe efficiency (NSE) criterion [Nash and Sutcliffe, 1970], which has been widely used for evaluation of hydrological and melt model performance [Legates and McCabe, 1999; Hock, 1999; Strasser et al., 2004; Pellicciotti et al., 2005].

[29] The complete calibration procedure is an iterative process and is repeated until the parameter values do not undergo any more significant changes from one iteration to another (in practice: if the difference between parameter values is less than inline image5%, which is the uncertainty in parameter values that we evaluate in the global sensitivity analysis).

[30] Because the calibration on the point scale is not affected by the results of the calibration on the distributed scale (loops 1 and 3), as long as initial conditions at the AWSs are represented adequately by the model and measured local data is used as input, the second calibration loop can be excluded from additional iterations of the calibration procedure.

3.3. Model Validation

[31] In a first step, the optimal parameter sets for the Juncal Glacier Basin for the ablation seasons 2005/2006 are validated against data from the ablation season 2008/2009 and vice versa. This allows us to assess the transferability of parameters from one season to the other.

[32] In a second step, the model is run for the entire Juncal River Basin (241 km2) with the parameters optimized for the small basin (23.49 km2). Runoff data from the outlet of the Juncal River Basin are available for a period of one year from May 2005 until April 2006. Validation of the two optimal parameter sets for the Juncal Glacier Basin on the Juncal River Basin provides evidence about the transferability of the parameter sets over a longer period and for a larger, less extensively glacierized catchment.

3.4. Model Sensitivity

[33] The physical basis of the calibrated values of the model parameters is analyzed and related to the characteristic climatic regime of the Dry Andes. However, a certain degree of uncertainty associated with the ranges and intervals we used and choice of the objective functions [Legates and McCabe, 1999] cannot be excluded. For this reason, analysis of parameter sensitivities is of particular importance because sensitivity quantifies the influence of parameters on model performance [e.g., McCuen, 1973; Kunstmann et al., 2006].

[34] We carry out two types of sensitivity analysis. First, the model sensitivity to the variation of individual parameter values is assessed. We define sensitivity by the derivatives of an expectation function of an explicit function [McCuen, 1973]. One by one parameters are varied by 5% intervals about the optimum values spanning a range of inline image10%. Our expectation function is a second-order polynomial which is fitted to the five resulting values of the model output (e.g., mean maximum runoff, Figure 4). The slope about the origin is used as an indicator of the sensitivity of the model to a given parameter [Anslow et al., 2008]. This procedure is applied both to the model setup for the smaller Juncal Glacier Basin and to the larger Juncal River Basin. We assess the model sensitivity to the calibrated parameters and compare it with model sensitivity to parameters not included in the calibration procedure (Table 3). This approach for assessing parametric sensitivity is a well-established method that is described by McCuen [1973], Helton and Davis [2003], and Oakley and O'Hagan [2004]. It is computationally affordable and was applied in a study with a distributed glacier melt model by Anslow et al. [2008] and Pellicciotti et al. (submitted manuscript, 2012). The results identify the parameters that strongly affect the optimal solution [Sulieman et al., 2001]. However, this sensitivity approach is not able to consider simultaneous variations in two or more parameters [Sulieman et al., 2001]. Therefore, we analyzed also the global model sensitivity to a fixed amount of parameter uncertainty, following Anslow et al. [2008]. This is done by examining the variation in computed runoff when the model is run for 103 parameter sets varying the calibrated parameters randomly within a range of inline image5% around the optimal values. This approach provides an estimate of the model global sensitivity, similar to various other examples in literature where a probabilistic-based sampling procedure is used to develop a mapping from analysis inputs to analysis results [Helton and Davis, 2003] (see also Saltelli et al. [2004] and Oakley and O'Hagan [2004] for summaries of global sensitivity methods). Using a global sensitivity technique, it is possible to assess how uncertainty in the model outputs can be apportioned to uncertainty in the model inputs [Saltelli et al., 2000]. This approach also allows to verify that the calibrated parameter values are optimal.

Figure 4.

Determination of model sensitivity to the variation of individual parameter values: schematic example for assessing the influence of a given parameter on mean daily maximum runoff.

4. Results

4.1. Model Calibration

4.1.1. Parameter Values and Transferability

[35] Table 4 shows the calibrated parameter values for the Juncal Glacier Basin for the ablation seasons 2008/2009 and 2005/2006 after one complete iteration of the calibration procedure (all three loops in Figure 3).

Table 4. Optimal Parameter Sets for the Two Ablation Seasons, 2005/2006 and 2008/2009, After One Complete Iteration of the Calibration Procedure for the Smaller Juncal Glacier Basina
ParameterAblation Season
2005/20062008/2009
  • a

    Symbols are as in Table 3. For all parameters calibrated at the AWSs in loop 2, the values shown for ablation season 2008/2009 are the arithmetic mean of the results at the two stations.

Precipitation Distribution
βMAX0.90.99
Pgrad0.0350.015
PT33
 
Melt Parameters
SRF0.01050.0105
TF00
TT65
α20.0650.075
 
Temperature Distribution and Storage Coefficients
Tgrad0.008750.0075
Tmod01
Kice4014
Ksnow200100

[36] Of the three parameters controlling the spatial distribution of precipitation ( inline image, Pgrad and PT), Pgrad shows variability from one year to the other, while PT (controlling the phase of the precipitation) is identical for the two years and inline image is only slightly different (Table 4).

[37] The melt parameters (optimized in loop 2) show no difference between the two seasons. The optimal values of SRF and TF are identical for both years (Table 4). The threshold temperature for melt onset (TT) is slightly different. As indicated in Table 4, this value is the arithmetic mean of the calibrated TT at AWS1 and AWS3 (equal to 6°C and 4°C, respectively). Therefore, TT at AWS1 is also identical in both years (6°C), but lower at AWS3 for 2008/2009 (4°C). Note inline image is higher in 2008/2009 than in 2005/2006 (Table 4). However, this difference might not be significant since there was only little snow left on the glacier tongue at the beginning of the measurement period and this value might therefore be not representative. We decided not to recalibrate both parameters of the albedo parameterization (equation (2)) for this study, because fresh snow albedo has never been measured on the Juncal Norte Glacier and more data for fresh snow conditions would be required for an accurate calibration. The value found by Brock et al. [2000] for inline image on the Haut Glacier d'Arolla, Switzerland, is therefore applied.

[38] The values of the temperature distribution parameters (Tgrad and Tmod) and storage coefficients (Ksnow and Kice), however, vary between the two seasons (Table 4). Differences are not very high for Tmod (see section 5) but are important for both the temperature lapse rate and the storage coefficients.

4.1.2. Step 1 of Calibration: Modeling of Initial Snow Cover

[39] The model shows satisfactory agreement with observed snow depths after calibration loop 1 (Table 5). Because the stakes on the glacier are concentrated on the glacier tongue, several data points may lie within the same grid cell of the 100 m DEM, therefore limiting the fitting capacity. However, the overall trend of increasing snow depths with altitude is reproduced well: the modeling results reflect clearly that modeled snow depths for December 2005 and December 2008 varied significantly at lower altitudes (Figure 5). The ablation season 2005/2006 was marked by much more abundant late winter snow: whereas there were still three meters of snow on 11 December at AWS1 during the ablation season 2005/2006, all snow had disappeared by then from AWS1 in 2008/2009. The differences in snow depths at locations above 4400 m asl are not significant; snow above this altitude is likely permanent and does not contribute to modeled runoff because the threshold temperature for melt onset (TT) is practically never reached. Carrasco et al. [2005] confirm that the mean of the altitude of the 0°C air temperature during summer at the latitudinal range of the Aconcagua Basin is around 4200 m. Photos from an automatic camera facing the lower areas of Juncal Norte Glacier show good visual agreement with modeled snow redistribution from slopes, thus confirming that the redistribution parameter inline image is adequate.

Figure 5.

Mean modeled snow depth per elevation band derived from the two snow initial condition maps for ablation seasons 2005/2006 and 2008/2009, Juncal Glacier Basin.

Table 5. Goodness of Fit Measures for the Three-Step Calibration Procedure for Both Ablation Seasonsa
 Ablation Season
 2005/20062008/2009
  • a

    For each loop, we indicate the reference data against which the goodness of fit measures are calculated. ΔMtot and ΔQ indicate the difference between total melt computed by EB2 and by TOPKAPI and between runoff computed by TOPKAPI and measured at the outlet of Juncal Glacier Basin, respectively. Total melt observed at the locations of the AWSs during the period of functioning (in Table 1) is between 3.5 and 4 m. Root-mean-square error (RMSE) and Nash-Sutcliffe efficiency (NSE) values for loops 2 and 3 are calculated on hourly data.

Loop 1: Snow Depth at Location of Stakes
RMSE183 mm230 mm
 
Loop 2: EB2
AWSAWS1AWS1, AWS3
ΔMtot−47.86 mm+86.29 mm, −23.20 mm
RMSE1.37 mm h−11.40 mm h−1, 1.61mm h−1
NSE0.860.89, 0.82
 
Loop 3: Runoff Juncal Glacier Basin
NSE0.250.72
ΔQ−0.02 m3 s−1+0.02 m3 s−1

4.1.3. Step 2 of Calibration: Modeling of Melt Processes at AWSs

[40] Figure 6 shows melt rates computed by TOPKAPI at AWS3 compared to EB2 simulations during the 2008/2009 ablation season. Agreement between the two time series is very good (see also Table 5). The diurnal cycle of melt rates simulated by TOPKAPI reproduces well the daily variability in the EB2 record (Figure 6). Some discrepancies are evident in the peak values of maximum melt (Figure 6b). The close up view of modeled ablation for the days 14 to 18 December (Figure 6b) reveals that model performance is sometimes limited by the use of a daily constant cloud factor in TOPKAPI, as subdaily variations associated with clouds cannot be reproduced by TOPKAPI, as on 17 January (Figure 6b).

Figure 6.

Comparison of hourly ablation rates at AWS3 modeled by EB2 [Pellicciotti et al., 2008] and computed by TOPKAPI with the optimal parameter set for ablation season 2008/2009 (Table 4). (a) Entire period of functioning of AWS3, ablation season 2008/2009. (b) Close-up view of 14–18 January.

[41] The transition from snowmelt to ice melt and corresponding increase in ablation rate is reproduced well by TOPKAPI (Figure 6a), although between 15 and 18 December TOPKAPI sometimes overestimates ablation because in reality snow disappears gradually from the glacier surface. The overall agreement with ablation rates computed by EB2, however, is very good (Table 5).

4.1.4. Step 3 of Calibration: Modeling of Runoff

[42] TOPKAPI reproduces accurately observed runoff, and its daily cycle in particular, when simulated with the corresponding optimal parameter set of each season (Figure 7). Discharge from the basin reaches its maximum between 1500 and 1800 h and then decreases over night until runoff starts to increase again at around 1000 h. The NSE value of the optimal model fit is considerably lower in 2005/2006 than in 2008/2009 (Table 5), but the difference to measured runoff is of the same order of magnitude. In Figure 8, modeled daily minimum, maximum and mean values are compared to measured values. The scattering around the 1:1 relationship is similar for both years. This confirms that scatter plots and absolute errors provide sometimes more information about model efficiency than single goodness of fit measures [Legates and McCabe, 1999]. The lower NSE value can be explained by the lower variability of daily runoff in 2005/2006: NSE is lower if the difference between model error and amplitude is small, in a similar way as the Nash & Sutcliffe index of a hydrograph is influenced by relative model bias [McCuen et al., 2006].

Figure 7.

Runoff at the outlet of Juncal Glacier Basin modeled by the optimal parameter sets of each ablation season and cross validation in time. Modeled total daily ablation simulated by the optimal parameter set of each year is plotted against the secondary Y axis, with the fractions of ice melt and snowmelt in different colors. In terms of volume, mean daily runoff of 6 inline image corresponds to 22.4 mm of daily mean ablation within Juncal Glacier Basin.

Figure 8.

Measured versus modeled daily minimum, mean, and maximum runoff (in m3 s−1) for the best model runs for ablation season (left) 2005/2006 and (right) 2008/2009. The black line denotes the 1:1 relationship, r2 is the coefficient of determination, and RMSE is the root-mean-square error of shown data points.

4.2. Model Validation

4.2.1. Parameters Transferability in Time

[43] When TOPKAPI is run for the ablation season 2005/2006 with the optimal parameter set of the 2008/2009 ablation season and vice versa, the daily runoff dynamics cannot be reproduced and the main differences between the two seasons become evident: the amplitudes of the diurnal modeled hydrographs overestimate or underestimate the observed amplitudes by a factor of three or more (Figure 7). The observed runoff time series in the two seasons have a similar mean value (Table 6) but different amplitudes: the diurnal cycle is less pronounced in 2005/2006 than in 2008/2009 (Figure 7 and Table 6), with differences between daily maximum and minimum runoff much larger in 2008/2009 than in 2005/2006 (Figures 7 and 8). If we compare the optimal calibrated parameter values for the two seasons, only the recalibrated parameters of loop 3 are different from one season to the other, while the parameters of loops 1 and 2 are identical or very similar (Table 4). Differences in runoff between the two seasons, therefore, do not seem to be controlled by substantial differences in the melt processes on the tongue but rather by the differences in the routing of meltwater and by different temperature lapse rates.

Table 6. Characteristics of Observed and Modeled Diurnal Hydrographs for the Two Ablation Seasons for the Smaller Juncal Glacier Basin: Average Minimum Daily Runoff, Mean Daily Runoff, and Average Maximum Daily Runoffa
 Ablation Season 2005/2006Ablation Season 2008/2009
 MeasuredModeledσMeasuredModeledσ
  • a

    Here σ are the standard deviations of the normal distributions fitted to the data in Figure 10 and represent the variation associated with a fixed amount of uncertainty (±5%) about the values of the calibrated parameters given by Table 4.

Minimum (m3 s−1)2.422.36±0.11 (±4.87%)1.821.96±0.10 (±5.05%)
Mean (m3 s−1)2.662.64±0.13 (±5.08%)2.692.71±0.14 (±5.09%)
Maximum (m3 s−1)2.872.96±0.16 (±5.44%)3.713.6±0.19 (±5.31%)

4.2.2. Parameters Transferability in Space

[44] Results of the validation on the larger basin are shown in Figure 9. We used the optimal values found for both the ablation seasons 2005/2006 and 2008/2009 (shown in Table 4). Runoff at the outlet of the Juncal River Basin starts to increase in October, reaches maximum values during the summer months and decreases again until end of April (Figure 9). The modeled streamflow reflects very well the observed runoff seasonality. Expressed in terms of NSE, the goodness of fit is above 0.83 for both parameter sets (Table 7). The agreement with measured runoff is better for the parameter set calibrated with the 2005/2006 Juncal Glacier Basin data, especially at the beginning of the ablation season (October to mid-December). Toward the end of the ablation season the simulations tends to underestimate runoff. Figure 9 shows that the model does not predict substantial snowmelt after February 2006, and ice starts to melt when the surface of the glacier becomes snow free.

Figure 9.

Measured and modeled runoff at the outlet of the Juncal River Basin. Modeled total daily ablation is plotted against the secondary Y axis, with the fractions of ice melt and snowmelt in different colors. In terms of volume, mean daily runoff of 70 m3 s−1 corresponds to 25 mm of daily mean ablation within Juncal River Basin. Modeled streamflow is obtained by running TOPKAPI with the optimal parameter sets for the smaller Juncal Glacier Basin for both seasons and total daily ablation by using the optimal parameter set for summer 2005/2006. Period of record is 1 May 2005 to 29 April 2006.

Table 7. Main Characteristics of Simulated Streamflow of the Juncal River Basin for the Period 1 May 2005 to 29 April 2006a
 Mean (m3 s−1)σ (m3 s−1)Maximum (m3 s−1)Minimum (m3 s−1)NSE
  • a

    Mean indicates the mean runoff, σ is the standard deviation of hourly runoff, and minimum and maximum are the extreme values during the period of record. NSE is the Nash-Sutcliffe efficiency criterion between measured and simulated streamflow.

  • b

    opt., optimal parameter set.

Measured8.031.6343.621.611
opt. 2005/2006b6.702.0630.340.840.845
opt. 2008/2009b8.152.6139.201.050.833

4.3. Sensitivity Analysis

[45] The parameters to which the model is most sensitive are the temperature lapse rate, Tgrad, the shortwave radiation factor (SRF) and the threshold temperature for melt TT at both scales (Table 8). Runoff in both basins is dominated by snowmelt and ice melt, explaining why these parameters are important. The model is generally more sensitive to the recalibrated parameters than to the nonrecalibrated parameters for both the small Juncal River and the larger Juncal Glacier Basin, as shown in Table 8. Of the set of nonrecalibrated parameters, inline image is the most influential (and more so at the larger scale, where snow contribution plays a more important role), and the model is more sensitive to it than to inline image, which was included in the calibration procedure. This result points to the importance of verifying the original value of inline image from Brock et al. [2000] for the central Andes of Chile.

Table 8. Parametric Sensitivity Computed for Both Basinsa
ParameterJuncal Glacier BasinJuncal River Basin
Mean (m3 s−1 %−1)Minimum (m3 s−1 %−1)Maximum (m3 s−1 %−1)Mean (m3 s−1 %−1)σmean(m3 s−1 %−1)Amplitude (m3 s−1 %−1)
  • a

    Juncal Glacier Basin (9 December 2008 to 29 January 2009): sensitivity with respect to mean runoff, mean daily minimum runoff, and mean daily maximum runoff. Juncal River Basin (1 October 2005 to 29 April 2006): sensitivity with respect to mean runoff, the standard variation of daily mean runoff (σmean), and the mean amplitude of daily runoff. Sensitivity is computed according to Figure 4. A higher slope value means higher sensitivity. A positive value indicates that an increase in model parameter corresponds to an increase in model output and vice versa. Numbers in bold correspond to the parameters to which the model is most sensitive.

Recalibrated Parameters
Tgrad−0.0312−0.0241−0.0405−0.1343−0.0760−0.0345
Tmod−0.0028−0.0021−0.0037−0.0112−0.00600.0023
Ksnow−0.00010.0003−0.0007−0.0001−0.0030−0.0009
Kice−0.00020.0046−0.0069−0.0003−0.0011−0.0062
TF0.00250.00180.00310.00500.00590.0003
SRF0.02560.01520.03870.05270.03830.0214
TT−0.0221−0.0168−0.0288−0.0817−0.0064−0.0132
α20.00380.00240.00560.00970.00950.0047
Pgrad0.01780.01460.0021
PT0.00350.00030.0057
βMAX0.00480.0129−0.0070
 
Not Recalibrated Parameters
α1−0.0141−0.0095−0.0207−0.0391−0.0425−0.0190
αice−0.0024−0.0013−0.0037−0.0044−0.0016−0.0013
c1−0.0010−0.0007−0.0017−0.0106−0.0055−0.0027
s0.00010.0013−0.00160.0059−0.0033−0.0179
θS−0.0013−0.0007−0.0017−0.0031−0.0115−0.0098
Ksh0.00130.00200.00000.00880.007−0.0087
Ksv−0.0019−0.0018−0.0021−0.0077−0.0051−0.0012

[46] The parameters Kice, Ksnow, s, inline image, Ksv and Ksh govern the discharge routing. The processes in the soil and the routing of melt water in the conceptual meltwater reservoirs influence the shape of the daily hydrograph but do not have an impact on the total amount of water routed to the outlet on longer timescales. Therefore the model sensitivity with respect to mean runoff is low for most of the soil or storage coefficient parameters.

[47] The high relative sensitivity of a model parameter points to the importance of correctly determining it through calibration in order to improve modeled processes. However, lower sensitivity values for parameters like TF or soil parameters do not exclude that they may still constitute an important source of errors for the modeling of runoff if they are drastically overestimated or underestimated. This is especially true for soil parameters, which can be only very roughly estimated because of the heterogeneity of the soil characteristics.

[48] The importance of soil, evapotranspiration, and surface characteristic parameters increase with the percentage of surface of a catchment that is not covered by glaciers (Table 8). The model of the larger basin is also sensitive toward the precipitation lapse rate (Pgrad) (Table 8). The sensitivity to the precipitation distribution parameters is not assessed for the Juncal Glacier Basin because of the shorter modeling period for the smaller Juncal Glacier Basin and the absence of precipitation during summer months.

[49] As far as the amplitude of the daily hydrograph at the outlet of the Juncal River Basin is concerned, the parameters to which the model is most sensitive are Tgrad and SRF. Storage coefficients are less influential on the amplitudes than the soil parameters s, inline image and Ksh because relative to the amount of water routed through the soil, less water is routed by the conceptual glacier melt reservoirs than it is the case for the Juncal Glacier Basin.

[50] While the amplitude refers to daily variation of streamflow, the variation of runoff ( inline image) refers to seasonal trends over a longer temporal scale. This indicator is only shown for the Juncal River Basin in Table 8, since the variation of daily mean runoff from the Juncal Glacier Basin was comparatively small during the ablation season. Variation of runoff inline image is most sensitive to Tgrad and SRF, as well as to inline image, inline image, inline image, and Pgrad. A higher value of inline image can effectively delay snowmelt. Also the snow redistribution parameter inline image and the saturated soil moisture content ( inline image) reveal a pronounced influence on inline image: redistribution of snow from steep slopes leads to a more aggregated distribution of snow and prevents the snow from being melted early in the season, while a higher inline image allows the soil to store more water and release is temporally shifted.

[51] For the simulations on the Juncal Glacier subbasin, the indicator that shows to be most sensitive is the mean maximum daily runoff. The absolute values of the sensitivity indicators decrease for the average daily mean runoff and mean daily minimum runoff. This correlates with the extent of the scattering of values observed for the 103 model realizations of the 2008/2009 ablation season for the Juncal Glacier Basin in Figure 10. The random parameter selection yields a normal distribution around the best estimate value obtained with the calibration procedure (Figure 10). The standard deviation of the results for the 103 model runs is an estimate of the variation that could be incurred for a fixed amount of uncertainty in physical parameters and can be used to quantify model uncertainty associated with it (reported in Table 6). The choice of a ±5% range in parameter values excludes a large range of physically realistic values, but the results show that the calibration procedure identified at least a local optimum for the fitted runoff modeled by TOPKAPI.

Figure 10.

(top) Scatterplot of simulated average daily minimum, mean, and maximum runoff for the 103model realizations around the calibrated parameter set (indicated by yellow markers) for the smaller Juncal Glacier Basin, ablation season 2008/2009. (bottom) Histograms with 0.05 m3 s−1 intervals of results of the 103 model realizations. The black curves show normal distributions fitted to the data.

5. Discussion

5.1. Parameter Values and Transferability

[52] A clear result of our work is that some of the parameters that we recalibrated are transferable from one season to the other while others are not. All of them, however, needed recalibration for the specific climatic setting of the Juncal River basin, confirming findings obtained by Pellicciotti et al. [2008, 2012]. They seem, however, to have a clear physical basis.

5.1.1. Temporal Transferability

[53] One of our key results is that the melt parameters TF, SRF and TT are transferable from one season to the other, despite the differences in melt processes in the two seasons. The robustness of this finding is enhanced by the fact that measured air temperatures were used for calibration of melt parameters (step 2 in Figure 3), precipitation was zero during the calibration period and initial conditions could be constrained by measured snow depths. Correlation with parameters from different calibration steps can therefore be excluded.

[54] The 2005/2006 ablation season was more snowmelt dominated in comparison to the 2008/2009 season, and the hydrograph of the Juncal Glacier Basin exhibits distinct characteristics in the two seasons, with more marked diurnal variability in 2008/2009 (Figure 7). Despite this difference, the melt parameters (TF, SRF, and TT) are stable. Their robustness is likely favored by the stable meteorological conditions that seem to be typical of the ablation seasons in the central Andes of Chile [Pellicciotti et al., 2010b], where ablation processes are dominated by incoming shortwave radiation and clouds, which normally provide most of the intraseasonal variability in the atmospheric forcing and energy balance fluxes [Pellicciotti et al., 2008; Giesen et al., 2008; Carenzo et al., 2009], are basically absent [Pellicciotti et al., 2008, 2010b].

[55] In contrast to the melt parameters of loop 2, the values of the parameters calibrated in the third calibration loop reveal a relatively large variability from one year to another (Table 4). While the differences between Tmod are linked to the variations of TT (the difference between TT and Tmod is identical for both studied seasons), our results suggest that Tgrad, Kice and Ksnow depend on the snow conditions, which in contrast to the meteorological conditions during summer can be significantly different from one year to another. The use of a temperature decreasing parameter such as Tmod makes sense only if the nonglacierized areas are not covered by snow, because Tmod is used to adjust temperature measured outside of the glacier into temperature in the glacier boundary layer. The optimized parameter Tgrad is almost identical to the mean lapse rate computed from the air temperature measurements on the glacier between AWS1 and AWS3 during the ablation season 2008/2009 (Table 2). Temperature gradients on glaciers are often shallower than off glacier [Greuell and Böhm, 1998; Petersen and Pellicciotti, 2011] because of katabatic winds and the effect of a surface at melting point on the 2 m observations of temperature [Greuell and Böhm, 1998; Pellicciotti et al., 2008]. Therefore, the shallower lapse rate for 2008/2009 compared to the value for 2005/2006 might be explained by the higher importance of glacier melt during the ablation season 2008/2009, so the calibrated value of Tgrad yielded a value which is appropriate to reproduce the particular conditions over melting ice surfaces. Synoptic weather conditions are also likely to have an influence on Tgrad.

[56] The values of the storage constants of the two conceptual reservoir for meltwater from glacier snow and ice, Ksnow and Kice, respectively, are considerably higher in 2005/2006 (snow rich season) than in 2008/2009 (with less snow at the beginning of the simulation period) (Table 4). They conceptually represent how quickly each reservoir empties (and have the units of time, Table 3). While meltwater from ice is routed through a combination of supraglacial, englacial and subglacial systems, snow meltwater has to percolate through the snowpack before flowing at the impermeable snow-ice interface and then entering the englacial and subglacial system [Hannah and Gurnell, 2001]. Its pathway is therefore longer. As snow temperatures can drop below zero during the night [Pellicciotti et al., 2008], refreezing can occur, further slowing down the process of transfer of surface meltwater from snow covered surface to the proglacial stream. Therefore, the Kice can be associated to a “fast” reservoir and Ksnow to a “slow” reservoir, and its value is usually greater than Kice. The storage constants for ice and snow both change with the retreat of the snowline [Hannah and Gurnell, 2001; Nienow et al., 1998] which is associated with the reduction of the snow amount and increasing meltwater input to the englacial and subglacial system because of enhanced ice melt. This has an influence on the characteristics of the runoff, and its diurnal cycle in particular, as it is evident from Figure 7. When the glacier becomes progressively more snow free, the runoff diurnal hydrograph becomes more peaked, because removal of the snowpack accelerates the water pathway to the glacier snout and the glacier drainage system evolves [Han et al., 2009; Helbing and Pellicciotti, manuscript in preparation, 2012]. As the melt season progresses, the drainage system tends to become more efficient at carrying large discharges through the glacier [Jansson et al., 2003; Hannah and Gurnell, 2001]. In terms of model parameters, this results in a decrease of the values of the parameters Kice and Ksnow as the catchment's reaction time to the meltwater input decreases. The results of the calibration therefore confirm that storage coefficients are connected to the extension and depth of the snowpack (higher for higher snow depth on the glacier) and decrease over the ablation period: summer was much more progressed in 8 December and 9 January, while the area was still snow covered by then in 2005/2006 because of the much larger amount of snow at the end of the 2005 winter.

5.1.2. Dependency of Parameters on Energy Fluxes and Effect of Climatic Setting

[57] Another important result of our work is that the values of the ETI model parameters are clearly related to the energy balance at the glacier-surface interface typical of this climatic setting, and to the partition of the single fluxes in particular (as demonstrated already by Carenzo et al. [2009] for the Alps and by Pellicciotti et al. [2012]).

[58] The optimal melt parameters obtained for Juncal Norte Glacier are remarkably distinct from those in the Alps, since TF is zero and SRF is very high. Carenzo et al. [2009] found higher temperature factors for Swiss Alpine glaciers, varying between 0.03 and 0.08, and lower SRFs, The zero value for TF can be explained by a compensation of temperature-dependent energy fluxes (sensible and latent heat fluxes, and net longwave radiation flux), which causes the sum of such terms to be on average zero [Pellicciotti et al., 2008, 2010b]. In the Alps, frequent overcast conditions reduce radiative cooling, while low-humidity values and absence of clouds cause strong radiative cooling on the Juncal Norte Glacier and corresponding higher negative longwave radiation flux [Pellicciotti et al., 2008]. The high SRF is caused by the very high solar radiation reaching the surface and by the absence of clouds, and agrees with values found in the Alps for clear-sky conditions [Carenzo et al., 2009]. Its value is very close to the physically based value of 0.01078 (the conversion factor for the conversion of units of incoming shortwave radiation (W m−2) to units of melt (mm we h−1)) and agrees with the value of 0.0106 obtained by Pellicciotti et al. [2008] for the ablation season 2005/2006 on Juncal.

[59] The calibrated melt onset temperature (TT), equal to 5°C and 6°C for ablation seasons 2005/2006 and 2008/2009, respectively, is fairly high (Table 4). The temperature threshold for melt onset is an empirical parameter that is normally considered equal to 0°C or 1°C in temperature index models [Hock, 1999; Pellicciotti et al., 2005], assuming a fairly close correspondence between air and surface temperature. This however is not always the case, because of the cold content of the snowpack and ice pack that needs to be removed by supplying heat to the surface before energy can be used for melting. This process is normally negligible once the melt season is ongoing, but it might be important at the beginning and end of the season and during the night [Pellicciotti et al., 2009]. Our results suggest that this effect is strong at the AWSs on Juncal Norte because of the strong radiative losses at night which cool the snow pack, so that its temperature drops below zero and needs to be brought back to melting point in the early morning hours, thus delaying effective melt, since part of the energy available is used to remove the snowpack cold content [Pellicciotti et al., 2008]. A high TT therefore parameterizes the temporal delay of melt onset associated with the removal of the snowpack cold content. Simulations with the EB model, which includes computation of the subsurface flux within the snowpack, show that surface temperature drops below zero during the night (Figure 11), thus reducing the effective amount of melt that takes place in the early morning hours. If we use a lower TT, which does not take into account this effect, melt is overestimated in the early morning and late evening (Figure 11, bottom).

Figure 11.

(top) Surface temperature at AWS1 and AWS3 calculated with the energy balance model EB2 (from Pellicciotti et al. [2010b]). (bottom) Difference in mean hourly melt per hour of the day between TOPKAPI and EB2, computed with the best parameter set for AWS1 ( inline image) and a parameter set with inline image. Location is AWS1. Period of record is 9 December 2008 to 6 February 2009.

5.2. Parameter Sensitivity and Optimality

[60] We have shown that the parameters the model is most sensitive to at both spatial scales are the temperature lapse rate, Tgrad, the shortwave radiation factor, SRF, and the threshold temperature for melt TT (Table 8). Sensitivity analysis is important to identify the parameters that most affect model outputs and therefore need to be estimated with care, as compared to others that count less for a given model output [Saltelli et al., 2000]. This is particularly important for models with numerous parameters and in data scarce regions, where data availability to identify model parameters is often limited. In this case, we have provided a clear indication of the parameters that need to be estimated with accuracy for correct model simulations. Of these, two depend on model structure (SRF and TT), while one, Tgrad, controls the spatial extrapolation of air temperature from point observations to the spatial scale of the basin.

[61] The two parameters related to model structure (SRF and TT) seem to be stable from one season to the other, and this is a reassuring finding because once their value has been correctly identified on the basis of field measurements, there is no need for recalibration from one year to the other. In addition, we have demonstrated that both parameters have a physical base (see section 5.1.2), so that their values can effectively be identified on the basis of devoted field experiments.

[62] The third parameter to which the model is most sensitive, Tgrad, is on the contrary an exogenous parameter, which could be determined from temperature records at two or more stations, if data allowed. For this study, two stations were available in 2008/2009 (Table 1). We decided however to recalibrate Tgrad rather than use measured values because these were available only for the lower glacier tongue and are therefore not representative of temperature variations over the entire glacier system, which ranges up to 5892 m. Petersen and Pellicciotti [2011], using a network of distributed air temperature observations on the tongue of Juncal Norte Glacier, have shown that there is large variability in the range of calculated temperature lapse rates over the glacier, and that high uncertainty is associated with values in the highest section of the tongue, so that the assumption of a constant lapse rate in space and time might be questionable. The value obtained for the 2008/2009 ablation season is in good agreement with temperature lapse rates calculated from the measurements on the glacier lower section. By determining the temperature lapse rate by calibration, we are aware that its value might correlate with other parameters, thus introducing possible additional dependencies among parameters. We argue that more research should be devoted to the determination of both temperature and precipitation lapse rates at high elevations and their variability in time and space, and to understand how this parameter covariates with other parameters of the model such as TT or Tmod.

5.3. Ice and Snowpack Contribution to Total Melt

[63] In the central Andes of Chile, very few studies have quantified the contribution of glaciers to total runoff. Using an empirical approach based on interpretation of available observations, Favier et al. [2009] argued that at the regional scale the seasonal snowpack is the main water source. Their study was conducted for the Norte Chico region (26°–32°S), northern than our study site, but their conclusions should have validity for other similar areas characterized by a arid or semiarid regime. The contribution of glaciers to the total runoff increases, however, when moving from the larger regional scale to the modeling of the headwaters catchments [Gascoin et al., 2011] and it depends on the period considered. Gascoin et al. [2011] examined the glacier contribution to the discharge of two headwaters in the Huasco River, in the Atacama region, using a combination of mass balance and discharge measurements. Calculated glacier contribution varied between 3% and 23% for various subcatchments. The authors, however, pointed to several knowledge gaps affecting their conclusions and to limitations of their approach, which include neglecting other hydrological contributions such as the seasonal snowpack and role of soils and groundwater. These can be taken into account only by using an integrated modeling approach [Favier et al., 2009].

[64] Our work is the first modeling work conducted in the Dry Andes of central Chile using a fully distributed and physically based hydrological model and the first study to quantify the separate contribution of snowmelt and ice melt for two spatial scales, and over the glacier ablation season in particular. For the smaller Juncal Glacier Basin, ice melt contribution varies between 16% and 44% over the period this study focuses on (Figure 12, first two columns). Strong differences are evident between the two seasons analyzed. The season 2005/2006 was characterized by much more abundant winter snow accumulation than the 2008/2009 (see also Figure 5). As a result, snowmelt contribution is higher (Figures 7 and 12), also because snow covers for a longer time the glacier, retarding the onset of ice melt. Ice melt becomes a significant contribution only from early January, and it increases gradually (Figure 7, top). In 2008/2009, which was a dryer season with less snow available both on the glacier and surrounding slopes, ice melt is an important source of water already in December, and becomes dominant in late January, once the snow has disappeared from the slopes where melt can occur (Figure 7, bottom). As a result, in this year the total contribution of snow and of ice over the period December to February is almost the same (Figure 10).

Figure 12.

Simulated sources of runoff: (top) mean absolute and (bottom) relative contributions to total streamflow. The two catchments for which they are calculated are Juncal Glacier Basin (JG) and Juncal River Basin (JR). Periods are September–November (0); 12 December to 27 January (1), corresponding to the common period of available streamflow records from Juncal Glacier Basin (Figure 7); February–April (2); and full hydrological year (HY).

[65] For the larger basin, the glacier contribution is obviously smaller (Figures 9 and 12), and equal to 10% (2005/2006) to 31% (2008/2009) for the period of the full glacier ablation season from December to February. It is very small and basically negligible (0.5%) over the period September to November, which is dominated by snowmelt, but represents the 44% of total melt in the late ablation season (February to April, sixth column in Figure 12). Over the entire year (May 2005 to April 2006), glacier contribution represents the 14% of total runoff in 2005/2006, according to our simulations. This value would likely be higher for 2008/2009 (simulations not carried out for the larger basin for lack of data), given that 2008/2009 was characterized by less snow at lower elevations (Figure 5).

[66] Our values are within the range of those calculated by Gascoin et al. [2011] and higher, depending on the size of basin considered. Glaciers in the Norte Chico region are much smaller than those in the central region [Nicholson et al., 2010]. The catchments studied by Gascoin et al. [2011] had a maximum of 11% glacier area and maximum glacier extension of less than 2 km2, which make results not comparable. Given the higher extent of glacier cover in our study area, it is to be expected that the glaciers of the central Andes of Chile would represent a major contribution to total streamflow.

[67] Our simulations are affected by some uncertainty, part of which we have discussed above (section 5.2). This is so particularly for the larger basin, for which other hydrological processes than snow melt and ice melt become increasingly important, while in this study we have focused on calibration and validation of glacier processes. Simulations for the larger basin seem plausible, however, on the basis of comparison with observed runoff (Table 5 and Figure 9). Some discrepancies are evident in the modeled and observed annual hydrograph (Figure 9). The uncertainty about soil parameter values and snow depths at higher elevations might cause the underestimation of runoff toward the end of the ablation season. If the model underestimates snow depths, runoff is underestimated after the beginning of March because the contribution of snowmelt is too low. Soil parameters, which are certainly more relevant for the larger Juncal River Basin than for the Glacier Basin, might not adequately reproduce a possible buffering effect of melted snow because of storage capacities in the soil. Optimization of these parameters might improve simulations of the late season low flows, but we decided to focus on this work on the recalibration of the parameters governing the main processes of snowmelt and ice melt and glacier runoff.

6. Conclusions

[68] We have analyzed the applicability of a distributed, physically based hydrological model to a glacierized basin in the Dry Andes of central Chile, with the aim of testing a newly developed approach for the simulation of snowmelt and ice melt and runoff. A key issue was the establishment of a rigorous multivariable calibration procedure that allowed identification of parameter values and their robustness. This was possible thanks to the availability of a rich data set of glaciometeorological data recorded during two separate field campaigns on one of the glaciers in the basin, Juncal Norte Glacier. We have assessed the parameter robustness both by applying the model to two different seasons and to a larger basin.

[69] Our main conclusions are as follows:

[70] 1. Once recalibrated, the model is able to predict accurately the processes of ice melt and snowmelt and glacier runoff (Table 5 and Figures 68 and 11). On the glacier tongue, where measurements and simulation of glacier ablation are available, TOPKAPI can reproduce the magnitude of hourly melt rates, their diurnal cycle and the seasonality pattern controlled by the transition from snow to ice. Uncertainty remains about melt processes at higher elevations (above 4200 m asl) and about how these processes affect the generation of streamflow. This work confirms that there is a strong need for understanding the melt processes at elevations above those of most meteorological observations, both on Juncal Norte Glacier and in the central Andes in general. Timing and magnitude of simulated discharge is in good accordance with observations at both spatial scales, indicating both that the model is accurate and that its parameters are transferable in space, at least for the basin sizes investigated in this work. This study focused on the characterization of glacier melt and runoff, and we therefore neglected a detailed analysis of the other components of the hydrological cycle. A more accurate determination of processes in the soil and related parameters, however, might improve simulations for the larger basin [Baraer et al., 2009].

[71] 2. We found a clear distinction between parameters that are transferable in time and parameters that are not. Melt parameters (TF, SRF, and TT) are transferable from one season to another and from one scale to another. Temperature lapse rates and the storage coefficients of the snow and ice linear reservoirs are not (the latter decrease as the ablation season progresses). Values of the storage coefficients of the snow and ice reservoirs are clearly related to the distribution of snow water equivalent, which has been shown in previous studies to affect the routing of surface meltwater to the glacier outlet. It is less clear what the causes are for the variability of the lapse rates and more work should be devoted to this, especially because the temperature lapse rate is one of the parameters the model is most sensitive to and which causes largest uncertainties in model predictions, as demonstrated by our sensitivity analysis. This finding is in agreement with those of several other recent studies [Minder et al., 2010; Shea and Moore, 2010; Petersen and Pellicciotti, 2011].

[72] 3. The calibration procedure (Figure 3) guarantees that simulated runoff corresponds to observed runoff for the correct physical reasons. The calibration procedure excluded in a best possible way the compensation of model errors during the calibration process. Such a multivariable and multistep approach necessitates nonconventional data such as observations of snow depth and density, glacier albedo and energy balance simulations. We therefore argue that an effort should be made to collect similar data sets and use them for calibration of physically based hydrological models. Despite the effort associated with such short-term field measurements, their value seems high since they allow determination of model parameters related to melt, glacier runoff and possibly changes in glacier geometry that can therefore be left out from traditional calibration against runoff or more conventional data sets, thus making them valuable to reduce parameter ambiguity.

[73] 4. The model is most sensitive to the temperature lapse rate that is used to extrapolate spatially distributed temperature fields across and outside the glacier, despite the fact that melt rates are not computed as a function of air temperature directly with our optimal parameter set. The lapse rate, however, controls the spatial extent of melt processes, which is important for a basin covering such a high elevation range as Juncal Norte Glacier. This work has demonstrated that on Juncal Norte Glacier good modeling results can be achieved also at the distributed scale without varying the intensity of ablation with air temperature. Here, the ETI model approach represents an advantage over conventional temperature index methods for modeling the contribution of glacier and snow melt to streamflow because it allows separation of the temperature-dependent from the shortwave radiation–dependent components of the energy balance. The other two parameters the model is sensitive to are the SRF and TT. These, together with Tgrad are therefore the parameters that should be carefully estimated for application of the model to other high-elevation catchments.

[74] 5. Estimated contributions from melted glacier ice to runoff vary from about 10% to almost 50% depending on basin area, glacier size and percentage of glacier cover during late summer months. For the larger Juncal River Basin, glacier contribution was 14% over the entire hydrological year for the snow rich season 2005/2006 but amounted to 47% over the late ablation season from February to April of the same year, an amount which is relevant in terms of water resources. In snow poor years, such as 2008/2009, these percentages could be even higher. Glacier retreat in the central Andes, indeed, has been documented [Rivera et al., 2002; Bown et al., 2008; Rabatel et al., 2011] but the role of such glaciers on the hydrology of the region is much less understood [Favier et al., 2009; Gascoin et al., 2011] and modeling studies are basically absent. Our work has provided the first quantification of glacier melt and contribution to total runoff in a key headwater of the central Andes of Chile for two different spatial scales. Favier et al. [2009] had concluded their paper by calling for such modeling exercises. We would like to encourage more studies of this type for a more exhaustive characterization of glaciers contribution to the hydrology of the region, which comprises key large catchments such as the Aconcagua or Maipo River Basin.

[75] The parameter values identified in this work will be used in a second paper for long-term simulations of the Juncal River Basin, thus testing their suitability over several years. For applications of the model at a larger spatial and for longer temporal scale, however, further investigations are necessary to assess TOPKAPI's capacity to reproduce snow cover and snow depths accurately, since both control the amount and timing of streamflow. While at the scale considered in this work, parameters derived from observations on glacier are likely to be valid also for snow, for larger scale and off glaciers areas, snow processes need to be observed directly, especially for the early spring period. The adequate extrapolation of input data (the spatial and temporal distribution of temperature and precipitation lapse rates within the Juncal River Basin) should also be better looked at to estimate the accuracy of modeled runoff that can be achieved with TOPKAPI. Finally, at the larger scale, where additional parameters controlling e.g. soil storage come into play, parameter correlation and interdependency should be explored more in detail to quantify the uncertainty in simulations.

Acknowledgments

[76] The authors would like to thank Darcy Molnar for reading the manuscript and Jakob Helbing for devising, setting up, and running the runoff measurement instrumentation during the two ablation seasons (2005/2006 and 2008/2009) and participating in the two field campaigns. Marco Carenzo's contribution to the data collection in the field in 2008/2009 was substantial. Stefan Rimkus did all the necessary modifications in the code of TOPKAPI and helped us with technical questions related to it. Fernando Escobar of the Dirección General de Aguas (DGA), Santiago, provided the temperature observations at Portillo, and Andrés Rivera from the Centro de Estudios Cientificos (CECS), Valdivia, provided the glacier inventory map we used to identify glacier boundaries. We are also grateful to all the people who contributed to the collection of data in the field in 2005/2006 and 2008/2009. The comments of three anonymous reviewers helped to considerably improve the paper and are gratefully acknowledged.

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