Sources of uncertainty in modeling the glaciohydrological response of a Karakoram watershed to climate change

Authors


Abstract

[1] In the headwater catchments of the main Asian rivers, glaciohydrological models are a useful tool to anticipate impacts of climatic changes. However, the reliability of their projections strongly depends on the quality and quantity of data that are available for parameter estimation, model calibration and validation, as well as on the accuracy of climate change projections. In this study the physically oriented, glaciohydrological model TOPKAPI-ETH is used to simulate future changes in snow, glacier, and runoff from the Hunza River Basin in northern Pakistan. Three key sources of model uncertainty in future runoff projections are compared: model parameters, climate projections, and natural climate variability. A novel approach, applicable also to ungauged catchments, is used to determine which model parameters and model components significantly affect the overall model uncertainty. We show that the model is capable of reproducing streamflow and glacier mass balances, but that all analyzed sources of uncertainty significantly affect the reliability of future projections, and that their effect is variable in time and in space. The effect of parametric uncertainty often exceeds the impact of climate uncertainty and natural climate variability, especially in heavily glacierized subcatchments. The results of the uncertainty analysis allow detailed recommendations on network design and the timing and location of field measurements, which could efficiently help to reduce model uncertainty in the future.

1. Introduction

[2] Mountain glaciers and snow are an important source of freshwater for lowland areas [Barnett et al., 2005; Kaser et al., 2010]. Worldwide, most mountain glaciers have been retreating and global warming will likely enhance continued recession [Solomon et al., 2007]. In the short term, negative mass balances, resulting from decreasing winter accumulation and/or increasing summer ablation, should lead to an increase of glacier runoff [Pellicciotti et al., 2010]. In the long run, when glaciers have reached a limiting size, runoff is likely to decrease and glacier recession will lead to a transition from a glacier-dominated to a snow and/or rainfed hydrological regime. The Himalaya-Karakorum (H-K) region is characterized by a high degree of complexity and variability of the processes controlling snow accumulation, snow- and glacier melt, and the overall response of glacierized basins. Rapid declines of glacier areas are reported from the Greater Himalaya and most of mainland Asia, but many central Karakoram glaciers began expanding in the late 1990s [Hewitt, 2005; Bolch et al., 2012; Gardelle et al., 2012; Kääb et al., 2012]. Topographic control on snow accumulation and the presence of debris covered glaciers, in combination with distinct climatic patterns, can partly explain differences in glacier fluctuations within the H-K [Hewitt, 2011].

[3] A thorough analysis of the hydrological significance of future glacier evolution in the H-K is severely hindered by a lack of data [Bolch et al., 2012; Pellicciotti et al., 2012]. Thus, previous modeling studies on effects of glacier retreat on streamflow trends have, in general, examined either just a single catchment or areas within a relatively limited geographical region [Singh and Kumar, 1997; Singh and Jain, 2002; Singh and Bengtsson, 2004; Singh et al., 2006; Immerzeel et al., 2012a]. Models that have been used for projections on a larger scale [e.g., Immerzeel et al., 2010] are conceptual and not sufficiently process based to take into account specific and spatially variable basins characteristics when simulating their response to climatic changes.

[4] Understanding the response of complex climate-basin systems to a changing climate requires appropriate models that can mimic the physics of the key controlling processes [Cogley, 2011]. Modeling the seasonal hydrographs in snow and glacier dominated, data scarce catchments with physically based models presents one major challenge: finding sufficient and suitable data for parameter estimation or model calibration to reduce the risk of a compensation of errors through different model components and model parameters [Pellicciotti et al., 2012]. If only single integrated response variables are used for calibration (in general streamflow and/or remotely sensed snow cover), more than one parameter set may exceed a defined performance benchmark, which in the literature has been referred to as an equifinality problem [e.g., Beven, 2001, 2002; Wagener et al., 2003]. If the model is sufficiently physically based, parameter values can be estimated directly from measurements or literature, but the lack of adequate data leads to uncertainty in parameter values that increases the uncertainty in final model output.

[5] Given the high difficulties in obtaining new data from the H-K region owing to logistical, financial, political, and even military obstacles to data collection [Cogley, 2011], it is thus worth investigating in more detail the main sources of uncertainty in glaciohydrological modeling. This may help to determine where resources should be allocated for field observations and how fieldwork can be most efficiently planned in order to collect the information that can most effectively reduce model uncertainty.

[6] In this study, we apply the physically oriented, distributed glaciohydrological model TOPKAPI-ETH to the Hunza River Basin in the Karakoram region (13,715 km2) with the aim of quantifying the importance of different sources of uncertainty on future streamflow projections. TOPKAPI-ETH has been successfully applied to simulate streamflow from high-elevation catchments [Finger et al., 2011, 2012; Ragettli and Pellicciotti, 2012; Pellicciotti et al., 2012; Ragettli et al., 2013]. The model requires, however, detailed information on single glaciohydrological processes for estimating model parameters and/or for model calibration [Ragettli and Pellicciotti, 2012]. While detailed ground data from the Hunza River Basin are scarce, this region has benefited from growing scientific interest in the past years due to recent evidence of glacier expansion in the Karakorum and the regions importance for downstream water supply: short-term monitoring programs and low-altitude weather stations [Hewitt, 2005], satellite laser altimetry and elevation models [Kääb et al., 2012; Gardelle et al., 2012] and remotely sensed analysis of the cryosphere [Tahir et al., 2011a] have led to a better understanding of the climatological and topographical control on glacier fluctuations. Two recent modeling studies have attempted to simulate the hydrology of the region [Tahir et al., 2011b; Pellicciotti et al., 2012]. These previous glaciohydrological studies provide the basis for setting up TOPKAPI-ETH for the Hunza River Basin and to evaluate model performance and uncertainty.

[7] We compare the effect of different sources of uncertainty—parametric uncertainty, climate projections, natural climate variability—and assess where additional effort should be placed to reduce it. This paper then presents a new methodology to assess the spatially and temporally variable capacity of individual parameters and model components to explain total uncertainty in simulated runoff, based on a regional sensitivity analysis [Spear and Hornberger, 1980; Hornberger and Spear, 1981]. We use this methodology to test how accurately individual parameters need to be defined for reliable projections of future water availability in the region and which type of field data are required to efficiently constrain model uncertainty. The strong topographical and climatological heterogeneity of the study catchment makes it particularly interesting to assess the spatial and temporal variability of the information content of model parameters and variables. The overarching objective of this study is thus to gain insight into glaciohydrological and meteorological processes controlling the uncertainty in model outputs, in an area where monitoring is demanding, but where prognostic tools are extremely useful to anticipate the impacts of climate change.

2. Study Site and Data

[8] This study focuses on the Hunza River Basin (Figure 1), located in the Karakoram Range at about 36°N and 75°E in the northern territory of Pakistan. The area of the basin is about 13,715 km2 and approximately 26% of the basin is covered by glaciers (Table 1). The Hunza River is a tributary to the Gilgit River, which eventually flows into the upper Indus.

Figure 1.

Map of the Hunza River Basin showing the position of the three meteorological stations, the outlines of the five subregions, the river network and glacierized areas (debris-covered glacier area and clean ice in a different color). The numbers on the map indicate the locations of glaciers listed in Table 7.

Table 1. Characteristics of the Hunza River Basin and Subregionsa
NameArea (km2)Mean Elevation (m asl)Glacierized (%)Mean Glacier Size (km2)Debris % of Glacier AreaInput Data
  1. a

    Input data denominates the meteorological station which is providing the meteorological input data to the associated subregion.

Hunza13,715.0451125.810.422.7 
Naltar4,567.5403823.914.626.1Naltar (2810 m asl)
Hispar1,864.3464141.551.626.0Naltar (2810 m asl)
Shimshal2,760.0485632.511.120.7Naltar (2810 m asl)
Ziarat2,204.0461218.25.823.2Ziarat (3669 m asl)
Kunjerab2,319.5483016.13.710.2Kunjerab (4730 m asl)

[9] One of the most important characteristics of the study area is that many glaciers are extensively debris covered (Table 1). Glacier debris originates mainly from surrounding rockwalls and accumulates as supraglacial debris, partially or totally covering the glacier ablation zone. At a depth of a few centimeters, debris cover reduces glacier melt rates [Mihalcea et al., 2006]. As glaciers act as a debris conveyor, the base of headwalls are continuously cleared off, which allows continued headwall retreat [Scherler et al., 2011a]. In turn, the steep topographic relief favors the appearance of avalanches.

[10] Glaciers in the Karakoram seem to behave anomalously in the sense that many glaciers, in particular at the highest elevations, show no volume loss in contrast to the global trend of glacier recession [Hewitt, 2005; Bolch et al., 2012; Gardelle et al., 2012; Kääb et al., 2012]. Recent glacier expansion in the Karakorum can be partly explained by distinct climatic patterns in combination with the region-specific accumulation and ablation regime [Hewitt, 2011]: the presence of debris on many Karakoram glacier tongues might retard the glacier response to climate warming [Scherler et al., 2011b], and downslope conditions are influenced more quickly by high-altitude snowfall due to avalanche nourishment of glaciers. Patterns of variable topographic shading, causing differential ablation because glaciers receive different amounts of surface irradiance, may also partly explain differences in glacier fluctuations within the same region.

2.1. Climatic and Hydrological Characteristics

[11] The climate of the Hunza River Basin is characterized by a varying influence of the south Asian monsoon and westerly airflow. The south of the Hunza River Basin receives precipitation from summer monsoon between June and September and from midlatitude Westerlies strongest in winter, when low-pressure systems reach the western margin of high Asia. The influence of westerly winds decreases from west to east, while the strength of the monsoon decreases from south to north, as wet air masses are orographically forced out. High-elevation areas in the north of the catchment are significantly more arid [Harper and Humphrey, 2003]. Precipitation from winter Westerlies can reach higher elevations than the summer monsoon, which may be related to the higher tropospheric extent of the westerly airflow [Scherler et al., 2011a]. Increasing precipitation and maximum precipitation occurring between 5000 and 6000 m in glacier source areas has been proposed as a possible explanation for the observed glacier expansion [Hewitt, 2005, 2011]. Valley weather stations indicate increases in precipitation since the early 1960s [Archer and Fowler, 2004; Hewitt, 2005; Fowler and Archer, 2006]. Mean summer temperatures slightly decreased until the turn of the century [Fowler and Archer, 2006] but have shown a noticeable increasing trend since 2001 [Sarikaya et al., 2013].

[12] Hydrometeorological data used in this study are provided by the Water and Power Development Authority of Pakistan (WAPDA): precipitation and temperature data are measured at three automatic weather stations in Naltar, Ziarat, and Kunjerab (Figure 1). Values of daily precipitation are calculated from 1 min measurements of accumulated precipitation recorded by an automated weighting system. Data are available for a 14 year period from 1996 to 2009. Runoff is measured at the gauging station (Danyior Bridge) at the outlet of the study catchment (Figure 1). Runoff data and observed trends in timing and magnitude of flow from the Hunza at Danyior are discussed in detail by Sharif et al. [2013]. An observed falling trend in runoff magnitude between 1966 and 1997 was associated to a declining proportion of glacial contribution and possibly increased storage and reduced glacier runoff due to positive glacier mass balances.

[13] Ziarat and Kunjerab are high-elevation weather stations in the north of the catchment, while Naltar is representative for the climate south of the main ridge. Mean annual precipitation is highest at Naltar with 625 mm and significantly lower in the North (Ziarat: 158 mm, Kunjerab: 162 mm). Measured mean annual temperatures decrease with higher elevation from 6°C at Naltar (2810 m asl) to 2.4°C at Ziarat (3669 m asl) and −6°C at Kunjerab (4730 m asl). Areas of influence of the three meteorological stations are attributed by using the drainage divides of five Hunza River Basins subregions, whose borders are shown in Figure 1. Data from the Naltar station are also used as an input to the Hispar and Shimshal subcatchments, both located in the southeast of the Hunza River Basin, as no other local meteorological data are available.

2.2. DEM, Glacier, and Debris Maps

[14] An ASTER Global Digital Elevation Model (GDEM) data set of 30 m resolution (available on http://gdem.ersdac.jspacesystems.or.jp) is used for the calculation of glacier thicknesses (section 3.1.1). The vertical accuracy is between 30 and 40 m in area with slopes less than 30° [Pieczonka et al., 2011]. For the glaciohydrological modeling, this DEM is resampled to a resolution of 500 m to reduce computational requirements. The glacier and debris map were provided by the International Centre for Integrated Mountain Development (ICIMOD). These maps were generated by a semiautomated object-based classification method based on Landsat TM7 imagery around the period 2003 [Bajracharya and Shrestha, 2011]. Debris-covered glacier area was corrected manually because the automated method cannot accurately enough separate bare rock from debris based on the spectral signatures [Bajracharya and Shrestha, 2011; Paul et al., 2004].

3. Methods

3.1. Model Description

[15] TOPKAPI-ETH is a fully distributed rainfall-runoff model that has been developed for applications to mountainous basins. It is applied in this study at a daily time step and a grid resolution of 500 m. The hydrological components of the model are almost identical to the version used by Ragettli and Pellicciotti [2012], Finger et al. [2011, 2012], Pellicciotti et al. [2012] and Ragettli et al. [2013]. In the study of Pellicciotti et al. [2012] the model was applied to the same basin as in this study. For a detailed description of the model components, we therefore refer to these publications, and only a brief overview of the most important components is provided here.

[16] Water routing is based on the kinematic wave concept, whereby soil drainage, overland flow, and channel flow are represented by nonlinear reservoir differential equations [Liu and Todini, 2002, 2005] that are resolved for each catchment grid cell. The soil water routing component of TOPKAPI-ETH has a strong physical basis, since the process can be described by soil properties that are physically measurable. In return for its physical basis, this component requires a relatively large number of model parameters (soil parameters in Table 2).

Table 2. Summary of TOPKAPI-ETH Parameters Classified in Six Model Componentsa
NameDescriptionCalibratedUnitLiterature
  1. a

    Literature values are provided by studies about the Himalaya-Karakoram (H-K) or by previous applications of TOPKAPI-ETH or partial model components to high-elevation catchments. Soil characteristic estimates and values of related parameters are not provided here due to the open range of plausible values named in literature [Saxton and Rawls, 2006].

  2. b

    Winiger et al. [2005],

  3. c

    Mayer et al. [2006],

  4. d

    Konz et al. [2007],

  5. e

    Immerzeel et al. [2012a],

  6. f

    Tahir et al. [2011b],

  7. g

    Kattel et al. [2013],

  8. h

    Ragettli and Pellicciotti [2012],

  9. i

    Ragettli et al. [2013],

  10. j

    Negi and Kokhanovsky [2011],

  11. k

    Brock et al. [2000],

  12. l

    Pellicciotti et al. [2005],

  13. m

    Adhikary et al. [2000],

  14. n

    Pellicciotti et al. [2008],

  15. o

    Carenzo et al. [2009],

  16. p

    Pellicciotti et al. [2012],

  17. q

    Müller [2010],

  18. r

    Finger et al. [2011].

Distribution of Meteorological Input
PgradPrecipitation gradient40%100 m−140b-e
TgradTemperature lapse rate0.00725°C m−10.0047–0.0076f, g
TmodTemperature decrease over glaciated surface2°C0–2.86h, i
Snow Redistribution by Gravity
SGRa, SGRCsnow holding depth dependent on the slope angle; exponential regression function (2 parameters)0.08, 20  
Snow- and Icemelt
α1Albedo of fresh snow0.90 0.82–0.97j
α2Decay of snow albedo0.12 0.112–0.155h, i, k, l
αglacierAlbedo of ice (glacier surface)0.15 0.10–0.28m
αresetThreshold precipitation rate to reset snow albedo1.2mm d−1 
PTThreshold temperature for precipitation state transition2°C−1 to 3d, e, h
SRFShortwave radiation factor, ETI model0.01m2 mm W−2 d−10.0048–0.0106n-p
SRFdebrisSRF for debris-covered glacier surface0.0025m2 mm W−2 d−10.0045q
TFTemperature factor, ETI model0.04mm d−1 °C−1−0.03 to 0.16n-p
TFdebrisTF for debris covered glacier surface0.06mm d−1 °C−10.01q
TTThreshold temperature for melt onset.2°C−6 to 6h, p
Glacial Meltwater Routing
KiceStorage constant for ice melt40h14–40h
KsnowStorage constant for snow melt on glaciers100h100–200h
Soil
ExphBrooks-Corey exponent for the permeability3.5  
Expvsaturation curve (horizontal and vertical)11  
Exph,lowExph, lower soil layer3.5  
KshHorizontal soil conductivity at saturationle−4 -le−2m s−1 
KsvVertical soil conductivity at saturationle−4 -le−2m s−1 
Ksh,lowKsh, lower soil layerle−6 −5e−5m s−1 
Ksv,lowKsv, lower soil layerle−7 -le−6m s−1 
sSoil depth0.7–5.0m 
slowSoil depth, lower soil layer1.0–6.0m 
θrResidual soil moisture content1.5–5.0% 
θr,lowθr, lower soil layer1.0% 
θsSaturated soil moisture content20–50% 
θs,lowθs, lower soil layer45% 
Clear Sky Irradiance/Evapotranspiration
αgroundGround albedo0.25 0.25r
CropFCrop factors of evapotranspiration0.05–1.20  
rhRelative humidity55% 
visibilityVisibility30km 

[17] Snow- and glacier melt is computed using an enhanced temperature index (ETI) approach [Pellicciotti et al., 2005, 2008]:

display math(1)

[18] TF is called temperature factor ( inline image) and is an empirical parameter. The equivalence between net shortwave radiation ( inline image) and units of melt ( inline image) is controlled by an empirical shortwave radiation factor ( inline image). TT is the threshold air temperature (°C) for melt onset. As an input to each cell i of the grid, the ETI approach requires extrapolated air temperature (T), distributed estimates of incoming shortwave radiation (I) and albedo (α). Snow albedo is calculated as a function of an empirical parameter α2 that controls the logarithmic decrease of albedo and the maximum albedo after snowfall (α1) [Brock et al., 2000]. Incoming shortwave radiation is simulated with a nonparametric model based on Iqbal [1983] for the position of the sun relative to the considered area during each time step and a vectorial algebra approach [Corripio, 2003] to account for the interaction between the solar beam and terrain geometry. Daily cloud transmissivity (CT) coefficients are derived from the range of diurnal variations of air temperature [Pellicciotti et al., 2011].

[19] TOPKAPI-ETH requires only temperature and precipitation data as input. This makes the model suitable for applications in remote high-elevation catchments, where data scarcity is a major issue. Station data are extrapolated to every model grid cell using linear lapse rates for temperature (Tgrad) and precipitation (Pgrad). Despite the fact that they might not reflect the actual distribution of the two variables, linear lapse rates are commonly assumed for studies in the region [e.g., Mayer et al., 2006; Tahir et al., 2011a].

3.1.1. Model Adaptations

[20] In comparison to previous applications of TOPKAPI-ETH [Finger et al., 2011, 2012; Ragettli and Pellicciotti, 2012; Ragettli et al., 2013; Pellicciotti et al., 2012], the model has been modified in this study to apply enhanced solutions for processes that are of particular importance for the selected study region as well as for long-term simulations of catchment response. The enhancements are (i) the Δh parameterization of glacier retreat [Huss et al., 2010b], (ii) a new routine for the calculation of gravitational snow transport using a slope-dependent maximum snow holding depth [Bernhardt and Schulz, 2010] and (iii) the inclusion of two empirical parameters (TFd and SRFd), which substitute the empirical parameters (TF and SRF, equation (1)) to compute melt from the debris-covered sections of glaciers.

[21] The reasons for the observed anomalous flow dynamics of Karakoram glaciers, including their propensity to surge, are not yet entirely understood [Mayer et al., 2011; Bolch et al., 2012]. The simple approach used in TOPKAPI-ETH to simulate glacier movement reflects the lack of understanding of glacier dynamics boundary conditions in the Karakoram: we use the Δh parameterization of glacier retreat proposed by Huss et al. [2010b], validated for large valley glaciers in the Swiss Alps. Although there are uncertainties related to the transfer of the Δh parameterization from the Alps to the Karakoram, the approach guarantees that ice accumulated above the equilibrium line altitude is redistributed to lower elevations and that declines in glacier area are delayed by flow dynamics. This approach is therefore preferred over the simple assumption of a static glacier mass balance. However, the approach cannot take into account long response times of glacier termini to climate change. The larger and flatter the glacier, the slower the reaction to changes in snowfall in the accumulation area under equal climatic conditions [Bolch et al., 2012]. The approach will therefore tend to underestimate glacier retreat in the case of negative mass balances but increasing precipitation. In the case of positive mass balances, glacier geometry changes are not allowed by the model for the same reason.

[22] Initial glacier thickness maps for the Hunza River Basin were generated as described in Immerzeel et al. [2012a], assuming that basal sliding is the dominant motion mechanism [Copland et al., 2009] and therefore that basal shear stress is at equilibrium shear stress, which then allows the estimation of initial ice thicknesses as a function of slope and the known extent of glaciers [Cuffey and Paterson, 2010]. The reader is referred to Immerzeel et al. [2012a] for technical details. Calculated glacier thicknesses are plausible when compared to estimates based on empirical nonlinear volume-area scaling [Bahr et al., 1997; Immerzeel, 2011]. The advantage of the equilibrium shear stress approach is that the estimates of ice thickness are provided at a high resolution, whereas empirical methods provide only an estimate for the average thickness of an entire glacier. Also, the equilibrium shear stress approach is independent of the shape of a glacier (valley, ice sheet, or cirque), whereas empirical methods show a strong dependence on glacier types and geometry [Bahr et al., 1997].

[23] Although TOPKAPI-ETH was modified to account for the processes that have been suggested in the literature to explain the response of Karakoram glaciers to climate change (debris insulation, avalanche nourishment, topographic shading, regional climatic patterns), projections of glacier fluctuations will remain uncertain as long as the model cannot sufficiently account for the physical processes controlling the glacier dynamics. The applicability of more complex procedures to estimate ice-thickness distributions [e.g., Farinotti et al., 2009] or to simulate glacier movement [e.g., Mayer et al., 2011] suffers from poorly documented boundary conditions of ice flow mechanics in the Karakorum. Future glacier extension simulated by TOPKAPI-ETH must therefore be treated with some care. In section 4.4, we use a sensitivity analysis to assess the effect on future runoff simulations of uncertainty about initial glacier thickness and the Δh parameterization.

3.2. GCM Data and Its Downscaling

[24] The general circulation models (GCMs) used in this work are: (1) the CGCM3.1(T47) model of the Canadian Centre for Climate Modelling and Analysis, Canada (CGCM3), (2) the CM2.0 model of the Geophysical Fluid Dynamics Laboratory (CM2), USA, and (3) the high-resolution version of the MIROC3.2 model of the Center for Climate System Research/National Institute for Environmental Studies/Frontier Research Center for Global Change, Japan (MIROC3). These three GCMs are selected because of their good performance in simulating present day climate [Immerzeel et al., 2010].

[25] We analyze the effect of climate change until the year 2050. Since the uncertainty due to the emission scenarios is rather small for the considered time period [Prein et al., 2011], only the emission scenario A1B is used.

[26] The outputs of the selected GCMs are at a monthly scale. They are downscaled to daily temporal resolution at the station locations using a stochastic approach that provides an ensemble of future scenarios. One of the main advantages of this type of downscaling is that it accounts for the natural variability of the climate by preserving the observed statistical properties of precipitation and temperature. In addition, the effect of the stochastic nature of these variables can be taken into account when simulating the hydrological response of a catchment.

[27] Precipitation is downscaled by reparameterization of the Spatio-Temporal Neyman-Scott Rectangular Pulses (ST-NSRP) model implemented in the RAINSIM package [Burton et al., 2008; Bordoy and Burlando, 2013a]. The methodology uses debiased climate model outputs and the scaling properties of the precipitation process to perturb the statistics needed for the model calibration at several temporal aggregations [Bordoy and Burlando, 2013b; Bordoy, 2013]. The model parameterized in this way is used to generate 100 stochastic realizations of 10 year length each, for each decade until 2050.

[28] Due to its different statistical characteristics, temperature is downscaled with a different approach. To capture the temporal and spatial correlations at daily resolution, a multivariate Markovian model is used to generate, in a Monte Carlo way, an ensemble of 100 standard series of 10 year length each. These time series are then shifted and rescaled on a monthly basis according to the debiased GCM temperature outputs following the change factor approach [Hay et al., 2000].

[29] For the debiasing of climate model outputs, as well as for the parameterization of the ST-NSRP and Markovian models, we use the signatures of 14 years of observed daily data (1996–2009, see section 2.1). Months with missing data (15.1% of all months in the case of precipitation and 27.5% in the case of temperature) are not considered. The performance of the stochastic approach can be assessed by comparing generated with observed meteorological data, without applying the change factors extracted from the GCMs. Figure 2 shows that the monthly characteristics of observed temperature and precipitation are well reproduced for the control period. Differences in total annual precipitation are less than 3% for each of the three stations.

Figure 2.

Precipitation and temperature measured at the locations of the three meteorological stations, and generated with the stochastic approach, for the control period 1996–2009. Error bars represent the standard deviation in monthly mean values.

[30] Time series of daily cloud transmissivity coefficients are generated randomly by using the probability distribution of cloud coefficients of the present as a function of precipitation intensity. In this way, we allow for a change of future cloud coefficients as a function of the predicted number of days with precipitation and precipitation intensity.

3.3. Model Calibration

[31] The main prerequisite for model parameters in this study is that they remain within realistic ranges of values. A systematic multicriteria calibration procedure could reduce uncertainties about parameter ranges. However, Pellicciotti et al. [2012] have shown that calibration data available for the Hunza River Basin (runoff measured at the outlet and remotely sensed snow cover data) are not sufficient for a univocal identification of optimal model parameters, and this resulted in problems of equifinality. In such cases, parameter uncertainty can be efficiently reduced by including “soft” process knowledge by the experimentalist in the calibration process [Seibert and McDonnell, 2002]. Therefore, we do not apply a systematic calibration procedure but make a best estimate of parameter values using values given in the literature and derived from the scarcely available observed data (see Table 2). This minimizes the risk of introducing physically unrealistic parameter values and perturbed estimates of the uncertainty.

[32] Model performance is evaluated using 3 years (2001–2003) of measured basin discharge. Although hydrometeorological data are available for a longer period (1996–2009), we use data only from this period because of large data gaps in the other years.

3.4. Future Simulations and Uncertainty Analysis

[33] Three different sources of uncertainty affecting simulations of basin response to future climate change are assessed in this work: (i) uncertainty associated with parameters, (ii) uncertainty due to the variability in GCMs outputs, and (iii) the uncertainty due to the natural interannual climate variability. Their effects are quantitatively assessed by looking at the spread of simulated model output.

[34] We run TOPKAPI-ETH for a period of 50 years using stochastic meteorological data generated for a control period (2001–2010) and for the following four decades (2011–2050) using the downscaled GCMs projections. A set of 100 simulations for each GCM allows estimating the uncertainty in simulated runoff due to the observed stochasticity in temperature and precipitation reflected in the generated meteorological data (see section 3.2). The optimal parameter set resulting from the model calibration is used for these simulations.

[35] To estimate the effect of parametric uncertainty on model outputs, we vary the model parameters randomly within a range of ±10%. The computational requirements for running TOPKAPI-ETH are minimized by choosing Sobolt's quasi-random number generator [Bratley and Fox, 1988] to sample the parameter space more efficiently. In this way, we generate 1000 random parameter sets, for each of which the model is run once. We use one single hypothetical time series of 50 year temperature and precipitation—chosen randomly from the ensemble of 100 scenarios—for each model realization.

[36] The importance of different sources of uncertainty varies in space. This variability is assessed by looking at the outputs for each subregion shown in Figure 1 separately. The temporal variability is investigated by computing uncertainty for each decade of model outputs. The structure of TOPKAPI-ETH allows for evaluation of uncertainty not only of the simulated runoff, but also of various intermediate model outputs such as glacier mass balance or glacier area (see Table 3).

Table 3. Mean Values of Simulated Runoff and Selected Variablesa for the Hunza River Basin as Well as for the Five Subregionsb
 2001–20102041–2050
Control PeriodCGCM3CM2MIROC3Param. ±10%
MeanσMeanσMeanσMeanσMeanσ
  1. a

    PrecS and PrecL are the mean annual liquid and solid precipitation, GMB is the glacier mass balance, Glac is the percentage of glacier area compared to initial glacier expansion, and ELA is the equilibrium line altitude.

  2. b

    Shown are the results of simulations forced with calibrated parameters and generated stochastic time series of meteorological data for the control period (2001–2010) and the last simulated decade (2041–2050) and of simulations forced by one time series of generated meteorological input but assuming ±10% uncertainty in parameter values (2041–2050). The 100 stochastic simulations are performed for each downscaled GCM (CGCM3, CM2, and MIROC3) and 1000 random parameter sets are used to assess the effect of parametric uncertainty (meteorological input provided by a CGCM3 time series). σ is the standard deviation in model outputs due to multiple model realizations.

Hunza
Runoff (mm/yr)650.9±25.0662.3±36.8588.5±33.2738.7±30.4694.1±39.7
Temperature (°C)−5.6±0.1−4.6±0.1−4.6±0.1−3.8±0.1−4.6±0.5
PrecS (mm/yr)590.0±39.1629.8±49.7567.3±48.4615.1±35.6667.3±21.2
PrecL (mm/yr)147.8±11.8183.4±20.8157.7±13.6217.5±18.5189.8±14.2
GMB (m/yr)0.12±0.100.30±0.130.28±0.110.07±0.110.38±0.17
Glac (%)98.6±0.280.0±0.683.7±0.479.7±0.580.4±3.6
ELA (m)4739±304912±434829±295022±384887±104
Naltar
Runoff (mm/yr)835.9±36.2840.1±55.3751.1±51.3907.6±43.8884.0±32.5
Temperature (°C)−2.9±0.1−1.9±0.1−1.9±0.1−1.1±0.1−1.9±0.5
PrecS (mm/yr)667.4±46.7714.9±59.3636.2±58.0685.4±42.6755.2±24.0
PrecL (mm/yr)249.7±19.5293.9±31.3268.3±22.7349.6±27.5302.1±17.0
GMB (m/yr)−0.09±0.100.13±0.110.10±0.10−0.07±0.100.19±0.14
Glac (%)98.2±0.281.0±0.883.6±0.780.2±0.881.0±4.9
ELA (m)4502±324659±454610±304785±424630±120
Hispar
Runoff (mm/yr)873.9±33.41048.0±50.7945.7±43.41206.8±45.81071.0±97.7
Temperature (°C)−7.4±0.1−6.3±0.1−6.3±0.1−5.5±0.1−6.3±0.8
PrecS (mm/yr)907.2±61.4965.3±77.2879.0±75.9955.3±56.31018.0±34.3
PrecL (mm/yr)158.3±14.3206.7±25.7171.8±17.2247.1±23.9210.3±22.4
GMB (m/yr)0.45±0.120.13±0.150.12±0.13−0.15±0.130.24±0.25
Glac (%)99.9±0.095.3±0.496.3±0.394.9±0.494.8±3.1
ELA (m)4496±334659±424610±294777±374628±109
Shimshal
Runoff (mm/yr)714.7±31.2907.6±47.9810.1±41.11027.4±42.6940.3±79.2
Temperature (°C)−8.8±0.1−7.8±0.1−7.8±0.1−7.0±0.1−7.8±0.9
PrecS (mm/yr)987.6±66.41054.6±83.6962.3±81.91052.4±61.31111.5±37.3
PrecL (mm/yr)130.8±12.6175.6±23.4140.7±15.3209.8±22.0177.8±22.6
GMB (m/yr)1.13±0.130.85±0.160.83±0.140.69±0.130.97±0.23
Glac (%)99.7±0.097.8±0.298.1±0.197.6±0.297.6±1.0
ELA (m)4489±344650±434603±314770±394616±112
Ziarat
Runoff (mm/yr)500.8±16.4183.3±15.3155.3±15.0192.3±13.2204.3±8.4
Temperature (°C)−4.5±0.1−3.4±0.2−3.4±0.1−2.6±0.1−3.5±0.4
PrecS (mm/yr)156.1±9.8170.9±13.6146.4±13.2160.5±12.1187.1±5.4
PrecL (mm/yr)58.6±6.072.1±10.158.6±6.682.4±7.479.0±4.4
GMB (m/yr)−2.07±0.10−0.58±0.12−0.47±0.10−1.01±0.13−0.51±0.10
Glac (%)93.5±0.815.9±1.227.3±1.115.8±1.217.5±7.8
ELA (m)5327±425523±465382±285625±365513±118
Kunjerab
Runoff (mm/yr)174.1±11.1165.7±12.8129.0±11.6205.8±14.4189.4±6.6
Temperature (°C)−6.7±0.1−5.7±0.1−5.7±0.1−4.9±0.1−5.7±0.0
PrecS (mm/yr)121.8±8.1123.0±10.4111.2±9.8114.8±6.9140.1±1.9
PrecL (mm/yr)43.8±5.062.1±9.042.8±5.571.0±8.171.4±1.8
GMB (m/yr)−0.31±0.06−0.24±0.08−0.11±0.05−0.56±0.10−0.23±0.06
Glac (%)99.5±0.172.0±1.684.1±0.872.7±1.575.2±3.8
ELA (m)5143±385345±385182±265412±295326±55

[37] Other sources of uncertainty that might be relevant for future projections, such as model structure uncertainties or the accuracy of measured meteorological data, are not assessed systematically in this work. The representativeness of measured climate data, however, is discussed qualitatively by comparing model outputs with the relevant literature in section 5.4.

3.4.1. Information Content of Model Parameters and Variables

[38] In order to assess the capacity of single parameters and variables to explain total model uncertainty, referred to as information content of parameters and variables hereafter, we apply a modified regional sensitivity analysis (RSA) approach. Regional sensitivity analysis is often applied in hydrology to assess model sensitivity to single model parameters [Wagener and Kollat, 2007; Tang et al., 2007; Sun et al., 2012]. It evaluates the effect of relative changes in a number of parameters on the model outputs. Usually, it is based on the partitioning of model outputs in at least one behavioral and one nonbehavioral group [Hornberger and Spear, 1981], using an objective function and a performance threshold to distinguish between “good” and “bad” model performance. The maximum vertical distance between cumulative distribution functions (CDFs) of single model parameters for behavioral and nonbehavioral parameter sets is then used to assess whether a parameter significantly impacts behavioral results [Sun et al., 2012].

[39] In this study, we use the RSA to identify parameters and variables that affect model outputs in terms of mean simulated streamflow. The 1000 parameter sets with parameters values varying randomly within a range of ±10% are partitioned in two groups: parameter sets that lead to more than average and to less than average total runoff, respectively, over a certain time period. For this purpose, it is not necessary to rank parameter populations in function of an objective function that requires measured streamflow, and the procedure can thus be applied to ungauged catchments. The larger the maximum vertical distance between two CDFs, the larger is the capacity of a parameter to explain differences in simulated mean runoff. Figure 3 provides an example of how the information content of parameters is calculated in this work. Of the four model parameters shown in this figure, parameter Tgrad is the parameter with the highest information content.

Figure 3.

Cumulative density functions (CDFs) of the parameters values of Tgrad, Pgrad, SRF, and α1, contained in each two groups of parameter sets for each decade, representing parameter sets resulting in higher resp. lower mean runoff per decade than the average runoff of all parameter sets together. The 1000 random parameter sets are considered for the analysis. The maximum difference between pairs of CDFs reflects the information content of a parameter with respect to runoff simulations for a specific decade.

[40] The information content of parameters and variables may vary significantly with the sampled initial range of parameters. However, there is a lack of prior knowledge about plausible ranges suitable for the study region. In order to prevent subjective choices, the parameters are thus varied only within ±10% of their calibrated value. This is a common approach when a priori ranges of parameters are not available [e.g., Anslow et al., 2008; Ragettli and Pellicciotti, 2012; Heynen et al., 2013]. Narrow ranges of parameter values also allow to better cover the entire parameter space with 1000 parameter sets, a number that is imposed by computational constraints. To prevent false interpretations of information content due to an insufficient number of model realizations, a Kolmogorov-Smirnov test is used to calculate the significance level α of the difference between the two groups of values [Spear and Hornberger, 1980]: a significance level of α = 5% corresponds to accepting the null hypothesis that the cumulative distribution curves are the same. If we test the significance level of the information content of a number n of parameters or variables, we evaluate each of the individual tests by a significance level of α/n.

[41] To validate the RSA results with an independent method and estimate the sensitivity of TOPKAPI-ETH to the glacier dynamics component in comparison to other components, we screen the main effects of all model parameters, of the Δh parameterization and of the initial glacier thickness by the Plackett-Burman sensitivity analysis (PBSA) technique [Plackett and Burman, 1946]. PBSA is a very efficient screening design in terms of numbers of model realizations needed, and, although not very often applied in hydrology, it is equally useful for any sort of model having many parameters [Beres and Hawkins, 2001]. In contrast to a one-at-a-time sensitivity method, it allows a simultaneous consideration of all parameters. PBSA is based on a two-level factorial design: for each model realization, either “high” or “low” values are assigned to each parameter (PBSA designs are readily available in MATLAB®). Parameters and initial glacier thickness are either plus or minus 10% of the original value, while we run the model with either the Δh function derived for large or for small glaciers in the Swiss Alps [Huss et al., 2010b], to assess the model sensitivity to the Δh parameterization.

4. Results

4.1. Calibration

[42] Measured daily runoff of the 3 year calibration period and daily runoff simulated by TOPKAPI-ETH using the calibrated parameter set are shown in Figure 4. The calibrated parameter set is consistent with values that are found in the literature (Table 2). Some doubts remain about the model parameters and associated processes that have been recently added to TOPKAPI-ETH and which were not considered by previous modeling studies from the study region (Snow redistribution by gravity: SGRa, SGRC; melt below glacier debris: TFdebris, SRFdebris).

Figure 4.

Measured runoff and calibrated runoff simulated by TOPKAPI-ETH for the period 2001–2003.

[43] The plausibility of the parameters for melt under debris can be evaluated by relating the model outputs to recent studies. In comparison to a TOPKAPI-ETH model run where debris is not considered, glacier melt from debris-covered glacier areas simulated with the optimal model run is lower by 60%. Mihalcea et al. [2006]; Kayastha et al. [2000], and Mattson et al. [1993] measured the variation of mean daily ice ablation in function of debris thickness on glaciers in the H-K region: according to these studies, a reduction of 60% of melt rates corresponds, in comparison to melt from clean ice, to a debris thickness of 20 cm [Mihalcea et al., 2006], 15 cm Mattson et al. [1993] and more than 40 cm [Kayastha et al., 2000]. A glacier survey by Bishop et al. [1995] on Batura glacier (in the Naltar subcatchment, Figure 1) estimated debris thickness on the terminus of the Batura glacier to be highly variable, but mainly above 30 cm. A mean debris thickness between 15 and more than 40 cm, corresponding to the calibrated melt parameters, therefore lies in the range of plausible values for glaciers in the Hunza River Basin.

[44] In order to assess the model performance corresponding to the calibrated parameter set, 2000 parameter sets are generated randomly within ±10% of their calibrated value. Model performance when running the model for each of the 2000 parameter sets is shown in Figure 5. In the explored region of parameter values, the calibrated parameter set is close to optimality (with a resulting Nash and Sutcliffe value of 0.93 and a total mass balance error of 3.1%). To further improve model performance, as well as to validate the consistency of simulated internal processes, detailed local information on physical processes would be required.

Figure 5.

Nash and Sutcliffe efficiency (NSE) and difference to total measured runoff (%): shown are the results for the calibration period (2001–2003) using 2000 parameter sets where parameters are varied randomly within ±10% of their calibrated values. The cross represents the model efficiency using the calibrated parameter set, which in this case is close to optimality.

[45] The analysis of parameter information content (sections 4.4 and 5.1) will provide more evidence about which parameter values need to be confirmed by measurements and which variables can be used for multivariate calibration, in order to identify a parameter set that can be used for reliable simulations of future response.

4.2. Future Projections

[46] Runoff projected with the three downscaled GCMs is shown in Figure 6, together with the snow- and icemelt, evapotranspiration, and rain. Results are shown for the entire Hunza River Basin and for the five subregions of the watershed. Simulated decadal mean runoff at the outlet of the Hunza River Basin is relatively constant in the next 50 years, but there are significant differences in the reaction of different subregions to a changing climate: while runoff from the Ziarat area will decrease to less than 50% with respect to the control period (2001–2010, Figure 6e), runoff from Hispar and Shimshal catchments might increase in the future (Figures 6c and 6d).

Figure 6.

Mean annual values of runoff and water balance components per decade projected by TOPKAPI-ETH using the three downscaled GCMs (CGCM3, CM2, and MIROC3) and the calibrated parameter set. Error bars represent the standard deviation in projected values, calculated from 100 model realizations for each stochastically downscaled GCM.

[47] The simulated decrease in runoff from Ziarat can mostly be attributed to reduced icemelt, as mean snowmelt, rain, and evapotranspiration show only little relative change (Figure 6). The ELA (calculated as the mean elevation where simulated annual accumulation equals ablation) on the glaciers in the Ziarat subregion is at 5327 m for the control period, which is higher than in any other subregion (Table 3) and is the result of both high temperatures and low precipitation. Only 14.5% of the present glacier area in the Ziarat subregion is located above this elevation. Even considering that for Karakorum glaciers the accumulation area ratio might be naturally small due to the steep topography and the large role of avalanches for snow accumulation, this value seems small and is an indication that already for the present climate, the glaciers in the Ziarat subregion might not be in an equilibrium state according to our simulations. As a consequence, projected future glacier area decreases drastically (Table 3). Figure 7 shows the seasonality of the simulated control period runoff compared to projected runoff for the period 2041–2050. The months that are most affected by a decrease of runoff in Ziarat are June to September. It is also evident that maximum annual runoff will occur earlier in the year (in June/July) as compared to July/August during the control period (Figure 7e).

Figure 7.

Hydrograph of mean monthly runoff, simulated with the calibrated parameter set and the three downscaled GCMs (CGCM3, CM2, and MIROC3): results are shown for the control period (2001–2010) and for the last simulated decade (2041–2050).

[48] Simulated runoff from the Hispar and Shimshal subcatchments increases due to enhanced snowmelt (Figures 6c and 6d), which is the result of increasing precipitation and higher (summer) temperatures (Table 3). However, those projections should be treated with some care, since no meteorological data from the present are available for these subregions (see the discussion in section 5.4).

[49] Figure 7 shows how projected runoff depends on the GCM used. While MIROC3 leads to a general increase in simulated runoff throughout the entire year, overall runoff will decrease in the next 40 years according to the CM2 GCM, especially for the months of July/August. This finding is valid for the overall Hunza River Basin as well as for subregions, except for Ziarat, where according to all applied GCMs, a decrease in future runoff can be expected. CGCM3 projections represent an intermediate scenario with no significant changes in the runoff regime of the Hunza River Basin.

4.3. Uncertainty in Future Response

[50] Error bars in Figure 6 show the uncertainty (95% confidence interval) in TOPKAPI-ETH projections related to the variability in model results in each set of 100 simulations for the three downscaled GCM. This uncertainty is due to the short-term natural climate variability. This source of uncertainty—the stochasticity of precipitation and temperature—is compared in Figure 8 to the parametric uncertainty and the uncertainty given by the ensemble of the three GCMs. The effect of sources of uncertainty on simulated runoff, snowmelt and icemelt is not constant in time and in space. In terms of absolute values, the strongest effect on decadal, mean simulated runoff is calculated for Hispar subbasin and parametric uncertainty (Figure 8c). Here, ±10% uncertainty in parameter values leads to 350–400 mm/yr uncertainty in simulated runoff (equivalent to 20.7–23.6 m3/s). For Kunjerab, parametric uncertainty affects simulated runoff only by 25–50 mm/yr (or 1.8–3.7 m3/s), which in this subcatchment is less than the uncertainty due to the two other sources. It is therefore evident that both the relative importance of different sources of uncertainty and absolute values vary in space. Regarding the variabiliy in time, the effect of parametric uncertainty on simulated runoff often decreases with time (especially if simulated glacier area and runoff are decreasing—e.g., Ziarat) while the uncertainty due to the climate model increases with time (for all subregions). Uncertainty in simulated runoff due to the stochasticity of meteorological variables also increases with time, but less than the uncertainty due to the climate model. Note that Figure 8 shows only the stochastic uncertainty resulting from CGCM3 climate simulations. Parametric uncertainty simulations were also conducted with CGCM3 time series of precipitation and temperature.

Figure 8.

Uncertainty in simulated runoff and snow- and icemelt: 95% confidence interval in model outputs resulting from ±10% parametric uncertainty (param. ±10%), from using stochastic time series of precipitation and temperature (reflecting the natural interannual climate variability) and the maximum difference in model outputs resulting from the climate model uncertainty (running the model with three downscaled GCMs).

4.4. Information Content of Parameters and Variables

[51] Figure 8 shows that the effect of only ±10% parametric uncertainty often introduces a greater amount of uncertainty than the climate model or the stochasticity of meteorological variables. Considering the limited information available about optimal parameters in the region, it is thus worth to investigate more in depth which parameters and variables affect simulated runoff uncertainty.

[52] Figure 3 shows the CDFs of parameters for which we calculate some of the highest information content. The increasing vertical distance between pairs of CDFs for the parameter Pgrad with time indicates that the information content of this parameter is not constant in time or might depend on the length of the simulation period. Table 4 ranks all parameters exceeding the significance level α = 5%/34 (34 parameters, see Table 2) according to their information content. The rank of sensitivity according to the Plackett-Burman sensitivity analysis is indicated in brackets. Because of the rigorous threshold criterion, only nine parameters exceed the significance level in any of the tests for the Hunza River Basin or any of the five subregions. According to the ranks indicated in Table 4, the temperature lapse rate (Tgrad) is the parameter with the highest information content. It is followed by the parameters α1 and SRF. After five decades of simulations, the information content of Pgrad exceeds that of SRF for the Hunza River Basin. Concerning the seasonal differences in information content (Table 5), it can be noticed that some of the soil parameters ( inline image and θs,low) control runoff during the low-flow period in winter, while the parameters listed in Table 4 are more important in summer.

Table 4. Ranks of Parameters According to Their Information Content Calculated for the Hunza River Basin, for Each Subregion and the First (2001–2010) and the Last Decade (2041–2050) of Runoff Simulationsa
 Decade 1Decade 5
NaltarHisparShimshalZiaratKunjerabHunzaNaltarHisparShimshalZiaratKunjerabHunza
  1. a

    In brackets the ranks according to the Plackett-Burman sensitivity analysis. The information content of all parameters listed in Table 2 was assessed but only parameters exceeding the α threshold in at least one of the Kolmogorov-Smirnov tests are shown here. Rank x denominates parameters that do not pass a significance test, and −99 indicates that the information content cannot be determined.

  2. b

    Δh parameterization: glacier movement component [Huss et al., 2010b], GlaH: initial glacier thickness.

Tgrad1 (1)1 (1)1 (1)1 (1)2 (2)1 (1)1 (1)1 (1)1 (1)1 (1)1 (1)1 (1)
α12 (2)2 (2)2 (2)x (3)1 (1)2 (2)3 (3)2 (2)2 (2)x (26)2 (2)2 (2)
SRF3 (3)x (3)x (3)2 (2)3 (4)3 (3)x (8)x (3)4 (4)x (9)5 (7)4 (4)
Pgradx (4)x (8)x (4)x (10)x (22)x (6)2 (2)x (6)3 (3)2 (3)x (28)3 (3)
CropFx (6)x (11)x (10)x (9)7 (6)x (7)4 (4)x (9)x (10)3 (2)3 (3)x (5)
Tmodx (5)x (4)x (6)3 (4)4 (3)x (4)x (7)x (5)x (7)x (8)6 (6)x (7)
Exphx (16)x (35)x (30)x (7)6 (7)x (14)x (36)x (21)x (24)4 (5)4 (5)x (18)
TTx (7)x (5)x (5)x (6)5 (5)x (5)x (21)x (13)x (6)x (7)x (11)x (8)
α2x (8)x (7)x (7)x (12)x (15)x (8)5 (6)x (4)x (5)x (29)x (8)x (6)
Δh parameterizationb−99 (21)−99 (14)−99 (13)−99 (24)−99 (21)−99 (16)−99 (5)−99 (16)−99 (8)−99 (11)−99 (12)−99 (14)
GlaHb−99 (9)−99 (9)−99 (11)−99 (5)−99 (11)−99 (9)−99 (14)−99 (26)−99 (11)−99 (4)−99 (4)−99 (10)
Table 5. Rank of Parameters According to Seasonal Information Content Calculated for the Hunza River Basin, for the First (2001–2010) and the Last Decade (2041–2050) of Runoff Simulationsa
 Decade 1Decade 5
Jan–MarApr–JunJul–SepOct–DecJan–MarApr–JunJul–SepOct–Dec
  1. a

    Only parameters exceeding the α threshold in at least one of the Kolmogorov-Smirnov tests are shown. Rank x denominates parameters that do not pass a significance test. Parameters are described in Table 2.

Tgrad31113113
α1723x623x
SRFxx2xxxxx
Pgradxxx6xx26
CropF5xx55xx5
Exphxxx4xxx4
θs1xx21xx1
s2xx32xx2
slow4xxx4xx7
Ksh,low6xxx9xxx
Expvxxxx7xxx
θs,lowxxxx8xxx

[53] The same procedure used for calculation of the information content of parameters is applied to assess the information content of water balance components and internal variables. We use the same model realizations obtained by varying model parameters: this allows to analyze how individual model components affect overall model uncertainty given the ±10% parameter uncertainty. A significance level of less than α = 5%/n for water balance components (n = 4) and α = 5%/n for variables (n = 10) is required for the water balance components and variables, respectively, to be identified as important (Table 6). The ranks for water balance components reflect the fact that the Hunza River Basin is a snow- and icemelt-dominated catchment. The uncertainty in these components affects most dominantly the uncertainty in total runoff. The uncertainty in modeled rain affects uncertainty in modeled runoff only during end of summer and autumn (with increasing importance until 2041–2050). The low rank of evapotranspiration (ETA) in Table 6 for the last decade 2041–2050 masks the fact that the information content of this water balance component increases with time: for Ziarat and Kunjerab, it increases by 0.36 and 0.12, respectively, from the first to the fifth decade of simulations (absolute values of information content are not shown). This is also why the crop factors (CropF, controlling crop evapotranspiration) and the parameter controlling the ratio between horizontal permeability and saturation (Exph) have high ranks for these subregions (Table 4), as these parameters control the amount of water available for evapotranspiration. As snow and ice cover are reduced over time and temperature increases, the importance of ETA in the overall water balance increases.

Table 6. Rank of Water Balance Components and Selected Variablesa According to Their Information Content Calculated for Each Subregion, the First (2001–2010) and the Last Decade (2041–2050) of Runoff Simulations, for the Entire Hunza River Basin and Each Seasonb
 Decade 1Decade 5
 NaltarHisparShimshalZiaratKunjerabHunzaJan–MarApr–JunJul–SepOct–DecNaltarHisparShimshalZiaratKunjerabHunzaJan–MarApr–JunJul–SepOct–Dec
  1. a

    PrecS and PrecL: liquid and solid precipitation, ETA: actual evapotranspiration, ELA: equilibrium line altitude, Snow cover: percentage of basin area covered by snow, GMB: glacier mass balance, SnowH: mean basinwide snow depth, Glac: percentage of glacier area compared to initial glacier expansion, RadCS*CT: global clear-sky irradiance corrected for clouds, SoilWV: soil water volume.

  2. b

    For the subregions, ranks according to the seasonal information content are not shown. Rank −99 denominates variables for which a seasonal information content cannot be calculated, since outputs are provided only on an annual basis. Rank x denominates variables or water balance components that do not pass a significance test.

Water balance components
Snowmelt22142221331111211143
Icemelt112111x211322213x322
PrecL3332433322233432x211
ETAx44334144xx44344243x
Variables
ELA131321−99−99−99−99222422−99−99−99−99
Snow cover212442x1121115615223
GMB324113−99−99−99−99545715−99−99−99−99
SnowH54353432236533342145
Glac477265−99−99−99−99334243−99−99−99−99
PrecL6557875444466886x311
Temperature76667623317776573432
RadCS*CT8989594566888978456x
PrecS989898x657999199x65x
SoilWVxx10xxx1xx5x1010xx1017x4

[54] Variables describing the cryospheric processes have the highest information content for runoff simulations (Table 6). The equilibrium line altitude (ELA), the percentage of area covered by snow, glacier mass balance (GMB), average snow depth (SnowH), or the total glacier area (Glac) have a higher information content than basinwide mean temperature. Noticeable is the increasing importance with time of the uncertainty in total glacier area on the uncertainty in simulated runoff. For the last decade, this is the variable with the overall third highest information content (Table 6).

[55] Total liquid precipitation (PrecL) often has a higher information content than total solid precipitation (PrecS). This can be explained by the long residence time of water fallen as snow in glacier-dominated regions: the residence time of solid precipitation in the accumulation area of a glacier might easily exceed the 50 years simulation time. As glacier area decreases, the residence time of solid precipitation decreases as well. As a consequence, the information content of PrecS and Pgrad for simulations over a 10 year period increases (Table 4: Pgrad Ziarat, Table 6: PrecS Ziarat). The main reason why in Kunjerab the parameter Pgrad does not have a significant information content is that for this subregion high-elevation meteorological data are available, provided by a station that is situated approximately at the same elevation (4730 m asl) as the mean elevation of the subcatchment (4830 m asl).

[56] The residence time of solid precipitation on glaciers does not depend only on glacier size but also depends on glacier movement. According to the Plackett-Burman sensitivity analysis, the model sensitivity to the glacier movement component increases with simulation time mainly for subregions with decreasing glacier area (Naltar: +11 ranks, Ziarat: +21 ranks, Kunjerab: +8 ranks; see values of information content in Table 4 and simulated glacier area in Table 3). For the entire Hunza River Basin, however, the choice of the Δh parameterization does not seem to have a significant effect on model outputs. A ±10% uncertainty in initial glacier thickness (GlaH) has a considerable effect on runoff uncertainty for Ziarat and Kunjerab (decade 5: rank 4), but for the entire Hunza River Basin, the model is more sensitive to ±10% uncertainty in model parameters (Table 4).

[57] Global irradiance (RadCS*CT) has a low information content compared to other variables (Table 6). This indicates that the radiation component of TOPKAPI-ETH is a robust model component with a strong physical basis and does not require major calibration. Total soil water volume has a high information content only during the low-flow period (Oct.–Mar.). Note that only annual information content can be calculated for the variables ELA, GMB and Glac because of the nature of these variables.

4.4.1. Information Content in Space

[58] While in the previous section the information content was assessed at the basin scale, it is also possible to calculate the information content for single grid cells, so as to assess the effect of uncertainty at the smallest spatial unit on total uncertainty in simulated runoff. While Table 6 provides an indication about variables that would best be observed in order to efficiently reduce total model uncertainty, analysis of cell-information content helps to determine where such observations should take place. We focus on snow- and icemelt, since these are the water balance components with the overall highest information content (Table 6). Following the modified RSA approach, we calculate cell-information content in monthly intervals, using distributed maps of monthly snow- and icemelt provided by 2000 model runs with ±10% parameter uncertainty (simulation period: 2001–2003, see section 4.1). The significance level is reduced to α = 5%/54,861 (the number of grid cells in our study area).

[59] Figure 9 shows the distributed cell-information content with respect to snow and icemelt. Only cell-information content exceeding the significance threshold is shown. Areas with high information content suggest that at these locations, the variability in simulated snow- and icemelt correlates with the variability in simulated monthly mean runoff. In order to understand what controls the spatial variability of information content, we applied a multivariate regression tree analysis to a number of predictors (glacier size, elevation, aspect, sky view factor, subregion, debris cover). This showed that the mean information content per glacier varies significantly among subregions and with the mean sky view factor and aspect of glacier tongues. The seasonal cell-information content is to a large extent controlled by elevation: Figure 10 shows for each month within which elevation range 95% of all cell-information content is located. As the ablation season progresses, the median elevation of monthly snow- and icemelt cell-information content increases and decreases again after August. Table 7 provides a ranking of glaciers with the highest mean monthly cell-information content (sum of snow- and icemelt cell-information content of every glacier grid cell) integrated over space.

Figure 9.

Spatial distribution of the information content (IC) of the water balance components Snowmelt and Icemelt regarding simulated runoff at the outlet of the Hunza River Basin: the map shows the information content calculated for each cell for September 2003. The 2000 random parameter sets are considered for the analysis (±10% parameter uncertainty). Runoff is simulated using measured precipitation and temperature input.

Figure 10.

Median elevation of snow- and icemelt cell-information content regarding simulated runoff at the outlet of the Hunza River Basin, calculated for each month in the period 2001–2003. Error bars represent the elevations within which 95% of all cell-information content is located. Dotted black lines indicate the 95% confidence interval of the total elevation range of the Hunza River Basin, meaning that 95% of its area is located between 2400 and 6100 m asl.

Table 7. Top 10 Glaciers Ranked According to the Sum of Total Glacier Cell-Information Content (Glacier IC), Calculated for Years 2001–2003 Runoff Simulationsa
 Glacier NameSubregionArea (km2)Debris (%)Glacier IC
  1. a

    Mean monthly snow- and icemelt information content of every glacier grid cell are added to calculate total Glacier IC. Area denominates the size of each glacier and debris the percentage of glacier area covered by debris.

1HisparHispar494.7526.7470.8
2BaturaNaltar320.7534.5257.3
3Sat Maro/KukuarNaltar117.7517.0126.7
4KhurdopinShimshal143.5022.0107.5
5VirjerabShimshal143.7519.0102.2
6BaltarNaltar89.2547.394.3
7HasanabadNaltar125.2529.192.0
8Yashkuk YazZiarat74.0042.284.2
9BarpuHispar99.0032.674.3
10Ku-ki-jerabZiarat51.5046.162.0
Mean top 10166.0031.6147.1

5. Discussion

5.1. Parametric Uncertainty

[60] The parameters with a high rank in Table 4 are the ones that should be monitored in the field to substitute calibrated by measured values when possible. Variables and water balance components with a high rank in Table 6 can be used to increase the accuracy of model projections by using their measured values in a multivariate calibration approach. Since it is difficult to obtain accurate distributed estimates of water balance components, these could be monitored at the point scale and values could be used in a multivariate, multistep calibration approach, where parameters governing, e.g., snow and icemelt, are first calibrated at the point scale, and other parameters are determined in a second step by using measured runoff as a calibration criteria. The feasibility of this approach to calibrate TOPKAPI-ETH model parameters was demonstrated by Ragettli and Pellicciotti [2012].

[61] In order to conduct effective field campaigns, information on snowmelt processes should be collected from April to June (Table 6) at elevations between 3500 and 4500 m asl. Icemelt processes should be monitored at approximately the same elevation from July to September (Figure 10). Since processes might vary from one glacier to another, Table 7 provides recommendations for possible study sites. According to Table 7, the uncertainty about snow- and icemelt on some of the largest glaciers of the Hunza River Basin (e.g., Hispar and Batura glacier) introduces most uncertainty into final simulated runoff. However, also some smaller glaciers with heavy debris cover appear to have a high information content, such as Baltar glacier (no. 6 on Figure 1), Yashkuk Yaz glacier (no. 8) or Ku-ki-jerab glacier (no. 10) (Table 7). Although debris-melt parameters (TFd, SRFd) do not seem to have a significant information content in comparison to other parameters, debris-covered glaciers taken as a whole do have a high information content for runoff modeling. The uncertainty in the spatial variability of debris thickness and its effect on runoff is not considered in the ranking in Table 7, because our model can only account for spatially and temporally uniform debris thickness. The actual information content of extensively debris-covered glaciers is therefore likely to be higher than indicated in Table 7.

[62] Figure 8 shows that the effect of parametric uncertainty on uncertainty in simulated runoff often decreases with time. For Ziarat subregion, this can be explained by the decreasing glacier area (Table 3) and therefore a change in hydrological processes controlling uncertainty in simulated runoff. Some subregions show an increase in future runoff and icemelt (e.g. Hispar, Figure 6) but still a decrease in the effect of parametric uncertainty (Figure 8). For the Hispar subcatchment, both mean temperature and annual precipitation increase until 2041–2050 (Table 3), while uncertainty in simulated icemelt and therefore in runoff decreases (Figure 8); a change in the seasonality of processes might explain the decreasing uncertainty in simulated icemelt, as more solid precipitation leads to a shorter period of glacier melt, which apparently reduces total uncertainty in this component. The physical properties of a watershed such as the elevation range or total glacier area define the effect of parametric uncertainty to a large extent. However, the effect of parametric uncertainty depends also on the climatic input and the selected GCM. The values of future information content of parameters and variables (Tables 4-6), might therefore also depend on the choice about a GCM and associated climate projections.

[63] Furthermore, parametric uncertainty and parameter information content depend on the sampled initial range of parameters (section 3.4.1). Tgrad is the parameter with the highest information content. Its calibrated value is 0.00725°C m−1, which is between the environmental and the dry adiabatic lapse rate. This is what we would expect for the relatively dry and cold environment of the Karakorum, in contrast to more shallow lapse rates in more monsoon-affected regions of the Himalaya [Kattel et al., 2013]. Similar high values were obtained for other dry high-elevation environments [e.g. Pellicciotti et al., 2008]. There is growing evidence about strong spatial and seasonal variability of this parameter [e.g., Petersen and Pellicciotti, 2011; Petersen et al., 2013], which cannot be taken into account in this case because of lack of data. This further justifies the high information content of Tgrad, as more accurate data about magnitudes of Tgrad in the Karakorum, as well as its seasonality and spatial variability could reduce model uncertainty substantially.

5.2. Climate Model Uncertainty

[64] Table 3 shows that all GCMs predict an increase in mean temperature until the decade 2041–2050 and an increase in liquid precipitation (PrecL). The GCM that leads to the strongest overall increase in runoff (Figure 6 and Table 3), MIROC3, projects the strongest increases in both temperature and precipitation compared to other GCMs. CM2 is the only GCM that projects a decrease in solid precipitation (PrecS) and the lowest values of projected future runoff, for the Hunza River Basin as well as for all subregions.

[65] Total projected glacier area (Glac) using the CGCM3 and MIROC3 climate scenario are very similar (20% decrease in 40 years, Table 3), while CM2 is slightly more conservative in terms of glacier area change (16% decrease in 40 years). Positive glacier mass balances (GMB) calculated for the Hunza River Basin correlate with a stagnation or decrease in total runoff (Table 3: CGCM3 and CM2), in agreement with findings by Sharif et al. [2013].

[66] Regarding the ELAs reported in Table 3, CGCM3 projects similar future temperatures and more solid precipitation than CM2, but the 2041–2050 ELA is higher on average. Therefore, differences in the seasonality of temperature and precipitation among GCMs are also affecting model results. Lower summer temperatures and more summer accumulation and cloudiness reduce glacier-ice ablation during the main melting season [Fujita and Ageta, 2000; Hewitt, 2011], and lead to lower ELAs in spite of less annual precipitation. Recent investigations from the Upper Indus report greater summer cloudiness and precipitation [Archer and Fowler, 2004], lower summer temperatures [Fowler and Archer, 2006], and increases in diurnal temperature ranges with lower minimum temperatures, a pattern that might not be sufficiently taken into account by current GCMs [Fowler and Archer, 2006].

[67] Differences among the GCMs are an indication that the number of GCMs included in the analysis might affect the conclusions about future basin response to climate change. Our results therefore suggest that for sound projections of future runoff and glacier response, GCMs outputs should be used in an ensemble manner. Since GCMs carry a large portion of uncertainty on regional scales [Prein et al., 2011], the use of only three GCMs in this study is a limitation, imposed by computational constraints.

5.3. Stochastic Uncertainty

[68] The stochastic variability in simulated future runoff is directly linked to future climate forcing, whose stochasticity can be derived from the climate statistics obtained from downscaled GCMs [Fatichi et al., 2011, 2013]. Table 3 shows that the stochasticity in temperature is very low, with a standard deviation in mean decadal temperatures of only 0.1°C for the Hunza River Basin (Table 3, control period and GCMs 2041–2050). The standard deviation in observed monthly mean temperatures is rather low also for the present (Figure 2). Stochasticity in temperature can thus not explain the stochastic variability in simulated runoff. The situation is different regarding precipitation: the stochastic uncertainty in liquid or solid precipitation exceeds the effect of the assumed parametric uncertainty on precipitation (Table 3, e.g., the standard deviation in Hunza 2041–2050 PrecS is more than 2 times larger in CGCM3 stochastic simulations than due to ±10% parameter uncertainty). In comparison to the control period, the standard deviation of solid and liquid precipitation increases in the future according to all GCMs (except for MIROC3 and solid precipitation). The higher probability of the occurrence of particularly wet or dry years is therefore responsible for the increasing uncertainty in projections about future decadal mean runoff (stochastic uncertainty in Figure 8).

5.4. Glacier Mass Balance and Climatic Input

[69] According to the modeling results, the total mass of glaciers in the Hunza River Basin is more or less stationary during the control period (Table 3; mean GMB Hunza 2001–2010: +0.12 m/yr). This is in accordance with recent studies based on geodetic mass balance observations [Gardelle et al., 2012; Kääb et al., 2012], which reported relatively stable glacier mass balance for the Karakoram for the early twenty-first century. However, Table 3 shows also that there are strong differences among subregions: while simulations indicate negative glacier mass balances in the north of the study catchment for the control period (Ziarat: −2.07 m/yr, Kunjerab: −0.31 m/yr), stable mass balances are calculated for the southwest (Naltar: −0.09 m/yr) and positive glacier mass balances for the southeast (Hispar: +0.45 m/yr, Shimshal: +1.13 m/yr). Such a strong spatially variable response of glaciers to climate change has been described previously by Scherler et al. [2011b], who used repeated satellite images to track glacier changes and found that 58% of the studied glaciers in the Karakoram were advancing or stagnant, while 42% of them were retreating. Sarikaya et al. [2013, 2012] identified a spatial trend in glacier fluctuations within northern Pakistan, with shrinking glaciers in the west and a greater frequency of advancing glaciers toward the east. This west-east gradient agrees with the pattern of simulated glacier mass balances in this study: Ziarat in the northwest shows more negative mass balances than Kunjerab in the northeast of the study catchment, and mass balances simulated for the subregions in the southeast (Hispar) and east (Shimshal) are more positive than in the southwest (Naltar). In glacier surveys by Hewitt [2005], 13 glaciers in the southeastern Karakoram (including three glaciers in the Shimshal valley, two Hispar glaciers, and two glaciers in Naltar) were found to be growing; some of the larger glaciers exhibited a thickening by 5–15 m over substantial ablation zone areas within only 5 years. Although glacier advances and elevation rise in the ablation zone may be the consequence of glacier surges [Mayer et al., 2011], these observations might also be an indication of positive mass balances, as mass balance has an important control on the frequency of glacier surging [Copland et al., 2011].

[70] The studies cited above confirm the plausibility of TOPKAPI-ETH simulations and indicate that the climatic input provided by the three stations might represent adequately the climate within the Hunza River Basin. However, the value of 1.13 m annual mass gain for Shimshal glaciers is very high. Likely, precipitation in the Shimshal basin is overestimated when using Naltar climate data and linear precipitation gradients. Winiger et al. [2005] identified the “Batura Wall” as the main precipitation divide between the wetter West Karakoram rainfall regime and the drier central Asian rainfall regime. Therefore, the northern part of Shimshal valley is likely drier than assumed in our simulations, as supported also by Immerzeel et al. [2012b]. However, no climate data are available for this area. To reduce the uncertainty due to the low density of meteorological stations, climate data representative of high-elevation regions, both South (Hispar) and North (Shimshal) of the Batura wall, are required.

[71] On the other extreme, mass balances for Ziarat are very negative, even compared to regions of the world where glacier retreat is well documented [e.g. Haeberli et al., 2007; Huss et al., 2010a]. Ziarat glaciers are extensively debris covered (Table 1), but very little is known about the characteristics of the debris mantles (thickness, conductivity, saturation conditions). Therefore, investigations should focus on the spatial variation of the debris layer characteristics and its effect on melt. If debris on Ziarat glaciers is thicker than in other subregions, mass balance may be less negative than simulated, as our model considers only uniform debris thickness.

[72] The uncertainty about the climatic input for areas where we calculate positive mass balances affects TOPKAPI-ETH simulations additionally because of the uncertainty about the correct representation of glacier advancement. The present version of TOPKAPI-ETH does not reproduce glacier advancements (section 3.1.1). Of the seven glaciers in the study region with positive mass balance studied by Hewitt [2005], terminus advances have been observed at four glaciers. We suggest that in order to increase the accuracy of models for the region, efforts should be made to better understand the dynamics of glaciers in the region and how to implement it in distributed glaciohydrological models.

6. Conclusions

[73] In this study the physically oriented, distributed glaciohydrological model TOPKAPI-ETH is used to assess and compare the effect of three sources of uncertainty on projections of future runoff from the Hunza River Basin, Karakoram, in northern Pakistan. The sources of uncertainty assessed are: (i) the uncertainty due to model parameters, (ii) the climate model uncertainty, and (iii) the uncertainty due to the natural interannual climate variability in precipitation and temperature. We investigate the spatiotemporal variable relevance of the sources of uncertainty and use an innovative approach to determine which model components are introducing the main uncertainty in model outputs.

[74] All the three sources of uncertainty have a significant effect on model projections, but we show that especially for heavily glacierized subregions, parametric uncertainty exceeds the effect of other sources of uncertainty. Also the lack of meteorological data about high-elevation temperature and precipitation strongly increases the effect of parametric uncertainty, as the extrapolation of meteorological input introduces additional uncertainty into model results. The uncertainty in simulated decadal mean runoff due to the stochastic nature of the meteorological input exceeds the simulated effect of climate model uncertainty 30–40 years into the future.

[75] The scarcity of data is characteristic of the vast majority of H-K catchments. In order to overcome this problem, modelers have until now applied relatively simple models, calibrated against sparse and short records of mountain climatic variables and runoff [e.g., Immerzeel et al., 2010; Tahir et al., 2011b] despite the fact that their accuracy cannot be systematically evaluated. We show that parameters drawn from the literature enable modelers to simulate a plausible response to climate change with a distributed, physically oriented model like TOPKAPI-ETH: simulated streamflow for the present agrees well with observed data and general patterns of modeled glacier mass balance are in accordance with recent studies in the region based on remotely sensed data or direct observations. However, the uncertainty about accurate internal process representation cannot be sufficiently constrained due to the lack of data for model calibration and validation. Aiming to improve the reliability of model projections, we make detailed suggestions about field data which could be used most efficiently to reduce model uncertainty. In a region where logistical, financial, and political obstacles severely complicate the collection of new data, detailed suggestions about the location and timing of fieldwork are of great value. We suggest an iterative approach where first the available process understanding provides the basis for setting up a physically oriented glaciohydrological model, then field data are collected on the basis of the results of an uncertainty analysis, which is a priori a modeling exercise. The data collected in this way will lead to better constraining the sensitive model parameters and an improvement in our understanding of processes, and in turn to more robust model simulations. A key advantage of our methodology is that it can be applied also to ungauged catchments. An application of the iterative approach to other H-K watersheds is thus encouraged and will allow a direct comparison with our results.

[76] Our work demonstrates that future efforts to predict the response of high-elevation catchments to climate change must consider ensembles of parameter sets and the entire range of available climate projections. The differences in climate projections concern differences in mean annual values of temperature and total precipitation but also in the variability and the seasonality of future climate. Model results show that all these characteristics of GCMs have significant effects on model output and should therefore be taken into account. Finally, future work should investigate the effect of interactions between sources of uncertainty, in order to attribute a full range of possible scenarios for future water availability in the region.

Acknowledgments

[77] The authors thank the Water and Power Development Authority of Pakistan (WAPDA) for providing the hydrometeorological data used in this study. Glacier and debris maps were provided by ICIMOD, which is gratefully acknowledged. We would like to thank very much Stefan Rimkus for support with TOPKAPI-ETH and Paolo Burlando for supporting Silvan Ragettli's work at ETH.

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