A methodology for monitoring and modeling of high altitude Alpine catchments

Abstract

Hydrological monitoring and modeling of high altitude Alpine catchments is of paramount importance. This is difficult, however, given the complex logistics of field campaigns and the need for long-term data. Here, we present a method for long term monitoring of high altitude catchments, which we tested within the Alps of Italy. This includes i) extensive gathering of climate data and hydrological fluxes, ii) high altitude field campaigns, and iii) robust physically based glacio-hydrological modeling, providing full account of ice flow, ice and snow ablation, and stream flows. We present an application of this method based on six years (2009–2014) of field monitoring in the Dosdè catchment, in the Italian Alps (17 km², average altitude 2858 masl, outlet 2133 masl), nesting 1.90 km² of glaciers. We demonstrate that i) high altitude Alpine catchments can be monitored in spite of geographical complexity, and ii) a data based approach delivers accurate stream flow estimates and improves our knowledge of flow components in the high altitudes. We then provide some estimates of the recent glaciers’ dynamics, and water resources from this high-altitude catchment, paradigmatic of the recent cryospheric evolution in the Alps of Italy. We estimated an average ice mass loss nearby −1.76E⁸ m³yr⁻¹, i.e. −20% of the ice mass in 2009, possibly pointing to accelerated glaciers’ down wasting. Instream discharges increased (+0.12 m³s⁻¹y⁻¹); however, this requires further monitoring. We then benchmark our findings against recent studies in the Alps, and other glacierized areas worldwide, displaying similarities in present glaciers’ dynamics. We suggest that our robust, yet flexible approach can be used for glacio-hydrological investigation in Alpine (and generally mountain) rivers, and for conjectures of potential future hydrological cycle under climate scenarios.

Keywords

Glaciers field campaigns glacio-hydrological modeling Alps climate change

I Introduction

The evidence of global change as set out by the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (AR5; IPCC, 2013) indicates a large impact on the highest altitude areas, where snow and ice cover ice is projected to shrink down and water resources will likely be modified (Barnett et al., 2005; Bocchiola et al., 2010, 2011; Hagg and Braun, 2005; Immerzeel et al., 2010; Kaser et al., 2010; Meybeck et al., 2001; Migliavacca et al., 2015; Soncini et al., 2015). In some largely populated areas there is a need to foresee the mountains’ fate and the potential extinction of permanent cryospheric areas (Barnett et al., 2005; Bolch et al., 2011, 2012; Diolaiuti et al., 2012a, 2012b; Kääb et al., 2012; Kaser et al., 2010; Viviroli et al., 2007). Change on cryospheric water has impacts on water and food security for downstream populations, and on the riverine environment (e.g. Aase et al., 2009; Groppelli et al., 2011a; Kaser et al., 2010; Viganò et al., 2015). Climate change in mountain areas changes water distribution in space and time (e.g. Bavay et al., 2009; Beniston et al., 1997; Laternser and Schneebeli, 2003; Rohrer et al., 1994), including the frequency of extreme floods and droughts (e.g. Bocchiola, 2014; Bocchiola et al., 2011; Braun et al., 2000; Confortola et al., 2013; Groppelli et al., 2011a; Liu et al., 2003). In the Italian mountain ranges, glaciers account for almost 4.5 km³ of solid water, and they are largely shrinking lately (Diolaiuti et al., 2012a, 2012b; Smiraglia and Diolaiuti, 2015; Smiraglia et al., 2015). In fact, D’Agata et al (submitted) analysed Sondrio Province glacier changes over the last three decades. They found a strong reduction of glacier coverage and the volume change between 2007 and 1981 equal to −1.3 × km³. The importance of the cryospheric water in the Italian Alps has emerged most clearly during the latest dry summers; for example, in 2003 when the contribution of glaciers’ melt saved most of the tributaries of the Po River from the severest droughts. The water budget of the cryosphere is driven on one side by snow cover forming during winter (Bocchiola and Groppelli, 2010; Bocchiola and Rosso, 2007), and on the other side by ablation of snow (Confortola et al., 2013; Groppelli et al., 2011a) and ice (Bocchiola et al., 2010; Hock, 2003, 2005). Ice ablation mechanism may be further complicated by the presence of surface rock debris, i.e. for debris covered glaciers (Azzoni et al., 2016; Bocchiola et al., 2015; Diolaiuti et al., 2006; Mattson and Gardner, 1989; Mihalcea et al., 2008). Knowledge of the response of high altitude areas to recent climate change (e.g. Bocchiola, 2014) is important per se, and as a tool to project forward the consequences of potential climate change within the century (e.g. Groppelli et al., 2011a; Migliavacca et al., 2015; Soncini and Bocchiola, 2011; Soncini et al., 2015). In spite of such, hydrology of the high Alpine areas is poorly studied and little understood, and most catchments are ungauged, thus posing major issues in flow prediction and water resources management within the Alps. Here, we present a generally valid strategy in the form of a template for long term monitoring of high altitude catchments and we report the results of a six-year-long test within the Alps of Italy. The manuscript is organized as follows. In Section II we report the critical issues in high altitude catchment observation and modeling, and we introduce our proposed template. In Section III we introduce the case study catchment. In Section IV we describe our data base, including historical weather and snow cover data, and recently gathered hydrological and glaciological field data, and we instruct on how to apply our methodology. In Section V we provide our outputs and we demonstrate the accuracy of the proposed approach. In Section IV we comment upon improved model performance using our template, we benchmark our results against available studies covering the Alps and other noteworthy areas worldwide and we discuss the model’s portability in other mountain areas. We then draw some conclusions, and implications for hydrological studies in high altitude areas and outline possible future efforts.

II Hydrology of high altitude catchments

2.1 Need for monitoring of high altitude catchments

Medium to long term monitoring of high altitude areas (and especially of snow and ice dynamics therein) entails effort, in terms of money and manpower. Such effort is important, scientific wise, given that it improves our knowledge of the dynamics of the cryospheric environment. However, one wonders whether a good depiction of cryospheric water cycles is only desirable per se, or it may also improve prediction of water resources. Most methods for flow modeling of data-scarce high altitude catchments (i.e. ungauged or poorly gauged catchments, e.g. Seibert and Beven, 2009; Sivapalan et al., 2003) include calibration of hydrological models against observed stream flows, if available (e.g. Konz et al., 2007; Ragettli et al., 2015). To account for ice/snow melt, one would test different values of melt factors, and possibly include/exclude ice flow (e.g. by modifying flow velocity, shear stress parameters, etc.) under a “blind” approach, i.e. with no knowledge of the actual phenomena. To do so, one would (manually/or automatically) modify all of the model’s parameters until a good score in stream flow depiction is reached (e.g. Ragettli et al., 2014). In some cases, even models with no explicit representation of relevant processes (e.g. in the high-altitude areas, with no ice melt and/or ice cover dynamics) may attain acceptable flow representation, at the cost of overly modifying the parameters set via tuning against data (e.g. Ragettli et al., 2014). Such circumstance is often referred to as “equifinality”, i.e. the recognition that “many different model structures and parameter sets that will be acceptable in simulating the available data” (Beven, 2001). However, when pursuing accurate hydrological modeling, including in the high-altitude areas, one may want to reduce the uncertainty in process estimation (i.e. cryospheric dynamics and flow partitioning) given by equifinality by constraining more properly the model’s tuning (e.g. Konz and Seibert, 2010). Here, we try and demonstrate that proper monitoring of high altitude catchments and subsequent constraining of the model’s tuning may indeed result in deeper understanding of the cryospheric fluxes and more accurate assessment of water resources. We do so by: i) providing a generally valid and flexible template for monitoring and modeling of high altitude catchments; ii) displaying an application of the template for a representative case study catchment in the Italian Alps; and iii) demonstrating the gain in accuracy in terms of flow prediction by way of a “sensitivity analysis” against tuning parameters. Our effort is to propose a general, flexible template for high altitude catchment monitoring that may be used by other scientists, providing improved flow prediction exercise.

2.2 A proposed template for modeling of high altitude catchments

Our proposed template is sketched in Figure 1(a), in the form of a flow chart. The framework derives from the authors’ experience of field work and modeling in several mountain areas in the Italian Alps (Bocchiola et al., 2010; Groppelli et al., 2011a) and worldwide (Migliavacca et al., 2015; Soncini et al., 2015, 2016), and it is here illustrated for a specific case in the Italian Retiche Alps. Yet, this is general and portable to other catchments. In Figure 1(b) we report the necessary components split into seven categories: domain of investigation (e.g. hydrology, cryosphere); tools (e.g. hydrological model, snow melt model, etc.); functions linking variables (e.g. snow melt M_s as a function of temperature, and radiation M_s (T, G), etc.); necessary field surveys (ice melt from stakes, etc.); network data (of weather, snow depth, SCA from remote sensing, etc.); model outputs (e.g. ice melt in time at different times and place M_i (t, s)); and model accuracy for end users (i.e. objective measure of matching against observed stream flows). The information necessary to model each component and the interactions between components is also sketched. Specific implementation of the proposed method clearly requires tailoring for each case study, and depends upon the characteristics of the area and the available data and tools. Here, the method is demonstrated with an application for a high-altitude catchment within the Italian Alps, the Dosdè catchment in Sondrio Province (17 km², average altitude 2858 masl, outlet 2133 masl), nesting 1.90 km² of glaciers. In the following, the case study is presented and each component of the methodology is illustrated with specific reference with that catchment.

Figure 1.

(a) Proposed methodology for hydrological modeling of high altitude catchments. In the flow chart they are reported the necessary components, split into seven categories: domain (e.g. hydrology, cryosphere); tools (e.g. hydrological model, snow melt model); functions linking variables (e.g. snow melt Ms as a function of temperature, and radiation Ms (T, G), etc.); necessary field surveys (ice melt from stakes, etc.); data (of weather, snow depth, SCA from remote sensing, etc.); model outputs (e.g. ice melt in time at different time and place M_i (t, s)); and model accuracy for end users (i.e. objective measure of matching against observed stream flows). T(t) is daily temperature, P(t) daily precipitation, G(t) is solar radiation, D(t) daily flow depth at hydro station, Q(t) is daily discharge at outlet section. Mi (t, s) is daily ice melt in a given place (cell) s, Ms (t, s) is daily snow melt, q(t, s) is daily runoff in cell s, h_ice (t, s) is daily ice depth, V_ice (t, s) is daily ice flow velocity. SCA is snow covered area. SWE is snow water equivalent. Bias is systematic error on average, NSE is Nash-Sutcliffe Efficiency. (b) Case study area, Dosdè catchment closed at Federico Dosdè hut, Italian Alps. Available data base is reported, including AWS stations, stream gauge and field surveys on the Dosdè East glacier. Explained in text.

III Case study area

3.1 Dosdè catchment

We demonstrate our method in the glacierized 17 km² Dosdè basin (Sondrio, Lombardia) within the Retiche Italian Alps, closed at Federico Dosdè hut (Figure 1(b)). This nests a number of glaciers of the Piazzi Campo area (e.g. Diolaiuti et al., 2011), covering a total area of 1.90 km² within the catchment. This area is largely paradigmatic of the recent evolution of glaciers in the Italian Alps (D’Agata et al., 2014; Diolaiuti et al., 2012a and b; Maragno et al., 2009). The climate is continental Alpine, with cold winter and moderate summer temperatures. The precipitation regime according to the Köppen-Geiger climate classification (e.g. Peel et al., 2007) belongs to the temperate/cool continental class, with seasonal snow cover above 1000 masl or so (e.g. Bocchiola, 2010; Bocchiola and Groppelli, 2010; Bocchiola and Rosso, 2007) and with a maximum of precipitation during the end of summer and a minimum during winter. The runoff is mainly influenced by snow melt in spring, by ice melt in summer at the highest altitudes and by rainfall in early fall. At the Federico Dosdè weather station (2000 masl) at basin outlet, average yearly temperature (2010–2014) is +1.9°C and average yearly precipitation is c. 1020 mm. The area nests some glaciers included within the Piazzi-Campo group, one of the six most notable glacier groups of the Lombardia region (Diolaiuti et al., 2011; Diolaiuti et al., 2012a). Most notably, the Dosdè East Glacier (0.81 km²), belonging to the Dosdè-Piazzi group, is nested in the catchment. The Dosdè East was recently used as a test site for the performance and efficiency of artificial covers, to reduce magnitude and rates of snow and ice melt (Diolaiuti et al., 2008; Mosconi et al., 2010; Senese et al., 2013). According to Diolaiuti et al. (2011), the glaciers in the Dosdè-Piazzi group covered an area of 8.21 km² in 1954 (17 glaciers and five glacierets), 6.53 km² in 1981 (19 glaciers and six glacierets), 5.55 km² in 1991 (19 glaciers and six glacierets), 4.10 km² in 1999 (13 glaciers and one glacieret) and 3.77 km² in 2003 (16 glaciers and six glacierets), so clearly undergoing large shrinkage lately (Diolaiuti et al., 2011: figures 1 and 2).

Figure 2.

Ice ablation model. Goodness of fit of the modeled values at stakes. Calibration and validation. Explained in text.

IV Data and methods

4.1 Available data base and field campaigns

To model the hydrological cycle of high altitude catchments according to our suggested approach in Figure 1(a), typically a mix of data can be used, coming from i) continuous/sporadic observation networks and data bases, and ii) field campaigns developed on purpose. In Table 1 the full report of the data base here is given. Topographic data come from a DTM (20 m resolution) of the Lombardy region. The Dosdè catchment and the glaciers therein (especially Dosdè East; e.g. Diolaiuti et al., 2011) have been subject to continuous monitoring from the authors during the last decade. Two automatic weather stations are installed in the area, one nearby the catchment outlet (AWS1, 2133 masl, installed in 2009) and one upon the Dosdè East glacier tongue (AWS2, 2850 masl, installed in 2007). These stations are fed via solar panels and measure air temperature, radiation and air pressure (AWS2), plus precipitation (AWS1 only, rain gauge, no heating). Complementary data coming from lower altitude stations were also used; these being the property of the Regional Agency for Protection of the Environment (ARPA Lombardia). These provide temperature, precipitation and snow depth, the latter used for snow melt model estimation (Table 1). Remote sensing data, i.e. 27 Landsat^® cloud free images during 2009–2014 (mostly during spring and summer, when snow dynamics is visible) were gathered to evaluate the snow-covered area for model validation. In July 2009, we installed nearby the Federico Dosdè hut a hydrometric station (2127 masl), measuring stream flows (the water level, plus the stage-discharge equation updated every year during 2009–2014 except for 2012). From 2009, seasonal field campaigns were carried out during spring and summer, including maintenance and data downloading, deployment of ice ablation stakes (14 in 2011 and four in 2014) upon the Dosdè East glacier for assessment of seasonal ice ablation, and snow trenches (snow depth and density profiling; two in 2010 and five in 2011) for snow accumulation and water equivalent estimation. Snow depth measurements were also carried out on the glacier (35 points in 2010, 66 in 2011). In the summer of 2009, ice thickness was estimated using a ground penetrating radar (GPR) along a number of transects and then subsequently interpolated.

Table 1.

Available data base. T is temperature, P is precipitation, HS is snow height, S is solar radiation, L is water level, M_i is ice melt, ρ_n is fresh snow density, ρ_s is snowpack density, SCA is snow covered area.

Station	Alt (masl)	Lat (°N)	Lon (°E)	Variable	Resolution used	Period
Federico hut	2133	46.421	10.198	T, P, S	daily	2009–2014
Dosdè East	2850	46.393	10.219	T, P, S	daily	2009–2014
Oga	2295	46.461	10.343	T, P, HS	daily	2004–2014
Bormio	1125	46.470	10.375	T, P, HS	daily	2004–2014
Vallaccia	2655	46.479	10.202	T, P, HS	daily	2004–2014
Cancano	1930	46.514	10.317	T, P, HS	daily	2004–2014
Livigno	2250	46.521	10.125	T, P, HS	daily	2004–2014
Dosdè hydro	2127	46.423	10.195	L	daily	2009–2014
Seven stakes	2600-2900	–	–	M_i	various	2011, 2014
101 points	2600-3000	–	–	HS	spot	spring–summer 2010, 2011
Three snow pits	2600-2800	–	–	ρ_s	spot	May 2010, June 2011
Landsat	–	–	–	SCA	27 images	April 2010 to September 2014

4.2 Temperature and precipitation modeling

Input of temperature and precipitation need to be added to the main hydrological model (Figure 1(a)). Using data available from all the AWS stations (AWS1, AWS2 within the catchment, plus AWSs from ARPA, as in Table 1), we estimated vertical lapse rates of temperature and precipitation for the area. Monthly temperature lapse rates were taken, ranging from −8°Ckm⁻¹ during July to −4.9°Ckm⁻¹ during December. Total precipitation lapse rate was substantially homogeneous monthly, so an average yearly value was taken of +23 mm/km⁻¹, with no substantial changes with altitude (until 2850 masl of AWS2). The total precipitation was calculated in five stations (Table 1) providing snow depth measurements by adding new snowfalls (with fresh snow density ρ_n = 120 kgm⁻²; Bocchiola and Rosso, 2007). Distributed (i.e. as per 80 m cell) modeling of temperature was pursued by assigning at each cell the temperature as per lapse rates applied upon the reference temperature at the Federico Dosdè station, AWS1. Distributed (i.e. as per 80 m cell) modeling of precipitation was pursued by assigning at each cell the precipitation as per lapse rates applied upon the reference temperature at the Federico Dosdè station, AWS1. Snow precipitation is simulated whenever the local temperature within a given cell is below 0°C. To model snow and ice ablation upon the glaciers’ area, we corrected daily temperatures therein, accounting for the Katabatic Boundary Layer (KBL) with the approach proposed by Braithwaite et al. (2002) and this provided acceptable results (Carturan et al., 2014).

4.3 Ice and snow ablation assessment and snow covered area

Ablation of bare/debris covered ice and snow have to be assessed for hydrological modeling of high altitude catchments (Figure 1(a)). Here, both these processes were modeled by way of a mixed (radiation plus temperature), or enhanced degree-day approach (Hock, 1999, 2003), namely

\begin{array}{l} M_{c i, s} = (T M F_{c i, s} (T - T_{t h}) + R M F_{c i, s} (1 - α_{c i, s}) G) i f T \geq T_{t h} \\ M_{c i, s} = 0 i f T < T_{t h} \end{array}

Therein M_ci,s [mm d⁻¹] is the melting of either clean-ice or snow within a cell, TMF_ci,s [mm d⁻¹°C⁻¹] and RMF_ci,s [mm d⁻¹ W⁻¹ m²] are the temperature and radiation melting factors for either debris-free ice or snow, α_ci,s is the debris free ice/snow albedo (here taken as 0.3/0.7 as an average value from radiation data), T_th is an air temperature threshold (0°C here as from data analysis), G [W m⁻²] is the theoretical clear sky, topographically corrected global radiation. Here, we used the theoretical radiation instead of the observed one, because i) several missing values were found in the radiation data base, ii) observed values in clear sky days substantially matched the theoretical ones, and iii) theoretical radiation values can be used for future projections of glaciers’ dynamics and hydrological fluxes (Confortola et al., 2013; Groppelli et al., 2011a; Soncini et al., 2016), so calibration of the melt model is functional to such application. Preliminary investigation using an additive mixed degree-day approach, as in Pellicciotti et al. (2005), provided less accurate results. The melting factors for snow were assessed using snow depth data from the three available snow gauges featuring a complete enough database (Oga, Vallaccia, Cancano; Figure 1(a)) for the period 2004–2014. Melting factors for bare ice (as no debris cover is present here) were calculated from the data gathered at the ablation stakes during two melting seasons (2011, from July 1 to October 12, and 2014, from August 21 to October 8). We suggest here that SCA images can be used for validation of the snow cover as simulated by the snow melt model (Figure 1(a)). Albeit SCA is a proxy for snow accumulation (and SWE), one is satisfied whenever the model-based estimation of SCA capture properly its remotely measured counterpart (see e.g. Bocchiola et al., 2011). Here, we pursue comparison of the snow covered area on the catchment SCA (%) from our model against Landsat images.

4.4 Ice flow modeling

In hydrological modeling of glacierized catchments it is important to avoid inconsistent “static” glacier cover, unfit for medium- to long-term assessment of ice bodies and especially for projection of hydrological scenarios (e.g. Soncini et al., 2015). Here, we adapted and used a model for glacier flow as driven by gravity (Oerlemans, 2001). We used a simplified force balance and pictured velocity as proportional to shear stress raised to n, i.e. the exponent of Glen’s flow law (n = 3; Cuffey and Paterson, 2010; Wallinga and van de Wal, 1998). When basal shear stress τ_b [Pa] is either known or estimated, and accounting for both deformation and sliding velocity as governed by τ_b , it is possible to model depth averaged ice velocity as

V_{i c e, i} = K_{d} τ_{b, i}^{n} h_{i c e, i}^{} + K_{s} \frac{τ_{b, i}^{n}}{h_{i c e, i}^{}}

with h_{ice, i} [m] ice thickness in the cell i, and K_s [m⁻³ yr⁻¹] and K_d [m⁻¹ yr⁻¹] parameters of basal sliding and internal deformation. Such a model was used in former studies, giving accurate results (e.g. in the Karakoram (Soncini et al., 2015) and in the Andes (Migliavacca et al., 2015)). Basal shear τ_b can be taken as

τ_{b, i} = ρ_{i} g h_{i c e, i}^{} \sin α_{i}

with ρ_i ice density [kg m⁻³], g gravity acceleration [9.81 m s⁻²] and α_i local slope. To estimate ice thickness on the whole glacier’s surface, we used the data from a field survey with GPR carried out during the summer of 2009 upon the Dosdè East glacier (Figure 1(b)). Using equation (3), we back estimated the value of τ_b given by the estimated (with GPR) thickness within each cell of the model. We observed that this value ranged mostly close to τ_b = 80 KPa (consistent e.g. with Baumann and Winkler, 2010). Using the same value as basal shear stress upon whole glaciers’ covered area, we back estimated ice thickness in the areas not covered by the GPR survey by solving equation (3) for unknown h_ice . Avalanche nourishment on the glaciers is accounted for by considering terrain slope (Soncini et al., 2015). When ground slope is larger than a given threshold, progressively more snow detaches (linearly increasing from 0 to 1 within 30–60°) and falls in the nearest cell downstream, where it could melt or start transformation into ice. Once a year, 10% of snow surviving at the end of the ablation season becomes new ice (i.e. full ice formation requires 10 years).

4.5 Glacio-hydrological modelling

A key tool of our proposed methodology for water resources assessment is the glacio-hydrological model, i.e. the one that takes ice and snow melt as input (Figure 1(a)), to assess flow discharge at the basin outlet Q(t) in time (t, daily). Here, we used a semi-distributed, cell based (80 m resolution) hydrological model, developed at Politecnico di Milano, suitable to represent the hydrological cycle of mountain basins (Bocchiola, et al., 2010; Groppelli et al., 2011a; Migliavacca et al., 2015; Soncini et al., 2015). The model tracks the variation of the water content in the ground within one cell W [mm] in two consecutive time steps (t, t+Δt), as

\begin{matrix} W^{t + Δ t} = W^{t} + R Δ t + M_{s} Δ t + M_{i} Δ t \\ - E T Δ t - Q_{g} Δ t \end{matrix}

Here, using the daily time step, R [mm d⁻¹] is the liquid rain, M_s [mm d⁻¹] is snowmelt, M_i [mm d⁻¹] is ice melt, ET [mm d⁻¹] is actual evapotranspiration and Q_g [mm d⁻¹] is the groundwater discharge. Overland flow Q_s occurs for saturated soil

\begin{array}{l} Q_{s} = W^{t + Δ t} - W_{M a x} i f W^{t + Δ t} > W_{M a x} \\ Q_{s} = 0 i f W^{t + Δ t} \leq W_{M a x} \end{array}

with W_Max [mm] the greatest potential soil storage. Potential evapotranspiration is calculated here using the Hargreaves equation, requiring temperature data. Groundwater discharge is expressed as a function of soil hydraulic conductivity and water content

Q_{g} = K {(\frac{W}{W_{M a x}})}^{k}

with K [mm d⁻¹] saturated permeability and k [.] power exponent. equations (4) to (6) are solved using a semi-distributed cell based scheme (Migliavacca et al., 2015). The flow discharges from each cell are routed to the outlet section based upon the conceptual model of the instantaneous unit hydrograph (IUH; Rosso, 1984). For calculation of the in-stream discharge, the model uses two (parallel) systems (groundwater, overland) of linear reservoirs (in series), each one with a given number of reservoirs (n_g and n_s ). Each of such reservoirs possesses a time constant, or lag time (i.e. t_g , t_s ). For each cell the lag time is proportional to the hydraulic path to the outlet section.

4.6 Gain in flow modeling accuracy

After the model’s setup, one has to evaluate its accuracy, measured as the capacity of objectively well representing flow variables (here, Q(t); Figure 1(a)). Here, we chose to use two largely adopted measures of accuracy, i.e. Bias (systematic error, or mean error) and NSE/R² (Nash-Sutcliffe Efficiency; or determination coefficient). We used these two measures to demonstrate the gain in flow modeling accuracy with our approach. We simulated a (hypothetic) condition where we did not carry out field campaigns (and so we have no knowledge) of ice/snow dynamics, but still we need to predict water resources using our hydrological model. We assumed that we knew the optimal parameters of hydrological response (i.e. lag times of the catchment t_g , t_s from calibration), and we could subsequently run the hydrological model using such “correct” (to the extent of our best guess based upon data) lag times. We modified each of the melt factors (TMR_ci,s , RMF_ci,s ) within a range −50% to +50% of the optimal values, and we calculated the resulting stream flows. Clearly, given the linearity of melt against melt factors, the changes in ice/snow melt estimates (against optimal values of TMR_ci,s , RMF_ci,s ) can easily be assessed (i.e. it is proportional to change in melt factors) and so it is not a finding. However, the corresponding error in stream flow modeling quantifies the misjudgment of stream flows when neglecting to investigate duly cryospheric water inputs. We did the same by increasing both TMR_ci,s and RMF_ci,s to quantify the error when changing both melt factors. Also, we tested the performance of the model when assuming “static” glaciers’ behavior. Normally, ice flow is only added if some knowledge of ice depth/velocity is available (and few studies in fact include such feature), so no “indirect” tuning is considered here (i.e. using stream flows). Eventually, we tested the situation when ice/snow dynamics would be measured (and melt models calibrated), and tuning of catchment response parameters was necessary (i.e. by changing t_g , t_s between −50% to +50%). As a result of this comparison, one should know i) how important it is to correctly measure and model cryospheric water fluxes, and ii) once cryospheric fluxes are well modeled, how important it still is to correctly calibrate catchment response (lag times) parameters. We pursued the analysis of performance in calibration and validation (i.e. using the optimal values of t_g , t_s from calibration). The comparison is made by considering two specific indexes, |Bias%| (taken in absolute value for readability), and (1−NSE)%, so that both indexes should be small as possible. We assessed whether any change (−50% to +50%) of the model’s parameters (TMR_ci,s , RMF_ci,s or both, no-ice flow, t_g , t_s ) does provide change in both |Bias%| and (1−NSE)%.

V Results

5.1 Ice and snow ablation and snow covered area

Table 2 reports the results of snow and ice melt modeling exercises. Figure 2 shows adaptation of ice melt to the observed values (18 stakes, with spot surveys, 31 values), including calibration (i.e. model tuning against ice stakes data) and validation (ice ablation back calculated by the model within the 80 m cells containing the stakes). The Bias in calibration (i.e. error on average) is +6%, with R² = 0.72. Estimates of two parameters for ice in equation (1) are TMF_ci = 0.4 mm d⁻¹°C⁻¹, and RMF_ci = 1.5E⁻³ mm d⁻¹ W⁻¹ m². Daily HS data (2004–2014) collected at three stations were used to calibrate the snow ablation model (Figure 3). After a preliminary test, we could use one only set of parameters for snow melt in equation (1), namely TMF_cs = 4 mm d⁻¹°C⁻¹, and RMF_s = 2.1E⁻³ mm d⁻¹ W⁻¹ m², with Bias = +2%, and R² = 0.69 globally (see Table 2 for single snow gauges). In Figure 4 we report the validation for the snow ablation model against data from summer snow surveys, providing cumulated SWE at thaw for years 2010 and 2011 (see details in Table 2). The estimated Bias is −6%, with R² = 0.42. This seemingly indicates that, in spite of the well know variability of snow distribution (Bocchiola and Groppelli, 2010; Tani, 1996), the model performs decently in providing at least average snow accumulation in the catchment. Notice further that resolution of the model is of 80 m, possibly making validation against point wise data more difficult (e.g. Bocchiola et al., 2010).

Table 2.

Glacio-hydrological model parameters, and goodness of fit statistics. Bold values are calibrated against observed values.

Parameter	Unit	Description	Value	Method
α_ci,s	[.]	Albedo, clean ice, snow	0.3, 0.7	AWS1,2
TMF_ci,s	[mmd⁻¹°C⁻¹]	Thermal melt factor, clean ice, snow	0.4, 4	ice stakes, nivometer
RMF_ci,s	[mmd⁻¹W⁻¹m²]	Radiation melt factor, clean ice, snow	1.5E⁻³, 2.1E⁻³	ice stakes, nivometer
t_g, t_s	[d]	Time constant, ground/overland	1, 2	hydrograph
n_g, n_s	[.]	Reservoirs, ground/overland	3, 3	Literature
F_v	[%]	Vegetation cover, average	21	soil cover
K	[mmd⁻¹]	Saturated conductivity	5	calibration flows
k	[.]	Ground flow exponent	2	calibration flows
W_Max	[mm]	Max soil storage, average	42	soil cover
θ_w,θ_s	[.]	Water content, wilting, field capacity	0.15, 0.35	literature
K_s	[m⁻³y⁻¹]	Ice flow basal sliding coeff.	1.5E⁻²¹	literature
K_d	[m⁻¹y⁻¹]	Ice flow internal deformation coeff.	1.9E⁻²⁵	literature
Goodness of fit
Variable	Unit	Description	Bias [%]	R² [.]
M_ci	[mmd⁻¹]	Clean ice ablation, calibration	+6.0%	0.72
M_ci	[mmd⁻¹]	Clean ice ablation, validation cells	+2.2%	0.49
M_s	[mmd⁻¹]	Snow ablation Oga, calibration	+3.4%	0.88
M_s	[mmd⁻¹]	Snow ablation Vallaccia, calibration	+5.9%	0.77
M_s	[mmd⁻¹]	Snow ablation Cancano, calibration	+2.0%	0.41
M_s	[mmd⁻¹]	Snow ablation all, calibration	+2.0%	0.69
SWE	[mm]	SWE thaw, 101 points, validation	−6.14%	0.42
SCA	[%]	Snow covered area 27 images, validation	+2.58%	0.94
Q	[m³s⁻¹]	Discharge outlet, calibration	−1.88%	0.92
Q	[m³s⁻¹]	Discharge outlet, validation	−0.44%	0.94

Figure 3.

Snow ablation model. Calibration using snow depth data at three stations: (a) Oga. (b) Vallaccia. (c) Cancano.

Figure 4.

Validation of snow ablation model vs snow surveys data. (a) 2010. (b) 2011.

In Figure 5 we provide a comparison of the snow covered area on the catchment SCA (%) from our model against our cloud free Landsat images. Table 2 provides Bias (+2.6%), and R² (0.94). Joint consideration of Figures 3, 4 and 5 seemingly indicate a good capability to capture distributed snow dynamics, of the utmost importance in this area.

Figure 5.

Snow covered area SCA from the model vs LANDSAT estimates.

5.2 Glacio-hydrological model

Figure 6 reports the glacio-hydrological model simulation during 2010–2014 against observed flows. In Table 2 we report the model’s performance during the calibration (2010–2011) and validation (2013–2014) phases. For calibration, we did not consider 2009 because i) the first installation of the flow gauging station occurred upon 26 July 2009, so giving a partial representation of stream flow, and ii) the estimated stream flows using the preliminary installation setup and stage-discharge curves would provide possibly inaccurate (and seemingly low) stream flows. Subsequent intervention provided an improved setup and new stage-discharge calibration curves with more credible stream flow estimates in thaw season, taken here to onset upon April 1 (Bocchiola, 2010; Bocchiola and Groppelli, 2010; Bohr and Aguado, 2001). During 2012, the hydrometric station underwent serious damage and no measurements could be made, so we report only modeled flow. As from Table 2, one has Bias = −1.9% and −0.4%, and R² = 0.92/0.94, respectively, for calibration and validation. Figure 6 also shows the modeled contribution of each process (i.e. ice melt, snow melt and rainfall plus base flow) to the river discharge. Figure 7 summarizes the mean monthly river discharge and the simulated contribution of each flow component. During 2009–2014, flow discharge was on average E[Q] = 1.04 m³ s⁻¹, the mean snow and ice melt contribution was E[Q_s] = 0.5 m³ s⁻¹, i.e. 48%, and E[Q_i] = 0.1 m³ s⁻¹, i.e. 10%, respectively, with basically the same shares during the melt months (MJJAS). Snow melt contribution is highest until May (74% or so), with ice melt peaking in August with 21% of the share. Yearly, flow generated from rainfall amounts to c. 0.44 m³s⁻¹, i.e. 42%, while it reaches up to 59% in September.

Figure 6.

Hydrological modeling of the Dosdè catchment. Daily simulations and observed stream flow. CAL is calibration. VAL is validation. Each flow component is reported (ice melting, snow melting, rainfall). Temperature and precipitation at Federico Dosdè station are also shown (right y axis, values upside down).

Figure 7.

Monthly share of flow components in the Dosdè catchment and mean monthly river discharge (right y axis, values upside down).

5.3 Ice thickness and flow model, and mass balance

Figure 8(a) reports estimated ice thickness and Figure 8(b) shows ice flow velocities. Average ice thickness is of 20.4 m (total surface area of 1.90 km²) with a largest value of 35 m within the ablation tongue of Dosdè East, given by ice flow convergence. Flow velocities range between 0.25 and 30 my⁻¹, averaging 8.3 my⁻¹, with the highest velocities in the lowest ablation tongues. Figure 9 displays yearly (2009–2014) estimated ice melt on the glaciers. Figure 10 reports mass balance (in m w.e., yearly, and cumulated) for the sole Dosdè East glacier. Therein are reported for reference the historically estimated mass balance from glaciological surveys (measurements from ice ablation stakes, plus linear regression of ablation against altitude and subsequent averaging on the glaciers) during 1996–2008 (Diolaiuti, unpublished data), joint with our estimates since 2009.

Figure 8.

Ice flow model. (a) Ice thickness (2009). (b) Ice flow velocity (average 2009–2014).

Figure 9.

Figure 10.

Yearly and cumulated mass balance estimates at the sole Dosdè East glacier during 1996–2008 (historical, Diolaiuti personal communication) and 2009–2014 (our estimates).

5.4 Gain in hydrological modeling using our template

Figures 11 and 12 demonstrate the gain in flow modeling accuracy when using our approach. Figure 11(a) and (b) reports the results for calibration and validation (with different color for sensitivity to snow/ice parameters and hydrological model parameters). As is easily seen, in some cases one index between |Bias%| and (1-NSE)% may be smaller than the reference one. Model calibration was pursued here by maximization of NSE, with the constrain of minimum Bias. One may pursue model tuning by only regarding either one of the indexes (i.e. minimum Bias or maximum NSE) so that parameters may exist that provide improvement of that index. However, no configuration of the parameters should exist providing improvement of both indexes. We therefore test the existence of cases when an improvement is found in both indexes, which we may call “dominating” against the optimal (reference) configuration. Figure 12(a) rearranges the indexes in Figure 11(a) and b into a |Bias%| vs (1−NSE)% chart, and shows that there is not one case (neither for calibration, nor for validation) when the models’ performance obtained using modified parameters dominates the performance with optimal values. Accordingly, the optimal model is always a dominating option in terms of combining |Bias%| vs (1−NSE)%, and each model’s set up with “wrong” parameters is lower performing. To account for variability in terms of both |Bias%| and (1−NSE)%, we introduced an “accuracy index” called A_c = [Bias _%* + (1−NSE)%], with Bias _%*= Bias%/Bias%, _max, i.e. the dimensionless ratio between Bias% and its maximum value (in Figure 12(a), Bias%, _max = 19.7%). Such A_c index has a range of variation of 0 ≤ A_c ≤ 200% (i.e. both 0 ≤ Bias _%* and (1−NSE)% ≤ 100%) and weighs equally the performance of the model in terms of Bias and of NSE. So doing, we provide a balanced judgment of the model capability (for each specific set of parameters) to i) capture accurately mean flows (important for water resources assessment on a yearly scale), and ii) capture accurately daily variation (important for flow management purposes, minimum instream flow assessment, hydropower production, etc.). In Figure 12(b) we report A_c , calculated as an average for each parameter’s set, consistently with Figure 11(a) and (b), namely E, _par[A_c ] = E, _par[Bias _%* + (1−NSE)%]. Such index provides a measure of the inaccuracy (weighted upon mean and flow variability) introduced by the wrong assessment of each of the parameters investigated. Figure 12(b) clearly shows that introducing inaccurately assessed cryospheric fluxes, and neglecting ice flow, lead on average to larger inaccuracy than the vice versa case (i.e. E[A_c ] is always larger than the reference case with correct cryospheric parameterization). Notice that this occurs for both calibration (expected, given the tuning of the lag times) and validation. Also, the inaccuracy introduced by improper parameterization of cryospheric fluxes (even in the case of properly tuned hydrological model lag times) is of the same magnitude (and even higher) of that given by improper tuning of the hydrological model (Figure 12(b), t_g , t_s ). Eventually, one can conclude that i) tuning of snow/ice melt/flow parameters using field measurements provides the best assessment of water resources with respect to other configuration of such parameters, ii) the inaccuracy given by mis-estimation of melt fluxes may reach, or even outweigh, that given by hydrological model tuning, and iii) even in the case of acceptable (and yet suboptimal, or “non-dominating”) performance using incorrect cryospheric process parameters, hydrological flux partition (rainfall, snow melt, ice melt) is not optimally represented (the magnitude of the inaccuracy being related, here linearly, to the mismatch between optimal parameters and those chosen for simulation).

Figure 11.

Sensitivity test. Absolute value of the percentage mean error |Bias|% and percentage lack of efficiency (1−NSE)%. In black (hollow/full) snow/ice melt parameters (|Bias|%, (1−NSE)%) and ice flow. In red (hollow/full) lag times (|Bias|%, (1−NSE)%). (a) Calibration case. (b) Validation case.

Figure 12.

Sensitivity test. (a) Dominating options. Absolute value of the percentage mean error |Bias|%, and percentage lack of efficiency (1−NSE)%. Shaded areas (grey/red) indicate areas of potentially dominating options against optimal values. (b) Average values of accuracy index A_c .

VI Discussion

6.1 Improved stream flow depiction

Our template, if reasonably well applied, does increase confidence in hydrological modeling, while delivering increased knowledge of cryospheric fluxes and flow partitioning. This is supported in the present literature. For instance, Ragettli et al. (2014), studying the high altitude Juncal River Basin in the Central Andes of Chile, concluded that data from short-term field campaigns (e.g. snow and ice melt and hydrological fluxes) are needed to complement long-term records (e.g. at low altitudes) for simulating changes in the water cycle, and these data can be used by a spatially-distributed physically-based model, as we did here. Konz et al. (2010), also based on Konz et al. (2007), investigated the use of remote sensing data of SCA to calibrate a distributed hydrological model of a Nepalese Himalayan headwater catchment. They concluded that SCA information (i.e. for snow melt validation) allows a reduction in the equifinality problem, thus producing more plausible partitioning of runoff components. Konz and Seibert (2010) studied hydrology of three glacierized catchments located in Austria and Switzerland, showing that, in addition to discharge observations, glacier mass balance data are needed to constrain model parameters.

6.2 Benchmarking against recent studies in the Alps

Our results further provide some hints for discussion and for benchmarking against recent results in the Italian Alps. Bocchiola et al. (2010) developed a simple hydrological model to evaluate daily flows during ablation season (May to September 2006–2009) for the 11 km² Pantano basin in the Adamello glaciers’ group (Maragno et al., 2009) in the Southern Retiche Italian Alps, 32 km south of Dosdè East glacier here. The basin embeds 2.14 km² of ice cover. Ice melt during ablation season (average 2006–2008, with 2009 being incomplete) was −2.2 m w.e. Here, ice ablation on average (2009–2014) amounted to −1.53 m w.e. Grossi et al. (2013) studied the Mandrone glacier (c. 12 km²) in the Adamello group. They estimated mass balance during 1995–2009 into −1.44 m w.e. per year, with the largest mass loss in 2003 (−3.05 m w.e.). They also provide mass balance of Presena glacier (nearby Adamello, covering ca. 0.95 km²; Figure 1 in Grossi et al., 2013), i.e. −1.50 m w.e. per year (−3.09 m w.e. in 2008), and of Caresèr glacier (c. 2.8 km², c. 15 km North of Adamello; Grossi et al., 2013), with −1.69 m w.e. per year (and −3.32 m w.e. in 2003), again during 1995–2009. Here, during 1996–2008, with the glaciological approach we obtained −1.06 m w.e. per year, with positive mass balance (+0.3 m w.e.) only in 2001 (seen also for Mandrone; see Table 6 in Grossi et al., 2013) and the largest loss in 2003, i.e. −1.8 m w.e. During 2009–2014, using our glacio-hydrological model, we estimated an average mass balance of −1.30 m w.e. per year, with a smallest loss of −0.31 m w.e. per year during 2013. Therein, lower than usual spring temperatures resulted in longer snow cover than normal (see Figure 6 for year 2010, with a low share of ice melt, and Figure 5, with large values of SCA, c. 90%). Garavaglia et al. (2014) investigated recent (1929–1981, 1981–2007) mass balance and flows from the Forni glacier, covering c. 11.4 km² in the Ortles Cevedale group in Valtellina valley, Italy, 27 km east of the Dosdè glacier here (D’Agata et al., 2014). They used a 1-D ice-flow model (Wallinga and van de Wal, 1998), and mass balance gradient (Zuo and Oerlemans, 1997). Recently, during 1981–2007, they found an average mass balance of −0.97 m w.e. yearly, with the largest loss ever in 2003, i.e. −6.36 m w.e. Diolaiuti (2001), Cannone et al. (2008) and, more recently, Smiraglia (personal communication 2015) provided assessment of the mass balance of Sforzellina glacier, covering 0.36 km² in the Ortles Cevedale group (D’Agata et al., 2014), 22 km south-east of Dosdè glacier here. During 1987–2014, the mass balance therein was, on average, −1.06 m w.e. More recently (2000–2014), it reached −1.19 m w.e., with the largest loss in 2003 (−2.20 m w.e.) and again slight gain in 2001 (+0.38 m w.e.). During 2009–2014, the average mass balance was −0.89 m w.e., consistent with our findings here for East Dosdè. Comparison with other glacierized catchments nearby may also help in assessment of flow components (i.e. ice and snow melt). Results from Bocchiola et al. (2010) indicated that c. 50% of the spring and summer flows in the Pantano catchment during 2006–2009 derived from ice and snow ablation, with ice melt share depending on the season, but around 35%. Here, during May to September, snow melt covers c. 47% of stream flows, with ice melt covering 10% or so. Even considering smaller ice cover here than there (15% vs 19%), our results indicate a lower share of ice melt. The Pantano basin covers an altitude range from 2375 masl and 3539 masl, averaging 2786 masl, with ice cover starting at 2562 masl or so (and average altitude of 2850 masl), while Dodsè here covers from 2113 masl to 3364 masl (average 2697 masl), with ice cover from 2595 masl to 3343 masl and average altitude 2950 masl. The difference in average altitude of the catchment and its glaciers is c. 65 m for Venerocolo and c. 250 m for Dosdè. Such circumstance, together with the higher altitude of the Dosdè glacier vs the Venerocolo glacier (100 m or so), may explain the largest share of ice melt for the former than for the latter. Ice flow velocity could not be validated in our study, and literature-based ice flow model parameters had to be used (taken from Garavaglia et al., 2014, valid for Forni glacier and slightly adapted to Dosdè glacier). Here, as reported, we obtained flow velocities in the range 0.25–30 my⁻¹, averaging 8.3 my⁻¹. By comparison, Grossi et al. (2013) used a simplified flow model to assess Mandrone glaciers’ flow velocity, which they estimated c. 16–32 my⁻¹. Garavaglia et al. (2014) validated their flow model of Forni glacier against ice flow velocity measured during 2006 in eight points of the Ablation tongue (2500–2700 masl) using stakes and the Differential Global Positioning System. Velocity therein ranged between 13 my⁻¹ and 37 my⁻¹, with an average value of 23 my⁻¹, however, valid in the ablation tongue.

6.3 The broader context of hydrological studies in mountain areas

Glaciers’ retreat as observed here is consistent with observations in other areas worldwide. In a recent study (Kaser et al., 2010), the Po River (nesting Dosdè) is ranked fourth of the rivers worldwide that is most impacted by shrinking glaciers, the first three being in central Asia (Aral Sea contributors, Indus, Ganges). We can highlight here some recent studies in these key areas. The mountain range of the Hindu Kush, Karakorum and Himalaya (HKKH) underwent measurable climate change in the last 50 years. This led to ice cover shrinking, especially in the southern most part (Bocchiola and Diolaiuti, 2013; Gardelle et al., 2012; Minora et al., 2016; Salerno et al., 2008), with subsequent implications hydrologically (Bocchiola et al., 2011; Soncini et al., 2015, 2016; Tahir et al., 2011). Among others, in Soncini et al. (2016) the authors used field data to model the stream flows in the upper Dudh Koshi River of Nepal (a contributor of the Ganges), at the toe of Mt Everest, nesting the Khumbu and Khangri Nup glaciers. They assessed changes of the hydrological cycle until 2100 based on climate projections from IPCC, AR5. At the half century, they projected yearly contribution of ice melt at 45%, on average, and snow melt at 28%. At the end of the century, ice melt would be 31% and snow contribution 39% or so. The glaciers in the area are projected to thin largely up to 6500 masl until 2100, reducing their volume by −50% or more and their ice-covered area by −30% or more. Soncini et al. (2015) used field data to model the hydrological cycle and ice cover dynamics in the Shigar River of Pakistan (a contributor of the Indus), fed by seasonal melt from two major glaciers (Baltoro and Biafo) at the toe of K2, c. 1000 km north of Khumbu. They assessed changes of the hydrological cycle until 2100, via climate projections from the IPCC AR5. Snowmelt is projected to occur earlier, while the ice melt component is expected to increase, with ice thinning considerably and even disappearing below 4000 masl until 2100. Similarly decreasing ice cover until 2100 for the Braldo River, sprouting from the Baltoro glacier, has been projected, e.g. by Immerzeel et al. (2013). A noteworthy area for investigation of hydrology and glacial dynamics under recent climate change is given by the central Andes of South America (e.g. Kaser et al., 2010). Therein, the water security is at stake under demographic growth, changing climate (Urrutia and Vuille, 2009) and accelerated glaciers’ shrinking (Bodin et al., 2011; Minora et al., 2015; Pellicciotti et al., 2008, 2014; Rivera et al., 2000, 2009). Migliavacca et al. (2015) used field data to assess the potential climate change impacts until 2100 for the Maipo River basin, near Santiago de Chile. They envisioned a decreasing trend of yearly flow until 2100, especially in (Austral) summer. The glacier’s down wasting was projected to largely speed up and, until 2100, the ice loss would range from −24% to −56% (−21% and −39% at 2050) vs ice volume in 1982. As a reference, Pellicciotti et al. (2014) studied the Juncal Norte glacier, north of the Maipo catchment. Using climate scenarios from AR4 of the IPCC, they projected the mass balance of the glacier until 2050 and water production in the Juncal Norte catchment. At the yearly scale, they projected a large (−30%, vs −11% in Migliavacca et al., 2015) decrease of runoff vs the three last decades. Similarly decreasing stream flows in the Maipo until 2100 have been projected by other scientists (Ahumada et al., 2013; Meza et al., 2012). One may thus guess that important continental glacierized areas worldwide undergo qualitatively similar processes of down wasting and subsequent modified hydrological processes. However, such phenomena now display different stages (e.g. in Pakistani Karakoram a relative stability of ice cover was observed so far, i.e. the “Karakoram anomaly;” e.g. Minora et al., 2016), and future evolution may display different timing. Accordingly, monitoring and modeling of the hydro-glaciological processes in these areas are of the utmost importance for water resources assessment. Gathering of field data of cryospheric dynamics represents a pillar of consistent hydro-glaciological modeling under present and potential future climate conditions.

6.4 Model portability and data requirement

Our proposed approach is generally valid for high altitude catchments, and it can be tailored depending upon local settings and data and tools available. First, topographic data are necessary, including ice cover maps. Then, climate data are required, including local observations of air temperature and precipitation (rainfall + snowfall, or snow depth whenever available), or at least some extrapolation to high altitudes. Here, we could count upon the ARPA network, and especially upon a near glacial and a supra glacial station installed for few years which provided usable information. Reading of snow depth or better SWE at melt near the glacier may be useful, but unavailable at times, given the harsh conditions at these altitudes. Here, besides snow depth at three ARPA stations, a large measured snow cover data base was available, including snow pits for snow density and a large array of seasonal snow depth measurements. Accordingly, we could pursue independent calibration and validation of snow melt and snow cover in our model, which, albeit not strictly necessary, still provides proof of robustness. Indirect assessment of the snow melt model may be pursued as reported using remotely sensed SCA (e.g. Bocchiola et al., 2011; Corbari et al., 2009; Parajka and Blöschl, 2008). Also, ice ablation is often indirectly inferred, e.g. by analysis of hydrograph flow components and sensitivity analysis (Ragettli et al., 2015). Here, we could use directly measured ice ablation as from ablation stakes, which are to be used whenever possible to constrain ice melt modeling, including upon debris covered glaciers (e.g. Bocchiola et al., 2010; Minora et al., 2015). Ice ablation stakes may also be used for flow velocity assessment (Migliavacca et al., 2015; Soncini et al., 2015) to calibrate/validate ice flow model, which we did not do here. Use of literature values of flow model parameters and comparison with glaciers nearby may still help in narrowing the range of possible flow velocity values. Here, however, ice thickness estimates were available on the Dosdè glacier, constraining ice flow modeling. Ice depth could be assessed by back estimation from equation (3) (Soncini et al., 2015) via some constraining of shear stress (e.g. Baumann and Winkler, 2010). Surveys of ice thickness would be carried out whenever possible, given that it provides an estimate of the stored water volume. Hydrological measurements at the outlet of high altitude catchments are seldom available, and our measurements here, albeit featuring very precious missing periods, allowed independent validation of the hydrological model. At least one or two years of flow data would be necessary for the model’s assessment (Ragettli et al., 2015; Soncini et al., 2015). Here, ice and snow melt modeling was pursued using a (daily) mixed melt index model, depending upon temperature and radiation (Hock, 1999, 2003). Solar radiation should be gathered near the study area whenever possible, and may also be used to assess snow/ice albedo. However, we have reported that topographically corrected theoretical radiation can be used with acceptable accuracy. More complex, sub-daily energy budget models could be used for melt modeling, pending upon data availability (Bocchiola et al., 2015; Michlmayr et al., 2008; Senese et al., 2012a, 2012b). Evapotranspiration is considered in our model, albeit not measured. This term is low given the high altitude, but in the future measurements of ET may be of interest, especially under increasing temperature for global warming (see e.g. potential increase of ET for mountain catchments in Groppelli et al., 2011a, 2011b; Ravazzani et al., 2014). A distributed, or semi-distributed glacio-hydrological model should be used, provided that it is fast enough to support repeated simulations as required for long term climate change impact assessment (e.g. Migliavacca et al., 2015) while reasonably capturing the observed pattern of snow and ice melt and ice and water fluxes.

VII Conclusions

We introduced here a methodology for monitoring and modeling hydrology of glacierized Alpine catchments, and we provided an application for a high-altitude catchment that we monitored for six years. Our methodology builds on, and benefits from, a decadal experience gathered by the authors working in several mountain areas worldwide, and displays a robust, yet flexible framework for consistent hydrological modeling in glacierized continental areas. Pillars of the method are: i) consistent data gathering from available networks; ii) high altitude field campaigns; and iii) robust physically-based glacio-hydrological modeling. We demonstrated that, in exchange for the burden of data collecting in possibly harsh conditions and of accurate process modeling, one has: i) wider knowledge of the fate of cryosphere and water; and ii) a more accurate depiction of flow timing and partitioning. We gave data-driven guidelines for portability, so that the method can be applied flexibly in a wide array of conditions. Also, our test site exercise suggests interesting pointers, given the need we claimed to unravel the glacio-hydrological dynamics of high altitude catchments in the Alps. Glaciologically-based mass balance in our catchment during 1996–2008 displayed a decrease, with a rate of −0.07 my⁻¹, i.e. with 7 cm more mass loss yearly. By adding our estimate during 2009–2014, one has −0.04 my⁻¹. Considering the sole ice cover depletion during 2010–2014 (with full yearly simulation) from our model, one has −0.037 my⁻¹, meaning a loss of three more centimeters of ice every year. Flow discharge during 2010–2014 increased by +0.12 m³s⁻¹. Several recent studies have indeed demonstrated that measurable climate change is ongoing in the Italian Alps (Böhm et al., 2001; Brunetti et al., 2000, 2006) and that the cryosphere therein is being impacted (Bocchiola and Diolaiuti, 2010; D’Agata et al., 2014; Diolaiuti et al., 2006, 2012a and b; Maragno et al., 2009; Nigrelli et al., 2015). Albeit the likelihood is high that cryospheric changes exert a strong influence upon the recently modified hydrological cycle (see e.g. Bocchiola, 2014), verification is still lacking within the Italian Alps (see e.g. Allamano et al., 2009, for an attempt in the Swiss Alps with reference to extreme floods) and needs to be tackled. Variability of the stream flows and potential effects of climate change in the mountain catchments may also have a tremendous impact upon riverine ecology because flow magnitude, seasonality and even temperature affect river biota (Palmer et al., 2008; Peeler and Feist, 2011; Loperfido, 2014; Viganò et al., 2015; Wilby et al., 2006, 2010) and strategies to monitor, model and manage freshwater ecosystems under climate change are urgently needed. Our proposed method is able to shed light upon the main mechanism of flow generation within high altitude areas, so being suitable for investigating flow variations under changing climate drivers. Our results here may therefore be of great interest for glaciologists, hydrologists, ecologists and policy makers, especially in the fields of water resources management and hydro-power production largely exploiting stream flows in high altitude catchments in the Italian Alps and at potential risk under climate change.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported financially by Sanpellegrino-Levissima under the umbrella of a scientific project aimed at studying the recent changes affecting Dosdè Piazzi glaciers. RS Azzoni is supported by a university grant funded by DARAS (Department of Regional Affairs, Autonomies and Sport) of the Presidency of the Council of Ministers of the Italian government in the framework of the GlacioVAR project (PI G Diolaiuti). Personnel of Politecnico di Milano acknowledges support from I-CARE project, funded by Politecnico di Milano. Bando 5 per Mille 2009.

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