Effect of snowpack removal on energy balance, melt andrunoff in a small supraglacial catchment - Willis, Arnold and Brock, 2002

Hydrological Processes and Snowpack Removal

• This study focuses on modeling melt and runoff from snow- and ice-covered catchments, using a physically based model to assess the impact of snowline retreat on meltwater routing. The study area is a small supraglacial catchment (0.11 km^2) on Haut Glacier d’Arolla, Switzerland.

Introduction

• Importance of Modeling Melt and Runoff:
  • Water resource management.
  • Hazard management (avalanches and floods).
  • Assessing glacier contribution to sea-level change.
  • Scientific study of glacier hydrology, dynamics, and hydrochemistry.
• Types of Models: statistical, lumped, conceptual, semi-distributed, and physically based distributed models.

Aims of the Study

• The study further develops, tests, and uses the surface melt and surface routing components of a physically based, distributed glacier hydrology model.
  1. Testing the Surface Melt Component:
     • The surface melt component of the model is tested against hourly ablation measurements in a supraglacial catchment.
  2. Testing the Coupled Surface Melt and Surface Routing Components:
     • The coupled model is tested against hourly runoff measurements at a supraglacial catchment outlet.
  3. Investigating the Effects of Snowpack Depletion:
     • The study uses the coupled model to investigate the effects of snowpack depletion on hourly patterns of energy balance, melt, and runoff.
     • This is important for understanding glacier hydrology, dynamics, and hydrochemistry, especially regarding changes in subglacial drainage systems and basal motion rates.

Field Site

• The study was conducted on Haut Glacier d’Arolla, Valais, Switzerland.
  • Glacier length: Approximately 4 km.
  • Area: About 6.3 km^2.
  • Altitude range: 2600 m a.s.l. to over 3500 m a.s.l.
• La Vierge Catchment:
  • Area: 0.11 km^2.
  • Elevation range: 2885 m a.s.l. to 2980 m a.s.l.
  • Orientation: Approximately due north with steep slopes (>20°) in the upper part and gentle slopes (<5°) near the outlet.
  • Drainage: A dendritic supraglacial stream network drains the catchment, terminating at a moulin.

Methods and Preliminary Data Reduction

• Measurement Period: July 22 (JD 203) to August 25 (JD 237), 1993.
• Digital Elevation Model (DEM):
  • 162 points surveyed using a Geodimeter 500 Total Station.
  • A Triangular Irregular Network (TIN) was created with a 10 m contour interval.
  • DEM created with a resolution of 5 x 5 m.
  • The supraglacial stream network position was calculated using the FLOWACCUMULATION routine.
• Calculated Energy Balance and Melt:
  • Spatial variations in energy balance and melt computed using a distributed surface energy balance model.
  • Requires initial snow depth distribution and meteorological data.
  • Initial snow depth distribution obtained by surveying snow depth at 12 locations and interpolating/extrapolating across the DEM.
  • Polynomial smoothing routine chosen with deeper snow on concave slopes and thinner snow on convex slopes.
• Meteorological Data:
  • An automatic weather station was installed near the catchment outlet.
  • Hourly averages of incoming shortwave radiation $(W/m^2)$, air temperature (K), wet-bulb temperature (K), wind speed $(m/s)$, and hourly totals of precipitation (m) were recorded.
  • Equations used to calculate radiation fluxes (Arnold et al., 1996) and turbulent fluxes (Brock et al., 2000b).
  • The model accounts for slope angle, slope aspect, shading, atmospheric emissivity, and atmospheric stability.
• Albedo and Roughness Length:
  • Spatial and temporal variations in albedo ($\,alpha$) and roughness length for wind speed ($z_0$) were determined empirically.

Albedo Equations:

• Ice albedo ($\alpha<em>i$) is calculated from: $\alpha</em>i = -490.880 + 0.344E + 6.077 \times 10^{-5}E^2$ where E is elevation (m a.s.l.).

• Snow albedo ($\alpha<em>s$) is calculated from: $\alpha</em>s = (1 - exp(-d/d^<em>))\alpha<em>{ds} + exp(-d/d^</em>)\alpha</em>{ss}$
  $\alpha<em>{ds} = 0.713 - 0.112 log</em>{10} T<em>{max}$$\alpha</em>{ss} = \alpha<em>i + 0.442 exp(-0.058T</em>{max})$
  where ds and ss refer to deep snow and shallow snow respectively, Tmax is the accumulated maximum daily temperature since the last snowfall (°C), and $d^*$ = 2.4 cm w.e.

• Roughness Length Equations
  $z<em>{0i} = 2.25$$z</em>{0s} = e^{[1.3343(\arctan(\frac{\log<em>{10}(T</em>{max}) - 1.6855}{0.0957}))-1.0460]}$

• Rainfall:

  • Rainfall measured at the weather station was assumed to fall evenly across the catchment.

• Melt:

  • A Campbell Scientific ultrasonic depth gauge (UDG01) was installed to measure melt near the catchment outlet.
  • Hourly averages of air-density-corrected distance measurements were recorded.
  • Ablation rates were calculated by differentiating these data and converted to units of water equivalent.

• Supraglacial Stream Discharge:

  • Spatial variations in water routing computed using a distributed supraglacial routing model.

  • Water flow assumed down the steepest slope from cell to cell to the catchment outlet.

  • Time taken for water to percolate vertically through the unsaturated snow pack $(t<em>u, s)$ calculated from: $t</em>u = \frac{\phi d}{(\frac{\rho<em>w g}{\mu</em>w})^{1/3} k^{2/3} q^{2/3}}$
    where $\phi$ is the effective snow porosity, d is snow depth (m), $\,mu_w$ is the viscosity of water ($1.8 \times 10^{-3} Pa \cdot s$), k is the relative unsaturated snow permeability $(m^2)$, and q is the water flux per unit area through the snow pack $(m/s)$.

    • Time taken for water to flow laterally through the saturated snow $(t<em>s, s)$ calculated from: $t</em>s = \frac{L}{(\frac{\rho<em>w g}{\mu</em>w}) k S}$
      where L is the cell length (m), S is the surface slope, $\phi$ is the snow porosity and k is the intrinsic saturated snow permeability $(m^2)$.

  • Manning's equation used to calculate water flow across ice:
    $t_i = \frac{nL}{R^{2/3}S^{1/2}}$
    where n is the Manning roughness coefficient $(m^{-1/3}s)$, R is the hydraulic radius of the ice surface (m).

• Supraglacial Stream Discharge:

  • A Druck pressure transducer was installed to measure water pressure in the supraglacial stream near the catchment outlet.
  • A stage-discharge curve was constructed to convert water level data to discharge.

Results

• Calculated Energy Balance and Melt
  • Diurnal net shortwave radiation fluxes were always directed towards the surface (positive)
  • Net longwave fluxes generally directed away from the surface (negative)
  • Turbulent fluxes generally directed towards the surface (positive)
  • Marked diurnal cycles ranging from a minimum of c. -1 mm w.e. h-1 at night to a maximum of c. 4 to 8 mm w.e. h-1 during the day
• Measured Ablation
  • UDG records show within 2-3 cm w.e. and 0.7 cm w.e. of the manual measurements over snow and ice respectively.
  • The time-series of measured ablation rate is also shown in Figure 8.
  • Apparent negative ablation rates occurred during most nights for several hours between 2000 and 0800.
• Calculated Supraglacial Stream Discharge
  • The discharge hydrographs are quite different depending on the parameter values used.
  • High values of Sw produce more flashy diurnal cycles with less pronounced recession limbs.
• Measured Supraglacial Stream Discharge
  • The measured discharge hydrograph shows many of the characteristics of the calculated hydrograph, including the gradual increase in the amplitude of diurnal variation and the gradual eradication of the ‘delayed-flow’ part of the diurnal hydrograph as the snow pack is removed.

Discussion

• Comparison of Calculated and Measured Ablation Rates
  • The agreement over the 33 days is very good although the model tends to slightly overestimate melt.
  • Negative QMc values represent radiation cooling of the glacier surface.
  • Negative QMa values imply apparent accumulation at night and may result from three factors: (i) error associated with thermal contraction of the UDG mast as it cools; (ii) error in the estimation of the distance between the UDG and the surface owing to the use of air temperature measured at the UDG height to represent the air temperature between the UDG and the surface; (iii) freezing of water or water vapour on the glacier surface.
  • It seems likely, therefore, that negative QMa values were mainly the result of surface freezing.
• Comparison of Calculated and Measured Supraglacial Stream Discharges
  • The agreement over the 21 days is good although the model overestimates low discharges and underestimates high discharges, suggesting that it does not quite account sufficiently for the delaying influence of the snow pack.
• Snow Pack Depletion and Effects on Energy Balance Components and Total Melt
• Over the whole measurement period, the radiation fluxes contributed 86% of the melt energy and the turbulent fluxes contributed the remaining 14%.
• During ice cover, air temperatures and vapour pressures were higher, and incoming shortwave radiation was lower than earlier melt periods indicating the meteorological conditions maskes the influence from snow to ice albedo.

Snow pack depletion and its effect on diurnal runoff cycles

• the effects of albedo on runoff characteristics
• the effects of the delaying influence of the snow pack on runoff characteristics
• the combined effects of albedo and snow pack delay on runoff characteristics

Snow pack depletion and implications for subglacial drainage

• Snowpack depletion within a supraglacial catchment increases peak diurnal discharges entering the moulin
• Snow pack depletion substantially reduces the minimum diurnal discharges entering the moulin.
• Hydraulic gradients between the main subglacial drainage system and surrounding areas of the bed will steepen, causing the drainage of water from the surrounding areas.

Summary and Conclusions

• A physically based, distributed numerical model was used to calculate melt and water routing across a supraglacial catchment on Haut Glacier d’Arolla.
• Minor discrepancies on an hourly basis of the melt model tested against hourly measurements of ablation at a site are caused by subsurface melting, surface water freezing, and melting of the frozen layer.
• Supraglacial stream discharge is impacted by five periods of anomalously high measured runoff corresponds with moulin overflow events.
• The snow pack decreases daily mean discharge, reduces maximum discharge, increases minimum discharge, lowers discharge range, and increases the lag between peak melt and discharge.
• Maximum and minimum discharges are altered as a result of both the higher albedo and the greater attenuating influence of snow than ice contributing to subglacial drainage from hydraulically inefficient to more hydraulically efficient.