Date Last Modified April 27, 1999
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Glaciers, Energy and Mass
By: Jennifer L. Aschoff and Megan O’Connor

 
Net Energy Balance
Positive Energy Balance
Negative Energy Balance
Mass Balance
Ablation
Accumulation
Positive
Negative
Equilibrium
Positive
Negative
Flow
Advance
Retreat

Energy Balance
The 1st law of Thermodynamics says:
 Energy is neither destroyed or created.
Newton's first law of thermodynamics correlates well with glaciers in that energy in a glacier are never destroyed
or created but instead cycles through the glacier as a system.

Energy Balance Equation: Qm = Qs + Ql + Qn + Qe
The energy balance equation is the sum of all inputs and outputs of energy into a glacier system. The two main components of energy in a glacier are net radiation and net convection.
                   Net Radiation: QR = Qs + Ql
There are two energy sources from radiation: short wave radiation and long wave radiation.  The tow together form the net radiation of a galcier.
                                                          Short Wave Radiation ( Irradiation) (Qs)
Qs = Gl + Ga + Gr
 insolation (G1)
 re-emission (Ga)
 irradiation flux (Gr)
Energy enters into a glacier in the form of short wave radiation from the sun.  This energy has three components:
insolation is the part of the sun's radiation that is transmitted to the surface to the glacier directly; re-emission is the
portion of the sun's radiation that is absorbed by particles in the atmosphere and then projected to the earth's surface; irradiation flux is when short wave radiation first strikes a surface other than the glacier on the ground and then is transmitted to the glacier surface.
                                                               Long Wave Radiation (Radiosity) (Ql)
 Ql = E + pQs
emission (E)
 reflectance (p)
Long wave radiation is produced when short wave solar radiation from the sun is absorbed into a system and re-emmited into the atmosphere.  Long wave radiation can either form by emission or reflectance.

                                                                                  Net Convection

Qc = Qn + Qe
  Sensible Heat (Qn)
Latent heat (Qe)
Convestion is heat transfer as a result of air movement close to the surface of a glacier.  Thus it depends on the temperature, velocity, and distribution of wind in an area.  There are two components of convesction: sensible heat is heat that you can sense; and latent heat is heat release due to phase changes between ice, water and vapor. Laten heat transfer is covered more in our mass budget section.



 
 
 
 
 
 

Geothermal Gradient

Geothermal heat is another factor to consider in a glaciers energy balance. As depth increases, geothermal heat also increases.  This change in geothermal heat with depth is defined by the geothermal gradient.  Therefor, at the base of a glacier heat from the subsurfcae may input heat into the system adding to the energy balance of a glacier. 
 
 
 
 
 
 
 
 

 



Mass Budget
Give me a Simple Explanation, something easier


Transformation
Snow- Firn- Glacial Ice
Snow 
no change since it fell - Least Dense (50- 400 Kg/m3) 
Firn 
Intermediate transformation stages (400-830 Kg/m3) 
   Glacial Ice 
No pore space, air as bubbles only Most Dense (830-910 Kg/m3)

 

Glaciers are not homogenous masses of ice, they contain zones ice, snow and debris that vary in density as well as in flow character. 
Each winter adds a new surface of ice and snow. Each summer ablates a portion of the winter surface.  This results in a mass balance, however the balance is not exact, and is termed here as a "budget". 

 
 Accumulation - Net gain of mass via. wind, snowfall, avalanching ect
Ablation- Net loss of mass via. melting
 

     Annual balance (budget) cycles - net gains/ losses of mass over the term of 1 year (May Not Balance Exactly)
     Long Term balance (budget cycles)- retreat/advance, thickening /thinning delayed Lag time accounted for
Balance Ratio
      Ration between Ablation Gradient and Accumulation Gradient
      BR=bnb/bnc
     summarizes the overall mass balance curve for a glacier- used to calc. ELA
       High Ratio= small area of ablation
       Low Ratio= Larger area of ablation

 
Mass Balance Velocity is the velocity of a glacier which depends only on the amount of mass within a given cross sectional area. 
 Mass Balance Velocity Equation
Q(x)= ?(wx*bx) 
   V(X)= Q(x)/ A(x) 
   Q(x)= cross sectional discharge (water equivalent) 
   V(x)= mass balance velocity 
   A(x)= cross sectional area 
    wx= width
                         bx= Net Balance

 


Flow
Give me a Simple Explanation, something easier
The flow of a glacier can be divided into three main sections: deformation of ice, sliding, and deformation of the bed.
Surging glaciers are also another topic related to the flow of a glacier.


Deformation of Ice
Zones of Deformation Within a Glacier 
A glacier has two zones of deformation, a plastic lower zone and a brittle upper zone.  Crevasses form in the upper brittle zone due to flow of ice where temperatures are low and stress is high.Temperature and pressure variations in the ice along with a density contrast create these two distinctive zones. The plastic zone of a glacier is higher in density with higher temperatures and will form features such as folds and will be the part of the glacier that is able to flow wiht out fracuring.
 
Visco-elastic type deformation 
Ice is a visco-elastic substance.  It deforms viscously at low shear stresses and elastically at higher shear stresses. An analogy to this behavior is silly putty.

This figure demonstrates the non-linear relationship between sheer stress and strain rate within the glacier. 
 

 
Glen's Flow Law
E =kTsn
 E = Strain Rate 
     k = Glen's Flow Law Constant (depends on Temp.) 
     Ts = Shear Stress 
    n = Glen's Flow Law Exponent (constant) Ranges 1.9-4.5
 Glen's flow law explains the behavior of a glacier with respect ot strain rates and shear stress.  The figure above displays that as temperature increase, the Glen's flow law parameter increases (n).  Synthisizing this inforamtion with the graph to the right, we can see that temperature decreases towards the top of a glacier, thus Gen's Flow Law (E) will decrease and thus the flow of the galcier will be slower.
  Temperature Variation within a glacier 

 
 
 
 
 

  Normal Stress
Tn= pgh
p = density
g = gravitational constant
h = thickness
Normal Stress is the stress acting down on a surface due to the pull of gravity. The equation above shows that the normal stess will increase with an increase in density and thickness of a glacier. The figure to the right shows the vaitions in normal stress over an irregular bed of a glacier.  The normal stress will be higher when the glacier flows on the upstream side of a bedrock knob and lower on the downstream side of the same obstacle. Normal stress parameters are further explained in the diagram delow.

 
 

     Shear Stress 
Ts=pghsina
p = density
g = gravitational constant
h = thickness
a = angle shown on the figure above

 
 Normal Stress and Shear Stess Components
The figure to the left shows that normal stress in the stress acting perpendicular on the surface of a glacier.  Shear Stress is the stress acting parallel to the surface of the glacier or its bed.  Normal stress increases with depth into the glacier as the overburden of ice increases.  As normal stress increases, shear stress also increases with respect to the bed. 

 
 
 
                  Creep 
                   (crystal dislocation) 
   Ice is polycrystalline, each crystal composed of atoms. During dislocation creep,(or just creep) the ice crystals deform by dislocation of atoms along the basal planes of the ice. As each crystal is deformed, recrystallization occurs allowing the crystal to maintain it's quisiequdimensional shape. This figures shows that glaciers move by the dislocation of individual crystals and not as a whole. 

A Few Surface Features Related to Flow of a Glacier
Crevasses generally form in regions of compression or extension.  These compressive and extensional regions are generally formed by a variation in flow velocity over a given area.  Therefor the glacier responds by brittle fracturing.


Sliding


One way that a glacier can flow is by regelation sliding.

Regelation- refreezing on downglacial and melting on upglacier side
Regelation depends on the normal stress (Tn) acting on a glacier.

Tn=Pi-Pw 
    Tn= Normal Stress 
     Pi = Ice Overburden Pressure

               Pw= Pore Water Pressure 

 Increased pressure on the upice side of the obstruction induces pressure melting.  Pressure melting thus increases the pore pressure and decreases the overall normal stress, allowing the ice to flow over the obstuction.  On the downice side of the obstuction the pressure is decreased and refreezing occurs.  Refreezing on the downice side of the obstruction releases heat which flows to the upice side of the obstruction where it facilitates melting.

Adhesion  is defined as a glacier near pressure melting point.  With increased adhesion the glacier will be able to slide more becasue of the effective pore water pressure at the base of the ice. 

Deformation of the Bed
The bed of the glacier is critical to glacier flow as well as glacier morphology.  Pore pressure, temperature and cohesion of the bed affect the resistance experienced by the glacier at the ice bedrock interface.  The resistance then, affects the shear stress, which increases or decreases the flow of the glacier as well as the types of features observed on the glacier surface.
 
Cohesion Values (kPa)

Sand                     0 
Gravel                   0 
Bentonite Clay      10-20 
Glacial Clay           70-150 
Till                        150-250 
Sedimentary Rock 1000-20000 
Igneous Rock        35000-55000 

Coulomb Equation 
                 Tst= c+ TnTan(phi)

        Tst= Total Shear Strength 

   c= Cohesion of bed material
Tn= Normal Stress
      Tan(phi) = Coefficient of Friction 

 

picture of a surging glacier here
Surging Glaciers
by definition are a glacier in which sudden, brief, large scale displacements occur (Ritter et al., 1995).
 The flow of a surging glacier is defined by two phases. The first is the
  Active Phase at which time ice transferred from the upper part of the glacier towards the
terminus (active to stagnant portion of the glacier)
   The second phase is the Quiescent Phase
   at which time ice builds up in upper portion of glacier and ablation of the terminus occurs.

 
 
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