Exercise: Glacier Elevation, Volume and Mass Change 1. Changes in the glacier density profile can result in changes in glacier elevation. Changes in glacier elevation therefore do not directly translate into changes in glacier mass. The following set of questions is designed to highlight the importance of density changes when inferring mass changes form measured volume changes. Below is the semi-­‐empirical densification rate according to Arthern et al., 2010: −3
d ρ ⎪⎧0.07A( ρi − ρ ), ρ <= 550 kg m
=⎨
dt ⎩⎪0.03A( ρi − ρ ), ρ > 550 kg m −3
⎡⎛ -60000 ⎞ ⎛ 42400 ⎞ ⎤
A = exp ⎢⎜
⎟⎠ + ⎜⎝
⎟⎠ ⎥ × ( b × 9.81) ⎝
T
×
8.314
T
×
8.314
⎣
⎦
A has units of yr-­‐1 T = temperature [K] T = mean annual temperature [K] b = average mass accumulation rate [kg m-­‐2 yr-­‐1] a. The following figure gives the steady state conditions for b = 250 kg m-­‐2 yr-­‐1 and: i. T = -­‐30, initial snow density of 300 kg m-­‐3 ii. T = -­‐20, initial snow density of 300 kg m-­‐3 iii. T =-­‐10, initial snow density of 300 kg m-­‐3 Match the profiles with the corresponding steady state conditions. 1 b. Draw profiles (i) and (iii) if the precipitation rate tripled. Think about this very carefully! c. Do you think that the overall density profile is going to be very sensitive to the assumed initial snow density, say in the range 200 – 400 kg m-­‐2? What is your reasoning behind your answer? d. In both (a) and (b) interannual and diurnal change in T were neglected (i.e. T = T ). If this had been accounted for how would they dρ
have affected the results? [hint: does change linearly with T?] dt
2 e. Redraw the density profile of (a.ii) if it had experienced a sudden warming of 5 K in the most recent 5 years. f. Can you think of a physical justification for the sharp change in the rate of densification once the firn density reaches 550 kg m-­‐3? 2. There are many sources of uncertainty in glacier volume change estimates. The most obvious source of uncertainty comes from the uncertainty of the elevation change estimates, which decreases as the area of sampling increases. a. What are the approximate areas of glaciers 1 and 2 (below). Area 1 = _____________ Area 2 = _____________ b. Determine the uncertainty of the volume change estimates for glaciers 1 and 2 (below) given the provided semivariogram and knowing that the uncertainty in a point elevation measurement is ±1m. Hint: the uncertainty ( σ ) of the mean of N uncorrelated values each with an uncertainty of E is: E
σ=
N
3 4 3. Horizontal offsets between different elevation products are common due to georeferencing errors and must be corrected for before elevation changes can be determined. a. If a glacier has a symmetric geometry, how will an erroneous horizontal offset between two DEMs acquired at times t1 and t2 affect the overall estimate of volume change? Now what if the glacier is not symmetric? b. If the uncertainty of the elevation change estimates are determined as the root-­‐mean-­‐square error of the elevation difference between the two products over ice free terrain, how will a horizontal offset affect the estimated uncertainty of the volume change? c. Would a 100-­‐meter offset have a large impact on the uncertainty estimate over a smooth ice cap or a steep icefield? 4. Below are two spatial maps produced from time series of filtered GRACE Level 2 data (spherical harmonics of gravity field in mm w.e.). For each map, describe what parameter is being plotted [i.e. trend, amplitude, phase, or frequency] and list at least 4 regional geophysical signals that can be identified in each figure. 5 parameter: regional geophysical signals: parameter: regional geophysical signals: 6 5. Unlike other instruments, GRACE is able to directly measure regional changes in mass. This means that GRACE is not sensitive to changes in the glacier density profile and, because GRACE has complete global coverage, mass change estimates do not require extrapolation of point observations. That said, GRACE is not able to directly separate changes in glacier mass from other mass change signals. To separate out other sources requires the use of land surface, climate reanalysis, and GIA models and/or well-­‐constrained regional observations. a. Do you think it is easier to separate glacier mass changes from other mass change signals for (a) continuous glacier systems or (b) highly dendritic glacier systems and why? Give real-­‐world examples of each. b. Why do GRACE derived glacier mass anomalies have much smaller uncertainty bounds for Greenland than for the Antarctic? Think about what the ground is doing? How can the large Antarctic mass change uncertainties be reduced? 7