Problem Set 07: Solution Key

Capstone: GIC Risk and Course-Long Synthesis

Worked Solutions

1. A more conservative dB/dt estimate

Conservative ratio = 500/375 = 1.33, implied GIC scaling factor = sqrt(1.33) = 1.15 -- both smaller than the lab's original values (ratio 1.87, factor 1.37), illustrating that even a more conservative reanalysis still implies a substantially elevated (not merely comparable) GIC risk relative to the modern benchmark.

CriterionPoints
Correct ratio and sqrt-factor arithmetic8
Correct comparison to the lab's original values7

2. Full chain for a different bracketing event

The equivalent Unit 6 quantity would be the Carrington Event's estimated Dst itself (rather than the 2017 event's published -142 nT). Given the genuine, disclosed uncertainty between the two published estimates (-800 nT conservative vs -1750 nT), a defensible choice is to headline the full estimated range rather than a single number, explicitly noting which study each endpoint comes from -- exactly the disclosure practice this course's own lectures and labs follow.

CriterionPoints
Correct identification of the Dst quantity as the Unit 6 equivalent5
Reasoned, non-overclaiming choice of range-vs-single-number presentation5

3. GIC scaling with grid length

Doubling the line length doubles the total GIC magnitude at fixed geoelectric field (since GIC ∝ E x length in this simple resistive model). High-latitude grids like Quebec's are both longer (spanning greater distances) and experience larger geoelectric fields during storms (since auroral/ring-current-driven magnetic disturbances are strongest at high geomagnetic latitude), so both factors compound to increase their GIC risk relative to shorter, lower-latitude grids.

CriterionPoints
Correct linear length-scaling statement5
Correct compounding-factors explanation for high-latitude grids10

4. Course-long synthesis

Example full-credit answer: "The Sun's hydrostatic interior structure (Unit 1) sets the stage for the dynamo-driven magnetic cycle and sunspots (Unit 2), whose stored free magnetic energy powers flares (Unit 3); a flare's associated CME propagates through the Parker solar wind (Unit 4) until it compresses Earth's magnetosphere and drives a ring current measured by Dst (Unit 6), whose rapid field changes ultimately induce the geomagnetically induced currents that can collapse power grids (Unit 7)."

CriterionPoints
At least four units named in correct order with correct one-clause physical link between each15

Grading Notes

Award full marks for correct method, units, and a numeric result consistent with the arithmetic shown (allow reasonable rounding). Verify that the student re-derives the number for this problem's specific inputs rather than quoting a lecture example without adaptation. Watch specifically for unit-conversion errors (Gauss vs Tesla, nT vs T, km/s vs m/s, hours vs seconds), for comparative-magnitude statements given in the wrong direction, and for level-1/level-2/level-3 data-provenance conflation (e.g., presenting the order-of-magnitude flare free-energy estimate as a precise measurement, or presenting a Carrington-Dst estimate as a directly measured historical value) -- these are the most common sources of mistakes in this course.