Title: Analyzing Linear Glacier Surface Elevation Change: A 10-Year Descent from 1,200m to 900m

When studying glacial dynamics, one key metric—surface elevation change over time—offers critical insight into climate impacts and environmental change. Consider a glacier whose surface elevation drops linearly from 1,200 meters to 900 meters across a 10-year period. Understanding the average annual rate of descent helps scientists, policymakers, and the public grasp the pace of glacial retreat.

The Linear Descent Pattern

Understanding the Context

The elevation begins at 1,200 meters and decreases steadily to 900 meters over 10 years. This straight-line decline reflects a consistent annual reduction in height, making it a prime example of linear change. Geospatial and glaciological studies often model such changes using basic mathematics to estimate trends and project future behavior.

Calculating the Average Annual Rate of Descent

To find the average annual elevation loss:

  1. Total elevation change = Final elevation – Initial elevation
    = 900 meters – 1,200 meters = –300 meters
A glacier’s surface elevation decreases linearly from 1,200 meters to 900 meters over 10 years. What is the average annual rate of descent?

Key Insights

  1. Time period = 10 years

  2. Average annual rate of descent = Total change / Time
    = –300 meters / 10 years = –30 meters per year

The negative sign indicates a decrease, but for reporting rates of decline, the magnitude is typically emphasized: the average annual rate of descent is 30 meters per year downward.

Implications of the Rate

This rate—30 meters per year—is significant in glaciological terms. While regional variations exist, a loss of 30 meters annually in surface elevation reflects rapid glacial thinning, often linked to warming temperatures, reduced snow accumulation, or increased melt rates. Monitoring such trends aids climate research, improves predictive models, and informs environmental policy affecting water resources and sea-level rise projections.

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Alternatively: The volumes form a geometric sequence with first term \(a = 729\), ratio \(r = 1/2\), and we want the number of terms \(n\) such that the sum \(S_n \geq 729\). But sum starts at 729, so \(n=1\). Not useful.
Correct model: The volumes are:
\(V_1 = 729\)

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Final Thoughts

Conclusion

A glacier surface elevation decreasing linearly from 1,200 meters to 900 meters over 10 years demonstrates a clear and measurable retreat. The average annual descent of 30 meters annually underscores the accelerating impact of climate change on cryospheric systems—data that is vital for understanding and responding to global environmental shifts.

Keywords: glacier surface elevation, linear decline, annual descent rate, 10-year change, glacial retreat, climate change impact, elevation loss, 1,200m to 900m over 10 years.