HolmesCo: Groundwater Assessment

Week 8 handout — Regression and extrapolation

This is a fictional document for teaching purposes.

HolmesCo

Geological Consultants Since 2019

“Our Trends Hold Water”™

GROUNDWATER RISK ASSESSMENT

Prepared for: Teesdale Aggregates Ltd

Project: Bollihope Quarry Expansion, County Durham

Report No.: HC-2026-0512

Date: March 2026

Classification: CONFIDENTIAL

1. Introduction

HolmesCo was commissioned by Teesdale Aggregates Ltd to assess groundwater conditions at Bollihope Quarry, near Frosterley, County Durham. The quarry operator is seeking planning permission to deepen extraction by 8 metres. The Environment Agency requires evidence that (a) the controls on groundwater levels are understood, and (b) the deepened quarry will not drain the local aquifer.

2. Data

HolmesCo installed a monitoring borehole at the quarry in January 2022. Groundwater levels and monthly rainfall have been recorded continuously since then — a total of 48 monthly observations (January 2022 to December 2025).

3. Analysis Part A: What controls groundwater level?

HolmesCo fitted a linear regression model to determine whether rainfall controls groundwater levels:

groundwater_level = β₀ + β₁ × monthly_rainfall + ε

Results

Parameter	Estimate	Std. Error	p-value
Intercept (β₀)	142.3 m AOD	1.8	< 0.001
Rainfall (β₁)	+0.038 m per mm	0.008	< 0.001

R² = 0.45 F(1,46) = 37.6, p < 0.001

Diagnostic plots

(Instructor: display the four diagnostic plots on screen. Key features described below for reference.)

Residuals vs Fitted:

     +2 ┤ ·  ·        ·  ·         ·  ·        ·  ·
        │  ·  ·        ·  ·         ·  ·        ·
      0 ┤       · ·         · ·          · ·
        │          · ·         ·  ·         · ·
     -2 ┤            ·  ·        ·  ·          ·  ·
        └──────────────────────────────────────────────
          Low fitted              →            High fitted

There is a clear wave pattern in the residuals, repeating approximately every 12 data points.

HolmesCo’s conclusion

“The regression is highly significant (p < 0.001), confirming that rainfall is the dominant control on groundwater levels at this site. R² = 0.45 demonstrates a strong relationship. Higher rainfall leads to higher groundwater levels, as expected.”

4. Analysis Part B: Future groundwater trend

During a site visit in December 2025, the quarry manager noted that groundwater levels had been declining. HolmesCo plotted the monthly groundwater level over time and fitted a linear trend:

groundwater_level = β₀ + β₁ × months_since_start + ε

Results

Parameter	Estimate	Std. Error	p-value
Intercept	148.2 m AOD	0.4	< 0.001
Trend	−0.21 m/month	0.05	< 0.001

R² = 0.52

Extrapolation

HolmesCo projected the linear trend forward:

Date	Predicted level (m AOD)	Status
December 2025 (observed)	138.5	Quarry floor at 140 m — water 1.5 m below
June 2026	137.2	Below quarry floor
December 2027	134.7	Well below quarry floor
March 2028	133.0	Aquifer effectively empty at quarry depth

HolmesCo’s conclusion

“The groundwater trend is unambiguous: levels are declining at a rate of approximately 0.21 metres per month and will reach critically low levels by early 2028. At current rates, the aquifer at quarry depth will be effectively exhausted within two years.

This is actually favourable for the proposed quarry expansion — the declining water table means deepened extraction is unlikely to encounter significant groundwater problems. HolmesCo recommends proceeding with the expansion.”

This report has been prepared by HolmesCo for the exclusive use of Teesdale Aggregates Ltd. HolmesCo accepts no liability for losses arising from use of this report by others.