Water Pollution, Graph Interpretation & Theory Testing – Week 5 Lecture 2 Study Notes

Session theme: interplay between water pollution, graph interpretation, and theory-data feedback in science.
Applies concepts to (1) a short math/biology scenario and (2) real field data from Meadowood Recreation Management Area (Virginia).
Deliverables announced
- Week 5 Lecture 2 Assignment (includes snake-spread math problem + graph questions).
- Short film–based assignment (“The Band”).
- A further video lecture/assignment still to come.

Situation
- Invasive snakes arrive via ship at island port.
- Population range expands radially at $v = 2\;\text{km yr}^{-1}$ in all directions (assume perfect circle).
Island dimensions shown on slide
- Short dimension $= 20\;\text{km}$ (likely width).
- Long dimension $= 50\;\text{km}$ (likely length).
Essential geometry
- Radius after $t$ years: $r(t)=2t$ .
- Range area: $A(t)=\pi r(t)^2 = \pi (2t)^2=4\pi t^2$ .
- To “occupy the entire island” we need $r(t)$ ≥ distance from port to farthest shoreline point.
- If port is at one end/corner → use half of island diagonal $d=\sqrt{20^2+50^2} \approx 53.85\;\text{km}$ .
- Required time (upper-bound worst case): $t_{req}=\dfrac{d}{2}=\dfrac{53.85}{2}\approx 26.9\;\text{yr}$ .
- Students must compute precise scenario based on given port location.
Task: Solve, record numerical answer, then resume lecture.

Always note axes labels & units
- $x$ (horizontal, independent), $y$ (vertical, dependent) – confirm reality, not assumption.
Count data series
- Colors/symbols = different variables, sites, treatments, etc.
Ascertain time frame if present
- Week, month, millennia – alters interpretation of “rapid” or “slow.”
Check data span
- $x<em>{min}, x</em>{max}, y<em>{min}, y</em>{max}$ tell absolute magnitudes.
Evaluate rate of change
- Increasing, decreasing, constant, accelerating, decelerating.

Linear
- Constant slope $m$ ; $\Delta y$ proportional to $\Delta x$ .
Exponential
- $y = a e^{bx}$ ; equal $\Delta x$ → ever-larger $\Delta y$ ; slope steepens.
Logarithmic
- $y = a \ln(x)+c$ ; rapid rise at small $x$ , then plateaus.
Parabolic (Quadratic)
- $y = ax^2 + bx + c$ (U-shape / inverted U); direction of effect reverses as $x$ passes vertex.
Instructional emphasis: “A graph tells a story—identify how the story changes with magnitude of $x$ .”

Watershed = drainage basin / catchment feeding a given water body (stream, lake, estuary, ocean segment).
Visual concept
- Ocean at base; river network inland; surrounding land (green on slide) funnels precipitation runoff → channel.
Nesting hierarchy
- Large Potomac River Watershed (red) contains Anacostia sub-watershed (blue) which contains Paint Branch sub-sub-watershed (smallest).
- People typically inhabit multiple overlapping watersheds simultaneously (local → regional → continental).
Scale examples
- Chesapeake Bay Watershed spans VA, WV, MD, DE, PA, NY.
- Mississippi River Watershed covers majority of continental U.S.; subdivided into Missouri, Upper Mississippi, Arkansas, Red, Ohio, Tennessee, Lower Mississippi basins.

Working theory: “More forested watersheds produce lower pollutant concentrations.”
- Rationale: Fewer anthropogenic sources + forest acts as buffer/sponge (filtration, uptake, infiltration).
Pollution type should mirror dominant land-use activity (heavy metals ↔ specific industry, salinity ↔ road salt, nutrients ↔ fertilizer/sewage).
Timing of concentration peaks should align with timing of inputs & hydrologic transport (e.g., winter de-icing salt spikes, spring nutrient runoff after application).
Scientific process roadmap
1. Establish theoretical expectation.
2. Collect observations (field monitoring).
3. Compare: fully consistent? partially? inconsistent?
4. Generate alternative explanations / refined hypotheses.
5. Design new studies → deeper understanding.

Location: ~1 hour south of American University, Virginia.
Three study watersheds (different land-use mosaics)
1. Giles Run – largest, most urban (red/pink land-use).
2. South Branch – medium urbanization; mix of forest & pasture.
3. Thompson Creek – smallest, most forested; some pasture & crops.
Monitoring campaign
- Duration: 2 years, weekly sampling.
- Team: Dr. (Rose?) + undergraduate researchers Jake, Jessica, Youngbae (photo shown).

Specific Conductance / Total Dissolved Solids (proxy for dissolved ions, esp. road salt $NaCl$ , $CaCl_2$ ).
Nutrients
- Nitrate $NO_3^-$
- Phosphate $PO_4^{3-}$
- Ammonia $NH_3$ (note: negligible in data set).
Sulfate $SO_4^{2-}$ – often from wastewater & atmospheric deposition.
pH – acidity/basicity (7 = neutral; >7 alkaline; <7 acidic).

Graph 1 – Specific Conductance vs. Time
- Colors: Blue = Giles (urban), Red = South Branch (medium), Green = Thompson Creek (forested).
- Time stamps: June 20 → winter (Dec 12) → spring (May 26).
- Expected theory match: highest conductance in Giles, lowest in Thompson, winter peaks (road salt season).
Graph 2 – Sulfate vs. Time
- Same site colors & timeline.
- Theoretical expectation: urban streams (Giles) display elevated sulfate, possibly tied to wastewater discharge events.
Graph 3 – Nitrate vs. Time
- Nutrient source mix: agriculture, septic, sewage; forested streams predicted low.
- Assignment prompt: judge full/partial/non alignment with theory.
Graph 4 – pH vs. Time
- Urban concrete can raise pH; acid deposition or mine drainage can lower it.
- Students analyze whether urban sites indeed show higher pH.

Policy/management often requires multistate coordination (e.g., Chesapeake Bay TMDL) because pollutants travel downstream.
Understanding nested watersheds helps prioritize remediation (start with smallest sub-basin for quickest effect).
Graph literacy is critical for accurately communicating environmental trends to stakeholders (public, agencies).
Linking land-use planning to water-quality monitoring enables targeted interventions: riparian buffers, green infrastructure, fertilizer management schedules, salt‐application optimization, storm-water retrofits.

Complete within Week 5 Lecture 2 Assignment
- Snake-expansion time calculation.
- Narrative/analysis questions for each of the four pollutant graphs (specific conductance, sulfate, nitrate, pH):
- "Fully consistent", "Partially consistent", or "Not consistent" with theory + justification.
Proceed to:
- Short film-based assignment (“The Band,” ~15 min view time).
- Remaining video lecture + assignment for week.
Instructor sign-off: “That’s it for now—see you later.”