How We Derived These Numbers: Methodology and Data Sources

1 Where the Data Comes From

Environment Canada Gauge 05DF001

The primary hydrometric station is North Saskatchewan River at Edmonton (05DF001),^{[1]Water Survey of Canada, station 05DF001. wateroffice.ec.gc.ca} operated by the Water Survey of Canada. Over the 10-year period (October 2016 through June 2026) this station recorded 986,540 readings at 5-minute intervals, measuring both water level (in meters above geodetic datum) and discharge (in cubic meters per second, m³/s).

Data is publicly available at wateroffice.ec.gc.ca.

AESO Generation Data

The Alberta Electric System Operator (AESO)^{[2]Alberta Electric System Operator. aeso.ca} publishes hourly generation data for every power plant in the province. We used data for two TransAlta hydroelectric facilities:

Data is publicly available at aeso.ca.

Upstream Tributary Gauges

Additional Environment Canada gauge stations used for tributary and regression analysis:

2 How We Converted Power Generation to Water Flow

Calibration Period

During 2016–2017, both AESO generation data and Environment Canada discharge measurements existed simultaneously for the dam sites, providing 564 days of overlapping observations.^{[3]Authors' calibration analysis from WSC and AESO data overlap, May 2016 – Nov 2017.} We used this overlap to fit linear regression models.

Regression Results

What R² Means

R² = 0.938 means 93.8% of the variation in actual water flow is explained by electricity generation alone. The remaining 6.2% is noise from factors like gate adjustments or measurement error.

Base Flow (Intercepts)

The intercept values (7.56 m³/s for Bighorn, 19.48 m³/s for Brazeau) represent environmental base flow — water that passes through or around the dam even when turbines are off. Brazeau's higher base flow reflects its larger reservoir and mandatory minimum release requirements.

Why This Proxy Matters

After 2020, Environment Canada stopped reporting dam discharge directly. AESO generation data is now the only available proxy for dam outflow. The strong R² values validate this approach.

Bighorn: Electricity vs. Discharge

Each dot is one day during the 2016–2017 calibration period. The line is the fitted regression. The tight clustering shows the strong linear relationship.

3 How We Calculated Dam Contribution Percentage

Transit Time

Water released from the Bighorn and Brazeau dams takes approximately 2 days (45–54 hours depending on flow conditions) to travel downstream to the Edmonton gauge. This lag was determined by cross-correlating dam release pulses with arrival signals at Edmonton.

Calculation Steps

1. Convert AESO generation data to discharge for each dam using the regressions from Section 2.
2. Sum the two dams: Dam discharge = Bighorn Q + Brazeau Q.
3. Lag dam discharge by 2 days to align with Edmonton measurements.
4. Apply the transit factor: Dam Q at Edmonton = Dam Q (lagged) × 0.8. Approximately 20% of released water is absorbed by channel storage (floodplains, gravel beds), evaporation, and infiltration during the 200+ km transit to Edmonton.
5. Calculate natural (non-dam) flow: Natural Q = Edmonton Q − Dam Q at Edmonton.
6. Calculate contribution: Dam % = Dam Q at Edmonton / Edmonton Q × 100.

Monthly Results

Why the Percentage Rises Through the Season

Natural tributaries are largely snowmelt-fed and decline sharply after July as mountain snowpack is exhausted. Dam releases, on the other hand, are driven by electricity demand and reservoir management — they remain more stable through the summer and fall. As natural flow drops, the dams become a larger share of Edmonton's total.

Transit Factor

Not all water released at the dam arrives at Edmonton. Some is absorbed by channel storage (floodplains, gravel beds) during transit. The analysis applies a transit factor of 0.8, meaning approximately 80% of released water arrives at Edmonton. The remaining 20% is temporarily stored or lost to evaporation and infiltration. This factor could range from 0.7 to 0.9 depending on antecedent conditions, which would shift the dam contribution estimates by approximately ±5 percentage points.

4 The Rating Curve — How Water Level Relates to Discharge

What Is a Rating Curve?

A rating curve maps discharge (how much water flows, in m³/s) to water level (how high the river surface sits, in meters). It is built from simultaneous measurements of both quantities.

Data Used

The curve was constructed from 10 years of simultaneous level and discharge measurements (October 2016 through June 2026) at the Edmonton gauge (05DF001), totaling nearly one million individual readings.

Key Reference Points

Sensitivity

In the normal operating range (150–500 m³/s), the relationship is approximately linear: each additional m³/s of discharge raises the water level by roughly 0.3–0.5 cm, depending on the base flow level. At lower flows the channel is wider and shallower, so extra water spreads out rather than rising significantly.

Rating Curve: Discharge vs. Water Level at Edmonton

Scatter of measured points with fitted curve, showing the operating-season range (150–500 m³/s). The horizontal dashed line marks the 3.75m target.

5 How We Calculated Required Dam Increases

Five-Step Process

1. Find the deficit: Target level (3.75m) minus current median level for each month.
2. Convert level to flow: Use the local rating-curve sensitivity (cm per m³/s at the current flow level) to convert the level deficit into a discharge deficit.
3. Apply transit factor: Divide by 0.8, because only ~80% of dam releases arrive at Edmonton.
4. Convert to generation: Translate the additional discharge back to MW generation increase using the calibration formulas from Section 2.
5. Calculate volume: Additional discharge × seconds per day × days in month.

Worked Example: September

6 Reservoir Sustainability

Combined Reservoir Capacity

Storage Required for Different Targets

Why 53% Does Not Mean "Empty the Reservoir"

• The reservoirs receive continuous natural inflow from their combined ~9,413 km² catchment throughout the season.
• Current operations already release ~130–207 m³/s combined while maintaining operating levels, meaning natural inflow roughly equals current outflow.
• The additional releases would draw down reservoir levels, but not by the full 53% because inflow continues replacing withdrawn water.
• Reservoirs refill during winter (November–April) when hydroelectric generation is partially replaced by other energy sources.

Comparison Context

The 3.5m target (21% of storage) is very conservative and almost certainly sustainable. The 4.0m target (114%) exceeds total capacity and is physically impossible even if the reservoirs were drained completely. The 3.75m target sits between these extremes and requires detailed operational modeling to confirm long-term viability.

7 The R² Regression — What It Tells Us

Five Regression Models

We tested five ordinary least squares (OLS) regression models, each predicting daily Edmonton discharge using different subsets of upstream data:

Interpreting the Models

• Model A (0.531): Dams alone explain over half of Edmonton's flow variance. This is remarkable since the dams control only 34% of the total watershed area.
• Model B vs. C gap: The jump from 0.605 (natural only) to 0.746 (natural + dams) = 0.141. This is the unique information dams add on top of natural flow.
• Model D (0.836): The Highway 759 gauge captures both dam and natural contributions in a single measurement, explaining 84% of downstream variance.
• Why not R² = 1.0? Local inputs between Hwy 759 and Edmonton (rain, groundwater, Whitemud Creek), measurement uncertainty, and lag variations all introduce unexplained variance.

Causation vs. Correlation

R² measures variance explained, not direct causation. Seasonal patterns are confounded — dam operations correlate with season (more generation in spring/winter for electricity demand). However, the direct flow contribution analysis in Section 3 confirms the causal relationship through physical mass balance.

R² Values by Model

Variance in Edmonton's daily discharge explained by each predictor set. Higher bars mean the model captures more of the variation.

8 Limitations and Caveats