Shelter Valley Brook Watershed Water Balance: 18-Env-B2 Water Resources, December 2018, Q5

Question 5: Shelter Valley Brook Watershed Water Balance (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

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Two working assumptions, both standard hydrologic-engineering convention rather than data stated in the question: (1) a 10:1 snow-to-water ratio is used to convert Table 1’s monthly snow depth (cm) to water-equivalent precipitation (mm) before summing with rainfall; (2) each month’s streamflow is compared and summed as a volume (mean flow rate × seconds in that specific month, so February’s 28 days are not weighted the same as March’s 31), not as a bare average of the rate.

Given. Drainage area 125 km²; eleven years of monthly mean streamflow (Table 1) and thirty years of monthly mean precipitation and evaporation (Tables 1–2), reproduced below.

Monthly means (from Table 1/Table 2 of the source)
Month	Mean flow (m³/s)	Snow (cm)	Rain (mm)	Watershed ET (mm)
Jan	1.15	27	31	10
Feb	1.35	23	28	15
Mar	3.46	17	49	25
Apr	2.16	4	75	40
May	0.63	0	79	90
Jun	0.56	0	82	100
Jul	0.36	0	82	95
Aug	0.27	0	75	65
Sep	0.29	0	58	50
Oct	0.18	0	61	40
Nov	0.43	10	52	20
Dec	1.40	23	41	10

Find. (a) the seasonal percentage split (Feb–May, Jun–Sep, Oct–Jan) of annual precipitation, streamflow, and evapotranspiration; (b) which month(s) need flow augmentation and the minimum reservoir volume required.

Monthly mean streamflow vs. the 30%-of-A.M. augmentation threshold (red bars = deficit months: Aug, Sep, Oct).

Approach. Convert precipitation, streamflow, and evapotranspiration to comparable monthly totals, sum each over the three seasonal groups, then separately compute the mean-annual-monthly (A.M.) flow rate and size the reservoir from the volume deficit in any month below 30% of it.

Convert every series to a monthly total. Precipitation: $P = \mathrm{SWE(snow)} + \mathrm{rain}$, with the snow water-equivalent taken as numerically equal to the snow depth in cm under the assumed 10:1 ratio (e.g. January: 27 mm SWE + 31 mm rain = 58 mm). Streamflow: monthly runoff volume $= Q_{mean}\times(\text{seconds in that month})$, expressed as an equivalent depth over the 125 km² area for comparison. Evapotranspiration: the Table 1 “watershed” evaporation column is used directly (already a monthly depth).
Sum by season and take percentages of the annual total. Grouping Feb–May, Jun–Sep, and Oct–Jan and dividing each group’s sum by the annual sum gives $$\boxed{\text{Precip: } 33.7\%,\ 36.3\%,\ 30.0\%\qquad \text{Streamflow: } 61.7\%,\ 12.1\%,\ 26.2\%\qquad \text{ET: } 30.4\%,\ 55.4\%,\ 14.3\%}$$ (each triple sums to 100%, Feb–May / Jun–Sep / Oct–Jan in order). Precipitation is spread almost evenly across the year, but streamflow is dominated by the Feb–May group (61.7%) — the spring snowmelt freshet — while evapotranspiration is dominated by the warm Jun–Sep group (55.4%), which is also why summer streamflow is disproportionately low despite near-average rainfall.
Compute the mean annual monthly (A.M.) flow rate and the 30% threshold. Averaging the twelve monthly means, $$\mathrm{A.M.} = \dfrac{1}{12}\sum Q_{mean,i} = 1.02\ \text{m}^3/\text{s}, \qquad \text{threshold} = 0.30\times \mathrm{A.M.} = 0.306\ \text{m}^3/\text{s}$$
Identify the deficit months. Comparing each monthly mean to the threshold, three consecutive months fall below it: $$\boxed{\text{August (0.27), September (0.29), and October (0.18 m}^3/\text{s) all need flow augmentation}}$$ (July, at 0.36 m³/s, and November, at 0.43 m³/s, both clear the 0.306 m³/s threshold).
Size the reservoir. For each deficit month, the required release volume is $(\text{threshold}-Q_{mean})\times(\text{seconds in that month})$: $$\text{Aug: } 96{,}422\ \text{m}^3 \qquad \text{Sep: } 41{,}472\ \text{m}^3 \qquad \text{Oct: } 337{,}478\ \text{m}^3$$ $$V_{total} = \boxed{475{,}373\ \text{m}^3\ (\approx 0.475\ \text{million m}^3,\ \text{or }475\ \text{ML})}$$

Final Results
Quantity	Value
Seasonal precipitation split (Feb–May / Jun–Sep / Oct–Jan)	33.7% / 36.3% / 30.0%
Seasonal streamflow split	61.7% / 12.1% / 26.2%
Seasonal evapotranspiration split	30.4% / 55.4% / 14.3%
Mean annual monthly (A.M.) flow	1.02 m³/s
30% of A.M. threshold	0.306 m³/s
Months needing augmentation	August, September, October
Minimum required reservoir volume	475,373 m³ (≈ 475 ML)

Concept & Theory

Topic: Watershed water balance and low-flow (reservoir) augmentation.

Key relations: Long-term water balance $P \approx Q + ET$ (storage change averages to near zero); reservoir yield for low-flow augmentation is the summed volume deficit below the target flow, over the deficit period.

Why this works: Comparing the precipitation, streamflow, and evapotranspiration seasonal fractions exposes the basin’s regime — here a snowmelt-and-groundwater-fed system (consistent with the sandy, high-conductivity soils and large baseflow contribution stated in the question) where spring runoff far outpaces spring’s share of precipitation, and summer ET consumes water that would otherwise sustain streamflow. The reservoir-sizing step is a simplified mass-balance (Rippl-type) calculation: sum only the shortfall below the target during the deficit months.

Common pitfall: Comparing monthly mean flow RATES directly as if they were volumes (a high-rate short month can hold less water than a lower-rate long one, so the seconds-per-month factor matters), and mixing snow depth (cm) with rain depth (mm) without first converting through a snow:water ratio.

Source: Linsley, Kohler & Paulhus, Hydrology for Engineers, water-balance and low-flow analysis chapters.

Question 5 of 6: Shelter Valley Brook Watershed Water Balance

Question 5: Shelter Valley Brook Watershed Water Balance (20 marks)