Reservoir Yield: Mass Curve, Evaporation Loss and a Demand Hike
An irrigation reservoir on a seasonal river is planned to meet a constant draft of 30 Mm³ per month at the canal headworks. The gauged monthly inflows for a representative 12-month period, in Mm³, are: 8, 6, 5, 4, 12, 38, 80, 92, 62, 33, 12 and 8 (total 360 Mm³). Dead storage is fixed at 5 Mm³. The water spread at full reservoir level is 8 km² and mean annual evaporation from the reservoir surface is 1.0 m. The design consultant has proposed a gross storage of 120 Mm³, describing it as the mass-curve requirement 'with a little extra for prudence'. In parallel, local public representatives are demanding a 20% increase in the command area, which would raise the draft to 36 Mm³ per month. The Chief Engineer must clear the storage and answer the command-area demand in writing.
1. Determine the live storage requirement by the mass curve method for a constant draft of 30 Mm³ per month, and state the gross storage needed.
Read the worked answer
Cumulative inflows (Mm³): 8, 14, 19, 23, 35, 73, 153, 245, 307, 340, 352, 360
Cumulative demand at 30 Mm³/month: 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, 360
Deficit (demand − inflow): 22, 46, 71, 97, 115, 107, 57, −5, −37, −40, −22, 0
The maximum deficit is 115 Mm³, occurring at the end of month 5, which is when the reservoir is at its lowest. The reservoir must therefore hold a minimum of 115 Mm³ of live storage at the start of the drawdown; the cumulative surplus from month 8 to month 11 (about 62 Mm³ in all) refills it before the next season. The mass curve closes at zero at month 12 because inflow exactly equals demand over the year - a necessary but not sufficient condition for a firma yield.
Gross storage = live storage + dead storage = 115 + 5 = 120 Mm³.
So the consultant's 120 Mm³ is arithmetically correct but leaves no allowance whatsoever for evaporation, sedimentation or freeboard. It should be treated as a bare minimum, not a prudent figure.
2. Evaluate the proposed gross storage of 120 Mm³ taking the evaporation loss into account, and comment on whether a 30 Mm³/month draft is actually sustainable.
Read the worked answer
Evaporation volume = 8 km² × 1.0 m = 8 Mm³ per year. Adding it to the annual demand of 360 Mm³ gives a total annual requirement of 368 Mm³ against an annual inflow of 360 Mm³ - a structural deficit of 8 Mm³ every year, entirely independent of how much storage is built.
Three consequences follow:
- The 30 Mm³/month draft is not a firm yield for this inflow series. The sustainable draft is (360 − 8)/12 = 29.3 Mm³/month. Either reduce the draft by about 2% or find the additional 8 Mm³ from augmentation.
- Gross storage of 120 Mm³ is inadequate. It provides 115 live and 5 dead, leaving nothing for the sedimentation wedge (typically 0.5% of gross per year, so about 0.6 Mm³/yr for this size of reservoir) and nothing for the fact that the last few metres of storage are lost to evaporation as the surface recedes. A gross of not less than about 130 Mm³ is a defensible figure, to be confirmed by a sediment survey and a reservoir routing.
- A single representative year is not sufficient for design. The mass curve assumes a repeating year and abandons all carry-over between years. Firm yield should be determined from at least 20–30 years of inflow data by a sequent-peak or behavioural simulation, including the worst drought in the record.
Recommended action: revise the draft to 29.3 Mm³/month, fix gross storage at about 130 Mm³, and rework the mass curve using a multi-year series before the reservoir level is fixed.
3. A 20% increase in command area would raise the draft to 36 Mm³ per month. Assess this proposal and state what data would be needed before any commitment is made.
Read the worked answer
The annual requirement would become 432 Mm³ against an inflow of 360 Mm³ - a shortfall of 72 Mm³/yr, or 20%, even before evaporation is added. Storage cannot manufacture water: within any year the mass curve can only redistribute surplus, and this inflow series has failed every single month from month 1 to month 7. A 20% increase is therefore not a capacity problem but a water-resource problem.
What storage could do is carry water over from a wet year to a dry one, which is exactly why a single-year analysis is unsafe in both directions. If the 12-month series happens to be a dry year in a multi-year record, some carry-over may exist; if it is an average year, the proposal is simply infeasible.
Before any commitment, require:
- A long-term (minimum 20–30 year) monthly inflow series and the reservoir simulation for the proposed draft, giving the firm yield and the reliability of supply at 50%, 75% and 90% dependability.
- Evaporation data from a pan or a nearby class-A station, and sedimentation from a catchment survey.
- The regulated release commitments downstream and any riparian/interstate allocation.
- Conjunctive elements, such as groundwater or canal diversions, if the shortfall could be met from them.
Until the firm yield is established, the 20% increase should not be committed; a defensible interim position is that the command area be held at the level supported by 352 Mm³/yr after evaporation.