Some reservoir concepts

Draft ratio is the ratio between mean annual withdrawal and mean annual inflow.

D = \dfrac{\mathbb{E}(Q_{out})}{\mathbb{E}(Q_{in})}

Storage ratio is the ratio between the total reservoir volume and mean annual withdrawal.

S = \dfrac{V}{\mathbb{E}(Q_{in})}

Some reliability concepts:

  • Annual frequency reliability (R_a) is the percentage of number of failure years over the total number of years in record.
  • Time reliability (R_t) is the percentage of the total failure duration over the total record time.
  • Volume reliability (R_v) is the percentage of total shortage volume over the total required volume in record.

Some uncertainty concepts for reservoir modelling:

  • Model uncertainty: the uncertainty due to the model structure.
  • Parameter uncertainty: the uncertainty due to parameter estimation method.
  • Intrinsic uncertainty (of the system): uncertainty that arises when assuming that the system will behave in the same way in the future as when it is modelled.

Model uncertainty and parameter uncertainty can be reduced with longer record lengths, but intrinsic uncertainty may not.

While the hydrologic aspects of a reservoir can be modelled universally, the socioeconomic aspects are very site specific and is up to the practitioner. Klemeš et al (1981) reported that long-memory and short-memory models are not statistically different (statistical significance), but the small statistical differences may lead to significantly different socioeconomic outcomes (socioeconomic significance). This idea reminds me of a thought my advisor told me at the beginning of our project: a model’s value may be more important than its skill. I’ll keep that in mind.


Klemeš, V., Srikanthan, R., & McMahon, T. A. (1981). Long-memory flow models in reservoir analysis: What is their practical value? Water Resources Research, 17(3), 737–751.