Hydrological cycle and mean precipitation methods

Hydrological cycle

The hydrological cycle is the continuous circulation of water between the oceans, atmosphere and land, driven by solar energy and gravity. It has no beginning or end; the total water on earth stays constant.

        Sun
         \   condensation -> clouds
          \   ~~~~~~~~~~~~~~~~~~~~
   evapo- ^        | precipitation
 transpir.|        v (rain, snow)
  _/\_/\__|___  infiltration    evaporation
  vegetation  \_______________   ^
     |   surface runoff ----> rivers --> OCEAN
     v   groundwater flow -----------^

Main processes:

1. Evaporation from oceans, lakes and rivers, and transpiration from plants (together evapotranspiration).
2. Condensation of vapour into clouds as air rises and cools.
3. Precipitation as rain, snow or hail.
4. Interception by vegetation and depression storage.
5. Infiltration into the soil and percolation to groundwater.
6. Surface runoff and groundwater flow (base flow) into rivers, lakes and finally the ocean.

Importance for hydropower: it decides the available river flow, its seasonal variation (monsoon high flows, dry-season low flows in Nepal), snow-fed contribution, and floods for spillway design.

Methods of finding mean precipitation over an area

Rain gauges give point rainfall; the mean (areal) depth over the catchment is found by:

1. Arithmetic mean method

$$\bar{P} = \frac{P_1 + P_2 + \dots + P_N}{N}$$

Simple; good only for flat areas with uniformly spread gauges and small rainfall variation.

2. Thiessen polygon method

• Plot stations on the map and join adjacent stations by straight lines to form triangles.
• Draw perpendicular bisectors of these lines; they form a polygon around each station.
• Measure the polygon area $A_i$ inside the catchment for each station.

$$\bar{P} = \frac{\sum P_i A_i}{\sum A_i}$$

Accounts for uneven gauge spacing; can use stations just outside the catchment. Does not consider orography; polygons must be redrawn if a gauge is added or removed.

3. Isohyetal method

• Draw isohyets (lines of equal rainfall) by interpolating between station values.
• Measure the area $a_i$ between successive isohyets $P_i$ and $P_{i+1}$.

$$\bar{P} = \frac{\sum a_i \left(\frac{P_i + P_{i+1}}{2}\right)}{\sum a_i}$$

Most accurate, especially in hilly areas like Nepal, as the analyst can use knowledge of topography; but needs skill and a dense network.

  Isohyets (mm)          Thiessen polygons
   ___80___               +-----+-----+
  /  _60_  \              |  A  |  B  |
 |  / 40 \  |             |  *  |  *  |
  \ \____/ /              +--+--+--+--+
   \______/                  | C *  |
                             +------+