--- title: "Hydrological cycle and mean precipitation methods" subject: "Hydro Power" chapter: 2 key: "semester_6/hydro_power:hydrological-cycle-mean-precipitation" source: https://www.bctengineer.com/q/semester_6/hydro_power/hydrological-cycle-mean-precipitation site: BCT Engineering --- # Hydrological cycle and mean precipitation methods Hydro Power · Chapter 2: Introduction to Hydrology - Asked in: 2082 Chaitra, 3+3 marks; 2078 Chaitra, 4+6 marks (asked 2 times) - Video: [Hydrologic cycle|| Engineering hydrology||Hydrological cycle|Water supply Engineering|| 4th semester](https://www.youtube.com/watch?v=NvkNoWIRaM4) — Hamro Engineering - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/hydro_power/hydrological-cycle-mean-precipitation - Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-2 ## Question Discuss hydrological cycle and describe about the different methods of finding the mean precipitation over an area. ## Short answer The hydrological cycle is the continuous circulation of water via evaporation, condensation, precipitation, infiltration, runoff, and groundwater flow, driven by solar energy and gravity. Mean areal precipitation is estimated by arithmetic mean (simple but less accurate), Thiessen polygon (area-weighted), or isohyetal method (contour-based, most accurate for hilly terrain). ## Answer #### 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. ```text 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. ```text Isohyets (mm) Thiessen polygons ___80___ +-----+-----+ / _60_ \ | A | B | | / 40 \ | | * | * | \ \____/ / +--+--+--+--+ \______/ | C * | +------+ ``` | Method | Accuracy | Effort | |---|---|---| | Arithmetic mean | Low | Least | | Thiessen polygon | Medium | Medium | | Isohyetal | High | Most | ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What drives the continuous circulation of water in the hydrological cycle? A. Wind and ocean tides B. Solar energy and gravity C. Earth's rotation and volcanic heat D. Groundwater pressure and lunar pull Answer: B. Solar energy lifts water as vapour through evaporation and gravity brings it back as precipitation and runoff. (Key point: Driving forces of the cycle) 2. How do clouds form in the hydrological cycle? A. Water vapour freezes on the ground and rises B. Rain evaporates again before reaching the ground C. Vapour condenses as moist air rises and cools D. Plants release liquid water into the sky Answer: C. Condensation of vapour into cloud droplets happens when air rises and cools. (Key point: Condensation) 3. Which method of finding mean areal rainfall is most accurate, especially in hilly areas like Nepal? A. Isohyetal method B. Arithmetic mean method C. Thiessen polygon method D. Simple average of the highest and lowest gauges Answer: A. The isohyetal method lets the analyst use knowledge of topography, but it needs skill and a dense gauge network. (Key point: Isohyetal method) 4. In the Thiessen polygon method, what weight is given to each station's rainfall? A. Equal weight for every station B. Elevation of the station C. Distance of the station from the outlet D. The area of its polygon inside the catchment Answer: D. P = sum(Pi Ai)/sum(Ai), so each station is weighted by the area it represents. (Key point: Thiessen weighting) ## Related in Hydro Power - [Arithmetic mean and Thiessen average precipitation](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Aarithmetic-thiessen-numerical) — Hydro Power, chapter 2 ## Related in other subjects - [Hydrological losses from precipitation](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Ahydrological-losses) — Engineering Hydrology, chapter 3 - [Define hydrological cycle, runoff, water balance, catchment](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Adefine-cycle-runoff-balance-catchment) — Engineering Hydrology, chapter 1 - [Human interference in the hydrological cycle](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Ahuman-interference-hydrologic-cycle) — Engineering Hydrology, chapter 1 - [Hydrological cycle and uses of engineering hydrology](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Ahydrologic-cycle-uses) — Engineering Hydrology, chapter 1