--- title: "Unit hydrograph, assumptions, base flow separation" subject: "Engineering Hydrology" chapter: 5 key: "semester_5/engineering_hydrology:uh-assumptions-baseflow-methods" source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/uh-assumptions-baseflow-methods site: BCT Engineering --- # Unit hydrograph, assumptions, base flow separation Engineering Hydrology · Chapter 5: Hydrograph Analysis - Asked in: 2080 Baisakh, 1+3+2 marks - Video: [Unit Hydrograph Theory - Part 1](https://www.youtube.com/watch?v=aDaOFf0IrTE) — HydroMohsen - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/uh-assumptions-baseflow-methods - Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-5 ## Question What is Unit Hydrograph? What are its assumptions and limitations? Describe the method of base flow separation. ## Short answer A unit hydrograph is the direct runoff hydrograph from 1 cm of uniform, constant-intensity rainfall excess over a basin for a given duration. Assumptions include spatial and temporal uniformity, linearity, superposition, and time invariance. Base flow separation methods are straight-line, recession extension, and variable-slope. ## Answer #### Unit hydrograph A **unit hydrograph (UH)** is the direct runoff hydrograph resulting from **1 cm (unit depth) of rainfall excess** falling uniformly over the whole basin at a uniform rate for a specified duration D (called the D-hour UH). It was proposed by Sherman (1932). #### Assumptions 1. Rainfall excess is **uniformly distributed** over the entire basin. 2. Rainfall excess has a **constant intensity** during the duration D. 3. **Time invariance:** for a given basin, the DRH for a given excess-rain duration is always the same, irrespective of when the rain occurs. 4. **Linearity (proportionality):** ordinates of DRH are directly proportional to the rainfall excess depth. 5. **Superposition:** the DRH from successive rainfall bursts is obtained by adding the individual responses with their proper time lags. 6. The **time base** of the DRH is constant for storms of the same duration. #### Limitations - It is valid for basins of about 25 to 5000 km² only; rain and flow are non-uniform in very small or very large basins. - Rain should not vary greatly over the basin; the UH is not reliable where there is storage (lakes, reservoirs) or for snowmelt. - Non-linear effects at large floods are neglected, and the UH of one duration cannot be used for a very different duration without conversion (S-curve). - It requires isolated, uniform-intensity storms and good rainfall-runoff data. #### Base flow separation The storm hydrograph = direct runoff + base flow. Base flow must be removed before deriving the UH. In the sketch, A is the point where the rising limb starts and B is the point on the recession limb where direct runoff ends. The usual methods are: ```text Q | /\ | / \__ | / \__ |___/ A \___ B ____ | base flow +------------------------- t ``` 1. **Straight-line method (Method I):** join A to B by a straight line (horizontal when A and B are at the same discharge). B is on the recession limb N days after the peak, where $N = 0.827A^{0.2}$ (A = catchment area in km²). It is the simplest method and suits small catchments with steady base flow. 2. **Method II:** extend the base-flow recession curve that existed before the storm forward, until it meets the ordinate at the peak (point C). Join C to B by a straight line. The base flow is then A–C–B. 3. **Variable-slope method (Method III):** extend the base-flow recession curve that follows the storm backward to a point below the point of inflection of the recession limb. Join this point to A by an arbitrary smooth curve. This suits large catchments with a good recession record. The area between the total hydrograph and the base-flow line gives the direct runoff volume; the direct runoff depth = volume / catchment area. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. A D-hour unit hydrograph is the direct runoff hydrograph from: A. 1 cm of rainfall excess falling uniformly over the basin at a uniform rate for D hours B. 1 cm of total rainfall including losses falling in any time C. 1 mm of rainfall excess falling over the basin in 24 hours D. Rainfall excess equal to the basin area, in one hour Answer: A. The UH is the DRH due to unit depth (1 cm) of rainfall excess, uniform over the basin and of constant intensity for duration D. (Key point: Definition of UH) 2. If the rainfall excess in a storm is 3 cm instead of 1 cm for the same duration, the UH assumptions imply the DRH ordinates are: A. Unchanged but with a longer time base B. Three times the UH ordinates C. One third of the UH ordinates D. Three times the UH ordinates with a base three times longer Answer: B. Linearity says ordinates are proportional to excess depth, and the time base is assumed constant for same-duration storms. (Key point: Linearity assumption) 3. Which is a limitation of the unit hydrograph method? A. It can only be used for basins smaller than 1 km2 B. It requires rainfall to vary strongly over the basin C. It is unreliable for very large basins and where lakes or reservoirs provide storage D. It works best with snowmelt-dominated runoff Answer: C. The UH is valid for roughly 25 to 5000 km2 and fails with storage or snowmelt, and with non-uniform rain. (Key point: Limitation of UH) 4. In the straight-line method of base flow separation, the base flow line is drawn: A. From the peak to the end of the recession limb B. Along the rising limb only C. From the point of inflection to the origin of the time axis D. From the start of the rising limb to the point on the recession limb N days after the peak Answer: D. A is where the rising limb starts and B is N = 0.827A^0.2 days after the peak (A in km2); they are joined by a straight line. (Key point: Straight-line base flow separation) ## Related in Engineering Hydrology - [Unit hydrograph, assumptions and limitations](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Auh-assumptions-limits) — Engineering Hydrology, chapter 5, asked 2× - [Base flow separation methods](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Abaseflow-separation) — Engineering Hydrology, chapter 5 - [Flood hydrograph, DRH, UH, baseflow separation](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Adefine-hydrograph-drh-uh-baseflow) — Engineering Hydrology, chapter 5 - [Storm hydrograph, DRH, baseflow separation](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Astorm-drh-baseflow-sketches) — Engineering Hydrology, chapter 5 - [Factors affecting flood hydrograph, baseflow separation](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Aflood-hydrograph-factors-baseflow) — Engineering Hydrology, chapter 5 - [Flood hydrograph from 4-h UH, 50 m3/s base](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Aflood-hydrograph-4h-uh-3-5) — Engineering Hydrology, chapter 5, asked 2× ## Related in other subjects - [Decoupled load flow assumptions and algorithm](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Adecoupled-assumptions-algorithm) — Power System Analysis II, chapter 2, asked 2× - [Hydrograph and flow duration curve](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Ahydrograph-flow-duration) — Power Plant Design, chapter 3, asked 3× - [Per unit circuit of three-generator system, 30 MVA base](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Apu-circuit-30mva-g1-g2-g3) — Power System Analysis I, chapter 3