1. Rainfall-Runoff Modeling
ATM 301 Lecture #20 (section 10.6)
Rainfall-Runoff Modeling
Homework#5: Due 12/05/2017. Accounts for 30% of your Final Exam.
See

2. Stream flow event-response (rainfall-runoff) modeling
Basic problem:
Given a time series of water input over a watershed, what is the resulting hydrograph at the outlet?
weff= w - “losses”
weff= w – ( ET Δ Sc ΔD Δθ)
“depression” storage
(to sfc water)
canopy storage
soil water storage

3. Applications of models:
Major applications:
Event forecasting
Use actual or forecast rainfall to predict conditions over hours to days
2. Engineering/design/hazard assessment
Use statistics of past rainfall (percentiles, exceedance probabilities, return intervals) to estimate the characteristics of potential future floods (design floods)

4. Physical vs. Empirical/Conceptual
Types of models:
Physical vs. Empirical/Conceptual
Physical
Based on physical laws & some assumptions / simplifications
Large system of equations. Must be solved on a computer
Requires extensive input information
Conceptual / Empirical
Not closely based on physical laws
Based on observations (empirical) or conceptual understanding of how a watershed works
Can be calculated quickly, sometimes without computer
Requires much less input information

5. Types of models: Lumped vs. Distributed Lumped Distributed
Most models explicitly consider the water budget, but they vary in the analysis domain(s) used:
Lumped
Treat the entire basin as a uniform unit
Use area-averaged water-input (no spatial rainfall variations)
Use single representative land properties (soils, vegetation, wetness) over entire basin
Solve a single water budget equation for the whole watershed
Predict hydrograph at the basin outlet
Distributed
Break the basin up into smaller pieces
Solve water budget separately for each “cell”
…then route water between them
Can account for spatial variations in water input
Can account for spatial variations in land properties
Can produce hydrographs for multiple locations
distributed
lumped

6. Physical models (Lumped): Sacramento Soil Moisture Accounting Model
Developed and used by NWS “River Forecast Centers“ (RFC’s).
Requires input time series of basin-averaged rainfall (temperature, winds, humidity, radiation, snowpack)
Requires basin-averaged soil & land use data
Uses physically based equations to predict: overland flow, interflow, base-flow, (snowmelt), and discharge
Flow routing based on unit hydrograph or “Lag & K method”

7. Physical models (Lumped): Sacramento Soil Moisture Accounting Model
Limitations:
No effects of spatial variations in:
water input
basin properties
“Time step” of 6hrs (does not capture “quick responses”)
Only single hydrograph output for a basin

8. Distributed Physical models:
Separate a basin into many sub-basins or with a grid
For each:
determine slope, soils, land use/vegetation, channels, initial soil moisture
input a distinct time series of rainfall (temperature, winds, incoming radiation, humidity)
Uses physically based equations to predict: overland flow, interflow, baseflow, (snowmelt), and discharge
Typically uses more-advanced routing than lumped models
Often can be used for long-term studies as well as

9. Distributed Hydrologic Models
Physical models:
Distributed Hydrologic Models
VIC model
Cole & Moore (2009, Adv. Water Res.)

10. Distributed Physical models:
Requires MUCH more data to run than a lumped model
Only makes sense to run distributed model if you have distributed input
Soil and land use info can come from soil databases (e.g., STATSGO)
Vegetation and soil moisture can come from ground-based or satellite mapping.
Precipitation can come from numerical models, radar, interpolated rain gauges, or combination

11. Distributed Physical models:
Distributed models use routing schemes to move water between cells and into channels following terrain-determined directions – River routing

12. Physical models: Distributed Advantages over lumped models:
More faithfully represent actual processes
More accurate when large precipitation variations occur over the watershed
More accurate when there are substantial variations in surface characteristics over watershed
Provides runoff info at many locations
Disadvantages over lumped models:
Require much more input data
Require much more computational resources

13. Flood forecasting & warnings in the U.S.:
Responsibility of National Weather Service (NWS)
US Geological Survey (USGS) monitors streams
NWS River Forecast Centers (RFC’s) model stream flow based on current observations and precipitation estimates
Local NWS weather forecast offices (WFO’s) issue watches and warnings and may do additional hydro modeling

14. US river forecasting
National (NOAA Advanced Hydrological Prediction Service)
Regional (Northeast River Forecast Center)
Local (Albany National Weather Service forecast office)

15. Common Lumped models (sec. 10.6.4, pp.514-529):
Three simple rainfall-runoff models:
The Rational Method: often for urban areas
The Runoff Curve-Number Method: for suburban and rural areas
These two simple methods are used for generating design flows from small watersheds for simple structures such as culverts, small bridges, surface-drainage systems, and runoff-detention basins.
3. The Unit Hydrograph Method: used to generate design flows from larger watersheds where measurements of rainfall and runoff from past events are available.

16. 1. The Rational Method:
This method postulates a simple proportionality between peak discharge qpk and rainfall intensity p*:
qpk = R CR AD p*
where R is a unit-conversion factor, AD is drainage area, and CR is a dimensionless runoff coefficient, which depends on watershed land use. For qpk in m3/s, p* in mm/hr, and AD in km2, R =0.278.
This eq. was derived from a simplified conceptual model for basins with negligible water storage, and is widely used for drainage design for small rural and urban watersheds.

17. The Rational Method: Runoff Coefficients, CR

18. 2. The Soil Conservation Service Curve-Number (SCS-CN), or Runoff Curve-Number Method:
The most widely used rainfall-runoff model for routine design purposes in the U.S.
This method uses soil information and a design rainfall volume P to
estimate
1) the effective rainfall P*
2) the peak discharge qpk
The effective rainfall is estimated as (see Box 10.9, p.517):
P* = 𝑃−0.2 𝑆𝑚𝑎𝑥 2 𝑃+0.8 𝑆𝑚𝑎𝑥
where P is the total rainfall, and Smax is the watershed water storage capacity, which is estimated using the curve numbers (CN) assigned to each hydrologic soil group under various land uses:
Smax = 𝐶𝑁

19. The SCS Curve Numbers (CN):

20. 2. The (SCS-CN) Method (cont’d):
Estimate of the peak discharge qpk
qpk = 𝑃 ∗ 𝐴𝐷 𝑇𝑟
where Tr is the time of rise in stream response,
qpk is in m3/s, P* in mm, AD in km2, and Tr in hr.
The advantages of the SCS-CN method:
Easy to compute
Uses watershed information
Gives reasonable results under various
conditions
4) No other better methods when there is no
detailed watershed information.

21. 3. The Unit Hydrograph Method:
Assumes the watershed response to rainfall input is linear:
qpk = 𝑃 ∗ ×𝑞𝑢𝑛𝑖𝑡
where qunit is the peak discharge in response to a unit of rainfall input that lasted over the same time period as the actual rainfall P* did.
The main task is to estimate the
unit-hydrograph for a given rainfall
duration, e.g., 2.5hr in this plot----
The linear assumption may induce
errors as the response also depends
on antecedent conditions.

22. Determination of the Unit Hydrograph:
Choose 4-5 hydrographs from intense storms of aprrox. equal duration, and with relatively uniform spatial and temporal distributions;
Determine the event response from the base flow, and the effective precipitation P*=Qef for each hydrograph;
Divide the measured discharge by P* to derive the response to unit rainfall input for each event;
Average over all the events to derive the composite unit hydrograph;
Unit hydrographs for other rainfall durations can be derived from the determined unit graph (see pp. 525).
Synthetic Unit Hydrographs: provide a means for estimating the unit hydrograph based on watershed characteristics when measurements of rainfall and runoff for previous storms are unavailable (see pp ).