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 http://www.atmos.albany.edu/facstaff/adai/ATM301/homework/hwk5_ATM301-2017.pdf

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

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) http://www.usbr.gov/river/iron.html

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

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

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” http://www.nws.noaa.gov/oh/hrl/general/chps/Models/Sacramento_Soil_Moisture_Accounting.pdf

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

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

Distributed Hydrologic Models Physical models: Distributed Hydrologic Models http://www.hydro.washington.edu/Lettenmaier/Models/VIC/Overview/ModelOverview.shtml VIC model Cole & Moore (2009, Adv. Water Res.) http://www.jircas.affrc.go.jp/english/publication/highlights/2004/2004_04.html

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

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

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

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

US river forecasting National (NOAA Advanced Hydrological Prediction Service) http://water.weather.gov/ahps/ Regional (Northeast River Forecast Center) http://www.erh.noaa.gov/nerfc/ Local (Albany National Weather Service forecast office) http://www.erh.noaa.gov/aly/

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.

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.

The Rational Method: Runoff Coefficients, CR

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 = 25400 𝐶𝑁 - 254

The SCS Curve Numbers (CN):

2. The (SCS-CN) Method (cont’d): Estimate of the peak discharge qpk qpk = 0.208 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.

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.

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.526-527).