1. Surface Water
Surface runoff - Precipitation or snowmelt which moves across the land surface ultimately channelizing into streams or rivers or discharging into lakes.
Watershed - Land area which contributes surface runoff to a specified point of interest  typically stream outlet Note: entire area within watershed may not contribute runoff due to depressions, detention ponds, etc.
Watershed divide - Imaginary lines delineating adjacent watersheds. Normally follow ridges and can be delineated with topographical maps.

2. Surface Runoff
Relationship between precipitation and runoff is influenced by various storm and basin characteristics:
Storm Basin (or Watershed)
intensity area, shape, slope
duration soil, vegetation, geology
areal extent stream patterns (length,branching)
uniformity antecedent moisture
land use

3. Surface Runoff
Initially large portion of precipitation goes into surface storage (initial abstraction), then soil moisture storage (governed by infiltration equations).
Both of these types of storage can be classified as either:
i) retention storage - long term, depleted by evaporation
ii) detention storage - short term, depleted by outflow
After detention storage volume begins to fill, outflow begins to occur. Can be
1) groundwater flow
2) unsaturated flow
3) overland flow
4) channel flow

4. Streamflow Hydrograph
Plot of volumetric flow rate vs. time at a particular point in stream or river. Gives spatially and temporally integrated measure of runoff production at a point in stream.
Annual streamflow hydrograph shows long term balance of precipitation, evaporation and streamflow.
Individual storm hydrograph - most widely used method of evaluating surface runoff. Shows relationship between peak streamflow and individual storms.
Hydrographs are used to predict peak flow rates so that hydraulic structures can be designed to accommodate flow safely and to evaluate water quality effects associated with surface runoff. Also integrating hydrograph over time gives volumes needed to design reservoirs, detention ponds etc.

5. Rainfall-Streamflow Relationships
If we take a systems approach to rainfall-streamflow relationship in a watershed:
Excess rainfall - rainfall not retained as storage on land surface or infiltrated into the soil, i.e., rainfall which becomes direct runoff
Graph of excess rainfall vs. time is called excess rainfall hyetograph.
interception
surface storage
rainfall rate
stream flow rate
infiltration
subsurface storage
overland flow
channel flow
subsurface flow
direct runoff
observed hyetograph
baseflow
time
time

6. Rainfall-Streamflow Relationships
Most excess rainfall-streamflow relationships use a systems approach to develop a deterministic lumped unsteady model of the rainfall-discharge relationship.
Watershed is treated as a “black-box” that produces output hydrographs in response to input hydrographs, without detailed consideration of the physical processes producing response.
Systems approach is necessary because of difficulty in obtaining spatial and temporal distribution of physical parameters and processes which affect response (i.e., parameters needed for overland flow and channel flow equations and to determine flow paths).
Best for predicting well-monitored watersheds within recorded bounds of climatic record.

7. Rational Formula
The simplest commonly used rainfall-discharge relationship is the rational formula.
Rational formula attempts to predict peak discharge for extreme events in small urban areas. Usually used to design ditches, canals and storm sewer networks.
Assumes a storm of constant excess rainfall intensity (precipitation-infiltration and initial storage losses) and long duration completely covering watershed.
Rational formula only gives peak discharge rate, no information on time distribution of discharge.

8. Rational Formula
tc - time of concentration - The time at which entire watershed begins to contribute runoff at outlet. Time of flow from farthest point in watershed to outlet.
tr - duration of storm
input = output storage filled ie
Qp = Aie Qp
detention volume
whole basin responding
drainage from remote areas reaches outlet
lag time as water accumulates on surface tc tr
response from nearby areas as gravity force overcomes surface resistance (overland flow)

9. Time of Concentration Formula for the time of concentration
tc= L0.77S-0.385
where
L=hydraulic length (the distance from the most remote point in the watershed to the outlet) in feet
S= average slope along the hydraulic length expressed as a fraction

10. Rational Formula Qp = CiA where Qp is the peak flow rate in cfs
C is an empirical runoff coefficient
A is watershed area in acres
Note: 1cfs= acre-in
For the rational formula to be valid must have rainfall duration > time of concentration for basin.
Typically used to design structures to handle peak flows from design storms with particular probability of exceedence for time of duration  time of concentration

11. Example
Determine the time of concentration and the peak flow rate for a 1:25 year 30 minute design storm with a rainfall intensity of 5 in/hr in a 100 acre agricultural catchment having a 4000ft hydraulic length with an average slope of 5%, hydrologic soil group B.
tc= L0.77S-0.385=14.6 minutes
Qp = ciA = 0.21*5 in/hr*100 acre=105 cfs