1. Precipitation Measurement

2. Area Average Precipitation
From Mays, 2011, Ground and Surface Water Hydrology

3. NOAA Hydrometeorological Design Studies Center Precipitation Frequency Data Server (PFDS)
The standard source for design storm data
CEE 3430 – Spring 2011

4. Terminology used in Precipitation Frequency Analysis
Duration (Td). The interval over which precipitation occurs.
Intensity (i). The average precipitation rate over a specified duration
Depth (D). The total precipitation over a specified duration
Exceedance probability (P). The probability associated with exceeding a given amount in any given period (usually year) once or more than once.
Recurrence interval or Return period (T). The average interval between events of a set magnitude, evaluated as the inverse of the exceedence probability
A 50 year return period event has a 1/50 = 0.02 probability of being exceeded in any one year
Frequency. General term for specifying the average recurrence interval or annual exceedance probability.
D = i Td
Rate i
Time Td
𝑃=𝑃𝑟𝑜𝑏(𝐷>𝑑)
𝑇=1/𝑃
Annual maximum series (AMS). Time series of the largest amounts in a continuous period (usually year).
Partial duration series (PDS). Time series that includes all amounts above a pre-defined threshold regardless of year; it can include more than one event in any particular year.
Based on

5. Water Budget in a Watershed
From Mays, 2011, Ground and Surface Water Hydrology

6. Evaporation Calculate Evaporation by Energy balance (p304)
Aerodynamic method
(p307)
Combined method
(p309)
Priestley-Taylor method

7. Method Information Requirements
Aerodynamic
Energy Balance
Combination RN

8. Summary Energy exchanges and energy balance
Turbulent diffusion into the atmosphere
Adjustment and balance RN + -
Conditions adjust to varying inputs. Calculations can interpret measurement, but should not be used to predict the effect of changing one variable without considering the adjustments of connected variables

9. Surface Runoff occurs when surface water input exceeds infiltration capacity. (a) Infiltration rate = rainfall rate which is less than infiltration capacity. (b) Runoff rate = Rainfall intensity – Infiltration capacity. (from Dunne and Leopold, 1978)

10. Green-Ampt model idealization of wetting front penetration into a soil profile
ℎ 1 = ℎ 0
ℎ 2 =−𝐿−𝜓
𝐹=𝐿∆𝜃
𝑓=−𝑞=𝐾 ℎ 1 − ℎ 2 𝑧 1 − 𝑧 2
=𝐾 ℎ 𝑜 − −𝐿−𝜓 𝐿
=𝐾 𝐹+𝜓∆𝜃 𝐹 for ho = 0
From Mays, 2011, Ground and Surface Water Hydrology

11. Infiltration capacity – Depth Function

12. Example
Consider a watershed with XXX soil and Green-Ampt parameters given in Mays Table (page 317). Consider a storm where X cm of rainfall occurs in X hours. Calculate the following using the Green-Ampt approach.
a) Time to ponding
b) Depth of infiltration excess runoff generated from this storm

13. Unit hydrographs
The unit hydrograph reflects the unchanging characteristics of a watershed that relates excess precipitation to direct runoff.
U(t) is the response to 1 unit of precipitation over a watershed in duration D.
Direct application. Given U(t) and P(t) calculate Q(t) (8.3.1, 8.3.2)
Inverse application. Given P(t) and Q(t) deduce U(t) for use with different P(t) inputs (8.3.2, 8.3.1)
Deduce losses and excess precipitation – CN,  index (8.2.1, 8.7.2, 8.2.6, 8.7.1, 8.7.3, 8.7.5)
Synthetic unit hydrograph. Determine U(t) from watershed attributes (8.4.1, 8.8.1, 8.4.1, #6, 8.8.1, 8.8.2)
S-Hydrograph. Technique to change the duration D associated with a unit hydrograph (8.5.1, 8.3.6, 8.5.4)
Example HW Problem

14. Synthetic Unit Hydrographs
1/3
2/3
A unit hydrograph is intended to quantify the unchanging characteristics of the watershed
The synthetic unit hydrograph approach quantifies the unit hydrograph from watershed attributes
Follow the procedure of table 8.4.1
𝑡 𝑝 = 𝐶 1 𝐶 𝑡 𝐿∙ 𝐿 𝑐 ℎ𝑟=1∙2∙ 4.45∙ =3.85 ℎ𝑟
𝑡 𝑟 = 𝑡 𝑝 /5.5=0.7 ℎ𝑟
𝑡 𝑝𝑅 = 𝑡 𝑝 𝑡 𝑅 − 𝑡 𝑟 = −0.7 =𝟑.𝟖 𝒉𝒓
𝑄 𝑝𝑅 = 𝐶 2 𝐶 𝑝 𝐴 𝑡 𝑝𝑅 =640∗0.625∗5.42/3.8=𝟓𝟕𝟎 𝒄𝒇𝒔
Widths
𝑊 75 = 𝐶 𝑄 𝑝𝑅 /𝐴 = / =2.88 ℎ𝑟
𝑊 50 = 𝐶 𝑄 𝑝𝑅 /𝐴 = / =5.04 ℎ𝑟
𝑇 𝑏 =2581 𝐴 𝑄 𝑝𝑅 −1.5 𝑊 50 − 𝑊 75 = −1.5∗5.04−2.88=14.1 ℎ𝑟
(3.09,427.5)
(4.05,570)
(5.97,427.5)
(7.41,285)
(14.1,0)
W50
W75
1/3
2/3

15. Effective Precipitation from the SCS Curve Number Equation
From Mays, 2011, Ground and Surface Water Hydrology

16. Hydrologic Response from the unit Hydrograph
Excess Precipitation
Precipitation
Infiltration Capacity
Excess Precipitation
Time

17. Calculating a Hydrograph from a Unit Hydrograph and visa versa
𝑄 1 = 𝑃 1 𝑈 1
𝑄 2 = 𝑃 2 𝑈 1 + 𝑃 1 𝑈 2
𝑄 3 = 𝑃 3 𝑈 1 + 𝑃 2 𝑈 2 + 𝑃 1 𝑈 3
...
𝑄 𝑀 = 𝑃 𝑀 𝑈 1 + 𝑃 𝑀−1 𝑈 2 +…+ 𝑃 1 𝑈 𝑀
𝑄 𝑀+1 =0+ 𝑃 𝑀 𝑈 2 + 𝑃 𝑀−1 𝑈 3 +…+ 𝑃 1 𝑈 𝑀+1
𝑄 𝑁 =0+0+… 𝑃 𝑀 𝑈 𝑁−𝑀+1
𝑄 𝑛 = 𝑚=1 𝑀 𝑃 𝑚 𝑈 𝑛−𝑚+1 for n=1 ... N
𝑀=3 𝑝𝑟𝑒𝑐𝑖𝑝 𝑖𝑛𝑝𝑢𝑡𝑠
𝐿=5 𝑢𝑛𝑖𝑡 ℎ𝑦𝑑𝑟𝑜𝑔𝑟𝑎𝑝ℎ
𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒𝑠
𝑁=7 𝑑𝑖𝑟𝑒𝑐𝑡 𝑟𝑢𝑛𝑜𝑓𝑓
ℎ𝑦𝑑𝑟𝑜𝑔𝑟𝑎𝑝ℎ
𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒𝑠
𝑁=𝐿+𝑀−1
From Mays, 2011, Ground and Surface Water Hydrology

18. Baseflow separation and hydrograph recession
Direct Runoff
Baseflow
End of direct runoff and beginning of baseflow recession

19. Determining the  index and Excess Rainfall Hyetograph

20. Rainfall – Runoff Analysis
From Mays, 2011, Ground and Surface Water Hydrology

21. S Curve to change the duration associated with a unit hydrograph

22. Practice Problem

23. Practice 2