Basic Hydrology & Hydraulics: DES 601 Module 7 Precipitation

Precipitation Module 7 Sun Clouds Precipitation Transpiration Surface Water Body Lake or Stream Ocean Groundwater Flow Surface Runoff Precipitation Transpiration Evaporation Sun Surface water hydrology really begins before the precipitate hits the ground. The form of precipitate is important (rain, sleet, hail, or snow). For example it takes about 10 inches of snow to produce the same water as 1 inch of rain. Other factors of importance are the size of the area over which the precipitation falls, the intensity of the precipitation, and its duration. Once the precipitation hits the ground several things can happen. It can evaporate immediately, especially if the surface is hot, and relatively impervious. If the surface is dry and/or porous, the precipitate may infiltrate into the ground or may just wet the surface. The process of just wetting leaves and blades of grass is called interception. Some of the infiltrated water is returned to the atmosphere by transpiration by plants. Collectively the return to the atmosphere is called evapotranspiration. The precipitate may be trapped in small depressions (puddles). It may remain in these puddles until it evaporates or until the depressions fill and overflow. Finally it may run off directly to the nearest stream or lake to become surface water. The four “processes” (evapotranspiration, infiltration, interception, and depression storage) that reduce the amount of precipitation available for direct runoff are collectively called abstractions. In drainage engineering, the loss model is how we account for these processes. Module 7

Precipitation There are four variables of engineering interest: Spatial: the average rainfall over the area Intensity: how hard it rains Duration: how long it rains at any given intensity Frequency: how often it rains at any given intensity and duration Module 7

Precipitation Unlike flood frequency the rainfall probabilities are expressed as a combination of frequency (same idea as AEP), depth, and duration. The inclusion of depth and duration reflects that different “storms” can produce the same total depth, but deliver that depth over much different times Consider a slow gentle rain for a long time versus a fast hard rain very rapidly Module 7

Precipitation The statistical relationships are expressed in either: Depth-Duration-Frequency (DDF curves) Intensity-Duration-Frequency (IDF curves) Module 7

Depth-Duration-Frequency Depth of rainfall is the accumulated depth (in a gage) over some time interval. Duration is that time interval. Frequency is the probability (like AEP) of observing the depth over the given duration. Module 7

Depth-Duration-Frequency DDF curve e.q. 12 hour, 100-year (AEP=1%), depth is 70 millimeters Frequency AEP; ARI Depth Duration Module 7

Intensity-Duration-Frequency An alternate form of DDF is to present the magnitude as an intensity (a rate). Intensity is the ratio of an accumulated depth to some averaging time, usually the duration. Intensity is NOT the instantaneous rainfall rate Module 7

Intensity-Depth Relationship Intensity (average rate) from depth e.q. 12 hour, 100-year (AEP=1%), depth is 70 mm average intensity is 70mm/12hr = 5.8 mm/hr Depth Intensity is related to depth and duration. The intensity is the ratio of depth to a particular duration. For example, if the duration or averaging time is 12 hours and the accumulated depth for 12 hours is 70 mm (about 3 inches), then the average rate is 70mm/12hours = 5.8 mm/hour. This average rate, if applied over 12 hours will produce the depth of 70mm. Duration Module 7

Intensity-Duration-Frequency IDF curves e.q. 20 min, 5-year (AEP=20%), intensity is 5.5 in/hr Frequency AEP; ARI Intensity The family of curves that depicts the relationship between the intensity, duration, and frequency of precipitation at a point is a fundamental part of the rational equation method for storm water drainage design. Module 7

How to Construct a DDF Curve DDF curves for a location can be constructed from maps of depth for a given duration and AEP. Such maps are available from: NWS TP40 (online) NWS HY35 (online) Texas DDF Atlas (online) Module 7

DDF Data Sources Module 7 Location Harris County 3 hour, 5-year (AEP=20%) depth = 3.6 inches ARI (AEP = 1/5 = 20%) Duration = 3 hour Module 7

How to Construct a DDF Select the AEP of interest. Locate the maps for that AEP – in the DDF Atlas, each duration for a given AEP is on a separate map. From each map, write the duration and depth into a table for the location of interest. A plot of depth versus duration for these tabulated values is a Depth-Duration curve for the particular AEP. Repeat as needed for different AEP to construct a family of DDF curves. Module 7

Example: DDF for Harris County Construct the DDF Curve for the 50%-chance storm for Harris County using the DDF Atlas. Step 1: Select the AEP (50%; 2-year storm) Step 2: Locate maps for 2-year storm (Figures 4-15 in the DDF Atlas) Step 3: From each map write the duration and depth into a table. (Next two slides illustrate finding this information) Module 7

Example: DDF for Harris County 1.1 inches Module 7

Example: DDF for Harris County 1.5 inches Module 7

Example: DDF for Harris County Construct the DDF Curve for the 50%-chance storm for Harris County using the DDF Atlas. Step 3: From each map write the duration and depth into a table. Module 7

Example: DDF for Harris County Step 4: A plot of depth versus duration for these tabulated values is a Depth-Duration curve for the particular AEP. Module 7

Exercise: Construct a DDF Curve Construct the DDF Curve for the 50%-chance storm for Bexar County using the DDF Atlas. Module 7

Depth, Intensity, and Duration Conversion from Depth-Duration to Intensity-Duration is obtained by the ratio of depth to duration. Conversion from Intensity-Duration to Depth-Duration is obtained by multiplication. using same duration! Module 7

A principal, but needed assumption: Frequency Matching A principal, but needed assumption: A particular discharge event is produced by a rainfall event of the same probability. The fundamental assumption in rainfall-runoff modeling is that a X-probability discharge event is produced by an X-probability rainfall event. It is only an assumption; there are situations where there is no reason to expect the probabilities to be equivalent. Although an assumption, it is the only way (currently) to proceed with rainfall-runoff modeling Module 7

Rational Runoff Equation The rational equation is a rainfall-runoff model that estimates peak discharge for small drainage areas. Dimensional coefficient, nearly 1.0 for U.S. Customary Units Drainage area Runoff coefficient, tabulated in HDM and other sources Rainfall intensity from DDF Atlas and appropriate duration Module 7

Rational Runoff Equation The duration is obtained from consideration of the drainage area’s flow paths, slopes and such – this duration is called the “Time of Concentration” The HDM and HDS-2 (as well as many other references) contain guidance on computing the time of concentration. The HDM and HDS-2 (as well as many other references) contain guidance on selecting appropriate runoff coefficients. Module 7

Rational Runoff Equation The rational equation produces estimates of peak discharge only – it does not produce a hydrograph The rational equation has limited applicability – the limits are listed in the HDM The equation should not be applied to drainage areas exceeding 200 acres (HDM) Module 7

Example: Apply Rational Equation Estimate the peak discharge for a 175 acre, undeveloped low-slope, sandy-loam drainage area in Harris County with a time of concentration of 40 minutes. Step 1: Use the DDF curve to estimate the average intensity for a 40 minute duration. Step 2: Look up appropriate runoff coefficient. Step 3: Compute the peak discharge. Module 7

Example: Apply Rational Equation Step 1: Use the DDF curve to estimate the average intensity for a 40 minute duration. Between 1.5 and 2.0 inches ~ 1.75 inches Module 7

Example: Step 2: Locate Runoff Coefficient Table 4-10 HDM CR=0.20 Module 7

Example: Apply Rational Equation Step 3: Compute the peak discharge This value would then be used to size a hydraulic structure (e.g. a culvert) or some similar application. Module 7

Exercise: Apply Rational Equation Estimate the peak discharge for a 200 acre, undeveloped sandy-loam drainage area with 3-5% slope in Bexar County with a time of concentration of 60 minutes. Step 1: Use your DDF curve to estimate the average intensity for a 60 minute duration Step 2: Look up appropriate runoff coefficient Step 3: Compute the peak discharge Module 7

Summary Rainfall is described by DDF or IDF curves Intensity is an average rate over the duration DDF values are obtained from NWS or similar sources – they are mapped to locations Module 7

Summary DDF curves can be constructed for a location by combining values for different durations and AEPs Rainfall-runoff analysis ASSUMES the X-probability rainfall event produces the X-probability discharge event Rational equation estimates peak discharge Module 7