Module 10: Average Rainfall Theodore G. Cleveland, Ph.D., P.E, M. ASCE, F. EWRI August 2015 Module 10 1

 FHWA-NHI Highway Hydrology  Chapter 2, Section 2.1; Chapter 3  Examine spatial distribution of rainfall and averaging techniques.  Examine how to put multiple gages into HMS and assign these gage depths to a particular watershed. Module 10 2

 The total amount (measured as depth) of rainfall that occurs in a storm is the important input characteristic for describing the response of a watershed to rainfall.  The depth-time of rainfall (hyetograph) is equally important. Module 10 3

 There are a number of time-related and space-related factors that are used in explaining rainfall input.  The four most important are:  Intensity (a rate: i.e. inches/hour)  Duration (a time: 15 minutes)  Frequency (a probability: 1%)  Average Depth (a length: inches) ▪Actually better thought of as volume/area, but dimensionally it is a length. Module 10 4

 HEC-HMS has precipitation input at “gages” that are assigned to basins.  The examples so far assume a single gage is assigned to a sub-basin.  HEC-HMS inputs are in depths, either incremental or cumulative  Intensity x Duration = Depth ▪These computations are typically external to HMS. ▪Here duration is simply used as a time interval, but the term really refers to an entire storm length and not some portion. Module 10 5

Watershed –Losses –Transformation –Storage –Routing Precipitation –Meterology, Climate  Runoff  Fraction of precipitation signal remaining after losses Spatial distribution – these precipitation arrows may not be identical. Unless we wish to route hydrographs, need some way to “average” the input. Module 10 6

 Averaging is used to generate uniform inputs for unit hydrograph applications  One implicit assumption of the UH is spatially uniform input time series.  Averaging avoids having to route hydrographs  Routing would probably be required on larger watersheds.  If the data justify distribution, then could route subdivided watersheds to capture storm patterns. Module 10 7

 The entire volume of rainfall applied to an entire basin is called the precipitation volume  If the basin area normalizes this volume the resulting value is called the equivalent uniform depth  Methods to compute equivalent depth  arithmetic mean  theissen polygon network  iso-heyetal method Module 10 8

 The mean value of all nearby gages is used  Not all gages actually on the watershed Module 10 9

 A weighted mean based on polygon area is used  Not all gages actually on the watershed  Polygons formed using Theissen method  Can use a minimum distance algorithm to semi-automatically generate the weights Module 10 10

 A weighted mean based on polygon area is used Area ratios are called Theissen weights Subarea A Subarea A Subarea C Subarea C Subarea D Subarea D Subarea E Subarea B Module 10 11

 A weighted mean based on iso-hyetal panel areas is used  Not all gages actually on the watershed  Areas formed by intersection of isohyetal contours and underlying drainage area Module 10 12

 A weighted mean based on isohyetal panel areas is used Module 10 13

 Theissen polygons and arithmetic mean are probably the most common because the weights are constants with respect to geography.  Arithmetic mean is easiest to automate Module 10 14

 Illustrate use of multiple gages on Ash Creek.  Known Theissen weights are ▪0.12 and 0.88  Simulate using these known weights. Module 10 15

 Multiple rain gage data can be used to estimate an equivalent uniform depth  Gage weights by a variety of methods  Arithmetic mean  Minimum distance (Theissen polygons)  Isoheyetal  Inverse distance methods Module 10 16

 HEC-HMS models multiple gages in the Meterological Model Manager  The example illustrates how to set-up multiple gages  Weights were supplied Module 10 17