# Rational Formula

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- Created by Unknown User (reynard.juanir), last modified by Abraham Toribio on May 17, 2018

**There are currently five** (5) different Intensity-Duration-Frequency methods and four (4) different Runoff Coefficient methods supported.

Rainfall intensity may be calculated in one of five ways:

- Using the method described in AR&R, 1977 (Pattison, 1977)
- The method described in AR&R, 1987 (Pilgrim, 1987)
- By using a user defined Intensity-Frequency-Duration Table
- A Generalized Equation
- The Alameda County Public Works (California) method

The coefficient of runoff may be calculated by one of five methods:

- The method described in AR&R, 1977 (Pattison, 1977), (Ordon, 1954)
- The method described in AR&R, 1987 (Pilgrim, 1987),
*(**Australia**only)* - Entering a Constant Runoff Coefficient for each subcatchment
- The Alameda County Public Works (California) method

There are no restrictions on combining any runoff coefficient with any intensity calculation method.

## AR&R 1977 IFD

This method follows the 1977 Australian Rainfall & Runoff procedures with polynomial coefficients obtained from that publication (*Pattison, 1977*).

Each rainfall intensity-frequency-duration curve can be represented by a polynomial equation as shown below:

where

*I* = rainfall intensity in mm/h

*t *= duration of rainfall in hours

ln *I *= natural logarithm of I

ln* t* = natural logarithm of t

a, b...g = coefficients

The coefficients a, b, c, d, e, f and g are extracted from the 1977 edition of AR & R for the 1, 2, 5, 10, 20, 50 and 100 AEP's. The intensities are then calculated as required for each catchment and each return interval requested. Coefficients must be entered for all return intervals (ie. 1 to 100), regardless of what return period is being analyzed.

The table below displays some typical data:

a | b | c | d | e | f | g | |
---|---|---|---|---|---|---|---|

1 | 2.8390000 | -.6530000 | -.0475000 | .0264700 | .0012400 | -.0021070 | .0002041 |

2 | 3.0970000 | -.6689000 | -.0541000 | .0299400 | .0019060 | -.0024570 | .0002390 |

5 | 3.3670001 | -.7178000 | -.0741000 | .0451000 | .0037260 | -.0041352 | .0004227 |

10 | 3.4970000 | -.7300000 | -.0853000 | .0446200 | .0055280 | -.0039794 | .0003366 |

20 | 3.6510000 | -.7471000 | -.0928000 | .0486800 | .0063370 | -.0044000 | .0003738 |

50 | 3.8100000 | -.7659000 | -.1036000 | .0526300 | .0075960 | -.0048175 | .0003939 |

100 | 3.9190000 | -.7775000 | -.1095000 | .0547800 | .0083970 | -.0049816 | .0003921 |

**Typical Rainfall-Intensity-Duration-Frequency Polynomial Coefficients (After AR&R, 1977)**

Although this procedure has been superseded by the method described in the 1987 edition of AR&R, it is probably still the most up to date method for calculating intensities as the Bureau can supply the latest polynomial coefficient information for any area in Australia.

** **AR&R 1987 IDF

This method follows the 1987 Australian Rainfall & Runoff procedure (Pilgrim, 1987). To use this procedure it is necessary to extract nine values from Volume 2 of 1987 AR&R. These are the 1 Hr, 12 Hr and 72 Hr intensities for both the 50 Yr and 2 Yr events, plus the Location Skew value and the F2 (events < 2 years) and F50 (events > 50 years) Frequency Factors.

** **Tabular IDF Input

The user creates a table of ARI (Average Recurrence Intervals) versus duration (in minutes). Both the ARI's and the durations are user definable and if the table does not cover the specific event then the program will linearly interpolate or extrapolate a value.

** **General IDF Equation

The Intensity is calculated from the equation:

**where:**

*I* = intensity (in/hr, mm/hr)

*t* = rainfall duration (min)

*ARI* = return period (yr)

*B*, *D*, *E* and *F* = user coefficients

Note that when *F *= 0, the equation becomes:

## Alameda County IDF Method

The Rainfall Intensity for the appropriate time of concentration is computed from the equation:

* Where*:

Ij = Rainfall Intensity for Return Period (frequency) j and storm duration i. (mm/hr, in/hr)

MAP = Mean Annual Precipitation (mm, in)

Ti = Storm Duration (hrs)

Kj = Frequency Factor

## AR&R 1977 Runoff Coefficient

The 1977 Australian Rainfall & Runoff Runoff Coefficients for urban catchments are based on Ordon Curves (1953).

The runoff coefficients for urban catchments are calculated from the following equation:

* where*:

C = Runoff coefficient

X = Calibrated constant

Y = Calibrated exponent

I = Rainfall intensity (mm/hr)

The values of the constants X and Y for each urban catchment category are tabulated below:

Category | Description | X | Y |
---|---|---|---|

1 | Semi Impervious Areas | 5.81 | 1.47 |

2 | Surface Clay, Poor Paving, Sandstone Rock | 4.46 | 0.96 |

3 | Bare Earth | 3.22 | 0.70 |

4 | Earth with Sandstone Outcrops | 3.14 | 0.594 |

5 | Bare Loam | 2.91 | 0.483 |

6 | Ordinary Loam | 2.31 | 0.376 |

7 | Park Lawns & Meadows | 2.09 | 0.313 |

8 | Cultivated Fields with Good Growth Sand Strata | 1.94 | 0.266 |

**Parameters for Urban Pervious Runoff Coefficients (After Ordon, 1953)**

A constant coefficient for impervious areas can also be entered directly.

## AR&R 1987 Runoff Coefficient

The user enters the 1 hour, 10 Yr intensity in this dialog. The coefficient of runoff is for the pervious portion of the catchment is calculated on the fly as the intensity is calculated. The coefficient of impervious runoff is input directly.

The figure relates the runoff coefficient for a 10 Year ARI, C10, to the pervious and impervious fractions of a catchment and to its rainfall climate characterized by the 10 Year ARI, 1 hour duration rainfall intensity (AR&R, 1987). For areas where the 10 Year, 1 hour intensity is between 25 and 70 mm/hr a line is linearly interpolated between the upper and lower bound curves.

For average recurrence intervals other than 10 years the C10 value is multiplied by frequency factors presented in the table below:

ARI (Years) | Frequency Factor |
---|---|

1 | 0.8 |

2 | 0.85 |

5 | 0.95 |

10 | 1.0 |

20 | 1.05 |

50 | 1.15 |

100 | 1.2 |

**Frequency Factors for Rational Method Runoff Coefficients (After AR&R, 1987)**

** Direct Input Runoff Coefficient**

A constant runoff coefficient may be directly entered. When this option is selected, a global runoff coefficient for all impervious surfaces is entered in Job Control with the pervious runoff coefficient entered at each sub-catchment.

** Alameda**** ****County**** Runoff Coefficient**

The Alameda County Public Works Department Method uses 3 components to calculate the Pervious C value:

**Where:**

C’ = Design Runoff Coefficient

C = Base C (entered at the sub-catchment level)

Cs = Slope adjustment factor

Ci = Intensity adjustment factor

S = Average ground slope (%)

I = rainfall intensity (in/hr)

__Section Pages__- Buildup and Washoff Data
- Erosion
- Groundwater
- Infiltration
- Initial Loads
- Landuse
- Runoff Pollutants
- Rainfall
- Snowmelt
- Sanitary Pollutant
- Sewer Dry Weather Flow
- Sewer Infiltration
- Waste Stream Temperature
- Temporal Variation
- Pump Rating Curve Global Data
- Pit Rating Curve
- Hydraulic Brakes
- Pavement Crossfalls
- HEC-12 and HEC-22
- User Defined File Type Global Data
- XP Tables Global Data
- Rational Formula
- Natural Section Shapes
- 2D Soil Type
- 2D Landuses
- User-defined Conduits
- Bridge Section Shapes
- LID - WSUD
- User Hazard Classifications
- User Hazard Values
- Rainfall Derived Inflow and Infiltration - RDII
- ARR Storm Generator