# 4.4: First-Flush Sizing

## Introduction

There is no single true method to determine the first-flush volume. This lack of assuredness is due to the great environmental variability of systems, including the level of pollution present, the ease of washing away pollution from roofing material, the time between rains, the strength of the rain, etc. As a rule of thumb, contamination is halved for each mm of rainfall flushed away. Area-based and exponential decay-based are the two ways to determine the appropriate size of a first-flush. Both methods contain assumptions. The exponential decay based model contains fewer assumptions. For a metal roof in a suburban neighborhood, the area based rule of thumb should suffice. For a clay tile roof on a dirt road, especially for water needed for drinking, the exponential decay model may be necessary.

A final consideration is the length of time between the reset of the first-flush and the next rain. A reset refers to the first-flush going from full to empty and, therefore, ready to catch the next rainfall. Ideally, all the first rain after a long dry season would be diverted from storage and discharged to untreated usage. Then, the first-flush would slowly evacuate so that subsequent rains would have only some of the initial water diverted. These aspects still need more study globally, in order to determine the best practices for the many different combinations of locations, roof materials, pollutants, etc.

## Area-Based Rule of Thumb

The area-based rule of thumb assumes a roof that is easily cleaned and in a clean environment. It is a simple and most commonly used rule of thumb, yet its effectiveness is currently being debated in literature and practice. The area-based rule of thumb is fast and works well in many settings such as a relatively clean environment and non-porous roof (such as metal). The following two formulae represent the area-based rule of thumb in imperial and SI units:

$First-flush\;Volume = \frac{1\;gal}{100\;ft^2\;of\;roof}$

$First-flush\;Volume = 0.41\frac{liters}{m^2\;of\;roof}$

## Exponential Decay Model

The exponential decay model is more explicit in its assumptions than the area-based rule of thumb. The model requires a decay value that has only been experimentally found for a few roofs, rains, and environments. In addition, the exponential decay model requires testing water turbidity (the cloudiness of the water). The exponential decay model is represented in the following formula:

$V(ff)=-\dfrac{\ln\left(\frac{\text{target turbidity}}{\text{runoff turbidity}}\right)}{λ} \times A \times k$

where:

• Vff = Needed volume of first-flush in liters
• ln = is the natural log function (it is present on most calculators and in Excel)
• Target turbidity = the target turbidity entering the tank in Nephelometric Turbidity Units (NTU).
• The World Health Organization states a target of 5 NTU for water leaving the storage tank (i.e. after storage and before use).
• 20 NTU entering the tank is usually sufficient.
• Runoff turbidity = the measured average runoff turbidity from the catchment area.
• A somewhat dirty roof might contribute just 20-100 NTU.
• A very dirty roof might contribute 1000 NTU.
• λ = the exponential decay value.
• These values are experimentally found.
• A very clean roof may be as high as 2.2/mm. A very dirty roof may be as low as 0.7/mm. 6 A = catchment area in square meters
• k= conversion factor to convert from $$mm*m^2$$ into liters. That conversion is 1.

Finally, for potable use, filtration should be used to bring the turbidity to below 1 NTU depending on any additional treatment.