41 Fake news and the “New UK” runoff equation

This episode was sparked by the response to Episode 39 on modelling inflow and infiltration that shouldn’t get into our sewerage systems.?I mentioned the “New UK” runoff equation in that and I thought that it was time for a proper discussion of what it was and what it was for and to debunk some of the misconceptions about it.

A history lesson

In 1975 in the UK the Flood Studies Report was published that introduced new modelling concepts for the hydrology of river catchments.?This introduced a Percentage Runoff (PR) equation based on the characteristics of the catchment upstream of the point of interest.?The equation included terms for the Soil class and the Catchment Wetness Index that combined the long-term Soil Moisture Deficit (SMD) with the shorter-term Antecedent Precipitation Index (API).

The same team from the Institute of Hydrology (IoH) then went on to adapt the PR equation for urban drainage systems and this was published in 1981 as The Wallingford Procedure.

The Wallingford PR equation:

• Was dominated by the Percentage of Impermeable area (PIMP) of the catchment.
• Still calculated the PR for the catchment as a whole but then distributed to each individual subcatchments based on the local value of PIMP.
• Changed to an Urban Catchment Wetness Index (UCWI) which was weighted towards the short-term API term by a factor of 8 to 1 compared to the SMD term.

All sensible changes – but it ended up with some inconsistencies.

By the mid 1980s those inconsistencies started to cause problems in poor modelling results.?So about 1987 I managed to raise funding to develop a new equation and got John Packman of the IoH team to do the analysis.?The rest is history – or possibly fake history.?

There are a lot of misconceptions about the “New UK” equation and I debunk some of the more prevalent ones below.

It is called the “New UK” equation

The original name of the new equation was the “Variable PR” equation and it intentionally stopped using the SMD parameter that was specific to the UK.?The plan was that it could readily be used in any country.?

The one UK specific piece of information was that maps were available in the UK to show the extent of the 5 different soil classes from well drained to impermeable.?However the appropriate class could be derived from similar geological mapping in other countries.?(Incidentally those soil maps are no longer published in the UK and old copies are carefully preserved by urban drainage teams up and down the country.)

I am not sure where the term “New UK” came from, but it is a) wrong and b) out of date, as the equation is now over 30 years old.?Maybe “Middle aged, not just UK” equation.

It was developed in 1993

Richard Allitt, in his paper “Rainfall, Runoff and Infiltration Re-visited” at the WaPUG Spring Meeting 2002, confidently stated that the new equation was introduced in 1993.?However the beta version was presented at the Spring Meeting in 1990 with the final version presented later that year, so it was available well before 1993.

It was intended to represent slow response (infiltration)

The equation was intended as a replacement for the Wallingford PR equation to represent the immediate runoff from a rainfall event.?The differences were that:

• it was less susceptible to imbalance between the different terms in the equation
• it allowed for increasing runoff as the catchment got wetter during the event
• it could be used for continuous simulation of long timeseries.

When I have explained this objective when lecturing on the topic, I have often had people correct me that it was definitely developed for slow response.?My response was generally unpublishable.

Thanks to that Richard Allitt paper for a great graph of exactly what it was supposed to do.

It uses fixed runoff from impermeable surfaces

The equation is often described as having fixed runoff coefficients for impermeable surfaces, but this is not strictly true.

The new concept was that a defined percentage of impermeable surface had 100% runoff but that the rest of the impermeable surfaces contributed additional runoff in wet conditions.?To represent this, these additional runoff surfaces were treated as being extra permeable surfaces.?See the diagram below.

It is therefore important not to change the runoff routing factors for the urban permeable surfaces as this messes up the extra runoff from the impermeable surfaces.?

You need 30 days rainfall to calculate API

The API term is an infinite series of previous precipitation on each day (I) of the form:

To be pedantic the precipitation is net after subtracting evaporation and so the term should be Net API (NAPI).

In the Wallingford PR equation the value of k was fixed at 0.5 and so it was not necessary to go back for more than 5 days of rainfall as at that point the value would be multiplied by 0.5 five times and so would have negligible effect.?The term was therefore called API5

The Variable PR equation used different values of k for different soil classes. ?The number of days that need to be included in the series therefore depends on the soil class as shown in the table.

To make sure that users took a long enough series the term was called API30.?But you don’t always need 30 days of rainfall data.

Incidentally the value for Class 5, completely impermeable soils, is meaningless as there was no data for any urban areas with those soils.

It wasn’t used for years as nobody trusted it

There was a slow take up of the Variable PR equation for several reasons:

• A general reluctance to adopt new methodologies.
• Updating existing models to the new equation would require expensive re-verification.
• But mostly, the lack of a standard methodology for deriving values of antecedent precipitation index for design storms.?

The lack of design values was because the funding obtained for development had not been enough to cover Phase 2 of the project to derive these values.?The problem wasn’t that there was no methodology, but rather that everyone had their own methodology, ranging from robust to guesswork.?However, in 2002 the late Jamie Margetts published his analysis relating design values to annual rainfall and Variable PR soon became the dominant equation in the UK.

It was replaced by the UKWIR equation in 2013

No sooner had it become the dominant equation than there was an UKWIR project to develop an improved equation.?This made the following changes:

• The definition of soil type changed from the old 5 classes to the new UK specific 29 HOST classes.?This makes it more difficult to use outside the UK.
• The “additional” paved and roof surfaces were transferred to a new intermediate surface rather than to the permeable surface.?The characteristics of this surface did not vary with soil type.

The UKWIR equation therefore had the complication of some extra parameters and was not seen to offer dramatic improvements.?It also suffered from the same early problem as the Variable PR equation of not having standard antecedent values for design storms.

The UKWIR equation has not taken off in the last 10 years, but it took longer than that for the Variable PR model to get established, so wait and see.