Calculating Flood Recurrence Intervals

Professor: Alright, this is your Geology
instructor.

Today we are going to talk about
how to calculate Flood Reoccurrence

Intervals, uh, discussion of
Flood Reoccurrence Intervals, as well

as flood probabilities is given in other--
other of my online materials, but, uh, so

we are going to focus instead on how we
actually, calculate those and to begin with

when we talk about floods, we typically
talk about discharge, which is the, uh,

volume per time in the river, so for
instance, gallons per minutes, but we also

talk about stage and today we're just
going to use stage.

Stage refers to the height of the, uh,
water surface and the channel relative to

some zero datum and you might be used to
thinking of, of, uh, for instance the

depth of water in a channel and we could
work with depth, the problem with depth

is that the bottom of the bottom of the
river channel, uh, may go down, it may go

up overtime and its--its--it's not
necessarily consistent between

individual floods, so we talk about stage
which, uh, by using, a zero datum then

we're always talking about where the
water surface is relative to something

that we know and that--that's our datum.

So, we're going to look at Flood
Recurrence Intervals as a function of

stage and, um, when we--when we look at
these things, one of the questions that we

might ask is, 'what is the stage of the
100-year Recurrence Interval Flood?'

and uh, this is a flood that we would
expect on average to see that once

every 100 years it has a 1% chance of,
uh, occurring any given year as well.

So, we think of, uh, a flood, we're going
to look at a hydrograph which shows us

the amount of water in a channel, uh,
overtime and in this case, stage again is

the height of the water surface above
some datum which is the black line right

here and we're going to see how-the
hydrograph-how stage changes during

the course of--of a flood.

So, the water gets deeper, the water gets
deeper, peaks at some point,

and then the water goes down.

When we talk about Flood Recurrence
Intervals, we're typically talking about

the largest flood that occurred in any
given year in the peak stage, so the

highest stage that the river reached in--
in any-any given year and that's what

we're going to work with today.

So, today we're going to ask, 'what is
the stage of the 100-year

Recurrence Interval Flood for, uh, an
example river.

To calculate river flood-Flood Recurrence
Intervals, we collect, uh, data for peak

floods, so this is the stage of the
largest flood in these particular years,

2003 through 2011, and to calculate, uh,
flood recurrence intervals, what we nee--

first need to do is rank these floods in
order from the largest to the smallest.

The largest will have a rank of one, the
smallest will have a rank of nine in this

case because we have nine years of data.

And, um, when we work with these things
we, uh, we're going to do a few simple

calculations, one of those calculations
requires us, uh, to know the total number

of--of years, which we're just going to
designate as n, and so in this case

we have nine years of data so n equals 9.

Once we have the rank, we're going to
calculate probability which is that rank

divided by n plus one, in this case,
that's going to be rank divided by 10

and then we'll multiply that times a
hundred to get the--the probability, uh,

here and, uh, conveniently in this case,
has rank of 1, then its 1 divided by 10

times 100, that's 10%, rank of 2,
2 divided by 10 times 100, 20%,

so things are going to, uh, work out easy
in terms of the-of the math on these, but

after we calculate probability, we can go
through then and calculate the recurrence

interval, which is again, um, what we're
most interested in--in--in this

particular case, but for the recurrence
interval, it's just n plus 1 divided by

rank, so this is going to be 9 plus 1 or
10 divided by the rank and we'll see that

again here shortly.

So, here is our table of data, we're going
to order the floods according to rank and

again, the largest flood is going to have
a rank of one, see that in the case,

it's, uh, the 2007 flood, which at a stage
of 26.

We'll look for the data and find the
second largest flood, oop, there it is,

2009, the third largest, the fourth
largest, fifth, sixth,

seventh, eighth, nineth.

So, we ranked the, uh, the floods in order
of their size and now that we have the

ranks, we can go ahead and calculate
probability and again that's going

to be rank divided by 10 in this case, so
n plus 1, so rank divided by 10 times 100,

and if we do that, uh, in order from top
to bottom, the probability of the 2003

flood becomes 30%, 2004, 70, and I'll just
go through quickly and we'll see what

these different values are.

So now we have the probabilities for the--
for the different sized floods,

and again, because we have nine years'
worth of data the math works out

conveniently in that, uh, the rank will
be 3, the probability will be 30, if the

ranks one, then the probability's 10, but
recurrence intervals typically don't work

out so neat, uh, we're going to calculate
recurrence interval again as n plus one

over rank, so nine plus one over rank,
and, uh, for the first of those then that

would be 10 divided by a rank of 3, so
3.33, we'll do this for 2004, 1.43, so 10

divided by 7, 10 divided by 8, 10 divided
by 6, 10 divided by 1,

that was a hard one, 10 divided by 4, 2.5,
10 divided by 2 so 5, 1, and finally

10 divided by 5 so a recurrence interval
of 2 years, and again this is the average

time between, uh, these different sized
floods, although there is a slightly more

technical definition that we're going,
uh, we're going to skip for now and you

can look at the other course
material for.

So, we have our data, and we need to plot
that data.

Now, I've posted a separate video which
shows you how to plot the data points and

so I'm not going to talk about the actual
plotting at the moment, instead I'm just

going to note that, uh, in the exercises
and assignments, we'll grab the data

points, drag them up, put them on the
graph pap-- in the appropriate

places on the graph paper and then draw
a trend line through them, so please refer

to the other video if you're not sure
how to plot or want to learn how to plot,

but when you do that, in this case again,
we're after the 100-year Recurrence

Interval Flood, our data would end up
looking something like this, and so how

are we going to use that to calculate the
size of the 100-year flood?

Welp, the 100-year flood has a probability
of 1% and so if that's the case, here we

have 1%, we come up 'till we hit the trend
line, where we hit the trendline then

we're going to turn and go to the left
to get to stage and so in this case, the

100-year Recurrence Interval Flood
has a stage of 32 feet.

So, we were able to plot those nine data
points, draw a trendline through them and

then from that estimate the size of the
32-year flood.

Now, we could just as easily estimate
the size of the 50-year flood and if we

did that, that would be right here, we
come across and that would be

approximately a stage of 30 feet, for
the--the 50-year flood.

What about the flood with 5% annual
probability?

Well, 5% annual probability, we'd come
up, we'd go over, 28 feet, okay, and that

actually, is the 20-year flood, note that
the 20-year Recurrence Interval Flood

is the same as the 5%, uh, uh, probability
flood, alright?

So, again, here's our completed data,
and, how to calculate things are--are shown

on the slides, I'll also be posting this
PowerPoint presentation as a PowerPoint

presentation with the course materials
online and, uh, as usual, if you have a

question, you're welcome to email me,
thank you.