Floods and droughts

Definitions

Flood: Floods occur when a

drainage basin experiences an

unusually intense or prolonged water

input. Flood is usually viewed as an

event in which the streamflow

exceeds the channel capacity,

resulting on overland flow (the

floodplain is inundated), but the

terms is also often applied more

generally to unusually high

discharge events.

Drought: A drought is an extended

period (months, years) that a region

experiences a deficiency in water

supply, generally because of

reduced precipitation.

http://www.11terra.com/rising_seas

http://library.thinkquest.org/03oct/00477/NatDisasterPages/Heidi

%20Draught/drought/droughtclassification.htm.htm

Floodplain

A floodplain is nearly flat land adjacent to a mature stream or river

extending from the stream channel to the base of the enclosing

valley. As the name implies, floodplains are water covered during

floods. Of course not all streams and rivers have floodplains.

Floodplains are fertile land for

agriculture (sediments are

deposited by floods) and they

can support rich ecosystems.

They are not particularly smart

places for human settlements.

Flood frequency

analysis

http://www.ceh.ac.uk/data/nrfa/data/timeseries_plots.html

Goal: Using a given record of stream

flows, such as a left, find the

exceedence probability and return period

of discharge events of a given size.

Flood frequency analysis useful for

developing floodplain management

strategies and informing infrastructure

design.

Getting exceedence probability Exceedence probability EP(Q) is the probability of discharge Q exceeding a

specified value of discharge Qsp

EP(Q) = Probability {Q > Qsp} = 1 – F(Q)

Where F(Q) is the cumulative distribution function (CDF) of discharge:

F(Q) = Probability {Q ≤ Qsp}

http://www.itl.nist.gov/div898/handbook/eda/section3/eda362.htm

Below: Probability density function (PDF) and cumulative distribution

function (CDF) for a normal distribution

Return period

If EP(Q) stays constant with time, then the interval between

occurrences of the event Q > Qsp is 1/EP(Q). Thus

exceedance probability can be expressed in terms of a return

period TR(Q), also know as a recurrence interval.

TR(Q) = 1/EP(Q) = 1/(1-F(Q))

If we consider the statistics using the largest discharge for each

year (as is typically done), then TR(Q) is the average number of

years between intervals when Q > Qsp.

Hence, by definition, the 100 year flood is the annual peak

discharge with an event probability of 0.01:

TR(Q) = 1/EP(Q)

TR(Q) = 1/0.01 = 100 years

Z-score transformation

http://www.thefullwiki.org/Z_scores

Assume for the moment that the largest discharge events for each year are drawn from

a normal distribution hence having the characteristics depicted in the figure below. For

each discharge value, we can compute a Z-score:

Z = [Q - <Q>]/SD

Where <Q> is the average of all of the largest annual discharge values, Q is the largest

discharge for a given year, and SD is the standard deviation of <Q>.

As seen in the figure:

For Q = <Q>, Z=0, EP(Q)=50%

For Q = <Q> + SD, Z=1, EP(Q) =16%

For Q = <Q> + 2.SD, Z=2, EP(Q) = 2.3%

For Q = <Q> + 3.SD, Z=3, EP(Q) = 0.01%

Dealing with non-normal distributions

Problem: The distribution of highest annual flows will

probably not be a normal distribution. It is more

likely to be a log normal distribution (example at

right). A log normal distribution is probability

distribution whose logarithm is normally distributed.

Solution 1: Non-parametric – make no assumptions

about the distribution:

•Rank the flows from lowest (i=1) to highest (i=N)

•Estimate the quantile value for each flow: qi =

i/(N+1)

•Make a plot of qi versus Qi (discharge) and

interpolate through the points.

Solution 2: Parametric - fit an appropriate PDF to

the discharge data (e.g., a log normal distribution).

The advantage of this approach is that one can

extrapolate beyond the bounds of the actual data to

estimate the high (floods) and low (droughts)

exceedence probability values. However, one must

be sure that the assumed distribution is the correct

one (see Section C-5 in Dingman, 2002).

http://www.danvk.org/wp/category/boggle/

The log Pearson III distribution is

used by federal agencies to

model flood flows.

Flow frequency curve

http://pubs.usgs.gov/wri/wri974073/report.html

At right is the flow frequency

curve for the Virgin River at

Littlefield AZ (gauging station

09415000) based on different

estimates. The 100 year

flood (annual exceedence

probability of 1%) is about

750 m3s-1. Half of the time

(exceedence probability of

50%) , the discharge

exceeds about 150 m3s-1

Source: USGS

Front Range Colorado: Mixed Population Floods

In the Front Range, the largest floods are due to rain

events, though snowmelt floods are more common

In the Alpine, rain storms are not large enough to create

significant floods, and the hydrology is dominated by snowmelt

Predicting flow at un-gauged sites

The techniques just discussed apply to gauged streams.

However, we may want to get exceedence probability relations

for ungauged streams:

•Get magnitude exceedence probability relations at gauging

stations from the surrounding area.

•Use multiple linear regression to relate the magnitude of floods

with specified exceedence probabilities at those gauging

stations to characteristics of their drainage basins (e.g., area,

slope, location, forest cover, elevation, geology, channel size).

•Apply the equation to the ungauged stream based on the

characteristics of its drainage

Regional equations for

predicting flood peaks

Source: USGS

Floodplain management

Flood control dams: These reduce

the peak flood discharge associated

with a given exceedence probability

at locations downstream of the dam.

Their effects decrease rapidly with

downstream distance and tend to be

less effective for larger floods.

Dikes and levees: Designed to

prevent flooding behind them. They

can increase flood levels

downstream. Overtopping of dikes

and levees can have catastrophic

consequences (e.g., New Orleans

after Hurricane Katrina, see

photograph at bottom right)

http://www.uwsp.edu/geO/faculty/ozsvath/images/flood_control_dam.htm

http://www.hurricanekatrina.com/

Floodplain management (cont.)

Channelization: This involves straightening,

deepening or lining a stream channel to enable

the channel to carry larger discharge without

overtopping its banks. Channelization turns out

to have only temporary beneficial effects and

environmental impacts can be severe.

http://www.streamteamok.net/projects/Pictures%20113.jpg

Floodproofing: Floodproof buildings

(through retrofit or as part of new

construction) so that they can handle

flooding without much damage.

http://www.wbdg.org/resources/env_flood.php

Floodplain management (cont.)

Removal of structures: Remove buildings in

harm’s way

Flood warning: Provide enough advance warning

of a flood (e.g., with a siren, as in Boulder) for

people to get out of the area anticipated to be

affected. Flood warning works best on large rivers

that respond relatively slowly and predictably to

water input events. Warning systems are less

effective when it comes to flash floods that require

rapid response time (e.g., Big Thompson River 1976,

we’ll look at this shortly).

Floodplain zoning: Land use controls that limit

development on flood prone areas

http://www.rcscomm.net/floodwarning.html

http://www.co.washington.wi.us/departments.iml?Detail=147

Boulder Creek, 1894

Bridge at 4th St.

Denver Public Library

Near 7th St., looking east

Between May 30-June 1, heavy rains fell in

the Boulder and South Boulder Creek

basins. Rainfall records for a 96-hour

period showed that the mountain drainage

area received from 4.5 to 6 inches of

precipitation which combined with

snowmelt runoff. The estimated flow on

Boulder Creek at 4th Street was 11,000 to

13,500 cfs, similar to the flow of a 100-

year flood of 12,000 cfs (from US Army

Corps of Engineers).

http://www.boulderfloods.org/Mapviewer/bo

ulder_centrall_floodhazardzone.htm

South Boulder Creek, 1938 Closeup of Dance Hall.

Both Denver Public Library

Houses on the brink

The storm produced general rains over all

of eastern Colorado, with over 6 inches

reported west of Eldorado Springs. Boulder

reported 3.62 inches of precipitation from

31 August to 4 September with 2.32 inches

falling during 2 September. Eldorado

Springs had 4.42 inches of rainfall.

Approximately 80 % of the total

precipitation falling in the South Boulder

Creek basin fell in the late afternoon and

evening of 2 September. The resulting

flood, with a peak discharge of 7390 cfs

arrived at Eldorado Springs at 10 PM on 2

September.

http://bcn.boulder.co.us/basin/history/1938flood.html

Big Thomson River, 1976

Denver Post, David Buresh

Denver Post, Dave Cupp

The flood was set off by a severe rainstorm (convection with easterly flow) that stalled

between Estes Park and Loveland on July 31, 1976. The storm dumped nearly 8 inches of

rain in one hour, and up to 12 inches of rain in four hours . The flood claimed 144 lives and

destroyed more than 400 homes. The peak flood flow on the Big Thompson was computed

to be just over 30,000 cfs. A 100 year flood? 1000 year? 10,000 year? There is debate.

Source:

USGS

Source:

USGS

Source: O’Connor et al., The Geology and Geography of Floods

Source: O’Connor et al., The Geology and Geography of Floods

The Missoula Floods – a glacial outburst : One of the largest floods known in geologic record

http://www.nwcreation.net/articles/missoulaflood.htm

Lake Bonneville flood, 15,000 BP

http://imnh.isu.edu/digitalatlas/

hydr/lkbflood/lbf.htm Lake Bonneville was the precursor of the Great Salt Lake

and once covered an area of more than 19,000 square

miles. Approximately 15,000 years ago, the lake suddenly

discharged to the north. This flood is thought to be caused

by capture of the Bear River which greatly increased the

supply of water to the Bonneville Basin. The flood waters

flowed over Red Rock Pass (where the failure occurred) in

southeastern Idaho and continued westward, following the

approximate path of the present Snake River. Peak flow

may have been 15 million cfs. The Melon Gravels

deposited by the flood average three feet in diameter, but

some well-rounded boulders range up to 10 feet in

diameter. Boulders were dumped in unsorted deposits up

to 300 feet thick.

(http://imnh.isu.edu/digitalatlas/hydr/lkbflood/lbf.htm)

http://travellogs.us/Miscellaneous/Geology/Melon%20R

ocks/Melon%20Rocks.htm

The Laurentide Ice Sheet and the routing of overflow from the Lake Aggasiz basin (dashed line) to the Gulf of Mexico just before the Younger Dryas (a) and routing of overflow from Lake Aggasiz through the Great Lakes to the St. Lawrence and northern North Atlantic during the Younger Dryas (b) [from Broecker et al., 1989, by permission of Nature]. Massive discharge of freshwater into the North Atlantic from the melting Laurentide Ice Sheet could have disrupted the ocean thermohaline circulation, initiating the YD cold event.

The Younger Dryas, 11,500 BP, initiated by a massive flood?

Open channel flow and flood waves

Stream discharge Q can be expressed as follows:

Q = U.Y.B (Eq. 1)

Where U is the average flow velocity (m s-1), Y is the average depth of the flow (m) and

B is the water surface width (m).

Open channel velocity U can be given by the Manning Equation :

U = (um.Y2/3.S1/2)/n (Eq. 2)

S is the water surface slope, Manning’s “n” is a factor characterizing channel

conductance/resistance (it depends on channel roughness and irregularity) and um is

a unit conversion factor.

Dingman (1984) has shown that the velocity of a flood wave UF is:

UF = 1/B.∂Q/∂Y (Eq. 3)

Where B is the water surface width (channel width), Q is the discharge, and Y is the

average depth of the flow.

Open channel flow and flood waves (cont.)

Q = U.Y.B (Eq. 1)

U = (um.Y2/3.S1/2)/n (Eq. 2)

Rearrange and combine the above two equations:

U = Q/(Y.B)

U = (um.Y2/3.S1/2)/n

Q/(Y.B) = (um.Y2/3.S1/2)/n

Q = Y3/3.B.(um.Y2/3.S1/2)/n

Q = B.(um.Y5/3.S1/2)/n (Eq. 4)

Differentiate with respect to Y

∂Q/ ∂Y = 5/3.(um.Y2/3.S1/2.B)/n (Eq. 5)

Substitute the Manning Equation (Eq. 2) and Eq. 4 into the equation for flood wave

velocity (Eq. 3) and we get

UF = 5/3.U

Meaning that the flood wave moves faster (1.67 times) than the water itself!

Dingman 2002, Figure 9-2

Open channel flow and flood waves (cont.)

Q = B.(um.Y5/3.S1/2)/n

UF = 5/3.U

These two equations work for flood waves that remain within the river channel. The

relationship between flow velocity and flood wave velocity may be altered of the stream

overtops the channel banks and inundates the flood plain.

Dingman 2002, Figure 9-2

Velocities tend to be lower in the overbank

portion of the flood because they the water is

shallower and encounters higher resistance due

to vegetation (e.g., trees get in the way). The

flood wave velocity equation can be adjusted to

account for such effects.

http://www.geograph.org.uk/photo/148021

Example: Glen Canyon Dam release

http://www.glencanyon.org/library/bureauhistory.php

In April 2009 there was a large water release

from the Glen Canyon Dam on the Colorado

River, intended to improve stream habitat by

mimicking the spring discharge peak that

would have naturally occurred without the

dam in place.

Consider the travel time of the flood wave

associated with the release from Lee’s Ferry

(in Glen Canyon) to the Grand Canyon.

http://www.grandcanyonairlines.com/gca/gcaimg/fulls/glencanyon4.jpg

Glen Canyon example (cont.)

Peak discharge Q at Lee’s Ferry: about 12,000

cfs at 2200h, 4/18/09

Peak discharge Q at Grand Canyon: was about

12,500 cfs at 1600h, 4/19/09

Travel time of flood wave = 18 hours = 64,800 s

Distance travelled = 87 miles = 459,360 feet

UF = 459,360 ft/64,800 sec ≈ 7 ft s-1

U = 2.5 feet s-1

Hence UF ≈ 2.7.U

Question: Why higher than 1.67?

Primary answer: Channel morphology

Channel width at Lee’s Ferry: 415 ft

Channel width at Grand Canyon: 290 ft

http://www.sangres.com/dimages/arizona/coconino-

county/Glen-Canyon-Dam.gif

Glen Canyon example (cont.)

Go back to the equation for flood wave velocity from Dingman

(1984):

UF = 1/B.∂Q/∂Y (Eq. 3)

Where B is the water surface width (channel width), Q is the

discharge, and Y is the average depth of the flow. Hence, because

the channel narrows, the flood wave propagates faster than

predicted.

290 ft/415 ft = 70%, i.e., Grand Canyon channel width is 70% of the

channel width at Lee’s Ferry

70% of 2.7 =1.9, closer to 1.67 but still high.

Explanation: Water velocity increases slightly downstream.

Drought

Drought is part of natural climate

variability. There are three basic

sequences of drought and associated

impacts:

Meteorological drought: Deficit in

precipitation, often (not always)

accompanied by above average

temperatures, high winds, low humidity

and high solar radiation.

Agricultural drought: Continued

precipitation deficit, leading to a soil water

deficit, hindering agriculture and natural

plant growth.

Hydrologic drought: The precipitation

deficit continues, and stream discharge,

lake wetland and reservoir levels drop,

with impacts on wildlife habitat.

http://www.drought.unl.edu/whatis/concept.htm

Low flow analysis: Flow duration curve

http://streamflow.engr.oregonstate.edu/analysis/flow/tutorial.htm

The flow duration curve is a useful

tool for streamflow analysis; it gives

the flow associated with any

exceedence or non-exceedence

probability. The flow which is

exceeded 95% of the time is an

index of water availability used for

design purposes. In the example at

right, for the Alsea River at

Tidewater (WY), the 95%

exceedence flow is about 80 cfs.

Flow duration curves are computed

using daily streamflow data.

Palmer Drought Severity Index (PDSI)

http://www.cpc.noaa.gov/products/analysis_monitoring/r

egional_monitoring/palmer/2010/

The Palmer Drought Severity

Index is a measure of dryness

based on recent precipitation

and temperature, developed by

Wayne Palmer in 1965. It is

based on a supply and demand

model of soil moisture. NOAA

prepares weekly PDSI maps

for the United States, the

example at right is for the week

ending 21 September 2002,

during the drought the gripped

much the western part on the

nation.

Calculating PDSI

“Computation of PDSI begins with the determination of monthly departure of moisture

from normal by estimating the gaps between actual precipitation and precipitation that

is climatically appropriate for existing conditions (CAFEC-P).

The CAFEC-P can be obtained from the basic terms of the water balance equation,

which deducts the expected supply from the expected demand factors to get the

water demand that must be met by precipitation.

Parameters of the CAFÉC-P include evapotranspiration, soil recharge, runoff, and

moisture loss from the surface layer. The monthly moisture anomalies are then

converted into the indices of moisture anomaly by multiplying by a weighting factor.

Finally, dryness or wetness severity is deduced from the moisture anomaly index and

the PDSI of the previous month. Theoretically, PDSI is a standardized measure,

ranging from about −6.0 to +6.0”

From: Spatial Variation and Trends in PDSI and SPI Indices and Their Relation to

Streamflow in 10 Large Regions of China, Jianqing Zhai, Journal of Climate, 23,

649-663.

Palmer Drought Severity Index (cont.)

PDSI for July 1934, during the “Dust Bowl”

Dust Bowl

The dust bowl of the 1930s was named for

immense dust storms which at times

reached east coast cities. The dust bowl

resulted from a combination of extended

drought and poor farming practices. Plowing

the topsoils of the plains eliminated deep-

rooted grasses that would normally have

kept soils in place during drought conditions

and high wind events. There were at least 4

distinct drought events: 1930–31, 1934,

1936, and 1939–40 (Riebsame et al., 1991).

Dust storm approaching Stratford, Texas Dust bowl

surveying in Texas

Image ID: theb1365, Historic C&GS Collection

Location: Stratford, Texas

Photo Date: April 18, 1935

Credit: NOAA George E. Marsh Album

June 4 1937, at Goodwell, Oklahoma. (Mrs. Emma

Love, Goodwell, Oklahoma)

M Hoerling, A Kumar Science 2003;299:691-694

Temperature and precipitation anomalies, 1998-2002

While Western U.S. drought was extreme in 2002, it was preceded by prolonged

below-normal precipitation and above-normal temperatures during 1998–2002 over

an extensive swath of the Northern Hemisphere mid-latitudes spanning the United

States, the Mediterranean, southern Europe, and Southwest and Central Asia

The figure above shows observed, standardized 4-year–averaged SST anomalies for June

1998 through May 2002 (top), and monthly anomalies for the climatological warm pool region of

the tropical Indian and west Pacific (left) and the climatological cold tongue region of the

equatorial east Pacific (right)

M Hoerling, A Kumar Science 2003;299:691-694

An unusual pattern of sea surface temperatures

Global climate models (GCMs) driven by the observed monthly varying anomalies in sea

surface temperature were able to reproduce the basic pattern of annual averaged surface

temperature (left) and precipitation (right) anomalies observed over the 4-year period June

1998–May 2002. Conclusion: the drought was largely driven by ocean conditions.

M Hoerling, A Kumar Science 2003;299:691-694

Modeling temperature and precipitation anomalies

The observed pressure height anomaly field at the 200 hPa level over the 4-year period June

1998–May 2002 (left) shows an almost uninterrupted zonal belt of unusually high pressure

spanning the middle latitudes. The anomaly field as simulated by atmospheric GCMs forced

with the observed, monthly varying SST and sea ice anomalies of the period is similar. Drying

of the lower atmosphere is consistent with this pattern.

M Hoerling, A Kumar Science 2003;299:691-694

Atmospheric circulation anomalies

Drought feedback processes

Drought can be exacerbated by

feedback processes. The figure

at right conceptualizes processes

in the Sahel of Africa. If the land

dries out, there will be less

vegetation, meaning less

evaporation from the land, and

more solar radiation will be

reflected from the surface

These processes weaken the

monsoon that brings rainfall to

the area. The feedback can

involve land degradation due to

human activities.

http://oceanworld.tamu.edu/resources/environment-

book/desertificationinsahel.html , from Dryland Systems in

Ecosystems and Human Well-Being: Current State and Trends

Rain follows the plow?

“Rain follows the plow” refers to a late 19th century theory of climatology, popular in

the American West and Australia. It finds it origin with Charles Dana Wilber, a land

speculator, journalist, author and champion of the American West as a site of

agricultural development. From his 1881 book The Great Valleys and Prairies of

Nebraska and the Northwest:

"Suppose (an army of frontier farmers) 50 miles,

in width, from Manitoba to Texas, could acting in

concert, turn over the prairie sod, and after deep

plowing and receiving the rain and moisture,

present a new surface of green growing crops

instead of dry, hard baked earth covered with

sparse buffalo grass. No one can question or

doubt the inevitable effect of this cooling

condensing surface upon the moisture in the

atmosphere as it moves over by the Western

winds. A reduction of temperature must at once

occur, accompanied by the usual phenomena of

showers. The chief agency in this transformation

is agriculture. To be more concise. Rain follows

the plow."

http://homesteadcongress.blogspot.com/2009/10/

homestead-myth-rain-follows-plow.html

http://science.discovery.com/top-ten/2009/science-

mistakes/science-mistakes-07.html

Rain follows the plow?

The basis of the theory is that agriculture would affect the climate of these semi-arid

and arid lands, increasing rainfall and hence making them lush and productive. The

theory was promoted as a justification for the settlement of the “Great American

Desert” (the Great Plains). It was also used to justify the expansion of wheat growing

in marginal lands in Australia.

Today, we would view the argument in terms of precipitation recycling (discussed

earlier in the semester). Precipitation recycling is the fraction of precipitation that

falls within a watershed (or region) due to water that is evapotranspirated from that

region and then falls back within the same region.

http://www.physicalgeography.net/fundamentals/7t.html http://severe-wx.pbworks.com/w/page/

15957990/Thunderstorms

Rain follows the plow?

F+

F+

PL/P = 1/(1+ 2.F+/ET.A)

P = Total precipitation

PL = Precipitation of local origin

ET = Evapotranspiration

A = Area of watershed

F+ = Vertically integrated vapor flux

directed into the watershed (advective

moisture term)

E

T

From the formulation of

Brubaker et al. (2003):

To get a high recycling ratio (P/PL)

you want a large ET rate

and a small advective moisture term.

P

Dingman 2002 Figure 2-3

http://www.bopmyspace.com/image_50/thunderstorm

Rain follows the plow?

The problem: For most regions, including the American west, the bulk of precipitation is

“imported” in that the water vapor associated with the precipitation comes from outside

of the region.

http://memory.loc.gov/award/nbhips/lca/107/10785r.jpg

Hence:

Plow the fields and plant crops.

Transpiration and bare soil

evaporation take soil moisture and put

it into the atmosphere as water vapor.

While some of the water vapor may

fall back as rain within the same

general region, most is carried away

downstream.

Rain does not follow the plow. The

plow needs to follow the rain.

Extra Stuff

Northern Colorado Water Conditions: A great web site

http://www.dwr.state.co.us/SurfaceWater/default.aspx

Colorado snowpack conditions, Jul 11 2011

ftp://ftp-fc.sc.egov.usda.gov/CO/Snow/snow/watershed/daily/co_update_snow_sites.pdf

http://www.dwr.state.co.us/SurfaceWater/data/detail_graph.aspx?ID=BOCOBOCO&MTYPE=DISCHRG

Boulder Creek at Boulder, Colorado July 2011

2012

Average

High July flow for July 2012 reflects:

1) Sharply above average winter snowpack

2) High July rainfall total (summer monsoon)

7/12/2011: 933 cfs

Water Resources Research

Bijou Creek

Big

Thompson

Source: O’Connor and Costa

Source: O’Connor and Costa

Source: O’Connor and Costa