Flood Hydroclimatology:

Insights into Mixed Flood Populations

Katie HirschboeckLaboratory of Tree-Ring Research

University of ArizonaApril 24, 2009

How do we transfer the growing body of knowledge

about global and regional climate change and variability

to individual watersheds

to develop useful scenarios about hydrologic

extremes?

Key Question:

Key Need: to understand the processes

that deliver precipitation (or the lack thereof)

to individual watersheds, at relevant

time and space scales

1. UNCERTAINTY: The Challenge of the “Upper Tails”

2. ASSUMPTIONS:The Standard iid Assumption for FFA

3. RE-THINKING:New Insights from “Flood Hydroclimatology”

4. ANTICIPATING THE FUTURE:Scenario building for a post-stationary world

A “Story” in Four Chapters:

1. UNCERTAINTY

SKEWED DISTRIBUTIONExtreme events tails of

distribution

Gaged Flood Record -- Histogram (Standardized Discharge Classes)

The Challenge of the “Upper Tails”

StandardizedMean Standardized

Mean

o = partial series

= annual series

Flow Time Series

The gage was shut downin 1980

A fairly long record with lots of variability . . . .

Flow Time Series

The flood of October 1983!

(WY 1984)

Santa Cruz River, Tucson Arizona Example

The record flood of October

1983!

Typical dry river bed or minor low flow

vs.

The Challenge of the “Upper Tails”

Flood Frequency Analysis:

Theoretical Dilemmas

(SOURCE: modified from Jarrett, 1991 after Patton & Baker, 1977)

. . . can fail when “outlier” floods occur !

SOURCE: modified from Jarrett, 1991, after Patton & Baker, 1977

Curves A & B indicate the range (uncertainty) of results obtained by using conventional analysis of outliers for 1954 & 1974 floods.

Pecos River nr Comstock,

TX

The Challenge of the “Upper Tails”

2. ASSUMPTIONS

http://acwi.gov/hydrology/Frequency/B17bFAQ.html#mixed

“Flood magnitudes are determined by many factors, in unpredictable combinations.

It is conceptually useful to think of the various factors as "populations" and to think of each year's flood as being the result of random selection of a "population”, followed by random drawing of a particular flood magnitude from the selected population.”

“ iid ” assumption: independently, identically

distributed

The standard approach to

Flood Frequency

Analysis (FFA) assumes

stationarity in the time series

& “iid”

The Standard iid Assumption for FFA

3. RE-THINKING

Meteorological & climatological flood-producing

mechanisms operate at

varying temporal and spatial scales

FLOOD-CAUSING MECHANISMS

Summer monsoon convective event

Synoptic-scale winter event

Tropical storm or other extreme event

The type of storm influences the shape of the hydrograph and the magnitude & persistence of the flood peak

This can vary with basin size (e.g. convective events are more important flood producers in small drainage basins in AZ)

Storm type hydrograph

HYDROCLIMATOLOGY

Weather, short time scales Local / regional spatial

scales Forecasts, real-time warnings

vs.

Seasonal / long-term perspective Site-specific and regional synthesis of

flood-causing weather scenarios Regional linkages/differences identified Entire flood history context

benchmarks for future events

HYDROMETEOROLOGY

It all started with a newspaper ad . . . .

Re-Thinking the “iid” Assumption

THE FFA“FLOOD PROCESSOR”

With expanded feed tube – for entering all kinds of flood data

including steel chopping, slicing & grating blades

– for removing unique physical characteristics, climatic information, and outliers

plus plastic mixing blade – to mix the populations together

Alternative Conceptual Framework:

Time-varying means

Time-varying variances

Both

SOURCE: Hirschboeck, 1988

Mixed frequency distributions may arise from:

• storm types

• synoptic patterns

• ENSO, etc. teleconnections

• multi-decadal circulation regimes

FLOOD HYDROCLIMATOLOGY

is the analysis of flood events within the context of their history of variation

- in magnitude, frequency, seasonality

- over a relatively long period of time

- analyzed within the spatial framework of changing combinations of meteorological causative mechanisms

SOURCE: Hirschboeck, 1988

This framework of analysis allows a flood time series to be combined with climatological information

To arrive at a mechanistic understanding of long-term flooding variability and its probabilistic representation.

APPROACH

Meteorological / Mechanistic / Circulation-Linked

Flood Hydroclimatology Framework / Link to Probability Distribution

“ Bottom–Up ” Approach(surface-to-atmosphere)

Observed Gage Record

WINTER &

Seasonality of Peak Flooding

Flood Hydroclimatology Example

• Peaks-above-base: 30+ gaging stations in Arizona

• Synoptic charts + precipitation data causal mechanisms

ANALYSIS

• Peaks-above-base -- 30+ gaging stations in Arizona

• Synoptic charts + precip data + decision tree

assigned causal mechanism / flood type

• Analyzed floods grouped by type

-- spatially-- temporally /

interannually

Sample Distributions of Gila Basin Gaged Peak

Flows:

Flood Hydroclimatology Example

Are there climatically controlled mixed populations within?

Santa Cruz River at TucsonPeak flows separated into 3 hydroclimatic subgroups

Hirschboeck et .al. 2000

Tropical storm Sumer

Convective

Winter Synoptic

All Peaks

Remember the Santa Cruz record?

What does it look like when classified hydroclimatically?

What kinds of storms produced the biggest floods?

Santa Cruz at Tucson

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

50000

1915 1920 1925 1930 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000

Water Year

Dis

char

ge in

(cf

s)52700 (cfs)

Convective

Tropical Storm

Synoptic

Hydroclimatically classified time series . . .

Hirschboeck et .al. 2000

Verde River below Tangle Creek

Peak flows separated into 3 hydroclimatic subgroups

Tropical storm

Sumer Convectiv

e

Winter SynopticAll Peaks

Historical Flood

Thinking Beyond the Standard iid Assumption for FFA . . . .

Based on these results we can re-envision the underlying probability distribution function for Gila Basin floods to be not this . . . .

Alternative Model to Explain How

Flood Magnitudes Vary over Time

Schematic for Gila River Basin based on different storm types

Varying mean and standard deviationsdue to different causal mechanisms

. . . but this:

IMPORTANT FLOOD-GENERATING TROPICAL STORMS

Tropical storm Octave Oct 1983

Hurricane Lili Oct 2002

Tropical

Storm Flood Events

When the dominance of different types of flood-producing circulation patterns changes over time, the probability distributions of potential flooding at any given time (t) may be altered.

Conceptual Framework for Circulation Pattern Changes

El Nino year

La Nina year

Blocking Regime

Zonal Regime

. . . or this:

Conceptual Framework for Low-Frequency Variations and/or Regime Shifts:. . . or this:

A shift in circulation or SST regime (or anomalous persistence of a given regime) will lead to different theoretical frequency / probability distributions over time.

Hirschboeck 1988

By definition extreme events are rare . . . hence gaged streamflow records capture

only a recent sample of the full range of extremes that have been experienced by a given watershed.

To fully understand flood variability, the longest record possible is the ideal . . .

especially to understand and evaluate the extremes of floods and droughts!

ADVANTAGES OF INTEGRATING THE PALEORECORD

Using Paleo-stage Indicators & Paleoflood Deposits . . .

-- direct physical evidence of extreme hydrologic events

-- selectively preserve evidence of only the largest floods . . .

. . . this is precisely the information that is lacking in the short gaged discharge records of the observational period

Flood Frequency Analysis

(SOURCE: Jarrett, 1991 after Patton & Baker, 1977)

Curves A & B indicate range (uncertainty) of results obtained by using conventional analysis of outliers for 1954 & 1974 floods.

Curve C is from analyses of paleoflood data.

Q (discharge) uncertainty

R.I. uncertainty

Pecos River nr Comstock,

TX

Compilations of paleoflood records combined with gaged records suggest there is a natural, upper

physical limit to the magnitude of floods in a given region --- will this change?

Envelope curve for

Arizona peak flows

Historical FloodLargest paleoflood

(A.D. 1010 +- 95 radiocarbon date)

1993

FLOOD HYDROCLIMATOLOGY evaluate likely hydroclimatic causes of pre-

historic floods

4. ANTICIPATINGTHE FUTURE

How do we transfer the growing body of knowledge

about global and regional climate change and variability

to individual watersheds

to develop useful scenarios about hydrologic

extremes?

Key Question:

Key Need: to understand the processes

that deliver precipitation (or the lack thereof)

to individual watersheds, at relevant

time and space scales

Web-based “course” by UA’s Roger Caldwell:

“Anticipating the Future” http://cals.arizona.edu/futures/

• Represent Events by Simple Curves

• Question Assumptions

• Watch for Groupthink and Fixed Mindsets

• Expect Both Surprises & ‘Expected Results’

• Several Solutions are Likely

MIXED POPULATION FAQ

Question: “Floods in my study area are caused by hurricanes, by ice-affected flows, and by snowmelt, as well as by rainfall from thunderstorms and frontal storms. How do I determine whether mixed-population analysis is necessary or desirable?”

Flood Hydroclimatology “in practice?”

“In practice, one determines whether the distribution is well-approximated by the LPIII by:

-- comparing the fitted LPIII --- with the sample frequency curve defined by plotting observed flood magnitudes versus their empirical probability plotting positions . . .

If the fit is good, and if the flood record includes an adequate sampling of all relevant sources of flooding (all "populations"),

then there is nothing to be gained by mixed-population

analysis.”

Answer:

from Hirschboeck 2003 “Respecting the Drainage Divide” Water Resources Update UCOWR

(Def): Interpolation of GCM results computed at large spatial scale fields to higher resolution, smaller spatial scale fields, and eventually to watershed processes at the surface.

ONE APPROACH: DOWNSCALING

PROPOSED COMPLEMENTARY APPROACH:

RATIONALE FOR PROCESS-SENSITIVE UPSCALING:

Attention to climatic driving forces & causes: -- storm type seasonality-- atmospheric circulation patterns

with respect to:-- basin size -- watershed boundary / drainage divide

-- geographic setting (moisture sources, etc.)

. . . can provide a basis for a cross-scale linkage of GLOBAL climate variability with LOCAL hydrologic variations

at the individual basin scale . . .

CONCLUSIONS

Insights on Flood Hydroclimatology & Mixed Populations

for AnticipatingFuture Floods

Mixed Distributions 1. Implications for predicting the

tails of a distribution

The distributions of key subgroups may be better for estimating the probability and type of extremely rare floods than the overall frequency distribution of the entire flood series.

Suggestion: Separate out causes & linkages by stratifying by subgroup.

Hydroclimatic Regions 2. Implications for spatial

homogeneity

-- Basins can be grouped according to how their floods respond to different types of mechanisms and circulation patterns

-- This grouping can change from season to season

-- This grouping is also basin-size dependent

Non-Stationarity & iid Implications for time series

homogeneity, stationarity & the iid assumption

The conceptual framework of climate-driven time-shifting means, variances and/or mixed distributions provides a useful explanation for non-stationarity in flood times series and challenges the iid assumption.

For floods, climatic changes can be conceptualized as time-varying atmospheric circulation regimes that generate a mix of shifting streamflow probability distributions over time.

This conceptual framework provides an opportunity to evaluate streamflow-based hydrologic extremes under climatic scenarios defined in terms of shifting modes or frequencies of known flood-producing synoptic patterns, ENSO, etc.

Climatic Variability Implications for evaluating how flood time series may vary under a changing

climate

PROCESS SENSITIVE UPSCALING: