Desirable Properties for a Drought Index, or

Alice’s Adventures in SWSI-Land

Kelly T. Redmond

Western Regional Climate Center

Desert Research Institute

Reno Nevada

Drought Index Evaluation and Implementation in a Geospatial Framework Linked to Hydrologic Data Web Services

Planning Workshop

ESRL, Boulder CO, August 18-19, 2009

Some Drought Background

Drought fundamentally involves the concept of a water budget

Supply minus Demand

Drought as accumulated Supply minus Demand

Need status of components of the water balance

Supply components

Demand components

Ideally, everywhere in space, at the necessary resolution

Past, present, future

Drought is defined by its impacts

A Working Definition of Drought (very hard to avoid this approach) :

Insufficient water to meet needs

Subjective / Objective Issue

What does “objective” mean?

An objective process is one that brings all relevant

information to bear - RSP discussion

There are many ground truths at once

There are many droughts – simultaneously

This approach is more complicated, but more useful

What is the purpose of the Drought Monitor?

Drought as a human construct (is there “natural” drought?)

Reinforcement of this notion in presentations at 2009 Climate Diagnostics

and Prediction Workshop, Lincoln NE, by

Dave Stooksbury, Tom Pagano, Andrea Ray

None of the foregoing decreases the need for quantitative

measures of water inputs, outputs, storage (human and natural)

DROUGHTS and RAINBOWs

share one common property:

Every person experiences their own RAINBOW.

Every person experiences their own drought.

In general, the most consequential droughts occur in the wettest portion

of the year … though not always.

Temperature seasonality is nearly the same everywhere:

Monthly USA Precipitation Climatologies Jan-Dec

www.wrcc.dri.edu/summary/sodusa.html

Madison Valley Seasonality Comparison Area.

Adapted from Phil Farnes, Western Snow Conference, 1995.

Oct-Mar Apr-May-June

Fraction of Annual Total Precipitation, by Season

July-Aug

WRCC / OSU

K. Redmond, 2003. p 29-48, Water and Climate in the Western United States. U Colorado Press.

Colorado Precip-Elevation Distribution

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1000 1500 2000 2500 3000 3500 4000

Elevation (m)

% o

f To

tal

%Total PPT Elev %

From PRISM, courtesy of Chris Daly

March 10, 2004

7.5” / 170 mm

12” / 300 mm

55” / 1400 mm

70” / 1800 mm

Assorted Points about Indices

The “why” question :

What is the purpose?

Who is the audience?

What do we want an index to tell them?

What do they want an index to tell them?

What are we expecting that people will do with the information?

Indices are human constructions

How do we want the index to behave?

In extreme or unprecedented cases ?

In unusual cases (with other factors present) ?

In known past episodes ?

Assorted Points about Indices … continued

A fascination with numerics

Diagnosis / evaluation / testing.

How to “ground truth” indexes.

Which reality / realities do we wish to describe?

Judging good indices on the basis of bad data.

SPI (transparent) vs. Palmer (obscure)

Use promotes use

Homogeneity of input records

A useful series of articles about drought.

August 2002

Bulletin of AMS

Desirable Properties of Climate Indices *

1) Detailed understanding of caveats, limitations, assumptions should not be critical to proper interpretation for indices in wide public use. Indices should not be too complex.

2) Indices should not be overly simplified (e.g., “Colorado statewide precipitation” lumps too many things together).

3) Indices should offer improved information over raw data values.

4) For routine practical usage, historical time series of data must be readily available, recent values must be quickly computable, and both must be compatible (homogeneous record).

5) It is helpful if social and economic impacts are proportional to the value of the indices.

6) Indices values should be open-ended. Unprecedented behavior yields unprecedented values.

7) Normalization to background climate, in non-dimensional units, greatly facilitates spatial comparisons across very different settings.

8) Statistical properties and sensitivities should be thoroughly evaluated before operational usage.

9) Subindices, component indices, or other spin-offs help debug or explain unusual, alarming, or otherwise interesting behavior.

10)Measures of placement within the historical context are invaluable and frequently requested, typically as percentiles. The goal should be a 50–100-year perspective.

From: The Depiction of Drought, Kelly Redmond, Bulletin of AMS, August 2002, 83, 1143-1147.Adapted from Redmond, K. T., 1991: Climate monitoring and indices, Proceedings of a Symposium on

Drought Management and Planning, D. A. Wilhite, D. A. Wood, and P. A. Kay, Eds, Lincoln, NE, University of Nebraska, Lincoln, 29–33.

The Quantification of Drought: An Evaluation of Drought Indexes. Keyantash and Dracup, BAMS, 2002.

Robustness

Usefulness over a wide range of physical conditions.

Tractability

Practical computability (high level numerics, sparse data, short or incomplete records, etc).

Transparency

Clarity of the objective, rationale behind the index.

Sophistication

Conceptual soundness. May oppose trnasparency. e.g., relativity theory is not transparent or tractable, but nonetheless is a superior description.

Extendability

Degree to which an index may be extended across time to alternate sequences and histories.

Dimensionality

Composed of fundamental physical units, or, of normalized, dimensionless, probabilistic forms.

Surface Water Supply Index Considerations

Purpose … Need for application specificity, to be of use

What is the index supposed to correlate with?

Which quantitative impact or economic measures?

Are these available?

And for a sufficient time?

Components are as important as the whole thing

Precipitation

Snowpack

Streamflow

Reservoir storage

Groundwater and soil moisture status … relevant to surface water

Surface Water Supply Index Issues

Manipulated water systems have non-stationarity and/or non-normal statistics

Changes through time to system infrastructure

Dams raised

Dams added

Reservoirs kept low for repairs or other reasons

Changes through time in system measurement points

Gages added

Gages removed

Gages moved

Changes through time in operational policy and practices - reservoirs

Operations guidance changes emphasis

Project operated for different or additional purposes

Reservoir levels bounded by full and empty

Preference toward keeping reservoirs full (power, recreation)

Lake Powell Storage Through July 23, 2009

As of 23 July 2009: 67 % full (capacity 24.17 MAF)

Minimum: 33 % full on April 8, 2005

Lake Powell Elevation Through July 23, 2009

Water level on July 23, 2009 was 3641.76 ft, - 58 ft below full. Minimum level on April 8, 2005 was 3555 ft, -145 ft below full.Source: www.usbr.gov/uc/water/index.htl

Surface Water Supply Index Issues

Different periods of record for input data yield different statistics

Different SWSI components have different periods of record (POR)

ex: Snow vs reservoirs vs streamgages vs precipitation

For a given component (eg, snowpack) not all sites have same POR

Not all past droughts may have been sampled by all components or sites

Inclusion (or not) of 1950s or 1930s drought can make a difference

Tails of the distributions are most affected, and of greatest interest

Intercorrelation among the components (how independent is the input info?)

There is always at least some correlation, and sometimes a lot

Intercorrelations among components vary through the seasonal cycle

For some components, significant correlation with adjoining months

Surface Water Supply Index Issuess

Elephant versus mouse issue

Applies to each component, but especially to reservoirs

How to account for large and small components in a basin

Large differences within many basins

See upcoming examples

When should large and small systems be normalized ?

Relative versus absolute water

Percentages vs percentiles

Which reservoirs to include or exclude ?

All reservoirs matter to somebody, otherwise why build them ?

Statistics of aggregated water vs Aggregated statistics of water

When should we do one, or the other ?

In the general case these are different. Sometimes very different.

0.783

0.055

0.027

0.004

0.011Capacity Total

31,058,490 MAF0.121

0.009

0.083

0.007 0.003

0.898

Capacity Total

4,175,850 MAF

0.014 0.090

0.015

0.099

0.0700.011

0.701

Capacity Total

1,182,954 MAF

0.1690.018

0.056

0.004

0.753Capacity Total

2,252,243 MAF

Surface Water Supply Index Issues

How to calculate the monthly or seasonal coefficients (weights) ?

What to optimize against (what criteria ?)

Multiple possibilities, but nothing seems to stand out as “best”

Monthly or seasonal “shocks” with step changes in coefficients

Create continuously varying coefficients (Fourier series, etc) ?

Use coefficients as mechanism to include/exclude components/sites

Should work in all climates in the US

In non-snowy climates, snow coefficients go to zero

Inter-correlation issue comes up here as well as other places

Predictive vs diagnostic applications

Some diagnostic information is also (highly) prognostic

This varies (substantially) by season

Surface Water Supply Index Issues

Is there quantifiable impact or criteria information ?

Much impact information does not have stationary properties

Changes through time in quantification procedures

Most impact information records are not very long

Impact information often very short records (1-20 years)

Most impact information records differ in length from physical records

Water rights, allocated water

Not all “available” water is available for every purpose

Much water is reserved for a specific purpose

A full reservoir is useless (to others) if one has no water rightsA nearly empty reservoir may be ok if remainder is for the user

Users are concerned only with water that is available / useful to them

With SWSI, all water is the same “color”

Surface Water Supply Index Issues

Index behavior

Sensitivity: change in index value per unit change in input values

Middle percentiles sensitive to small changes in water amounts

Tail percentiles not very sensitive to large changes in amount

Tails are where there is most interest ( = drought)

Bounded values

Percentiles bounded at 0 and 100

Good and bad implications

SWSI is bounded at -4.17 and +4.17

-4.07 or -4.00 seem almost the same as -4.17 …. not!

Nothing intuitive about these values, like 0 and 100

No unprecedented values allowed

Is this a desirable property ?

Surface Water Supply Index Issues

Practical and logistical issues

All data must be available in a timely manner

Generalized access to water information

Has to be on a publicly accessible system

Water data often hard to get

Especially reservoir time series

Double-especially private reservoir time series

Metadata often in poor shape, scattered, not quality controlled

Need the actual data time series, not just the statistics

Infilling of missing segments

Quality control to produce a working copy operational data base

Automated ingest for nearly everything

What is the updating cycle?

Some data only available manually (weakest link problems)

Surface Water Supply Index Issues

Migrate from monthly to daily ?

A lot can change in a month, and right after a new month starts

Some data readily available daily, others hard to obtain even monthly

Social Issues

Neutral information broker is needed

Who calculates it ?

Is this even a relevant question ?

All components available for a user to create their own SWSI

SWSI versus “BWI”

Why leave out groundwater ?

BWI … Basin Water Index

Recommended by participants in 2002 NRCS workshop

SWSI comes from setting groundwater coefficient to zero

Can have many flavors of indices by setting coefficients to zero

Surface Water Supply Index Issues

Testing and validation

Drought trigger (SWSI or any other) behavior in past droughts

Case studies of past drought episodes

As earlier droughts evolved, which information was superior ?

Are there certain situations where SWSI is the more useful index ?

Is one particular component driving a low SWSI value ?

Occam’s Razor

Most drought indicators are correlated

Simpler approach often almost as good (SPI versus Palmer example)

Might we be letting the perfect be the enemy of the good ?

Too simple vs Too complicated

Presentation

Need creative ways to show all components at once

The Quantification of Drought: An Evaluation of Drought Indexes. Keyantash and Dracup, BAMS, 2002.

Robustness

Usefulness over a wide range of physical conditions.

Tractability

Practical computability (high level numerics, sparse data, short or incomplete records, etc).

Transparency

Clarity of the objective, rationale behind the index.

Sophistication

Conceptual soundness. May oppose trnasparency. e.g., relativity theory is not transparent or tractable, but nonetheless is a superior description.

Extendability

Degree to which an index may be extended across time to alternate sequences and histories.

Dimensionality

Composed of fundamental physical units, or, of normalized, dimensionless, probabilistic forms.

Keyantash and Dracup, BAMS, 2002

Thank You

DISCARDS

The Standardized Precipitation Index. McKee, Doesken, Kleist, 1995.

From Experience, Five Commonly Asked Questions:

How much precipitation have we had? Absolute Amount in units.

How much more or less than usual is this? Absolute Departure in units.

What percent of average is this? Relative Departure in Percentage units.

How often does this happen? Historical context.

Is there some kind of description comparable across space? “Standard”

Plus

We can be in different situations in different time scales.

Rationale for use of Standardized Precipitation Index

Straightforward interpretation

Depends only on precipitation

Similar to Palmer Index in some ways

Correlates well and best at 8-12 month time scales

But, disagreement is not necessarily undesirable

… they measure different things

Several useful associated quantities

Basic time step is now monthly

Consideration of shorter, sub-monthly, time scales

Precipitation data easiest to get

R. Seager, M.F. Ting, I.M. Held, Y. Kushnir, J. Lu, G. Vecchi, H.-P. Huang, N. Harnik, A.

Leetmaa, N.-C. Lau, C. Li, J. Velez, N. Naik, 2007. Model Projections of an Imminent Transition to a More Arid

Climate in Southwestern North America. Science, DOI:

10.1126/science.1139601

Average of 19 climate models.

2007.

Figure byGabriel Vecchi.

www.ldeo.columbia.edu/res/div/ocp/drought/

science.shtml

Seager et al, 2007. Average of 19 climate models. Figure by Naomi Naik.

www.ldeo.columbia.edu/res/div/ocp/drought/science.shtml