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