Robust Adaptation to Multi-Scale Climate Variability

Abstract

Evaluating and optimizing investments in climate adaptation requires projecting future climate risk over the operational life of each proposed investment. While many studies have considered that different climate change scenarios may emerge over the course of this M-year future period, adaptation policies remain vulnerable to the temporal and spatial clustering of climate risk which dominates much of the observational record. Large-scale, low-frequency climate variability can induce spatial shocks by favoring simultaneous extremes around the world, and can also cause a historical record to be a misleading indicator of future risk. In this work we consider whether the limited information in an N-year observational record permits the identification and projection of quasi-periodic climate variability and secular change, and what the resulting bias and uncertainty portends for risk mitigation instruments with a service life ranging from a few years to several decades. We present a set of stylized experiments to assess how well one can learn and predict the two kinds of risk for the design life (M years) and the probability of over- or under-design of a climate adaptation strategy based on these projections. We consider different temporal structures for the underlying risk which encompass quasi-periodic, regime-like, and secular variability, as well as statistical models for estimating this risk from an N-year historical record. The relative importance of estimating the short- or long-term risk associated with these extremes depends on the design life M, but the potential to understand and predict these different types of variability depends on the informational uncertainty in the N-year historical record. Though we use floods as an example, the framework also applies to other forms of climate extremes.

Full text

H52F-05H: Robust Adaptation to
Multi-Scale Climate Variability
Toward Better Water Planning and Management in an
Uncertain World I
James Doss-Gollin1, David J. Farnham2, Scott Steinschneider3, Upmanu Lall1
14 December 2018
1Columbia University Department of Earth and Environmental Engineering
2Carnegie Institution for Science
3Department of Biological and Environmental Engineering, Cornell University

Motivating Example
What to do after Sandy? [City of New York, 2013]
James Doss-Gollin (james.doss-gollin@columbia.edu)1

Hypotheses

Idea 1: Risk Estimates over Finite Future Periods
Typical Approach:
Cost-Benet Analysis (CBA), probably with discounting, over a nite
planning horizon of Myears.
Project should be evaluated on climate conditions over this nite
planning period:
• For “mega-project”, M≥50 years
• For small, exible project, M≤5 years
James Doss-Gollin (james.doss-gollin@columbia.edu)2

Idea 2: Hydroclimate Systems Vary on Many Scales
Inter-annual to multi-decadal cyclical variability key (for small M)
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1920 1940 1960 1980 2000
0 50 100 150 200
American River at Folsom
Water Year
Annual Maximum Streamflow
1500 1600 1700 1800 1900 2000
−6 −4 −2 0 2 4 6 8
Living Blended Drought Analysis
Year
Drought Severity
Annual
20−Year Moving Average
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average wavelet power
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Figure 1: (a) 500 year reconstruction of summer rainfall over Arizona from LBDA [Cook et al.,
2010]. (b) A 100 year record of annual-maximum streamows for the American River at Folsom.
(c),(d): wavelet global (average) spectra.
James Doss-Gollin (james.doss-gollin@columbia.edu)3

Idea 3: Physical Drivers of Risk Depend on M
The physical drivers of hazard depend on the projection horizon (M),
but our ability to identify these mechanisms depends on information
available (e.g., the length of an N-year observational record).
James Doss-Gollin (james.doss-gollin@columbia.edu)4

Stylized Experiments

Experiment Setup
Research Objective
How well can one identify & predict cyclical and secular climate signals
over a nite planning period (M), given limited information?
Let P∗(X>X∗). Note that the insurance premium (or risk factor) is:
R=E[P∗] + λV[P∗]
Systematic, stylized experiments:
what happens as we vary M,N,
climate structure, estimating model?
James Doss-Gollin (james.doss-gollin@columbia.edu)5

Stationary Scenario (LFV Only)
With limited data, the uncertainties caused by extrapolating from
complex models lead to poor performance.
James Doss-Gollin (james.doss-gollin@columbia.edu)6

Nonstationary Scenario I (Secular Change Only)
Long planning periods need trend estimation, but this demands lots of
information. For short planning periods, simple models may be better.
James Doss-Gollin (james.doss-gollin@columbia.edu)7

Nonstationary Scenario II (Secular Change + LFV)
As the system becomes more complex, more data is needed to
understand it.
James Doss-Gollin (james.doss-gollin@columbia.edu)8

Discussion

Summary
Assertions:
• Investment evaluation depends
on climate condition over nite
planning period
• Physical hydroclimate systems
vary on many scales
• Physical drivers of risk depend
on planning period
Implications:
•Ability to identify and predict
dierent climate signals
depends on information
available (e.g., N)
•Importance of predicting
dierent climate signals
depends on extrapolation
desired (i.e., planning period)
• In general, low risk tolerance
and/or limited information
favor investments with short
planning periods.
James Doss-Gollin (james.doss-gollin@columbia.edu)9

References i
Carpenter, B., et al., Stan: A Probabilistic Programming Language, Journal Of Statistical
Software,76(1), 1–29, doi:10.18637/jss.v076.i01, 2017.
City of New York, A Stronger, More Resilient New York, Tech. rep., New York, 2013.
Cook, E. R., R. Seager, R. R. Heim Jr, R. S. Vose, C. Herweijer, and C. Woodhouse,
Megadroughts in North America: Placing IPCC projections of hydroclimatic change in a
long-term palaeoclimate context, Journal of Quaternary Science,25(1), 48–61,
doi:10.1002/jqs.1303, 2010.
Doss-Gollin, J., D. J. Farnham, S. Steinschneider, and U. Lall, Robust adaptation to multi-scale
climate variability.
Rabiner, L., and B. Juang, An Introduction to Hidden Markov Models, IEEE ASSP Magazine,
3(1), 4–16, doi:10.1109/MASSP.1986.1165342, 1986.
Ramesh, N., M. A. Cane, R. Seager, and D. E. Lee, Predictability and prediction of persistent cool
states of the Tropical Pacic Ocean, Climate Dynamics,49(7-8), 2291–2307,
doi:10.1007/s00382-016- 3446-3, 2016.
Schreiber, J., Pomegranate: Fast and exible probabilistic modeling in python, arXiv.org, 2017.
Zebiak, S. E., and M. A. Cane, A Model El Niño-Southern Oscillation, Monthly Weather Review,
115(10), 2262–2278, doi:10.1175/1520-0493(1987)115<2262:AMENO>2.0.CO;2, 1987.
James Doss-Gollin (james.doss-gollin@columbia.edu)10

Thanks for your attention!
Interested in making these ideas more
concrete? I’d love to collaborate!
G,I@jdossgollin
ajames.doss-gollin@columbia.edu
Òwww.jamesdossgollin.me
James Doss-Gollin (james.doss-gollin@columbia.edu)10

Supplemental Discussion

Idealized Experiments ⇐⇒ Real World
The idealized models used here are analogs:
Analysis Real World
N-year record Total informational uncertainty of an
estimate
Statistical models of increasing
complexity and # parameters
Statistical and dynamical model
chains of increasing complexity and #
parameters
Linear trends Secular changes of unknown form
low-frequency climate
variability (LFV) from the El
Niño-Southern Oscillation
(ENSO)
LFV from many sources
LFV and trend additive LFV and trend interact

Generating Synthetic Streamow
Sequences

Example Sequences and Fits
Figure A1: Example of sequences generated with M=100 and N=50

Equations for Synthetic Streamow Generation
First
log Q(t)∼ N (µ(t), σ(t)).(A1)
Where σ(t) = ξµ(t), with σ(t)≥σmin >0. Then,
µ(t) = µ0+βx(t) + γ(t−t0),(A2)
and where x(t)is NINO3.4 index from realistic ENSO model [Zebiak and
Cane, 1987; Ramesh et al., 2016]

Spectrum of LFV Used
Figure A2: Wavelet spectrum of (sub-set of) ENSO model used to embed synthetic streamow
sequences with low-frequency variability. ENSO data from Ramesh et al. [2016].

Climate Risk Estimation

Stationary LN2 Model
Treat the Nhistorical observations as independent and identically
distributed (IID) draws from stationary distribution
log Qhist ∼ N (µ, σ)
µ∼ N (7,1.5)
σ∼ N +(1,1)
(A3)
where Ndenotes the normal distribution and N+denotes a half-normal
distribution. Fit in Bayesian framework using stan [Carpenter et al.,
2017].

Trend LN2 Model
Treat the Nhistorical observations as IID draws from log-normal
distribution with linear trend
µ=µ0+βµ(t−t0)
log Qhist ∼ N (µ, ξµ)
µ0∼ N (7,1.5)
βµ∼ N (0,0.1)
log ξ∼ N (0.1,0.1)
(A4)
where ξis an estimated coecient of variation. Also t in stan.

Hidden Markov Model
Two-state hidden Markov model (HMM) [see Rabiner and Juang, 1986]
implemented using pomegranate python package [Schreiber, 2017]. See
package documentation for reference.