Analogs: Or How I Learned to Stop Worrying and Love the Past…

Analogs: Or How I Learned to Stop Worrying and Love the Past…

10 April 2003

Robert Hart

Penn State University

Jeremy Ross, PSU

Mike Fritsch, PSU

Charles Hosler, PSU

Richard Grumm, SOO/NWS CTP

Richard James, PSU

As meteorologists we may be somewhat familiar with analogs…

Hurricane forecasting…

“Snowstorms along the Northeastern U.S. Coast of

the United States: 1955-1985”

Kocin & Uccellini 1990

AMS Monograph

Major snowstorms….

Analogs• Looking for patterns in historical meteorological data

that are similar to those occurring today.

• Also used extensively in other areas with relatively low predictability:

– Stock Market– Species evolution & extinction– Sports– Planetary evolution – Politics– War– History in general

Analog forecasting

• The oldest forecasting method?

• Compare historical cases to existing conditions

• Subjectively: Memory• Analog forecast skill a function of human age…?

• Objectively: Objective pattern comparison• Analog forecast skill a function of dataset length?

How long of a dataset is required?

As with most things in life, great insight is provided by “The Simpsons”

1996, Episode “Hurricane Neddy” “The Simpsons” provide insight on the perils of analog forecasting:

Homer Simpson:“Oh Lisa! There's no record of a hurricane ever hitting Springfield.“

Lisa Simpson: “Yes, but the records only go back to 1978 when theHall of Records was mysteriously blown away!”

Simpsons argue 20 years not enough…..

A sobering perspective…

“…it would take order 1030 years to find analogues that match over the entire Northern Hemisphere 500mb height field to within current observational error.”

From: Searching for analogues, how long must we wait?

Van Den Dool, 1994, Tellus.

We have decided not to wait, and instead have

drastically reduced our expectations.• We are not looking for an exact replication of patterns

• We want to determine on which side of climatology we are most likely to reside.

• We do not need to forecast departures from climatology all the time: Only when confidence measures allow.

• With these lesser expectations: Is 50 years of archive sufficient for skillful seasonal analog forecasts?

An exploratory study

• Goal: To test feasibility of analog approach using longest continuous global datasets

• Methods will be improved with additional work

• Many parameter choices probably not ideal, but based upon physical insight

• Limit forecasts to tropics where seasonal forecast skill is more easily obtained

• Results are preliminary

An exploratory study 2• Historical archive:

1948-2002 NCEP/NCAR Reanalysis Dataset

– Consistent method of data assimilation

– Incorporates majority of available observations

– Global, 2.5°x2.5°, 6-hourly resolution

– Dynamically grows in time: updates daily

– Areal weighting for pattern matching & skill evaluation

An exploratory study 3• Strengths of analog approach

– Forecasts confined to what has occurred– Quick compared to NWP– Do not need to understand cause/effect– Can predict any variable for which historical data is available

• Weaknesses:– Forecasts confined to what has occurred– Do not need to understand cause/effect– Requires lengthy archive

1000-500hPa Thickness as Global Pattern Descriptor

• Fewer degrees of freedom than other atmospheric variables

• Great integrator of:– Long wave pattern– Global temperature pattern– Global lower tropospheric moisture pattern

• Large inertia: Not greatly influenced by transient fluctuations (e.g. short-lived convection)

• Pattern matching performed using MAE of global thickness pattern comparison

Matching instantaneous thickness analysis

MRF Thickness Analysis at 00Z 19 Jan 2003

#1 Analog: 12Z 10 Jan 1981

Analogs: How to pattern match?

• Instantaneous (unfiltered) thickness analyses?

• Filtered thickness analyses?– Spatial? [EOF]– Temporal?

• Choice likely depends on desired forecast length– Short term forecast: compare instantaneous analyses– Long term forecast: compare filtered analyses

Analog Forecast• For any given initialization, the closest matching N

members are chosen – Leads to an ensemble of analog matches with spread

– Significant difference from most current analog methods which use constructed analog approaches

• Their ensemble mean evolutions are used to produce the analog forecast thickness anomaly:

)(1

)()(1

ttZN

ttZttF a

Na

aANOMCLIMO

Initial experiment:Pattern matching instantaneous analyses

• Initial tests matched instantaneous thickness analyses Lead to forecast skill out to 8 days.

We can reproduce current NWP range with 0.00001% NWP cost?

No forecast skill

Forecast skill

Climatology

5 10 15 20 25 30 35Forecast length (days)

MAE

Method

)(125

1)(

30

iZtZti

daystiSMOOTH

• Since our goal is seasonal forecasting, we next matched the 31-day lagged mean smoothed thickness fields

Method • Global pattern matching of smoothed thickness

• Allow analog matches to occur within 2-week window about initialization date/time to increase variety of available analogs.

e.g. analogs for July 1 come fromJune 24 – July 8 in each of the

available years

Matching Window for July 1

J D1998

J D1997

J D1996

J D1948

J D1949

J D

J D

J D

J D

J DMatch exact time/date # = 51

Match within 2 wk window # 3000

J D

J D

J D

J D

J DMatch allowed over entire year # 75000

1998

1997

1996

1948

1949

Method • For each 6-hour initialization time in 1948-1998, the top

200 analogs were selected from the available 3000 (about 6%).

51 years of Analog

Selection:

The DNA of atmospheric recurrence?

P e r c e n t

The “1976 Fracture”• Cause of abrupt change in pattern matching after 1976:

– Data changes• Observation network change?• Buoys, satellite availability?

– Rapid Surface condition changes• Deforestation?• Ocean conveyor & salinity changes?

– Long-term global change?• Global warming?• Frequency of ENSO events changed?

– Global seasonal pattern change?• Actual synoptic to long-wave patterns have changed?

• Why abrupt and not smooth change?

Trying to understand abruptly changing analog selection patterns: A meteorological explanation

Annual Mean Thickness

NH

SH

Globe

Trying to understand abruptly changing analog selection patterns: A dataset explanation

1950 1960 1970 1980 1990

Approx.Daily # Obs (Log)

Land Rawinsondes Aircraft Satellites Radiances108

106

104

Year

What area to forecast for?• Tropical (20°S-20°N) monthly mean thickness forecast is

evaluated

• Not a signal to noise ratio as some have feared!• Tropical thickness responds to changes in magnitude of

sustained convection

How to measure skill?• Persistence, anomaly persistence?

• Convention for seasonal forecasting: Climatology. – 54-year mean? 10-year mean?– 30-year mean? Previous year?

• Skill measured here against 54-year mean. The impact of climatology period choice will be shown.

• Skill here = MAECLIMO - MAEANALOG

Forecast Skill Benchmarks

Forecast Skill Benchmarks

Forecast Skill Benchmarks

Forecast Skill Benchmarks: Climatology

Forecast Skill Benchmarks: Climatology

Forecast Skill Benchmarks: Climatology

Forecast Skill Benchmarks: Climatology

Forecast Skill Benchmarks: Climatology

Harshest competition: Adjust climatology linearly for long-term trend…

Annual mean thickness

Adjusted climatology for skill benchmark

NH

SH

Globe

Forecast Skill Benchmarks: Detrended climatology

Analog Forecast Skill: 51 year mean

Analog Forecast Skill: 51 year mean

Skill to 8.5 months

Skill to 25 months

Skill to 12 months

Analog Forecast Skill: 51 year mean• Forecast skill extends to:

– 25 months against 54-year climatology– 12 months against previous 10-year climatology– 8.5 months against a trend-adjusted climatology

• This argues analog forecast skill is a combination of:– Correctly forecasting seasonal pattern (majority of skill)– Correctly forecasting mean pattern: global trend

• The latter two skill results argues we are able to forecast seasonal thickness pattern evolution in the tropics

• How does the forecast skill vary from year to year?

Winter/spring 1997 Forecast of 1998 El Niño

Pinatubo hinders analog matching

Spring 1986 prediction of 1987 El Niño

Spring 1982 prediction of 1983 El Niño

Successful forecast of a non-ENSO anomaly

Skill (shaded) = MAECLIMO – MAEANALOG: [Red: Skill > 2m ]

2

The importance of matching globally

January 1997 Obs 12 month forecast

January 1996 Obs 12 month forecast

January 1952 Obs 12 month forecast

Implications:There may be signs of an upcoming ENSO event 12 months in advance

outside the tropics?

Summary• Highest skill and longest lead times occur for large

tropical thickness anomalies (e.g. ENSO)

• 5-12 month lead on ENSO events often precedes infamous “April” barrier

• Forecast skill exists during non-ENSO anomalies

• 1992-1994 forecasts were unusually poor. Evidently, Pinatubo produced a global pattern unlike any observed in the 54-year period

Future Work: Many unanswered questions…

• How does analog forecast skill vary with filtering of thickness in time and space

• How does de-trending the raw dataset impact analog selection (and forecast skill)?

Lost analog potential b/c of climate change?

Future Work: Many unanswered questions…

• How does trajectory matching rather than single analysis impact skill? – Match thickness evolution (trajectory) through Jan 1-31 rather

than Jan 1-31 mean?

• But the current approach views them as the same…

Many unanswered questions…• What is the impact of using another reanalysis

dataset (ECMWF, JMS)?

• Where outside the tropics do ENSO indications lie?

• How can mid-latitude forecast skill outside ENSO (NAO/PNA predictability?) be obtained? [NCEP/CDC/CPC: It can’t]

• Is skill possible in surface parameters?

52-Year Temporal Correlation of Monthly MEI and PrecipitationTeleconnection pattern between ENSO and Global Precip

Acknowledgments

• Resources:– Penn State University– NCEP & NCAR through CDC: Reanalysis

• Insightful discussion & guidance:– Jenni Evans, PSU– Paul Knight, PSU– Robert Livezey, NOAA/CDC– Huug Vandendool, NCEP/CPC– Chris Landsea, HRD/AOML

Current Analog ENSO Forecasts

Jan 2002 Forecast of Extended 2002 El Niño

2003 Forecast: Initialized Dec. 2002

2003-4 Forecast: Initialized Jan. 2003

2003-4 Forecast: Initialized Feb. 2003