Objective Digital Analog Forecasting

“Is The Future In The Past?”

We’re Going Back …..

Back to the Future

Pattern Recognition Important to recognize the shape and influence of

patterns and teleconnection indices.

Teleconnections: AO, NAO, NAM, PNA, AAO, EA, WP, EP, NP, EAWR,

SCA, POL, PT, SZ, ASU, PDO,

El Nino/La Nina MEI, SOI, Nino1, Nino2, Nino3, Nino4, Nino3.4

Complex interactions in the mid and high latitudes makes forecasting most teleconnection indices difficult beyond a week or two.

55-yr Monthly Temporal Correlation of AO and 1000-500 mb Thickness

55-yr Monthly Temporal Correlation of AO and Precipitation

55-yr Monthly Temporal Correlation of AO and 500 mb Zonal Wind

55-yr Monthly Temporal Correlation of NAO and Surface Temperature

55-yr Monthly Temporal Correlation of PNA and 1000-500 mb Thickness

55-yr Monthly Temporal Correlation of MEI and 1000-500 mb Thickness

55-yr Monthly Temporal Correlation of MEI and Precipitation

Analog Motivation

Monthly/seasonal pattern evolution affected by?

Sea surface temperature anomalies ENSO Snow Cover / Icepack Solar cycle Phytoplankton Vegetation Atmospheric Chemistry Stratospheric Phenomena

Analog forecasting The oldest forecasting method?

Compare historical cases to existing conditions

Previous analog forecasting research yielded limited success

New digital age of analog forecasting

1. Dataset availability 55 Year NCEP Reanalysis 40 Year ECMWF Reanalysis 109 Year Climate Division Data Etc

2. Computational resources – statistical forecasting - ensembling

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.

Goals

Not seeking exact replication of patterns

Instead, determine sign of the climatological departure using an analog ensemble (on a weekly to monthly time scale)

Analogs require keys keys to matching keys to extracting

Statistically extracting information relevant to current patterns and removing noise.

Analog Components1. Data

Dataset length, frequency, area, variables, filtering

2. Matching Method Parameters, region, search window, threshold method (MAE,

anomaly correlation, RMSE, etc), statically or dynamically

3. Ensemble Configuration Match/date selection, top (1,10,100,1000 matches), ensemble

of single match analysis / ensemble of match analyses / both

4. Forecast Forecasts made from dates acquired from matching Integrate historical dates forward in time to generate

ensemble forecast – mean, probabilistic distributions

Example Analog Forecasts

1. Seasonal tropical thickness forecasts

2. Seasonal San Diego precipitation forecasts

3. 2-4 week mid-latitude forecasts

Seasonal Tropical (20N-20S) Analog Thickness Forecasts

1000-500hPa Thickness as Pattern Descriptor

Fewer degrees of freedom (Radinovic 1975)

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)

Matching Method?

Instantaneous (unfiltered) thickness analyses?

Filtered thickness analyses?

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

Optimal Filtering F = f(t,L)t = forecast length (lead time)L = verification increment (hour, month, season)

Filtering

30

1( ) ( )

125

i t

SMOOTHi t days

Z t Z i

Seasonal forecasting30-day lagged mean

smoothed thickness

Matching Window for July 1

J D2003

J D2002

J D2001

J D1948

J D1949

J D

J D

J D

J D

J DMatch exact time/date # = 55

Match within 2 wk window # 3000

J D

J D

J D

J D

J DMatch allowed over entire year # 80000

2003

2002

2001

1948

1949

Analog selection for 00 UTC 12 January 2001.

Choose the top 200 (out of 3000 possible or 6%) matches from a 2-week window around the initialization date.

Exclude matching between the year before and after the initialization

Consensus forecast made for each 6-hour initialization time in 1948-1998, approx 80,000 forecasts.

51 years of Analog

Selection:

The DNA of atmospheric recurrence?

P e r c e n t

Skill? Persistence, anomaly persistence?

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

Tropical (20°S-20°N) monthly mean thickness forecast is evaluated

Skill = MAECLIMO - MAEANALOG

Analog Forecast Skill: 51 year mean

Skill to 8.5 months

Skill to 25 months

Skill to 12 months

Winter/spring 1997 Forecast of 1998 El Nino

Pinatubo hinders analog matching

Spring 1982 prediction of 1983 El Nino

2

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

Seasonal Precipitation Forecasts

“Dependent” Analog Forecasts

Analogs allow for forecasts of any dependent variable which has a historical record, regardless of what is matched.

Forecasts of dependent variables requires some relationship to the matching parameter

For example – electrical usage – long term record of electrical usage could be determined from dates provided by thickness matching, thanks to the dependence of electricity on temperature, and temperature on thickness.

Precipitation Forecasts

Need an analog ensemble of matching datesAcquired from global thickness matching

Daily historical records of surface parameters with a period as long as that from which the analogs matches were extracted51 years (1948-1998)

MEI and Precipitation CorrelationWith Available GSN Data

Method San Diego precipitation forecasts

Global thickness matching dates Surface precipitation observations Forecast length (1- 365) days

Forecasts averaged over the length of period which is to be forecast e.g., a seasonal (3 month) forecast is composed of an

average of 3 months of 6 hourly forecast initializations (~360 forecasts)

1983 El Nino 1998 El Nino

Seasonal Precipitation Forecast For San Diego Initialized 1982

Seasonal Precipitation Forecast For San Diego Initialized 1997

Mid-Latitude 2-4 Week Thickness Forecasts

Method

Technique similar to seasonal tropical forecasts with the following exceptions:

1-day filtered thickness analysesNH matchingMatching window - 4 weeksForecast length 1-30 days

Observed Analyses 00Z14MAR1993

Analog Ensemble Size

Analog Ensemble Consensus Top (1,10,100,500 analogs)

00Z14MAR1993

Optimal Analog Ensemble Size at Analysis

Analog Skill Length as a Function of Year and Season

Forecast Skill Variability

Distinct periods where analog forecast skill extends to 30 days or beyondENSOBlockingWell represented patterns - good analogs

Forecast confidence?

Example Forecast00Z15JAN1995

Analysis

Week 1

Week 2

Week 3

A flood of unanswered questions…

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

What is the impact of using another reanalysis dataset (ECMWF, JMS)?

How will mutli-parameter analogs impact skill?

Will temporal sequence matching vs static matching improve analog selection?

Can we blend dynamical prediction systems with analogs to further improve the skill of both?