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 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 mb Thickness

55-yr Monthly Temporal Correlation of MEI and 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 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 Components 1. 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 week mid-latitude forecasts

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

hPa 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  Seasonal forecasting  30-day lagged mean smoothed thickness

Matching Window for July 1 JD 2003 JD 2002 JD 2001 JD 1948 JD 1949 JD JD JD JD JD Match exact time/date # = 55 Match within 2 wk window #  3000 JD JD JD JD JD Match allowed over entire year # 

Analog selection for 00 UTC 12 January 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 , approx 80,000 forecasts.

51 years of Analog Selection: The DNA of atmospheric recurrence? PercentPercent

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 = MAE CLIMO - MAE ANALOG

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) = MAE CLIMO – MAE ANALOG : [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 dates  Acquired from global thickness matching  Daily historical records of surface parameters with a period as long as that from which the analogs matches were extracted  51 years ( )

MEI and Precipitation Correlation With 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 Nino1998 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 analyses  NH matching  Matching window - 4 weeks  Forecast 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 beyond  ENSO  Blocking  Well represented patterns - good analogs  Forecast confidence?

Example Forecast 00Z15JAN1995 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?