# Presentation: 447824

## Predictability of Week-2 to Monthly Climate

- Tom Hamill (+ Jeff Whitaker, Randy Dole)
*NOAA Earth System Research Lab, Physical Sciences Division (Formerly Climate Diagnostics Center)*
- tom.hamill@noaa.gov

- NOAA Earth System
- Research Laboratory

## Disclaimer

- Statistics and Ensembles

- Climate Dynamics

- I am no 44.45 kg
- (98-pound)
- weakling!

- “I know nothing!”

## Topics

- Main sources of potential predictability
- Tools for improving 2-4 week predictions, with a focus on reforecasts

## Sources of potential predictability:the atmospheric initial condition

- from LaLaurette et al (2006), ECMWF tech memo

- Still some skill
- in week 2. Will
- continued NWP
- improvements
- affect weeks 3
- and 4 positively?

## Views of predictability: Inverse error cascade or baroclinic error growth?

- Growth of errors in
- Lorenz (1969)
- experiment [assuming
- -5/3 power law for
- spectrum of energy
- per unit wavenumber.]
- Implies very rapid
- upscale cascade of
- errors, fully saturating
- by week 2.
- However, -3 power law
- more typical for synoptic
- scales.

**Notes:**
In this conventional picture, errors in small scales (high wavenumber) propagate upscale with a constant flux of error energy in spectral space. The main 
addition to Thompson’s work is that small-scale errors grow and eventually   contaminate all the skill remaining in larger scale. The implication f  o
r weather forecasting is that eventually even the smallest amplitude small-scale error will creep up scale and amplify in time, rendering practical, a
ccurate prediction feasible only for a finite length of time.

## Views of predictability: inverse cascade or baroclinic error growth?

- Tribbia and Baumhefner (2004):
- Rapid error growth between 0 - 0.25 days.  Thereafter, more exponential til saturation.
- “In our alternative view the inverse cascade becomes of lesser importance than in the traditional view. The primary role of the inverse cascade is to seed disturbances
- in the baroclinically active region of the spectrum. Once in the synoptic scales, the errors organize within the synoptic structures and amplify, extracting energy from the large-scale background flow, not the smaller scales.”

**Notes:**
solid line is  spectrum of full field, dashed perts.  Shading between is spectrum change in 5 days.

## Sometimes predicting planetary scales well will dramatically affect skill...

- from Pettersen 1956

- Positions of fronts every 24h

- unblocked

- blocked

## Sources of predictability:the stratospheric initial condition

- Baldwin and Dunkerton (1999)

**Notes:**
signature of the AO at 10, 1000 hpa .  Gotten by regressing AO index with geopotential.. Contour units meters.   AO is the leading mode (1st EOF) of low-frequency  variability of winter geopotential betw 1000 and 10 hpa.  Data normalized by dividing by std dev at each level. 90-day low-pass filtered data north of 20N.  Dec.- Feb data. 5 levels of data  agglomerated for EOF analysis.  leading EOF of temporal covariance matrix..  Accts for 23 % of variance. 

weakening of the NH  strat polar vortex tend to be followed by episodes of  anomalously low sfc air temp and increased frequency of occurrence of extreme cold events in eastern N.  Amer. and Europe that can persist for several months.

## NAO surface pattern predicted by previous month’s 10 hPa AO? 

- Baldwin and Dunkerton (1999)

- But: (1) convincing dynamical explanation of this not yet proposed, and (2) presumably the
- mechanism involves large-scale dynamics, so they wouldn’t well-represented in
- current models?  Hence will this be a *future* source of improved predictability?

**Notes:**
Major winter stratospheric warmings preferentially occur during the easterly phase of the QBO, Holton and Tan (1980).

## Sources of predictability:ENSO

## How tropical heating can affect extratropical circulations

- Schematic of the dominant changes in the upper troposphere in response to increases in SSTs, enhanced convection, and anomalous upper tropospheric divergence in the vicinity of the equator (scalloped region).  Anomalous outflow into each hemisphere results in subtropical convergence and an anomalous anticyclone pair straddling the equator, as indicated by the streamlines.  A wave train of alternating high and low geopotential and streamfunction anomalies results from the quasi-stationary Rossby wave response (linked by the double line).  In turn, this typically produces a southward shift in the storm track associated with the subtropical jet stream, leading to enhanced storm track activity to the south (dark stipple) and diminished activity to the north (light stipple) of the first cyclonic center.

- from Trenberth et al (1998); see
- also Sardeshmukh and Hoskins (1988)

## Altered position of jet in El Niño vs. La Niña

- El Niño

- La Niña

- from Shapiro et al. (2001)

## Characteristics of cyclones changes from + to - phase of ENSO

- 1998 El Niño

- 1999 La Niña

- forward-breaking PV wave

- 300 K PV (colors) on 6 Feb 1998

- rearward-breaking PV wave

- from Shapiro et al. (2001)

## El Niño and hurricane activity

- El Niño is one of many
- large-scale predictors
- of western-Atlantic
- tropical cyclone activity.
- ENSO forces increased
- vertical wind shear in
- trades.

- Blake and Gray (2004)

- inactive

- active

## July patterns for active August-October hurricane season in U.S.

- July 925 - 400 hPa average
- wind pattern in the month preceding

- August wind pattern associated with the top
- quintile of years with U.S. hurricane landfalls

- Saunders and Lea, 2005

- 35-40 % skill relative to climatology

- Northward displacement of Bermuda high, Rockies anticyclone, La Niña signature, etc..

**Notes:**
Tropospheric height wind

## Sources of potential predictability: Madden-Julian Oscillation

- orange-yellow
- are cold cold tops

**Notes:**
other lines equatorial Rossby?

## MJO: the optimistic perspective (Ferranti et al. 1990)

- ECMWF T42 forecasts in times of active MJO; test skill of “perfect” tropical forcing vs. existing model.  However: (1) small sample size, (2) we’re not yet anywhere near perfect tropical prediction, (3) MJO active only small percentage of time.

- relax tropics to analyzed
- state
- control
- relax tropics to persisted
- initial condition

## 91-day

- running
- mean of
- RMM12 +
- RMM22

- from Wheeler’s http://www.bom.gov.au/bmrc/clfor/cfstaff/matw/maproom/RMM/ts.PCvar91drm.gif

- long periods
- with no
- significant
- MJO activity

- ?

## Predictability from land-state anomalies?

- 1-2 month response to observed
- SST forcing (warmer than avg).

- response to dry initial root layer
- (note: EMCWF model diminishes amplitude
- of seasonal soil moisture perturbations, so
- had to force dry soils in model)

- response to dry soil over all layers

- Case: 2004 European heat wave;
- (dry soils preceding that spring)

- Ferranti and Viterbo (2006)

## Tools for improving weeks 3-4 predictions

- Linear Inverse and other statistical models (see Newman, Penland, Sardeskmukh’s work).
- Reforecasts (I’ll concentrate on this).

## Linear Inverse Modeling

- Newman et al. (2003)

-  Good for diagnosing
- sources of linear
- predictability.
-  Better than circa 1998
- MRF (GFS) in week 3.
-  But: models may improve,
-  LIM won’t much.

**Notes:**
assumes dynamics of weekly avgs are linear, asymptotically stable, and stochastically forced.   Predictable signal is associated with deterministic linear dynamics,
and the forecast error with unpredictable stochastic noise..  Tropical heating main source of predictability in wintertime   Predictability increases with increasing projection
onto growing structures..  Very ENSOish SST part of initial structure. 

## Tools for improving predictions:reforecast data sets (e.g., our prototype with the T62 model)

**“****Reforecast” definition: **a data set of retrospective numerical forecasts using the same model as is used to generate real-time forecasts.
**Model**:  T62L28 NCEP GFS, circa 1998
**Initial States**: NCEP-NCAR Reanalysis II plus 7 +/- bred modes.
**Duration**: 15 days runs every day at 00Z from 19781101 to now. (_[http://www.cdc.noaa.gov/people/jeffrey.s.whitaker/refcst/week2](http://www.cdc.noaa.gov/people/jeffrey.s.whitaker/Manuscripts/multimodel.pdf)_*).*
**Data**:  Selected fields (winds, hgt, temp on 5 press levels, precip, t2m, u10m, v10m, pwat, prmsl, rh700, heating).  NCEP/NCAR reanalysis verifying fields included (Web form to download at _[http://www.cdc.noaa.gov/reforecast](http://www.cdc.noaa.gov/people/tom.hamill/skill_overforecast_QJ_v2.pdf)_).

**Notes:**
As promised - details of dataset.

11 months done - dataset will be complete in about a month.

## WHY?

- 850 hPa temperature
- bias for a grid point in
- the central U.S.

- Spread of yearly bias
- estimates from 31-day
- running mean F - O
- Note the spread is often
- larger than the bias,
- especially for long leads.

## Calibrating ensemble forecasts: raw, bias correction, logistic regression

- Hamill et al. (2004)

## surface temperature

- precipitation

## Calibrating Z500 CRPSS

## Calibrating T850 CRPSS

## Calibrating T2m CRPSS

## Are reforecasts still necessary with improved models?

- ECMWF produced
- a short reforecast
- data set.
- Calibration using
- their week-2
- reforecasts
- produced a skill
- increase of ~11%;
- for our reforecast,
- skill improvement
- was ~ 16%

- Whitaker and Vitart (2006)

## Multi-model reforecasts

- Whitaker and Vitart (2006)

- may be worth keeping old reforecasts around

**Notes:**
One forecast every 2 weeks, T159L40, 12 years, every 2 weeks..  850T north of 20N.  ERA_40.  DJF.

## Reforecasts as a tool for studying predictability

- Hamill et al. (2006)

**Notes:**
CCA; linear combination  of the data from predictand field that have maximum linear correlation , in space of  truncated principal components (leading PCs of 
ens mean week-2 500Z fcst as predictors, anals as predictands).  Pattern 1 like tropical-North American pattern (Mo and Livezey 1986). 2nd like PNA, 3rd like NAO.

## Skill of predicting these patterns

- Hamill et al. (2006)

**Notes:**
Don’t yet know the source of skill of these patterns, but refcsts a good tool for getting started at this.

## General areas where more research is needed to improve weeks 3-4 forecasts.

- What is the value of coupled ocean / atmosphere models for these leads?
- Are the predictable aspects in weeks 3-4 that emerge from nonlinear ensemble forecasts ones that are essentially linear and can be obtained by cheaper LIM techniques?
- What are the mechanisms for error growth of *planetary* scales?

## My hunches

- Still some sources of predictability that are nonlinear in weeks 3-4, hence NWP will be useful supplement to purely statistical techniques. But we should be systematic in determining whether nonlinear effects are important.
- However, if you’re adopting an NWP approach, reanalyses / reforecasts will be crucial.  Model biases are huge at these leads.

## References

- Hamill, T. M., J. S. Whitaker, and X. Wei, 2003: Ensemble re-forecasting: improving medium-range forecast skill using retrospective forecasts. *Mon. Wea. Rev*., **132**, 1434-1447. _[http://www.cdc.noaa.gov/people/tom.hamill/reforecast_mwr.pdf](slide36.xml)_
- Hamill, T. M., J. S. Whitaker, and S. L. Mullen, 2005: Reforecasts, an important dataset for improving weather predictions.  *Bull. Amer. Meteor. Soc*., **87**, 33-46.
- _[http://www.cdc.noaa.gov/people/tom.hamill/refcst_bams.pdf](slide18.xml)_
- Whitaker, J. S, F. Vitart, and X. Wei, 2006:   Improving week two forecasts with multi-model re-forecast ensembles. *Mon. Wea. Rev*., **134**, 2279-2284. http://www.cdc.noaa.gov/people/jeffrey.s.whitaker/Manuscripts/multimodel.pdf
- Hamill, T. M., and J. S. Whitaker, 2006: Probabilistic quantitative precipitation forecasts based on reforecast analogs: theory and application. *Mon. Wea. Rev*., in press. http://www.cdc.noaa.gov/people/tom.hamill/reforecast_analog_v2.pdf
- Hamill, T. M., and J. Juras, 2006: Measuring forecast skill: is it real skill or is it the varying climatology? *Quart. J. Royal Meteor. Soc*., in press. http://www.cdc.noaa.gov/people/tom.hamill/skill_overforecast_QJ_v2.pdf
- Wilks, D. S., and T. M. Hamill, 2006: Comparison of ensemble-MOS methods using GFS reforecasts. *Mon. Wea. Rev*., in press. http://www.cdc.noaa.gov/people/tom.hamill/WilksHamill_emos.pdf
- Hamill, T. M. and J. S. Whitaker, 2006: White Paper.  “Producing high-skill probabilistic forecasts using
- reforecasts: implementing the National Research Council vision.”  Available at http://www.cdc.noaa.gov/people/tom.hamill/whitepaper_reforecast.pdf .

## 1st EOF (RMM1) and 2nd EOF (RMM2) of MJO

- We performed EOF analysis on the combined daily fields of equatorially-averaged (15°S to 15°N) OLR, 850hPa zonal wind, and 200 hPa zonal wind for the period of 1979 to 2001 (23 years). We did this on the covariance matrix with each field normalized by the square-root of its global mean variance first. This is necessary so that each field contributes the same amount of variance to the combined field. Before the EOF analysis, however, we also performed the following:
-     * Remove the long-term mean and climatological seasonal cycle (3 harmonics) from each field at each grid-point.
-     * Remove the variability associated with El Nino (that which is linearly related the ENSO SST1 index).
-     * Remove a 120-day mean of the most recent 120 days at each point..

- from Wheeler’s http://www.bom.gov.au/bmrc/clfor/cfstaff/matw/maproom/RMM/eof1and2.htm

- back

## Predictability from tropical boundary conditions (SSTs)

- Rossby wave energy dispersion from steady, localized heat sources

- Horel and Wallace’s (1981) schematic illustration of geopotential height anomalies introduced by warm SSTs along the dateline.

- Sardeshmukh and Hoskins (1988) (a) divergence perturbation and (d) streamfunction perturbation on day 48 assuming fully nonlinear response

## MJO: a note of caution

## MJO: a note of caution

## MJO: a note of caution

## Issues: (1) should reanalyses be part of reforecast process?

-  Want homogeneous
- characteristics of forecasts; skill the same for 1980’s forecasts as 2006 forecasts.
-  Part of better skill of current forecasts is the better initial condition.
-  Reanalysis would improve skill of old forecasts.
-  Reanalyses should use same or similar model as used in reforecasts.