Jun 26, 1995 - UNCERTAINTY IN WEATHER AND. CLIMATE PREDICTION. Julia Slingo (Met Office). With thanks to Tim Palmer, James Murphy, Ken Mylne, ...
“… one flap of a sea-gull’s wing may forever change the future course of the weather” Edward Lorenz 1963
UNCERTAINTY IN WEATHER AND CLIMATE PREDICTION Julia Slingo (Met Office) With thanks to Tim Palmer, James Murphy, Ken Mylne, David Sexton and Glenn Shutts
Outline • Ed Lorenz and the concept of chaos • Initial condition uncertainty in weather forecasting • Stochastic processes and forecast uncertainty • Predictability on climate timescales • Reducing uncertainty in climate change • Future directions: moving from uncertainty to probabilities
X = −σX + σY The Lorenz Attractor: Y = − XZ + rX − Y The prototype chaotic model…..
Edward Lorenz (1917 – 2008)
Z = XY − bZ
In a nonlinear system, predictability is flow dependent – and predictable “Climate” of the Lorenz model Z Evolution of three different ensembles: X
• Underlying equations are non-linear; • Growth of initial uncertainty is strongly dependent on the starting conditions; • Predictability of forecasts is variable.
Basics of Ensemble Forecasting Time Forecast uncertainty Initial condition uncertainty
Analysis
Possible States
Dependence of accuracy on flow and forecast variable 10-day forecasts of London temperatures (0C) 26th y June 1994
26th June 1995 y 30 28 26 24 22 20 18 16 14 12 10
UK
UK
8 0
1
2
3
4
5 6 Forecast day
7
8
9
100
1
2
3
4
5 6 Forecast day
7
Individual member forecast Ensemble mean forecast Actual observations
8
9
10
Great Storm of 15/16 October 1987 “…….a woman rang the BBC and said she had heard that there was a hurricane on the way. Well if you are watching, don't worry there isn't.“ – Mike Fish, BBC Weather Forecaster
Benefits of ensemble prediction systems • Ensembles are used to capture forecasting uncertainties and estimate probability. • Ensemble forecasts provide a range of equally probable forecast solutions which allows forecasters to: – assess possible outcomes. – estimate risks and probabilities. – gauge confidence.
• Probability forecasts help end-users to assess and manage risk in an uncertain world.
Problem of under-dispersion of the ensemble system Northern Hemisphere 500hPa Height Forecasts Forecast Error Forecast Spread
RMS error grows faster than the spread Ensemble is underdispersive. Ensemble forecast is overconfident.
Buizza et al., MWR, 2004
Ensemble spread increased by identifying initial perturbations (singular vectors) that give maximum error growth.
Stochastic parameterizations: Reducing model error and enhancing internal variability Stochastic parameterizations can change mean and variance of PDF:
Potential
Weak noise
Strong noise
PDF
• Impacts variability of model and increases ensemble spread • Impacts systematic error (e.g. blocking, precipitation error)
Unimodal
Multi-modal
Stochastic physics in Ensemble Prediction Systems Met Office employs three schemes to address different sources of model error: – Random Parameters (RP) • Error due to approximations in parameterisation
– Stochastic Convective Vorticity (SCV) • Unresolved impact of organised convection (MCSs)
– Stochastic Kinetic Energy Backscatter (SKEB) • Excess dissipation of energy at small scales
Kinetic energy spectra from aircraft
Unresolved processes and upscale energy transports in models • Traditionally assume that effects of unresolved scales can be represented through parametrizations based on bulk formulae. • Inherently assumes that there is no coupling between dynamics and physics on these unresolved scales. • Essentially ignores upscale energy cascades
Nastrom and Gage, 1985
Phase changes of water drive weather and climate Moist processes in a complex, multi-scale system
Process Weather Climate model model model © Crown copyright Met Office
Stochastic Physics: Spectral Backscatter Scheme Rationale: A fraction of the dissipated energy (D) is scattered upscale and acts as forcing for the resolved-scale flow, Ψ∗
∆ψ * ∝
D ⋅ Fψ
Smoothed Total Dissipation
Total dissipation rate, D, from numerical dissipation, convection, gravity and mountain wave drag. Forcing pattern, Fψ , describes spatial/temporal correlations of the backscattered energy
Model Uncertainty and Stochastic Physics: Essential elements in probabilistic predictions Temperature at 850 hPa (200-900N)
+Forecast Error
Initial condition uncertainty only Including stochastic physics backscatter
Forecast Spread
Forecast Day Number
Basics of Ensemble Forecasting Time Forecast uncertainty Initial condition uncertainty
Analysis Model Uncertainty
Model uncertainty arises from stochastic, unresolved processes
Possible States
‘Predictability in the midst of chaos’
If we can't predict the weather beyond the next week or so, why is it possible to make seasonal forecasts?
What is the impact of boundary forcing, f, on Lorenz Attractor?
−σ X + σ Y + f X = Y =− XZ + rX − Y + f = Z XY − bZ
Adding external steady forcing f to the Lorenz (1963) equations
f=0
f=2
f=3
f=4
The influence of external forcing, f, on the state vector probability function is itself predictable. Weak forcing: Number and spatial patterns of regimes remain the same, but their frequency of occurrence is changed (“Lorenz model paradigm”) Strong forcing: Number and patterns of regimes are modified as the atmospheric system goes through bifurcation points In other words, it’s not possible to say what the weather will be like at any particular place on any particular day, but it should be possible to say what the statistics of the weather might be over the coming season or decades.
Birth of Seasonal Forecasting ‘Predictability of Monsoons’ J. G. Charney and J. Shukla, 1981
‘It is shown by numerical simulation that the variability of average pressure and rainfall for July due to short-period flow instabilities occurring in the absence of boundary anomalies can account for most of the observed variability at midlatitudes but not at low latitudes. On the basis of the available evidence it is suggested that a large part of the low-latitude variability is due to boundary anomalies in such quantities as sea surface temperature, albedo and soil moisture, which, having longer time constants, are more predictable than the flow instabilities.’
Seasonal to decadal prediction of the coupled ocean-atmosphere system • Use fully coupled models of the ocean and atmosphere circulation • Initialise both the atmosphere and ocean from observations • Combine initial condition and stochastic physics perturbations • Systematic and model-specific errors grow more strongly in fully coupled system • Multi-model ensembles often used to provide better sampling of forecast phase space
Seasonal predictability is highly dependent on location Global Impacts of El Nino
UK and Western Europe are among the least predictable places on the planet!
Different phases of El Nino are more predictable than others Initiation of warm event is difficult to forecast due to stochastic forcing from the atmosphere e.g. westerly wind events.
Decay of warm event is more predictable due to the role of equatorial ocean dynamics - the delayed oscillator.
How reliable are the forecasts? Lower tercile tropical JJA rainfall
• Because of systematic model errors, the distribution of probable outcomes may not reflect the observed distribution – i.e. the forecasts may not be reliable. • Forecast reliability has to be assessed using large sets of model hindcasts. • Final probabilities can be calibrated based on assessment of reliability • Use of multi-model ensembles can improve reliability • For seasonal and longer term predictions this is challenging because of the limited observational base
Ensemble prediction in a changing climate FUTURE Climatology Time Forecast uncertainty Initial condition uncertainty
Analysis
Model Uncertainty
Model uncertainty arises from stochastic, unresolved processes
CURRENT Climatology
Non-stationarity of the climate UK Temperature Record, 1914-2009: Anomalies from 1971-2000 mean UK Monthly Mean Temperature Anomalies
Uncertainties in Climate Change Projections Characterised by the spread in a multi-model ensemble of climate projections run at different international centres, and collected in a common archive.
Responses of annual mean surface temperature (left) and precipitation (right) to SRES A1B emissions, in 21 coupled AOGCMs contributed to IPCC AR4.
Multi-model ensembles (MMEs) Strengths: •Each member extensively tested – credibility derived from tuning and validation against a wide range of observables • Constructed from a large pool of alternative components – samples different structural assumptions • The source of much of our knowledge of projected future changes Limitations: • Not designed to sample modelling uncertainties in a systematic fashion (“ensemble of opportunity”) • Rather small. Difficult to get robust estimates of most likely changes, or associated uncertainties, in noisy quantities like regional changes in extreme events • Difficult to use MMEs to assess climate risks as there is no obvious “best” way of determining the distribution of possible changes of which the MME is a sample.
Perturbed physics ensembles (PPEs): An alternative approach • Relatively large ensembles designed to sample modelling uncertainties systematically within a single model framework • Executed by perturbing poorly constrained model parameters within expert-specified ranges • Key strength: Allows greater control over experimental design cf “ensembles of opportunity” • Key limitation: does not sample “structural modelling uncertainties”, e.g. changes in resolution, or in the fundamental assumptions used in the model’s parameterisation schemes.
Atmosphere Parameters Boundary layer
Large Scale Cloud
Turbulent mixing coefficients: stabilitydependence, neutral mixing length
Ice fall speed Critical relative humidity for formation Cloud droplet to rain: conversion rate and threshold
Roughness length over sea: Charnock constant, free convective value
Dynamics
Cloud fraction calculation
Diffusion: order and e-folding time
Convection Entrainment rate
Gravity wave drag: surface and trapped lee wave constants
Intensity of mass flux
Gravity wave drag start level
Shape of cloud (anvils) Cloud water seen by radiation
Radiation Ice particle size/shape Cloud overlap assumptions Water vapour continuum absorption
Land surface processes Root depths Forest roughness lengths Surface-canopy coupling CO2 dependence of stomatal conductance
Sea ice Albedo dependence on temperature Ocean-ice heat transfer
Summer precipitation changes in response to doubled CO2 in a perturbed physics ensemble
UKCP09: Moving from uncertainty to probability
UKCIP02 gave a single estimate of changes
Using many models in IPCC AR4 gave a range of estimated changes
UKCP09 uses over 400 model projections to give the probability of estimated changes
Moving from uncertainty to probabilities/likelihoods UKCP09
UKCIP02
Very unlikely to be less than (10%) Summer Rainfall 2080’s
Single projection
Central estimate (50%)
Very unlikely to be more than (90%)
Quantifying uncertainties 2020’s Improved model physics e.g. clouds
2080’s
Winter rainfall in south east England
22
25
35
43 15 31
9
20
Natural Variability
Carbon Cycle
Downscaling
Model Uncertainty
© Crown copyright Met Office
Using weather forecasting for reducing climate model uncertainties
MetUM: proto-HadGEM3
CloudSat
Real time comparison of vertical cloud properties using space-borne radar on CloudSat
© Crown copyright Met Office
Quantifying uncertainties 2020’s Improved model physics e.g. clouds
25
2080’s
Winter rainfall in south east England
22
Benefits of initialisation for near-term 35 projections
43 15 31
9
Natural Variability
Carbon Cycle
Downscaling
Model Uncertainty
© Crown copyright Met Office
Increased 20of earth understanding system processes – more uncertainty?
Decadal Prediction system: Effects of initialisation on projections of UK temperature for the next 30 years 360m ocean T, March 2007
UK 9-year mean temperature
© Crown copyright Met Office
Probabilistic predictions of climate change FUTURE Climatology Time Forecast uncertainty Initial condition uncertainty
Analysis
Model Uncertainty
Model uncertainty arises from stochastic, unresolved processes and parameter uncertainty
CURRENT Climatology
Multi-Model (1960 – 2005)
Methods of Handling Uncertainty: Strengths and Weaknesses RMSE of anomaly persistence Ensemble mean RMSE Ensemble Spread
Perturbed Parameter (1960 – 2005)
Courtesy Antje Weisheimer, ECMWF
Stochastic Physics (1991 – 2005)
Structural uncertainty • Model resolution: – Will increasing horizontal resolution reduce uncertainties at the global/regional level? – What resolution is required in global models to drive regional/local downscaling? – What vertical resolution is required in the atmosphere and ocean?
• Is it time for a coordinated study of the effects of model resolution?
What will happen to rainfall? Systematic patterns of change are emerging, but large uncertainty in the magnitude of those changes
Surface Pressure
Potential Vorticity on 315K
Persistent Blocking Anticyclone Climate Models typically undersimulate persistent anticyclonic blocking Slide 45
Blocking Index. 13 month integrations of ECMWF model (at T159 and T1259). DJFM 1960-2003
ERA-40
T1259 T159
Slide 46
T1259 run on NSF Cray XT4 “Athena” (two months of dedicated usage)
The importance of interactive upper-ocean thermodynamics for monsoon active-break cycles Lag correlations of intra-seasonally (30-50 day) filtered July and August rainfall
The “Real Butterfly Effect” raises fundamental unanswered questions about convergence of climate simulations with increasing resolution: 1. Is there an irreducible level of uncertainty in predictions of climate chang? What is it? 2. How much will uncertainties in climate-change predictions of the large scale reduce if models are run at 20km, 2km or even 0.2km resolution rather than say 200km resolution? 3. Once we reach a certain resolution (eg 20km), is it just as good to represent small scale motions using stochastic equations, than to try to resolve ad infinitum? 4. Will the development of stochastic parametrisations give more reliable estimates of uncertainty than current ad hoc multi-model methodologies? Slide 48 5. What is the most efficient way of using finite computer resources for climate prediction – eg how to best partition resources between resolution, Earth-system complexity and ensemble size?
V. Ramaswamy, GFDL, Princeton
Natural Variability
Concluding remarks •
Lorenz’s theory of the atmosphere as a chaotic, non-linear system pervades all of weather and climate prediction.
•
Estimating (and reducing) uncertainty and moving to more reliable (and confident) predictions requires:
•
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Improved representation of multi-scale physics
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Higher resolution and more complete models
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More complete observations of the climate system
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More comprehensive ensemble prediction systems
But there will always be an irreducible level of uncertainty – ‘flap of the seagull’s wings’ – on all timescales
Questions
