Numerical Weather Prediction Numerical Weather Prediction and Data Assimilationand Data Assimilation

David Schultz, David Schultz, Mohan Ramamurthy, Mohan Ramamurthy, Erik Gregow, John HorelErik Gregow, John Horel

What is a model?What is a model?

• Resource: Kalnay, E., 2003: Atmospheric Modeling, Data Assimilation and Predictability

• model: tool for simulating or predicting the behavior of a dynamical system such as the atmosphere

• Types of models include:– heuristic: rule of thumb based on experience or common sense– empirical: prediction based on past behavior– conceptual: framework for understanding physical processes

based on physical reasoning– analytic: exact solution to “simplified” equations that describe the

dynamical system– numerical: integration of governing equations by numerical

methods subject to specified initial and boundary conditions

What is Numerical Weather What is Numerical Weather Prediction?Prediction?

• The technique used to obtain an objective forecast of the future weather (up to possibly two weeks) by solving a set of governing equations that describe the evolution of variables that define the present state of the atmosphere.

• Feasible only using computers

A Brief History A Brief History • Recognition by V. Bjerknes in 1904 that forecasting

is fundamentally an initial-value problem and basic system of equations already known

• L. F. Richardson’s (1922) attempt at practical NWP• Radiosonde invention in 1930s made upper-air

data available• Late 1940s: First successful dynamical-numerical

forecast made by Charney, Fjortoft, and von Neumann

• 1960s: Edward Lorenz shows the atmosphere is chaotic and its predictibility limit is about two weeks

NWP SystemNWP System

• NWP entails not just the design and development of atmospheric models, but includes all the different components of an NWP system

• It is an integrated, end-to-end forecast process system

Data Assimilation

Components of an NWP Components of an NWP modelmodel

1. Governing equations• F=ma, conservation of mass, moisture, and thermodynamic

eqn., gas law

2. Numerical procedures:

• approximations used to estimate each term (especially important for advection terms)

• approximations used to integrate model forward in time • boundary conditions

3. Approximations of physical processes (parameterizations)

4. Initial conditions:• Observing systems, objective analysis, initialization, and data

assimilation

Model PhysicsModel Physics• Grid-scale precip. (large scale condensation)• Deep and shallow convection• Microphysics (increasingly becoming

important)• Evaporation• PBL processes, including turbulence• Radiation• Cloud-radiation interaction• Diffusion• Gravity wave drag• Chemistry (e.g., ozone, aerosols)

Grid spacing (resolution) defines the scale of the features you can simulate with the model.

Good Numerical Forecasts Good Numerical Forecasts Require…Require…

• Initial conditions that adequately represent the state of the atmosphere (three-dimensional wind, temperature, pressure, moisture and cloud parameters)

• Numerical weather prediction model that adequately represents the physical laws of the atmosphere over the whole globe

Sources of error in NWPSources of error in NWP• Errors in the initial conditions• Errors in the model• Intrinsic predictability limitations

• Errors can be random and/or systematic errors

Sources of Errors - continuedSources of Errors - continued Initial Condition Errors

1 Observational Data Coveragea Spatial Densityb Temporal Frequency

2 Errors in the Dataa Instrument Errorsb Representativeness Errors

3 Errors in Quality Control4 Errors in Objective Analysis5 Errors in Data Assimilation6 Missing Variables

Model Errors

1 Equations of Motion Incomplete

2 Errors in Numerical Approximations

a Horizontal Resolution

b Vertical Resolution

c Time Integration Procedure

3 Boundary Conditions

a Horizontal

b Vertical

4 Terrain

5 Physical Processes

Source: Fred Carr

Given all these assumptions and Given all these assumptions and limitations, limitations, we have no right to we have no right to do as well in forecasting the do as well in forecasting the

weather as we do!weather as we do!

• What other disciplines forecast the future with as much success as meteorology?

Dave sez:

NWP in FinlandNWP in Finland

• Currently, NWP models are run by FMI (limited domain over Europe) and by the European Centre for Medium-Range Weather Forecasts (global)

• Currently the FMI model is run at about 9 & 22 km and the ECMWF model is run at 25 km grid spacing, meaning that these models can resolve features about 6 times those grid spacings.

• The new AROME experimental model is running at 2.5 km grid spacing.

22 km HIRLAM9 km HIRLAM2.5 km AROME

9 km HIRLAM2.5 km AROMEobserved radar reflectivity

9 km HIRLAM2.5 km AROME

The Hopes of the TestbedThe Hopes of the Testbed

• Higher-resolution observations will provide higher-resolution initial conditions, which could be put into a higher-resolution NWP model, producing higher-resolution forecasts.

• The hope is that precise forecasts of convection, the sea breeze, rain/snow forecasting, and winds could be made up to a few hours in advance.

• BUT…

Difficulties Lie Ahead…Difficulties Lie Ahead…

• The reality is often that you end up with a higher-resolution, less-accurate forecast.

• Results from forecasting/research experiments at the NOAA/Storm Prediction Center show value can be added sometimes with high-resolution forecasts.

• When that value can be added is a very important forecasting/research question!!!

Difficulties Lie Ahead…Difficulties Lie Ahead…

• Producing the initial conditions from sparse resolution (in space and time) and incomplete observations is not easy.

• Creating a gridded 3-D/4-D dataset suitable for initializing a NWP model is called data assimilation.

• How it is proposed to be done in the Helsinki Testbed is described next…

Erik Gregow Project Manager LAPS

• Numerical weather prediction model that adequately represents the physical laws of the atmosphere over the whole globe

• Initial conditions that adequately represent the state of the atmosphere (three-dimensional wind, temperature, pressure, moisture and cloud parameters)

2/6/07

LAPS

Radar

SoundingProfilers

Satellite

Sfc obs.

GPS

Good Numerical Forecasts Good Numerical Forecasts Require…Require…

• Numerical weather prediction model that adequately represents the physical laws of the atmosphere over the whole globe

• Initial conditions that adequately represent the state of the atmosphere (three-dimensional wind, temperature, pressure, moisture and cloud parameters)

2/6/07

HIGH RESOLUTIONANALYZE & NOW-CASTING

LAPS

Radar

SoundingProfilers

Satellite

Background analysisfields; MM5

FORECAST 0-6hMM5

Sfc obs.

GPS

Monitoring

Current

Conditions

September 6

20GMT

ADAS

Potential Discussion PointsPotential Discussion Points• Why are analyses needed?

– Application driven: data assimilation for NWP (forecasting) vs. objective analysis (specifying the present, or past)

• What are the goals of the analysis?– Define microclimates?

• Requires attention to details of geospatial information (e.g., limit terrain smoothing)

– Resolve mesoscale/synoptic-scale weather features? • Requires good prediction from previous analysis

• What’s the current state-of-the-art and what’s likely to be available in the future?– Deterministic analyses relative to ensembles of analyses

(“ensemble synoptic analysis”–Greg Hakim)

• How is analysis quality determined? What is truth?– Why not rely on observations alone to verify model guidance?

Observations vs. TruthObservations vs. Truth

• “Truth? You can’t handle the truth!”• Truth is unknown and depends on

application: “expected value for 5 x 5 km2 area”

• Assumption: average of many unbiased observations should be same as expected value of truth

• However, accurate observations may be biased or unrepresentative due to siting or other factors

What’s an appropriate analysis given the What’s an appropriate analysis given the inequitable distribution of observations?inequitable distribution of observations?

???x

x x

= observation x = grid cell

Case 1 Case 2 Case 3

What’s an appropriate analysis given What’s an appropriate analysis given the variety of weather phenomena? the variety of weather phenomena?

Front Elevated Valley InversionsO

O

? O

O

?

OO ?

T

z

Analyses vs. TruthAnalyses vs. Truth

Analysis value = Background value + observation Correction

- An analysis is more than spatial interpolation- A good analysis requires:

- a good background field supplied by a model forecast- observations with sufficient density to resolve critical weather and climate features- information on the error characteristics of the observations and background field- good techniques (forward observation operators) to transform the background gridded values into pseudo observations

- Analysis error relative to unknown truth should be smaller than errors of observations and background field- Ensemble average of analyses should be closer to truth than single

deterministic approach IF the analyses are unbiased

Truth: Continuum vs. DiscreteTruth: Continuum vs. DiscreteT

empe

ratu

re

West East

Truth

Truth

Truth = (Truth)

Truth is unknownTruth depends on application

Discrete Analysis ErrorDiscrete Analysis Error

Goal of objective analysis: minimize error Goal of objective analysis: minimize error relative to relative to Truth Truth not Truth!not Truth!

Tem

pera

ture

West East

Truth

Truth

Analysis

AnalysisError

ADASADAS•Near-real time surface Near-real time surface analysis of T, RH, V analysis of T, RH, V (Lazarus et al. 2002 (Lazarus et al. 2002 WAF; WAF; Myrick et al. 2005Myrick et al. 2005 WAF; WAF; Myrick & HorelMyrick & Horel 2006 2006 WAFWAF))

•Analyses on NWS GFE Analyses on NWS GFE grid at 5 km spacing grid at 5 km spacing

•Background field: RUCBackground field: RUC

•Horizontal, vertical &Horizontal, vertical & anisotropic weighting anisotropic weighting

Description:

In the following slides, temperature results from LAPS/MM5 analysis are shown.

The objective is to compare a normal MM5 analysis with LAPS/MM5 analysis, also verify against some observations that are not included into the LAPS analysis

Input to LAPS analysis is here:

- MM5 9-km resolution (input to MM5 is ECMWF 0.35 deg)

- 52 surface observations from HTB area

MM5 analysis: Temperature at 9 m height, with 1 km resolution

The analysis is based on 0.35 degree boundary fields from ECMWF operational analysis.

09 Aug 2005,15 UTC

09 Aug 2005,15 UTC

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MM5 analysis: Temperature at 9 m height, with 1 km resolution

Verification: The figures, within the plot, are measurements from certain stations not included in the LAPS analysis

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LAPS/MM5 analysis: Temperature at 9 m height, with 3 km resolution

Verification: The figures, within the plot, are measurements from certain stations not included in the LAPS analysis

09 Aug 2005,15 UTC

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LAPS/MM5 analysis: Temperature at 9 m height, with 1 km resolution

Verification: The figures, within the plot, are measurements from certain stations not included in the LAPS analysis

09 Aug 2005,15 UTC

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LAPS/MM5 analysis: Temperature at 9 m height, with 1 km resolution

Verification: The figures, within the plot, are measurements from certain stations which are not included in the LAPS analysis

09 Aug 2005,15 UTC

WHAT IS TRUTH?

Data Assimilation SurprisesData Assimilation Surprises• Torn and Hakim (unpublished) have applied an ensemble Kalman filter for several hurricanes to determine

the most sensitive regions for forecasts in the western Pacific Ocean. The largest sensitivities are associated with upper-level troughs upstream of the tropical cyclone. Observation impact calculations indicate that assimilating ~40 key observations can have nearly the same impact on the forecast as assimilating all 12,000 available observations.

• Sensitivity of the 48 hour forecast of tropical cyclone minimum central pressure to the analysis of 500 hPa geopotential height (colors) for the forecast initialized 12 UTC 19 October 2004. Regions of warm (cold) colors indicate that increasing the analysis of 500 hPa height at that point will increase (decrease) the 48 hour forecast of minimum central pressure. The contours are the ensemble mean analysis of 500 hPa height.

More Data Assimilation WoesMore Data Assimilation Woes• Adaptive observations: collecting data where the

forecast is most sensitive

• Sometimes assimilating more data produces a worse forecast (Morss and Emanuel)

• Heretical thought: What if none of the hundreds of observations from the Helsinki Testbed made any difference to the forecast?

Challenges Ahead for Testbed/LAPSChallenges Ahead for Testbed/LAPS

• The Testbed only samples the lower troposphere at best, not the mid and upper troposphere.

• Weather phenomena, even adequately sampled by the Testbed data, will move out of the Testbed domain within an hour or two.

• Weather phenomena inadequately sampled by the Testbed data will move into the domain and screw up your forecast.

• Predictability of mesoscale weather features is unknown.• All of this assumes a perfect model.

Challenges Ahead for ForecastersChallenges Ahead for Forecasters

• Determinism is dead—long live probabilistic forecasting!• High-resolution model output cannot be interpreted the

same way as a coarser-resolution model output. • Forecasters need to be retrained.• Communication of high-resolution forecasts to end users

is not simple (i.e., you cannot just send raw model output to users and expect them to use it).

• This ensures jobs for good forecasters in the future.