SO441 Synoptic MeteorologyNumerical weather prediction

24-hour precipitation totals ending 0000 UTC 30 Jan 2018

Climate Forecast System (CFS): 56km Δx

NAM (US): 4km Δx

NAM (US): 12km ΔxGFS (US): 13km Δx

SO441 Synoptic MeteorologyNumerical weather prediction

24-hour precipitation totals ending 0000 UTC 30 Jan 2018

Climate Forecast System (CFS): 56km Δx

NAM (US): 4km Δx

NAM (US): 12km ΔxGFS (US): 13km Δx

A bit of important history . . .• What is numerical weather

prediction?– An integration forward in time

(and space) of fundamental governing equations: 6 equations, 6 unknowns• Equation of state• Navier Stokes (from F=ma)• Continuity equation• Thermodynamic energy equation

(from 1st & 2nd laws of thermodynamics)

• Why is it so important?– Moved meteorology away from a

collection of rules-of-thumb and educated guesses to an analytic science grounded in physics and calculus

Source: https://www.ecmwf.int/en/forecasts/charts/catalogue/plwww_m_hr_ccaf_adrian_ts?time=2018011100

“Anomaly correlation scores are spatial correlation between the forecast anomaly and the verifying analysis anomaly; anomalies are computed with respect to ERA-Interim-based climate. Verification follows updated WMO/CBS guidelines as specified in the Manual on the GDPFS, Volume 1, Part II, Attachment II.7, Table F, (2010 Edition - Updated in 2012).”

What, exactly, is a dynamical model?

• A set of computer programs/lines of code (often written in FORTRAN), designed to simulate the real atmosphere– Integrates the governing

equations forward in time– Uses finite differencing

techniques to integrate the partial derivatives

• What does a dynamical model need to succeed?– A good set of governing

equations– Accurate initial and boundary

conditions• Remember Dr. Lorenz’s

experiments from the 1960s? What did he find that was so important?

Grid spacing in a model

From: http://www.drjack.info/INFO/model_basics.html

In the upper-left figure, the point represent the centers of hypothetical grid boxes. Most models stagger their solutions, solving the wind (u,v,w) at the edges of the boxes and the mass (temp, mixing ratio, height/pressure) at the centers

Parameterizations• For all processes that take place

inside a grid box, i.e., they are smaller than the grid spacing of the model, the model cannot “resolve” them explicitly

• Processes requiring parameterization:– Planetary boundary layer

• Turbulence (energysmaller scales)• Flux of momentum, heat, and water

vapor– Land-surface

• Water and water vapor cycle– Microphysics (clouds)– Precipitation

The effects that model physics parameterizations attempt to simulate are generally unresolvable at grid scales

Parameterizations: planetary boundary layer

• Turbulent fluxes need to be “transported” from within the planetary boundary layer to outside it– Example: momentum flux in

the governing equation for u:

• Similar equations exist for other flux quantities:– Heat– Water vapor

0

1Du p u wfvDt x z

Example of the “boundary layer”

w q w

Parameterizations:Land-surface models

• Many complex processes to “pass” on to the model:– Evaporation– Transpiration– Infiltration/runoff– Sublimation– Condensation

• Note that nearly all have something to do with water!

Parameterizations:Cloud microphysics

• Imagine a cloud occupies a model 3-d grid box– How many water molecules are

there?– What shapes/sizes are those

molecules?– What phases of water (gas, liquid,

solid) are present?– Is there more condensation/freezing

• And thus heat being added to the atmosphere

– Or is there more evaporation/melting• And thus heat being removed?

Parameterizations:Cumulus parameterization

• Clouds come in many shapes and sizes– Most clouds are between 0.5-3 km in diameter

• Thus smaller than model grid boxes

• To get precipitation in the model, need to parameterize clouds– “Trigger” precipitation when certain thresholds

are met: relative humidity above 70-80%, positive w (rising motion), CAPE

– Effect is to warm and dry the atmosphere above the surface

• Multiple “schemes” for cumulus parameterization: each differs in how it adjusts the atmosphere column in response to precipitation– Betts-Miller-Janic– Arakawa-Schubert– Kain-Fritsch

Parameterizations:Cumulus parameterization

• Example: how to handle precipitation in a model grid cell

• Difference in cloud water for an explicit (a) vs. parameterized (b) precipitation event

Data assimilation• What is data assimilation?

– A means of combining all available information to construct the best possible estimate of the state of the atmosphere

• What data are assimilated?– In-situ surface observations: temp, dew

point, pressure, cloud cover, wind speed and direction, current weather, visibility• Like the weather station we have on the field

out at the corner of Hospital Point• Ships, buoys

– In-situ upper-air observations• Radiosondes, aircraft

– Remotely sensed observations• Satellites: clouds, but also temperature, water

vapor, and even vertical profiles• Radar: precipitation, air motion• GPS radio occultation

Radiosonde network

ACARS observations

Data assimilation• How does it work?

– Observations must be blended together and interpolated to the nearest model grid point (horizontal and vertical)• Not an easy process!

• Which data source is most important?– Sensitivity studies (data

denial) show that it depends

Flow chart for the GFS

model

Data sources: Radiosondes, ACAR, and surface

Sensitivity of the u-wind forecast to the various components

Ensemble modeling• Predicting future weather using a suite of

several individual forecasts– Idea began with Ed Lorenz at MIT in 1950s:

tried to repeat an experiment he had made with an equation. Found that very small rounding differences completely changed the mathematical answer!• This is now known as the “butterfly effect”: an

even miniscule difference in the initial state will eventually amplify and result in a different forecast

– Lorenz proposed an upper-limit on weather forecasts of 2 weeks• Also found that some situations “degrade”

much faster than others

• Ensemble weather prediction attempts to show how fast the solutions “degrade”

Why are there still errors in NWP today?

• Grid spacing– The atmosphere is divided into cells, and the

center point (or edge points) is (are) forecasted– Topography, ground cover, etc. vary –

sometimes dramatically – inside one grid box (but the forecast for that grid box gives only one unique value)

• Equations of motion are non-linear– Changes in one variable feed back to all others

• Differential equations are solved by discretizing them in time– Rounding occurs in finite-differencing

techniques– This noise, as found by Dr. Lorenz, leads to

growing error• Initial conditions

– Current atmospheric state is unknown at all points

• Parameterizations– Sub-grid processes are estimated