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Brief History of Meteorology and NWPLecture 1

Brief History of Meteorology

• 340 B.C.– Meteorologica - Aristotle

• 1400's– Hygrometer - Cryfts (1450)

– Anemometer - Alberti (1450)

• 1500's– Thermoscope - Galileo

• 1600's– Barometer - Torricelli (1643)

– Les Meteores - Descarte (1637)

• 1700's– Trade winds - Hadley (1730)

• 1800's– Three-cell model - Ferrel (1855)– Weather maps of surface pressure

• 1900's– Weather prediction from maps -

Bjerknes (1903)– Polar front theory - Bjerknes

(1921)– Numerical weather prediction -

Richardson (1922)– First computer forecast - Charney

/ von Neumann (1948)– Daily balloon observations

(1940's)– Weather satellites (Tiros I, 1960)

Excerpts from Aristotle’s Meteorologica

• There are two reasons for there being more winds from the northerly than the southerly regions. First, our inhabited region lies toward the north; second, far more rain and snow is pushed up into this region because the other lies beneath the sun and its course. These melt and are absorbed by the earth and when subsequently heated by the sun and the earth’s own heat cause a greater and more extensive exhalation.

• Let us now explain lightning and thunder, and then whirlwinds, firewinds and thunderbolts; for the cause of all of them must be assumed to be the same. As we have said, there are two kinds of exhalation, moist and dry; and their combination (air) contains both potentially. It condenses into cloud, as we have explained before, and the condensation of clouds is thicker toward their farther limit. Heat when radiated disperses into the upper region. But any of the dry exhalation that gets trapped when the air is in process of cooling is forcibly ejected as the clouds condense and in its course strikes the surrounding clouds, and the noise caused by the impact is what we call thunder.

Scales of Motion

Molecular scale (<< 2 mm)Molecular diffusionMolecular viscosity

Microscale (2 mm- 2 km)EddiesSmall plumesCar exhaustCumulus clouds

Mesoscale (2 - 2000 km)Gravity wavesThunderstormsTornadosLocal windsUrban air pollution

Synoptic scale (500-10,000 km)Pressure systemsWeather frontsTropical stormsHurricanesAntarctic ozone hole

Planetary scale (>10,000 km)Global wind systemsRossby wavesStratospheric ozone lossGlobal warming

Atmospheric Model• Aerosol processes (Microphysics)

– Nucleation/condensation– Phase changes

• Cloud processes– Conden./evap./deposition/sublim.– Precipitation– Stability (Vertical/Slantwise Ascent)– Convection– Entrainment

• Radiative transfer– UV/visible/near-IR/thermal-IR– Scattering/absorption– Snow, ice, water albedos

• Meteorological processes– Velocity – Geopotential– Pressure– Water vapor– Temperature– Density– Turbulence

• Surface processes– Temperatures and water content of

• Soil Water Snow• Sea ice Vegetation Roads• Roofs

– Surface energy/moisture fluxes– Ocean-atmosphere exchange – Ocean dynamics, chemistry

An Overview of Numerical Weather

Prediction

(Originally Prepared by Marty Baxter)

Highlights

• 1955 – First Operational Numerical Model – Barotropic Model (Charney)• 1962 – First Operational Baroclinic Model (Cressman)• 1966 – 6-layer Primitive Equation (PE) model (PEs by Shuman and Hovermale) –

– First Global PE Model.– 381 km grid – First model to have QPF

• 1971 – Limited Fine-Mesh Model (LFM) (Howcroft) – – First operational regional model.– 190 km grid, 6 vertical layers– Improved resolution had positive impact on QPF

• 1978 – 7-Layer PE mode: mesh size/time step halved from 6-layer model• 1980 – Global Spectral Model (Sela) replaced 7-layer PE model

– 30 Spherical harmonic modes (resolves to 30 waves) and 12 levels

• 1985 – Nested Grid Model (NGM) (Phillips, Hoke) – – Model part of Regional Analysis and Forecast System (RAFS)– 3 grids: 381, 190, and 80 km and 16 levels– Used optimum interpolation (OI)– Later frozen for MOS since 1990

Highlights

• 1991 (August) – RAFS updated for last time, NGM run with only two grids with inner grid doubled in size

– Implemented Regional Data Assimilation System (RDAS) – included 3-hourly updates from an improved OI analysis using all off-time data including profiler and ACARS wind reports & complex quality control procedures

• 1993 (June) – Early Eta (Mesinger, Janjic, Black) – Replaced the LFM as the early run model (for 00 and 12 UTC)

– 80 km grid with 38 vertical levels

• 1994 (September) – Rapid Update Cycle (RUC) (FSL, Benjamin)– 60 km grid, 25 vertical levels, forecasts out to 12 hours 8 times a day– CONUS domain with 3-hourly OI updates at 60 km resolution on 25 hybrid (sigma-theta) vertical levels.

• 1994 (September) – Early Eta analysis upgrades• 1995 (August ) – Mesoscale version of the Eta model implemented at 03 and 15 UTC for an

extended CONUS domain with 29 km and 50-layer resolution run out to 30 hours– Included NMC’s first predictive cloud scheme and new coupled land-surface atm. Package

• 1995 (October) – Major upgrade of Early Eta model– 48 km grid with 38 vertical levels (replaced 80 km Eta as the early run)

• 1996 (January) – New coupled land-surface-atmosphere scheme put into early Eta

Highlights

• 1996 – AVN/MRF changed to T126, 28 levels• 1997 (February ) – Upgrade package implemented in the early and Meso Eta

runs• 1998 (February) – Early Eta upgraded to 32 km grid and 45 levels with 4 soil

layers.– OI analysis replaced by 3D-Variational Analysis (3D-VAR) method with new data

sources

• 1998 (April) – RUC (3-hourly) replaced by hourly RUC II system with extended CONUS domain

– 40 km gird and 40 level resolution– Additional data sources and extensive physics upgrades

• 1998 (June) – Meso Eta runs 4 times a day for North America domain at 32 km grid and 45 vertical level resolution

– Used new snow analysis– All runs started from EDAS which is fully cycled for all variables

• 1998 (November) – Eta 03 UTC run moved to 06 UTC. – 06 and 18 UTC productions run out to 48 hrs (instead of 33 and 30 hrs)

Highlights

• 2000 (January) – Resolution upgraded from T126L28 to T170L42 in AVN/MRF. – MRF run at T170L42 through day 7, then at T62L28 through day 16. – AVN run at T170L42 out to 84 hrs four times a day

• 2000 (March) – ETA 00 UTC and 12 UTC runs out to 60 hrs• 2000 (May) – AVN available out to 126h at full T170 resolution at 00Z• 2000 (June) Resolution of AVN/MRF ensemble members increased from

T62 to T126 for first 60 hr of forecast.• 2000 (September) – Eta model resolution changed to 22 km, 50 layers for

all four daily runs and domain expanded to match old 48-km domain.• 2000 (December) – High-resolution satellite added to Eta assimilation• 2001 (April) –Eta 00 UTC and 12 UTC runs extended to 84 hours• 2001 (May) – List of changes implemented in the AVN/MRF

Highlights

• 2001 (November) – Major changes to Eta – resolution changed to 12 km, 60 layers for all four daily runs – major upgrades to grid-scale precipitation.

• 2002 (March) – AVN runs four times a day out to 384 hrs. – Resolution T170L42 to180 hrs thereafter T62L28

• 2002 (April) – RUC-20 replaced RUC-2. – 50 levels, 20 km grid spacing, – improved microphysics and convection– boundary conditions from 6 and 18 UTC Eta instead of using older 00 and12 UTC Eta.

• 2002 (April) – MRF is replaced by the 00Z AVN• 2002 (Sept-Oct) – AVN now referred to as the Global Forecast System model (GFS)• 2002 (October) – Resolution in GFS changed to T254L64 to 84 hr, T170L42 to 180 hr,

T126L28 to 384 hr• 2003 (May) – Change from OI to 3D-VAR in RUC• 2003 (July) – Eta 06 UTC and 18 UTC runs extended to 84 hr. (all 4 daily runs to 84 hr)• 2004 (March) – GFS ensemble run 4 times daily. Resolution T126 0-180 hrs, then T62 to

384 hrs.• 2004 (April) – multiple changes and updates implemented in the RUC• 2005 (January) – Eta model renamed as North American Model (NAM)

Barotropic Atmosphere

• Surfaces of constant pressure coincide with surfaces of constant density

• Temperature is the same at every point meaning there is no thermal wind.

• No change in intensity with height and no slope of systems

• No isotherms on a constant P chart

Equivalent-Barotropic Atmosphere

• Constant-pressure surface now has isotherms on it everywhere parallel to the contours

• Wind can change speed with height but not direction

• Systems are vertically stacked, no temp advection exists

• Equivalent-barotropic level presumed to be near the LND, usually assumed to be at 500 mb

• Atmosphere often close enough to the equivalent-baroclinic state (i.e. tropics) such that barotropic dynamics may be dominant

Baroclinic Atmosphere

• No assumptions about the patterns of density or temperature on a pressure surface

• Thermal wind can now change speed and direction

• Systems slope with height• Real atmosphere always

baroclinic

Thermal Wind (Remember?)

The thermal wind is a measure of the Geostrophic wind shear:

Written in vector form:

Can also be related to:

If the lines are Z, GWIf the lines are T, TW

Basic Principles of NWP (Fred Carr)

• In 1905 Bjerknes recognized that NWP was possible in principle– Eqs governing time rate of change of

meteorological values are known– Can integrate these eqs forward in time to get new

values– Must have “suitable” initial conditions (observations)

in order to do this

Written in general form:

Ai = dependent forecast variables such as u, v, T etc…

F(Ai) = advection and physical forcing terms that can be calculated from obs of Ai

To get a forecast, integrate from an initial time t0 to some time in the future t1

Using a forward difference expression for gives us:

Δt = time step on the order of minutes – repeated several hundred times to get a 24 and 48 hour forecast

iiAF

t

A

dtAFdtt

A t

t

i

t

t

i

1

0

1

0

We get dtAFAA

t

t

ii

t

i

t

1

0

01

t

Ai

it

i

t

i

ttAFtAA

Seek equations between variables you want to know and the forcing mechanisms that cause changes in these variables

In Other Words:

Example of a prognostic equation:

In Meteorology we would solve for Du/Dt

OR

Written as:

Example of a diagnostic equation:

0 and DW

Dtp pg

gz RT

Consider the vertical component of:

Right hand side balances perfectly for large-scale flow:

Hydrostatic eq. - used to deduce Z from T

0

0

1DW pg

Dt z

Essential components of NWP models are:

• Physical Process– RHS of equations

• i.e. PGF, friction, adiabatic & diabatic heating, advection terms …

• Numerical Procedures– Approximations used to estimate each RHS term– Approximations used to integrate model forward in

time– Grid used over model domain (resolution)– Boundary conditions

• Quality and quantity of obs are vital

Primitive equations of motion: – Set of governing equations that describe large-scale atmospheric

motions derived from conservation laws governing momentum, mass, energy, and moisture

– Best suited for development of comprehensive dynamical-physical models of the atmosphere

– Equations expressed in the Eulerian (fixed obs) framework in x-y-p coordinates written as:

(6)

(5)

(3)

(1)

(4)

(2)Horizontal Momuentum Eqs

of u and v

Vertical Momentum Eq

Continuity Eq

First Law of Thermodynamics

Conservation of Moisture Eq

• Eqs. (1), (2), (5), and (6) are prognostic equations (involve a time derivative) and thus require initial conditions. – Initial conditions are derived from observations

or the use of some balance relationship• Eqs. (3) and (4) are diagnostic equations and

can be computed once the initial conditions are provided

The dependent variables in this set of equations are u, v, , , T, and q which are assumed to be continuous functions of the

independent variables x, y, p, and t.

Thus, Eqs (1) to (6) constitute a set of 6 equations and 6 unknowns

6 primitive equations are considered a closed system if:

1. Expressions can be found for Fx, Fy, H, E, and P in terms of the known dependent variables

2. There are suitable initial conditions over the domain3. Suitable lateral boundary conditions for the

dependent variables are formulated (for regional models); all models need boundary conditions at the top and bottom levels

Problems in finding suitable lateral boundary conditions and expressions for Fx, Fy, H, E and P

For lateral conditions – effect of (topography) mountains have to be included in the model via the lower boundary condition and choice of vertical coordinate.

Fx and Fy are “friction” terms which modify the momentum equations – raises need for the addition of physics to primitive eqs.

The diabatic heating term H also consists of several effects which can be written: H = HL (ascent) + HC (convection) + HR + HS

Parameterization problem – trying to express subgrid–scale processes in terms of the large-scale dependent variables

Evaporation (E) can be due to moisture flux from surface and evaporation of precipitation

Precipitation Rate—related to HL and HC, precipitation efficiency…

Once three conditions are “suitably” met, primitive equations are a closed system and can

be solved by:

1. Obtain observations of the prognostic variables u, v, T, and q over the domain

2. Compute from (3) and from (4)

3. Compute Fx, Fy, H, E, P and the other terms on the right-hand sides of (1), (2), (5), and (6)

4. Integrate the four prognostic equations forward in time to obtain new values of u, v, T, and q

5. Repeat steps 2 to 4 until the forecast is complete

• Conditions which make the primitive equations a closed system are never perfectly met – Leads to a large part of the total forecast error seen in

models

• No two numerical models are alike – There are nearly an infinite number of ways to formulate

the physics and many numerical procedures for the solution of the eqs

• Each model may have its own systematic errors or biases

Important to be aware of these limitations in order to make intelligent use of model data

One BIG Caveat

5 Major Steps in the Production of an NWP Model

Observations• All models require obs from an area larger than their forecast domain• Forecasts longer than 2-3 days require global data sets• Global Telecommunications System (GTS) gathers and disseminates conventional

data to nearly all countriesAnalysis• Objective analysis – obs checked for errors and interpolated to grid on which model

atmosphere is representedInitialization• Adjusts the analyzed data so that the model and data are dynamically consistent• Ensures no “noise” is generated when forecast beginsForecast• System of forecast eqns marched forward in time until desired forecast length is

reachedOutput• Forecast maps produced and sent to users, including computations of many quantities

not directly forecast by the model• Forecasts verified to document model errors and biases in order to formulate

improvements in the future.

Courant-Friederichs-Lewy criteria

• Criteria states that the (Maximum) time step of the model must be small enough to capture the fastest moving wave on the model grid

• This is determined by

t = time step, d = grid distance, c = speed of fastest wave

c

dt

2

Example: If you know d = 150 miles and the speed of the fastest wave is 700 mph, the length of the time step needed to capture the wave can be calculated.

min1.9min60152.7002

150

hr

hrmi

mit

Courant-Friederichs-Lewy criteria cont.

If the time step and grid spacing is known, this criteria can be used to determine the fastest wave the model will be able to resolve

Example d = 30 km and t = 90 sec (MM5 model)

hr

kmkmkm

t

d8503600

sec236.

2sec90

30

2

If this criteria is not obeyed, small scale waves amplify rapidly and overwhelm the solution leading to

computational instability

Note – smaller than the speed of sound which is 1152 km/hr

Map Scale Factor

When a curved earth is projected on a flat map, a scale factor must be used in to assure that the distance between grid points stays constant.

Map projections will always have one true latitude and have to use a scale factor for all others, because as you move away from the true latitude, the distance between grid points will change.

Example: A polar stereographic projection of the earth with a true latitude of 90° N would use the following map scale factor.

sin1

90sin1

m m = map scale factor = your latitude

Note: 90° is the true lat. of the map, this can change from one map to another.

x

Tm

mxT

x

T

To provide accuracy, the map factor is included

Setting up a Numerical Model

• Grid point models – models that solve the forecast equations at equally spaced grid points. – Forecast variables specified on a set of grid points

• Spectral models – models that emulate the process of drawing contours through a data field to represent the forecast variables.– Forecast variables at all locations using a combination of

continuous waves of differing wavelength and amplitude

Hydrostatic vs. Non-Hydrostatic

• Hydrostatic models assume hydrostatic equilibrium– Valid for most synoptic and global systems and some

mesoscale phenomena

• Non-hydrostatic models include equations for vertical motions that hydrostatic models lack

• Most grid-point models and all spectral models in operation are hydrostatic

• Many mesoscale models are non-hydrostatic• Non-hydrostatic processes and effects become

important when length of a feature is approximately equal to its height– Typically features 10 km and less in size

Horizontal resolution

• Horizontal resolution is related to the spacing between grid points for grid point models or the number of waves that can be resolved for spectral models

• Directly related to size of weather feature it can simulate• Higher the resolution – smaller the weather feature it can depict• Typically takes at least 5 grid point to define a feature (grid

point model)– Example – a model with 20 km grid spacing cannot resolve

anything less than 100 km in length• Increasing horizontal resolution increases computation

– Additional intermediate forecast steps are required to make same length of forecast

Vertical Resolution

• Can be set arbitrarily• Highest vertical resolution used where it is

needed most– Highest is set near Earth’s surface to capture

boundary layer processes and near and below tropopause to accurately predict jet stream

– Not as detailed between 600-300 mb

• Variety of vertical coordinate types used to represent atmospheric layers– Most common is sigma coordinate system

• Defined as ; p= pressure level, ps=station pressure

• Bottom and top are levels where vertical motion are negligible• Bottom is near the earth’s surface (σ = 1.0)• Top is set to a very small pressure value (σ = 0.0)

Sigma Coordinate System (σ)

• Near surface sigma levels closely mimic terrain

• Aloft sigma levels flatten out horizontally

• Sigma levels eliminate problem of constant height or pressure surfaces intersecting the ground

sp

p

Parameterization

The representation of the effects of sub-grid scale processes in terms of grid-scale variables predicted by the model

• NWP models cannot resolve features and/or processes within a grid box realistically

• Parameterization has its greatest impact on predictions of sensible weather at the surface

• Physical processes typically parameterized– Soil moisture/temperature– Longwave radiation– Solar isolation/reflection– Evaporation– Convection – Cloud and precipitation processes– Friction/turbulence

Convective Parameterization Schemes

• Most NWP models use these• Designed to reduce atmospheric instability in

the model• Prediction of precipitation is a by-product of

how the scheme reduces instability• Expectations of schemes to accurately predict

location and timing of convective precipitation is usually low

3 reasons processes need to be parameterized

1. Phenomena are too small or too complex to be resolved numerically – computers aren’t powerful enough to directly treat them

2. Processes are often not understood well enough to be represented by an equation

3. Effects profoundly impact model fields and are crucial for making realistic forecasts

Problems associated with using parameterizations result from:

1. Increasing complexity of parameterization

2. Interactions between parameterization schemes – these are harder to trace than errors occurring in a single scheme