Intro to NWP
numerical weather prediction
Compiled by Henrik Vedel
Center for Meteorological Models (CMM), Research and development
department, Danish Meteorological Institute (DMI)
Weather Prediction by Numerical Process
Lewis Fry Richardson, Cambridge University Press, 1922
Fundamental equations
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Newton's second law
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Conservation of mass
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Equation of state for ideal gases
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Conservation of energy
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Conservation of water mass
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Effects of radiation, condensation, turbulence, surface
friction, lower boundary conditions, etc.
Discretization and solution by finite differences
Kopieret fra ”Atmospheric Data Analysis”, R. Daley, Cambridge Univ. Press
Richardson estimated 64000 people would be necessary for doing global NWP
in a ”forecast factory”.
For various reasons his test, for part of Europe, failed, with huge deviations
between forecast and observations.
• In 1950 NWP was done again, for the US using a real computer,
taking about 24 h to make a 24 h forecast.
• Due to more and better observations, faster computer, and better
model physics, this time with success.
• One reason for the improvement in observations was World War II,
where knowledge about current and future weather was in many
situation crucial to the planning of military actions.
Fundamental equations
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Newton's second law (3 equations for 3D vind)
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Conservation of mass (continuity equation)
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Equation of state for ideal gases (p, rho, T relation)
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Conservation of energy (first law of thermo dynamics)
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Conservation of water mass
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Effects of radiation, condensation, turbulence, surface
friction, lower boundary conditions, etc.
By analysing the equations with atmospheric motions on the
Earth in mind simplifications can be made.
Some of these divide NWP models into categories.
Momentum equations
See ”An introduction to Dynamical Meteorology”, J. R. Holton, Elsevier Press
Momentum equations
See ”An introduction to Dynamical Meteorology”, J. R. Holton, Elsevier Press
Most NWP models are based on the so-called ”primitive equations”,
describing the atmospheric flow under the assumption the vertical
flow is much slower than the horisontal, and under the assumption the
height of the atmosphere simulated is small compared to the radius of
the Earth.
The primitive equations were first written down by Vilhelm Bjerknes,
before Richardson had his go on a numerical solution.
Example of primitive equations (for a system with pressure as vertical
coordinate, catesian tangent plane in the horisontal, and neglecting curvature
of Earth.
Geostrophic wind
equations
Hydrostatic balance
Continuity equation (mass conservation),
relating horisontal divergence to vertical
motions under the hydrostatic approximation
Conservation of energy
In addition an equation for conservation of water mass and equation of state
Hence the main variables are 2D horisontal wind, temeperature, water vapour
NWP model coordinate systems
It varies from model to model, in each case care must be taken to ensure
proper transformation between coordinate systems when trying to estimate
a property based on NWP data.
In general:
A NWP model space is spherical or flat (LAM)
Typically g, the graviational acceleration is a fixed constant.
The height of the model surface is typically the geometric height wrt. mean
sea level (geoid), when determining heights further up, it is typically the
geopotential height increment above the surface, derived from pressure,
density and the hydrostatic approximation, delta_p = -g rho delta_z , which
is added to the surface height.
The horisontal coordinates differ from model to model, typically being some
type of lat-lon-grid in regional models, to spherical harmonics and more
sofisticated grids in global models. Some models are run in grid space,
some in spectral space.
In most current models the vertical coordinate is tied to pressure, but is not
pressure itself, most common are,
Both have the benefit of being ”terrain following”, the coordinate being 1 at
the surface, which simplifies the equations to solve in the lower
atmosphere. The latter has constant pressure surfaces in the upper
atmosphere, which among other things benefits the use of important
satellite data.
In some of the newer, non-hydrostatic, models the vertical coordinate is
height
Parametrisations
• Operational NWP is mainly done on with horisontal gridsizes of the order 1 to
50 km.
• Higher resolution enables more phenomena to resolved explicitly by the
model.
• But at any resolution, many processes occur on too small scale, or are simply
too complex, to be explicitly included in the model.
• Convective clouds have sizes of about 1 km, and are currently not resolved
properly in operational NWP.
• Clouds droplet formation occur on molecular scale, is not resolved, and far
from understood in detail. Similarly the transfer of solar radiation is related to
cloud microphisics. Interactions with the ground, related soil type, vegetation
type, soil moisture and resulting evaporation are parametrised.
When the horisontal resolution is increased, to order few km scale, we
expect the hydrostatic approximation to become increasingly invalid.
Hydrostatic NWP models cannot model the formation of individual
convective systems, even the big ones. They are not good at modeling the
airflow in regions with strong orography. They do not model gravity waves
well at all, which can be of importance sometimes on even larger scales.
•(Figure from Arakawa, presentation at workshop on Non-hydrostatic Modelling 8-10 Nov., 2010
ECWMF)
Parameterizations
Land surface
Cloud microphysics
Turbulent diffusion and interactions with surface
Orographic drag
Radiative transfer
From J. Knievel
In NWP ”language” processes that are resolved are often referred to
as ”dynamics”, whereas processes not explicitly resolved are
referred to as ”physics”.
The ”physics” is in general ”tuned” for the model to perform the best
in the area of interest. For this reason the NWP models of different
met offices or universities can perform quite differently in different
areas, without it being a real model error . Sometimes even for the
same model, that is just tuned differently.
It is important to have this in mind, when using results from different
models or from different institutions for a specific area.
MENU
Ingredients of a numerical weather
prediction system
Observations
Data assimilation system
provide ”Analysis”
(=initial conditions)
Boundary values
from external
model
Numerical
weather
prediction
model
Old model state
Combined and done on a
very powerfull computer
Computer
generated
forecasts
Forecasts by
forecasters
From NN
Examples of HIRLAM (high resolution limited area model) run at DMI
Example: HIRLAM S03/SKA details
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HIRLAM = High Resolution Limited Area Model
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Boundary conditions = ECMWF global model
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Horizontal grid resolution = 0.03° (approx 3 km)
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Vertical layers = 65
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Grid points = 978 * 818 * 65
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Approximately 8 variables
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Forecast length=54h, time step=90s
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Runs on 50 nodes (700 cores) using MPI parallelization;
asynchronous I/O on 8 cores
Much of the progress in NWP skill is due to faster computers enabling us
to increase resolution, improve the data assimilation systems,
improve the representation of physical processes. In addition the
observing system is gradually improving, with more and novel types
of observations.
Global models are typically run 2 – 4 times a day, with forecasts out to
about 15 days.
Higher resolution, local area models (LAMs) are run 4 to 24 times a day,
with forecasts typically in the range of 12 hours to several days.
About non hydrostatic NWP
Idealised test of N-H versus H NWP model Aladin
From a presentation by Jan Masek
Slovak HydroMeteorological Institute (28th EWGLAM meeting 2006)
Very high resolution
Test of N-H model, by run at double resolution.
OK
Test of N-H model, by run at double resolution.
OK
Now at 1 km resolution
Findings in idealised tests
From Jan Masek
Some examples from DMI
More realistic regarding a focus on real weather phenomena
Less easy to conclude from..
Piteraq i Tasiilaq Feb. 6 1970
See Emilie Harmansson, Vejret 126, 2011. Thanks also to Niels Voetmann
•Night time radiation results in colder
air near surface. In steep orography
the denser air slides toward lower
levels, accelerating if it continues to
be denser.
•Hypothesis that N-H NWP is better to
model this than hydrostatic NWP
because of better handling of vertical
dynamics and of orografic forcing.
•If air mass moves in an area
channeling the air, and into a low
pressure area that can “absorb” the
air, the wind speed is further
increased.
•Possibly gravity waves also
strengthens the phenomon (similar in
foen situations).
• NH Arome versus H Aladin, rated by Meteo France forecasters
•
(from Benard, Meteo France, at workshop 8-10 Nov, 2010, ECMWF)
Hydrostatic versus non-hydrostatic
•The naming ”non-hydrostatic” is confusing to non-experts. Non-hydrostatic
models do not miss something. It is the other way around!
•In N-H models one includes a vertical acceleration term in the dynamic equations.
In hydrostatic models this term is replaced by the simplifying assumption of
hydrostatic balance (+inclusion of extra parametrisations).
•On large scales, many km, the differences are in general not important. Running a
hydrostatic model can be preferable – as it leaves cpu for other calculations.
•On smaller scales, order one kilometer, differences become marked, N-H is
superior.
•On scales in between the situation is currently more complicated. If orographic
forcing or gravity waves are of importance, N-H models have benefits. But in other
cases, more typicical of the Danish area, the skill of other components of the NWP
system (parametrisations, data assimilation, etc.) of importance to the particular
weather type can be more important than non-hydrostatic versus hydrostatic.
Verification
• It is extremely important to monitor and to verify model performance.
Both in order to improve models, and in order to choose between
models for forecasting this and that. Different models and model setups
have different skils – it is not one model always being better than the
rest.
• Divided into ”objective” and ”subjective” verification.
• SUBJECTIVE: A forecaster, or other expert, compare by eye model
output to observations or fields derived from observations.
• OBJECTIVE: Traditionally two methods are used
1. Point comparision of model to observations. Typically done for 2mT,
2mRH, 10 m wind, and against radiosonde observations of wind,
temperature and humidity at select pressure levels. Can in principle
be done for any type of meteorological observation. Common is to
derive bias and standard deviations. In case of precipitation, slightly
more complex methods are used.
2. Model fields comparisons, between a forecast field and the
”analysis” valid at the same time. The analysis is the initial
condition field from which an NWP run is started, and represents the
current state of the atmosphere better than the forecasts. (or..)
Example:
Mslp, 2mT and 10m wind as
function of forecast length
over a month long period for 4
different models
Example:
10m wind as function of day
of month during one month,
for 5 different models.
Monitoring example:
Meteogram for one location
comparing 48 hour forecasts
of 2mRH, 2mT, 10m wind
direction and speed, and
mslp.
Monitoring example:
Average 2mT and 10m wind
speed for one month as
function of time of day and
forecast length. For 7 models
started the same time very
day.
HIRLAM prediction case of
EXTREME PRECIPITATION
Forecasted 100 mm
Observed 100 mm
To improve forecasts: Improve resolution, increase forecast
frequency, include extra observations to benefit the extra
forecast cycles.
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To improve results from increased NWP resolution, observations with
higher spatial density are needed.
To improve results from higher NWP cycling rate (e.g. hourly instead of
6 hourly) more frequent observations are needed.
The “traditional” meteorological observing system is not built for high
resolution, rapid update cycling meso scale NWP.
There is a particular lack of high resolution, rapid update observations
related to humidity and precipitation in most current operational NWP
setups.
•
•
The purpose of the NWP nowcasting is to predict important weather
phenomena that has low predictability because they occur on small scales in
time and space, leaving them very difficult to predict properly with traditional
NWP setups.
Examples of importance to DMI/Denmark are:
–
Convective, heavy, local precipitation (risk of floodings, risk of waste
water overflow).
–
Road temperatures, humidity, precip., cloud cover (e.g. slippery road
forecasts, used by road authorities when planning salting etc.)
–
Short term changes in wind and cloudiness, changing energy production
from wind turbines and solar panels.
The basic idea in NWP nowcasting (even more in general nowcasting), is to
utilise very recent observations to predict near future events.
Cycling a forecasting system 4 times a day, every 6 hour, to predict the exact
strength and location of a one or two hour convective precipitation event is
beyond the capacity of the current observing systems and NWP models.
Possibly beyond physics as well (chaos/un-predictability).
CASE 1 – 2/7-2011
Copenhagen
10-minute output
15 UTC simulation
CASE 2 – 14/8-2010 - Copenhagen
Subjective verification
Objective verification of precipitation
The ”double penalty problem” of high resolution models when using
standard point verification
At half the resolution
Point comparisons of precipitation tend to punish high resolution
models relative to coarser resolution models, even if to a forecaster they
appear superior.
FSS (fractions skill score)
CASE 1 – 2/7-2011
Uniform
Fractions skill score
CASE 1 – 2/7-2011
CASE 2 – 14/8-2010
Fractions skill score
Ensemble forecasting
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The NWP models are far from perfect. Both
because of lack of computer power and lack of
physical knowledge about important processes.
The initial conditions are heavily under-determined
by the observations.
Some of the most severe weather events in Europe
are related convective precipitation, which can
have very short lifetime, hour to hours, and very
low predictability.
The atmosphere is a chaotic system. Small
variations in initial conditions can lead to large
variations in the forecast.
Ensemble forecasting
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By making variations of the initial conditions and the
unknowns of the NWP model, in a systematic and
realistic way, we can assess the quality and
robustness of the forecasts, enabling estimation of
the uncertainty of the forecasts, as well as identify
situations where several outcomes (forecasts) are
possible, given our lack of perfect models and lack of
a perfect observing system.
Running such a suite of forecasts in called
“Ensemble forecasting”.
Originally ensembles where global, with a focus on
large scales and several days ahead.
Now many regional ensembles exist, with a focus on
the near future and smaller scale phenomena, such
as severe, convective precipitation.
Example from the ECMWF
ensemble system with 50
members (different forecasts).
Ensamble prediction for a
single location.
Next slides show results from a DMI ensemble with a resolution of 5
km and 25 members (different forecasts).
Ensemble prediction, rainfall 14 Aug 2010
Ensemble mean and forecast “probabilities”
Access to NWP models
• Some NWP models, such as WRF and MM5 are open software, that you
can download and run on your pc. They are used extensively for
research at universities, resulting in a wealth of different software
packages to choose between for simulations of various physical
processes, assimilation of different observations, etc.
• In addition it is possible to download freely GFS data, which can be
used as initial data and boundary data for your own NWP run.
• In contrast the majority of the NWP models and associated data
assimilations systems used for operational weather forecasting at the
national met offices are not open software. They are developed by
consortias of met offices, some by single met offices. They benefit from
being developed in a ”balanced” way, each component constructed to
work well with the other components.