Transcript Slide 1

Lec. 27+28: Weather Forecasting & Analysis (Ch 13 + Appendix)
• complexity of the problem
• forecasting methods
• NWP
• Limitations of NWP
• Physics/dynamics
This 0-3 month
forecast made
using NWP models
Historical skill of
this long-range
dynamical forecast
Modern NWP for the Normandy (D-day) landings based on data available at the
time… http://www.ecmwf.int/research/era/dday/
This 3 month leadtime forecast made
using statistical
method
Historical skill of
this long-range
statistical forecast
• courtesy of Edward Hudson, Prairie &
Arctic Aviation Weather Centre,
Edmonton
• taken 15 Nov., 2006
RAIN FELL FROM overcast skies and gale force winds drove large waves on to
the beaches of Normandy as dawn broke on Monday June 5, 1944. To the Germans
watching their defences, there was nothing to show that this was the moment the
Allied Armies had planned to invade Europe. In fact, the operation had been put on
hold because the bad weather had been forecast 24 hours before. Had it gone ahead
in these conditions, the invasion would have been a catastrophic disaster.
Nevertheless, the invasion had to occur on either the 5th, 6th or 7th of June to take
advantage of the right conditions of moon and tide. Darkness was needed when the
airborne troops went in, but moonlight once they were on the ground. Spring low
tide was necessary to ensure extreme low sea level so that the landing craft could
spot and avoid the thousands of mined obstacles that had been deployed on the
beaches. If this narrow time slot was missed, the invasion would have to be
delayed for two weeks.
From “The Most Important Forecast in History,” by E. Brenstrum (N.Z. Meteorological
Service). Published in New Zealand Geographic, pp11-16, Vol. 22, 1994,
Fluxes of solar radiation
(interact with clouds)
Fluxes of longwave radiation
(temperature-and composition- dependent)
Cloud
vertical wind
water/ice
/vapour
temperature
pressure
horizontal wind
winds on range of scales down to
millimeters - cause advection,
entrainment, etc.
variables inter-linked by consv. of
mass, heat & momentum. Relations
expressed as partial differential eqn’s
Boundary fluxes of heat and moisture (QH, QE) and
momentum (frictional drag t ) on complex terrain
Forecasting** methods
Value of a given technique depends on “range” of the forecast. For now, focus on
“weather” forecast… ie. range of up to a couple of weeks
• Climatology: hard to beat for f/c ranges beyond about 10 days.
– “The average.” eg., this afternoon’s weather in Edmonton will equal the
average observed 1961-1990 for Nov. 15 in Edmonton
– or, (eg.) this afternoon’s weather will be that associated with one of a set
of “map types,” ie. previously observed on an afternoon having similar
maps. Called an “analog method”... Ah! We’ve seen this… in 1901 …
– or, forecast the anomaly associated with (eg.) Southern Oscillation Index
• Persistence: hard to beat for f/c range of a few hours
- eg. This afternoon’s weather same as this morning’s, except for influence of
local processes (eg. solar heating)
• Numerical Weather Prediction: hard to beat for f/c range out to about 10 days
(esp. if supplemented by experienced human interpretation)
** “nowcasting” and “hindcasting”
“Causal” weather prediction
(pre-computer age)
 Detailed analysis of “initial state,” using hand-plotted weather maps & charts
 Interpretation using rules and conceptual models (such as Polar Front theory,
etc) having a physical basis, eg.
• Atmospheric stability
• air-sea interaction
• local diurnal cycle - surface energy balance
 Richardson’s pioneering hand-computation
• science degree Cambridge 1903
• applied calculus to help Nat’l Peat Co. cut drains in peat
• 1913 joined Meteorol. Off. (supervised an observatory)
• ambulance driver, WW1 France
• in off-duty time, embarked on test of his mathematical
forecasting system… had taken with him to
France observations for 7 a.m., 20 May 1910.
• by 1916, wrote Weather Prediction by Arithmetic Finite
Differences… published 1922
Lewis Fry Richardson
(1881-1953)
Richardson divided a map of Europe into squares… for each he tabulated atmospheric
pressure… armed with a slide rule and mathematical tables, he began the laborious
task of 'forecasting' what was going to happen to the weather at 1 p.m. on his selected
day… producing by hand a six-hour weather forecast which he could check against
observations. For each square on his map, he applied his numerous equations, to
calculate changes of pressure, wind and temperature… The six-hour forecast took him
six weeks. And when he had finished, the forecast was horribly wrong.
Images and quotation from P. Holper, Australian
Broadcasting Corp.,
http://www.abc.net.au/science/slab/forecast/story.htm
For an excerpt from Richardson’s book, see
http://alumnus.caltech.edu/~zimm/weather.html
Numerical Weather Prediction
 Based on the physics as expressed in equations… conservation of
mass, momentum, energy + equations of state + (etc.)
  set of coupled “partial differential equations” for U,V,W,T,Q…
versus x,y,z,t (or more typically lat., long., pressure and time)
 which can be solved numerically given “initial” and “boundary”
conditions (eg. sea surface temperature + much more)
 produces gridded fields of U,V,W,T,Q,…
 to produce forecast numerical output supplemented by rules of
thumb, statistical packages, subjective guidance
Stages in NWP
 data acquisition
 analysis phase
 initialisation (t=0)
 prediction phase (numerical integration)
 post-processing phase
The decision to postpone the invasion for 24 hours had been taken by Eisenhower and
the Supreme Command at 0430 on Sunday June 4. It was not taken lightly, because so
many ships were already converging on Normandy that the risk of detection was grave.
Nor had the forecast which prompted the postponement been easily arrived at.
Eisenhower's weather advice was provide by Group Captain Stagg, a forecaster
seconded from the British Meteorological Office who was coordinating the advice of
three forecasting teams: one from the Meteorological Office, one from the Admiralty
and one from the United States Army Air Forces.
The advice of these groups was often diametrically opposed. The American team used
an analog method, comparing the current map with maps from the past, and were often
over-optimistic. The Meteorological Office, aided by the brilliant Norwegian
theoretician Sverre Petterssen, had a more dynamic approach, using wind and
temperature observations from high altitude provide by the air force, and were closer to
the mark.
The decision to invade on Tuesday June 6, taken late on Sunday night and finally
confirmed early Monday morning, was based on a forecast of a short period of
improved weather caused by a strengthening ridge following the front that brought
Monday's rain and strong winds. In the event, Monday's bad weather had already given
the Allies a crucial advantage: it had put the Germans off guard.
From New Zealand Geographic, pp11-16, Vol. 22, 1994
Data acquisition
 regional or global? (depending on f/c range)
 obs. coordinated by World Meteorol. Org.
 10K land obs stations, 7K ship obs, 300 buoys, weather satellites, 1K
radiosondes twice daily + (still in research phase) sensors on scheduled
commercial aircraft +…
 “synoptic times” 0000 and 1200 UTC (GMT), but increasing amount of data
comes in off the synoptic times… challenge to incorporate these
Doppler wind sounders
(acoustic & electromagnetic)
Surface winds
from satellite
scatterometry
The traditional in-situ synoptic data…
Fig. 13-3
Rawindsonde
Analysis Phase
• quality control… criteria of physical acceptability (eg. no negative pressures)
and plausibility relative to climate
• interpolation onto a regular “grid” of points
• numerical analysis: adjustment to form
fields that are consistent with allowable
physics (eg. winds must be such that air
mass is conserved) and consistent with the
numerical model being used (eg. initial data
must not contain features the model is
unable to resolve, eg. reduced winds in a
small valley not “visible” in model’s terrain)
• the “adjustment” blends the observations
for time t0 with a 6 hour forecast valid for t0
Data on a grid (shown in 2-d), example of “interpolation”, and
finite-difference representation of a gradient
Te 
J+1
TI , J  TI 1, J
2
n
J
TI-1, J
J-1
w
e
TI, J
TI+1, J
Dx
TI 1, J TI 1, J
 DT 



 Dx  I , J
Dx
I-1
I
I+1
Building an equation to express conservation of air mass on the grid
Fz(z2)
“flux” of air is a vector
with components
Fx,y,z [kg m-2 s-1]
Wind components: U,V,W
z2
rI , J
Fx(x1)
Dz
Fx(x2)
z1
Since flux is convective,
Fz(z1)
rI-1 , J-1



F (x)  U (x)r (x)
x
x1
Dx
x2
Dx Dy Dz DrI , J  Dt Dz Dy Fx ( x1 )  Fx ( x2 )  Dt Dx Dy Fz ( z1 )  Fz ( z2 )
… expresses the change DrIJ in time Dt
of the mass [kg] of air in box IJ.
(Note: Dy is the face length along y)
Fz(z2)
z2
rI , J
Fx(x1)
Fx(x2)
Dz
z1
Fz(z1)
rI-1 , J-1
x1
Dx
x2
Thus we need to
interpolate values
of U and r on
“control volume
faces”
Numerical integration (prediction phase)
Governing equations have form (eg.)
 DT 


 Dt 
n
 U
I ,J ,K
n
I , J ,K
 DT 


 Dx 
n
 ...
I ,J ,K
(term shown on r.h.s. is advection of heat along the x-axis). On re-arrangement one
has a formula to advance the temperature at gridpoint (I,J,K) over time interval Dt
(15 minutes, GEM global, Nov. 06) from time “n” to time “n+1”
T
n 1
I ,J ,K
T
n
I , J ,K
 DT 


 Dt 
n
Dt
I ,J ,K
Repeat the process to go from time “n+1” to “n+2”… out to 12, 24, 36, 48 hours (or
longer).
End result: forecast fields of U,V,W,T,P, r, Q (humidity) on the grid
Post-processing phase
 Forecast products usually involve
subjective human involvement.
Forecaster compares models, knows
which aspects of which models have
proven reliable
 produce and distribute maps for
mandatory levels, to convey model
output to forecasters
ALERT: Received the following bulletin at Mon
Dec 02 08:04:08 UTC.
MAIN WX DISCUSSION, UPPER LEVEL
PATTERN
WHILE OVER W CST THE L/W UPPER RIDGE
WILL PERSIST, CONDITIONS WILL BE QUITE
ACTIVE IN THE VAST CYCLONIC
CIRCULATION COVERING ALMOST ENTIRE
CANADA AND ARCTIC... HOWEVER DESPITE
THIS HIGHLY CHANGING UPPER LEVEL
PATTERN, MODELS ARE IN QUITE GOOD
AGREEMENT FOR THE UPPER LEVEL
PATTERN EVOLUTION NEXT 48 HRS. SINCE
REGGEM HAS VERIFIED THE BEST PAST RUN
AND IS VERY CONSISTENT, WE ACCEPT ITS
SCENARIO.
 may use rules of thumb and/or
supplementary statistical algorithms
to forecast weather elements, eg.
tomorrow’s max or visibility for an
airport
The “omega-block” (or “omega high”)
• tends to persist
• predictable weather
• useful hint to forecaster
Fig. 13-17
Weather in relation to Operation Uranus – Soviet encirclement of
besieging German 6th Army at Stalingrad; 19 Nov., 1942
From Ch15 of A. Beevor’s “Stalingrad. The Fateful Siege: 1942-1943”
“All through the night, Soviet sappers in white camouflage suits had been crawling
forward in the snow, lifting anti-tank mines… One Soviet general said that the
freezing white mist was `as thick as milk’… Front headquarters considered a further
postponement, due to the bad visibility, but decided against it…
`Once again, the Russians have made masterly use of the bad weather,’ wrote
(General von) Richthofen
During the afternoon of 19 November, the Soviet tanks advanced southwards in
columns through the freezing mist… it was Butkov’s 1st Tank Corps which finally
encountered the gravely weakened 48th Panzer Corps. The German tanks still
suffered from electrical problems, and their narrow tracks slid around on the black
ice. The fighting in the gathering dark was chaotic. The usual German advantages of
tactical skill and coordination were entirely lost.”
Model Output Statistics (MOS)
Forecasting algorithm that employs an established (historical)
statistical correlation between:
• past observed values of weather variables (eg. visibility
V), and
• corresponding forecast values of a set of “relevant” variables from
NWP model (eg. local 500 mb height H500, wind speed and direction
at 850 mb, U850, b850, etc.)
• of form V = V (H500, U850, b850, ... )
• used predictively with machine forecasts to predict future weather
• this partly “corrects” flaws in NWP model. But MOS correlations
must be re-calculated (“re-trained”) for each revision of NWP model
Medium-range forecasting
 Numerical forecast for ranges of order 3-15 days
 not much skill beyond one week
 increasingly common to perform “ensemble forecast” (multiple model runs
starting from slightly different initial conditions that attempt to mimic possible
errors in the initial data). Variability of the forecast amongst ensemblemembers implies greater uncertainty
Long-range seasonal anomaly forecasting
 Statistical techniques presently the most important
 where numerical models involved, must be coupled land-atmosphere-ocean
 at present, low skill
Attributes of NWP models
• domain & boundary conditions (eg. if global, no lateral boundaries)
• spatial and temporal resolution
trade-offs
in speed
vs. detail
• grid or spectral representation?
• model “dynamics” (approximations in the equations, eg. hydrostatic?; choice
of dependent variables, eg. velocity or vorticity?...)
• model “physics” (which includes “parameterizations” of effects of unresolved
scales of motion):
• radiation as function of model’s diagnosed cloud and possibly other
resolved properties such as humidity, CO2 concentration…
• convection (deep & shallow), clouds (stratiform & cumuliform) & precip
• surface exchange (momentum, heat, vapour, CO2…) based on surface
state, analyzed or forecast
• drag on unresolved terrain features
Compromising limitations of numerical weather forecasting
 extreme sensitivity to initial data (growth of initial errors)
 data-sparse regions
 inability to represent all scales of motion, from the planetary down to the scale
of a cloud droplet
 at present, grid-spacing order 10 km in horiz… thus for example no
possibility to model cumulus… effects of cumulus must be
“parametrized” (eg. diagnose cloud base and cloud top height from
model’s temperature and humidity profiles: re-mix heat and vapour
uniformly in that layer)
 some processes entirely missing
 others (eg. land-atmosphere exchange, drag on small hills)
oversimplified/poorly represented
Quality
Forecast Assessment
skill
---
Value
accuracy
 considered “skillful” if provides (in a statistical sense) greater accuracy than
persistence or climatological forecasts
 forecasting extremes: valuable when right, penalizing when wrong - forecasters
reluctant to forecast extremes, more likely to be correct if f/c near-average
conditions
 types of f/c include qualitative (categorical), quantitative, probability f/c
 many criteria exist for accuracy of f/c, eg. mean absolute error (MAE) average
magnitude of difference between f/c and actuality