Transcript Sources of Error in NWP Forecasts

Sources of Error in NWP Forecasts
or
All the Excuses You’ll Ever Need
Fred Carr
COMAP Symposium 00-1
Monday, 13 December 1999
Introduction
NWP has become an indispensable tool for the forecaster, but it is
important to understand its limitations. There are many sources of
possible error in an NWP forecast. If you keep these sources in mind as
you examine NWP products, you should be able to make more
intelligent use of the products in your forecasts.
These sources of error can be grouped into three categories:
A.
Errors in the Initial Conditions
It is a complicated process to collect data from observations and
get them into a form that an NWP model can use. Errors can
occur at several steps along the way, as well as grow out of
limitations of the data sources themselves.
Intrinsic Predictability Limitations
Errors in the Initial Conditions
1 Observational Data Coverage
a Spatial Density
b Temporal Frequency
2 Errors in the Data
3
4
5
6
a Horizontal Resolution
b Vertical Resolution
c Time Integration Procedure
3 Boundary Conditions
a Horizontal
b Vertical
a Instrument Errors
b Representativeness Errors
4 Terrain
5 Physical Processes
Errors in Quality Control
Errors in Objective Analysis
Errors in Data Assimilation
Missing Variables
a Precipitation
Errors in the Models
1 Equations of Motion Incomplete
2 Errors in Numerical Approximations
i Stratiform Precipitation
ii Convective Precipitation
b Radiation
c Surface Energy Balance
d Boundary Layer
i Surface Layer
ii Ekman or Mixed Layer
Intrinsic Predictability Limitations
Introduction
B. Errors in the Model
A model is by definition an approximation of reality, and although
NWP models continue to grow in complexity, they cannot take into
account all factors that affect the weather. The numerical solution of
these models by computers introduces additional error.
C. Intrinsic Predictability Limitations
Even with error-free observations and a “perfect” model, forecast error
will grow with time. There is an intrinsic limit to the range of a useful
forecast. This range is short for small-scale phenomena and increases
for synoptic and planetary-scale features.
Intrinsic Predictability Limitations
Errors in the Initial Conditions
1 Observational Data Coverage
a Spatial Density
b Temporal Frequency
2 Errors in the Data
3
4
5
6
a Horizontal Resolution
b Vertical Resolution
c Time Integration Procedure
3 Boundary Conditions
a Horizontal
b Vertical
a Instrument Errors
b Representativeness Errors
4 Terrain
5 Physical Processes
Errors in Quality Control
Errors in Objective Analysis
Errors in Data Assimilation
Missing Variables
a Precipitation
Errors in the Models
1 Equations of Motion Incomplete
2 Errors in Numerical Approximations
i Stratiform Precipitation
ii Convective Precipitation
b Radiation
c Surface Energy Balance
d Boundary Layer
i Surface Layer
ii Ekman or Mixed Layer
Intrinsic Predictability Limitations
Intrinsic Predictability Limitations
Even with error-free observations and a “perfect” model, forecast
errors will grow with time.
No matter what resolution of observations is used, there are always
unmeasured scales of motion. The energy in these scales transfers both
up and down scale. The upward transfer of energy from scales less
than the observing resolution represents an energy source for largerscale motions in the atmosphere that will not be present in the
numerical model. Thus, the real atmosphere and the atmosphere that is
represented in the numerical model are different. For this reason, the
model forecast and the real atmosphere will diverge with time. This
error growth is roughly equal to a doubling of error every 2-3 days.
Therefore, even very small initial errors can result in major errors for a
long-range forecast.
The problem just stated is the essence of chaos theory applied to
meteorology. This theory proposes that nothing is entirely predictable,
that even very small perturbations in a system result in unpredictable
changes in time.
Intrinsic Predictability Limitations
This graphic illustrates the
effect of intrinsic
predictability limitations on
forecast skill.
Forecasts based on
climatology will have a
relatively high level of error,
but will remain constant over
time. Forecasts based on
persistence (i.e., whatever is
happening now will happen
later) are nearly perfect at
extremely short range, but
quickly deteriorate. Current
models do well at short
ranges, but eventually do
worse than climatology. A
forecast that is worse than
climatology is considered
useless.
Intrinsic Predictability Limitations
Even the best model we can
envision will, for reasons just
discussed, produce forecasts
that deteriorate over time to a
quality lower than those based
on climatology.
Our current forecast models
have skill up to the 5-7 day
range on the synoptic scale for
500 hPa heights. (Occasionally
they have skill at 15-30 days
for time-averaged planetary
waves.) They show much less
skill for derived quantities such
as vorticity advection or
precipitation.
Intrinsic Predictability Limitations
A related predictability limitation is that intrinsic error
growth will contaminate smaller scales faster than larger
scales. In other words, a small-scale phenomenon will be
less well forecast than a large-scale phenomenon in the
same range forecast.
However, mesoscale/convective scale predictability may
not follow this smooth progression due to its highly
intermittent nature. For example, a rotating supercell
thunderstorm may have more predictability (2-6 hr) than
an airmass thunderstorm (1 hr). Topographically and/or
diurnally-forced circulations such as drylines and sea
breezes are more predictable than squall lines.
Concluding Comment
It used to be thought that the errors due to horizontal resolution
constituted about 30% of the total forecast error. However, due to
faster computers (which have allowed more accurate numerical
schemes and higher resolution) this is no longer the case.
Currently, the largest source of error is more likely to be the
unavailability of high resolution data over the entire forecast domain.
One might now say that new (and accurate) observing systems, which
measure the variables we need under all weather conditions, are the
best way to improve NWP forecasts. Improvements in computers
(which may allow higher horizontal and vertical resolution) and in the
parameterizations of physical processes within the models will help,
but to a lesser degree than new observing systems.