Scale
dependence of predictability (top)
Limits of Predictability
The skill of precipitation forecasts is limited by both
practical and fundamental constraints. The practical constraints
include the accuracy of the forecast model and the accuracy
of its initial conditions. The accuracy of the initial conditions
is in turn determined by the available observations and their
quality and by the scheme used to assimilate those observations.
The fundamental constraint is the finite limit of predictability,
which arises from the influence of unresolved scales even
in the case of an accurate model and initial conditions.
Fuqing Zhang (Texas A&M University), Chris
Snyder and Richard
Rotunno explored the limits of predictability
for precipitation within the context of the snowstorm
that paralyzed Washington, D.C. on 25 January 2000
(Zhang et al. 2003). Rapid growth of forecast differences
in their simulations is associated with regions of
moist ascent and moist convective instability. Using
an embedded, three-km grid, they showed that initial
differences with scales of less than 100 km and amplitudes
of less than one K, grow rapidly by altering the position
and timing of individual convective elements (in this
case, in a region of negative lifted index over Louisiana).
The differences then contaminate larger scales, altering
the mature cyclone and the precipitation over the East
coast 36 h later. It is clear that this growth from
small to large scales places an upper bound of a few
tens of hours on skillful, deterministic precipitation
forecasts.
Zhe-Min Tan (Nanjing University, China), together
with Zhang, Snyder, and Rotunno, generalized these
results beyond a single case study by considering the
growth of small perturbations to an idealized, moist
baroclinic wave developing in a channel (Tan et al.
2003). They also found rapid growth of forecast differences
in regions of (parameterized) moist convection although
the amplification rate is smaller by roughly a factor
of four than that found in the previous case study.
A key remaining question is the mechanism by which
errors at the convective scale spread across the mesoscale
to synoptic scales.
Ensemble
forecasting on the mesoscale (top)
Predictability of Synoptic-scale Flows
While the work of Zhang et al. has focused on the intrinsic
limits of predictability, the practical predictability of
synoptic-scale flows, given realistic observing systems,
is also of interest. Analysis error statistics and their
influence on forecast-error growth are crucial factors in
determining practical predictability, and are poorly understood
at present.
Thomas Hamill, Jeffrey Whitaker, both of NOAA Climate Data
Center (CDC), and Chris
Snyder used the simplified,
primitive-equation general circulation model of Held
and Suarez to examine the analysis and forecast errors
produced by the ensemble Kalman filter (EnKF). They
calculated for the first time approximate analysis-error
covariance singular vectors given the ensemble from
the EnKF. These are changes to the analysis that, among
all equally likely errors in the analysis, produce
the greatest forecast error (in the absence of error
in the forecast model itself). They found that, unlike
more familiar singular vectors based on the energy
norm, these covariance singular vectors are deep structures
that span the troposphere and have weak vertical tilts
(Hamill et al. 2003).
Empirical Covariance Norm vs. Energy Norm
Snyder and Gregory Hakim (University of Washington)
also examined singular vectors under various norms,
but in the more idealized context of the quasigeostrophic
Eady model. They proposed an empirical covariance norm
based on the assumption that potential-vorticity variance
for analysis errors is small in the interior of the
troposphere relative to the surface and tropopause.
To the extent that analysis error statistics are consistent
with that assumption, the empirical covariance norm
may be more appropriate than the energy norm for use
in numerical weather prediction.
Calibrating for Forecast Model Error
Error in the forecast model is of course another factor
that determines practical predictability. One way to
account for forecast model error in ensemble forecasts
is to correct or calibrate present forecasts based
on the characteristics of forecast errors from previous
forecasts. One particular class of model error, deficient
spatial variance properties, results in under-dispersive
ensembles that cannot envelope the true evolution of
the atmosphere. A collaboration between Joshua
Hacker (ASP) and David Baumhefner (CGD)
produced a simple scale- and flow-dependent calibration
that corrects
for this type of error. It depends only on the current
forecast case and requires only one superior (typically
more expensive) forecast to compute calibration coefficients
in Fourier space. Its performance is summarized by
the error-growth curves in Fig.
1, where curve DMP
is corrected to curve COR, which agrees with the "correct" error
growth in weather research and forecast (WRF).The effects
of other sources of model error, some of which cannot
be corrected
with this method, are measured as the residual error-growth
differences after calibration. The calibration has
applications to ensembles with limited-area models
and ensemble-based data assimilation.
 |
| Figure
1: Shown is improved
performance obtained by implementing a simple scale-
and flow-dependent
calibration that corrects
deficient
spatial variance properties in forecast models. Performance
is summarized
by the error-growth curves in Fig. 1, where curve
DMP
is corrected to curve COR, which agrees with the "correct" error
growth in weather research and forecast (WRF). |
Verification
of mesoscale model forecasts based on mesoscale predictability (top)
Object-based Verification Approaches
Christopher Davis and Kevin
Manning, as part of a group
led by Barbara Brown (RAP) and including Randy Bullock
(RAP), Rebecca Morss,
and Cynthia Mueller (RAP), continued to investigate
object-based verification
approaches appropriate for forecasts of phenomena covering
a range of scales. The primary focus is development
of a rain-area detection and comparison algorithm,
applied to Quantitative Precipitation Forecasts (QPF)
verification. They investigated nontraditional verification
techniques for QPF in mesoscale models. The method
uses a highly tunable smoothing and thresholding method
to isolate significant precipitation regions. Simple
geometric shapes are fit to each region and the statistics
of rain areas are computed from forecasts and observations.
Further, matching of rain areas in forecasts and observations
is currently being implemented. Collectively this approach
allows systematic model areas in size, shape, location,
and intensity of rain areas to be evaluated, and it
will allow easier interpretation of model errors than
can be done with traditional verification schemes.
Davis and Manning,
in collaboration with John
Tuttle, David Ahijevych,
and Richard Carbone,
concluded their examination of the ability
of numerical weather prediction (NWP) models,
including the National Centers for Environmental Prediction's
Eta model and the WRF model, to reproduce time-space
statistics of warm season rainfall. While forecasts
tend to exhibit some propagating rainfall features
in time-longitude representations of meridionally averaged
rainfall that are similar to observations, they poorly
represent the diurnal and systematic zonally
propagating signals of convection. In general, the
models appear more able to predict the corridors along
which convective systems propagate than the actual
propagation. Errors in the diurnally averaged time-longitude
rainfall frequency result both from propagation errors
linked to shortcomings of parameterized convection
and from a lack of phase-locking convection to terrain
and the diurnal cycle as observed. The latter is believed
to be a combined error of the boundary layer and cumulus
parameterization schemes (see Figure 2).
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| Fig. 2. Examination
of the ability of numerical weather prediction
(NWP) models, including the National Centers for
Environmental Prediction's Eta model and the WRF
model, to reproduce time-space statistics of warm
season rainfall. While forecasts tend to exhibit
some propagating rainfall features in time-longitude
representations of meridionally averaged rainfall
that are similar to observations, they poorly represent
the diurnal and systematic zonally propagating
signals of convection. This is believed to be due
to combinded errors in the boundary layer and cumulus
parameterization schemes. |
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