Assimilation of NCEP multisensor hourly rainfall data using 4DVar approach: A case study of the squa

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Assimilation of NCEP multi-sensor hourly rainfall
data using 4D-Var approach A case study of the
squall line on April 5, 1999
Speaker Shao-Fan Chang
Reference Peng. S. Q., and X. Zou. 2000
Assimilation of NCEP multi-sensor hourly rainfall
data using 4D-Var approach A case study of the
squall line on April 5, 1999. Meteorol. Atmos.
Phys., 81, 237-255.
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Outline
1. Introduction
2. Case description and the control experiment
3. 4D-Var experiments
4. Numerical results
5. Summary and conclusions
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1. Introduction

• New satellite and radar observing systems provide
  a large amount of rainfall/rainrate measurements.
• The improvements to the forecasts depend on the
  ability of a data assimilation system.

• 4D-Var not only allows rainfall observations to
  be directly assimilated at their time of
  observation, but also provides a natural
  multivariate constraint on model variables,
  maintaining a dynamical and physical consistency
  defined by the forecast model itself.

• Data
• ---- One rainfall data set is the hourly
  multi-sensor rainfall data from NCEP/Climate
  Prediction Center (NCEP/CPC).
• ---- These rainfall observations are available at
  4-km resolution
• ---- Combine 3000 automated hourly raingage
  observations available over the contiguous 48
  states with radar precipitation estimates from
  the Next Generation Weather Radar (NEXRAD)
  network.

• A systematic evaluation of the impact of these
  rainfall observations on summer QPFs.

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2. Case description and the control experiment
2.1 A brief description of the selected case and
the forecast model

• The squall line case that occurred over Oklahoma
  and Texas from 00 UTC April 5, 1999 to 00 UTC
  April 7, 1999 is chosen for this study.
• Strong moisture ,temperature gradients and a
  convergence line.

Surface temperature and pressure
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Accumulated precipitation

• Western precipitation follow the squall line.
• Eastern precipitation area was induced by the
  intense moisture convergence from the Gulf Mexico
  behind a strong ridge and ahead of a trough

• In the following 6 h (06-12 UTC), the western
  precipitation intensified and moved northeastward.

00-06UTC April 5, 1999
06-09UTC April 5, 1999
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• Forecast model MM5
• The version used for this study includes the
  Blackadar high resolution planetary boundary
  layer parameterization, surface friction, surface
  heat and moisture fluxes, radiative cooling of
  the atmosphere, inflow/outflow boundary
  conditions, grid-resolvable precipitation, and
  the Kuo-type cumulus parameterization scheme.
• The MM5 adjoint model was developed by Zou et al
  (1997). The same set of model physics was used in
  the non-linear and adjoint models.

• Numerical experiments are carried out over a
  domain centered at (35N, 98W). There are 68 74
  27 grid points. The horizontal resolution is 30
  km.

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2.2 Control forecast

• The model precipitation also covered a larger
  area than the observations.

• The model-simulated precipitation was not
  separated initially.

00-06UTC April 1997
06-09UTC
09-12UTC
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3. 4D-Var experiments
3.1 Experiment design
The hourly multi-sensor rainfall data during the
6-h assimilation window from 00 UTC to 06 UTC
April 5, 1999 were incorporated into the model.
The cost function
H interpolation of model-predicted hourly
rainfall from 30-km to 4-km resolutions for EXP3
and EXP4.
Jp a term which applied the digital fiter (DF).
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Jp a term which applied the digital fiter (DF).
xN the vector of model forecast variables at
the Nth time step (the middle of the assimilation
window) xDFN the model forecast in the middleof
the assimilation window after a DF has been
applied.
Assimilation window
00UTC
06UTC
09UTC
12UTC
Fordward model (forecast model MM5)
Backward model (adjoint model)
Iteration ? minimize J(x0) ?get optimal initial
condition x0 at 00UTC ? Forecast
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4. Numerical results
4.1 Impact of observed no-rain information and
data resolution

• The 6-h accumulated rainfall from 00-06 UTC both
  EXP1 and EXP2.

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The Threat Score (TS) is a typical measure for
the verification of forecasts.

• Nf the number of points on which the forecast
  rainfall is greater than a given threshold,
• No the number of points on which the observed
  rainfall is greater than the threshold
• Nc the number of points on which both the
  forecast and observed rainfall are greater than
  the threshold.
• A perfect rainfall forecast ? NfNcNo ?TS 1
  

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The figures show the threat scores of
precipitation from EXP1, EXP2 and EXP3

• EXP1, EXP2 and EXP3 are all higher than CTRL ?
  assimilation improve the forecast.

• EXP1 is higher than EXP2
• ? no-rain information is important.

• EXP2 ,EXP3 difference is small
• ? different resolution data sets are small
  improvements.

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• Errors of all the 4D-Var experiments are smaller
  than CTRL except for the mean errors from EXP1
  from 00-06 UTC.
• EXP2 are consistently better than EXP1
• ?Including the observed no-rain information is
  better.
• The data resolution impact, however, is
  relatively small.

Mean error
RMS error
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• Heavy rainfall over the border of Oklahoma and
  Texas
• CTRL and EXP1 is rather weak.
• EXP2 the rainfall amounts over the border of
  Oklahoma and Texas were increased.

Accumulated rainfall 09-12UTC
OBS
CRTL
EXP1
EXP2
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threat scores of EXP2 are higher than those of
both CTRL and EXP1.
the threat scores for CTRL, EXP1 and EXP2
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Differences in the specific humidity at a
mid-level between EXP2 and CTRL at different
times at 9 UTC April, 1999.
light shading ? positive values greater than 0.3
g/kg dark shading ? negative values less than
-0.3 g/kg)
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4.2 Effect of a digital filter
Surface pressure perturbations at 03 UTC April 5

• Observation errors and the inconsistency between
  model and observations
• ? high-frequency oscillations.

• The assimilation of rainfall observations (EXP3)
  introduced stronger high frequency oscillations,
  especially.
• Adding the DF penalty constraint (EXP4)
  effectively reduced these high frequency
  oscillations.

CTRL
EXP3(without DF)
EXP4(with DF)
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The absolute surface pressure tendency at a
selected grid point (27N,54W)
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• EXP4(with DF) is slightly higher than that
• EXP3(without DF) in the periods from 00-06 UTC
  and 06-09 UTC.
• Forecast skill is degraded from 09-12 UTC.

• Uccellini and Koch (1987) pointed out that
  mesoscale gravity waves with wavelengths of
  50-500 km and periods of 1-4 h may have important
  effects on rainfall in the way of organizing the
  individual cloud bands.

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Specific humidity on the 700 mb level (contour
interval 0.5 g/kg).CTRL overlayed (thin solid
line, contour interval1.0 gkg)
5. Adjustments in model state variables resulting
from rainfall assimilation
Differences (EXP2 minus CTRL.)
Predicted precipitation (contour interval 2 mm)
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Type I grids observed rainfall greater than
zero ? CRTL under-predicted Type II grids
observed rainfall equal to zero but
model-forecasted rainfall greater than zero ?
CRTL over-predicted

• The averaged vertical profiles of the differences
  (EXP2 minus CTRL)
• Type I (solid line) and Type II (dashed line) at
  00 UTC 5 April, 1999

• The decrease of moisture in the middle and lower
  levels at Type II grids is a result of weak
  divergence and weak upward motion.

specific humidity
temperature
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in the rain areas, moisture and temperature in
the lower levels decreased in favor of the
convective development.
T environment T rising air parcel
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• Separation between temperature and dew point
  became larger below 700 mb
• A supersaturation occurred between 700 mb and 500
  mb.

CRTL
EXP2
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Type I grids, the vertical velocity increased in
the middle levels for EXP2. Type II grids, the
situation is reversed.
averaged vertical velocity
Thick ? Type1 ? CRTL under-predicted Thin ?
Type2 ? CRTL over-predicted
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SeCpT gz Lvr
moist static energy
The decrease of moist static energy over Type I
was caused by the cooling effects of the
evaporation and the drying effects of the
downdraft.
moist static energy
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Sensitivity experiment for adjustment variables.

• All model variables gives the best result.
• Adjusting only temperature or moisture is better
  than only adjusting wind components.
• Adjusting both temperature and moisture is
  comparable to adjusting all model variables
  during 00-09 UTC.
• Adjustments of temperature and moisture are of
  the most importance to forecast.

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5. Summary and conclusions

• Improvements in QPFs can be obtained through
  assimilation of the multi-sensor rainfall
  observations.
• (2) The observed no-rain information included in
  the rainfall assimilation plays an important
  role.
• (3) The assimilation of high-resolution (4 km)
  observed rainfall produces slightly more
  improvement in QPFs than the assimilation of
  low-resolution (30 km) observed rainfall.

(4)The adjustments of temperature and moisture
are found to be the primary factors for
improving QPFs. (5) The assimilation of rainfall
observations could introduce high frequency
gravity wave oscillations. These oscillations can
be removed by applying a digital filter in 4D-Var.
END.
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Further improvements of QPFs can be expected if
additional observations, such as precipitable
water, are available and can be incorporated into
the rainfall assimilation. This is important to
reduce the uncertainty in adjusting 3-dimensional
variables of temperature and moisture from
2-dimensional rainfall data. We also plan to test
some of the ideas used in traditional methods
such as physical initialization for the use of
precipitation observations in the 4D-Var
framework, or to adjust model parameters
involved in the formulation of moist physical
parameterization schemes, to find out if the
improvement in QPFs beyond the assimilation
window can be maintained at a similar level as
that during the assimilation window. Finally, the
rainfall assimilation will be carried out over an
ensemble of spring and summer precipitation
cases. Results from these experiments will be
presented in future papers.
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SeCpT gz Lvr
                                                  
        where g is gravitational acceleration, Lv
is the latent heat of vaporization, Cp is the
specific heat at constant pressure for air, T is
absolute temperature, z is height above some
reference level (either the local surface at z
0 or the height where the ambient pressure is 100
kPa), and r is the water vapor mixing ratio in
the air. Compare dry static energy, liquid water
static energy, saturation static energy.
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Only approximated variances were included in the
background weighting matrix W, which is
calculated based on the difference between the
6-h forecast and the initial condition. The
weighting parameter for precipitation
observations was set to 100 cm 2 corresponding to
an estimated precipitation observation error of 1
mm. The third term in (1) is a penalty term
which applied the digital fiter (DF).
The lateral boundary conditions are fixed in all
the data assimilation experiments since a
relatively large model domain is used in this
study.
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2.2 Control forecast
The large precipitation produced by CTRL occurred
over areas where there was no observed
precipitation. For example, the model produced
heavy precipitation over eastern Colorado and
southern Texas where there was no observed
precipitation in the first 6 hour and following
3 hour observation periods (Fig. 2a,b and Fig.
3a,b). The model also over-predicted
precipitation amounts over Arkansas from 06-09
UTC and under-predicted the precipitation amounts
from 09-12 UTC over the Oklahoma-Texas border.
The observed heavy precipitation from 00-06 UTC
over Louisiana and southern Arkansas was
signifiantly weaker and remained as a separate
system from the squall line during the following
6-h period. On the contrary, the
model-simulated precipitation, initially over
Louisiana and southern Arkansas, was not
separated from the precipitation associated with
the OK squall line, causing large errors in both
the predicted position and intensity of this
system (Fig. 3a,b).
The large discrepancy between observed and
model-simulated precipitation could be due to
uncertainties in the initial conditions and model
errors (such as the cumulus parameterization).
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Why are the QPFs of EXP2 for the subdomain
better than those of EXP1? The evolution of the
moisture field provides some answers. Figure 9
shows the positions of the largest differences of
the specific humidity between EXP2 and CTRL in
the middle levels at 06, 09, and 12 UTC April 5,
overlayed by the wind field in the same levels at
09 UTC. It can be seen that the moisture amounts
were reduced over the false-forecasted rain
region in southern Texas (also see Figs. 2a and
3a) at 06 UTC after the assimilation of observed
no-rain information. An increase of moisture
amounts (positive center) occurred downstream
(next to the negative center). Afterward, this
positive and negative couplet of moisture
adjustment developed and advected northeastward
following the wind flow. By 12 UTC, a strong
increment of moisture was seen over southern
Oklahoma and northern Texas. This feature of
moisture adjustment was not seen in the
assimilation without observed no-rain information
(EXP1). Therefore, the observed no-rain
information had a role not only in correcting the
local false forecast of rainfall, but also in
improving the rainfall forecasts in other
regions.