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 rainf

all data using 4D-Var approach: A case study of the squall line on April 5, 1999. Meteorol. Atmos. Phys., 81, 237-255.

Outline:

1. Introduction

2. Case description and the control experiment

3. 4D-Var experiments

5. Summary and conclusions

4. Numerical results

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.

1. Introduction

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.

2.1 A brief description of the selected case and the forecast modelThe 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.

2. Case description and the control experiment

Surface temperature and pressurespecific humidity and wind field

Accumulated precipitation:

00-06UTC April 5, 1999

06-09UTC April 5, 1999 09-12UTC April 5, 1999

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.

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.

Observation

Control experiment

2.2 Control forecast

00-06UTC April 1997 06-09UTC 09-12UTC

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

The model-simulated precipitation was not separated initially.

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.

3. 4D-Var experiments3.1 Experiment design

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).

Assimilation window

00UTC 06UTC 09UTC 12UTC

Iteration minimize J(x0) get optimal initial condition x0 at 00UTC Forecast

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 windo

w after a DF has been applied.

Jp : a term which applied the digital fiter (DF).

Backward model (adjoint model)

Fordward model (forecast model = MM5)

4.1 Impact of observed no-rain information and data resolution

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

4. Numerical results

ObservationControl experiment

EXP1EXP2

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 thresholdNc : the number of points on which both the forecast and observed rainfall are greater than the threshold.

A perfect rainfall forecast Nf=Nc=No TS =1

NfNo

Ncforecast observed

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.

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

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.

OBS CRTL

CRTL

OBS

EXP1 EXP2

Accumulated rainfall 09-12UTC

threat scores of EXP2 are higher than those of both CTRL and EXP1.

the threat scores for CTRL, EXP1 and EXP2

Control experiment(00-06 UTC)

EXP2(00-06 UTC)

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/kgdark shading negative values less than -0.3 g/kg)

4.2 Effect of a digital filterObservation errors and the inconsistency between model and observations high-frequency oscillations.

CTRL

EXP3(without DF) EXP4(with DF)

Surface pressure perturbations at 03 UTC April 5

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

The absolute surface pressure tendency at a selected grid point (27N,54W)

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.

Differences (EXP2 minus CTRL.)

00-06UTC

00UTC

06UTC

Specific humidity on the 700 mb level (contour interval: 0.5 g/kg).CTRL overlayed (thin solid line, contour interval:1.0 g=kg)

Predicted precipitation(contour interval: 2 mm)

5. Adjustments in model state variables resulting from rainfall assimilation

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

Type I grids : observed rainfall greater than zero CRTL under-predictedType II grids : observed rainfall equal to zero but model-forecasted rainfall greater than zero CRTL over-predicted

specific humidity temperature

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

in the rain areas, moisture and temperature in the lower levels decreased in favor of the convective development.

T : environmentT’ : rising air parcel

Separation between temperature and dew point became larger below 700 mb

A supersaturation occurred between 700 mb and 500 mb.

EXP2CRTL

Thick Type1 CRTL under-predictedThin Type2 CRTL over-predicted

averaged vertical velocity

Type I grids, the vertical velocity increased in the middle levels for EXP2. Type II grids, the situation is reversed.

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

Se=CpT+ gz + Lvrmoist static energy

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.

Sensitivity experiment for adjustment variables.

5. Summary and conclusions

(1) 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 impor

tant role. (3) The assimilation of high-resolution (4 km) observed rainfall produces slightly more i

mprovement 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….

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.

                                                         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.

Se=CpT+ gz + Lvr

The lateral boundary conditions are fixed in all the data assimilation experiments since a relatively large model domain is used in this study.

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).

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).

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.