Task 5. Development of Digital Filter Initialization for WRF

Xiang-Yu Huang, Min Chen, Ju-Won Kim, Wei Wang, Bill Skamarock, Tom Henderson

5.1 A short introduction to DFI

Imbalance between the wind and mass in the initial field can be introduced, e.g., by objective analyses like 3D-Var or by simple interpolations. The noise could cause spurious precipitation, lead to numerical instabilities, degrade the forecast, and damage the subsequent data assimilation through noisy first-guesses. The digital filter initialization (DFI) is one of the methods to remove the imbalance (Lynch and Huang, 1992). It was also shown to construct consistent fields which are not analyzed or do not exist initially, e.g., cloud water content and vertical velocity; and to reduce the spin-up problem (Huang and Lynch, 1993; Huang and Sundqvist, 1994; Chen and Huang, 2006).

5.2 DFI options

A few options of DFI, as defined by (Huang and Yang, 2002), were implemented to WRF (see Fig.5.1):

• DFL (Digital Filter Launching). A short forecast is made first to produce a time series of the model state. A digital filer is then applied on the time series to produce a filter model state. The final forecast will be launched from the filtered state. DFL does need a backward integration and is relatively easy to implement. It removes noise efficiently and should be able to provide noise free background model state for the next data assimilation cycle. However, DFL is not really a initialization scheme, as the filtered state is not at the initial time. For example, if the analysis is at 00UTC and the filter span is 4 h, then the filtered state is valid at 02 UTC.
• DDFI (Diabatic Digital Filter Initialization). In order to center the time series at the analysis time, e.g. 00 UTC, an adiabatic backward integration is run first, e.g. for 2 h, followed by a diabatic forward integration, in this case, 4 h, to produce the time series for the filter. After the filtering, the initialized model state valid at the analysis time is used as initial state for the final forecast. This is a real initialization scheme, but may have problems due to backward integration. As diabatic processes are basically nonreversible, they were all switched off during the backward integration. This brings some inconstancies to the time series of model state.
• TDFI (Twice Digital Filter Initialization). It is similar to DDFI, but the filter is also applied to the time series from the backward integration. As the filter is applied twice, it requires shorter time integrations.

Fig.5.1 Options of DFI implemented to WRF. See the text for further explanations.

The WRF implementation of DFI includes the following steps:

1. Develop a diagnostic package for WRF.
2. Understand the WRF registry and solver structure. Code and test DFL.
3. Reverse the clock used by WRF.
4. Reverse numerical filters in WRF.
5. Code and test DDFI.
6. Code and test TDFI.
7. Solve the problems due to parallelization.

5.3 Experiment configuration

A 7-day period, 12 UTC 4 May – 12 UTC 11 May 2006, was chosen for assessing the impact of DFI on the data assimilation and forecasts. The period is characterized by a developed cyclone moving from the west sea cross the Korean peninsula, causing heavy precipitation (Fig. 5.2).

Fig.5.2 Surface map for 06 UTC 6 May 2006.

The current KMA operational 10 km domain was chosen for all the experiments. The model domain and model terrain are shown in Fig.5.3. The model top is at 50hPa. The model domain of 178x160x31 grid points uses 10 km horizontal grid spacing. The time step used for the integrations is 60 s. The physics package includes WSM6 microphysics, LSM surface scheme, YSU PBL scheme, and Kain-Fritch cumulus parameterization.

Fig.5.3. Model domain and model terrain used in all experiments.

All three DFI options are tested. In these experiments, the Dolph filter is selected (Lynch, 1997), the cutoff is 1 h (this should filter out oscillations with frequency shorter than 1/1h). The filter span is 3 h for DFL, 4 h for DDFI and 2 h for TDFI.

Both cold start and cycling experiments are conducted. For cold start experiments, the initial model states are obtained by interpolating the 30 km operational model fields to the 10 km grid. The experiment without DFI is named as COL. Experiments with DFI are named following the options: NCDFL, NCDDFI and NCTDFI. Here NC stands for No Cycling. Two 24 h forecasts per day for each experiment are run.

For cycling experiments, WRF 3D-Var is used with 6 h cycling. The 6 h forecast from previous cycle is used as background and conventional observations are assimilated. The experiment with DFI is named as CYC. Experiments with DFI are named following the options: DFL, DDFI, TDFI. Two 24 h forecasts per day for each experiment are run.

5.4 Results

5.4.1 Noise control

The main motivation of using DFI is to filter out the noise. The noise level during the time integration of a numerical model can be measured by the mean surface pressure tendency, N1. For the WRF model, the dry surface pressure (MU) is used as a prognostic variable and the mean MU tendency, N2, is therefore a better measure of the noise. In Fig.5.4, we compare the noise level of forecasts from different experiments.

Fig.5.4 N1 (left) and N2 (right) as functions of forecast time are shown for experiments COL, CYC, DDFI and TDFI from the 8^th cycle.

The initial noise level in COL is very high, indicating that the interpolation from 30 km domain to 10 km domain and the terrain difference between the two domains lead to imbalance between the model wind and mass fields. The initial noise level in CYC is much lower than COL and the imbalance is mainly caused by analysis. It is evident that both DDFI and TDFI efficiently remove the noise. Without initialization, the noise level decreases in both COL and CYC runs due to other filtering mechanism of WRF model and its lateral boundary formulation. For a 6 h cycling configuration like the one used by CYC, the noise level in the background fields (6 h forecast) is already reduced to an acceptable level. However, for 3 h or even shorter cycling configurations, the noise in the background can be high and may have detrimental effect on the following analysis. The difference between N1 and N2 are due to the nonhydrostatic effect and model physics. The difference shows clearly only on the first a few time steps. Although only the 8^th cycle is shown, other cycles have very similar pictures.

Fig.5.5 Initial dry surface pressure tendency in hPa/3h for COL, CYC, DDFI and TDFI.

Another way to study the initial noise level is to use the initial (dry) surface pressure tendency maps. For the same set of experiments, these maps are shown in Fig.5.5. From the figure, we can find terrain related noise patterns (in COL) and analysis increment related noise patterns. The initial dry surface pressure tendency maps for DDFI and TDFI show reasonable tendency related to weather systems.

5.4.2 Spin up

Most DFI implementations have shown reduction of spin up due to a better balance between the model dynamic fields and humidity fields (Huang and Lynch, 1993; Chen and Huang, 2006). Our preliminary results, shown in Fig.5.6, indicate mixed results. DDFI has a reduction of spin up clearly. TDFI, on the other hand, seems make the problem worse. Further tuning is needed.

Fig.5.6. Domain averaged precipitation rate as a function of forecast time for COL, CYC, DDFI and TDFI.

5.4.3 Conventional observation verification

The impact of DFI on forecast is assessed by conventional observation verification. Using the radiosonde observations as a reference, DFI pushes the initial state slightly way from observations, but has no impact on later forecasts. Fig.5.7 shows the verification for T. Verification scores for other variables are similar. These results are consistent with those of Lynch and Huang (1992), Huang and Yang (2002), Chen and Huang (2006).

Fig.5.7 RMS difference between model T and radiosonde observations. DFL has no model state at t=0, the score at initial time should be ignored.

Using the surface observations (SYNOP) as a reference, DFI has a similar impact on cycling experiment, i.e., pushes the initial state slightly way from observations, but makes little difference on later forecast scores (Fig.5.8). It is interesting to see DFI has a clear positive impact on the initial state of all cold start experiments (Fig.5.9), indicating DFI can be used as a part of the interpolation procedure (SI for MM5 or WRF) as discussed in Chen and Huang (2006).

Fig.5.8. RMS difference between model variables and SYNOP observations, as functions of forecast time. DFL has no model state at t=0. These are cycling experiments.

Fig.5.9. RMS difference between model variables and SYNOP observations, as functions of forecast time. DFL has no model state at t=0. These are cycling experiments.

5.4.4 Precipitation verification

Precipitation skill scores are calculated and averaged over 7 days and 73 observation points over South Korea. The scores are defined as following:

Hit (H) event forecast to occur AND did occur

Miss (M) event forecast NOT to occu r BUT did occur

False_alarm (F) event forecast to occur BUT did NOT occur

Correct_negative (C) event forecast NOT to occur AND did NOT occur

Bias Score = ( H + F ) / ( H + M )

Threat Score = H / ( H + M + F )

Fig.5.10. Bias (upper) and TS (lower) for 3 h (left) and 24 h (right) accumulated precipitation as functions of precipitation thresholds. These are all cold start experiments.

DFI has a positive impact on the precipitation forecast in all cold start experiments (Fig.5.10), but mixed (both positive and negative) impact on cycling experiments (Fig.5.11). Further tuning is necessary.

Fig.5.11. Bias (upper) and TS (lower) for 3 h (left) and 24 h (right) accumulated precipitation as functions of precipitation thresholds. These are all cycling experiments.

5.5 Conclusions

An implementation of DFI for WRF has been made successfully. Several difficult problems were solved, including the handling of ESMF clock and numerical filters in the backward integration.

Tests have been conducted over a 7-day period, covering a heavy rain case, using the 10 km KMA operational configuration. The results indicate a satisfying noise reduction, a reasonable spin-up reduction, satisfying conventional observation verification scores, and reasonable precipitation scores. However, further tuning DFI parameters may lead to further improvements, especially for the precipitation scores.

References

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Huang, X.-Y. and H. Sundqvist, 1993: Initialization of cloud water content and cloud cover for numerical prediction models. Mon. Wea. Rev. 121, 2719-2726.

Huang, X.-Y. and Yang, X. 2002. A new implementation of digital filtering initialization schemes for HIRLAM. HIRLAM Technical Report No. 53, 36 pp.

Lynch, P. 1997: The Dolph-Chebyshev Window: A Simple Optimal Filter.
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