The HIRLAM forecasting system defines two prognostic variables to describe atmospheric moisture: the specific humidity (Q) and cloud water content (Cw). In addition, precipitation rate as well as total and cumulus cloud covers are calculated during forecast steps as diagnostic quantities and used for routine weather forecast. Since the analysis scheme only treats specific humidity, the cloud water is assigned, at the start of forecast, the first guess value from the forecast of the previous cycle. To overcome the obvious inconsistency between the Cw and the other analysed fields, a Diabatic Digital Filter Initialization scheme (DDFI) was designed by Huang and Lynch (1993) and the sheme has been shown to be superior to the traditional Nonlinear Normal Mode Initialization (NNMI), in terms of the reduction of spin-up in moisture fields ( e.g., Cw and precipitation) as well as in noise fields (represented by surface pressure trendency). A refined version of the DDFI was implemented in the HIRLAM reference system in late 1999 (Lynch et al, 1999).
Recently, however, significant moisture spin-up was found in the DMR runs. The manifestation of the problem is most obvious in the daily forecasted cloud cover for individual stations. The two-dimensional cloud cover (COV2D) fields are found to go through an unrealistic and abrupt change, rising from near-zero to a more realistic value during the short period after the forecast start. This is also shown in the results from our control runs in the present work which is configured similar to the DMR runs (dashed line in Fig. 1a). Further examinzation of the forecasted time series reveals severe spin-up problems exist also in the cloud water and precipitation rate fields. For Cw, the forecast time series display an initial severe loss followed by a V-shaped slow recovery in following integration (see dashed line in Fig. 1b). In the corresponding time series for precipitation rate, there is an initial shock release of rain water due to the imbalance in moisture fields (Fig. 1c, dashed line). Similar spin-up feature has since also been observed in operational HIRLAM runs at several member services using either DDFI (the reference initialization procedure in HIRLAM 4.7) or NNMI as initialization procedure.
The fact that severe spin-up appears in both forecasts using NNMI and DFI indicates, obviously, that the initialization scheme might not be the only culprits. In searching for the origin of the problem, it is found that the lack of proper initialization of cloud cover in the reference HIRLAM condensation scheme (STRACO) may be an important contributing factor. In this note, a modification to the forecast model has been proposed to reduce the shortcoming, and the parallel experiment results are presented as a validation of the modification.
The STRACO (Soft TRAnsition COndensation) scheme, is a parameterization scheme for moist processes including deep convection(Sass, 1997, Sass et al. 1999). The scheme includes the cloud microphsics that is simliar to Sundqvist scheme, and the convective part is a modified Kuo-type scheme with a moisture convergence closure. The novel feature of the STRACO is the gradual transition between the convective and stratiform regime. Very briefly, in STRACO, a certain time scale is assumed in description of the transition between condensation regimes. E.g., the Cw is assumed to undergoes an exponential delay towards zero when convection criteria breaks down. Moreover, such a transition mechanism is assumed to apply for the three dimensional total and cloud cover fields, in similar fashion as those for the temperature (T), Q and Cw. i.e., the relaxation scheme for cloud cover is defined to reflect the transition needed for adjustment to new regime in 'equilibrium',
where C refers to total (TOTCOV) or cumulus cloud cover(CUCOV), Ceq is the diagnostic total cloud cover corresponding to the equilibrium state, kad is a coefficient representing relaxation time scale. (For more details, see Sass, 1997, and Sass et al. 1999).
In discretized form, (1) is reformulated as:
where the coefficient
zads = [( dtime)/( 2T0 )]
dtime is time step, T0 is 15 min. and represents the assumed time scale for condensation regime transition.
The above formulation represents a distinguished feature of the STRACO scheme in comparison to other condensation scheme. Extensive tests have been made on the STRACO scheme and the results show that it can indeed avoid effectively the noise/instability generation in connection with transition of condensation regimes, as has been seen in the earlier HIRLAM condensation schemes. On the other hand, it is obvious that, with the formulation as in (1), the estimation of cloud cover at current time step now relies also on the value from previous time step, thus the cloud cover (both TOTCOV and CUCOV) are now effectively prognostic. It is immediately clear that these cloud cover fields face similar initialization problems as for other prognostic quantities such as Cw. In the current reference HIRLAM model (version 4.7.3 as is used for DMR runs), TOTCOV and CUCOV are not analyzed quantities, nor are they initialized using input data from the first guess or initialized model state. In the absence of a initial non-zero value for TOTCOV and CUCOV, the formulation as (1) results in behavior as is reflected in the two-dimensional total cloud cover time series (Fig 1a). The lack of (or unrealistically small) cloud cover in each grid-box is obviously inconsistent with the cloud water, thus resulting in massive rain-out which are manifested in the initial precipitation peak and severe loss of cloud water (b and c in Fig 1).
To alleviate the spin-up problem due to that shortcoming, we suggest here a modification in forecast model through introduction of a relaxation scheme to the discretized formulation for calculation of cloud covers in STRACO scheme. The relaxation coefficient zads in (2) is suggested to be modified as:
zads = [((T1 - kstepdtime))/( T1)]+ [(kstepdtime)/( T1)] [( dtime)/( 2T0 )],
for kstep*dtime £ T1, and
zads = [( dtime)/( 2T0 )],
for kstep*dtime > T1, where kstep is integration step, T1 is the relaxation period suggested as 1 h. With such modification, the cloud cover TOTCOV and CUCOV at initial forecast step will be determined diagnostically and the scheme is gradually adjusted back to the original STRACO formulation.
Experiments are set up to test the suggested scheme on Fujitsu 700 at ECMWF. The runs are configured to be similar to those of DMR runs, with the exception that the 6-hourly ECMWF analyses instead of forecasts are used as lateral boundaries. For diagnostic purposes, additional statistics have been introduced into the forecast model to calculate the domain averaged time series for precipitation rate, two dimensional cloud cover, etc. In the corresponding test runs, the suggested modification to forecast model is implemented and the results are compared to control runs, mainly in terms of the forecasted time series of domain averaged cloud cover, precipitation and liquid cloud water.
The experiments are made for a four-day period from 20000506 to 20000509. The data assimilation cycle is run with 6 hour interval and 30 hour forecasts. Qualitatively similar results are seen from each individual cycles but only the cycles in the middle of the period, from 2000050712 to 2000050900, are presented here.
Fig. 1 displays the time series of the domain averaged quantities which are often chosen to represent the spin-up feature in the NWP forecast: 2D-cloud cover (a), liquid cloud water content (b) and precipitation rate (c). The dashed line represents the control run and the solid line for the runs with modified STRACO scheme. The contrast in the parallel results seem to indicate convincingly that the modification has resulted in a much more 'soft' start in the initial forecast for moisture fields, most significantly in cloud cover and precipitation fields, but also in the cloud water content. Meanwhile, it is also apparent from Fig 1 that the spin-up in moisture fields are largely confined in the first 3-6 hours in both control and modified runs. Beyond such a spin-up period, the difference in initialization do not seem to have significant impact on the forecasts in remaining hours.
Apart from the experiments with modification to the forecast model as examined, parallel runs have also been made to test different initialization strategies. E.g., Fig 2a shows comparison of simulated cloud water using NNMI and DDFI, and 2b shows corresponding comparison between DDFI and Adiabatic DFI (ADFI). Both results seem to be in favor of the DDFI. On the other hand, even with the modified forecast code and DDFI, the initial loss of cloud water in the forecasts still seem to be a bit excessive. Obviously, further development efforts in moisture initialization would still be needed.
Spin-up of moisture fields is typically an initialization problem. However, the lack of realistic initial cloud cover fields in the reference HIRLAM system is found to cause additional spin-up problem, due to the quasi-prognostic treatment of cloud cover in the STRACO condensation scheme. The proposed modification of forecast model in this work removes that abnormal feature. However, further improvement in initialization technique to overcome moisture spin-up (especially in the cloud water field), is desirable. This is believed to be particularly important for the NWP system with short data assimilation interval and for nowcasting.
It should also be pointed out that another obvious approach to alleviate the spin-up problem would be to simply treat the cloud cover fields in similar fashion as for Cw in analysis and initialization step. This requires that the forecasted three dimensional TOTCOV and CUCOV are included in the first guess input. In the forward DDFI step, filter is applied to TOTCOV and CUCOV in similar fashion as to Cw. This approach has also been tested and the desired effects in reduced spin-up of moisture fields are achieved. However, such an approach suffers the undersirable feature in requiring storage of two additional three dimensional fields (TOTCOV and CUCOV) and is therefore not preferred.
Gerard Cats reported problem with abnormal spin-up feature in forecasted cloud cover in DMR runs. Xiang-Yu Huang, Ray Mcgrath and Peter Lynch contributed in discussion issues related to the digital filter initialization. Ben W. Schreur performed parallel investigations which has helped this work. The Management Group of HIRLAM 5 Research Project offered useful comments.
Huang, X.-Y. and P. Lynch, 1993: Diabatic digital filtering initialization: application to the HIRLAM model. Mon. Wea. Rev., 121, 589-603.
Lynch, P., R. McGrath and A. McDonald, 1999: Digital Filter Initialization for HIRLAM. HIRLAM Technical report 43.
Sass, B. H. 1997: Reduction of numerical noise connected to the parameterization of cloud and condensation processes in the HIRLAM model. HIRLAM Newsletter 29, 37-45.
Sass, B. H., N. W. Nielsen, J. U. Jørgensen and B. Amstrup, 1999, The operational DMI-HIRLAM system. DMI Technical Report, 99-21, pp 43.