Nudging - Data Assimilation

An option to nudge towards a large scale analysis or forecast exists in ASP. The model uses a digitally-filtered cold start, but while filtered, this initial state might not be optimal in terms of accuracy for the best weather forecast. Thus ASP uses the so-called “Big-Brother” data assimilation (BBDA) method, which essentially means it nudges the forecast fields early in the forecast towards the driving model forecast (which is used to input the lateral boundary conditions). Thus, the model assimilates the large scale forecast fields early in the forecast presumably when the large scale model forecast is most accurate (owing to it's own DA system).

The method consists in modifying the $K_r$ coefficient in the nudging term as shown in Eq. 118 such that it is no longer zero in the interior zone (i.e. outside of the lateral sponge zone) of the domain. The mask is a function of height and time: it is unity above about $\eta=0.9$ currently (below which it linearly decreases to zero). The time varying part of the weight is computed from

$$f_w(t) = \frac{1}{2}\,\Bigg\lbrace 1 - {\rm cos}\left[ \pi\, {\rm... ...rac{2\,\pi\, t}{\tau_f}\right)\right] \hskip0.5in \left(0\leq f_w \leq 1\right)$$ (120)

where $t=j\Delta t$ and $j$ is the number of time steps since the forecast start, $\tau_f$ is the forecast input frequency in seconds (corresponding to 6 hours here), $\tau_{min}$ is the length of time since the forecast start that the weights can attain their maximum value (currently set to 12 hours), and $\tau_{min}$ is the time at which the weights decrease to a constant value of 0.

The time varying weight, $f_w$, is shown in Fig. 4. In this example, the weights are at their maximum at each point when a large scale field is input into the model (here every 6 hours, which corresponds to the default input large scale forcing frequency in forecast mode) and is in full force during the first 12 hours of the forecast: the weights then rapidly fall to zero by 18 hours into the forecast. Currently, the model simply nudges $T$, $u$ and $v$ when BBDA is active. In order to implement this method currently, $K_r$ is modified each time step owing to the temporal weights, with no other changes to the equations or code. The results are rather dramatic: using this method, the forecasts are much closer to those made by forecast systems during the duration of the forecast (3.5 days currently) than those using a DF-cold start, and very close even out to 2-3 days (so the effect can be felt for some time, depending on the flow regime etc.) without the need to implement a complex and costly DA method (the additional cost of DA on the forecast run time is negligible).

Figure 4: The time varying weight applied to the nudging term which assimilates certain prognostic variables. The weights are at their maximum at each point when a large scale field is input into the model (here every 6 hours) and is in full force during the first 12 hours of the forecast: the weights then rapidly fall to zero by 18 hours into the forecast.