Scale-dependent Inflation for Multiscale Ensemble based Data Assimilation
Abstract
The degree of the background ensemble deficiency, often manifested as ensemble underdispersion, can vary at different scales in the ensemble-based data assimilation. This study develops the new scale-dependent inflation (SDI) methods based on two scale-unaware inflation approaches, RTPS (Relaxation To Prior Spread) and SE (observation-dependent Sampling Error inflation). In the new scale-dependent RTPS inflation (RTPS-SDI), the posterior ensemble spread is relaxed toward the prior ensemble spread at each scale separately. In the Scale-dependent SE inflation (SE-SDI), mathematical derivation is performed so that posterior ensemble variance is individually adjusted toward the mean square error of ensemble analysis mean at each scale. The impact of RTPS-SDI and SE-SDI are examined and evaluated by implementing both approaches within the Multiscale Local Gain Form Ensemble Transform Kalman Filter (MLGETKF).
Four continuously cycled MLGETKF experiments are performed with the four inflation methods using a two-layer surface quasi-geostrophic turbulence model. During the DA cycling, RTPS-SDI and SE-SDI outperform RTPS and SE, respectively, in the reduction of analysis errors and the enhancement of ensemble spread nearly at all scales and all cycles. In addition, the improvements in RTPS-SDI over RTPS are greater than those of SE-SDI over SE. These improvements in both SDI methods are associated with their larger inflation at all scales, especially at larger scales, compared to their scale-unaware counterparts. In the subsequent forecast, both SDI methods show statistically significantly better forecast performance than their scale-unaware inflation experiments. RTPS-SDI is more accurate than RTPS for all scales in 1-4 days lead time. SE-SDI is more accurate than SE at all scales for 3-6 days lead time during the early cycles and shows a smaller forecast error with significance for 2-3 days.
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