Abstract
When there exist catchment-wide biases in the distributed hydrologic model states, state updating based on streamflow assimilation at the catchment outlet tends to over- and under-adjust model states close to and away from the outlet, respectively. This is due to the greater sensitivity of the simulated outlet flow to the model states that are located more closely to the outlet in the hydraulic sense, and the subsequent overcompensation of the states in the more influential grid boxes to make up for the larger scale bias. In this work, we describe Mean Field Bias (MFB)-aware variational (VAR) assimilation, or MVAR, to address the above. MVAR performs bi-scale state updating of the distributed hydrologic model using streamflow observations in which MFB in the model states are first corrected at the catchment scale before the resulting states are adjusted at the grid box scale. We comparatively evaluate MVAR with conventional VAR based on streamflow assimilation into the distributed Sacramento Soil Moisture Accounting model for a headwater catchment. Compared to VAR, MVAR adjusts model states at remote cells by larger margins and reduces the Mean Squared Error of streamflow analysis by 2–8% at the outlet Tiff City, and by 1–10% at the interior location Lanagan.
Highlights
Streamflow observations are used extensively to update hydrologic model states via various forms of data assimilation (DA) [1,2,3,4,5,6,7,8,9,10,11,12]
We describe and evaluate Mean Field Bias (MFB)-aware VAR, referred to as MFB-aware variational assimilation (MVAR), for state updating of distributed hydrologic models based on variational assimilation of streamflow data
Type-II conditional bias (CB) is conditioned on streamflow observation ZQ,k which quantifies a failure of detecting existing events
Summary
Streamflow observations are used extensively to update hydrologic model states via various forms of data assimilation (DA) [1,2,3,4,5,6,7,8,9,10,11,12]. The premise of this work is that one may improve the performance of DA significantly by updating the model states at the catchment scale first and the resulting states at the grid box scale Correcting spatiotemporal biases such as MFB, local bias (LB) and conditional bias (CB) in the data or modeled variables has been extensively explored in statistical pre- and post-processing, calibration, and DA. We describe and evaluate MFB-aware VAR, referred to as MVAR, for state updating of distributed hydrologic models based on variational assimilation of streamflow data. The significant new contributions of this paper are the development of MFB-aware DA for streamflow assimilation into the distributed model and the comparative analysis and evaluation of MVAR and VAR.
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