This study investigates the suitability of the asynchronous ensemble Kalman filter (AEnKF) and a partitioned updating scheme for hydrological forecasting. The AEnKF requires forward integration of the model for the analysis and enables assimilation of current and past observations simultaneously at a single analysis step. The results of discharge assimilation into a grid-based hydrological model (using a soil moisture error model) for the Upper Ourthe catchment in the Belgian Ardennes show that including past predictions and observations in the data assimilation method improves the model forecasts. Additionally, we show that elimination of the strongly non-linear relation between the soil moisture storage and assimilated discharge observations from the model update becomes beneficial for improved operational forecasting, which is evaluated using several validation measures.

Understanding the behaviour of extreme hydrological events and the ability of
hydrological modellers to improve the forecast skill are distinct challenges
of applied hydrology. Hydrological forecasts can be made more reliable and
less uncertain by recursively improving initial conditions. A common way of
improving the initial conditions is to make use of data assimilation (DA),
a feedback mechanism or update methodology which merges model estimates with
available real-world observations

Data assimilation methods can be classified from different perspectives.
Traditionally, we distinguish between sequential and variational methods. The
sequential methods are used to correct model state estimates by assimilating
observations, when they become available. Examples of sequential methods are
the popular Kalman and particle filters

A next distinction can be made between synchronous and asynchronous methods.
Synchronous methods, also called three-dimensional (3-D), assimilate
observations which correspond to the time of update. The ensemble Kalman
filter

The essential difference between a smoother and a filter is that a smoother
assimilates “future observations”, while a filter assimilates “past
observations”. This implies that for operational forecasting purposes, we
need a filter rather than a smoother. A smoother can help improve the model
accuracy in the past (e.g. for re-analysis), but it does not help improve
forecast accuracy

Discharge represents a widely used observation for assimilation into
hydrological models, because it provides integrated catchment wetness
estimates and is often available at high temporal resolution

The Kalman type of assimilation methods were developed for an idealized
modelling framework with perfect linear problems with Gaussian statistics;
however, they have been demonstrated to work well for a large number of
different non-linear dynamical models

Illustration of the model updating procedure for the ensemble Kalman
filter (EnKF), the ensemble Kalman smoother (EnKS), and the asynchronous
ensemble Kalman filter (AEnKF). The horizontal axis stands for time,
observations (

In this study we present a follow-up of the work of

We carried out the analyses for the Upper Ourthe catchment upstream of
Tabreux (area

For a more detailed description of the catchment and model structure and
definition of the hydrological states and fluxes we refer to

Topographic map of the Upper Ourthe (black line) including the river
network (blue lines), rain gauges (crosses), six river gauges (white circles
labelled with numbers: 1 – Tabreux, 2 – Durbuy, 3 – Hotton, 4 – Nisramont,
5 – Mabompré, and 6 – Ortho). Projection is in the Universal Transverse Mercator
(UTM) 31N coordinate system. After

In contrast to

The import and export of hydrological and meteorological data to the system
is done using Delft Flood Early Warning System

As stated in the introduction, we investigate the potential added value of
the asynchronous EnKF (AEnKF)

First, we define a dynamic state space system as

Left: catchment discretization using a grid-based approach including
the channel delineation. Arrows indicate flow direction. Right: schematic
structure of the HBV-96 model for each grid cell. Model states are in bold
and model fluxes in italics

Second, we define an observation process as

After the model update at time

The AEnKF should not be considered as a new method but rather a simple
modification of the (synchronous) EnKF (Sect.

From the operational point of view, it is preferable to have a longer
assimilation window, because less frequent assimilation eliminates
a disruption of the ensemble integration by an update and a restart. When
assimilation is done more frequently, it will cause considerably higher
calculation costs, which can often be a burden for real-time operational
settings

Overview of the periods used in this study.

In this study, we assume the source of model uncertainty to be the HBV soil
moisture, which provides boundary conditions for surface runoff and
represents interaction from interception, evapotranspiration, infiltration
and input uncertainty by rainfall. The uncertainty is represented as a noise
term

This section provides a configuration setup of the filtering methods
(Sect.

The ensemble of uncertain model simulations is obtained by perturbing the
SM state with the spatio-temporally correlated error model
(Sect.

Four partitioned state updating schemes (indicated in the first
column) for five model states (indicated in the first row) being updated and thus
included in the model analysis. Model states are described in Sect.

The experimental setup scrutinizes the problem of asynchronous filtering from
two perspectives. First, we investigate the effect of state augmentation
using the past observations and assimilation of distributed observations on
the state innovation (Sect.

Discharge ensemble forecasts (grey lines) and observations (points)
at four locations (gauges 1, 3, 5, 6; see Fig.

The performance of the data assimilation procedure regarding discharge
forecasting is evaluated using the Ensemble Verification System (EVS):
a software tool for verifying ensemble forecasts of hydrometeorological and
hydrological variables at discrete locations

To investigate and understand the effect of augmented operators
(Eqs.

The mean difference between the forecasted and updated model states for the
whole ensemble is illustrated in Fig.

Mean difference between the forecasted (

Let us first consider the traditional EnKF (i.e. no state augmentation with

The presented educational examples shows an update for several scenarios starting from the same initial conditions. This enables a fair comparison between scenarios; however, the sensitivity of state augmentation needs to be further scrutinized in terms of its cumulative effect over time.

Ensemble of discharge forecasts for a typical event at the catchment
outlet (Tabreux, gauge 1) for three updating scenarios: all, noSM, and HQ (see
Table

Scaled difference between the ensemble mean for the three partitioned
update schemes and the control run without data assimilation at four gauging
locations (shown by different colours) within the Upper Ourthe catchment using
the AEnKF with

We present a qualitative interpretation of the hydrological forecasts with
a lead time of 48 h in Fig.

Besides a qualitative interpretation of the forecasted hydrographs presented
in Fig.

Figure

Validation of the model setup in terms of the RMSE is presented in
Fig.

To present the results in a more robust way, we also analysed them (at
Tabreux) in terms of other probabilistic verification measures: the ROC score and the BS score (see
Fig.

To reveal the temporal nature of the model being updated using the AEnKF,
using

For the AEnKF using

We applied the asynchronous ensemble Kalman filter (AEnKF)

We investigated the effect of a partitioned update scheme recently suggested
by

We would like to thank Arno Kockx and Martin Verlaan for their help with the
OpenDA configuration and Jaap Schellekens for help with the OpenStreams
configuration (all from Deltares). We thank Paul Torfs (Wageningen
University), Seong Jin Noh (KICT, Korea), Ming Pan (Princeton University),
two anonymous reviewers and the editor for their comments on the manuscript.
This project is financially supported by the Flood Control 2015 program
(