A partial ensemble Kalman filtering approach to enable use of range limited observations

Borup, Morten; Grum, Morten; Madsen, Henrik; Mikkelsen, Peter Steen

doi:10.1007/s00477-014-0908-1

Cited by 15 publications

(20 citation statements)

References 30 publications

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“…As a way to do that, Borup et al. s*() proposed a DA scheme, namely PDEnKF, to solve the Bayesian system in Equation . The authors assumed the OR observation likelihood to be constant outside the observable range.…”

Section: Methodology and Algorithmmentioning

confidence: 99%

“…Whereas the geostatistical techniques are well established for variables without dynamical evolution (Chiles and Delfiner, ; Emery and Robles, ), only one study (Borup et al. , ), to the best of our knowledge, has dealt with the issue of OR observations in an ensemble‐based data assimilation framework. The issue has been addressed in variational methods (see (Bocquet et al.…”

Section: Introductionmentioning

confidence: 99%

“…Borup et al. s*() proposed the Partial Deterministic Ensemble Kalman Filter (PDEnKF) to assimilate observations with a detection limit. The main idea of the PDEnKF is to assume a virtual observation at the detection limit in the absence of hard data and defining a constant OR observation likelihood in the unobservable region from the detection limit.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Assimilation of semi‐qualitative observations with a stochastic ensemble Kalman filter

Shah¹,

Gharamti

Bertino³

2018

Quart J Royal Meteoro Soc

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The ensemble Kalman filter assumes observations to be Gaussian random variables with a pre-specified mean and variance. In practice, observations may also have detection limits, for instance when a gauge has a minimum or maximum value. In such cases, most data assimilation schemes discard out-of-range values, treating them as "not a number," with the loss of possibly useful qualitative information. The current work focuses on the development of a data assimilation scheme that tackles observations with a detection limit. We present the Ensemble Kalman Filter Semi-Qualitative (EnKF-SQ) and test its performance against the Partial Deterministic Ensemble Kalman Filter (PDEnKF) of Borup et al. Both are designed to assimilate out-of-range observations explicitly: the out-of-range values are qualitative by nature (inequalities), but one can postulate a probability distribution for them and then update the ensemble members accordingly. The EnKF-SQ is tested within the framework of twin experiments, using both linear and nonlinear toy models. Different sensitivity experiments are conducted to assess the influence of the ensemble size, observation detection limit and number of observations on the performance of the filter. Our numerical results show that assimilating qualitative observations using the proposed scheme improves the overall forecast mean, making it viable for testing on more realistic applications such as sea-ice models.

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Section: Methodology and Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Assimilation of semi‐qualitative observations with a stochastic ensemble Kalman filter

Shah¹,

Gharamti

Bertino³

2018

Quart J Royal Meteoro Soc

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“…This approach is more efficient for large non-linear models than non-ensemble based Kalman filters [5]. Furthermore, research has shown that the EnKF can even be used to utilize information from range-limited observations when the observed quantity is outside the observable range of the gauge [10], which is a very common situation for gauges in urban drainage systems.…”

Section: Introductionmentioning

confidence: 99%

Technical Note on the Dynamic Changes in Kalman Gain when Updating Hydrodynamic Urban Drainage Models

Borup

Madsen

Grum³

et al. 2018

Geosciences

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To prevent online models diverging from reality they need to be updated to current conditions using observations and data assimilation techniques. A way of doing this for distributed hydrodynamic urban drainage models is to use the Ensemble Kalman Filter (EnKF), but this requires running an ensemble of models online, which is computationally demanding. This can be circumvented by calculating the Kalman gain, which is the governing matrix of the updating, offline if the gain is approximately constant in time. Here, we show in a synthetic experiment that the Kalman gain can vary by several orders of magnitude in a non-uniform and time-dynamic manner during surcharge conditions caused by backwater when updating a hydrodynamic model of a simple sewer system with the EnKF. This implies that constant gain updating is not suitable for distributed hydrodynamic urban drainage models and that the full EnKF is in fact required.

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“…Computer based dynamic operation of urban drainage systems in real-time is therefore an attractive tool to avoid combined sewer overflows, minimise the risk of pluvial flooding, achieve better wastewater treatment during wet-weather and to optimise the • methods for updating model states (directly from measurements as in [14,15], or by using Kalman filtering approaches as in [16][17][18]), • error correction methods (e.g., using time series models as in [19], or neural networks as in [20]), • and in some cases joint state and parameter estimation approaches (for example, using particle filtering approaches as in [21] or an evolutionary algorithm as in [22]). …”

Section: Introductionmentioning

confidence: 99%

Evaluation of Maximum a Posteriori Estimation as Data Assimilation Method for Forecasting Infiltration-Inflow Affected Urban Runoff with Radar Rainfall Input

Pedersen

Lund

Borup

et al. 2016

Water

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High quality on-line flow forecasts are useful for real-time operation of urban drainage systems and wastewater treatment plants. This requires computationally efficient models, which are continuously updated with observed data to provide good initial conditions for the forecasts. This paper presents a way of updating conceptual rainfall-runoff models using Maximum a Posteriori estimation to determine the most likely parameter constellation at the current point in time. This is done by combining information from prior parameter distributions and the model goodness of fit over a predefined period of time that precedes the forecast. The method is illustrated for an urban catchment, where flow forecasts of 0-4 h are generated by applying a lumped linear reservoir model with three cascading reservoirs. Radar rainfall observations are used as input to the model. The effects of different prior standard deviations and lengths of the auto-calibration period on the resulting flow forecast performance are evaluated. We were able to demonstrate that, if properly tuned, the method leads to a significant increase in forecasting performance compared to a model without continuous auto-calibration. Delayed responses and erratic behaviour in the parameter variations are, however, observed and the choice of prior distributions and length of auto-calibration period is not straightforward.

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A partial ensemble Kalman filtering approach to enable use of range limited observations

Cited by 15 publications

References 30 publications

Assimilation of semi‐qualitative observations with a stochastic ensemble Kalman filter

Assimilation of semi‐qualitative observations with a stochastic ensemble Kalman filter

Technical Note on the Dynamic Changes in Kalman Gain when Updating Hydrodynamic Urban Drainage Models

Evaluation of Maximum a Posteriori Estimation as Data Assimilation Method for Forecasting Infiltration-Inflow Affected Urban Runoff with Radar Rainfall Input

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