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Edited by: Paul Bates, University of Bristol, United Kingdom

Reviewed by: Andrew Mark Ireson, University of Saskatchewan, Canada; Juan Pablo Rodríguez Sánchez, University of Los Andes, Colombia

This article was submitted to Hydrosphere, a section of the journal Frontiers in Earth Science

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

Flood models predict inundation extents, and can be an important source of information for flood risk studies. Accurate flood models require high resolution and high accuracy digital elevation models (DEM); current global DEMs do not capture the topographic details in floodplains, and this often leads to inaccurate prediction of flood extents by flood models. Flood extents obtained from remotely sensed data provide indirect information about topography. Here, we attempt to use this information along with model predictions to produce better floodplain topography. The algorithm we describe is a two-step process: first, we reduce the noise along the observed flood boundaries for all particles. Then, the model predictions from these modified DEMs are assimilated with observations using a particle batch smoother. We implemented the algorithm for a synthetic test case. For the nominal case, we observed a significant improvement in accuracy in terms of RMSE (35% reduction), bias (20%), and standard deviation (40%). We conducted sensitivity analysis by using priors of varying bias (0.5, 1, and 2 m) and standard deviation (1, 2, and 4 m). The bias reduced to ∼0.5 m or below in all the cases: the reduction in bias varied from 11 to 76%. The standard deviation of errors in the final estimate was almost half of the prior: the reduction varied from 40 to 49%. The reduction in RMSE ranged between 35 and 67%. For the case with 2 m bias and 4 m standard deviation (SRTM-like error levels), bias went down to 0.48 m (76% reduction), and standard deviation reduced to 2.24 m (44% reduction). Flood inundation maps produced from the final estimate DEMs also improved on its prior. For the 2 m bias cases, true positive rate (TPR) for peak inundation went from ∼30% to more than 57% in all three cases. The algorithm produces promising results, and this type of analysis can be performed in data-poor floodplains where high resolution DEMs do not exist.

Prediction of inundation extents from flood models is an indispensable source of information for assessing flood risk in the context of hazard studies, but inundation prediction accuracy is often limited by the quality of topographic data available globally. Topographic data, generally in the form of digital elevation models (DEMs), are the primary input data for flood inundation modeling. Airborne light detection and ranging (lidar) DEMs offer the best horizontal resolution and vertical accuracy. However, high resolution lidar DEMs are not available globally and are expensive to obtain. Globally, the best available DEMs are obtained from satellite data: the shuttle radar topography mission (SRTM, spatial resolution 30 m) (

Spaceborne remote sensing observations of inundation extent contain indirect information about floodplain topography. Remotely sensed data is widely used to study floods (

Because inundation images reflect the complex flow paths that water takes during flooding events that can only be captured by flood models, methods such as

To our knowledge, assimilation has not been used to estimate floodplain DEMs, though related work has been done.

In the present study, we present and test (using synthetic observations) a new algorithm designed to infer floodplain topography using globally available DEMs and inundation imagery. The algorithm consists of two steps: smoothing and data assimilation, that capitalize on the strengths of each method.

We tested our algorithm for a synthetic case of small domain. This allowed us to explore the sensitivity of the algorithm to errors of various magnitude. We used the Buscot model, a tested example model distributed with LISFLOOD-FP, as our synthetic test case. LISFLOOD-FP (^{3}/s at time 0, 200 m^{3}/s at its peak and back to 20 m^{3}/s at the end of the 5-day simulation. Figure

To obtain best results from this method, we require multiple unique flood extent observations. We used 9 flood inundation maps obtained between day 1 and peak inundation on day 3 as observations. Our primary objective was to test the efficacy of the algorithm itself, and we did not focus on studying the impact of less or more flood inundation observations. In order to focus on the effect of prior DEM error on the analysis, we did not add white noise to the classified imagery; we leave for future work how observational uncertainty and temporal revisit would impact the algorithm accuracy. Figure

Flood inundation area and available flood maps.

In the design of the synthetic experiment, we attempt to simulate a realistic situation where we attempt to correct a noisy “prior” estimate of the floodplain DEM. We accomplish this by taking the DEM distributed with the Buscot model to be the “truth.” We then create a prior estimate of the DEM by adding errors to the truth. Here we chose to add spatially uncorrelated errors when creating the prior; the level of the errors varies among the various cases. We define the “nominal case” to be addition of 0.5 m bias and 1 m standard deviation of errors, which is referred to as the prior henceforth. We performed sensitivity analysis by considering 8 additional cases, by exploring bias ranging from 0.5, 1, and 2 m, and standard deviation of 1, 2, and 4 m. The case with bias of 0.5 and 2 m is similar to the TanDEM-X errors, which was used by

We evaluated the performance of the algorithm by calculating bias, standard deviation of DEM errors and root mean squared error (RMSE) for all the pixels modified by the algorithm. We also evaluated the DEM’s ability to predict inundation by using true positive rate (TPR), a statistical measure of binary classification. TPR is the proportion of predicted inundation area from the model that is accurate (from observations).

Our approach merges smoothing and data assimilation to better extract floodplain topography information from inundation maps. We will use the PBS concept described by

Outline of the methods.

It has been established from empirical evidence that DEM errors are not completely random, and often have spatial correlation (

The set of randomly perturbed DEMs thus obtained might be inefficient as the process may generate many unrealistic DEM particles. Data assimilation style approach will require a large set of particles to capture the complex spatial pattern of topography, making the process computationally inefficient. One way to deal with this problem is to make the ensemble of particles more realistic. We make this ensemble of particles more realistic by using the process described in Section “Smoothing Along Flood Boundary”.

We exploited the indirect information about elevations along the flood boundary to produce a set of realistic particles. For each particle in the ensemble, we extracted the elevations along the flood boundary. We extracted two adjacent pixels along the boundary: one flooded pixel on the edge (the “wet boundary”), and the adjacent pixel on the non-flooded side (the “dry boundary”). Then, we performed linear regression along both boundaries, considering the wet and dry boundaries separately. We consider the length along the boundary going from upstream to downstream as the independent variable and the extracted elevations as the dependent variable. We modified each particle by updating the elevations along the flood boundary as the weighted average of extracted elevations, and its regressions. By doing this, the noise in elevations along the boundary was reduced (Figure

Elevations along the boundary for four sample ensemble members for the nominal case. Weight refers to the inverse of RMSE of the best fit line, and is used to smooth the elevations along the boundary.

We used the estimate of bias and standard deviation of errors for the prior to calculate RMSE of the prior. We use this RMSE to compute the ensemble weight, _{en}

where _{fit,j}_{en}_{fit,j}_{fit,j}_{en}_{fit,j}

Figure

When we modify elevations along the observed flood boundary, we introduce sub-optimality into the analysis, because the errors in the smoothed DEMs are now dependent on errors in the observations. Thus the errors in the LISFLOOD-FP predictions are also correlated with the errors in the observations, whereas the PBS assumes that they are not correlated. However, we assume that the degree of sub-optimality introduced by using the observations is relatively small compared to the large errors in the prior DEM.

We ran a forward simulation of LISFLOOD-FP using the updated particles (_{j}_{j}_{j}

where _{j}

where ^{+}^{-}_{j}_{j}_{j}

Agreement between observed and predicted flooded area for a sample of nine particles, and their corresponding weights for the nominal case. TPR is the true positive rate; weight refers to the particle weights assigned using the exponential distribution.

In most continents, the mean SRTM error is less than 2 m, and standard deviation is ∼4 m (

Root mean squared error for the prior for the nominal case (errors of 0.5 m mean and 1 m standard deviation) was 1.10 m. The set of particles generated from this prior had an RMSE of was 1.10 m. The RMSE of height errors along the flood boundaries reduced to 0.78 m in the updated set of particles where we smoothed elevations along the flood boundary. Table

Statistics for height errors along the flood boundary before and after smoothing.

Standard deviation (m) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|

Mean (m) | ||||||||||

0.50 | 0.50 | 0.52 | 0.40 | 0.55 | 0.56 | 0.49 | 0.42 | 0.38 | 0.32 | |

1.00 | 0.98 | 0.96 | 0.35 | 0.93 | 0.93 | 0.43 | 0.94 | 0.90 | 0.45 | |

2.00 | 1.94 | 1.95 | 0.50 | 2.00 | 2.00 | 0.50 | 2.02 | 2.02 | 0.48 | |

0.50 | 0.98 | 0.59 | 0.59 | 1.92 | 1.13 | 1.13 | 4.13 | 2.41 | 2.40 | |

1.00 | 1.03 | 0.59 | 0.60 | 1.96 | 1.09 | 1.09 | 3.76 | 2.04 | 2.04 | |

2.00 | 1.03 | 0.50 | 0.53 | 2.03 | 1.07 | 1.07 | 4.03 | 2.20 | 2.24 | |

0.50 | 1.10 | 0.78 | 0.71 | 1.99 | 1.26 | 1.23 | 4.15 | 2.44 | 2.42 | |

1.00 | 1.42 | 1.13 | 0.69 | 2.16 | 1.43 | 1.18 | 3.88 | 2.23 | 2.09 | |

2.00 | 2.20 | 2.01 | 0.73 | 2.84 | 2.27 | 1.18 | 4.51 | 2.99 | 2.29 | |

Sensitivity analysis also showed similar trends, improving upon priors in terms of bias, standard deviation of errors and RMSE. We found that the process of smoothing did not have an effect on the bias before and after smoothing. The difference between prior bias and smoothed bias is less than 4 cm for all the cases (Table

When this smoothed set of particles was put through a PBS, the bias reduced in the final estimate from the prior and the smoothed ensemble. Table

Figure

Error histograms for all cases.

When we used the final estimate DEMs to predict flood inundation, there was a consistent increase in TPR when compared to the prior. Figure

Total area where inundation is in both the observation and prediction for all cases.

Predicted flood inundation from prior and estimated DEM for two cases.

True positive rate (TPR) at peak inundation.

Standard Deviation (m) | |||||||
---|---|---|---|---|---|---|---|

1 | 2 | 4 | |||||

Prior | Estimate | Prior | Estimate | Prior | Estimate | ||

Mean (m) | 0.5 | 72 | 82 | 66 | 74 | 50 | 62 |

1 | 63 | 85 | 44 | 63 | 34 | 52 | |

2 | 33 | 82 | 28 | 75 | 29 | 57 | |

We successfully implemented a new algorithm to improve topography information in a floodplain by exploiting indirect information of ground elevations from observed flood extents. In synthetic tests, the algorithm reduced the bias, standard deviation of errors and RMSE. Our primary motivation to produce better topography was to obtain DEMs that are more suitable for flood inundation simulations. The improved DEM we obtained from this algorithm also predicted flood inundation much better than the prior. We implemented the algorithm for nine different cases with varying mean and standard deviation of errors, and obtained similar trends in the reduction of bias and standard deviation of errors. In fact, the magnitude and percentage reduction in bias increases in cases with higher errors. The results from the synthetic tests show potential, and we believe that the method could be used to improve DEM accuracy. For example, SRTM DEM could be used as prior, along with flood inundation observations obtained from Landsat or radar to obtain a DEM with better elevation accuracy.

Digital elevation models are the primary source of topographic information, and accurate DEMs are hard to obtain in the developing world. Globally available open-source products are easy to obtain, but are not accurate. Hence, they not suitable for flood inundation modeling (

All authors designed the model and the computational framework and wrote the manuscript. AS performed the analysis and interpretation of data.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The handling Editor declared a past co-authorship with one of the authors MD.