# Improved predictions in ungauged basins using flood marks

Ludovic Oudin, Romain Caupin, Pierre Brigode

► To cite this version:

Ludovic Oudin, Romain Caupin, Pierre Brigode. Improved predictions in ungauged basins using flood marks. Journal of Hydrology, 2025, 657, pp.133145. 10.1016/j.jhydrol.2025.133145. hal-05006074

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Submitted on 26 Mar 2025

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Research papers

# Improved predictions in ungauged basins using flood marks

Ludovic Oudin<sup>a,* ID</sup>, Romain Caupin<sup>a ID</sup>, Pierre Brigode<sup>b ID</sup>

## ARTICLE INFO

This manuscript was handled by Marco Borga, Editor-in-Chief, with the assistance of Nadav Peleg, Associate Editor

**Keywords:**

Rainfall–runoff modeling
Regionalization
Prediction in ungauged basins
Flood marks
Citizen science

## ABSTRACT

Hydrological models are crucial for predicting river flow and managing water resources, but they face challenges in ungauged basins where flow data are absent. Since most of the world’s basins are ungauged, regionalization techniques are often employed, which transfer parameters from similar and/or neighboring basins; however, this process frequently yields poor results. This study investigates the use of flood marks, specifically event dates, as alternative data to calibrate hydrological models in ungauged basins. Utilizing over 80,000 flood marks from the French Repères de Crue database, we assess whether these historical records can improve flow predictions in ungauged catchments using the GR4J model. Results suggest that while flood marks alone are insufficient, their combination with neighboring gauged data enhances model performance, indicating the potential for improved hydrological simulations in data-scarce regions.

## 1. Introduction

Hydrological models are commonly used to anticipate river flow fluctuations and thus mitigate risks such as flooding; to manage water resource allocation for human, environmental, or economic needs; to predict the concentrations of chemical elements; or to study the water cycle. These models simulate catchment behavior using parameters that are calibrated on observed flow data at the outlet of the catchment. The calibration process involves simulating discharge with various parameter sets and selecting the set that optimizes a performance function between observed and simulated discharges (Gupta et al., 1998). Once calibrated, the model is validated by assessing its ability to reproduce observed discharge over a different period in order to ensure the robustness of the parameter selection (Beven and Binley, 1992).

However, this widely used methodology, which relies heavily on time series of observed discharge data, has significant limitations when applied to ungauged basins—those without hydrometric stations to record water flow. Ungauged basins present a major challenge in hydrological modeling, as there is no direct discharge data available for calibration. This issue is particularly critical, as most of the world’s river basins remain ungauged (Hrachowitz et al., 2013; Sivapalan et al., 2003). In such cases, hydrologists often resort to regionalization techniques, where calibrated parameters from neighboring basins or from basins that share similar geographical, climatological, or

geomorphological characteristics are transferred to the ungauged basin (Blöschl et al., 2013; Oudin et al., 2008). These approaches assume that basins with similar physical and climatic characteristics will respond similarly to hydrological processes, thus allowing for the transfer of parameter sets (Merz and Blöschl, 2004). However, these assumptions often lead to disappointing model performance due to variability in local factors that cannot be captured by the regionalization process (Oudin et al., 2010; Parajka et al., 2007). As a result, hydrological simulations for ungauged basins using these methods tend to show significant performance degradation, limiting the reliability of the models for predicting flow behavior or extreme events such as floods. Consequently, achieving reliable and robust predictions in ungauged catchments by regionalization is still a major challenge of hydrological science (Pool et al., 2021).

Given the limitations of regionalization, point flow measurements (Perrin et al., 2007; Pool et al., 2017; Rojas-Serna et al., 2016; Seibert et al., 2024) and/or alternative sources of local hydrological information must be considered so as to improve the calibration of models in ungauged catchments. One such potential source is flood marks, which provide physical evidence of past flood events, including information on peak water levels and in some cases the specific date of the event. Flood marks have been used historically for purposes such as risk assessment, floodplain delineation, and public awareness of flood risks (Bösmeier et al., 2022; Luu et al., 2018; Machado et al., 2015; Naulet et al., 2005).

<footnote><sup>a</sup> Sorbonne Université, Université PSL, EPHE, CNRS, Milieux Environnementaux, Transferts et Interactions dans les hydro systèmes et les Sols, METIS, F-75005 Paris, France</footnote>

<footnote><sup>b</sup> Univ Rennes, CNRS, Géosciences Rennes – UMR 6118, Rennes F-35000, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: Ludovic.oudin@sorbonne-universite.fr (L. Oudin).</footnote>
<figure><img src="image_2.png" /><figcaption>Fig. 1. The 58,279 flood marks and 603 hydrometric stations considered in this study.</figcaption></figure>

Recently, they have been more systematically recorded and stored in databases. In France, since 2016, the public database Repères de Crue has aggregated flood marks across the country (MTES, 2024). This database, which in early 2024 contained over 80,000 georeferenced flood marks, offers an unprecedented resource for hydrological studies, particularly for ungauged basins. The majority of these flood marks include the precise dates of the flood events, while some also provide the corresponding water heights. These marks represent a valuable, albeit underutilized, source of information for hydrological modeling. Previous studies have shown the potential of using historical flood marks to improve flood quantile estimation (Leese, 1973; Macdonald, 2012; Macdonald and Black, 2010; Payrastre et al., 2005; Renard, 2023). However, no studies to date have explored the possibility of using flood dates as a calibration tool for hydrological models.

In this study, we propose to explore the utility of flood marks, particularly flood event dates, as a new source of calibration data for hydrological models in ungauged basins. Specifically, we aim to investigate whether the flood dates recorded in the Repères de Crue database can be used to calibrate hydrological models and improve predictions of river flow behavior during flood events. This approach represents a novel application of flood marks, as it shifts the focus from traditional discharge time series to an event-based calibration method. Although it is reasonable to expect that calibration using flood dates may not achieve the same level of accuracy as calibration based on continuous discharge data, it is essential to assess the potential of this method, particularly for basins where no other data are available. By focusing on flood dates, we aim to determine whether this approach can offer insights into river dynamics that are otherwise inaccessible in ungauged

contexts.

For this purpose, we will employ the GR4J hydrological model (Perrin et al., 2003), a conceptual, global model with a daily time step. Using GR4J is advantageous for several reasons: (i) it requires only four parameters, making it a low-degree-of-freedom model for daily simulations; (ii) studies have shown that the parameter calibration can be achieved with relatively small datasets, sometimes as few as a dozen daily discharge observations (Perrin et al., 2007); and (iii) a reduced set of 27 parameter sets has been shown to capture a wide range of hydrological behaviors across various catchments, offering a robust alternative to traditional calibration (Andréassian et al., 2014). This reduction was achieved by selecting the 27 sets from an initial pool of 106, where 22 sets achieved a high performance on at least 10 % of the catchments studied and the remaining 5 covered additional hydrological behaviors. These parameter sets have been demonstrated to outperform classically calibrated sets, particularly in cases of short calibration periods (<1 year), and are recommended for use in ungauged or poorly gauged basins (Rojas-Serna et al., 2016).

## 2. Data

### 2.1. Flood marks

The Repères de Crue database, established in 2016, is a collaborative database enriched by contributions both from citizens and from government field agents. As of mid-2024, the platform contains more than 80,000 georeferenced flood marks. For many of these flood marks, additional information is provided, such as the floodwater level, the date
<figure><img src="image_3.png" /><figcaption>**Fig. 2.** Some characteristics of the flood mark database used in this study (top) and examples of photographs (bottom) showing the diversity of information. ". Source : "Plateforme nationale collaborative des repères de crues https://www.reperesdecrues.developpement-durable.gouv.fr/</figcaption></figure>

of the event, the type of flooding, and the river involved in the overflow, among others. For this study, only flood marks with an associated date—specifically with daily precision—and unrelated to maritime events were selected. This subset includes 58,279 flood marks, the spatial distribution of which is shown in Fig. 1.

It is important to note the heterogeneity in the distribution: Certain river networks and Mediterranean basins, particularly those subject to flash floods, are prominently represented with a higher density of flood marks.

Flood marks come in various forms: permanent markings, flood debris lines, water stains, and even eyewitness accounts. However, the majority of marks are temporary, with flood debris lines being the most common type. Additionally, the number of flood marks reported annually has significantly increased over time, most likely due to the growing awareness of flood risks (Fig. 2).

## 2.2. Hydrometeorological data

For meteorological data, we used the FYRE Climate reanalysis dataset (Devers et al., 2021). The FYRE Climate reanalysis builds upon an earlier reanalysis called "SCOPE Climate" (Caillouet et al., 2019), based on analogous atmospheric pressure fields and daily observational

records to enhance accuracy. FYRE Climate provides daily time series of air temperature and precipitation at an 8-km spatial resolution, covering the period from 1871 to 2012 across metropolitan France and neighboring regions (including non-French parts of transboundary catchments). As a probabilistic ensemble, FYRE Climate is composed of 25 members. The long temporal coverage enables the use of many historical flood marks. FYRE temperature reanalyses were used to determine potential evapotranspiration using a temperature-based equation (Oudin et al., 2005). In the discussion section, SAFRAN gridded values since 1958 provided by Météo-France (Vidal et al., 2010) were also used to investigate the sensitivity of our results to the forcing data used.

Streamflow data were collected from the HydroPortail French hydrometric database (Leleu et al., 2014). For this study, we used 603 stations located in metropolitan France with a hydrological regime that is neither nival nor pluvio-nival, as provided by the classification proposed by Hashemi et al. (2022) and a fraction of solid precipitation to total precipitation <0.10, to avoid increased parameter uncertainty of an eventual snow routine module in the hydrological model. Besides, these 603 catchments were chosen due to their long-term monitoring, with at least 20 years of data available. Last, we selected catchments that present low influence due to artificial reservoirs and dams. To this aim, we used the MADAM dataset v1.0 (Delaigue et al., 2024) and estimated the
<figure><img src="image_4.png" /><figcaption>Fig. 3. Two flood events on the Tarn at Montbrun as reported in the flood mark database and streamflow simulations obtained by the 27 parameter sets. For this example, the first member of the FYRE reanalysis is used only, but the methodology considers all FYRE members in turn.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 4. Selected hydrometric stations and associated flood mark information.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 5. Location and flood mark selection for the Tarn at Montbrun catchment.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>Fig. 6. Effect of filtering out the events within the same temporal window of 3 days and 6 months. In the first case, the event date retained is selected based on the proximity of the flood mark to the hydrometric station and in the second case, the date retained is the one leading to the maximum number of flood marks.</figcaption></figure>

equivalent water depth of the total water storage capacity of all dams on the catchment (sum of capacities divided by catchment area). If this equivalent water depth was greater than tenth the annual water runoff of the catchment, we excluded the catchment from the dataset. The spatial distribution of these stations is shown in Fig. 1, illustrating a good coverage of the territory, excluding high mountain areas. The catchment set includes a wide variety of catchment areas, ranging from 10 to 100,000 km² (interquartile range: 120–760 km²).

## 3. Method

### 3.1. Pairing flood mark information to hydrometric stations

The objective of matching flood marks with gauging stations was to calibrate the model based on available flood dates at locations where streamflow data have been observed, enabling an evaluation of this calibration strategy. We applied the following method to each of the 603 stations:

*   **River Name Match:** First, only flood marks that were associated with the same river name as the station were selected.

*   **Proximity Along the River:** Next, we selected flood marks where the nearest river point was located within 40 km of the station, following the river course. The purpose of this selection was to avoid assigning dates to the station that differed from the flood marks due to travel time between the two points. The 40-km threshold approximately corresponds to 12 h of travel at a velocity of 1 m.s⁻¹, which is consistent with the daily time step of the model and the level of precision for most flood marks.

*   **Catchment Area Match Criterion:** Flood marks were further filtered based on the difference in catchment area: the ratio between the catchment area of the station and that of the flood mark must be between 60 % and 160 %. This criterion was meant to prevent matching floods that did not involve the catchment studied, either due to floods occurring in a downstream tributary or floods being masked by a major tributary between the flood mark and the catchment outlet.

*   **Temporal Consistency:** Finally, only flood marks with dates falling within our study period (1874–2012) were retained, which corresponds to the period covered by the FYRE Climate reanalysis, with

the first 3 years (1871–1873) being used for model initialization, ensuring that the model’s reservoir states were independent of the initial conditions at the start of the study period.

This methodology ensures that the matched flood events are spatially and temporally relevant to the hydrological conditions observed at the gauging stations, providing a robust framework for evaluating the calibration approach.

### 3.2. Hydrological model

The method outlined in this paper can be applied to any daily lumped rainfall–runoff model. In this study, the four-parameter GR4J model (Perrin et al., 2003) was used. GR4J is a widely used hydrological model, often applied in water resource management, flood forecasting, and climate change impact studies due to its efficiency and adaptability across various catchments.

GR4J involves four free parameters: production store capacity (X1), groundwater exchange coefficient (X2), routing store capacity (X3), and time base of unit hydrograph (X4). The model operates by partitioning rainfall into effective precipitation and water storage in the production store, which is then divided between direct runoff and slow, subsurface flow processes. The production store (X1) accumulates and releases water based on soil moisture conditions, simulating the infiltration and evapotranspiration processes. GR4J uses a unit hydrograph to route surface flow toward the catchment outlet, while the routing store (X3) handles delayed flow through the system, representing the subsurface flow contributions. The exchange coefficient (X2) accounts for ground-water exchanges between the river and the surrounding aquifers.

Classic calibration of the model involves adjusting the four parameters to fit observed streamflow data, by exploring the four-dimensional parameter space. In this study, we also performed so-called discrete calibration, allowing us to move from a four-dimensional search for parameter values to a one-dimensional search for parameter sets, i.e., the dimension of a list of 27 parameter sets provided by Andréassian et al. (2014). The GR4J model was manipulated using the R (R Core Team, 2020) package airGR (Coron et al., 2017, 2023).
<figure><img src="image_8.png" /><figcaption>**Fig. 7.** Results of the selection of the parameter set using flood dates on the Tarn at Montbrun. For this example, the first member of the FYRE reanalysis is used only, but the methodology considers all FYRE members in turn. Timing errors in days are reported, but only the number of hits (0 time error) is used to choose the optimal parameter set.</figcaption></figure>

### 3.3. Determining parameter sets on ungauged catchments

In an ungauged catchment context, two primary methods were considered for determining the parameters of the GR4J model. The first method involved the classic “nearest neighbor” approach (denoted as the “NN” approach), where parameters calibrated from the nearest gauged catchment were transferred. In this approach, parameters X1, X2, and X3 were transferred directly without any modification, while X4 was adjusted to account for differences in catchment area between the

gauged and ungauged catchments (see Andréassian et al., 2014). The distance between catchments was calculated using a weighted Euclidean distance, considering both the outlets (weight 0.2) and the centroids (weight 0.8), as suggested by Lebecherel et al. (2016). Following the recommendations of Rojas-Serna et al. (2016), instead of using a single locally calibrated parameter set for the gauged catchment, the method tested 27 parameter sets, ranking them based on their KGE (Kling-Gupta efficiency) score (Gupta et al., 1998). The parameter set transferred was the top-ranked one, i.e., the set with the highest KGE score on the
<figure><img src="image_9.png" /><figcaption>Fig. 8. Distribution of KGE values of the different strategies used to determine parameter sets on the pseudo-ungauged catchments. The lower and upper hinges correspond to the first and third quartiles, and the upper and lower whiskers extend from the hinge to the largest value no further than 1.5 * IQR from the hinge (where IQR is the interquartile range).</figcaption></figure>

neighboring gauged catchment.

$$X_{NN} = \arg \max_{X_i \in \{X_1, X_2, \dots, X_{27}\}} \sum_{i_m=1}^{25} KGE_{NN1}[Q(P_{im}, ETP_{im}, X_i)]$$

where $X_{NN}$ was the parameter set with the highest KGE over the 25 FYRE members of precipitation ($P_{im}$) and potential evapotranspiration ($ETP_{im}$) for the nearest neighbor gauged catchment (NN1), with the $X_{4i}$ parameter (time base of unit hydrograph) being adjusted to account for differences in catchment area between the gauged and ungauged catchments (see Andréassian et al., 2014).

The second method (denoted as the “FM” approach) utilized flood marks from the ungauged catchment and counts the number of times the model predicts peak flows on the same dates as indicated by these flood marks. In this approach, all 27 parameter sets were used to generate daily discharge simulations. For each dated flood event, a 1-year time window was opened, centered on the flood mark date, and the day of maximum flow within that year is determined. For each of the 27 parameter sets, if the peak day matches the flood mark date, the objective function was incremented by 1. This was repeated for each flood event and for each of the 25 members of the FYRE climate reanalysis. After counting how many times the peak day matches the flood mark, the 27 parameter sets were ranked, and the one that maximizes the number of hits was selected:

$$X_{FM} = \arg \max_{X_i \in \{X_1, X_2, \dots, X_{27}\}} \sum_{i_m=1}^{25} \sum_{i_e=1}^{nb\_events} \text{Hits}_{i_m, i_e}(X_i)$$

where $X_{FM}$ is the parameter set that maximizes the number of matched peak dates, $i_m$ is a member of the FYRE reanalysis and $i_e$ is one flood event from the flood marks database and $X_i$ is the i-th parameter set from the 27 parameter sets in the short list.

Fig. 3 illustrates the assessments made for two flood events. As shown in this figure, the approach enables the discrimination of several parameter sets, whether within a very narrow time window around the flood event (in which case the differing dynamics between the parameter sets become particularly important) or within a broader time window. In the latter case, the model’s ability to distinguish between two different flood events in terms of magnitude is also assessed. This assumes implicitly that the flood mark dates the most significant event within the 1-year period under consideration.

In a narrow time window, the key factor for discriminating between parameter sets is the capacity of each to accurately capture the timing and peak of the specific flood event. Different parameter sets may simulate varying responses to rainfall events due to their distinct internal dynamics, which influences the simulated hydrograph’s shape and timing. Therefore, a finer focus on the event’s immediate vicinity enables the assessment of how well each parameter set models the short-term runoff response and flood behavior.

On the other hand, when considering a broader temporal window, the model’s performance extends beyond individual flood event dynamics. It also reflects the model’s overall ability to correctly simulate the relative magnitudes of distinct flood events that occur within the year. This implicitly assumes that the flood mark represents the largest flood during this period. By distinguishing parameter sets based on their capacity to correctly rank the magnitudes of different floods, the method evaluates the model’s capacity for representing both the timing and the intensity in flood scenarios.

Finally, the third approach, denoted as the “JOINT” approach, combined the two previous methods by calculating a weighted average of the ranks associated to each parameter set according to the nearest neighbor approach and the flood-mark-based method. Last, the parameter set transferred was the top-ranked one. This combined rank provided a balanced solution, leveraging both proximity-based parameter
<figure><img src="image_10.png" /><figcaption>Fig. 9. Distribution of KGE values of the JOINT calibration procedure using both nearest neighbor information and flood mark information. The lower and upper hinges correspond to the first and third quartiles, and the upper and lower whiskers extend from the hinge to the largest value no further than 1.5 * IQR from the hinge (where IQR is the inter-quartile range).</figcaption></figure>

transfer and flood event matching for improved parameter selection in ungauged basins:

$$ \text{rank}_{\text{JOINT}} = a \cdot \text{rank}_{\text{NN}} + (1 - a) \cdot \text{rank}_{\text{FM}} $$

The weight a allows us to go from the NN approach (for a = 0) to the FM approach (a = 1). To assess the sensitivity of the joint approach to this weighting procedure, we tested 11 values of a, from 0 to unity using an increment of 0.1.

This combination approach is similar to the one developed by Rojas-Serna et al. (2016), who combined regional information (parameter sets of neighboring gauged stations) and local information. The main difference lies in the local information being used: streamflow point measurements in the Rojas et al. (2016) study versus flood mark dates in this study. Besides, FYRE ensemble precipitation and temperature (Devers et al., 2021) are used in this study, rather than the SAFRAN gridded values provided by Météo-France (Vidal et al., 2010) used in Rojas-Serna et al. (2016), in order to benefit from the maximum flood marks available before 1958.

### 3.4. Benchmarking the performance of the regionalized model

Each simulation was then evaluated based on its ability to reproduce streamflows in the pseudo-ungauged catchment. For this evaluation, the KGE (Kling-Gupta efficiency) criterion was used, calculated over the observation period of the catchment discharge data. This allowed us to assess the performance of each method compared to upper and lower benchmarks, as advocated by Seibert et al. (2018).

To contextualize the performance of the methods developed for the ungauged case, the results were compared against three reference approaches:

(1) full local calibration as an upper benchmark, which represents the performance of a model calibrated directly on the catchment using observed discharge data;

(2) discrete calibration, where the best-performing parameter set from the 27 pre-determined sets is selected based on local conditions. This configuration can be seen as another upper benchmark, representing the best performance that can be achieved by drawing parameter sets from the short list; and

(3) the performance obtained using a single parameter set applied uniformly across all catchments. This single set was chosen as the one among the 27 available that most frequently performed best across the set of 603 catchments. This configuration can be seen as a lower benchmark since it is probably the strategy that would be followed without any regional or local information.

This comparison enabled a clear evaluation of how well the ungauged basin methods performed relative to established calibration techniques in hydrological modeling. The KGE provides a quantitative benchmark to gauge the accuracy of the simulated flows in replicating observed discharge patterns across different methods.

## 4. Results

### 4.1. Selection of flood marks and catchments

In this section, we analyze the selection of catchments based on the number of flood marks identified near the hydrometric station. By applying the automatic selection process for flood marks detailed in Section 3.1, we find that 231 out of 603 catchments have at least one usable flood mark. The number of flood marks and the number of flood events for each of these 231 catchments vary significantly (Fig. 4). Catchments in the Mediterranean arc are overrepresented compared
<figure><img src="image_11.png" /><figcaption>**Fig. 10.** Distribution of KGE element values of the JOINT calibration procedure using both nearest neighbor information and flood mark information. The lower and upper hinges correspond to the first and third quartiles, and the upper and lower whiskers extend from the hinge to the largest value no further than 1.5 \* IQR from the hinge (where IQR is the inter-quartile range). Alpha is the ratio between the standard deviation of the simulated values and the standard deviation of the observed ones, beta is the ratio between the mean of the simulated values and the mean of the observed ones and r is the Pearson product-moment correlation coefficient.</figcaption></figure>
<table><caption>**Table 1**
Correlation coefficients between calibrated parameter values (full calibration) and estimated values from the three regionalization approaches. Pearson's product-moment correlation coefficient values are shown for each parameter. Spearman's rank correlation coefficient values are in brackets.</caption><thead><tr><th>Parameter</th><th>Nearest Neighbor (NN)</th><th>Flood Marks (FM)</th><th>Joint with a ranking weight of 0.2 (JOINT)</th></tr></thead><tbody><tr><td>X1</td><td>0.449 (0.388)</td><td>-0.024<br>(0.013)</td><td>0.365 (0.352)</td></tr><tr><td>X2</td><td>0.638 (0.353)</td><td>-0.026<br>(0.008)</td><td>0.356 (0.347)</td></tr><tr><td>X3</td><td>0.373 (0.454)</td><td>-0.059<br>(0.102)</td><td>0.353 (0.432)</td></tr><tr><td>X4</td><td>0.678 (0.734)</td><td>0.72 (0.715)</td><td>0.639 (0.757)</td></tr></tbody></table>

with northern France because the database of flood marks contains more records in this region. This is primarily linked to the frequency and severity of extreme flood events in southern France.

It is also important to note that a few significant events can lead to a large number of flood marks, explaining why the number of flood events is considerably lower than the number of marks for each station.

Fig. 5 illustrates the event selection process for a specific hydrometric station. In this example, it shows that flood marks can be located relatively far upstream or downstream of the hydrometric station, as long as the hydraulic distance and catchment size rules are respected. This can introduce some uncertainty regarding the exact date of the event. In the event date database, small discrepancies of 1 or 2 days between dates are common. In such cases, only one date is retained, with priority given to the mark closest to the hydrometric station. This also contributes to reduce the distance between the gauging stations and the finally selected flood marks and also the discrepancies between corresponding catchment areas. Over the final selection of 1090 dates of

historical events, the distances range from 0 to 39 km (interquartile range: 0–12 km) and 90 % of ratios between the catchment area of the station and that of the flood mark lie between 75 % and 133 %.

Even after filtering, it is sometimes possible for two significant events within the same sliding 1-year window to be retained. This may reflect the occurrence of two major flood events within a single year. Since the sliding window around each flood mark date is 1 year, we only retain a single event date in such cases. The selected date corresponds either to the event with the highest number of recorded marks or, if this is not a distinguishing factor, to the date of the flood mark closest to the hydrometric station. The effects of these two filtering operations are reported in Fig. 6.

## 4.2. Calibrating hydrological model using flood marks

Fig. 7 illustrates the selection process for the parameter set using the FM approach on the Tarn at the Montbrun catchment. Depending on the flood event considered, the parameter sets for which the simulations yield a peak discharge on the same day as recorded in the flood mark database may vary. In this example, we observe that significant equifinality can occur, but this equifinality diminishes as the number of available events increases.

Fig. 8 shows the performance results obtained for all 231 catchments, as well as for those with more than 3 (126 catchments) and more than 7 flood events (43 catchments) recorded by flood marks. As expected, the performance in the gauged mode—obtained using full and discrete calibration—is significantly higher than that of the other approaches. Discrete calibration is less efficient than full calibration. However, Andréassian et al. (2014) showed that the performance gaps were reduced during validation. The discrete calibration provides the maximum that could be achieved by FM, NN, and JOINT approaches, making it a useful benchmark. The regionalization method, which

<figure><img src="image_12.png" /><figcaption>**Fig. 11.** Distribution of KGE values of alternative strategies used to determine parameter sets on the pseudo-ungauged catchments using a) FYRE reanalyses dataset and b) SAFRAN dataset. The lower and upper hinges correspond to the first and third quartiles, and the upper and lower whiskers extend from the hinge to the largest value no further than 1.5 * IQR from the hinge (where IQR is the interquartile range).</figcaption></figure>
transfers the parameter set from the nearest gauged catchment, ranks
third but remains far behind the gauged-mode methods in terms of
performance.

The method that calibrates parameters using flood marks ranks below the approach that applies the same parameter set to all catchments. This indicates that using flood marks alone is not sufficient to effectively guide parameter determination in ungauged catchments. The flood marks fail to provide enough precise information for robust model calibration.

However, the performance gap between the three approaches for ungauged parameter determination (nearest neighbor transfer, flood-mark-based calibration, and uniform parameter set) decreases when focusing on catchments with more than 7 flood events. This suggests that the availability of a larger number of flood events improves the calibration potential, but even then, the flood mark method struggles to match the effectiveness of other regionalization techniques.

4.3. *Joint use of regional information and flood marks*

Fig. 9 illustrates the performance of the method that jointly uses flood marks and information from the nearest gauged basin. The results show an interesting complementarity between the two data sources, as the optimal weight for combining the parameter set rankings from 27 simulations ranges between 0.20 (when considering all basins with at least one recorded event) and 0.60 (when considering all basins with at least 7 recorded events). When using all basins, the median KGE is 0.74 for the nearest neighbor approach and 0.61 for the flood mark approach, reaching 0.755 for a ranking weight of 0.2.

For basins with at least 3 (resp. 7) recorded events, the median KGE is 0.77 (resp. 0.73) for the nearest neighbor approach and 0.62 (resp. 0.64) for the flood mark approach, peaking at 0.78 (resp. 0.77) for a ranking weight of 0.2 (resp. 0.3). It is also worth noting that these improvements are more pronounced for the lower quantiles of the KGE distribution, indicating that the combined approach is particularly robust and effectively filters out parameter sets that lead to poor performance in pseudo-gauged basins. Using a ranking weight of 0.3, the performance obtained on ungauged catchments using the JOINT approach is equal to or better than that obtained with the nearest neighbor approach on over 82 % of catchments. However, the two approaches lead to strictly equal performance on 67 % of catchments (for a number of events greater than 1) and 53 % of catchments (for a number of events greater than 7).

Lastly, the choice of weight appears to be relatively unimportant, as improvements are almost optimal with weight values as low as 0.1 or as high as 0.9. This suggests that even a slight inclusion of flood mark information can enhance the nearest neighbor regionalization approach, while knowledge of the parameter set performance from the neighboring basin also significantly improves the calibration approach based on flood marks.

Fig. 10 shows how the different components of the KGE criterion evolve as a function of the weight assigned to the NN and FM approaches. This figure highlights the complementarity of the two methods in selecting the optimal parameter set: The NN approach tends to provide discharge simulations with less bias in terms of mean and variance since beta (ratio of means) and alpha (ratio of standard deviations) values are closer to unity. Conversely, the FM approach helps select parameter sets that result in better correlations (greater r Pearson coefficient values) between observed and simulated discharges. This outcome is expected, as the FM approach does not exploit information on flood magnitude but focuses solely on the timing of peak discharge occurrence. Conversely, the NN approach provides insights into the regional context of the catchment (e.g., available water storage, lithology, topography), which are valuable for accurately representing the catchment's water balance behavior.

To get an idea of how the use of flood marks can help in the cali-
bration of ungauged parameters, Table 1 shows the correlation co-
efficients between the locally calibrated parameters (full calibration

method) and the parameters obtained by the three regionalization
methods (NN, JOINT, and FM). This type of comparison is always
difficult to interpret, given the non-uniqueness of optimal parameters,
potential compensations between parameters, and the parameter dis-
tribution laws, even with a model that only has 4 free parameters. That
said, the table provides interesting insights, as the so-called production
parameters (those responsible for the water balance in the watershed)
are much better determined by the NN (nearest neighbor) approach,
while the parameter X4, related to the base time of the unit hydrograph,
is better determined by the FM approach using flood marks.

5. Discussion

This study aimed to evaluate the added value of flood marks in
streamflow prediction for ungauged basins. In this section, we address
two key limitations that may constrain the generalization of the pro-
posed approach to other hydrological models or regions: (i) the reliance
on a predefined parameter library i.e. the short list of 27 parameter sets
and (ii) the use of FYRE reanalysis data, which inherently contain
uncertainties.

The methodology presented in this study is based on a predefined
shortlist of parameter sets previously developed for the GR4J hydro-
logical model (Andréassian et al., 2014). The use of this shortlist was
essential to reduce the dimensionality of parameter calibration, given
that historical flood dates alone were deemed insufficient in both
quantity and quality for conventional model calibration techniques.
However, this reliance on a predefined shortlist poses a challenge for
extending the methodology to other hydrological models that lack an
equivalent parameter sets library.

To address this limitation, we propose an alternative strategy that
utilizes parameter sets calibrated on neighboring gauged catchments in
place of the short list of parameter sets. The core principle of the method
remains unchanged: filtering parameter sets based on their ability to
reproduce flood dates recorded in the flood mark database.

The refined approach proposed here leverages the parameter sets
from the *n* nearest neighboring gauged catchments. These *n* sets are
tested for their capacity to reproduce flood dates observed locally on the
ungauged catchment. The *m* best-performing parameter sets are then
used to simulate streamflow in the ungauged basin. Ensemble averaging
is thus used in this context since it often yields improved discharge
simulations on ungauged basins by compensating for errors associated
with individual parameter sets (see e.g. McIntyre et al., 2005). Thus, as
recommended by Oudin et al. (2008) for the GR4J model over France,
we considered taking the *m* = 3. Then the streamflow simulations ob-
tained with the 3 parameter sets are averaged to determine the
streamflow over the ungauged catchment. Averaging streamflows was
preferred compared to averaging model parameter values as this pre-
serves the correlation structure of the parameter (Neri et al., 2020;
Oudin et al., 2008). Various combinations of *m* and *n* were tested, and
for clarity, we present here the one that yielded optimal regionalization
results (*n* = 20, *m* = 3).

Another critical point is the use of FYRE reanalysis data. The FYRE dataset offers a substantial temporal depth, enabling the identification of several significant historical flood events. However, two limitations must be considered. First, the forcing data uncertainties are evident in the variability across the 25 precipitation and air temperature ensemble members. These uncertainties can propagate into the streamflow simulations, potentially leading to inaccuracies in the predicted flood event dates. Second, the extensive historical depth of the FYRE dataset includes flood data of varying intensity and quality. To evaluate the impact of these limitations, we propose replicating the experiments using the SAFRAN dataset for the post-1958 period (Vidal et al., 2010). SAFRAN offers improved precision for more recent periods, which may reduce the uncertainties associated with older flood date records.

Fig. 11 illustrates that using SAFRAN slightly reduces the number of basins with historical flood dates available, while the overall sample
remains largely comparable. The conclusions previously drawn regarding the tested regionalization approaches remain largely consistent when using SAFRAN instead of FYRE. Additionally, the alternative approach, which selects the three neighbors that best reproduce historical flood events among the 20 closest basins, yields performance equal to or better than the JOINT approach previously tested. This approach outperforms the other regionalization approaches tested, particularly for catchments with a large number of events, underlining the benefits of collecting flood marks on a regular basis.

## 6. Conclusion

The main finding of this study is that flood marks indicating past flood events can be beneficially incorporated into classic methods to determine parameter sets for ungauged catchments. These results are promising, particularly given that extreme hydrological events, which are often considered outliers in data series, have proven crucial in improving the simulation of more common events. This finding opens promising perspectives for small ungauged catchments that are prone to extreme events. For such catchments, continuous measurement data are often lacking but local knowledge or anecdotal evidence related to past extreme floods is available (Borga et al., 2008). In these regions, leveraging historical knowledge of extreme events could serve as a valuable tool for hydrological modeling. These methods are particularly relevant in regions where the cost or logistics of installing gauging stations make long-term monitoring unfeasible. Another important aspect to consider is the potential for collecting additional qualitative data through field surveys or interviews near the outlet of the catchment considered. Gathering oral histories and community recollections of past floods could provide valuable supplementary data points, especially in these regions where official measurements are lacking. These events often leave a strong emotional impact on local populations, making them likely to recall the dates, the severity, and the impacts of the events with a high degree of accuracy (McEwen et al., 2017). Such an approach aligns with recent trends in participatory and citizen science, which increasingly values the contributions of local knowledge to environmental research (Buytaert et al., 2014).

In this study, we chose to use only the dates of flood marks to help determine the parameter set. Using this information as a simple metric in our study shows the potential of exploring alternative calibration methods that place greater emphasis on minimizing timing errors, which is a relatively unexamined topic in calibrating hydrological models (Ewen, 2011). Using information on the intensity of the past flood, as given by water levels, could also be considered. This could potentially offer substantial benefits in refining the determination of model parameters. However, using such water level data raises concerns about uncertainties related to their measurements but also to changing river morphology over time, which could affect the conversion of water levels to streamflow values (Benito et al., 2015; Payrastre et al., 2005). This would require extensive effort to reconstruct past river geometries and floodplain changes, making it a challenging task to generalize over large datasets or multiple basins.

It is likely that other hydrological models would perform similarly when calibrated against extreme events. The principle of using limited flow data for model calibration is widespread in hydrology, particularly for regions with sparse data (Seibert and McDonnell, 2015; Singh and Bárdoossy, 2012). Many models are designed to be flexible enough to incorporate a few key reference points, and their performance can be significantly improved by incorporating even minimal data, such as historical flood marks. This suggests a broader applicability of our findings to different hydrological models and regions.

In summary, this study illustrates how leveraging knowledge of past extreme events can significantly improve hydrological models, especially in data-scarce regions. Future research could benefit from integrating water-level data, gathering community-based information, and exploring novel calibration techniques to further enhance the reliability

and accuracy of flood simulations.

## CRediT authorship contribution statement

**Ludovic Oudin:** Writing – review & editing, Writing – original draft, Supervision, Project administration, Methodology, Funding acquisition, Conceptualization. **Romain Caupin:** Writing – review & editing, Methodology, Investigation, Formal analysis, Data curation. **Pierre Brigode:** Writing – review & editing, Supervision, Project administration, Methodology, Funding acquisition, Formal analysis, Conceptualization.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgments

Flow measurements were extracted from HydroPortal (available at [https://www.hydro.eaufrance.fr/](https://www.hydro.eaufrance.fr/)). Flood marks were collected from the national collaborative platform of flood marks developed by the Viganies network of the French Ministry of Ecological Transition ([https://www.reperesdecrues.developpement-durable.gouv.fr](https://www.reperesdecrues.developpement-durable.gouv.fr)). We thank Jan Seibert and the anonymous reviewer for their relevant suggestions.

## Data availability

Data will be made available on request.

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