In order to simulate flow intermittence, a spatially distributed process-oriented hydrological model (JAMS-J2000) was implemented on the three mesoscale DRNs (detailed description of the model in Sect. ). Once calibrated and validated, the JAMS-J2000 hydrological model enables daily streamflow time series to be simulated in each reach of the river network.

Then, the deterministic hydrological model was coupled with a stochastic model, using the model outputs and physical information to train a random forest (RF) classification model with some flow state observations. The outputs of the RF model enables the daily flow state (flowing or dry) to be predicted in each reach of the DRN, thus predicting the spatio-temporal patterns of flow intermittence.

The modelling method to simulate flow intermittence is summarised in Fig.  and is described in detail in the following sections.

Table  shows general statistics on the distribution of the observed flow state between the different datasets and the coverage of the river networks. The gauging stations are the main source of observed data in terms of number of observations. They give information on long time periods with a regular time step, but the number of stations in the DRN is limited (one station in the Genal and Lepsämänjoki DRNs and five stations in the Albarine DRN), which means that stations cannot provide useful information about the spatial patterns of drying in the DRNs. The field campaigns (with expertise) are the second source of observed data. They cover a shorter time period than the stations (3 months in Lepsämänjoki and 3.5 years in the Albarine) but have a better spatial coverage of the river network than the stations. In the Genal DRN, observed data from Google Earth images show a very good spatial coverage with about 38 % of the river network, with at least one observation along the period of available data. It also covers a long time period (11.5 years) but with only a few observations per reach (between one and eight observations per reach). Crowdsourced data only represent a very small fraction (0.6 % to 2.8 %) but have a good spatial coverage, with around 14 % of the Albarine and Genal river networks covered.

Observed data have different distributions in time and space in the DRNs (Fig. ). For the three DRNs, there are observed data on the different classes of reaches (classified according to their drainage area), but there are more data available in the class of reaches with the largest drainage area. This is due to the data from gauging stations that are located along the main river and which represent the largest share of the data. The Albarine basin is the only one to have a full seasonal coverage on the different types of reaches. Reaches with small drainage areas in the Genal and Lepsämänjoki DRNs have mainly observed data between June and September and have missing data during the other months of the year (especially December and January). This shows that the collection of observed data on flow intermittence tends to be focused on the dry season and that there is almost no information on the state of flow for small river sections during winter.

Figure  also shows a seasonal distribution of the no-flow observations along the river networks. There is a clear spatio-temporal distribution of the no-flow observations in Lepsämänjoki DRN, with most of the drying events occurring in June and July in reaches with the smallest drainage area. Drying events gradually decrease with the size of the reaches drainage area, and the main river is perennial. However, drying events seem to be over-represented during the summer season because in the smallest reaches, 100 % of the observations are dry, whereas it is known that in this catchment, not all small reaches dry up, and they do not dry for more than a few weeks. In the Genal DRN, the peak of the drying season seems to be between June and September, but drying events are also observed in early spring and autumn. Most of the dry events are observed in the small reaches, but a few dry events are also observed in the downstream part of the Genal river due to water abstraction of irrigation (around 4 % of the observations in June and July). Drying events are observed later in the season – from August to October – in the Albarine DRN and are localised in small reaches but also in the main river due to the seepage of the Albarine river into the soil (around 30 % of dry observations in the Albarine between July and August). The smallest reaches (with a drainage area lower than the 25th percentile) only show flowing observation, which shows that no-flow observations may be lacking in these reaches.

This section presents the results of the simulation of flow intermittence with the JAMS-J2000 + RF modelling.

Figure  shows an example of the state of flow prediction in one reach of the Albarine DRN. Comparison of the observed state of flow and the discharge simulated with the JAMS-J2000 model shows that the hydrological model alone is not sufficient to reproduce the periods with no flow. The transition from a flowing to a dry state cannot be easily inferred from the simulated flows alone since there are periods when the simulated discharge is relatively high (e.g. in late 2020) while the phototrap indicates a dry state, whereas on other periods, the simulated discharge is low while the phototrap indicates a flowing state (e.g. late summer 2019). However, the flow state predicted by the RF model is in good agreement with the observed flow states, which shows the usefulness of the coupling between the spatialised hydrological JAMS-J2000 model and the RF model.

To enhance the precision of evaluating the coupled JAMS-J2000 + RF model to represent flow intermittence across the entire river systems, the model underwent training and testing using two distinct configurations: configuration 0 involved training the RF model with 100 % of the observed data, while configuration 1 involved training the RF model with 75 % of the observed data and validating its performance on the remaining 25 %. The SEN, SPE, ACC, and FAR values obtained with the reduced training sample (configuration 1) are indicators of the RF model error to extrapolate the prediction of the state of flow on reaches and dates that are not represented in the training dataset. With configuration 0, the model perfectly reproduces the observed drying and flowing events in the three DRNs (SEN and SPE = 1), whereas the performance of the RF model is decreased with configuration 1 (Fig. ). The Albarine and Lepsämänjoki DRNs only show a slight decrease in the performance: the model still correctly predicts more than 90 % of the no-flow observations and has a FAR around 5 %. The Genal DRN is more impacted by the removal of some of the observed data; the mean SEN drops to 65 %, and the mean FAR is 19 %. Specificity is above 0.99 for the three catchments, which means that the RF model predicts flowing events almost perfectly with configuration 1. ACC is also very close to 1 (>0.98); this is due to the fact that flowing events are much more represented than drying events in the observed dataset, so prediction errors for dry events are negligible compared with the near-perfect predictions of flowing events.

These results show that there is a high confidence of the prediction in the general dynamics of drying in the Albarine and Lepsämänjoki DRNs but higher uncertainty for the Genal DRN (see discussion in Sect. ).

The next sections firstly present flow intermittence modelling results obtained with configuration 0 in Sect.  and  and secondly the uncertainty related to the input data (size of the training sample with configuration 1, type of flow state observed data, and geology data) in Sect. .

Regarding the spatial pattern of flow intermittence, the model simulates more drying in the small tributaries for the three DRNs (Fig. ). For the Albarine and Genal DRNs, the flow intermittence of the main river in the downstream part of the catchment, due to seepage for the Albarine and water abstraction for irrigation in Genal, is well reproduced by the model. Simulated spatial patterns of drying have been validated by local experts, who confirmed that they are consistent with their observations (Figs. S13 and S14).

Figure  shows the mean interannual variations of the fraction of the dry river network through the year. It shows that the drying is limited to the end of May until the end of August in the Lepsämänjoki DRN, and then the mean annual maximum of drying usually does not exceed 9 % of the river network. In the Albarine DRN, the mean annual maximum of drying occurs in early September with between 24 % and 27 % of the dry river network. More than 10 % of the river network is continuously dry between July and the end of September. The model predicts some flow intermittence throughout the year (between 1 % and 4 % of the dry river network during the winter season). In the Genal DRN, the river network can dry up to 78 %–80 % in August, and more than 50% of the river network is dry from June to mid-September. The fraction of dry river network in Genal during the winter season stays relatively high (between 6 % and 26 %), but the lack of observed data over this period makes the results particularly uncertain.

Overall, the model successfully represents the general spatio-temporal patterns of drying in the three contrasted European DRNs, with intense and long periods of drying in the Genal catchment, characterised by a dry and warm climate; regular and localised drying up due to the geological context in the Albarine catchment; and short and limited in space drying in the Lepsämänjoki catchment, characterised by a more humid climate but that is mild in summer.

The ranking of the most important covariates in the RF models reflects the different contexts of flow intermittence in the DRNs. In the DRNs with more complex spatial patterns of drying, the RF gives more weight to the variables describing the reach characteristics. For all three DRNs, the drainage area of the reaches and their slopes are the two most important variables for the prediction of the flow state (Fig. ).

For the Lepsämänjoki DRN, the next most important variables are the mean catchment air temperature during the previous 30 d (T30), the simulated discharge, and simulated groundwater contribution to the discharge (GW10 and GW). These three variables give information on the hydro-meteorological situation in the catchment and define the temporal variability of drying. T30 allows seasonal variability to be captured and makes a distinction between winter low flows, when precipitation is stored as snow in the basin, and summer low flows, when drying is observed in small streams.

For the Genal DRN, the third and fourth most important covariates are the mean discharge during the 10 previous days and the current discharge, which shows that the temporal dynamics of drying is mainly controlled by the simulated discharge in the reaches. The fifth most important variable is the land use, which reflects the more concentrated agricultural areas, with a water demand for irrigation, in the downstream part of the basin.

In the Albarine DRN, the most important variables, after the reaches drainage area and slope, are the land use and soil types around the reaches and the current discharge. The four most important variables do not reflect the main cause of drying in the Albarine, which is the seepage of the river in moraine deposit areas. The classes of geology causing flow intermittence in the Albarine are not represented in the IHME1500 dataset, which may explains why other spatial characteristics are used in the RF model to reproduce the spatial pattern of drying.

The coupling between a spatially distributed model and a random forest model has a number of benefits for predicting intermittence in river systems. First, the JAMS-J2000 model represents the spatially distributed hydrological physical processes in the catchments. This enables several hydrological variables to be simulated at the HRU and the reach scale, such as evapotranspiration, soil water content, groundwater level, and discharge, which can be used as spatially distributed covariates in the RF model. Second, the JAMS-J2000 represents lateral flow routing between the HRUs and the reaches and thus represents the hydrological connectivity which cannot be represented in a RF model. However, the simulation of flow intermittence with JAMS-J2000 alone is not yet possible. The JAMS-J2000 model has difficulties in simulating periods with no flow. Even after long periods without precipitation input, the model tends to simulate residual low flows, and the reaches never completely dry up. There are also a multitude of processes causing the drying of rivers (e.g. interaction between the riverbed and the water table, seepage into karst, pumping of water from aquifers and rivers), and it is difficult to represent them all and accurately in a physical model . Despite the JAMS-J2000 model's ability of simulating seepage through the alluvial riverbed or water abstraction for anthropogenic uses , the data needed to parameterise these processes are seldom available and were not available in our case studies (e.g. daily amounts of water withdrawals and their precise locations). The use of the RF model enables flow intermittence to be simulated, even if the processes causing the drying up are not known or understood precisely beforehand since it does not require a representation of physical processes but links covariates to observed states of flow. In addition, RF models have the advantage of providing variable importance metrics which, in our case, allow the processes leading to the drying in the DRNs to be better understood.

The question can be raised about the contribution of the RF model compared to applying a threshold on the discharge simulated by the JAMS-J2000 model below which would determine zero flows. Figure  shows the distributions of simulated discharges for the two types of flow conditions (flow or dry) in reach 2443600 of the Albarine (same example as in Fig. ). For simulated discharges ranging from 0 to 4 m3 s-1, there is an intersection of the distributions for observed dry and flowing events. Setting a threshold would mean truncating the tails of these distributions. For instance, by setting a threshold to achieve a SEN of 98 % on this reach, a FAR of 26 % is obtained, as low discharges are all predicted as dry events. In contrast, with the RF model, the intersection of the distributions is well reproduced, and a FAR of 1.7 % is achieved for the same SEN (98 %). The differences in distributions between observed and simulated flow conditions can be explained by the fact that there are few “flowing” observations during winter periods with high flows in this reach. It is also challenging to extrapolate a discharge threshold value across all reaches of the network. Looking at the spatial pattern of flow intermittence in the DRNs (Fig. ) it is clear that the threshold value should be spatially distributed to take account of local effects, but this raises the question of how this spatial distribution should be achieved.

The use of a spatialised hydrological model combined to a RF model is therefore very advantageous in order to be able to simulate flow states at fine time steps and in a spatialised way over the entire river network.

However, the use of a RF model has several limitations. A first limitation is that the RF model can predict the right state of flow for the wrong reasons if the causes of drying are not represented in the covariates. For the three studied DRNs, drainage area is the most important covariate, which is consistent with other studies using RF models to predict flow intermittence , but in the Albarine and Genal DRNs we know that the drying is in fact due to the geology and water abstraction, respectively. The results of the RF model do not necessarily provide a better understanding of the origin of drying in river networks if the covariates are not sufficiently precise. Most importantly, this means that a RF model trained on a specific DRN may not be robust enough to predict flow intermittence in another DRN.

One major application of this flow intermittence modelling approach is to simulate the flow states under different climate change scenarios and predict tipping points in the flow regime of the river sections, such as transitions from a perennial to an intermittent flow regime. However, the robustness of such a model for extrapolating flow intermittence in climate change projections is questionable. The RF model is trained with observed data over a relatively short period, with no observed change in the flow regime of the reaches, and it is known that RF models cannot predict events that have never been observed before , which represents a major limitation for predicting the future evolution of drying spells in the DRNs. While it can be expected that the drying spells of currently intermittent reaches will be prolonged under climate change scenarios, the ability of the RF model to predict a shift from a perennial to an intermittent flow regime is not guaranteed. However, the results of this study show that the average annual number of dry days simulated for the reaches known to have perennial flow is rarely zero but can vary between 0 and 3 d yr-1. This means that in the present period, the model only simulates completely perennial flow in a few reaches. This bias in predicting the state of flow in the present period is a drawback for characterising current drying dynamics in river systems and studying the impact on biodiversity but may facilitate the prediction of drying in the context of climate projections as most of the reaches are already considered intermittent in the present period.

The results of the RF model are highly dependent on the training dataset. This study highlights the challenges of obtaining observed flow state data to train or validate the models. To accurately represent flow intermittence along river networks, the observed data ideally need to be uniformly distributed both spatially and temporally, which can be difficult to achieve.

Most studies focusing on the catchment scale collect observations from field campaigns e.g., but such surveys generally do not allow rivers to be monitored over many years and are usually limited to portions of the river network as they can be very time-consuming.

This study shows the interest of combining different types of data with heterogeneous spatial and temporal patterns in order to maximise the information on flow condition in the river networks. This is consistent with the results of , who showed that combining data from citizen science and aerial photographs afforded more robust information.

The results obtained in the three basins demonstrate the need to adapt the data collection to the context of each DRN. Ideally, a large amount of homogeneously distributed data along the river network and throughout the year will introduce the least possible bias into the model, like in the Albarine DRN. However, the case of the Lepsämänjoki DRN shows that even with a small amount of data concentrated on the summer season, the predicted patterns of drying are consistent with the observations made by local experts. In contrast, with a similar amount of data, the variability of the prediction of flow intermittence in the Genal DRN is higher due to more complex spatio-temporal patterns of drying. To reduce the uncertainty in the Genal DRN, more years of observed data would be necessary, with data more evenly spread over the year to better capture the length of dry spells.

The analysis of the Albarine and Lepsämänjoki DRNs shows that data from field campaigns provide essential information on the spatial and temporal dynamics of drying, making them the most useful type of data for predicting flow intermittence in river networks. However, in the Genal DRN, where phototraps were not installed during field campaigns, remote sensing seems to be a good alternative for collecting data. Although remote sensing data can be used to detect the state of flow adequately, have nevertheless pointed out several limitations: images are available at too low a frequency to study temporal patterns, and dense vegetation near the rivers may prevent the detection of the state of flow.

As shown in the results of this study, citizen science can also be a useful way of obtaining intermittence data and increasing the spatial coverage of observations. Several studies have shown the advantages of working with citizens to monitor temporary streams, especially to obtain observations in streams that would otherwise not be monitored . and studied the accuracy of data provided by citizen scientists and showed these data give an overall good indication of the hydrological state of the streams.

Expertise data indicating reaches with perennial flow proved to be crucial in reducing the over-representation of data from intermittent reaches in the RF model training data across all three DRNs. However, this raises questions about the value of such data, which is based on human perception and the error it may contain. Expert elicitation in hydrology has already shown benefits, particularly when tangible data are missing . These studies do show differences in the individual perceptions of the experts consulted, but by consulting a larger number of experts (in this study, only one or two experts were consulted per studied DRN) and by applying protocols similar to the ones proposed in these studies, the uncertainty linked to individual perception could be reduced, or at least quantified.

The general indications for data collection emerging from this study are to (1) favour a good spatial distribution of the observations by collecting data reaches with different characteristics (e.g. in terms of drainage area, geology and water abstractions), (2) collect data on intermittent sections as well as on reaches with a permanent flow regime, and (3) have time series of observations covering at least a whole year on a few points of the river network.

Another limitation of the study arises from the delineation of river networks. The delineation needs to be as accurate as possible to ensure that observations of flow state are assigned to the correct reaches. However, several studies such as those by , , and have shown that river networks are dynamic systems: they extend or retract according to landscapes and climatic conditions and can also be disconnected. It is therefore difficult to delineate a fixed reference river network with a density, enabling the spatial variability of drying in the DRNs to be predicted accurately.

In this study, the density of the delineated river networks was chosen so that all observations could be assigned to a reach, but the results show that the density of the river network has an impact on the simulated patterns of drying in the DRNs. In the three studied DRNs, contradictory states of flow were observed in reaches on the same day, indicating that the density of the river networks is not high enough to capture very local processes of drying. In contrast, the density of the river network should not be too high, as it may lead to the representation of reaches with an unrealistically small drained area, for which there are no observed data available to train the RF model. This situation occurred in the Albarine DRN where the resolution of the river network had to be increased in order to capture the locations of observed data (Fig. S2), resulting in some unrealistic prediction of small perennial reaches in the upstream part of the catchment (Fig. ).