The parameterized DROP model has been developed based on the scheme. The model works at the level of each reservoir individually and is based on the mass balance (as shown below in Eq. ) of each reservoir to calculate the release at its outlet. 1dVdt=Qin-Qout Qin and Qout stand, respectively, for the net inflow to the reservoir and its outflow at the outlet. In fact, the net inflow, Qin, combines different physical processes, as shown in Eq. (): it includes water inputs from precipitation P, direct runoff Rd representing water flows running off the surrounding ground surface that also feeds the reservoir, and tributary streamflows Qtrib flowing into the reservoir. Evaporation E and groundwater exchange Qgw are also included in Qin. 2Qin=(P-E)×Areservoir+Qtrib+Rd±Qgw, where Areservoir is the reservoir surface area.

In order to simulate dam releases, Qout, the reservoir model categorizes reservoirs as irrigation and non-irrigation reservoirs, computes the mass balance for each reservoir individually, and calculates releases based on inflow and water demands. A schematic of the DROP model is shown in Fig.  with its six parameters (in blue). To give an overview of its overall functioning, the model takes as input inflow and water demands and calculates at a monthly time step dam releases according to the reservoir management purpose and its relative capacity compared to inflow, denoted as c. Operating rules are set following an “operational year”. This type of year has been introduced by , and it differs from hydrological and calendar years. It starts the first month of the water release period and is therefore specific to each reservoir. This specific month, representing the first parameter of the model, will be denoted as mstart in the remaining sections of this article. At the beginning of each operational year, defined by mstart, reservoir storage volume Sinit is compared to the ideal filling value Sideal, defined as a ratio, α, of storage capacity C. Reservoir-simulated releases are impacted by this step as they are retrospectively revised upwards or downwards depending on whether the reservoir has more or less water storage than the ideal rate. Dam monthly releases are then computed following two steps: first, a provisional release is calculated based on water demands and the annual mean inflow. In irrigation reservoirs, two parameters are involved: dmax, setting the control area of the reservoir and thus the water needs to be supplied, and M, defining the minimum release to be provided for environmental requirements. The calculation scheme remains simplistic for other management purposes where releases are set to mean annual inflow. The provisional release is then corrected by incorporating a “demand-controlled release” ratio R, controlled by two parameters cthreshold and b, which accounts for inflow pattern influence in reservoirs with low storage capacities compared to inflow. The DROP model therefore has six parameters, as shown in Fig. .

The operating rules are detailed below. First, at the beginning of each operational year, an annual release coefficient Ky is computed to determine the filling rate of the reservoir. Ky is a ratio between the reservoir storage at the beginning of the year Sfirst,y and the long-term target storage Sideal: 3Ky=Sfirst,y/Sideal, where Sideal=α×C, α being a nondimensional constant, and C is the total storage capacity of the reservoir. Sideal represents the ideal filling level at the beginning of each year; α was set semi-empirically to 0.85 of the maximum capacity for all reservoirs based on sensitivity tests conducted in . This annual release coefficient is the one used to weight the provisional releases calculated afterwards depending on whether the reservoir has more (Ky>1) or less (Ky<1) water storage than the ideal rate. The underlying aim is to reduce interannual variation in streamflow.

The following steps describe how reservoir releases are computed. The provisional monthly releases, rm′, are set depending on the reservoir's main purpose. The scheme is simplified for a non-irrigation reservoir since it constantly releases the mean annual inflow imean calculated over the whole simulation period (noted “long-term” in the remaining sections of this article): 4rm′=imean. For an irrigation reservoir, monthly releases are proportional to water demands. They are parameterized here following as 5rm′=imean(M+(1-M)dmdmean,y if DPI>1-M,imean+dm-dmean,y if DPI≤1-M, where dm and dmean,y are, respectively, monthly and annual mean water demands. DPI (demand per inflow) is, as introduced by , the ratio between dmean,y and imean, and M represents the minimum monthly release as a percentage of imean. It is set to 0.5 by and and to 0.1 by and .

When the DPI is above the set threshold (1-M), water needs are considered to be very high and can only be partially fulfilled by the water stored throughout the coming year. The priority is to first ensure a minimum release, M×imean, in order to meet the environmental flow requirements. The remaining part of the annual inflow is released throughout the year on a monthly basis following the sub-annual water demand fluctuation curve. Otherwise, when the DPI is below (1-M), the reservoir releases all the monthly water demand that is needed.

In this scheme, only irrigation demand is considered. Since dams provide water for the downstream demand within a certain distance, a maximum distance, dmax, is a parameter to define, for each reservoir, the irrigated grid cells within the river basin to be supplied and thus delimits a “command area” for each reservoir. In contrast to (where a crop growth model is considered to calculate the irrigation demand), here the distribution of irrigated areas is based on ECOCLIMAP SG , which is used by the irrigation module in the ISBA LSM to compute irrigation demands for 5×5 km-resolution grid cells (see Sect. ). The irrigation water demands are aggregated within the command area for each reservoir. Unlike the scheme, the DROP model entirely separates irrigation from non-irrigation reservoirs and only accounts for irrigation water demands for this category of reservoirs. Moreover, industrial and domestic demands are highly uncertain and hardly accessible. In fact, these consumptions are strongly linked to each country's specific political and economical policies, and extensive records are generally not made public. Some global databases, such as the Food and Agriculture Organization of the United Nations (FAO) global information system AQUASTAT , provide estimates of average annual water withdrawals by activity sector and by water resource publicly accessed at the country level. However, such estimates are still limited in terms of temporal and spatial resolution and would consequently add a non-negligible source of error to the model. They are therefore neglected in this study.

In all possible cases, regardless of the reservoir purpose, the water released over the operational year is equivalent to the long-term mean annual inflow.

The release computed so far is provisional. The real monthly release is calculated as follows: 6rm=Ky×rm′ if c≥cthreshold,(1-R)×im+R×Ky×rm′ if 0≤c<cthreshold, where c is the relative capacity of a reservoir and is defined as the ratio between storage capacity C and the long-term mean annual inflow water volume (c=C/Imean). The parameter R, as introduced by (and also parameterized as β by ), is a so-called “demand-controlled release ratio”. It is parameterized in the current study as 7R=ccthresholdb, where R describes the influence of the inflow regime on release for small storage capacity reservoirs. It varies between 0 and 1 and includes two parameters: cthreshold and the b coefficient. In fact, the smaller the reservoir capacity is compared to inflow, the closer it gets to run-of-river dams where release is close to the natural river flow and thus the influence of the inflow annual pattern. Otherwise, when c is above the threshold (large-capacity dams), then R=1 and the release is fully controlled by water demand. cthreshold and b are set, respectively, as 0.5 and 2 in both and . , on the other hand, proposed an analytical formula to compute R, which is reproduced in this study, and set cthreshold and b, respectively, to 1/α and 1. The monthly releases are also weighted by the annual coefficient, Ky from Eq. (), which is calculated at the beginning of the operational year and describes how full the reservoir is relative to the ideal rate. Reservoir releases can therefore be revised upwards or downwards depending on whether the reservoir had more or less water storage than the ideal rate.

The modifications brought to the model from the previous version of and the parameterization can be summarized in the following list.

The starting month of the operational year, which was calculated in previous versions at the level of each reservoir based on observed inflows and dam releases, is considered in this model version as a parameter, denoted as mstart. This overcomes the challenge faced by the old versions when applying the model in ungauged basins. Within our version, mstart is to be set separately for irrigation and non-irrigation reservoirs.

The Sobol sensitivity analysis method has been widely used in hydrological models in order to identify the parameters that contribute the most to the model output uncertainty. It is a global variance-based approach where, for a chosen variable of interest Y, the total variance is decomposed into fractions attributed to each individual input as well as the interactions between them. If Y=f(X) is a goodness-of-fit metric of the model with X representing the set of parameters X1,X2,…Xp of size p, the total variance of Y, D(Y), is decomposed as follows : 8D(Y)=∑iDi+∑i<jDij+∑i<j<kDijk+…+D12..p, where Di is the amount of variance due to a parameter Xi alone, Dij is the amount of variance arising from the interaction between the parameters Xi and Xj, and so on. Equation () is known as Hoeffding decomposition .

The sensitivity indices, called Sobol indices, are computed as ratios between the component variances and total variance in order to measure the contribution of each single parameter and each parameter interaction. The first-order Sobol index, S1, captures the sensitivity of Y to each input parameter Xi taken alone. The second-, S2, and higher-order indices describe the contribution of the multiple interactions between parameters. A model with p parameters requires 2p-1 indices to be evaluated, which rapidly becomes computationally challenging for high values of p. The total-order index, ST, measures the full influence of a parameter by including all of the variance caused by its interactions with the rest of the parameters, all orders included. The first-, second- and total-order Sobol sensitivity measure formulas are 9S1i=DiD,10S2ij=DijD,11STi=1-D∼iD, where D∼i is the amount of variance due to all of the parameters except for Xi.

Model parameter sampling and Sobol index estimation are performed here using the open-source Python library SALib . The parameter samples are generated following quasi-random sequences in order to scatter the sample points as uniformly as possible over the parameter space. Following the theorem, the different orders of Sobol indices are estimated from a total number of model runs of N×(2×d+2), where N and d are, respectively, the sample size and the number of parameters. The package also provides confidence intervals of the index estimates at the 95 % confidence level.

Spain has an estimated area of 505 983 km2 , representing more than 85 % of the Iberian Peninsula (estimated area 583 254 km2, ). It has river basins with sizes ranging from a few square kilometers to more than 80 000 km2 (i.e., the Ebro basin). The five largest river basins are the Ebro, flowing into the Mediterranean Sea, and the Duero, Tajo, Guardiana and Guadalquivir, flowing into the Atlantic Ocean. They also represent the river basins where the natural river flow pattern is the most significantly altered in the country, with high degrees of regulation resulting from extensive reservoir construction. These different rivers have a Mediterranean hydrological pattern, which is characterized by high flows during the wet season (i.e., fall and winter) and low flows during its dry season (i.e., late spring, summer). This seasonality explains the strong anthropization of the Spanish hydrographic basins and, in particular, the construction of more than 1200 dams mainly in the second half of the 20th century. They are essential for retaining enough water to meet irrigation and domestic water demands as well as for hydropower production, which represents ∼13 % of Spanish electricity generation in 2020,.

The data series required as inputs to the model and the ones used to validate the outputs are taken from the Spain database. Reservoir characteristics are taken from the global GRanD database. Irrigation demands are simulated by the ISBA irrigation module. The needed input data are detailed below.

Local (Spain) database. In situ observations of natural and anthropized flow and volume data are made publicly available by the Center for Hydrographic Studies of Spain (CEDEX, Ministry of Public Works and Ministry for Ecological Transition, Spain). The national database includes the location and daily time series of discharge for 1119 gauge stations and outflows from 347 reservoirs over the period 1900–2014.

A sensitivity analysis with respect to the six parameters was conducted on the performance of a Nash–Sutcliffe efficiency NSE, bounded version, called C2M , on outflows using the Sobol method. In fact, the NSE values in some reservoirs were highly negative for some simulations, and thus this metric was not suitable for a variance-based sensitivity analysis method like Sobol's. C2M is used instead as it is a normalized version of NSE that varies between -1 and 1 and where all negative values are bounded between 0 and -1. Parameter default values, bounds and distributions are listed in Table . The parameter distributions were all considered uniform except for relative capacity, for which the distribution is logarithmic to align with the observed pattern on the modeled reservoirs (Fig. ).

The default values for α, M, cthreshold and b are those considered in . α-selected bounds cover a realistic range of ideal reservoir filling rates. The distribution and bound values of the cthreshold parameter are drawn from the relative capacity distribution of the 215 modeled reservoirs (Fig. ). The b lower limit is 0.5, below which the shift to the demand-controlled state of a reservoir becomes too abrupt once c exceeds cthreshold. The upper limit considered for b is 5, beyond which the transition curve between the behavior of a low relative capacity reservoir and a high relative capacity one becomes unchanged, following the sensitivity test run conducted on this parameter. For dmax, both the default value and the lower and upper limits were set to be consistent with the sizes of Spanish river basins. The operational year starting month, mstart, is set to April for irrigation reservoirs in order to match the beginning of the crop irrigation season considered in the irrigation model. For other reservoirs, mstart is chosen empirically to be May as the default value based on the observed filling curves of the reservoirs, which tend to be at the maximum filling level near May.

The sensitivity analysis was performed on each of the 215 reservoirs separately, distinguishing between irrigation and non-irrigation reservoirs since the number of parameters involved depends on the main purpose of the reservoir (six and four, respectively, as dmax and M are only considered in irrigation reservoirs).

Using Saltelli's quasi-random sampling method , a sample size of 4096 was used for this analysis in each category, resulting in 4096×(2×6+2)=57344 and 4096×(2×4+2)=40960 model runs for each of the 107 irrigation and 108 non-irrigation reservoirs, respectively. By comparing with smaller sample sizes, the confidence intervals estimated by SALib show that the Sobol indices converged and that the chosen sample size is sufficient to reliably represent the results.

Using the default parameterization with the parameters listed in Table , an operating rule is determined for each of the 215 reservoirs, and both outflows and water storage variations are simulated through complete operational years within the overall period 1979–2014. Figure  shows the C2M values at reservoir outlets by evaluating the simulated monthly outflow time series against in situ observations. Panel a shows the results obtained using a reference simulation where rivers are considered in their natural state (Qout=Qin). Panel b shows the C2M improvement rate when considering the DROP model.

Overall, with DROP, the river flow representation is clearly improved at nearly all the reservoirs' locations. The median C2M index for flows is 0.52, which corresponds to a 43 % improved flow representation when compared to natural river representation. For storage volume representation, the mean correlation is 0.53 with a standard deviation of 0.3. Half of the reservoirs have a correlation greater than 0.63 between observed and simulated storage volumes.

The results reveal the model's positive contribution in representing the seasonal cycle of river flow, specifically for irrigation large-storage capacity reservoirs, as the model reproduces the seasonal shift between inflows and outflows caused by irrigation management rules with reasonable accuracy. For these reservoirs, the correlation between simulated and observed discharge increases from 0.49 (reference simulation) to 0.75 in the median. Regarding storage volumes, correlation reaches 0.74 in the median. As an example, the Gonzalez Lacasa reservoir located in the Ebro basin shows typical results in Fig. . In fact, this irrigation reservoir stores incoming water during winter/early spring, which explains a lower outflow than inflow (in blue and orange, respectively, for observed discharges, panels (a) and (b) in Fig. ) between October and March and releases the water in summer when there is insufficient water to supply all crops' irrigation needs. The period of release, from April to September in this case (shown in the annual cycle, Fig. c), corresponds to the crop-growing period and therefore to high irrigation water needs. As a result, the discharge seasonal curve is shifted and the maximum monthly discharge, in this example, is reached in July instead of April. This management scheme is well reproduced by the DROP model, as the simulated outflows (shown in red) align well with the observations (in blue), and consequently so do the volume variations.

The improvement of the C2M distribution for each category of dams, in terms of main purpose and relative capacity, is shown in Fig. . Note that, for irrigation reservoirs, the improvement rate reaches 80 % in terms of the median and 123 % for those considered of high relative capacity (here c≥0.5) and which are fully demand-controlled. The flow improvement rates for the rest of the high relative capacity reservoirs are dispersed but remain positive at the median despite the simplistic approach of DROP. For low relative capacity reservoirs (here c<0.5), and independent of the management purpose, the model's contribution is almost null since the reservoirs are considered “run-of-river” and the influence of the inflow regime is predominant.

The distributions of first-order Sobol indices for each parameter calculated at each of the 107 irrigation and 108 non-irrigation reservoirs are shown in Fig.  with a box plot. Overall, it emerges from Fig.  that the most influential parameter is cthreshold. In fact, based on the definition of S1, ∼48 % of the total variance in C2M is attributed to cthreshold alone within irrigation reservoirs. In non-irrigation reservoirs, this parameter accounts for ∼74 % of C2M variance. The M parameter is ranked second in irrigation reservoirs and accounts for 15 % alone in the median of all of the variance, followed by dmax with an S1 index of 0.03. The parameter controlling the month for which the operational year starts, mstart, alone has very little influence on the overall outflow C2M variance, although the effect is slightly more noticeable in the non-irrigation reservoirs. α and b are considered the least influential parameters for most reservoirs.

To better illustrate how each parameter individually affects the model outputs, the Gonzalez Lacasa reservoir (GRanD ID 2699; c=0.65) is set as an example. Given the sensitivity analysis results, a screening step is added on cthreshold, M and α separately and the rest of the parameters are set to their default values. The means of monthly outflows over the simulation period (1979–1994) are shown in Fig. .

Regarding the first parameter and for values of cthreshold below the relative capacity of the reservoir (lower than 0.65 for the Gonzalez Lacasa case), the reservoir is considered with high storage capacity, and so monthly releases are completely driven by demand, resulting in a seasonal shift between inflow and outflow and a peak of discharge in July in order to meet the irrigation needs. Conversely, when the cthreshold is higher, the dam is considered to have a low storage capacity, which reduces the buffering effect and increasingly aligns the simulated release curve (in red) with the seasonal trend cycle of inflow (in orange), as shown in Fig. a. The buffer role of the reservoir is therefore conditioned by the value of the cthreshold.

The influence of M on the minimum release is shown in Fig. b. The higher the value of M, the greater the part of mean inflow set as minimum release and the lower the remaining part of water dedicated to meeting irrigation needs during peak demand. Since the Gonzalez Lacasa reservoir is considered to have a relatively large storage capacity (with cthreshold=0.5 as the default value) among the considered reservoirs, the outflow will still follow the seasonal curve of water demand, but M will influence the release peak by extending or flattening the outflow curve to maintain a minimum release level required through the year. For run-of-river dams, M is irrelevant since the release follows the monthly inflow. dmax also controls the variation of outflows over the year in the same way, but only when the DPI ratio is low. Its impact remains limited beyond the (1-M) threshold, as the release curve is fixed to maintain the required minimum outflow.

The parameter α, on the other hand, does not affect the long-term mean pattern of release. In fact, α only operates on outflows on an inter-annual basis, through Ky, to offset the excess or shortage of stored water from one year to the other, especially when the critical filling zones are reached (reservoir in a dead storage zone or overflowing), in order to bring the reservoir water state to the ideal filling curve over the long term (Fig. c). The same behavior is noted for mstart, which is not shown in Fig. .

The cthreshold, α and mstart parameters have the same effect on non-irrigation reservoirs. The influence of each of the three parameters on [1979–2013] monthly mean outflows from the “Alcantara II” reservoir (GRanD ID 2800) in the Tagus River basin, which has a relative capacity of 0.6 and is mainly used for electricity generation, is shown in Fig. . For this specific reservoir, the simulated period includes several wet years, and there were periods when water flowed over the spillways during winter, which explains the alignment of the outflow with the inflow during this season.

The distributions of total sensitivity indices ST (in grey), alongside S1 (in white), of each parameter are shown in Fig. . A significant gap is observed between the first- and total-order index distributions. This confirms the non-negligible effect of the parameters' interactions on the output variance involving mainly cthreshold. In the median, based on the ST definition, ∼62 % of C2M variance in irrigation reservoirs and ∼87 % in non-irrigation reservoirs are attributed exclusively to cthreshold and its interactions with other parameters: it is indeed the most important parameter of the DROP model. α and b, on the other hand, were in the median low values, which makes them the least important parameters.

The distributions of second-order Sobol indices for each parameter couple for the irrigation and non-irrigation reservoirs considered separately are shown in Fig. . The results reveal that the parameter with the most interactions overall with other parameters is cthreshold. This is mainly due to its position at the end of the model chain, where provisional releases are corrected. For the rest of the parameters, the interaction between mstart and α is more marked in non-irrigation reservoirs since the scheme is simplistic and the outflow depends mainly on the Ky annual coefficient that is driven by both mstart and α. In irrigation reservoirs, the coefficients dmax and M interact because they control irrigation water demand and the reservoir water storage allocated to it. As they are both involved in the reservoir water balance, they jointly control the outflow. The b coefficient meanwhile interacts only with cthreshold when computing the demand-controlled release ratio R calculation. The total influence of b, mostly resulting from the interaction with cthreshold, is only seen in reservoirs with low relative capacities.

Since c is a defining characteristic of each reservoir and is involved in the outflow computation, the first- and total-order Sobol indices were rearranged according to their reservoir-correspondent c values, here grouped into six ranges to simplify the presentation of the results to better identify the impact on parameter ordering and interactions (Fig. ).

For low values of c (less than 0.01), cthreshold is the only relevant parameter. The total influence of b, on the other hand, is mostly related to its interaction with cthreshold. The remaining parameters are negligible since their first-order Sobol indices are almost zero and the total order is very low. For reservoirs with a medium storage capacity (0.01≤c≤1), a significant part of total variance is due to parameter interactions, apart from b, as all Sobol indices increase significantly from first to total order. This is even more noticeable when 0.1≤c≤0.3. Above a relative capacity of 0.3, the M parameter in irrigation reservoirs gains in importance and increases interactions with the cthreshold as c is bigger. For non-irrigation reservoirs of the same category, cthreshold takes on more importance as the storage capacity increases (less spreading and very high S1). The remaining parameters lose relative importance. For the very high relative capacity values, α and mstart are almost irrelevant, regardless of the operating objective. Finally, for nearly all reservoirs combined (except those with very small values of c), the b coefficient has almost no influence and can therefore be set to a nominal value.

When using Sobol indices, the representation of model output uncertainty is limited to the variance only, which is not fully representative of all the statistical characteristics (or moments) of the C2M distribution. Using the distribution function instead provides a complete description of uncertainty in the model output. Here, we evaluate the sensitivity of parameters by assessing their influence on the entire C2M distribution without reference to a specific moment of the output moment-independent methods. This method is used as a validation step for the overall conclusions found with the variance-based Sobol method. The deviation of the C2M distribution function caused by two different parameters cthreshold and α over the irrigation reservoirs is shown in Fig. . Here, the same samples generated for Sobol's index calculation were used. First, the unconditional probability distribution function (PDF) of the model output C2M is obtained when all input parameters are randomly sampled from their distributions. Then, for each input parameter, conditional PDFs of C2M are computed following different value ranges from the total parameter distribution: here, five ranges are considered. The importance of each parameter is proportional to the magnitude of the conditional PDF deviation from the unconditional one.

The large dispersion of the conditional PDFs (colored) shows the strong impact of cthreshold in the model outlet in Fig. a. All PDFs are nearly aligned for α, and thus the value of this parameter has very little significance for C2M distribution. Moment-independent sensitivity indicators like “Kolmogorov”, “Kuiper” and “Delta” were used to measure the deviation from the unconditional PDF, and the results were consistent with the conclusions made with the Sobol index. It is also noted that DROP tends to have very poor performance scores for high values of cthreshold (above 2.76) where all the reservoirs are considered run-of-river and the release would be close to the lines alignments with inflow as shown in Fig. . This figure indirectly demonstrates the reservoir model contribution in terms of improving river flow representation in anthropized basins where the magnitude and seasonal flow dynamics are significantly altered by large storage capacity reservoirs, especially those for irrigation purposes.

The DROP model outputs are affected by several uncertainties linked to the model inputs and the algorithm. The parameterized model is based on a generic scheme of reservoir operation, which inevitably implies a simplification in terms of water release. Concerning the representation of operational purposes, the algorithm fails to differentiate between other purposes than irrigation and considers that a constant release is expected by the rest of the reservoirs. In addition, only the main objective of the reservoir is represented, and the releases of the multi-purpose reservoirs are not entirely represented since their management rules are more complex to describe. This explains the poor performance of the model at the level of reservoirs that are used for irrigation, though it is not their main objective: DROP is very simplistic for the rest of its possible purposes, so that the seasonal shift in water discharge is not always well reproduced. This is the case of the reservoir “Los Bermejales”, for example, a multi-purpose reservoir located in the basin of the Guadalquivir River, southern Spain, which is mainly used for water supply, but it is also used to meet irrigation water demands (Fig. ).

In addition, the model computes releases independently on each reservoir. The cascades of reservoir operations, which can be coordinated with each other, are thus not captured. More specific studies on multi-objective reservoirs and multi-reservoir systems have been conducted , but they all remain complex and are reservoir-specific. These methods were evaluated only at the local scale and are very difficult to extend to a global scale because they need a significant amount of observed input data and require detailed operating rule knowledge.

Regarding the representation of releases from non-irrigation reservoirs more generally, the scheme remains very simplistic since release policy is not driven by physical processes. In fact, operation rules of these types of reservoirs involve complex socioeconomic and political factors that are different in each country. Simulating other management purposes is mainly based on optimization algorithms, as is the case for hydro-power dam releases, for instance, where the objective functions are economically oriented (i.e., to maximize energy production; ). These methods remain very reservoir-specific and are currently deemed to be too complex to be applicable at a large scale.

The model provides a relatively good performance in representing irrigation reservoir operations because of its physical approach that links water releases to crop water demands. However, some simplifications are to be noted which could be improved in the future. The irrigation water demand estimation is based on the irrigation scheme in ISBA LSM, which has its own limitations . Also, in this version of the reservoir scheme, water demands for each irrigation reservoir are reduced to considering pixels that are downstream of the reservoir at a given maximum distance dmax. This creates inconsistencies because water demand is not linked to the reservoir water storage capacity, which leads for some reservoirs to much higher water demands compared to water supply. Moreover, here there is no proportionality rule set between reservoirs with common irrigation grid cells. They are recorded on multiple reservoirs when their command areas are overlapping because the model runs on each reservoir independently. We end up repeatedly counting shared pixels, and this leads to overestimation of water demands at the level of each reservoir. According to results from the sensitivity analysis, parameter dmax alone (ranging from 1 to 250 km) does not have much influence on outflow variance, and this is even more true when irrigation demands are considered excessive compared to inflow (DPI ≥1-M), because in that case the amount of irrigation demand is not more significant in outflow computing; only the seasonal variation defines the reservoir release curve. suggested an efficient way to overcome this issue by defining a least-cost adduction network, based on and , to connect each irrigation grid cell to a unique abstraction point, either a river or a reservoir, by using topographic information, distance and upstream areas of the river abstraction points. This approach has the advantage of considering not only the downstream grid cells, but all the surrounding ones. Most importantly, it ensures that reservoir command areas do not overlap anymore and that each pixel irrigation demand is only counted once. The method is implemented in the routing model of ORCHIDEE (ORganizing Carbon and Hydrology In Dynamic EcosystEms; ) and can be easily implemented in other routing models. It is also interesting at this stage to account for all possible sources of water withdrawals, including underground water, canals, but also the abstractions made directly from the reservoirs' storage, in order to have a more realistic representation of reservoir releases.

Another aspect which is not explicitly simulated in the model is water abstraction. In this study, abstractions are taken into account indirectly since the inflow is reconstructed from observations at the inlet of each reservoir. However, once the DROP model is implemented in a hydrological model, the tributary inflows will correspond to river flows simulated by the routing model, and therefore there should be a deterioration of the performance index on discharge with an error spreading along the anthropized rivers. However, by coupling the above with a model that takes irrigation into account, such as the new version of the ISBA land surface model, for example , the water releases from the reservoir model can be linked to crop irrigation needs, and thus river water withdrawals can be represented as well as those taken directly from the reservoirs.

The sensitivity analysis has revealed the most influential parameters and those that can be set using predefined values without impacting the model output uncertainty distribution. It emerged that cthreshold is the most influential parameter in representing reservoir releases, and this result is consistent with the analysis of on the role of the release ratio R where cthreshold is involved. Indeed, the aforementioned study showed the positive contribution of this formulation to the R ratio (R=αc, i.e., cthreshold=1/α) and its optimization in improving the representation of release and stabilizing water storage in the simulated reservoirs, especially those with 0.21≤c≤1.18 (the values of c for which 4c2=αc and c=1/α, α being set at 0.85).

conducted a sensitivity test on the α parameter for a case study of a large relative capacity hydroelectric reservoir (c=2.28). The model was tested with four different values of α (0.65, 0.75, 0.85, and 0.95) and found that this parameter had a low impact on the simulated release but a high impact on the simulated storage, except when the reservoir is full. α showed high sensitivity to releases when events with water passing over spillways were more frequent. Their conclusions concerning the sensitivity to outflows are also in line with the results found here.

Actually, the sensitivity analysis undertaken in this study focused on the model sensitivity in the average representation of releases rather than on the filling levels of reservoirs since the focus of the study is on flow representation and the effect of anthropogenic factors in altering the flow dynamics along the rivers. If we were to focus on water resource availability and water management issues, the sensitivity analysis should also focus on the uncertainty in representing water storage levels in the reservoirs, considering the C2M over volumes as the variable of interest. In this configuration, as shown in Fig. , the parameters α and mstart, alongside cthreshold, will emerge as the most influential parameters with significantly high sensitivity indices of both first and total orders.

Both α and mstart directly affect the bias in the filling curve representation. In the ideal case where the reservoir state is not on the boundary conditions, the filling curve is vertically shifted following the value of α and the chosen month in order to bring the reservoir volume at the beginning of each operating year in line with the ideal filling rate αC, as shown in Fig. , without changing the seasonal release pattern. The larger the seasonality of reservoir water levels, the greater the effect of both parameters, which is very noticeable in large-storage capacity reservoirs used for water supply and hence explains the two parameters' interaction with cthreshold.