Comparison of Generalized Non-Data-Driven Reservoir Routing 1 Models for Global-Scale Hydrologic Modeling

1 Models for Global-Scale Hydrologic Modeling 2 Joseph L. Gutenson, Ahmad A. Tavakoly, Mark D. Wahl, Michael L. Follum 3 Research Civil Engineer (Hydraulics), US Army Engineer Research and Development 4 Center, Coastal and Hydraulics Laboratory, 3909 Halls Ferry Rd., Vicksburg, MS 39056 5 University of Maryland, Earth System Science Interdisciplinary Center, College Park, 6 Maryland, USA 7 Corresponding Author: joseph.gutenson@noaa.gov 8 9 Abstract: Large-scale hydrologic simulations should account for attenuation through lakes 10 and reservoirs when flow regulation is present. Generalized methods for approximating 11 outflow are required since reservoir operation is complex and specific real-time release 12 information is typically unavailable at global scales. There is currently no consensus on the 13 best approach for approximating reservoir release rates in large spatial scale hydrologic 14 forecasting. This research compares two parsimonious reservoir routing methods 15 previously implemented in large-scale hydrologic modeling applications, requiring 16 minimal data so as not to limit their usage. The methods considered are those proposed by 17 Döll et al. (2003) and Hanasaki et al. (2006). This paper compares the two methodologies 18 across 60 reservoirs operated from 2006-2012 by the U.S. Army Corps of Engineers. The 19 authors vary empirical coefficients for both reservoir routing methods as part of a 20 sensitivity analysis. The Döll method generally outperformed the Hanasaki method at a 21 daily time step, improving model skill in most cases beyond run-of-the-river conditions. 22 The temporal resolution of the model influences performance. The optimal model 23 coefficients varied across the reservoirs in this study and model performance fluctuates 24 between wet years and dry years, and for different configurations such as dams in series. 25 Overall, the Döll and Hanasaki Methods could enhance large scale hydrologic forecasting, 26 but can be subject to instability under certain conditions. 27


Introduction 1.Importance of Dams in Hydrologic Simulations
Improvements in numerical weather prediction, the increasing abundance of computational power, and greater precision of remotely sensed observations make global hydrologic forecasting and flood warning systems increasingly feasible (Alfieri et al., 2013;Wu et al., 2014;Emerton et al., 2016;Salas et al., 2017).Lack of information concerning anthropogenic influences on runoff is a major deficiency of large-scale flood forecasting systems (Emerton et al., 2016).Reservoir operations tend to distort natural flow patterns, effectively redistributing surface water spatially and temporally (Zhou et al., 2016).Impoundments significantly influence the downstream flow regime at small and large spatial scales (Batalla et al., 2004;Magilligan and Nislow, 2005).Over half of the world's large river systems are now substantially altered by dams (Nilsson et al., 2005) resulting in a seven-fold increase in water storage within the global river system (Vörösmarty et al. 1997).Furthermore, the cumulative alterations from global reservoir impoundments are so significant that it has been suggested that they could buffer global sea-level rise (Chao et al., 2008).
Dams primarily impact the hydrologic cycle by changing the magnitude and timing of the discharges downstream (Haddeland et al., 2006;Döll et al., 2009;Biemans et al., 2011;Wu et al., 2014;Zajac et al., 2017), often with the specific intent to mitigate hydrologic extremes (i.e., floods and droughts) (Zajac et al., 2017).Dams reduce peak discharges by roughly a third on average while dampening the daily variation by a similar amount (Graf, 2006).In hydrologic forecasting, accuracy of the timing and magnitude of hydrologic extremes is fundamentally important to the usefulness of the forecasts.approaches require training data or specific knowledge of a particular reservoir to effectively parameterize and apply them.This is often an insurmountable limitation for data-driven approaches.For that reason, the focus of this paper is on non-data-driven reservoir routing methodologies as an incremental improvement over schemes that effectively neglect dams when information is scarce.

Non-Data-Driven Reservoir Storage and Outflow Simulation
Non-data-driven approaches to reservoir routing rely on conceptualizing reservoir responses without explicitly observing the actual reservoir operations.The optimal method for a given application depends on a balance between complexity and available information (De Vos, 2015).Therefore, this manuscript focuses on selecting for parsimony.
Existing non-data-driven reservoir models range from simple approaches to sophisticated methods.Solander et al. (2016) showed that temperature-based schema best fits the modeling of discharge,  , .The Solander et al. (2016) rule is driven by temperature shifts at each model time step above and below the mean temperature.The Solander et al. (2016) method indicates that temperature is the main proxy governing reservoir release, due to the assumption that seasonality drives agricultural production and reservoir operation.However, the Solander et al. (2016) study focuses on long-term climatic forecasting.Diurnal temperature variations will not likely describe day-to-day reservoir operations.Zhao et al., (2016) developed a reservoir routing scheme based on reservoir stage and storage rules.However, real-time insights related to current reservoir stages throughout a region can involve considerable remotely sensed information.The stage information must then be related somehow to storage volume making this a much more a data-driven process.Burek et al. (2013) also developed a non-data-driven approach to reservoir routing which was implemented by Zajac et al. (2017).This approach is built into the LISFLOOD model.The Burek et al. (2013) model requires a number of assumptions about storage capacity limits and naturalized streamflow thresholds.For example, the minimum, normal, and maximum storage are assumed to be 0.1, 0.3, and 0.97, respectively.To maintain the objective of investigating parsimonious models, the approach by Burek et al. (2013) was not included in this evaluation.Döll et al. (2003) and Wisser et al. (2010) were presented non-data-driven methods to simulate reservoirs operation that can be considered as simple approaches.
The Wisser et al. (2010) method follows a simple, rule-based approach to define the reservoir outflow at each time step ( , ).The rule that Wisser et al. (2010) enact is that when the inflow at each model time step moves above and below long-term average inflow, the behavior of the reservoir release changes.De Vos (2015) suggested that this model is too simple to effectively model reservoir outflow.Döll et al. (2003) derived a natural lake reservoir routing scheme.Hence, this methodology is applicable to man-made reservoirs and natural water bodies.The Döll et al. (2003) methodology found genesis in the reservoir outflow model proposed by Meigh et al. (1999).Meigh et al. (1999) proposed a simple reservoir release methodology, which intended to mimic outflow at reservoirs from a theoretical rectangular weir.A more substantive version of the Meigh et al. (1999) method is formulated by Döll et al. (2003).Despite its simplicity, the Döll method demonstrated good performance compared to several other methods previously mentioned (De Vos, 2015).Compared to the aforementioned methods, Hanasaki et al. (2006) derived a demand driven approach to reservoir routing, which can be considered as complicated non-data-driven reservoir routing model.They distinguished between irrigation and non- De Vos (2015) also proposed a within-year/over-year reservoir routing method, which they considered a non-data-driven approach.Within-year reservoir operations are driven by yearly fill and release cycles and typically have a small storage capacity relative to their total annual demand.Thus, water accumulates during wet periods and decreases during dry periods.Over-year reservoir operation, on the other hand, is based on long-term, multi-year drawdowns.Over-year reservoirs have storage which is sufficiently large, relative to inflow, so that yearly cycles of water storage and release are not necessary (Adeloye and Montaseri, 2000;Vogel et al., 1999).De Vos (2015) compared his methodology to the Hanasaki et al (2006), Döll et al. (2003), andNeitsch et al. (2011).The De Vos (2015) over-year simulation assumes knowledge of the mean and standard deviation of reservoir storage and is still too data-driven for the purposes of this study.
The non-data driven reservoir routing methods developed by Döll et al. (2003) and Hanasaki et al. (2006), which will be referred to as Döll and Hanasaki methods, were considered in this research for several reasons.Both models require minimal input data to implement.They consider only reservoir inflow and storage volume, i.e. current, minimum, and maximum storage volume that can be estimated when detailed reservoir information is not available.Additionally, both models have been implemented in large-scale hydrologic models.The Döll method was used in the WaterGAP model and the application of the Hanasaki method was implemented in the TRIP model by the same authors.
The aim of this study is to assess non-data-driven reservoir routing methods for use in hydrologic forecasting schemes applicable across the global domain.The Döll and Hanasaki methods were found to be sufficiently parsimonious for wide-scale implementation.The following research questions are addressed with respect to the two approaches: (1) How well do the chosen reservoir routing models improve outflow estimates relative to simulation of naturalized flow (i.e.neglecting dams altogether)?(2) How do reservoir routing coefficients affect model performance?(3) How does the time step affect model performance and stability?This is a critical point for the current regionalto continental-scale forecasting schemes that operate at daily, or sub-daily, time steps.( 4

Simulation Specifications
The storage ratio (Vogel et al., 1999) or Impoundment Ratio (impoundment ratio) is an important metric in previous work generalizing reservoir operation by De Vos (2015) and Hanasaki et al., (2006).The impoundment ratio is described as follows:  = (  −  )  _  * 86400 * 365 (1) where   and   are the maximum and minimum volumes of the reservoir's active storage, and  _  is the mean annual inflow to the reservoir.
A higher impoundment ratio indicates that the capacity of the reservoir is large relative to mean inflows, while the opposite is true of low IR values.De Vos (2015) considered IR values greater than unity "large" reservoirs, as they are capable of storing the average yearly volume of water flowing into them.To utilize the Hanasaki method, the release coefficient (  ) needs to be determined.
where S begin is the storage at the beginning of the each year and  is a dimensionless coefficient, which was set to 0.85 in the Hanasaki et al. (2006) study.In the current study, the  parameter was varied from 0.45-0.95by increments of 0.10 and solve   for each  value.
Outflow is the quantity of most interest for hydrologic forecasting.The Hanasaki Method relates outflow based on the incoming flow.In this study, only the non-irrigation methodology from the Hanasaki Method was used to simulate reservoir outflow at each time step ( , ) since one cannot assume seasonal irrigation demands will be known globally.Further, the primary of selected reservoirs is not irrigation.Hanasaki estimates outflow as follows: ) where  , is the inflow at time t and   is the release coefficient which is calculated based on Equation 2. The 0.5 threshold value for IR is an empirical condition derived by Hanasaki et al. (2006).
Unlike Hanasaki method, the Döll method relates outflow (  , ) to current available storage capacity of the reservoir: (4) Where Döll empirically derives the release coefficient,   = 0.01, Δ is the simulation time step (s), and   is the current volume of storage at time "t".For analysis of the Döll methodology,   was varied at values of 0.01, 0.02, 0.04, 0.06, 0.08, 0.10, 0.20, 0.40, 0.50, 0.60, 0.70, 0.80, and 0.90 in this study.The results for the sensitivity analysis are discussed in the section 3.3.
The sensitivity analysis can provide useful information on how coefficients may vary based on geographical and reservoir characteristics such as the impoundment ratio.
The two methods were evaluated and results compared to actual outflow records provided by the USACE Districts.Two approaches were used to evaluate model performances: hydrograph assessment of daily and monthly reservoir outflow and statistical evaluation.the statistical evaluation was performed for daily and monthly averaged simulated results vs. observations using the Kling-Gupta efficiency (KGE, Gupta et al., 2009), coefficient of determination (R-Squared), and root mean square error (RMSE).The KGE value ranges from negative infinity to one.Four levels of performance were defined for KGE in this study (Tavakoly et al., 2017): poor performance (KGE < 0), acceptable (0 < KGE < 0.4), good (0.4 < KGE < 0.7), and very good (0.7 < KGE).Goodness-of-fit values were evaluated to compare simulated discharge to the actual outflow records provided by the USACE Districts.These are indicators of how well the models perform.The same goodness-of-fit values are calculated to compare actual discharge with observed inflow to assess baseline performance.The baseline condition represents the treatment of reservoir outflow as naturalized, altogether neglecting reservoir operations.Thus, the baseline condition is that inflow into the reservoir equals outflow from the reservoir.To be viable, the reservoir routing scheme should improve results over the baseline condition in virtually all cases.

Study Area
The model tests and evaluation were conducted on 60 reservoirs in the United States maintained by the U.S. Army Corps of Engineers (USACE).Figure 1 illustrates reservoirs used in this study.The primary purpose of 43 of the reservoirs are flood control, six are hydroelectric, four are recreation, three are water supply, two are classified as other, one is irrigation, and one is a fish and wildlife pond.Table 1 describes pertinent characteristics of each reservoir in this analysis.The goodness-of-fit metrics were calculated for each reservoir in the study.240 Observed inflow is compared with observed outflow to establish a benchmark used to show 241 whether implementing the two non-data driven reservoir routing schemes improves 242 reservoirs and tends to preserve high KGE values at locations where the baseline is already 265 good or very good estimator of outflow.Figure 3a illustrates the wide range of reservoir 266 operating conditions present in the study.The reservoir dataset contains reservoirs in which 267 the outflow correlates poorly with the inflow regime as others that correlates well.Figure 268 3a also portrays significant geographic clustering where reservoirs in certain regions tend 269 to be less correlated with inflow and other clusters where observed inflow and observed outflow correlate strongly.This could indicate that operations at these reservoirs may have a particularly regional context and may bias towards a particular reservoir routing scheme.
However, it can be seen that correlation between observed inflow and observed outflow and geographic proximity of the reservoirs do not influence the implementation of either the Döll or Hanasaki method.Thus, the results of this research indicate no significant geographic constraints in the context of this study.that the   = 0.01 is not necessarily the optimum coefficient to maximize model performance.

Sensitivity Analysis of Models
Investigating the linkage between dam characteristics and the best performing   yields no clear relationship.Evaluation of correlation between impoundment ratio, coefficient of variation of inflow, ratio of average inflow to average outflow, and geographic location shows low correlation between each variable and best performing   value.However, the range of best performing   within this analysis and as demonstrated in Figure 5 suggests that the value is not constant across all reservoirs.Thus, as one implements the Döll Method within their hydrologic modeling framework,   may be adjusted when comparing streamflow estimates to gage observations, like those curated by the Global Runoff Data Centre (GRDC, 2017).

Dam Systems and Reservoir Routing
Reservoirs in the Vicksburg and Omaha districts were selected to evaluate performance of the Döll Method in complex drainage systems.Although these reservoirs are not directly connected, the reservoir operators coordinate in order to minimize flooding in the Louisiana Delta regions near the mouth of the Mississippi River.The operation of these reservoirs presents an interesting case in which the non-date driven models in this study do not characterize the nature of the dam releases well.The modeled results at four Vicksburg District dams yield only minimal improvement over unregulated (i.e.naturalized) flow at these reservoirs.The decrease in reservoir routing performance can be attributed to the large impoundment ratios at these dams indicating the reservoir storage is large relative to annual volume of inflow.
The reservoirs of interest in the Vicksburg District include Arkabutla, Sardis, Enid, and Grenada.These dams function in parallel on tributaries of the lower Mississippi River, namely the Coldwater River, Little Tallahatchie River, Yocona River, and Yalobusha River, respectively.Together, these dams control flooding in northern Mississippi as part of the Yazoo Basin Headwaters Project (USACE, 2017;USACE, 1987).The Yazoo Basin reservoirs discharge directly into the heavily regulated Mississippi River (Meade and Moody, 2010).The reservoirs operate to ensure high releases are not concurrent with large flows upstream on the Mississippi to avoid devastating flooding to the low-lying Louisiana delta regions.This requires a high level of coordination throughout the Yazoo Basin Headwater Project and with regulation upstream on the Mississippi.Additionally, each of the Yazoo Basin reservoirs have a substantial impoundment ratio, ranging from 2.96-3.95.
In other words, the reservoirs are capable of containing large volumes of water to mitigate downstream impacts.Thus, current pool levels and forecasted inflow at these four reservoirs do not substantially influence release decisions.The reservoirs also have the capacity to absorb large flood events.As a result, they do not seem follow the same functional form as other dams in this study.
Figure 6 from Sardis Dam in the Yazoo Basin Headwaters Project demonstrates the hydrograph comparing observed inflow and outflow and the modeled outflow that provides the highest KGE (Döll method, krd=0.90)for the year 2008.Figure 6 demonstrates that peak outflows do not tend to correspond to the time at which peak inflow occurs.In fact, release rates at Sardis Dam are at a minimum during the peak inflow time period.This pattern repeats at each of the reservoirs in the Yazoo Basin Headwaters Project indicating that inflow and consumed storage are not substantial predictors of outflow timing at these reservoirs.This exemplifies the lack of correlation between observed inflow and observed 346 outflow at reservoirs within the Yazoo Basin Headwaters Project.347 348 Dams operating in series represent a specific case where compounding model error 349 is a particular concern.USACE operates several large dams in series on the Missouri River.350 These include Fort Peck, Garrison, Oahe, Big Bend, Fort Randall, and Gavins Point within 351 in the Omaha District (Lund and Ferreira, 1996).For this cascading system on the Missouri 352 River, inflow appears to be a progressively stronger predictor of outflow from upstream to 353 down.At the upstream end inflow yielded a KGE=0.43 at Fork Peck with a KGE=0.99 354 downstream at Gavins Point Dam. Figure 7   However, the differences are almost trivial considering how well inflow alone performed in this case.The Döll method is particularly accurate during peak inflow conditions, for example the large hydrologic event in mid-2011 at Gavins Point Dam in Figure 7.The performance of non-data driven approaches in this instance is promising since compounding errors are a large concern in this type of system.Other instances involving dams in series should be evaluated to find out if these findings hold more generally.
The reservoir management is unique in both the Yazoo Basin Headwaters Project and the Missouri River.The operators of dams within the Yazoo Basin Headwaters Project tend to regulate outflow in a manner that is more in line with downstream conditions.The attention to downstream conditions is due mainly to the impact that downstream floods will have on the low-lying communities within the Louisiana Delta.The dams in the Yazoo Basin Headwaters Project have among the highest impoundment ratios, which inherently reduces the influence of upstream conditions in discharge decisions.The non-data driven approaches evaluated here do not account for downstream conditions and thus do not perform well in this instance, particularly where large impoundment ratios allow operators considerable leeway.
On the other hand, the non-data driven approaches tend to perform well when inflow conditions dictate discharge decisions as we see on the Missouri River system.
Reservoirs with smaller impoundment ratios are naturally more responsive to inflow requiring greater consideration for upstream conditions.The Döll Method showed relatively small improvement of outflow estimates compared to inflow as a predictor of outflow in the Yazoo Basin Reservoirs, while the method provided reasonable estimates in dam systems like the Missouri River system.Therefore, it can be inferred that the Döll method is more applicable for dam systems where reservoir management focuses on upstream hydrologic conditions, while large impoundment ratios may be indicative of reservoirs where downstream conditions are more likely to prevail.This would likely apply for the Hanasaki Method as well since that method links outflow more directly.Results for wet years and dry years appear to be fairly mixed.Indications are that the performance of the Döll Method could be somewhat site specific.However, reservoirs that tend to be less responsive to storage fluctuations are not represented well in the Döll Method since storage fluctuations drive the model.Arcadia Lake has an IR of about 4.75 which is relatively high.Union City Dam has an IR of about 0.24, which is relatively low.

Wet and Dry Year Comparison
IR is a good indicator of reservoir responsiveness to storage fluctuations.A lack of reservoir responsiveness to storage fluctuations could result in two different types of error when the Döll Method is implemented within a large-spatial-scale hydrologic model.First, forecasted outflow could easily mistime a hydrologic event, particularly during wet years, as Figure 8b demonstrates.Second, the authors anticipate that if the storage does not dramatically fluctuate during a dry year the estimated reservoir release likely will not anticipate sporadic releases for irrigation and other purposeful discharges.Unaccounted for, these large but short duration releases may lead to a consistent overestimation of reservoir outflow for the entire dry year period.2  431 illustrates the results at Fort Peck, Garrison Dam, Oahe Dam, and Fort Randall Dam, each 432 of which appears in the Hanasaki et al. (2006) study and this research.Table 2

also contains 433
Sardis Dam, Mosquito Creek Dam, and Prado Dam, which are not included in Hanasaki et 434 al. (2006).Results illustrate that the time scale can influence simulation results.The 435 monthly comparison amongst Fort Peck, Garrison, Oahe, and Fort Randall is in agreement 436 with the conclusions of Hanasaki et al. (2006).However, when the simulation time step 437 changes to a daily time step, the skill of Hanasaki Method and the Döll method reverse and 438 the Döll method tends to outperform the Hanasaki Method.In additional reservoirs (Sardis 439 The time-scale effect upon model performance may relate to how well observed inflow correlates with observed outflow.Examining Table 2, Hanasaki Method outperforms the Döll Method when observed inflow and observed outflow are relatively well correlated.The effect is nullified when the inverse is true.The Hanasaki Method estimates outflow as a ratio of inflow, which may be a better estimate of outflow at the monthly time scale, particularly when discharge tracks closely with inflow.However, the Hanasaki Method will fluctuate at the smaller time steps due to inherent variations in inflow.The Döll Method tends to vary less at a daily time step and may be a better estimate of outflow at sub-monthly time steps. The hydrographs from Fort Randall Dam further illustrate the relationships between time step and model skill, particularly during high flow events.Daily and monthly comparisons between observation and simulations for Fort Randall Dam are shown in Figure 9.This figure compares the daily and monthly simulations with observations.Figure 9a shows that the Hanasaki simulations perform better than the Döll Method for monthly time steps, particularly during the high inflow events in 2011.The Döll method tends to overestimate reservoir outflow, while the Hanasaki Method correlates well with inflow and better matches the peak flow of 2011.At a diurnal time step (Figure 9b), the Hanasaki Method tends to be hypersensitive to inflow variations and overestimates outflow, whereas the Döll method provides a better approximation of outflow during the 2011 high flow event.
It is possible that the conclusions of Hanasaki et al. (2006) suggesting better 464 performance of the Hanasaki Method at the monthly-scale depend on how closely 465 discharge from the dam tracks inflow.The Döll method may be a better candidate for 466 integration into daily flow forecasting models.467 (5) 491 This condition prevents the reservoir from falling below the minimum storage.Outflow 492 from Old Hickory Dam was re-simulated with   = 0.9 and the new minimum storage 493 condition (Equation 5).The proposed modification resulted in simulated outflow shown in 494 Figure 10.Outflow is substantially overestimated for one-time step and drops to zero at the 495 next time step.While an oversimplification of actual operations, this condition is similar 496 to an emergency spillway discharge to prevent overtopping.The dam releases tremendous 497 flow for a brief period, when the maximum storage is nearly exceeded and then inhibits the 498 discharge when the storage is at the minimum capacity.The benefit of this modification is 499 that additional reservoir information is not required.However, further testing and 500 evaluation should be performed to validate this refinement.501

Limitations 503
This study is limited to models that require only reservoir inflow and storage, 504 primarily to provide insight into the reliability of these measures as indicators of reservoir 505 outflow.The inclusion of additional demand and evapotranspiration parameters could 506 improve the results, but could also add considerable uncertainty.Of the two models, only 507 Hanasaki et al. (2006) currently includes an estimate for withdrawals of any nature.508 Another limitation of this study is the inflow that drives the simulations.All inflow 509 utilized in this study, except for the Nashville district, is back-calculated from observed 510 changes in storage and known discharges.This indirect method can lead to negative inflow 511 values when losses due to seepage, evapotranspiration, or other types of withdrawals are 512

Future Work
The non-data driven approaches evaluated consistently improved simulated streamflow estimates over naturalized flow conditions suggesting these approaches can potentially improve global streamflow forecasting.The Döll Method performed particularly well at daily time steps commensurate with many large-scale stream routing models.The incorporation of the Döll Method into to the RAPID code, a large-scale river routing model for simulating streamflow throughout distributed stream networks over large spatial extents (David et al., 2011), is under development.This will enable widespread testing and evaluation over large hydrologically diverse areas.
Reservoir routing schemes could be enhanced by assimilating remotely sensed data, e.g.near real-time changes in storage resolved from satellite altimetry, and eventually the planned NASA Surface Water and Ocean Topography (SWOT) Mission.This information could constrain reservoir simulations to improve global streamflow forecasts (Yoon and Beighley, 2015).These simulations could provide the training data necessary for more data intensive reservoir routing approaches, e.g.applying Artificial Intelligence and Machine Learning techniques to infer reservoir rule curves.Eventually, global streamflow forecasting models should leverage all available data to account for anthropogenic influence, utilizing techniques that range from simple to extremely complex.

Conclusions
This research compares two parsimonious reservoir routing methods that have previously been implemented in large-scale hydrologic modeling applications, namely the  There is a significant relationship between reservoir IR and two of the skill metrics applied (KGE and R-Squared).Given that reservoirs with high IR typically are less responsive to short-term fluctuations in inflow and storage, the correlation between these variables is plausible.Further investigation of dam characteristics, such as if the dams operate in series or in parallel and wet and dry year considerations are further evidence of the correlation between the IR and Döll and Hanasaki Methods. The best value for the empirical Döll coefficient,   , can vary.Optimal values were typically greater than the krd=0.01value which Döll et al. (2003) derived.This suggests that   could be a potential calibration parameter within a large-scale hydrologic modeling framework much like a weir coefficient, which is specific to a particular type of weir.
 The Yazoo Basin Headwaters Project (USACE, 2017;USACE, 1987) is an interesting case study in how reservoir system complexity can be difficult to model.
The Yazoo Basin Headwaters Project considers downstream flow conditions as the dominant criteria in dam operation.Thus, the inflow and available storage volume are poor predictors for determining reservoir discharge in this type of management scheme.The Döll Method appeared to scale flow correctly at these reservoirs and improve reservoir overall skill, but timing of the releases well represented and thus skill improvement is only minimal.
 Dam discharges in the Missouri River Reservoir System (Lund and Ferreira, 1996) are more correlated with storage volume and inflow conditions, which lends itself to the two non-data-driven approaches evaluated here.The Döll Method is particularly capable of accurately modeling reservoir outflows in reservoir systems that correlate well with storage and inflow fluctuations.Concerns related to model error being compounded through a series dams may be mitigated somewhat by the fact that inflow appears to be a progressively stronger predictor of outflow further downstream in these types of systems.
 Numerical stability of the Döll Method is a concern, particularly with higher   values.These stability concerns originate at reservoirs with small active storage https://doi.org/10.5194/hess-2019-264Preprint.Discussion started: 4 July 2019 c Author(s) 2019.CC BY 4.0 License.
https://doi.org/10.5194/hess-2019-264Preprint.Discussion started: 4 July 2019 c Author(s) 2019.CC BY 4.0 License.irrigationreservoirs and offered two distinct algorithms for each.Water demands for irrigation, domestic, and industrial uses are considered in the irrigation reservoirs, whereas the releases from non-irrigation reservoirs are simply a ratio of inflow.

)
How sensitive are the reservoir routing schemes to various real-world dam operations and climate variability?To achieve research objectives of the study, reservoir data including daily inflow and outflow from 2006-2012, for 60 USACE reservoirs were used to evaluate the reservoir routing schemes.The data were obtained from nine USACE districts: Pittsburg, Nashville, St. Paul, Rock Island, Omaha, Tulsa, Sacramento, Los Angeles, and Vicksburg.The selected dams are representative of a wide range of reservoir sizes, flow regimes, and climatologic settings.The results of this analysis will benefit readers in determining if the reservoir routing models implemented within existing large-scale hydrologic models adequately represent reservoir effects.https://doi.org/10.5194/hess-2019-264Preprint.Discussion started: 4 July 2019 c Author(s) 2019.CC BY 4.0 License.

Figure 1 .
Figure 1.USACE districts and location of reservoirs in this study.

Figure 3
Figure 3 is a geographic representation of the KGE values from the baseline 261 scenario as well as the two routing models for each reservoir.In general, the Döll Method 262 outperforms the baseline and Hanasaki Method, particularly in the Tulsa and Pittsburg 263 Districts.Furthermore, the Döll Method tends to improve KGE values at nearly all 264

Figure 2 .
Figure 2. Scatter plots of skill metrics between the use of daily observed inflow as outflow (Baseline) and simulated outflow.The dashed line indicates the plane separating increased and decreased skill that results from using either reservoir routing method.

Figure 3 .
Figure 3. Spatial distribution of KGE comparing observed daily outflow to the each estimate of outflow: a) observed inflow b) Döll Method simulated outflow, c) Hanasaki Method simulated outflow for all reservoirs in this study.KGE values for the Döll Method and the Hanasaki Method are the maximum KGE from all coefficient treatments.

Figure 4 .
Figure 4. Comparison of IR and KGE from goodness of fit metrics.

291
Figure 5. Bar charts of   values that maximize KGE and correlation and minimize nRMSE.
provides a comparison of observed inflow and 355 outflow along with simulated outflow for Gavins Point Dam.The Döll method tends to 356

Figure 7 .
Figure 7. Hydrographs of observed inflow and outflow versus simulated outflow with the highest KGE value at Gavins Point Dam (Döll method kr=0.04).KGE comparing observed Inflow and outflow = 0.99; KGE comparing simulated and observed outflows= 0.99.

Figure 8
Figure 8 shows results for wet and dry years at two reservoirs considered to be representative of this study.The Döll Method provides a relatively good estimate of outflow at Union City Dam (Pittsburg District) in Figure 8a and Figure 8c.It performs

Figure 8 .
Figure 8. Two reservoirs where the Döll Method tends to perform very good and poor: outflow: a) wet year Union City Dam 2011; b) wet year Arcadia Lake 2007; c) dry year Union City Dam 2012; and d) dry year Arcadia Lake 2006.
Lake, Representative Dry Year (2006) and Prado), the results indicate that the Döll method outperformed the Hanasaki Method at both daily and monthly time steps, based upon KGE.However, the results at Mosquito Creek reservoir tend to follow the original Hanasaki et al. (2006) results.

Figure 9 .
Figure 9.Comparison of simulated outflow for the Fort Randall Dam with Hanasaki and Döll methods for (a) monthly and (b) daily time steps

Figure 10 .
Figure 10.Outflow simulation for the Old Hickory Dam using the proposed modification of the Doll method for krd=0.4.
Döll and Hanasaki Methods.These methods were compared across 60 USACE operated reservoirs at a daily time step.Results show that the Döll Method tends to outperform the Hanasaki Method at a daily time step.An in depth examination of these results yields the following conclusions. The complexity and data requirements of both Döll and Hanasaki Methods are low and thus computationally inexpensive.Both can be feasibly implemented at large spatial scales at a daily or sub-daily time step.


schemes.At overlapping locations, this study replicates the results reported by Hanasaki et al. for monthly time steps.However, the Hamasaki et al. findings do not hold for a daily time step.
capacity during high inflow events.Additional model refinement can overcome 579 these stability concerns.580  The Döll Method showed minimal bias during relatively wet and dry years.Timing 581 of releases can be influenced by wet years and the magnitude appears to be affected 582 during dry years.The Döll Method appears to be most applicable for dam systems 583 where reservoir management focuses on upstream hydrologic conditions.Large 584 impoundment ratios could indicate reservoirs where downstream conditions are 585 more likely to influence release decisions at the reservoir.586 587 https://doi.org/10.5194/hess-2019-264Preprint.Discussion started: 4 July 2019 c Author(s) 2019.CC BY 4.0 License.

Table 1 .
Select statistical characteristics of reservoirs analyzed in this study.

Table 2 .
Comparison of daily and monthly KGE values at selected reservoirs.The α and krd values represent the highest KGE values for Hanasaki and Döll methods respectively.