A Model for Assessing the Importance of Runoff Forecasts in Periodic Climate on Hydropower Production

Round 1

Reviewer 1 Report

The comments are presented in the attached file.

Comments for author File: Comments.pdf

Author Response

1. Make the title simpler

The title has been modified to ‘A model for assessing the importance of runoff forecasts in periodic climate on hydropower production’.

2. Keywords should not be in the title

The Keywords have been edited: ensemble forecasting; biennial periodic climate; hydropower optimization; hydropower management; production efficiency; forecasting error.

3. Add innovation

The innovation has been added in the paper line number 89-95. The context is as below.

The innovations of this study comprise the following aspects a) the model framework that facilitates investigation of the impact of forecasting periodic climate on hydropower operations; b) an ensemble forecasting method based on classification of dry and wet 12-month periods in historical records; c) the assessment model is implemented in a MATLAB environment, including stochastic forecasting and applied to a cascade hydropower system.

4. This reference is not based on format

The reference format has been edited. See paper line number 185-188.

5. This figure have low resolution. Please correct.

The high-resolution version can be found in a separate pdf document. I have uploaded all high–resolution figures separately.

6. There is no discussion in this version. You should discuss the results

The conclusions section includes the discussion of the results. Section 5 has modified the title to Conclusions and Discussions.

7. This section should be re-written. The authors should be guided by components of a good discussion and conclusion remarks.

• Interpretation of the results: What do the results imply in the context of your study;
• Implication: why do the results matter to the problem being addressed;
• Limitations: what can’t the results tell us; based on the methods, data etc
• Recommendation: what practical actions or scientific studies should follow?

Ok, we have rescheduled section 5. Paragraphs one and two of section 5 provide the interpretation of the results and their implications based on the results of sections 4.1 and 4.2, respectively. And the limitations are addressed in the following paragraph. The last paragraph describes the possibilities that this study can support hydropower operations.

Reviewer 2 Report

Line 14: Quasi-linear is wrong here. See my comment on line 147.

Line 58: Usually, for dam operators most important is to have less flood damage and a high level of dam safety. Does this apply here, too?

Line 83: The word “simulate” in brackets is unclear. Do you intend to simulate the importance?

Line 99 ff: This seems to be text from the template. Deleatur.

Line 117: “Optimizing reservoir levels and water spillage” reads imprecisely. Usually, the optimization addresses a control variable, the reservoir release. Water levels and spillage are results (states) and the release is adjusted such that the objectives are met in the best way. Optimization of water spillage sounds a bit paradox, because spill is in principle undesired at all times. And with optimal water levels and spillage, there is not yet hydropower. The release through the turbines is the key. Consider to write: “minimize spillage” or “optimize reservoir operation” or “reservoir release such that the storage in the reservoir is used in an optimal way and no water is spilled”. By the way: Optimization of water spillage can be also an optimization task. In the Federal Columbia River Power System (Schwanenberg et al. 2015) there are environmental obligations of “fish spill”: a certain portion of water must not go through the turbines, but through the spillway to allow downstream migration of fish. If this type of spill optimization applies for your case, it needs additional description.

Line 133: Consider writing “carried out for each forecast” instead of “repeated N times”. The repetition can be misleading, because a repetition implies that only the last repetition is used (“repeat until it works well”).

Figure 1: This figure should be carefully revised. There are standards how to design a flow chart (parallelogram for conditions, rectangular for actions, and there is also a shape for data etc.). Now it looks as if “Optimized decisions of qT, qS, power, profit for time period tu” flows into the “Forecasted sceanario of runoff”, and we need a forecasting error to carry out a Simulated scenario of real runoff.

Line 147: “Quasi-linear” must be “quasi nonlinear” or better “linear”. “Quasi” is Latin and means “as it were” or “almost”. So “Quasi-linear” means “almost linear but non-linear”. The reader is left with the impression that you approximate a linear process with a nonlinear equation. This makes no sense in an optimization context, because linear optimization problems can be solved easier than nonlinear optimization problems. If I am not mistaken, you just do the opposite: a linear equation is used to simplify a nonlinear equation.

Line 149: t_u is defined as simulation period for the system updating, so it should be TH here, according to Figure 1. You don’t use the optimization model for the update, right? I think it is worth to mention that the simulation model does not need the assumption of a constant head.

Line 149: The statement “is acceptable when t_u is sufficiently short” needs more support. It is quite common to hold the head constant in reservoir optimization constant. But what is short? I would rather say that the assumption for a constant head works better for a long optimization period (100 years of climate change scenario with monthly time steps), and that the variation should not be too big. More important is the size of the reservoir: The assumption works for large reservoirs, but not for small reservoirs where a change in release changes the head very quickly. And instead of the water level in the reservoir it should be the head (head difference between reservoir level and tailwater level). Both vary.

Line 157: “Linear optimization programming with receding horizon control” looks a bit odd to me. Receding horizon control needs no optimization, it can be done with a simulation model, too. The modelling – either simulation, or optimization, or both – is part of the receding horizon control. Consider turning it around: “Receding horizon control with linear optimization”.

Line 162: “Ensemble forecasting is one of the statistical methods …” I would not categorize ensemble forecasting as a statistical method. It is rather a method to address forecast uncertainty. And statistical methods (stochastical methods, to be more precise) can be used to generate ensemble forecasts. See Cloke & Pappenberger (2009).

Line 180: “… affects the management of the cascade hydropower system”: This expression implies that the forecasted runoff actually effects the operations of the cascade. Do you mean “improve the management of the cascade”? If you are interested how a forecast affects the management of the cascade, interviewing the operators or analysis of historic data would be an appropriate method, but not optimization of some synthetic forecasts.

Figure 2: Add a third line that shows the average of all years.

This is an interesting hydrograph, it looks as if there is hardly any seasonal variation. It would be interesting to learn a bit more on the reservoir cascade. In most areas of the world, reservoirs must balance the water supply between dry (summer) and wet season (winter). Not here, apparently. Maybe worth to mention that the dams are mainly there to create head rather than to store water.

Note that the Dalälven case has not been introduced yet. Consider moving this section to the case study.

Line 190: I don’t understand this sentence.

Line 216: Replace “ensembles” with “ensemble members”.

Line 218: Why is TH shorter than the classified segments? How long is TH?

Line 225: Replace “quasi-linear” with “linear”. See comment on line 147. It is a linear optimization problem, isn’t it?

Line 239: How can you update after each time step tu? Are you optimizing for one time step only?

Line 241: What is “this period”? Can you make a picture that explains the different time horizons? The simulation period, the optimization period, the forecasting period, and the corresponding time steps.

Line 233, Equation 1: Is A constant for all time steps? This is quite a severe assumption and requires far more consideration.

Line 247: n is not a time step index, it is an index that indicates a forecast ensemble member.

Line 248: What is the time step length of k?

Line 265, Equation 3: V = A * h is a linear relationship between V and h, this very inaccurate assumption for a real reservoir. This should be explained and verified. Typically, lookup tables or polynominal functions that relate V and h are used.

Line 265, Equation 4: Use constraints on V instead of h, because h introduces nonlinearity to the optimization problem (see above).

Line 265, Equation 2: qr denotes a product of q and r (q times r). Variables must have one letter, not more. Put r into the index.

Line 285-287: The downstream water demand can be satisfied with turbine flow, too. Instead of a lower limitation of spillage discharge set a minimum flow to Q_out = Q_turbine + Q_spill. If there is a minimum spill flow requirement this should be explained, because spill is usually undesired at all times. I reckon that the upper limitation will account for the spillway capacity rather than an environmental requirement. Is there no maximum discharge for flood protection?

Line 290: Equation (1) is not a quadratic equation. It is important to highlight that the equation contains the product of two optimization variables. This makes the optimization problem nonlinear. A product of variables alone not necessarily makes a nonlinear optimization problem as long only one optimization variable is involved.

Line 296: The optimization period TH is 90 days and tu is 2 days according to Table 1. How can you update within the optimization for each tu? The optimization uses a constant head, but this must apply for the whole period of TH, otherwise it would be a nonlinear problem according to line 290. But in line 157 you classify the optimization problem as linear. This must be explained.

I stopped my review here, following instructions from the editors.

References

Cloke, H. L.; Pappenberger, F. (2009): Ensemble flood forecasting: A review. Journal of Hydrology Vol. 375 (2009) No. 3 pp. 613–626. DOI: 10.1016/j.jhydrol.2009.06.005.

Schwanenberg, D.; Becker, B. P. J.; Xu, M. (2015): The Open RTC-Tools Software framework for Modeling Real-Time Control in Water Resources Systems. Journal of Hydroinformatics Vol. 17 (2015) No. 1 pp. 130–148. DOI: 10.2166/hydro.2014.046.

Author Response

Line 14: Quasi-linear is wrong here. See my comment on line 147.

See comment response on line 147.

Line 58: Usually, for dam operators most important is to have less flood damage and a high level of dam safety. Does this apply here, too?

The management operations involve different constraints, such as maximum and lowest reservoir levels as well as minimum discharge. However, in the application to Dalälven River basin there is no consideration of multiple objectives involving flood protection.

Line 83: The word “simulate” in brackets is unclear. Do you intend to simulate the importance?

“Simulate” here refers to the fact that the procedure simulates a difference between the forecast of future runoff and the actual future runoff scenario. Such a deviation between the weather forecast and the actual result is rarely considered in research models and which is what prevents investigations of the importance of forecast accuracy on operational efficiency. Here we solve this problem by generating stochastic forecasts and real scenarios of runoff.

Line 99 ff: This seems to be text from the template. Deleatur.

Ok. It has been deleted.

Line 117: “Optimizing reservoir levels and water spillage” reads imprecisely. Usually, the optimization addresses a control variable, the reservoir release. Water levels and spillage are results (states) and the release is adjusted such that the objectives are met in the best way. Optimization of water spillage sounds a bit paradox, because the spill is in principle undesired at all times. And with optimal water levels and spillage, there is not yet hydropower. The release through the turbines is the key. Consider to write: “minimize spillage” or “optimize reservoir operation” or “reservoir release such that the storage in the reservoir is used in an optimal way and no water is spilled”. By the way: Optimization of water spillage can be also an optimization task. In the Federal Columbia River Power System (Schwanenberg et al. 2015) there are environmental obligations of “fish spill”: a certain portion of water must not go through the turbines, but through the spillway to allow downstream migration of fish. If this type of spill optimization applies for your case, it needs additional description.

We agree that ‘water spillage’ is unclear on Line 117, since it includes both water turbine discharge and spillway flow.

In this paper, hydropower planning model optimizes three variables (states): water level, turbine discharge, and spillage. The primary aims behind maximize the energy in the reservoirs are maximizing water level and turbine discharge, and minimizing the spillage. The ‘fish spill’ and water demand have been considered in the optimization model by setting the lower boundary of the water spillage, which ensures the water requirement from agriculture, industry, and cities. The detailed optimization statement is described in section 2.2.

Line 133: Consider writing “carried out for each forecast” instead of “repeated N times”. The repetition can be misleading, because a repetition implies that only the last repetition is used (“repeat until it works well”).

Ok! Have edited this sentence.

Figure 1: This figure should be carefully revised. There are standards how to design a flow chart (parallelogram for conditions, rectangular for actions, and there is also a shape for data etc.). Now it looks as if “Optimized decisions of q_T, q_S, power, profit for time period t_u” flows into the “Forecasted sceanario of runoff”, and we need a forecasting error to carry out a Simulated scenario of real runoff.

A completely new figure is proposed that follows the ISO 9001 standard and which also makes more clear how different time variables appear in the simulation scheme; The time horizon of forecasts (T_H), the updating period (t_u) and the simulation period (T_sim).

Line 147: “Quasi-linear” must be “quasi nonlinear” or better “linear”. “Quasi” is Latin and means “as it were” or “almost”. So “Quasi-linear” means “almost linear but non-linear”. The reader is left with the impression that you approximate a linear process with a nonlinear equation. This makes no sense in an optimization context, because linear optimization problems can be solved easier than nonlinear optimization problems. If I am not mistaken, you just do the opposite: a linear equation is used to simplify a nonlinear equation.

Stepwise linear might be more specific here. The optimization problem is solved for the constant reservoir head and the optimal decisions are applied for a limited updating period, but for the next updating period the head is generally different from that of the last step. Hence, one interpretation of “Quasi-linear” is that this is almost linear, but the word might be unclear. We have modified it to “stepwise linear” followed by some explanations.

Line 149: t_u is defined as simulation period for the system updating, so it should be TH here, according to Figure 1. You don’t use the optimization model for the update, right? I think it is worth to mention that the simulation model does not need the assumption of a constant head.

The reason why the t_u is applied as the system updating period is that we implement the receding horizon approach in the optimization planning model. It allows the optimization to be carried out on time horizon T_H, but apply decisions of turbine discharge and spillage only for the updating period t_u in combination with (simulated) real runoff and then move forward in the simulation period with the updated system.

Line 149: The statement “is acceptable when t_u is sufficiently short” needs more support. It is quite common to hold the head constant in reservoir optimization constant. But what is short? I would rather say that the assumption for a constant head works better for a long optimization period (100 years of climate change scenario with monthly time steps), and that the variation should not be too big. More important is the size of the reservoir: The assumption works for large reservoirs, but not for small reservoirs where a change in release changes the head very quickly. And instead of the water level in the reservoir it should be the head (head difference between reservoir level and tailwater level). Both vary.

We agree that this statement is not clearly motivated. The constant head is assumed for the entire horizon of the optimization (T_H), but the outcome of the optimization is applied only for the updating time step. Hence, if the updating time-step is short the application of the simulation framework catches the variation of the water head. As mentioned above the assumption of a constant head works for large reservoirs with minor changes of head over the updating time-step, and also it is suitable to small run-of-the-river dams. Therefore, we make this simplified assumption, which introduces one source of error in the optimization in addition to forecasting. The latter has been pointed out in the revised discussion and conclusion section.

Ok, "water level" has been edited to water head.

Line 157: “Linear optimization programming with receding horizon control” looks a bit odd to me. Receding horizon control needs no optimization, it can be done with a simulation model, too. The modelling – either simulation, or optimization, or both – is part of the receding horizon control. Consider turning it around: “Receding horizon control with linear optimization”.

It can be “Linear optimization combined with receding horizon control”

Line 162: “Ensemble forecasting is one of the statistical methods …” I would not categorize ensemble forecasting as a statistical method. It is rather a method to address forecast uncertainty. And statistical methods (stochastical methods, to be more precise) can be used to generate ensemble forecasts. See Cloke & Pappenberger (2009).

Have been modified.

Line 180: “… affects the management of the cascade hydropower system”: This expression implies that the forecasted runoff actually effects the operations of the cascade. Do you mean “improve the management of the cascade”? If you are interested how a forecast affects the management of the cascade, interviewing the operators or analysis of historic data would be an appropriate method, but not optimization of some synthetic forecasts.

The sentence has been edited as “…, the suggested model investigates how improvements of the forecasted runoff with biennial periodicity can enhance the management of the cascade hydropower system.”.

Figure 2: Add a third line that shows the average of all years.

This is an interesting hydrograph, it looks as if there is hardly any seasonal variation. It would be interesting to learn a bit more on the reservoir cascade. In most areas of the world, reservoirs must balance the water supply between dry (summer) and wet season (winter). Not here, apparently. Maybe worth to mention that the dams are mainly there to create head rather than to store water.

The diagram shows daily averages not how the runoff varies over the year. The figure shows a systematic difference in yearly averages depending on odd vs. even years and start month of the averaging. This direct result indicating a biannual periodicity complements earlier studies that have shown such a periodicity using spectral decomposition.

Note that the Dalälven case has not been introduced yet. Consider moving this section to the case study.

Sure, Figure 2 has been moved to Results section. And a green line has been added as the average of all years.

Line 190: I don’t understand this sentence.

The sentence has been modified to “Previous studies have indicated a biennial periodicity in runoff by the use of spectral analysis [10], [11], which suggests, for example, that there could be dry and wet years. Such biennial periodicity should be possible to identify directly in runoff time series by assessing the yearly average using different start month and then classifying segments of runoff time-series in the categories odd and even years.”

Line 216: Replace “ensembles” with “ensemble members”.

Ok!

Line 218: Why is T_H shorter than the classified segments? How long is TH?

This model framework is implemented to the hydropower operations in Dalälven River basin (see section 4), in which the length of T_H is 3 months. Each classified wet segment or dry segment has a length of 12 months. The segment is used for a forecast along the time horizon T_H cannot be longer than one year. The numeric time-step is set as 0.5 days. It’s not possible to regulate one year’s operation with this high accuracy and for the demonstrative purpose, we think that a longer forecast horizon is not needed.

Line 225: Replace “quasi-linear” with “linear”. See comment on line 147. It is a linear optimization problem, isn’t it?

We have edited it, see the comment on line 147.

Line 239: How can you update after each time step tu? Are you optimizing for one time step only?

According to receding horizon method, the decisions are only kept for the first updating period (t_u) period after one optimization with horizon (T_H).  The meaning with this procedure is that the update is conducted after a simulation along the future horizon T_H, but decisions are implemented only for the short updating period (t_u). We have edited the text to make this clear.  

Line 241: What is “this period”? Can you make a picture that explains the different time horizons? The simulation period, the optimization period, the forecasting period, and the corresponding time steps.

We have made an application of this model framework and attached the parameters, definitions and the value of the parameters in the application. Please see Table 1, and Section 4. The updated Figure 1 also includes the most essential time variables.

Line 233, Equation 1: Is A constant for all time steps? This is quite a severe assumption and requires far more consideration.

Yes. Area is the mean area of a reservoir and is assumed as a constant in the application to the Dalälven River basin. However, it is not a limitation of the suggested model framework.  

Line 247: n is not a time step index, it is an index that indicates a forecast ensemble member.

We agree and it has been clarified.

Line 248: What is the time step length of k?

“k” has been defined in section 2, paragraph 2. And the length of K has been defined as 45 in the application, see section 4.

Line 265, Equation 3: V = A * h is a linear relationship between V and h, this very inaccurate assumption for a real reservoir. This should be explained and verified. Typically, lookup tables or polynominal functions that relate V and h are used.

This study aims to develop a model framework that can assess the importance of forecasts of periodic water availability for hydropower operations. In the application to River Dalälven, we assumed reservoirs volumes V= A*h, where data covers the reservoir mean area and it keeps this particular relationship linear for numerical simplicity. But the relationship between V and h can be changed in the future if important to specific applications.

Line 265, Equation 4: Use constraints on V instead of h, because h introduces nonlinearity to the optimization problem (see above).

The constraints in V and h are interchangeable through V = A h (or any other non-linear functional form). Hence, we would like to stress the nonlinearity of the parent optimization problem that was converted to a stepwise-linear problem.

Line 265, Equation 2: qr denotes a product of q and r (q times r). Variables must have one letter, not more. Put r into the index.

It is possible to use two letters, like in Reynolds number Re etc. However, we agree to use q_r instead of qr because many indexes are already subscripts, like i, j, n, k. To avoid confusion, we would like to keep all indexes as subscripts and two letters for variable q_r.

Line 285-287: The downstream water demand can be satisfied with turbine flow, too. Instead of a lower limitation of spillage discharge set a minimum flow to Q_out = Q_turbine + Q_spill. If there is a minimum spill flow requirement this should be explained, because spill is usually undesired at all times. I reckon that the upper limitation will account for the spillway capacity rather than an environmental requirement. Is there no maximum discharge for flood protection?

Yes, but this depends on the actual situation at the power plant. Often the spillage occurs in a separate river channel, whereas turbine flows come back to the river tens of kilometers further downstream. So in certain situation the spillage requirement could be set as Q_turbine + Q_spill > requirement 1, but in other situations it could be that Q_spill > requirement 2.

Line 290: Equation (1) is not a quadratic equation. It is important to highlight that the equation contains the product of two optimization variables. This makes the optimization problem nonlinear. A product of variables alone not necessarily makes a nonlinear optimization problem as long only one optimization variable is involved.

Ok. We agree. Has been edited.

Line 296: The optimization period TH is 90 days and t_u is 2 days according to Table 1. How can you update within the optimization for each t_u? The optimization uses a constant head, but this must apply for the whole period of T_H, otherwise it would be a nonlinear problem according to line 290. But in line 157 you classify the optimization problem as linear. This must be explained.

Yes, the optimization is conducted for a future horizon T_H and the constant head is applied for the whole period. Such optimization informs the user what decisions of turbine discharge and spillage are optimal for the coming short-term updating time step t_u as well as for the entire horizon. However, the information about the optimal turbine and spillage discharges are only applied to t_u. At that time, the actual runoff did not follow the forecast exactly and, hence, the users realize that the forecast should be updated for another future horizon (now extending from t = t₀ + t_u to t = t_u + T_H). Another optimization is conducted and another set of decisions is taken.

I stopped my review here, following instructions from the editors.

References

Cloke, H. L.; Pappenberger, F. (2009): Ensemble flood forecasting: A review. Journal of Hydrology Vol. 375 (2009) No. 3 pp. 613–626. DOI: 10.1016/j.jhydrol.2009.06.005.

Schwanenberg, D.; Becker, B. P. J.; Xu, M. (2015): The Open RTC-Tools Software framework for Modeling Real-Time Control in Water Resources Systems. Journal of Hydroinformatics Vol. 17 (2015) No. 1 pp. 130–148. DOI: 10.2166/hydro.2014.046.

Reviewer 3 Report

1. In the introduction section, similar model frameworks are presented, but in the results section there is no comparison of the results obtained by the developed model and those already existing.

2. It is also not entirely clear in which software the proposed algorithm was released? what program produced the results.

Author Response

1. In the introduction section, similar model frameworks are presented, but in the results section there is no comparison of the results obtained by the developed model and those already existing.

Previous research has developed model frameworks for studying the impacts of climate variations on hydropower; however, it has not sufficiently acknowledged a model framework that can assess the importance of forecasting periodic hydroclimatic fluctuations for hydropower planning and generation. The model framework developed in this study doesn’t have a particularly similar model from the previous. As the study case and area are different, there might not be necessary to carry out a comparison.

2. It is also not entirely clear in which software the proposed algorithm was released? what program produced the results.

We agree. The model framework is programmed by MATLAB. The optimisation model for cascade hydropower stations is developed by MATLAB also, using the linear algorithm. We have edited the text.

Round 2

Reviewer 2 Report

Dear authors, 

thank you for addressing my review comments, in particular for the revision of the flow chart. I am looking forward to the publication!

Kind regards