Bias correction of simulated historical daily streamflow at ungauged locations by using independently estimated flow duration curves

Farmer, William H.; Over, Thomas M.; Kiang, Julie E.

doi:https://doi.org/10.5194/hess-22-5741-2018

Articles | Volume 22, issue 11

https://doi.org/10.5194/hess-22-5741-2018

© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/hess-22-5741-2018

© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 22, issue 11

Research article

|

08 Nov 2018

Research article |

| 08 Nov 2018

Bias correction of simulated historical daily streamflow at ungauged locations by using independently estimated flow duration curves

William H. Farmer, Thomas M. Over, and Julie E. Kiang

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Final revised paper (published on 08 Nov 2018)
Preprint (discussion started on 19 Mar 2018)

Interactive discussion

Status: closed

AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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RC1: 'Good paper that would benefit from a synthesis diagram to better explain the method', Anonymous Referee #1, 18 Apr 2018
- AC1: 'Author Response to Anonymous Referee #1', William Farmer, 24 May 2018
RC2: 'Review', Anonymous Referee #2, 30 Apr 2018
- AC2: 'Author Response to Anonymous Referee #2', William Farmer, 24 May 2018
RC3: 'Comments on "Bias correction of simulated historical daily streamflow at ungauged locations by using independently estimated flow-duration curves"', Anonymous Referee #3, 15 May 2018
- AC3: 'Author Response to Anonymous Referee #3', William Farmer, 24 May 2018

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

ED: Publish subject to revisions (further review by editor and referees) (04 Jun 2018) by Monica Riva

AR by William Farmer on behalf of the Authors (09 Jul 2018) Author's response Manuscript

ED: Referee Nomination & Report Request started (30 Jul 2018) by Monica Riva

RR by Benoit Hingray (23 Aug 2018)

Suggestions for revision or reasons for rejection

The authors have significantly improved their manuscript and clarified their work. The methodology is now clear to me and the discussion of results are fair, including the poor performance of the overall bias correction method (as mentioned in the manuscript, rooms for improvement obviously exist with a better estimation of regional Flow Duration Curves). Almost all my previous suggestions / questions have been addressed. The manuscript now just requires some minor revisions. I do not need to review the forthcoming corrected version.

P1/20 : over the last 20years at least..
P2/16 : what is a categorical truism. Please give a more accessible formulation.
P2/20 : “rank-order of simulated streamflows”
P2/22 : “the temporal sequence of relative…”
P2/25 : the expression is not clear : “to rescale the streamflow simulations by interpolating the nonexceedance probabilities of the simulated streamflow along the FDC (see Material and Methods, below).

Reformulate to : to rescale each streamflow value based on the streamflow value of the regional FDC for the corresponding nonexceedance probabilities (see Material and Methods, below).

P2/30 : “hydrograph” typically refers to a given hydrological event, not to the time series of discharge for a n-years period. Next the spatial issue is missing in the first part of the sentence.

Reformulate to : “The approach tested here seeks to bias-correct a simulated time series of daily discharge using an independently estimated FDC, when viewed in another way, presents a novel form of nonlinear spatial interpolation”.

P3/15 : typo : simulation

P7/19-20 : “sequential” and “distributional” is used in the different figures but not defined. Introduce both terms here :

In the same fashion, evaluation of the complete hydrograph can be assessed sequentially (sequential evaluation in the following), retaining the contemporary sequencing of observations and simulations, or distributionally (distributional evaluation in the following), considering the observations and simulations ranked independently.

P8/22 : Figure 7 is introduced but not commented > please comment.

P9/35 : You can conclude this. Figure 4 and 6 do not discuss the bias but the accuracy. Please reformulate.

P9/33 : I do not see those numbers (30%, 20%) in the table.

P10/38 : “from errors in the simulated temporal structure”

P12/2 : “independent evaluation cases…. … “ and again “independent evaluation case….

P13/12. I do not understand what you conclude from the figure. How can you state that there is a “general move towards unbiasedness” > I do not think the figure allows such a conclusion (I would even conclude the reverse from graph d) : we should see a compaction in the Y axis but nothing is obvious !!! Perhaps give the limits of the standard deviations (or some high /low percentile) of the cloud in both X and Y directions

P13/31-32 : I do not understand. Please clarify the “principle” of this alternative approach

P14 /14-16 : already discussed previously > to be removed.

P15/20 : “While using the nonexceedance probabilities of kriged streamflow simulations
5 improves upon the use of single index streamgages to obtain nonexceedance probabilities,”. The use of single index streamgages has not been considered here. You can not say your method “improves…. “ > refomulate

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RR by Anonymous Referee #3 (18 Sep 2018)

RR by Anonymous Referee #4 (09 Oct 2018)

Suggestions for revision or reasons for rejection

The paper presents a method to bias correct streamflow by modifying an existing approach of using independent FDC. Although the paper addresses a very interesting topic, the readability of the manuscript and presentation of results are unfortunately very poor. For instance, abstract contains words like '... bias arising from distributional properties of residuals', '... a method for rescaling simulated streamflow to correct...', '... pooled ordinary Kriging simulation', '... regional regression on basin characteristics', '... using an idealized case', 'region of neighbors to ...'. I noticed that these words are mostly coming from Authors' previous papers. However, to make it an independent paper and easily readable, Authors should consider clarifying these points in the abstract.

There are many sentences in the Introduction which appear confusing because of the kind of words used or complex way of trying to say too many things in a sentence. For example, '... distributional bias in simulated streamflow is a failure to reproduce....'. Bias is not a failure, it is an error. '... effective squeezing of the streamflow distribution'; what does the word squeezing mean here? '.... distributional compaction...', so it means squeezing lead to compaction; compaction of what? 'This bias is particularly concerning, as examinations of extreme high-flow events are a common and influential use of historical simulation and long-term forecast.' What does this sentence mean? 'Consider, for example, the motivation for work by Archfield et al.' Does it mean that the readers should go through all the cited papers?

On page 2, Authors are talking about nonlinear spatial interpolation of daily streamflow using FDCs. The claim is that in previous studies, only single neighbour was used and the nonexceedence probabilities were interpolated along a FDC. It is not clear then how it became nonlinear spatial interpolation when interpolation has to be performed along FDC. All these concepts are presented in few sentences which need further explanation unless the assumption is that the reader will go back and read all the referred papers.

'Furthermore, though necessarily explored in this study through the use of a single technique for hydrograph simulation, this approach may be a means to effectively bias-correct any simulation of streamflow, including those from rainfall-runoff models, as presented by Pugliese et al. (2017). Pugliese et al. (2017) used a geostatistical tool...... underlying methods.... the approach proposed by Pugliese et al. is the same as that explored here.' What is the single technique; which geostatistical tool was used; what are the underlying methods mentioned here; etc. need to be explained properly.

More information is required to explain how by estimating nonexceedence probabilities directly or indirectly affect the nonlinear spatial interpolation.

On page 2 and at the beginning of page3: 'Although the results presented here are promising, they demonstrate that the performance of two stage modeling, where timing and magnitude are largely decoupled, is limited by the less well performing stage of modeling.' This sentence doesn't connect with the previous sentences in the same paragraph. Does it mean that by improving nonlinear spatial interpolation, both timing and magnitude of simulated streamflow are going to improve?

On page 3: Please use SI units in the paper. '.... the small additive value applied was 0.0049cfs...... the bias in streamflow plus a correction factor.' It appears that Authors are trying to avoid logarithm of a zero. Why not add this correction to only zero streamflow values? Are you adding 0.0049 cfs to entire data or only zero values?

Section 2 says materials and methods; what does the materials mean here? I recommend separating the description of data and study area in a section, then present another section describing the methodology in detail? The methodology is presented in a summary form assuming that readers will go through Authors' previous papers on this topic. I am sure it will take at least two pages description along with equations and figures to describe what is written in a paragraph citing other papers: 'Though the potential for distributional bias applies to any hydrologic simulation (Farmer and Vogel, 2016), for this study, initial predictions of daily streamflow values for each streamgage were obtained by applying the pooled ordinary kriging approach (Farmer, 2016) to each 2-digit Hydrologic Unit (figure 1) through a leave-one-out cross-validation procedure on the 25 streamgages within the 2-digit Hydrologic Unit. This approach considers all pairs of common-logarithmically transformed unit streamflow (discharge per unit area) at each day and builds a single, time-invariant semivariogram model of cross-correlation that is then used to estimate ungauged streamflow as a weighted summation of all contemporary observations. A spherical semivariogram was used as the underlying model form. Additional information on the time series simulation procedure is provided by Farmer (2016).' There are so many concepts involved here, Authors should try to try to explain the steps systematically with the help of equations and figures.

The last sentence on page 3 about the pooled Kriging is very general. It has to be specific whether the methodology used here is applicable to other study area or not.

On page 4, again Authors refer to Farmer et al. (2018) and present all the details of regional regression in a paragraph. Without reading the cited paper, there is no detail available for the reader to figure out the form of regression equation, three streamflow regimes, fitted coefficients, percentile groupings etc.

On page 5, Authors present two methods to discuss about the biases in the tails - observation dependent and observation independent tails. Authors should present some figure to explain the concepts rather than summarizing all the analysis in a paragraph.

Instead of commenting on the rest of the paper, I would like to strongly recommend that Authors should use hydrographs, flow duration curves etc. in presenting results. Explaining all the results using box plots is not very practical and it is hard to evaluate what Authors have presented in Section 3.

In my opinion, the manuscript needs to be re-written thoroughly. Technical contents and novelty can be evaluated only when all the necessary details are present.

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ED: Publish subject to minor revisions (review by editor) (17 Oct 2018) by Monica Riva

AR by William Farmer on behalf of the Authors (25 Oct 2018) Author's response Manuscript

ED: Publish as is (26 Oct 2018) by Monica Riva

Short summary

This work observes that the result of streamflow simulation is often biased, especially with regards to extreme events, and proposes a novel technique to reduce this bias. By using parallel simulations of relative streamflow timing (sequencing) and the distribution of streamflow (magnitude), severe biases can be mitigated. Reducing this bias allows for improved utility of streamflow simulation for water resources management.