the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 23 Sep 2024
Influence of Spatial Heterogeneity of Runoff Generation on the Distributed Unit Hydrograph for Flood Prediction
Abstract. The spatial scale mismatch between runoff generation and runoff routing is an acceptable compromise but a common issue in hydrological modeling. Moreover, there is hardly any report available on whether a unit hydrograph (UH) that is consistent with the spatial scale of runoff generation can be computed. The objective of this study was to explore the influence of spatial heterogeneity of runoff generation on the UH for flood prediction. To this end, a novel GIS-based dynamic time-varying unit hydrograph (DTDUH) was proposed based on the time-varying unit hydrograph (TDUH). The DTDUH can be defined as a typical hydrograph of direct runoff which gets generated from one centimeter of effective rainfall falling at a uniform rate over the saturated drainage basin uniformly during a specific duration. The DTDUH was computed based on the saturated areas of the watershed instead of the global watershed. The saturated areas were extracted based on the TWI. Finally, the Longhu River basin and Dongshi River basin were selected as two case studies. Results showed that the proposed method exhibited consistent or better performance compared with that of the linear reservoir routing method, and performed better than the TDUH method. The proposed method can be used for watersheds with sparse gauging stations and limited observed rainfall and runoff data, as for the TDUH method. Simultaneously, it is well applicable to humid or mountain watersheds where saturation-excess rainfall is dominant.
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Status: final response (author comments only)
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RC1: 'Reviewer Comment on hess-2024-274', Anonymous Referee #1, 17 Nov 2024
The paper by Yi et al. describes a unit hydrograph (UH) model that combines a time varying parameter with a restriction of its effective rainfall input to the saturated part of the catchment. The model is applied to two catchments in China and a selection of floods from these catchments within an event-based simulation approach. The UH model presented by the authors is ambitious with intensive data processing done to configure it on the two test catchments. However, despite this commendable effort, the considerable literature available on UH models imposes that any new development be extensively tested and compared with a wide range of alternatives. Unfortunately, the paper by Yi et al. is lacking such a detailed comparison. In addition, the UH model presented by Yi et al. suffers from several theoretical issues that are detailed below.
Consequently, we are unable to recommend this paper for publication. Our major and minor comments are provided in the two sections below.
>>> Major comments
Comment #1 – Lack of clarity in method description
A UH model is a routing scheme that aims at propagating effective rainfall towards a catchment outlet. Consequently, the presentation of the XAJ rainfall-runoff model in sections 2.1 and 2.3 is irrelevant and could be summarised simply as the need to use a rainfall-runoff model to estimate the saturated area fraction of the catchment and effective rainfall. Details on the XAJ model can be moved to appendix. It is also worth noting that many other rainfall-runoff models with similar concepts (e.g. TOPMODEL, VIC, PDM, see (Kavetski et al., 2003)) could be used.
At the same time, a key part of the method underlying the proposed UH model is the conversion of a lumped estimation of catchment saturation to a distributed map of saturation area. This is done by the author based on the TWI index as indicated at lines 360. This point is important and should be moved from the result to the method section with extensive discussion on the choices made and their implications. This point is critical because the link between saturation area and topography is far from simple.
Finally, the assumptions behind Equation 9, which is the foundation of the whole UH model, are not discussed in the paper and rely on the reference to Yi et al (2022). This paper is written in Chinese and difficult to access for an international audience. Consequently, the rationale behind this equation needs to be repeated and justified here.
Comment #2 – Clarify the role of Muskingum routing
At line 249, the authors state that “When the watershed is divided into multiple sub-basins, the Muskingum method will be used to confluence the runoff of each sub-basin to the outlet of the basin.” This sentence is confusing because it is not clear why an additional routing model is needed aside of the UH models or linear reservoir previously introduced by the authors.
To be clear, Muskingum routing model should not be used in this work because the combination of UH and Muskingum makes it impossible to distinguish the performance of the UH model from those of the Muskingum model.
Comment #3 – UH model relies on questionable hydraulic assumptions
The UH model presented by the authors relies on equation 9 which introduces a relationship between velocity, excess rainfall and soil moisture content. The application of this equation to a source cell, i.e. a cell with no inflow from upstream areas, seems reasonable although more justification should be provided on its formulation as indicated in Comment #1.
However, when the cell is not a source, the flow in the cell combines two types of routings: (1) hillslope routing which propagate locally generated flow, (2) river routing which propagates flow from upstream cells. This distinction is not needed in a linear UH model due to the superposition principle. However, Equation 9 introduces a dependency of the velocity to excess rainfall which makes the UH model presented by the authors non-linear. In this case, both routing should be distinguished as is done by Bunster et al. (2019). More precisely, Equation 9 becomes irrelevant when the second type of routing dominates, typically at the end of a flow path (or “road” as labelled by the authors), because soil saturation in the cell has a limited impact on flow routing compared to the geometrical characteristic of the channel (e.g. storage on floodplain).
Consequently, it is suggested to introduce a second type of routing similar to Bunster et al. (2019) which takes into account flow routing within channel.
Comment #4 – Lack of clarity regarding initial conditions at the beginning of each flood event
The authors rely on an event-based approach to run each flood event. The difficulty with such choice is the identification of initial conditions for the XAJ model. Such initialisation is far from trivial because XAJ states are not simple functions of climate inputs due to the non-linearities in the XAJ equations. The authors allude to their initialisation briefly at line 326 where they say that “to consider the initial condition, the antecedent precipitation was calculated based on the daily recession coefficient of the water storage.” This is clearly inappropriate and is likely to introduce errors potentially larger than the ones related to the choice of the routing scheme.
To circumvent this problem and avoid hazardous initialisation procedures, we recommend switching to a continuous simulation approach where both rainfall-runoff and routing models run continuously for the whole simulation period.
Comment #5 – Validation protocol is too limited
Unit hydrograph models were invented in the 1930 with a very long history in hydrology (Beven, 2020). Consequently, any new addition to this theory should be justified thoroughly from a practical point of view. The authors applied their UH model to one rainfall-runoff model, two catchments and a total of six validation events (two in the Longhu basin and four in the Dongshi basin). In addition, the paper does not present any simulation hydrograph which are important, albeit not sufficient, to judge on model performance.
Overall, we suggest expanding the testing to at least 10 catchments (perhaps using one of the various CAMELS datasets), two rainfall-runoff models and use a continuous simulation approach (see comment #4). In addition, it is important to incorporate performance metrics that are evaluating low flow regimes as well as floods. The validation of model outputs outside of high flow event is important because a sophisticated UH model such as the one introduced by the authors should remain efficient for a wide range of flow regimes.
>>> Minor comments
In general, we recommend using the present instead of past tense when possible.
L10, “there is hardly any report available”: Please be more specific with this comment. “Hardly” is too vague.
L11, “that is consistent with the spatial”: Please clarify what is meant by “consistent”.
L15, “hydrograph of direct runoff”: Please clarify what is meant by “direct”. I suggest removing this word to avoid entering into the details of runoff processes.
L18, “based on the TWI”: Please define TWI.
L28, “The assumption that basins behave as linear systems (i.e., there is proportionality and additivity between excess rainfall and total storm response) has been the core of hydrology”: I disagree with this statement. Many hydrological models rely on non-linear dynamic, especially related to the modelling of catchment saturation as shown later in the paper in the case of the XAJ model.
L30, “a single response function named the UH has been widely applied”: I suggesting clarifying that a response function is a convolution operator applied to effective rainfall inputs. A simple equation could be added here to precise the mathematics similarly to Lee et al (2008). More precisely, a UH model can be written as
Y = sum(X[i-k+1].H[k], k=1, T)
The discussion in the following paragraph could then precise (1) what is meant by X, (2) how to obtain H.
L32, “For gauged basins, unit hydrographs are derived from observed data by measuring rainfall and runoff data.”: Developing a UH in this case is not straightforward. The process generally relies on deconvolution technique which are known to be unstable if not smooth properly. I recommend highlighting this point here.
L79, “Hydrologists have made great efforts to address the nonlinear issues of the UHs in the past decades, while these approximations are still acceptable compromises in challenging hydrology research.”: I suggest removing this sentence which does not add much to the content.
L92, “confluence theory is prevalent”: Please clarify what is meant by confluence theory.
L93, “hydrologists almost ignore the forecasting errors associated with this issue”: Please clarify what is meant by forecasting errors. So far, the paper discusses general modelling concepts and not their application to a particular engineering problem such as forecasting. In addition, forecasting errors are generally driven by errors in forecasts in rainfall forcings, especially at long lead times. I am not sure the authors are prepared to discuss the whole chain of uncertainty leading to forecasting errors in this paper. I suggest leaving forecasting out of this paper and replacing it by prediction throughout the paper.
L100, “there is hardly any report available on whether UH that is consistent with the spatial scale of runoff generation”: This sentence is unclear. Please clarify what is meant by “consistent” and also be more specific about the availability of reports. “Hardly” means that there are indeed report, so please summarise them.
L105-108: These points are not contributions. They describe the method but do not clarify what novelty the method brings compared existing alternatives.
L134-137: Please clarify the mathematics of this part and more precisely the algorithm behind the XAJ model . What is said here can be interpreted in various ways.
L165, “fully distributed models use routing methods which are usually computationally intensive because they solve the St. Venant equations”: The full solution of the Saint Venant Equation is rarely implemented in distributed models. More frequently, a simplified solution based on the kinematic or diffusive wave is used leading to small runtimes. Consequently, I disagree with argument. Please consider how the proposed method compares with simplified routing methods.
Table 1: This table can be removed. The difference between the existing UH and DTDUH is simply the restriction to the saturated part of the catchment.
Section 2.3: This section should be merged with 2.1 and moved to appendix (see comment #1).
>>> References
Beven, K. J. (2020). A history of the concept of time of concentration. Hydrology and Earth System Sciences, 24(5), 2655–2670. https://doi.org/10.5194/hess-24-2655-2020
Bunster, T., Gironás, J., & Niemann, J. D. (2019). On the Influence of Upstream Flow Contributions on the Basin Response Function for Hydrograph Prediction. Water Resources Research, 55(6), 4915–4935. https://doi.org/10.1029/2018WR024510
Kavetski, D., Kuczera, G., & Franks, S. W. (2003). Semidistributed hydrological modeling: A “saturation path” perspective on TOPMODEL and VIC. Water Resources Research, 39(9). https://doi.org/10.1029/2003WR002122
Citation: https://doi.org/10.5194/hess-2024-274-RC1 - RC2: 'Reviewer Comment on hess-2024-274', Anonymous Referee #2, 02 Dec 2024
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