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4 Methods to estimate changes in flood flows

4.1 Introduction

After estimating the change in rainfall, as described in chapter 3, the next step is to convert that rainfall change into a flood flow (an amount of water flowing in a river). This chapter looks at both screening and advanced tools that can be used to help river managers estimate changes in flood flows.

Historical data and ongoing data campaigns are vital components of any forecasts of flood flows. Although climate change means that future flow statistics will be different from those in the past, they are necessary to calibrate any model of river flow. Past extreme events can be used as indicators of future trends and are invaluable for assessing how climate change has affected river flows.

4.2 Screening methods

There are many different screening methods available to assess changes in flows in a changing climate. Common to each is relative ease of use and the ability to tune the method to replicate historical events, because they are all simple empirical methods. This ease, however, comes at a cost. By restricting themselves to historical data and by only vaguely representing real-world processes, screening methods generally offer less confidence in making forecasts for events that fall outside the range of historical observations.

Empirical screening methods generally draw on a few basic approaches: the Rational Method, the US Soil Conservation Service (SCS) method, and the unit hydrograph. Here we discuss the Rational Method and one approach presently used in New Zealand that employs both the SCS and unit hydrograph methods.

4.2.1 Unit hydrograph and SCS methods

The unit hydrograph method reflects how a catchment converts a hyetograph (a graph of the distribution of rainfall over time) into a hydrograph (a graph showing changes in river flow over time), while the SCS method empirically relates peak flood flow to rainfall using land-cover-related parameters. To illustrate how the unit hydrograph and SCS methods can be adapted to incorporate climate change, TP108 is used as an example, although these approaches can be generalised across other implementations of the basic methods.

TP108 is a standard model for computing design flood hydrographs in small catchments in the Auckland region (Auckland Regional Council, 1999). It has been used outside the region, but it must be stressed that the model was not developed to do so. Also note that it is currently being updated by the Auckland Regional Council to GD2009/001.

A key input to TP108 is the 24-hour rainfall total, P, which is mapped for the Auckland region (Auckland Regional Council, 1999). The formula for event run-off is:

Q = (P – Ia)2 / (P – Ia + S)

where:

  • Q is run-off depth (millimetres)
  • P is rainfall depth (millimetres)
  • S is the potential maximum retention after run-off begins (millimetres)
  • Ia is initial abstraction (millimetres), which is 5 millimetres for permeable areas and zero otherwise.

The retention parameter S (measured in millimetres) is related to catchment characteristics through:

S = (1000/CN – 10) 25.4.

The value of the curve number (CN) ranges from 0 for zero run-off to 100 for complete run-off; its value depends on a catchment’s characteristics. The TP108 method for estimating CN values is given in the TP108 manual (Auckland Regional Council, 1999, section 2.2 and Appendix B). Note that TP108 does not give detailed guidance on how to adjust CN values for the effect of antecedent conditions, but does mention they influence CN values.

The remaining steps of TP108 convert the run-off depth (Q) into a flow hydrograph by assuming a particular temporal pattern for the storm rainfall and estimating a characteristic lag time for the catchment to respond to rainfall. In a screening approach, these calculations will be assumed to be the same for both the current and future climates and are not discussed further here. In a more sophisticated approach, you might consider whether the temporal rainfall pattern or initial abstraction might change, but this level of detail is generally not appropriate when the method is used as a screening tool.

To use this method as a screening tool in the Auckland region, apply it once with the current 24‑hour rainfall from the map in the Auckland Regional Council guidelines (Auckland Regional Council 1999), and apply it a second time with: (i) the rainfall changed to reflect the expected changes in rainfall described in section 3.2; and (ii) the CN value changed to reflect any available information on how antecedent conditions may change with climate. Thus, the extreme daily rainfalls might be approximately 8 per cent higher by 2040, since extreme rainfall is expected to increase 8 per cent per degree of warming, and approximately 1 degree of warming is expected by 2040 in many parts of New Zealand. Tables 1 and either 2 (for 2040 estimates) or 3 (for 2090 estimates) from this manual can be used with this method.

It is important to note that TP108 is designed specifically for use in Auckland: it includes supporting information to guide its application, and this is what allows it to be used as a screening method. TP108 is an example of the wider class of unit hydrograph methods for estimating river flow from rainfall. For example, the HEC-HMS computer modelling system (eg, Scharffenberg and Fleming, 2006) is a freely available and more generic implementation of the unit hydrograph approach. However, without detailed guidance on assigning values to model parameters, HEC-HMS would be considered an advanced technique in the context of this manual rather than a screening method.

Although the simplicity of the SCS and unit hydrograph approaches offers an advantage over advanced techniques, both have their disadvantages. CN values have not been widely assessed for New Zealand and often reflect local hydrology poorly, and both the SCS and unit hydrograph discount the importance of changing pre-storm initial conditions (ie, antecedent soil moisture).

4.2.2 The Rational Method

The Rational Method is a widely used technique in engineering hydrology, although it is known to produce results that have large uncertainty (see McKerchar and Macky, 2001). It can be used as a screening tool in much the same way as described previously for TP108. Other similar models, such as the Modified Rational Method, can also be used as screening models. (For a comparison of the New Zealand performance of the Rational Method with two other methods, see McKerchar and Macky, 2001.)

The formula for the Rational Method can be written as:

Q = C i A /3.6

where:

  • Q is the estimate of the peak design discharge in cubic metres per second
  • C is the run-off coefficient
  • i is rainfall intensity in millimetres per hour, for a duration equal to the time of concentration of the catchment
  • A is the catchment area in square kilometres.

Selection of the run-off coefficient, C, relies partly on knowledge of physiographic conditions and engineering judgement. It also depends on the rainfall intensity (eg, see Maidment, 1993, and Ministry of Works, 1978). When applying the formula (Q = C i A /3.6) for future climates, the important point to note is that both i and C must be changed when considering climate change.

4.2.3 Rules of thumb for changes in regional flood frequency

As more detailed studies of the impacts of climate change on floods are undertaken, it may be possible to synthesise the results into ‘rules of thumb’. This would be particularly true if the results from a variety of methods and locations produced robust and similar results. For example, an advanced method may have been applied to several river basins in a region and in all cases it is found that a consistent change in flood magnitude is predicted. At the time of writing we are not aware of any such rules of thumb, but it is conceivable that a rule of the form “the 100-year flood in the current climate will be an X-year flood by 2050” could be applicable (where X might be 60, or 40, or even less). For preliminary screening these rules of thumb may be suitable, provided evidence is available to support them. They are mentioned here not to recommend them but to alert the reader to their possible future existence.

Consider two hypothetical cases where all flood peaks on a given river increase by either 10 per cent or 30 per cent as a result of climate change. How would the recurrence interval of a 100‑year ARI flood change in these two hypothetical cases? It is possible to use results from McKerchar and Pearson (1989) to suggest that over much of New Zealand (places where the 100-year ARI flood is between two and three times the mean annual flood), the average recurrence interval would approximately halve if flood peaks all increased by this hypothetical 10 per cent. For example, the flood size that is presently exceeded once every 100 years on average would in future be exceeded once every 50 years on average (based on the slopes of flood frequency curves presented by McKerchar and Pearson). If, instead, flood peaks were to increase by 30 per cent as a result of a more severe climate scenario, then the flood that is presently exceeded once every 100 years on average would be exceeded on average approximately once every 20 years.

A future edition of Regional Flood Estimation in New Zealand, updating McKerchar and Pearson, 1989, will provide national guidance on the impacts of climate change on flood magnitude. The 1989 edition of this estimation technique provides national coverage for estimating flood magnitudes, but it is becoming outdated because it does not use any flood data collected in the last 20 years. The regional flood estimation method is being updated and revised at present, and a national revision is expected to be available in 2015.

4.3 Advanced methods

As with screening methods, there are many different rainfall run-off methods available internationally, distinguished by the complexity with which they treat the processes of run-off generation and run-off routing through the catchment. These can be divided into storage-routing models and catchment hydrology. The incorporation of climate change into each of these classes of models is illustrated with two particular cases that have been used in New Zealand, although the general principles can be applied to all similar models.

4.3.1 Storage-routing models

The simpler of the advanced methods for predicting the effects of climate change on river flow are the storage-routing models. These models represent the downstream flow of water by way of linked reservoirs, devoting less attention to the physics of the rainfall run-off processes themselves. Two widely used models are HEC-1 and RORB. Incorporating climate change considerations into these models requires simulations driven by synthetic rainfall time-series under climate change, as obtained in chapter 3. For illustrative purposes only RORB is discussed here.

RORB 11 is a general run-off and stream-flow-routing programme used to calculate flood hydrographs from rainfall and other channel inputs (Laurenson et al, 2007). It converts time-series of storm rainfall for the sub-catchments of a river into a flood hydrograph at the outlet of the catchment. It subtracts losses from rainfall to produce rainfall excess and routes this through catchment storage to produce the hydrograph. It can also be used to design retarding basins and to route floods through channel networks.

The model is areally distributed, non-linear, and applicable to both urban and rural catchments. It makes provision for temporal and areal variation of rainfall and losses, and can model flows at any number of gauging stations. In addition to normal channel storage, specific modelling can be provided for retarding basins, storage reservoirs, lakes or large flood-plain storages. Base flow and other channel inflow and outflow processes, both concentrated and distributed, can be modelled.

A suitably verified rainfall run-off model of the catchment can be used to assess the impacts of climate change on flood magnitude. For example, the model of the Waimakariri River described by Griffiths et al (1989) could be used to assess the impacts of climate change on Waimakariri River floods. The key steps are the development of changed rainfall time-series to use with the model (see chapter 3 of this manual) and verification that the catchment model is applicable (as in Griffiths et al, 1989).

4.3.2 Catchment hydrology models

The most advanced approach for incorporating climate change into river flow estimates is to use a fully distributed, physically-based catchment hydrology model. These models represent a catchment in great detail, including topography, soil and land uses, and discard empirical representations of hydrological processes in favour of general physical and biophysical principles. Their greater complexity brings both benefits and costs. Although there are many such models in operation worldwide (eg, TopNet, MIKE SHE), the method for addressing climate change is similar across all of them. For the purposes of this discussion, TopNet, a model developed specifically for New Zealand conditions, will be used.

TopNet (Bandaragoda et al, 2004; Clark et al, 2008) is a spatially distributed, time-stepping model of water balance. This physically-based catchment hydrology model differs from RORB and other storage-routing models in its highly detailed representation of hydrological processes and in its use of kinematic wave theory to route run-off. It is driven by time-series of rainfall and temperature data (hourly resolution or better), and of additional weather elements where available. TopNet simulates water storage in the snowpack, plant canopy, rooting zone, shallow subsurface, lakes and rivers. It produces time-series of modelled river flow throughout the modelled river network. It is used for both flood modelling and water balance modelling. A detailed description of the model equations is published in Clark et al, 2008.

As with RORB, the key steps in using TopNet for assessing climate change impacts on floods are the development of changed rainfall time-series (see chapter 3) and verification that the catchment model is applicable (see Gray et al, 2005). The key advantage of TopNet and other complex catchment and routing models is they are designed to reflect the underlying processes of floods. This gives modellers greater confidence in their ability to make inferences about events that fall outside the range of historical observations – as will be the case with climate change. A notable disadvantage, however, is they require greater attention in their development, in terms of both the underlying biophysics and calibration. A further consideration regarding the choice of catchment models is the degree of user expertise: a great deal of experience is required to operate these models soundly. Lastly, it should be noted that TopNet is currently more applicable for use in research, while models such as MIKE SHE are used more in the engineering domain.

4.4 Summary

  • A range of methods have been presented that provide estimates of how altered rainfall predictions may affect river flow. The aim of each method is to convert extreme rainfall data into an estimate of peak flow.
  • As with the methods presented in chapter 3, each method differs in its complexity, data requirements and reliability of results, as well as its user experience needs. Unlike the methods presented in chapter 3, all but the research models (ie, TopNet) are currently usable by practitioners.
  • If more confidence in flow prediction is desired, research models are still valuable options.
  • As was recommended in chapter 3, you should consider three factors when deciding how to develop predictions of flood flows:
    • what weather and landscape data is available?
    • what accuracy and precision do we need?
    • do we have access to the expertise and computing facilities to undertake the analysis and modelling?
  • The summaries in table 6 will help you to choose the most appropriate method.

Table 7:Summary of advanced methods for estimating inundations as a guide to selecting the appropriate method

Table 6: Summary of advanced methods for estimating flood flows as a guide to selecting the appropriate method
Method (example) Description Advantages Disadvantages Data and climate change requirements
Rules of thumb General approach based on past, more complex studies. Easy to use; based on comprehensive analysis. Uncertain applicability outside the rivers where studies were conducted. Case-by-case considerations
Rational method Empirical method to estimate peak flow. Rapid implementation; low data requirements; widely used in the engineering community; guidelines for estimating run-off coefficient. Not suitable where rainfall varies significantly across the catchment; limited accuracy in validation tests. Design rainfall intensity; run-off coefficient, which depends on catchment characteristics (ie, slope, land cover, soil); time of concentration and catchment area.
SCS method (TP108) Empirical and graphical method to estimate peak flow. (As for the Rational Method.) Limited database for New Zealand conditions; limited to small to medium-size catchments; limited accuracy in validation tests. Rainfall; land-use description; hydrological soil group.
Unit hydrograph (HEC-HMS, TP108) Empirical approach that converts a hyetograph into a hydrograph. Relatively simple approach. Limited to gauged catchments. Storm hyetograph.
Storage-routing models (RORB, HEC-HMS) Route rainfall or run-off through a simple catchment. Moderate data requirements. Lacks catchment complexities and detailed routing procedure. Rainfall or run-off time-series; defined storage-routing network.
Kinematic wave models (TopNet) Flow is routed through a catchment’s river network based on kinematic wave theory. Can be used for operational flood forecasting; more accurate than screening methods when in large complex catchments; ongoing scientific development. Longer computation time; larger data requirements; larger cost of model calibration. Time-series of distributed catchment run-off; digital river network calibrated parameters.
Catchment water balance models (TopNet, MIKE SHE) Models river flow and other hydrological variables across a catchment based on biophysical principles. Suitable for assessing both climate and land-use change impacts on water resources; ongoing scientific development. Longer computation time; larger data requirements; larger cost of model calibration. Rainfall and temperature time-series; digital river network; GIS data for soil, land cover and topography.

Note: Data requirements specifically related to climate change are underlined.


11 Griffiths et al (1989) provide a brief description of the model, and more details are available from http://civil.eng.monash.edu.au/expertise/water/rorb