In this study, sensitivity analysis is used to identify which parameters are most influential in determining catchment hydrologic response, and therefore which ones should receive more attention in parameter refinement.
Adjustments were made to some parameter ranges to improve model calibrations.
For example, in the Waitahanui catchment the range of values for field capacity were widened from a maximum of 800 mm and the rainfall multiplier was reduced
160 | Model calibration and sensitivity analysis
to 0.4. KGE values for the fit to the time series increased from 0.88 to over 0.91 (an improvement of 4%).
Identifiable parameters present a clear relationship between objective function value and parameter value. Those that are well-defined (in the parameter space, refer Section 6.3.1) converge toward a narrow range of values for which the highest objective function values are found. The most identifiable parameters also tend to be the most sensitive in each of the sub-catchments. Table 7.1 lists sensitive parameters in order of importance for each of the modelled sub-catchments. The four most sensitive and identifiable parameters are the rainfall multiplier, lag time, fastflow proportion and baseflow proportion. Scatterplots (Figure 7.1 to Figure 7.4) of the respective parameters demonstrate that these four parameters are well defined within the parameter space for most catchments. It is not unexpected that the catchment lag time and rainfall multiplier are sensitive. The rainfall multiplier converts the observed rainfall into a catchment areal estimate. This is based on achieving mass balance (minimising the overall bias) in each sub-catchment. The fact that such high calibration values have been obtained in a number of catchments suggests that the inputs to the system are representative of overall dynamics, if not the magnitude of catchment rainfall which the rainfall multiplier accounts for.
Although sensitive, the rainfall multiplier parameter is less identifiable in the lower Tongariro, Whanganui, Tutaeuaua and Poutu catchments. The first three catchments use observations from gauges several kilometres away which may lack some representativeness. In terms of the lower Tongariro catchment the rainfall multiplier is not only used to adjust for mass balance and areal rainfall estimates but also for the area of the catchment which now drains through the Tokaanu Power Station rather than to the Tongariro River. A lack of identifiability for this parameter in the Poutu catchment is most likely to be a result of the complex regulation which is difficult to model. More information on the regulation of the catchment, particularly in regard to the discharge from the Rangipo Station would improve overall performance.
It is not surprising that catchment lag times are also generally well-defined and sensitive, particularly in some of the more flashy catchments. Catchment lag times account for the time it takes for input rainfall to move through the catchment and be measured at the gauge. Adjusting the timing of the modelled output for this time difference allows a closer fit to the observations.
Model calibration and sensitivity analysis | 161 Table 7.1 Results of sub-catchment sensitivity analyses. Parameters are in order of descending statistic value. The darker shading indicates parameters which are classified as sensitive and lighter shading for moderately sensitive parameters. Insensitive parameters are not shaded. Insensitive parameters that are still significant (at the 5% level) are in italics.
Waitahanui Hinemaiaia TaurTaupo Waimarino L. Tongariro Poutu Waipakihi Waihohonu Waihi Kuratau Whareroa Whanganui Waihaha Tutaeuaua Baseflow Rain mult. Rain mult. Rain mult. Rain mult. Baseflow Lag time TB Tf Rain mult. Lag time Rain mult. Rain mult. rain mult Rain mult. Lagtime Fastflow Fastflow Lag time Rain mult. Tf Tf Fastflow Lag time Rain mult. Fastflow Lag time Tf
Lag time Baseflow Baseflow Lag time Fastflow Fastflow Rain mult. rain mult Rain mult. Baseflow Fastflow Lag time Fastflow lagtime Interflow Fastflow Lag time Interflow Baseflow Tf Fastflow baseflow Baseflow Fastflow Baseflow Baseflow Baseflow fastflow
TB Interflow Tf Baseflow Tf Interflow Baseflow fastflow Field cap TB Interflow TB Interflow baseflow
Fastflow Tf Field cap Tf TB Lag time Interflow interflow Curve Interflow Tf Ti Tf Field cap.
Field cap TB Interflow Ti Field cap Ti Min. release lagtime Interflow Tf TB Tf TB Curve
Ti Ti Ti Curve Interflow Field cap Field cap Field cap. Lag time Field cap Curve Interflow Min. release Min. release Curve Field cap Curve Min. release Min. release Min. release FC to sat Ti Ti Curve Max. infiltr. Max. infiltr. Curve Ti Min. release FC 2 sat FC to sat TB Curve Curve Curve Max. infiltr. Min. release Min. release Min. release Field cap Field cap interflow
Max. infiltr. Max. drain. Max. infiltr. Max. infiltr. FC to sat Max. infiltr. Max. infiltr. Min. release TB Ti Field cap Curve Ti TB Max. drain. Max. infiltr. Min. release FC to sat Max. infiltr. TB Max. drain. Curve FC to sat Max. drain. Ti Min. release FC to sat Max. drain
Tf Curve Max. drain. Field cap Max. drain. FC to sat TB Max. drain Max. drain. Max. infiltr. Max. drain. FC to sat Max. drain. Max. infiltr.
FC to sat Min. release TB Max. drain. Ti Max. drain. Ti FC to sat Max. infiltr. FC to sat FC to sat Max. drain. Max. infiltr. FC to sat
162 | Model calibration and sensitivity analysis
Figure 7.1 Scatterplot of rainfall parameter – most sensitive parameter over all
Model calibration and sensitivity analysis | 163
Figure 7.2 Scatterplot of lag parameter – most sensitive parameter over all
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Figure 7.3 Scatterplot of fastflow parameter – most sensitive parameter over all
Model calibration and sensitivity analysis | 165
Figure 7.4 Scatterplot of baseflow parameter – most sensitive parameter over all
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In catchments which have a more defined flood peak, it may be easier for this parameter to be identified. In catchments with longer residence times and less direct runoff (such as the baseflow dominated Waitahanui), flood response may be dampened. Lag times in these catchments are less easily obtained because there is often no well-defined peak to fit to.
In terms of dominant flow pathways, the fastflow and baseflow proportions are the most sensitive. There is strong bivariate sensitivity between all three store proportions as they are directly constrained by the physical requirement that together they must not exceed one. The fastflow parameter is vital for simulating the flood (direct runoff) response of a catchment.
Baseflow is a considerable contributor to flow in all catchments, regardless of their physiographic attributes. This is consistent with the findings in Chapter 5 in which the range of baseflow index values is relatively small (0.69 – 0.76). Although the range of parameter values for baseflow proportion are wider, it is still very identifiable. Baseflow residence time is sensitive in only five catchments. This does not undermine the importance of this and other less sensitive parameters.
Univariate sensitivity analyses are unable to identify parametric interaction, which can result in the non-identification of influential parameters (Wagener and Kollat, 2007). Bivariate sensitivity analysis directly compares the sensitivity of one parameter to another. In this study, baseflow residence times are sensitive to baseflow proportion in five catchments. It is least sensitive in catchments which are more variable and have lower baseflow volumes.
In the Waihi, Tutaeuaua and Tongariro catchments, the residence time for the fastflow store is one of the most sensitive and identifiable parameters found. This parameter influences flood peak attenuation. The shorter the residence time, the flashier the flood response. The Tutaeuaua and Waihi catchments are the smallest sub-catchments studied, allowing water to exit quickly. The steeper nature of the Waihi catchment reduces the amount of time water remains in the stores while the rounder shape and higher drainage density of the Tutaeuaua catchment has a similar effect.
Fastflow residence time is also important in the sub-catchments of the Tongariro as well, despite being much larger in size compared to the Waihi and Tutaeuaua catchments. Although the Waihohonu, Waipakihi, Poutu and lower Tongariro catchments are generally steep, draining the higher elevation areas of the Lake
Model calibration and sensitivity analysis | 167 Taupo catchment, there are some clear differences. The Waihohonu catchment is largely covered in tussock grassland so there is less interception than would be expected in the Waipakihi catchment. Further, a large proportion of its soils consist of weakly developed raw soils with little water holding capacity. It also has one of the highest drainage densities. Despite a high baseflow contribution, these factors allow water to run through the fastflow reservoir more quickly. In contrast, the Waipakihi catchment is more elongated but also has a relatively high drainage density. Baseflow contribution is one of the lowest. The steepness of this catchment, in conjunction with the underlying geology and density of the drainage network, results in a flashy and responsive catchment.
It is not surprising that the fastflow residence time is also sensitive in the Poutu catchment, given that the Waipakihi and Waihohonu both drain into the Tongariro River upstream of the Poutu Intake. This time governing constant of fastflow recession is also important in the lower Tongariro catchment, albeit to a lesser extent. This sub-catchment is, in general, less steep which means that water travels through the catchment more slowly than steep catchments. It also has a large amount of permeable pumice soils and a range of vegetation types. This parameter is least sensitive in the spring fed Waitahanui catchment where baseflow is the highest of all sub-catchment of Lake Taupo.
Although not classified as sensitive in the Tauranga-Taupo and Waimarino catchments the fastflow residence time is significant in terms of the Kolmogorov-Smirnoff (KS) statistic. These two catchments (plus the Waipakihi catchment) have the highest streamflow variability index values and flood flow variability values of all catchments studied. Bivariate sensitivity analysis revealed that the catchment lag time is sensitive to this parameter. As the fastflow residence time increased the lag time also increased. Longer residence times tend to delay or subdue the peak response.
Finally, field capacity is sensitive in catchments that tend to have higher baseflow, such as the Waitahanui, Kuratau and Waihohonu catchments. Field capacity reflects the permeable and water holding capacity of the soil. However, field capacity parameter values are wide ranging and there is little interaction between this parameter and other parameters of the model, with the exception of the rainfall multiplier. The rainfall multiplier tended to increase as field capacity increased in eight sub-catchments, most of which tend to have a more variable and flashy response (Tauranga-Taupo, Waimarino, Waihi, Waipakihi and Tutaeuaua).
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It was hoped that correlation analysis of parameter values against the physiographic attributes used in Chapter 5 would be able to provide further insight into catchment hydrologic behaviour. While this analysis has been undertaken, many relationships could not be discerned with certainty because of a lack of identifiability (in a univariate sense) for some model parameters of some catchments. Multi-variate analyses, such as Sobol‟s global sensitivity analysis, would provide a more robust analysis of individual parameter influence and parameter interactions, but can be computationally expensive (Yang, 2011). Although the results of the correlation analysis are not included in this chapter, they are presented in Appendix E.