Calibration and evaluation data selection

Model calibration is the process of adjusting parameter values to effect a closer matched simulation of the real world. Model performance is evaluated by how well it provides acceptable representations of the real world (Refsgaard and Henriksen, 2004; Wagener, 2003). The term „evaluation‟ is used in this study since the commonly used term „validation‟ implies some degree of „truth‟ or legitimacy in the model (Oreskes et al., 1994), which is difficult to achieve with models which are made up of simplified representations of the complex reality (Beven, 2009).

Past observations of discharge, precipitation and potential evapotranspiration are used for calibration of this hydrological model. Successful calibration requires the identification of model parameters that can reliably simulate the catchment‟s hydrological response over a range of conditions (Singh and Bárdossy, 2012). The data is often split for calibration and evaluation periods, with the location of the split between the two selected subjectively. Although there have been a number of attempts to quantify a suitable length of time for model calibration, it is commonly accepted that it is the information content of the data used rather than the length of data that is more important for parameter identification (Gupta and Sorooshian, 1985; Liu and Han, 2010; Singh and Bárdossy, 2012). The information content of hydrological data is, however, largely unknown (Singh and Bárdossy, 2012)

The calibration period should ideally represent the range of phenomena experienced in the catchment including periods of floods, drought and normal flow conditions (Gupta and Sorooshian, 1985; Singh and Bárdossy, 2012). In the Lake Taupo catchment, however, many of the records for the sub-catchments are over relatively short periods (often less than five years). The corresponding rainfall record may be, in some cases, longer but may have lengthy gaps in the record limiting the selection of suitable calibration periods. Where data permits, calibration periods are selected from the longest continuous period of rainfall data for which there is a corresponding flow record. One third of the calibration data length up to a maximum of one year is used for model warm-up, to minimise effect of initial conditions (Madsen, 2003). At least one year is kept for model evaluation. In catchments for which suitable calibration and evaluation data is limited, calibration is undertaken on as much information as possible to identify model parameters (Singh and Bárdossy, 2012). Evaluation is not performed.

122 | A rainfall-runoff model for the Lake Taupo catchment

For those catchments used in the Lake Taupo Inflow Model (LTIM), the periods selected have undergone extensive analysis in terms of their suitability for model calibration. The periods are assessed in terms of the range of hydrological responses represented in the period selected and the consistency between the rainfall and discharge records. Four separate analyses of the data are undertaken. First, periods of no rainfall (and evapotranspiration) are plotted and negative recessions (rising streamflow) highlighted with the aim of ascertaining the representative of the rainfall gauges for capturing the majority of events in the hydrograph.

Secondly, flow duration curves for the calibration data and the entire record are compared. Thirdly, residual mass curves are used to identify periods where there is consistency between the period in terms of the cumulative departure of rainfall and flow from their respective means. Finally, the rainfall data for the period is assessed for catchment representativeness in terms of how adequately it captures the events that are observed in the hydrograph.

Optimal parameters are evaluated on a separate and non-overlapping set of data.

They are also evaluated over the 1998-2011 period as this is the critical period for evaluating the performance of the model in terms of predicting lake level over certain events. This 14 year period overlaps with many of the calibration data periods; any gaps are infilled irrespective of length.

Identifying negative recessions

The consistency between the rainfall and streamflow records is undertaken by identifying periods of no rainfall and or evapotranspiration and highlighting where streamflow is significantly rising during these recession periods (Figure 6.4). This assessment aims to show how representative the selected rainfall gauge is by illustrating how adequately it captures the events that are observed in the hydrograph. This analysis helps to identify suitable periods of data for calibration and evaluation purposes.

Representativeness of calibration period

To compare the representativeness of the calibration period selected, flow duration curves are compared of the calibration data and the entire record. Ideally the calibration period would reasonably cover the main range of flows that are seen in the whole record, as shown in Figure 6.5, although it is noted that depending on the

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Figure 6.4. Plot of recession periods (light blue dots). Negative recessions (rising streamflow during periods of no rain or evapotranspiration) are highlighted (dark blue dots) (a) Entire record and (b) corresponding rainfall (mm/15 minutes). (c) Calibration period and (d) corresponding rainfall.

Figure 6.5 Comparison of flow duration curves for calibration period and entire record. This calibration period represents the range of hydrological responses reasonably across the entire range of flow.

1980 1985 1990 1995 2000 2005

Percentage of time flow is equalled or exceeded

Streamflow (cumecs)

All data Calibration Data

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length of the record there may be more extreme responses that have not been observed.

Residual mass curves

Residual mass curves are used to identify abnormalities in the monthly and annual records of individual rainfall and runoff records. They show the departure of the monthly (and annual) values to the mean. Comparison of residual mass curves for both rainfall and flow may indicate if a rainfall record is suitable for input to the model for a particular sub-catchment. Ideally both would follow a similar pattern. In Figure 6.6 (top), the monthly rainfall and stream flow show significant differences in the residual mass plots, indicating that the rainfall record is not suitable as model input for this catchment. Conversely, in Figure 6.6 (lower) the residual mass plots show little difference between the monthly rainfall and streamflow curves, suggesting this rainfall record is appropriate for model calibration for this particular catchment. It should be noted that in catchments where precipitation falls as snow there may be some discrepancies in the rain and flow residual mass curves during periods of snowfall and subsequent snowmelt.

Figure 6.6 Residual mass curves compare monthly rainfall and streamflow data to provide an indication of suitability for rainfall-runoff modelling. The top chart shows a catchment where there is considerable divergence between the time series indicating that the rainfall record should not be used for calibrating this catchment. Conversely, in the lower chart both time series show consistency in the curves suggesting that this catchment can be calibrated using this rainfall time series as input.

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Rainfall-runoff event analysis

Residual mass curves can identify periods of record which are suitable for model calibration in general. The next stage is to assess whether the rainfall record over the period is able to capture the majority of events in the catchment. Corresponding event rainfall and flow observations are reviewed to find inconsistencies between event rainfall and runoff. For example, small scale intense convective events may occur over the gauge itself, resulting in observed rainfall but only a small (if any) response in the hydrograph. Similarly, rainfall in areas away from the gauge would result in a hydrograph response but no observed rainfall. Figure 6.7 shows an example of such an occurrence which has resulted in a hydrograph in the flow time series for the event but no corresponding rainfall for the period. If numerous instances of such inconsistencies are evident, then the rainfall record may not be suitable for representing the spatial and temporal rainfall over the catchment.

Figure 6.7 A rainfall event is observed a number of days before the response is seen at the outlet of the catchment. This is unlikely to be a lag time issue. The rainfall event recorded may not be representative of catchment areal rainfall. In addition, the response in the hydrograph suggests that there may have been a significant event in the catchment which was not adequately captured at the rainfall gauge site. Many occurrences of these may render the rainfall record unsuitable for model calibration in this catchment.

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Flow (cumecs)

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June 1985

Rainfall (mm)

126 | A rainfall-runoff model for the Lake Taupo catchment