5.8 Sensitivity and uncertainty analysis
5.8.1 Sensitivity analysis
A sensitivity analysis is a systematic evaluation of the effect of varying each model‟s parameters on the model output. One model output is considered, and a base line simulation is chosen (e.g. using calibrated values). A number of simulations are then run by repeatedly increasing then decreasing each parameter value by a fixed percentage (Parkin, 2000a).
In this research, all parameters were subjected to sensitivity analyses including the un-calibrated parameters of runoff generation, runoff concentration, and channel flow and transmission losses routines discussed in sections 5.6.6.2, 5.6.6.3 and 5.6.6.4 respectively.
The generated runoff value of the model output was considered to conduct the sensitivity analysis for each parameter. Stated clearly, the generated runoff is the sum of two components: runoff (as either IEOF or SEOF) and transmission losses (portion of the generated runoff which is lost to the ground). Therefore, for those parameters, which affect the transmission losses like active alluvium depth and alluvium infiltration rate, the transmission losses value as output was considered to evaluate the model sensitivity.
5.8.1.1 Runoff generation parameters
A set of four simulations were run for 13 parameters of different model routine; by a decrease of 25% and 50% of the calibrated value, then by an increase in the calibrated value of 25% and 50%. For runoff generation parameters, the simulations were done for infiltration rate, initial losses and the soil depths (Fig. 5.37). The soil depth is the most sensitive parameter to any changes because it directly determines the amount of rainfall required to saturate the soil before a runoff is generated. By decreasing the soil depths to 50% of all terrain, discussed in (5.6.5.1), the runoff amount almost doubles (190%). On the other hand, with higher soil depths more rain is required to saturate the soil and consequently less runoff is generated. An increase in 50% in the soil depths will reduce the amount of the generated runoff to 62% of the calibrated value. The thickness of the soil has a more substantial role in Saturation Excess overland Flow (SEOF) mechanisms. Therefore, with deeper soil, more rain is required to saturate the soil. If Infiltration Excess overland Flow (IEOF) is the dominating process, the infiltration rate has a greater role in determining the amount of generated runoff.
The infiltration rate is also a sensitive parameter, and the generated runoff amounts are more influenced by a decrease in infiltration rate rather than an increase. A decrease of 50% of the calibrated infiltration rate value of all soil units will increase the generated runoff amount by 44% while a 50% increase will reduce the runoff amounts by 11%. Similar to soil depth and infiltration rate, the initial loss parameter also has an inverse relation with the generated runoff, and with a decrease of 50% of the initial loss, an increase of 21% in the generated runoff amount occurs. An increase of 50% will reduce the runoff amount by 14%.
These variations in increase or decrease in the runoff amounts are controlled by the runoff mechanism which is specific for every runoff event and it is possible to have in the same rain storm one or more runoff mechanisms. The initial loss parameter is dependent on soil type and the vegetation cover. Generally, their values for the different terrain are low. Therefore, the increase in value will not reduce the runoff amounts very much when compared with the influence of soil depth.
50%
80%
110%
140%
170%
200%
-50% -25% 0% 25% 50%
parameter change factor
Runoff change
Inf.rate Initial losses Soil depth
Fig. 5.37: Sensitivity analysis for runoff generation parameters.
5.8.1.2 Runoff concentration parameters
Sensitivity analyses were conducted to Fisher-Tippet distribution parameters “a” and
“b.” The first parameter describes the required time for the generated runoff to be transformed from each sub-catchment to a lateral flow of the adjacent channel while the second parameter determines the shape of the synthetic unit hydrograph of every sub-catchment. Variations in the values of these parameters will effect the time to concentration and the width of the curve and do not influence the runoff volume.
5.8.1.3 Routing parameters
To evaluate the effect of parameter changes on transmission losses, six parameters were subjected to sensitivity analysis. These parameters are: channel length, channel slope, channel width, channel roughness coefficient Manning n, percentage covered by the inner channel, and depth to bankfull stage. Channel slope and the depth to bankfull stage have no significant influence on the generated runoff amount rather;
they do influence the time arrival of the flood. Channel length and width influence the volume of the transmission losses (Fig. 5.38). In case of shorter and narrower channels, less runoff is lost along and within the channels. An increase of channel lengths and widths by 50% leads to more loss of runoff to the channel beds as transmission losses with 30-40% more losses compared with the calibrated value.
50%
70%
90%
110%
130%
150%
-50% -25% 0% 25% 50%
parameter change factor
Trans. Loss. change
Channel length Channel width
Fig. 5.38: Sensitivity analysis for routing parameters (physical).
Other parameters which influence the amount of transmission losses are the channel roughness coefficient and the percentage of the inner channel to the total width of the channel. A roughness coefficient was assigned for every channel type based on field observations and surface characteristics of the channels; therefore Manning n, in addition to its influence on the flood peak and flood arrival, does influence the amount of transmission loss (Fig. 5.39). By having higher friction between the flood wave and the channel surface, larger volumes of runoff, which have came from the adjacent sub-catchments of every channel segment, will be lost to the channel beds as transmission losses. A decrease of the roughness coefficient by 50% will yield an 8%
reduction in transmission loss while an increase of 50% in the roughness coefficient will cause a 7% increase in transmission losses compared with the calibrated value.
The c% parameter is the percentage of the inner channel relative to the total width of the channel, and is acquired through field measurements. When the total channel is wide and the inner channel is narrow, relatively low transmission losses occur. When the total channel is narrow (similar to channel type 4), the percentage of the inner channel is usually higher and transmission losses will also be low due to the inner channel being the part of the channel which will be flooded first (Fig. 5.39).
A decrease of 50% in the inner channel percentage will increase the transmission losses by 8%, while an increase of 50% of the inner channel percentage will cause a reduction of 16.5% in the transmission losses.
80%
90%
100%
110%
-50% -25% 0% 25% 50%
parameter change factor
Trans. Loss. change
Manning n c%
Fig. 5.39: Sensitivity analysis for routing parameters (empirical).
5.8.1.4 Transmission losses parameters
The depth of active alluvium (Ad) and the infiltration rate of the alluvium (kf) have a direct influence on transmission losses. Deep alluvia along channels means a greater proportion of the flood water will infiltrate into the channel bed, effectively increasing transmission losses. Over the same time with a higher infiltration rate into the alluvium, more transmission losses occur (Fig. 3.40). The increase or decrease in the alluvium depth by 50% will cause an increase and decrease of 5% and 4%
respectively, while the infiltration rate of the alluvia has a greater influence on the transmission losses in which 50% reduction will cause 30% reduction in transmission losses and 50% of increase will cause 25% more transmission losses.
60%
75%
90%
105%
120%
-50% -25% 0% 25% 50%
parameter change factor
Trans. Loss. change
Ad kf
Fig. 5.40: Sensitivity analysis for transmission losses parameters.
5.8.2 Uncertainty analysis
As mentioned earlier, some error or uncertainty in the model is attributed to the input data or the forcing data used in the model. The criteria which have been followed to reduce the uncertainty of the measured rainfall using the automatic tipping bucket rain gauges were mentioned in section 4.3.1, and for the climatological data, they were mentioned in section 4.3.2. Still, for the climatic stations an important criterion of their final locations was considered to secure them during the monitoring period;
therefore, both weather stations were installed on the roofs of governmental buildings which violate the 2 m height rule required to calculate the evapotranspiration.
Therefore, a correction should be considered to adjust wind speed data to standard height to reduce the uncertainty of wind effect.
Wind speed is measured with anemometers. Anemometers are composed of cups or propellers in a weather station, which are turned by the force of the wind (Fig. 4.15).
By counting the number of revolutions over a given period of time, the average wind speed over the measuring period is computed and this value is important to calculate the evapotranspiration process in hydrological modelling. Wind speed is affected by the height above the soil surface which is slowest at the surface and increases with height. Therefore; the anemometers are placed at a chosen standard height which is 2 meters above the surface for the calculation of evapotranspiration and they are required to be adjusted in case of higher elevations as recommended by Allen et al.
(1998) using the following equation: z: height of measurement above ground surface, (m)
The two weather stations of King Hussein Gardens and Wadi Es Sir WWTP were installed 6 m and 6.5 m from the surface, respectively. Therefore, the wind speed effect was corrected for both stations, using the above mentioned equation in order to reduce the uncertainty value in the measured wind speed. After correcting the raw data of both stations for wind speed, the grids were interpolated and prepared in the proper format to run the model.
The uncertainties resulting from model parameters are given in Table 5.11. All values are within the range of ± 50%, which are included in the sensitivity analysis discussed earlier. The uncertainty values were estimated based on the experience acquired during the parameter assessment and on previous studies conducted in arid and semi arid regions (e.g. Lange, 1999; Shadeed, 2008).