Problem Formulation
Chapter 6 Synthetic Streamflow Generation
6.4 Comparison of Results of ANN, Thomas-Fiering and Actual Streamflow Series
component in the streamflow generation model to prevent the network from generating repetitious sequence of streamflow. A small random component calculated on the basis of the standard deviation of the observed streamflow is added to the output produced by the network (Ahmed and Sarma 2007). Thus repetitive generations of streamflow were handled by introducing a random component t t in the model. Where, t is an independent standard normal random variable with mean zero and variance unity, t is the standard deviation of observed streamflow of the corresponding month. Synthetic streamflow series of hundred years are generated by feeding the known value of inflow of previous period, inflow of current period, periodical mean of the historical flow of next period and periodical standard deviation of the historical flow of next period, maximum and minimum of historic flow of next period and average time rate of change of discharge in different periods of the series of flow. The output of the model will be the predicted inflow of the succeeding period and it will serve as input for the next iteration. If negative flow occurs during synthetic streamflow generation, would be replaced by the minimum value of the historic flow for the particular period (Ahmed and Sarma 2007).
6.4 Comparison of Results of ANN, Thomas-Fiering and Actual
those models along with the corresponding parameter for which they are working best.
Several trials have been made to work out the best ANN model for different time step discretization by considering different number of hidden neurons and input parameters.
Trial made for monthly model is detailed in Table- 6.1. The ANN30D1 with 8 neurons in hidden layer, momentum factor = 0.05 and learning rate = 0.05 was found to be the best. The results showing the comparisons of ANN and Thomas-Fiering models with the observes mean monthly time series and standard deviation of observed monthly time series are presented in Fig 6.2 and Fig 6.3 respectively. It is clear from the curve that synthetic streamflow generated by ANN series though generates slightly higher value in case of periodical mean, periodical standard deviation of the generated series is quite close to the actual series. The skewness value of the series generated by ANN30D1 is found closer to the skewness value of actual series in comparison to that of the Thomas-Fiering model.
Fig.6.2 Mean of synthetic series –ANN30D1 0
1000 2000 3000 4000 5000 6000
1 2 3 4 5 6 7 8 9 10 11 12
Monthly mean of streamflow (m3/s)
Month
ANN Actual
Thomas Fiering
Fig.6.3 Standard deviation of synthetic series –ANN30D1
Fig.6.4 Mean of synthetic series –ANN10D1
In case of the ten daily ANN models, ANN10D1 is found best. It has 3 neurons in hidden layer (Table 6.3) with = 0.5 and = 0.05. Fig 6.4 and Fig 6.5 are the plots showing the comparisons of ANN10D1 and Thomas-Fiering with the actual ten daily series for mean
0 200 400 600 800 1000 1200 1400
1 2 3 4 5 6 7 8 9 10 11 12
Monthly standars deviation of streamflow (m3/s)
Month
ANN Actual
Thomas Fiering
0 1000 2000 3000 4000 5000
1 4 7 10 13 16 19 22 25 28 31 34
Ten daily mean of streamflow (m3/s)
Period (10 days)
ANN Actual
Thomas-Fiering
and standard deviation of the synthetic series. The results depicts that both ANN generated series and Thomas-Fiering model generated series are in good agreement with the actual series in respect of periodical mean. In respect of standard deviations and skewness of the series ANN10D1 outperform the Thomas-Fiering model.
Fig.6.5 Standard deviation of synthetic series –ANN10D1
It has been found from the Table 6.1, Table 6.4 and Table 6.8 that the ANN08D1 having 10 neurons in hidden layer, = 0.02 and = 0.04 is performing better among others ANN models for eight daily time step. The comparative results are presented in Fig 6.6 and Fig 6.7; periodical mean of the ANN generated series has been found to give slightly lower values in the pre-monsoon period and slightly higher value in the dry period as compared to actual series, but it follows quite well to the observed series in case of periodical standard deviation. As observed in the previous cases regarding Thomas-Fiering model, here also it can capture the periodical mean very well but it fails to capture the periodical standard deviation. The skewness coefficient of the entire series generated by ANN08D1 is relatively
0 500 1000 1500 2000 2500
1 4 7 10 13 16 19 22 25 28 31 34
Ten daily standard deviation of streamflow (m3/s)
Period (10 days)
ANN Actual
Thomas Fiering
close to skewness value of the actual streamflow series as compared to the skewness value of the series generated by Thomas-Fiering model.
Fig.6.6 Mean of synthetic series –ANN08D1
Fig.6.7 Standard deviation of synthetic series –ANN08D1
For six daily time step discretization the ANN06D3 model having four input parameter (Table 6.1), 8 neurons in hidden layer, = 0.9 and = 0.09 found to be the most
0 1000 2000 3000 4000 5000 6000
0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45
Eight dialy mean of streamflow (m3 /s)
Period (8 days)
ANN Actaul
Thomas -Fiering
0 500 1000 1500 2000 2500 3000 3500
0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45
Eight daily standard deviation of streamflow (m3/s)
Period (8 days)
ANN Actaul
Thoams -Fiering
efficient as compared to others. The comparisons of mean and standard deviation of each period of the series are shown in Fig 6.8 and Fig 6.9.
The results reveals that though the periodical mean of the series generated by Thomas–Fierings methods follows good except for the period during second seasonal peak i.e. during months of August and September, the series generated by ANN predicts relatively low values during pre monsoon period. On the other hand the periodical standard deviation of series generated by ANN is in close agreement with the actual series while the series generated by Thomas-Fiering model gives very high values. Moreover, the skewness value of the whole series generated by Thomas Fiering is also found high than the skewness of the actual series as compared to ANN (Table- 6.8).
Fig.6.8 Mean of synthetic series –ANN06D3
Fig 6.10 and Fig 6.11 gives a comparison of the synthetic series generated by Thomas-Fiering’s method and ANN method for five daily time step. The ANN05D6 model having 10 neurons in hidden layer, = 0.9 and = 0.04 performs better as compared to other models.
0 1000 2000 3000 4000 5000
0 5 10 15 20 25 30 35 40 45 50 55 60 65
Six daily mean of streamflow (m3/s)
Period (6 days)
ANN Actaul
Thomas-Fiering
Fig.6.9 Standard deviation of synthetic series –ANN06D3
Fig.6.10 Mean of synthetic series –ANN05D6
The periodical mean of series generated by ANN05D6 gives marginally low values as
compared to actual observed series while Thomas-Fiering generated series follows quite well to the actual series.
0 500 1000 1500 2000 2500 3000 3500
0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68
Six daily standard deviation of inflow (m3 /s)
Period (6 days)
ANN Actaul
Thomas-Fiering
0 1000 2000 3000 4000 5000 6000
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
Five daily mean of streamflow (m3/s)
Period (5 days)
ANN Actual
Thomas-Fiering
Fig.6.11 Standard deviation of synthetic series –ANN05D6
In case of periodical standard deviation ANN05D6 follows the actual series far better as compared to Thomas-Fiering generated series. From the Table 6.8 it is clear that the skewness of whole series generated by ANN05D6 is quite close to the skewness value of the actual series.
For the daily time step discretization, the result of the both model are shown in Fig 6.12 and Fig 6.13 respectively. The periodical mean of series generated by ANN01D5 follows well in lean season; it gives rather low values in the beginning as well as end of wet season and high values in peak wet season as compared to actual observed series. On the contrary Thomas –Fiering is found better in case of periodical mean. The comparisons of the periodical standard deviation shows that most of the time ANN01D5 is quite close to actual series except for a few periods.
0 500 1000 1500 2000 2500 3000 3500
0 6 12 18 24 30 36 42 48 54 60 66 72 78
Five daily standard deviation of streamflow (m3/ s)
Period (5 days)
ANN Actual
Thomas-Fiering
Fig 6.12 Mean of synthetic series -ANN01D5
Fig.6.13 Standard deviation of synthetic series –ANN01D5
In this case the skewness value of the series generated using ANN01D5 model is also closer to the value of actual historical series as compared to Thomas-Fiering model. The best models for each time step discretization and their network as well as input parameters are summarized in the Table 6.8.
0 1000 2000 3000 4000 5000 6000 7000 8000
1 16 31 46 61 76 91 106121136151166181196211226241256271286301316331346361
Daily mean of streamflow (m3/s)
Period (1 day)
ANN Actaul
Thomas-Fiering
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
1 19 37 55 73 91 109 127 145 163 181 199 217 235 253 271 289 307 325 343 361
Daily standard deviation of streamflow (m3 /s)
Period (1 day)
ANN Actual
Thomas-Fiering
Table 6.8 Different ANN models and their selection parameters