| 1 Introduction |
|
1 | (10) |
|
|
|
1 | (7) |
|
|
|
8 | (2) |
|
1.2.1. The extrapolation problem |
|
|
8 | (1) |
|
1.2.2. Network architecture |
|
|
8 | (1) |
|
|
|
9 | (1) |
|
|
|
10 | (1) |
| 2 Artificial Neural Networks |
|
11 | (12) |
|
|
|
11 | (1) |
|
2.2 What is an Artificial Neural Network |
|
|
12 | (1) |
|
2.3 Multilayer Perceptron |
|
|
13 | (2) |
|
2.4 Delta learning rule for Feed-Forward Multilayer Perceptron |
|
|
15 | (2) |
|
|
|
17 | (4) |
|
2.5.1 The unipolar binary function or sigmoid function (S) |
|
|
17 | (1) |
|
2.5.2 The bipolar binary function (B) |
|
|
18 | (1) |
|
2.5.3 The hyperbolic tangent function (T) |
|
|
19 | (1) |
|
2.5.4 The linear function (L) |
|
|
20 | (1) |
|
2.6 Recurrent Multilayer Perceptron |
|
|
|
2.6.1 Elman Recurrent Network (ERN) |
|
|
21 | (1) |
|
2.6.2 Jordan Recurrent Network (JRN) |
|
|
22 | (1) |
| 3 Preliminary considerations |
|
23 | (6) |
|
|
|
23 | (1) |
|
3.2 The choice of a suitable time interval |
|
|
23 | (3) |
|
3.3 The choice of goodness-of-fit indices |
|
|
26 | (3) |
| 4 Extrapolation management for Artificial Neural Network models of Rainfall-Runoff relationships |
|
29 | (18) |
|
|
|
29 | (1) |
|
4.2 Standardisation: key to managing the extrapolation problem |
|
|
30 | (1) |
|
4.3 Standardised range of other activation functions |
|
|
31 | (1) |
|
4.4 Case studies without including the EMF in the raw data |
|
|
32 | (4) |
|
4.4.1 Silk Stream catchment |
|
|
32 | (3) |
|
4.4.2 Dollis Brook catchment |
|
|
35 | (1) |
|
|
|
35 | (1) |
|
|
|
35 | (1) |
|
4.5 Case studies with including EMF in the raw data |
|
|
36 | (3) |
|
|
|
39 | (1) |
|
4.7 Case studies with different activation functions |
|
|
39 | (4) |
|
4.8 Different values of the factor K2 |
|
|
43 | (3) |
|
|
|
46 | (1) |
| 5 Recurrent Neural Networks |
|
47 | (14) |
|
|
|
47 | (1) |
|
|
|
48 | (5) |
|
5.2.1 Case I: the Brue River |
|
|
48 | (1) |
|
5.2.2 Case II: the Thrushel River |
|
|
49 | (2) |
|
5.2.3 Case III: the Chumporn River |
|
|
51 | (2) |
|
5.3 Elman recurrent network |
|
|
53 | (3) |
|
5.4 Jordan recurrent network |
|
|
56 | (3) |
|
5.4.1 Case I: the Brue River |
|
|
56 | (1) |
|
5.4.2 Case II: the Thrushel River |
|
|
57 | (2) |
|
5.5 Jordan recurrent network with Future Errors |
|
|
59 | (1) |
|
|
|
60 | (1) |
| 6 Choice of input |
|
61 | (20) |
|
|
|
61 | (1) |
|
6.2 Average rainfall or Distributed rainfall |
|
|
61 | (4) |
|
6.3 Forward shift operator |
|
|
65 | (1) |
|
6.4 Implementation of the FDTF Method |
|
|
66 | (13) |
|
|
|
68 | (6) |
|
6.4.2 Case II: Mole river |
|
|
74 | (5) |
|
6.5 Discussions and Conclusions |
|
|
79 | (2) |
| 7 Conclusions and recommendations |
|
81 | (4) |
| 8 Samenvatting |
|
85 | (4) |
| 9 References |
|
89 | (12) |
|
I Data used for the study |
|
|
95 | (6) |
|
|
|
95 | (1) |
|
|
|
96 | (1) |
|
|
|
97 | (1) |
|
1.4. The Dollis Brook river |
|
|
97 | (1) |
|
|
|
98 | (1) |
|
1.6. The Silk Stream river |
|
|
99 | (1) |
|
|
|
99 | (1) |
|
1.8. Estimated Maximum Flood (EMF) of the Dart and Thrushel rivers |
|
|
99 | (2) |
| Curriculum vitae |
|
101 | |