Risk in Water Resources Management (Proceedings of Symposium H03 held during IUGG2011 in Melbourne, Australia, July 2011) (IAHS Publ. 347, 2011).

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1 Risk in Water Resources Management (Proceeings of Symposium H3 hel uring IUGG211 in Melbourne, Australia, July 211) (IAHS Publ. 347, 211). 121 Reucing the uncertainty associate with water resources planning in a eveloping country basin with limite runoff ata through AI rainfall runoff moelling ADEBAYO J. ADELOYE School of the Built-Environment, Heriot-Watt University, Riccaton, Einburgh EH14 4AS, UK a.j.aeloyehw.ac.uk Abstract A major bane of water resources assessment in eveloping countries is the insufficiency or total lack of hyrometeorological ata, resulting in huge uncertainties an ineffectual performance of water schemes. This stuy reports on the application of the Kohonen Self-organizing Map (KSOM) unsupervise artificial neural networks in harnessing the multivariate correlations between the rainfall an runoff for an inaequately gauge basin in southwest Nigeria, for the sole purpose of extening the runoff recors, an through them, reucing water resources planning uncertainty associate with the use of short ata recors. The extene runoff recors were then analyse to etermine possible abstractions from the main river source at ifferent exceeence probabilities. The stuy emonstrates the successful use of emerging tools in reucing the uncertainty associate with lack or insufficiency of ata for water resources planning assessment. Key wors water resources assessment; hyrological ata; Kohonen Self Organising Map (KSOM); reliability; water abstractions; Nigeria INTRODUCTION Planning an management of water resources systems require that aequate an reliable hyrometeorological ata are available (Aeloye, 1996). However, this is often not the situation in most eveloping countries where the runoff ata are either unavailable or when available, they are too short an rile with numerous gaps an outliers. One commonly aopte solution in such situations is to reconstruct an exten the available runoff ata recors using the typically much longer rainfall ata recors from rainfall runoff moelling such as regression analysis. However, traitional rainfall runoff moelling, incluing regression, can only analyse for one epenent variable an is unfeasible for preiction if the preictor is missing (Aeloye, 29). To overcome this problem, artificial intelligence (AI), multivariate techniques unhinere by missing values an noise in the available ata can be use. The Kohonen Self-organising Map, KSOM (Kohonen et al., 1996) is a class of unsupervise artificial neural networks whose powerful clustering capability can reuce a multi-imensional ata array into a two imensional array of features or best matching units (BMUs), which then form the basis for multivariate preiction. This approach was use to reconstruct an exten monthly rainfall an runoff ata for stations within the lower Osun basin in southwest Nigeria for the purpose of water resources assessment. In the next Section, further etails about the KSOM moelling are given. This is then followe by the methoology applie for the Osun catchment stuy. Finally, the results are presente an iscusse. KSOM MODELLING The KSOM (also calle feature map or Kohonen map) is one of the most wiely use artificial neural network algorithms (Kohonen et al., 1996) an its principal goal is to transform an incoming signal pattern of arbitrary imension into a two-imensional (2-D) iscrete map. It involves clustering the input patterns in such a way that similar patterns are represente by the same output neurons, or by one of its neighbours. The KSOM consists of two layers: the multi-imensional input layer an the competitive or output layer; both of these layers are fully interconnecte as illustrate in Fig. 1. The output layer Copyright 211 IAHS Press

2 122 Aebayo J. Aeloye Fig. 1 Illustration of the winning noe an its neighbourhoo in the Kohonen Self-organizing Map. Fig. 2 Preiction of missing components of the input vector using the Kohonen Self-organizing Map (BMU = best matching unit). consists of M neurons arrange in a 2-D gri of noes. Each noe or neuron i (i = 1, 2,, M) is represente by an n-imensional weight or reference vector Wi = [w i1,., w in ], where n is the imension of each input vector, i.e. the maximum number of variables in the input vector. In training, an input vector is ranomly selecte an its most similar reference vector, i.e. BMU, is ientifie by etermining the closest to it in terms of the Eucliian istance, D i : n 2 ( x w ) ; i = 1,2 M Di = m j j ij,..., j= 1 where x j is the jth element of the current input vector; w ij is the jth element of the coe vector i; an m j is the so calle mask which is use to inclue in (m j = 1), or exclue from (m j = ), the calculation of the Eucliian istance, the contribution of a given element x j of the input vector. Once ientifie, the elements of the BMU are upate an the process continues until some state stopping criteria are reache. Rustum & Aeloye (27) present aitional comprehensive information about training the KSOM, incluing various inices for assessing its performance. The application of the KSOM for preiction purposes is illustrate in Fig. 2 (see also Rustum & Aeloye, 27). First, the moel is traine using the available ata set. Then the eplete vector, i.e. with the preictan either missing or eliberately remove, is presente to the KSOM to ientify its BMU using the compute Di (equation (1)). The values for the missing variables are then obtaine as their corresponing values in the BMU. (1)

3 Reucing the uncertainty associate with water resources planning in a eveloping country basin 123 METHODOLOGY Case stuy an ata The Osun basin in southwest Nigeria is highly evelope with many water abstractions an impouning schemes, as shown in Fig. 3. The latest evelopment being propose on the river is an off-line, pumpe storage scheme at Igbonla, just before the river enters the Lagos lagoon. To achieve this, probabilities associate with ifferent pumpe abstraction scenarios, as shown in Table 1, for filling the reservoir will nee to be etermine. Without runoff ata at Igbonla, however, this prove an impossible task. Fig. 3 The Osun basin map showing isohyets an location of main towns, ams, runoff an rainfall stations. Table 1 Propose abstraction scenarios from River Osun at Igbonla. Target year Desire aily pumping rate (MCM)

4 124 Aebayo J. Aeloye Rainfall ata are wiely available within the basin, incluing: monthly ata for Osogbo an Ibaan ( ); Lagos Marina, Ijebu-Oe an Abeokuta ( , albeit with several missing values); an Lagos Islan, Ikeja an Ibaan ( ). Thus potentially, it coul be assume that rainfall ata are available for , i.e. 66 years, which can be use as the basis for extening/reconstructing monthly runoff recors at esire locations in the basin. Stations with runoff recors in the basin inclue STN 44 (monthly, ) an STN 25 (monthly, ), both upstream of the Igbonla site an with far too short recor lengths to carry out any meaningful statistical analysis. One way of improving the situation is to harness the multivariate correlations between the rainfall an runoff, an thus exten the runoff recors. All other gauging sites in Fig. 3 have no time series runoff recors. KSOM moelling The KSOM analysis use monthly rainfall at four stations, namely Ibaan (no. 6528), Ikeja (no. 6521), Lagos Islan (no. 6523), an Osogbo (no ) an the two runoff stations (25 an 44) for the multivariate, KSOM moelling. This le to the reconstruction of runoff at stations 25 an 44 for the perio The self-organizing map (SOM) toolbox for Matlab 5 was use for this case stuy. The toolbox was evelope by the SOM team at the Helsinki University of Technology, Finlan ( Runoff reconstruction an quantiles at Igbonla Simple area-ratio scaling (Loucks et al., 1981) was use for transposing runoff ata to Igbonla. Since STN 25 is closer to Igbonla, its reconstructe ( ) ata forme the basis of the transposition using the respective catchment areas, i.e km 2 at Igbonla an 4325 km 2 at STN 25. Allowance was also mae for the Asejire am (catchment area = 5646 km 2 ) an its ownstream compensation releases, which was taken to be 1% of STN 25 mean runoff. Finally, runoff quantiles at Igbonla were etermine by fitting the 3-p lognormal istribution as escribe by McMahon & Aeloye (25) to the 1-month annual low-flow series. RESULTS AND DISCUSSIONS Rainfall runoff analysis using the KSOM The KSOM component planes which visually illustrate the correlations between the various variables are shown in Fig. 4. The runoff component planes at both stations 44 an 25 are broaly similar with coinciental occurrences of high an low runoff magnitues. However, in relation to the rainfall stations, runoff at both stations 44 an 25 appears to correlate more with the Osogbo rainfall. This woul suggest that Osogbo rainfall woul be a much better preictor for the runoff at both stations 44 an 25. Information such as this if available a priori woul have mae Osogbo rainfall to be sole preictor variable for runoff at the sites if a univariate regression approach were to be aopte. The time series plots of the monthly ata are shown in Fig. 5 both for the observe an those estimate by the KSOM an confirm the goo performance of the KSOM. In general, the Nash- Sutcliffe efficiency was above 94%, which is very goo. Low flow quantiles The probabilities corresponing to the planne abstractions rates (see Table 1) as estimate from the fitte 3-parameter lognormal istribution are summarise in Table 2. As seen in Table 2, except for the 211 abstraction, where the probability of achieving the require abstraction or higher was 59%, all the other abstraction scenarios ha unacceptably low probabilities. Table 3 shows the abstractions at Igbonla for a range of acceptable reliabilities, from which it is clear that achieving such reliabilities woul entail large water shortages especially in years 215 an 22.

5 Reucing the uncertainty associate with water resources planning in a eveloping country basin 125 Rainfull Ibaan 328 Rainfull Ikeja 444 Rainfull Lagos Rainfull Osogblo 282 Runoff Runoff Fig. 4. KSOM component planes for rainfall an runoff ata, Osun Basin, Nigeria. Ranfall Ibaan Observe Data Preicte Data Using KSOM Preicte Missing Values Rainfall Ikeja Rainfall Lagos Rainfall Osogbo Runoff Station 25 (MCM) Runoff Station 44 (MCM) Data number (Month) Fig. 5 Performance of the KSOM in preicting monthly rainfall an runoff.

6 126 Aebayo J. Aeloye Table 2 Assesse probabilities of projecte abstractions at Igbonla. Year Abstraction rate, q Cumulative probability (MCM/month) Exceeence probability (%) Table 3 Assesse shortfall at Igbonla for acceptable exceeence probability levels. Exceeence Possible abstraction rate Shortfall (%) probability (%) (MCM.month -1 ) Year 211 Year 215 Year CONCLUSIONS This stuy has emonstrate the usefulness of the KSOM as a viable rainfall runoff ata extension tool in situations where the available ata for water resources assessment are limite. Because of its powerful clustering ability, the implementation of the KSOM is unhinere by missing values; inee, as seen in this work, one of the outcomes of the KSOM moelling is the provision of reliable estimates for the missing values. Also, as a consequence of this, ata extension an reconstruction using the KSOM can be accomplishe even when some of the preictor variables are unavailable, something that will be impossible with traitional rainfall runoff moelling tools such as univariate regression. The methoology thus offers huge potential for combating the wicke problem of inaequate an insufficient ata for meaningful water resources planning an management, an the associate uncertainty. On the basis of the results obtaine here, the runoff at Igbonla will only provie the projecte abstraction rates with a low level of reliability. In the UK, it is customary for supply sources to have at least 98% reliability. Achieving such a high level of reliability at Igbonla woul require significant reuctions in the abstraction rates, as shown in Table 3, or supplementing the supply with water from other sources, e.g. grounwater which is abunant in the basin or esalination which is feasible but potentially expensive. REFERENCES Aeloye, A. J. (1996) An opportunity loss moel for estimating value of streamflow ata for reservoir planning. Water Resources Management 1(1), Aeloye, A. J. (29) The relative utility of multiple regression an ANN moels for rapily preicting the capacity of water supply reservoirs. Env. Moelling & Software 24(1), Kohonen, T., Simula, O. & Visa, A. (1996) Engineering applications of the self organising map. IEEE 84(1), Loucks, D. P., Steinger, J. R. & Haith, D. A. (1981) Water Resources Systems Planning an Analysis. Prentice-Hall, Inc., Englewoo Cliffs, New Jersey, USA. McMahon, T. A. & Aeloye, A. J. (25) Water Resources Yiel. Water Resources Publications LLC ( Colorao, USA. Rustum, R. & Aeloye, A. J. (27) Replacing outliers an missing values from activate sluge ata using Kohonen self organising map. J. Environ. Engng, ASCE 133(9),