5.1. Site Description and Data
 South Bison Hill (SBH) (57° 39′N and 111° 13′W), a waste rock overburden pile located north of Fort McMurray, Alberta, Canada, is considered in this study. SBH was constructed with waste rock material from oilsands mining in stages between 1980 and 1996. The area of SBH is 2 km2, rises 60 m above the surrounding landscape, and has a large flat top several hundred meters in diameter. To reclaim the overburden so that revegetation can occur, the underlying shale is covered by a 0.2 m layer of peat on top of a 0.8 m layer of till. The top of SBH is dominated by foxtail barley (Hordeum jubatum); also present are other minor species such as fireweed (Epilobium angustifolium). Estimation of evaporation from the reconstructed watershed is of vital importance as it plays a major role in water balance of the system, which links directly to ecosystem restoration strategies.
 Micrometeorological techniques were used to directly measure evaporation and the surface energy balance. A mast located in the approximate center of SBH was equipped to measure air temperature (AT) and relative humidity (RH) (HMPFC, Vaisala, 3 m) housed in a Gill radiation shield, ground temperature (GT) (TVAC, Campbell Scientific, averaged 0.01–0.05 m depth), all-wave net radiation (Rn) (CNR-1, Kipp and Zonen, 3 m), and wind speed (WS) (015A Met One, 3.18 m). All instruments were connected to a data logger (CR23X, Campbell Scientific) and sampled at 10 s, and an average or a cumulate record was logged every half hour. The energy balance of the surface is given by:
where LE is the latent heat flux (evaporation when divided by the latent heat of vaporization), H the sensible heat flux, G the ground heat flux, and ɛ the residual flux density, all expressed in W m−2. G was measured using a CM3 radiation and energy balance (REBS) ground heat flux plate placed at 0.05 m depth. LE and H were measured directly via the open path eddy covariance (EC) technique [Leuning and Judd, 1996] using a CSAT3 sonic anemometer (Campbell Scientific) and an LI-7500 CO2/H2O gas analyzer (Li-Cor) with the midpoint of the sonic head located on a boom 2.8 m above the ground surface. Measurements of H and LE were taken at 10 Hz, and fluxes were calculated using 30-min block averages with 2-D coordinate rotation. Sensible heat fluxes were calculated using the sonic virtual temperature [Schotanus et al., 1983], and latent heat fluxes were corrected for changes in air density [Webb et al., 1980]. Fluxes were removed when friction velocity was less than 0.1 m/s due to poor energy balance closure at low wind speeds [Twine et al., 2000; Baker and Griffis, 2005]. Flux measurements were also removed during periods of rainfall and during periods of unexpected change in state variables. No gap filling was performed.
 Variation of evaporation is commonly perceived as highly dependent on climatic variables such as temperature, humidity, solar radiation, and wind speed [Brutsaert, 1982; Sudheer et al., 2003]. Hence in this study, the climatic variables AT, GT, Rn, RH, and WS, which are commonly measured at weather stations, are used to estimate the evaporation flux measured by the EC system. As a common practice, a training set is used for model development, and an independent validation set is used to test the efficiency of the developed model. Hourly data between 20 May 2003 and 9 June 2003 comprise the training set, and the data between 18 June 2003 and 28 June 2003 comprise the testing set. The training set consists of 500 instances while the testing set consists of 247 instances. Plots showing the correlation of input variables AT, GT, Rn, and RH with LE are presented in Figure 3. The correlation plot between WS and LE is not shown as there is no significant correlation between them. The correlation plots shown in Figure 3 are based on the training set alone. As expected, air temperature (R2 = 0.227), ground temperature (R2 = 0.405), and net radiation (R2 = 0.569) are shown to have a positive trend with LE, while relative humidity (R2 = 0.114) has a negative relationship with LE.
Figure 3. Correlation plot between latent heat and (a) air temperature, (b) ground temperature, (c) net radiation, and (d) relative humidity.
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 Traditionally, Penman-Monteith is the most widely used method for estimating evapotranspiration due to the widespread availability of the input variables. The hourly FAO Penman-Monteith [Temesgen et al., 2005] equation is given by equation (6):
where, Rn is net radiation at the grass surface (MJ m−2 hr−1), G is soil heat flux density (MJ m−2 hr−1), Δ is the saturation slope vapor pressure curve at AT (K Pa °C−1), γ is the psychrometric constant (K Pa °C−1), e0 is saturation vapor pressure at air temperature AT (K Pa), ea is the average hourly actual vapor pressure (K Pa), and WS is the average hourly wind speed (m/s). It should be noted that the evaporation calculated by the Penman-Monteith equation is potential evaporation for a well-watered surface and not actual evaporation. Several methods of converting ET0 to actual evaporation which estimate actual evaporation based on water balance or by empirical equations have been illustrated by Saxton  and Jensen . Eddy covariance (EC) offers a convenient way to directly measure actual evaporation, and hence in this study, an attempt has been made to model EC-measured evaporation flux using neural networks.
5.2. Estimation of Evaporation Flux Using FFNNs
 The FFNN model considered for modeling evaporation flux consists of five input neurons, representing AT, GT, Rn, RH, and WS. The output layer consists of a single neuron representing LE. As explained in section 2, the optimal number of hidden nodes is found by the trial-and error method and is found to be four. Hence the neural network architecture adopted in this study is of the form ANN(5,4,1). The Bayesian regularization algorithm is used for training the networks. For this case study, 5000 epochs is found optimal for training the FFNNs.
5.3. Estimation of Evaporation Flux Using SMNNs
 The performances of both variants of SMNNs (SMNN(Competitve) and SMNN(SOM)) are tested with regard to estimating the EC-measured evaporation flux. The SMNNs considered in this application consist of five input neurons. By the trial-and-error method, as detailed in section 3, the optimal number of neurons in the spiking layer is found to be eight for both SMNN(Competitive) and SMNN(SOM). The spiking layer consists of eight neurons, representing individual clusters in the input space. Eight hundred epochs are found optimal for training the spiking layer. Corresponding to each cluster, eight different associator neural network models specializing in mapping input-output relationships at different domains of the mapping space are constructed. The associator neural network models employ Bayesian regularization algorithm for training the networks. The optimal network architecture of associator neural networks is ANN(5, 4, 1). Symbolically, the optimal architecture of SMNNs can be represented as SMNN(8, ANN(5, 4, 1)).