w xy» w (Keski ad Terzi, 2006; Deswal ad Pal, 2008; Rahimi Khoob, 2009). Sudheer et al.(2002) w Class A d mw, d e» œ Stephes ad Stewart œ. w» l xy w»
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1 ª Œª Œ 30ƒ 4B Á œ pp. 399 ~ 412 ª x w w x The Temporal Disaggregatio Model for Noliear Pa Evaporatio Estimatio ½ Á½ xá» Á½x Kim, SugwoÁKim, Jug-HuÁPark, Ki-BumÁKim, Hug Soo Abstract The goal of this research is to apply the eural etworks models for the temporal disaggregatio of the yearly pa evaporatio (PE) data, Republic of Korea. The eural etworks models cosist of multilayer perceptro eural etworks model (MLP-NNM) ad geeralized regressio eural etworks model (GRNNM), respectively. Ad, for the performaces evaluatio of the eural etworks models, they are composed of traiig ad test performaces, respectively. The three types of data such as the historic, the geerated, ad the mixed data are used for the traiig performace. The oly historic data, however, is used for the testig performace. From this research, we evaluate the applicatio of MLP-NNM ad GRNNM for the temporal disaggregatio of oliear time series data. We should, furthermore, costruct the credible mothly PE data from the temporal disaggregatio of the yearly PE data, ad ca suggest the available data for the evaluatio of irrigatio ad draiage etworks system. Keywords : pa evaporatio, temporal disaggregatio model, stochastic model, MLP-NNM, GRNNM w w x w. x ƒƒ d r p x(mlp-nnm) y z x(grnnm). š x wsƒ w z l p. x z w d, yw ƒ xk ƒ, l p w d. mw x w w MLP-NNM GRNNM sƒw. ƒ w l w, p j l sƒ w ƒ w œw. w :, w x, w x, MLP-NNM, GRNNM 1. y l ùkü, w l,, l z w (Molia Martiez et al., 2005; Gudekar et al., 2008). (Mass trasfer) w d, d w wù (Eslamia et al., 2008). z š y» w v pƒ w ew x, yw d ƒ e ù y ƒ w ƒ w w (Kisi, 2006). w d,, y w, d k ƒ w w (Jese et al., 1990). ƒ œ w w, w» w w ƒ š (Kisi, 2006). x w x, w w ü x ùký x m w w (Kisi, 2006; Eslamia et al., 2008). z Á Á w m w Áœw Á» ( swkim1968@dyu.ac.kr) z Á w w m w z Á w m w Áœw z Á w w z» lœw Áœw 30ƒ 4B œ 399
2 w xy» w (Keski ad Terzi, 2006; Deswal ad Pal, 2008; Rahimi Khoob, 2009). Sudheer et al.(2002) w Class A d mw, d e» œ Stephes ad Stewart œ. w» l xy w» w,,, t d» w w w. Bruto et al.(2000) d» w w» w. w xz Priestly-Taylor œ w w, x e w.,, k t d» w w w. Kisi(2006) d» w w w -r x w. -r x w, k, t,» d» w w w. w» w l xyw -r x œ ùkü. w Kim ad Kim(2008) ù qq» xy w š ü x w, d y mw x w, ƒ w lw w š œw qq» w. w w x x w ½ ½x (2008)ƒ qq» xy w w x x w mw w w. mw w qq» xyƒ ƒ w. ù x w w w x w (Buria et al., 2000, 2001; Gutierrez-Magess ad McCue, 2004; Ta, et al., 2007; Zhag et al., 2008; Choi et al., 2008) w x, w w. ù» d d ƒ x w wš w. x w w x z w w z ƒ, ƒƒ d, ( w x w ) yw ( d w x w k yw) ƒƒ. š z w w d l p wš w. w x w w w x wš w. 2. x š 2.1 dr p x(multilayer Perceptro, MLP-NNM) MLP-NNM d, d 1 y d, ƒ d d y ¼ w. w MLP-NNM w z l p. z mw MLP-NNM w, w MLP-NNM l p ww (Hayki, 2009). MLP-NNM d 1, d 12, d 12, z 10,000z, e w. w QuickProp q z š w. MLP-NNM d 1, 6 12 (1a)-(1c) ùký, Fig. 1 MLP-NNM ùkü. 12 PE 1 () t = Φ 2 W Φ 1j W 1 PE () t B ji + + B y 1 2 j = 1 = j 1 12 PE 6 () t = Φ 2 W Φ 6j W 1 PE () t B ji + + B y 1 2 j = 1 = PE 12 j 1 12 () t = Φ 2 W 12j Φ 1 W PE () t B ji + + B y 1 2 j = 1 = j 1 Fig. 1 The developed architecture of MLP-NNM (1a) (1b) (1c) 400 ª Œª Œ
3 2.2 y z x(geeralized Regressio, GRNNM) y z x(grnnm)» w x(radial basis fuctio eural etworks model, RBFNNM) x xk x. GRNNM d, d, w d d 4 d, x z» x. d, d w d x ù, d w d. w d(summatio layer) w (Summatio ode) wù (Divisio ode) 2. w d w. w w š d ƒ (Weighted trasfer value) ww. GRNNM ƒ d w d w, w d d. ƒ d w d w l l ù w. GRNNM z MLP-NNM ƒ š. d d z RBFNNM z (Usupervised traiig) K- measù OLS š p w š v w, š z w» w. w d w d z d w s³ y» z (Supervised traiig) (Specht, 1991; Wasserma, 1993; Tsoukalas ad Uhrig, 1997; ½, 2001). GRNNM d d w l x i u ji w s w w ùküš, (2) ùký. m R j = ( x i u ji ) 2» i, j ƒƒ d d ùküš, R j l ùkü l (3) ùký. X = [ x 1, x 2,, x m ] T» U (j) (4) ùký. ( ) = [ u j1, u j2,, u jm ] T U j š (2) (5) ùký. R j = X U j ( )». j (Euclidea legth). R j d w Φ 1 (Á) w (6) ù ký. S j = Φ 1 ( R j ) = Φ 1 ( X U j ( ) ) d w Φ 1 (Á)» w ƒ Ÿ (2) (3) (4) (5) (6) w. ƒ ww (GKF)ƒ, l 0 1 š l ƒ w l ƒw. GKF (7) ùký. m ( x 2 Φ 1 exp( B 1 R j ) i u ji ) 2 = = exp σ » B 1 2 ùküš m w ƒ, 2σ» w s ùküš. w d S j d w d l e (8) ùký. T k = W kj S j = W Φ X U j ( ) kj ( ) 1 j = 1 j = 1» k w d, T k w d, W kj d w d ùkü (8) l w d 1, 6 12 w (9a)-(9d) ùký. S 1 = Φ 2 W 1j Φ 1 ( X U j ( ) ) j = 1 S 6 = Φ 2 W 6j Φ 1 ( X U j ( ) ) j = 1 S 12 = Φ 2 W 12j Φ 1 ( X U j ( ) ) j = 1 D 1 = W 13j Φ 1 ( X U j ) j = 1 (7) (8) (9a) (9b) (9c) (9d)» Φ 2 (Á) w d w, x w (Pure liear trasfer fuctio, PLTF) w. w S 1 1 w, S 6 6 w, S w š D 1 ùküš. d w ƒ w wù ù. GRNNM d 1, 6 12 (10a)-(10c) ùký. S 1 FE 1 () t = D 1 PE 6 () t = PE 12 S 6 D 1 S 12 () t = D 1 (10a) (10b) (10c)» PE 1 (t) 1, PE 6 (t) 6 š PE 12 (t) 12. GRNNM d 1, j l l 20, d 12, w d 30ƒ 4B œ 401
4 3. w x»»z s³ x»»z (Periodic Autoregressio, PAR) x» s³ sww y w PARMA(p,q) ùkü. PARMA x» xy. PARMA (1,1) x (11) ùký. Fig. 2 The developed architecture of GRNNM 13, d 12, z 10,000z, e w. w z (Supervised traiig) QuickProp q z š w. Fig. 2 GRNNM ùkü. 2.3 š (Geetic Algorithm, GA) GA w GRNNM z d»y l w. GRNNM d w e. w w ƒ w z Ÿ w(global solutio) w t w wù. GA j» w ƒ w öe w ƒ ƒ v w (Deb, 2001). ˆ w j» 100 w w, 1% 20 w w x d x w ¾ w w. GA z w GRNNM z j, x GRNNM w l p w w mw (Kim ad Kim, 2008). GA ƒ d w sy (Multiplier) š, z w k» GA w l p w ƒ yw GRNNM w (Neuroshell 2, 1993). = + ( y v, τ 1 ) + ε v τ µ τ 1 y v, τ µ τ Φ 1, τ (11)» v (year), τ (Seaso) š τ = 12,,, ω ùküš. (11) x (Salas et al., 1980). w (½ ½x, 2008) PM œ w qq» z g ƒ yw w PARMA (1,1) x w. š w t 2 t w, 500 w g. t kw, t kw. w t» r (Bias) w» w» 50 w, ƒ PARMA (1,1) x (Method of approximate least square) w w (Kim, 2004). 4., θ 1 τ, ε v, τ 1» w 76» d» d»»»,»» wš w, ƒ «tw» d s ww» w w.» d,,,, s d w. v w» mw w ƒ w l(water maagemet iformatio system, WAMIS) yr ( œ l v w w.» wš» d d w. d » d w z 1919, ƒ d ù, yw k. d » d w z 1919, ƒ d ù, d yw k.» wš» d d w. d » d w z ƒ d ù, yw. š d l» d w š d k, yw.» wš» d s d w. s d l» 402 ª Œª Œ
5 d w š d k, yw. 5. z w w w wùƒ w xk ƒ w ƒ w ƒ š w. w d sww š, w yw w ƒ v w. x z. x ƒ yw w w» w w ƒ, x ƒ j z ù sƒw w (Kim et al., 2009). 5.1 x w m t MLP-NNM GRNNM z l p w d MLP-NNM GRNNM w m w sƒ w. m w t (Correlatio coefficiet, CC), s³ s (Root mea square error, RMSE), Nash-Sutcliffe (Nash-Sutcliffe coefficiet, E) s³ (Average absolute relative error, AARE). Table 1 MLP-NNM GRNNM w s ƒw» w m w t ùkü.» y i ( x) = (mm), y i ( x) = d (mm), u y = s³(mm), = d s³(mm) =š u y Idex CC RMSE E AARE Table 1. Summary of statistical idex Equatio 1 -- [ y i ( x) u y ][ y i ( x) u y ] [ y i ( x) u y ] 2 -- [ y i ( x) u y ] [ y i ( x) y i ( x) ] 2 [ y i ( x) y i ( x) ] [ y i ( x) u y ] 2 y i ( x) y i ( x) % y i ( x) Model Evaluatio Efficiecy Efficiecy Efficiecy Effectiveess. AARE m w t z x l yw x yw x z (Effectiveess) sƒw, CC, RMSE E m w t wš x x» w x z (Efficiecy) yw (Kim ad Kim, 2008). 5.2 d d w z.» d 1908 l 2002 ¾ d» w 86 kw, d 1912 l 2002 ¾ d» w 88 kw.» d 1949 l 2002 ¾ d» w 52 kw. d 1965 l 2002 ¾ 38 kw. š» s d 1980 l 2002 ¾ 23 kw. š MLP-NNM GRNNM z w d t yw w. d t yw w wù ƒ d d ùkü Table 2. Statistical aalysis of the mothly PE for the traiig performace (Historic data) Statio Seoul Kagreug Icheo Busa Jeju Mokpo Statistical Idex CC RMSE E AARE CC RMSE E AARE CC RMSE E AARE CC RMSE E AARE CC RMSE E AARE CC RMSE E AARE ƒ 4B œ 403
6 š» w d t ywš d ew, ƒ d z w» w q (Kim ad Kim, 2008; Kim et al., 2009). Table 2 d w MLP-NNM GRNNM z w ùküš. Table 2 w MLP-NNM z w w m CCƒ 0.869~0.985, RMSEƒ 5.963~18.775(mm), Eƒ 0.754~0.970 AAREƒ ~0.0035(%) š, GRNNM z w w m CCƒ 0.714~0.974, RMSEƒ 7.847~27.560(mm), Eƒ 0.471~0.949 AARE ƒ ~0.0073(%). k 6» d MLP-NNM z w ƒ GRNNM z w yw. 5.3 w z 5.2 d d w w. MLP-NNM GRNNM z w d w w x PARMA (1,1) w 500 g.» w r (Bias) w» w» 50 w, ù 450 w. d w w ƒ ww w. MLP-NNM GRNNM z w d 450. Table 3 w MLP- NNM GRNNM z w ùküš. Table 3 w MLP-NNM z w w m CCƒ 0.853~0.941, RMSEƒ ~ (mm), Eƒ 0.727~0.886 AAREƒ ~0.0006(%) š, GRNNM z w m CCƒ 0.790~0.910, RMSEƒ ~22.967(mm), Eƒ 0.623~0.827 AAREƒ ~0.0008(%). k 6» d MLP-NNM z w ƒ GRNNM z w yw. 5.4 yw yw w z 5.2 d d 5.3 Table 3. Statistical aalysis of the mothly PE for the traiig performace (Geerated data) Statio Seoul Kagreug Icheo Busa Jeju Mokpo Statistical Idex CC RMSE E AARE CC RMSE E AARE CC RMSE E AARE CC RMSE E AARE CC RMSE E AARE CC RMSE E AARE Table 4. Statistical aalysis of the mothly PE for the traiig performace (Mixed data) Statio Seoul Kagreug Icheo Busa Jeju Mokpo Statistica Idex CC RMSE E AARE CC RMSE E AARE CC RMSE E AARE CC RMSE E AARE CC RMSE E AARE CC RMSE E AARE ª Œª Œ
7 w w yw w. MLP-NNM GRNNM z w d ƒƒ d 536, d 538, d 502, d 488, s d 473 yw. Table 4 yw w MLP-NNM GRNNM z w ùküš. Table 4 w MLP-NNM z w w m CCƒ 0.854~0.941, RMSEƒ ~19.508(mm), Eƒ 0.730~0.886 AAREƒ ~0.0005(%) š, GRNNM z w w m CCƒ 0.786~0.910, RMSEƒ ~23.217(mm), Eƒ 0.618~0.828 AAREƒ ~0.0013(%). k 6» d MLP-NNM z w ƒ GRNNM z w yw. w MLP-NNM kw 6» d d w z w ƒ yw w z w yw. GRNNM s d wš yw w z w ƒ d w z w yw. 6. l p w l p ü x xy k w w wš. x z m w ƒƒ w l p w. MLP-NNM GRNNM d, yw w z 6 z mw w. w z ƒƒ d, yw w, e w j ƒ. ù l p 6» d w w x z ƒ ƒ yw q w» w q. 6.1 d d w z mw MLP-NNM GRNNM w l p w. l p l p,,,, s d w 2003 l 2007 ¾ 5 kw, 5. Table 5 d w z w w MLP- NNM GRNNM l p w ùküš. Table 5 w MLP-NNM l p w m CCƒ 0.789~0.952, RMSEƒ ~20.015(mm), Table 5. Statistical aalysis of the mothly PE for the testig performace (Historic data) Statio Seoul Kagreug Icheo Busa Jeju Mokpo Statistical Idex CC RMSE E AARE CC v RMSE E AARE CC RMSE E AARE CC RMSE E AARE CC RMSE E AARE CC RMSE E AARE Eƒ 0.574~0.899 AAREƒ ~0.0312(%) š, GRNNM l p w m CCƒ 0.643~0.903, RMSEƒ ~27.396(mm), Eƒ 0.140~0.723 AAREƒ ~0.3160(%). k 6» d d w MLP- NNM l p w GRNNM l p w w x y w w» ƒ w q. Fig. 3(a)-(f),,,, s d d w z w w MLP-NNM GRNNM l p w w ùkü. 6.2 w z mw MLP-NNM GRNNM w l p w. l p l p,,,, s d w 2003 l 2007 ¾ 5 kw, 5. Table 6 w z w w MLP- NNM GRNNM l p w ùküš 30ƒ 4B œ 405
8 Fig. 3 Compariso of the mothly PE for the testig performace (Historic data). Table 6 w MLP-NNM l p w m CCƒ 0.811~0.952, RMSEƒ ~16.999(mm), Eƒ 0.622~0.900 AAREƒ ~0.0509(%) š, GRNNM l p w m CCƒ 0.754~0.941, RMSEƒ ~24.188(mm), Eƒ 0.300~0.868 AARE ƒ ~0.2659(%). k 6» d w MLP-NNM l p w ƒ GRNNM l p w yw. Fig. 4(a)-(f),,,, s d w z w w MLP-NNM GRNNM l p w w ùkü. 6.3 yw yw w z mw MLP-NNM GRNNM w l p w. l p l p,,,, s d w 2003 l 2007 ¾ 5 kw, 5. Table 7 yw w z w w MLP- NNM GRNNM l p w ùküš. Table 7 w MLP-NNM l p w m CCƒ 0.811~0.952, RMSEƒ ~17.086(mm), Eƒ 0.618~0.899 AAREƒ ~0.0320(%) š, GRNNM l p w m CCƒ 0.746~0.950, RMSEƒ ~23.834(mm), Eƒ 0.256~0.887 AARE ƒ ~0.2502(%). k 6» d yw w MLP-NNM l p w ƒ GRNNM l p w yw. Fig. 5(a)-(f),,,, s d yw w z w w MLP-NNM GRNNM l p w w ùkü. 406 ª Œª Œ
9 Table 6. Statistical aalysis of the mothly PE for the testig performace (Geerated data) Statio Seoul Kagreug Icheo Statistical Idex CC RMSE E AARE CC RMSE E AARE CC RMSE E AARE Statio Busa Jeju Mokpo Table 6. Cotiued Statistical Idex CC RMSE E AARE CC RMSE E AARE CC RMSE E AARE Fig. 4 Compariso of the mothly PE for the testig performace (Geerated data) 30ƒ 4B œ 407
10 Table 7. Statistical aalysis of the mothly PE for the testig performace (Mixed data) Statio Seoul Kagreug Icheo Statistical Idex CC RMSE E AARE CC RMSE E AARE CC RMSE E AARE Statio Busa Jeju Mokpo Table 7. Cotiued Statistical Idex CC RMSE E AARE CC RMSE E AARE CC RMSE E AARE Fig. 5 Compariso of the mothly PE for the testig performace (Mixed data) 408 ª Œª Œ
11 Table 8. Results of the ANOVA test o the mea Model MLP-NNM GRNNM Statios Level of Sigificace Critical t statistic Mea Two-sample t test Computed t statistic Null hypothesis Historic Geerated Mixed Historic Geerated Mixed Seoul 0.05/ / Accept/Accept Accept/Accept Accept/Accept Kagreug 0.05/ / Accept/Accept Accept/Accept Accept/Accept Icheo 0.05/ / Accept/Accept Accept/Accept Accept/Accept Busa 0.05/ / Accept/Accept Accept/Accept Accept/Accept Jeju 0.05/ / Accept/Accept Accept/Accept Accept/Accept Mokpo 0.05/ / Accept/Accept Accept/Accept Accept/Accept Seoul 0.05/ / Accept/Accept Accept/Accept Accept/Accept Kagreug 0.05/ / Accept/Accept Reject/Accept Reject/Accept Icheo 0.05/ / Reject/Reject Reject/Accept Reject/Accept Busa 0.05/ / Reject/Accept Reject/Accept Reject/Accept Jeju 0.05/ / Accept/Accept Accept/Accept Accept/Accept Mokpo 0.05/ / Accept/Accept Accept/Accept Accept/Accept d, yw w MLP-NNM GRNNM l p w w. yw z mw w l p w ƒ d z mw w l p w yw. w d MLP-NNM l p w GRNNM l p w w y w q ù, yw MLP-NNM l p w ƒ GRNNM l p w yw ùküš. 7.,,,, s d l p d d, yw w z mw MLP-NNM GRNNM ƒ w l p w w mw (Homogeeity test) w.,,,, s d w s³ w (Oe-way aalysis of variace, ANOVA) Ma-Whitey U (Test) w (McCue 1993; Salas et al., 2001). 7.1 d MLP-NNM GRNNM w w s³ w w. 2t t- (Two-sample t-test) w m (Test statistics) (Degrees of freedom) w, (Level of sigificace) 5% 1% m (Critical test statistics) w t w s³ w ƒ (Null hypothesis) k (Accept) y (Reject)w w. Table 8 s³ w e ùküš. Table 8 w d MLP-NNM w d, yw z mw w l p w s³ w,,,, s d 5% 1% s³ w ƒ k. w d GRNNM w d, yw z mw w l p w s³ w, s 5% 1% s³ w ƒ k. ù d 5% 1% s³ w ƒ k š, y w 5%, 1% k. d 5% 1% s³ w ƒ š, yw 5%, 1% k. d, yw 5%, 1% k. w 5% 1% F- m e(f-test statistics) w, F- m e mw w ƒ k y w w. Table 9 w e ùküš. Table 9 w d MLP-NNM w d, yw z mw 30ƒ 4B œ 409
12 Table 9. Results of the ANOVA test o the variace Model MLP-NNM GRNNM Statios Level of Sigificace Critical F statistic Variace F-test statistics Computed F statistic Null hypothesis Historic Geerated Mixed Historic Geerated Mixed Seoul 0.05/ / Accept/Accept Accept/Accept Accept/Accept Kagreug 0.05/ / Accept/Accept Accept/Accept Accept/Accept Icheo 0.05/ / Accept/Accept Accept/Accept Accept/Accept Busa 0.05/ / Accept/Accept Accept/Accept Accept/Accept Jeju 0.05/ / Accept/Accept Accept/Accept Accept/Accept Mokpo 0.05/ / Accept/Accept Accept/Accept Accept/Accept Seoul 0.05/ / Accept/Accept Accept/Accept Accept/Accept Kagreug 0.05/ / Accept/Accept Accept/Accept Accept/Accept Icheo 0.05/ / Accept/Accept Accept/Accept Accept/Accept Busa 0.05/ / Accept/Accept Accept/Accept Accept/Accept Jeju 0.05/ / Accept/Accept Accept/Accept Accept/Accept Mokpo 0.05/ / Accept/Accept Accept/Accept Accept/Accept Table 10. Results of the Ma-Whitey U test Model MLP-NNM GRNNM Statios Level of Sigificace Critical Z Ma-Whitey U test Computed Z Null hypothesis Historic Geerated Mixed Historic Geerated Mixed Seoul 0.05/ / Accept/Accept Accept/Accept Accept/Accept Kagreug 0.05/ / Accept/Accept Accept/Accept Accept/Accept Icheo 0.05/ / Accept/Accept Accept/Accept Accept/Accept Busa 0.05/ / Accept/Accept Accept/Accept Accept/Accept Jeju 0.05/ / Accept/Accept Accept/Accept Accept/Accept Mokpo 0.05/ / Accept/Accept Accept/Accept Accept/Accept Seoul 0.05/ / Accept/Accept Accept/Accept Accept/Accept Kagreug 0.05/ / Accept/Accept Accept/Accept Reject/Accept Icheo 0.05/ / Reject/Reject Reject/Accept Reject/Accept Busa 0.05/ / Reject/Accept Reject/Accept Reject/Accept Jeju 0.05/ / Accept/Accept Accept/Accept Accept/Accept Mokpo 0.05/ / Accept/Accept Accept/Accept Accept/Accept w l p w w,,,, s d 5% 1% w ƒ k. w d GRNNM w d, yw z mw w l p w w,,,, s 5% 1% w ƒ k. 7.2 Ma-Whitey U Ma-Whitey U t 2t t- (Two-sample t-test) w wù, w l t w w» w. w t w Kruskal-Wallis w. Table 10 Ma-Whitey U w w e ùküš. Table 10 w d MLP-NNM w d, yw z mw w l p w Ma-Whitey U,,,, s d 5% 1% t ƒ ƒ k. w d GRNNM w d, yw z m w w l p w Ma-Whitey U, s 5% 1% 410 ª Œª Œ
13 t ƒ ƒ k. ù d 5% 1% t ƒ ƒ k š, yw 5%, 1% k. d 5% 1% t ƒ ƒ š, yw 5%, 1% k. d, yw 5%, 1% k. MLP-NNM w d m w ƒ k q ù, GRNNM d ƒ q. r MLP-NNM w ƒ GRNNM w yw š q. 8. z ù» d d MLP-NNM GRNNM w w ƒ x mw. MLP-NNM GRNNM w w x z d, yw ƒƒ w. š w t 2 t w, 500 w g. t kw, t kw. w t» r (Bias) w» w» 50 w. z w w d l p w w. 1. MLP-NNM GRNNM z w MLP- NNM d w w ƒ yw w w yw š, GRNNM s d wš yw w w ƒ d w w yw. 2. MLP-NNM GRNNM z w MLP-NNM w ƒ GRNNM w yw. ù z z d, yw w e w j ƒ q. 3. MLP-NNM GRNNM z w ƒ 6 w l p ww. yw z mw w l p w ƒ d z mw w l p w yw. mw x w w öe q. 4. MLP-NNM GRNNM l p w, d z mw w MLP-NNM l p w GRNNM l p w w yw q ù, yw z m w w MLP-NNM l p w ƒ GRNNM l p w yw ùküš. 5.,,,, s d d MLP-NNM GRNNM w d, yw z m w w l p w w w s³ w Ma- Whitey U w. MLP-NNM w d mw ƒ k q ù, GRNNM d ƒ q. r MLP-NNM w ƒ GRNNM w yw š q. mw x w w w x w mw, w. ù x» w w x r w w» w w w v w, x w ƒ v w q. š x mw (2007) w l yr ½, ½x (2008) qq» xy w mw. wm wz, wm w z, 28«, 2By, pp ½, k, (2001) w Hybrid Neural Networks w w d. w wz, w wz, 34«, 4y, pp Bruto, J.M., McCledo, R.W., ad Hoogeboom, G. (2000) Estimatig daily pa evaporatio with artificial eural etworks. Tras. of the ASAE, ASAE, Vol. 43, No. 2, pp Buria, S.J., Durras, S.R., Nix, S.J., ad Pitt, R.E. (2001) Traiig artificial eural etworks to perform raifall disaggregatio. J. of Hydrol. Egr., ASCE, Vol. 6, No. 1, pp Buria, S.J., Durras, S.R., Tomic, S., Pimmel, R.L., ad Wai, C.N. (2000) Raifall disaggregatio usig artificial eural etworks. J. of Hydrol. Egr., ASCE, Vol. 5, No. 3, pp Choi, J., Socolofsky, S.A., ad Olivera, F. (2008) Hourly disaggregatio of daily raifall i Texas usig measured hourly precipitatio at other locatios. J. of Hydrol. Egr., ASCE, Vol. 13, No. 6, pp Deb, K. (2001) Multi-objective optimizatio usig evolutioary algorithms, Joh Wiley & Sos, Chichester. Deswal, S. ad Pal, M. (2008) Artificial eural etwork based mod- 30ƒ 4B œ 411
14 elig of evaporatio losses i reservoirs. Proceedigs of World Academy of Sciece, Egieerig ad Techology, Vol. 29, pp Eslamia, S.S., Gohari, S.A., Biabaaki, M., ad Malekia, R. (2008) Estimatio of mothly pa evaporatio usig artificial eural etworks ad support vector machies. J. of Appl. Sci., Vol. 8, No. 19, pp Gudekar, H.G., Khodke, U.M., ad Sarkar, S. (2008) Evaluatio of pa coefficiet for referece crop evapotraspiratio for semiarid regio. Irrig. Sci., Vol. 26, pp Gutierrez-Magess, A.L., ad McCue, R.H. (2004) Accuracy evaluatio of raifall disaggregatio methods. J. of Hydrol. Egr., ASCE, Vol. 9, No. 2, pp Hayki, S. (2009) Neural etworks ad learig machies, 3 rd Editio, Pearso Educatio Ic., NJ, USA. Jese, M.E., Burma, R.D., ad Alle, R.G. (1990) Evapotraspiratio ad irrigatio water requiremets, ASCE Maual ad Report o Egieerig Practice No. 70, ASCE, NY, pp Keski, M.E. ad Terzi, O. (2006) Artificial eural etworks models of daily pa evaporatio. J. of Hydrol. Egr., ASCE, Vol. 11, No. 1, pp Kim, S. (2004) ad Embedded Stochastic Processes for Hydrological Aalysis i South Korea. KSCE J. of Civil Egr., KSCE, Vol. 8, No. 1, pp Kim, S. ad Kim, H.S. (2008) Neural etworks ad geetic algorithm approach for oliear evaporatio ad evapotraspiratio modelig. J. of Hydro., Vol. 351, pp Kim, S., Kim, J.H., ad Park, K.B. (2009) Statistical learig theory for the disaggregatio of the climatic data. Proc. 33rd IAHR Cogress 2009, IAHR/AIRH, Vacouver, British Columbia, Caada, pp Kisi, O. (2006) Daily pa evaporatio modelig usig a eurofuzzy computig techique. J. of Hydro., Vol. 329, pp McCue, R.H. (1993) Microcomputer applicatios i statistical hydrology, Pretice Hall, NJ, USA. Molia Martiez, J.M., Martiez Alvarez, V., Gozalez-Real, M.M., ad Baille, A. (2005) A simulatio model for predictig hourly pa evaporatio for meteorological data. J. of Hydro., Vol. 318, pp Neuroshell 2 (1993) Ward systems group, Ic., MD, USA. Rahimi Khoob, A. (2009) Estimatig daily pa evaporatio usig artificial eural etwork i a semi-arid eviromet. Theor. Appl. Climatol., Doi : /s Salas, J.D., Delleur, J.R., Yevjevich, V., ad Lae, W.L. (1980) Applied modelig of hydrologic time series, Water Resor. Pub., Littleto, CO, USA. Salas, J.D., Smith, R.A., Tabios III, G.Q., ad Heo, J.H. (2001) Statistical computig techiques i water resources ad evirometal egieerig, Upublished book i CE622, Colorado State Uiversity, Fort Collis, CO, USA. Specht, D.F. (1991) A geeral regressio eural etwork. IEEE Tras. o Neural Networks, Vol. 2, No. 6, pp Sudheer, K.P., Gosai, A.K., Raga, D.M., ad Saheb, S.M. (2002) Modelig evaporatio usig a artificial eural etwork algorithm. Hydro. Process., Vol. 16, pp Ta, K.S., Chiew, F.H.S., ad Grayso, R.B. (2007) A steepess idex uit volume flood hydrograph approach for sub-daily flow disaggregatio. Hydro. Process., Vol. 21, pp Tsoukalas, L.H. ad Uhrig, R.E. (1997) Fuzzy ad eural approaches i egieerig, Joh Wiley & Sos Icorporated, New York, NY, USA. Wasserma, P.D. (1993) Advaced methods i eural computig, Va Nostrad Reihold, New York, NY, USA. Zhag, J., Murch, R.R., Ross, M.A., Gaguly, A.R., ad Nachabe, M. (2008) Evaluatio of statistical raifall disaggregatio methods usig rai-gauge iformatio for west-cetral florida. J. of Hydrol. Egr., ASCE, Vol. 13, No. 12, pp ( : / : / : ) 412 ª Œª Œ
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