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»

ª Œª Œ 30ƒ 4B Á 2010 7œ 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» (E-mail : 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 2010 7œ 399

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 0.001 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

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 ---------------------------- 2σ 2 1 --------» 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 12 12 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 2010 7œ 401

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 0.001 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 (www.wamis.go.kr) œ l v w w.» wš» d d w. d 1907 10» d w z 1919, 1950-1953 1991-1994 ƒ d ù, yw k. d 1912 1» d w z 1919, 1950-1951 ƒ d ù, d yw k.» wš» d d w. d 1949 1» d w z 1950-1951 ƒ d ù, yw. š d 1965 1 l» d w š d k, yw.» wš» d s d w. s d 1980 1 l» 402 ª Œª Œ

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 ] ------------------------------------------------------------------------------------- 1 1 -- [ y i ( x) u y ] 2 -- [ y i ( x) u y ] 2 1 -- 1 -- [ y i ( x) y i ( x) ] 2 [ y i ( x) y i ( x) ] 2 1 ----------------------------------------- [ y i ( x) u y ] 2 y i ( x) y i ( x) -------------------------- 100% 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 00.948 00.889 RMSE 13.970 20.295 E 00.899 000.787 AARE 0.0018 00.0028 CC 00.869 00.714 RMSE 18.775 27.560 E 00.754 00.471 AARE 0.0027 00.0030 CC 00.948 00.877 RMSE 12.836 19.513 E 00.898 00.764 AARE 00.0024 00.0034 CC 00.899 00.745 RMSE 11.733 18.708 E 00.808 00.511 AARE 00.0029 00.0038 CC 00.963 00.832 RMSE 10.678 23.019 E 00.928 00.665 AARE 00.0035 00.0073 CC 00.985 00.974 RMSE 05.963 07.847 E 00.970 00.949 AARE 00.0013 00.0022 30ƒ 4B 2010 7œ 403

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 0.0013~0.0035(%) š, GRNNM z w w m CCƒ 0.714~0.974, RMSEƒ 7.847~27.560(mm), Eƒ 0.471~0.949 AARE ƒ 0.0022~0.0073(%). 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 12.026~19.579 (mm), Eƒ 0.727~0.886 AAREƒ 0.0003~0.0006(%) š, GRNNM z w m CCƒ 0.790~0.910, RMSEƒ 14.574~22.967(mm), Eƒ 0.623~0.827 AAREƒ 0.0004~0.0008(%). 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 00.940 00.906 RMSE 14.869 18.423 E 00.884 00.821 AARE 00.0004 00.0005 CC 00.853 00.790 RMSE 19.579 22.967 E 00.727 00.624 AARE 00.0006 00.0008 CC 00.938 00.893 RMSE 13.710 17.817 E 00.880 00.797 AARE 00.0003 00.0005 CC 00.873 00.790 RMSE 13.132 16.495 E 00.761 00.623 AARE 00.0003 00.0004 CC 00.941 00.906 RMSE 13.409 16.824 E 00.886 00.820 AARE 00.0003 00.0004 CC 00.939 00.910 RMSE 12.026 14.574 E 00.883 00.827 AARE 00.0003 00.0004 Table 4. Statistical aalysis of the mothly PE for the traiig performace (Mixed data) Statio Seoul Kagreug Icheo Busa Jeju Mokpo Statistica Idex CC 00.940 00.910 RMSE 14.842 18.118 E 00.884 00.828 AARE 00.0003 00.0013 CC 00.854 00.786 RMSE 19.508 23.217 E 00.730 00.618 AARE 00.0005 00.0006 CC 00.938 00.898 RMSE 13.707 17.471 E 00.880 00.806 AARE 00.0003 00.0004 CC 00.873 00.798 RMSE 13.108 16.221 E 00.762 00.636 AARE 00.0003 00.0004 CC 00.941 00.906 RMSE 13.398 16.781 E 00.886 00.821 AARE 00.0003 00.0004 CC 00.940 00.910 RMSE 11.994 14.556 E 00.883 00.828 AARE 00.0003 00.0004 404 ª Œª Œ

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 11.994~19.508(mm), Eƒ 0.730~0.886 AAREƒ 0.0003~0.0005(%) š, GRNNM z w w m CCƒ 0.786~0.910, RMSEƒ 14.556~23.217(mm), Eƒ 0.618~0.828 AAREƒ 0.0004~0.0013(%). 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 11.800~20.015(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 00.952 00.903 RMSE 11.800 20.596 E 00.899 00.692 AARE 00.0004 00.1407 CC v0.801 00.735 RMSE 18.037 25.362 E 00.574 00.158 AARE 00.0189 00.1603 CC 00.825 00.866 RMSE 18.452 25.240 E 00.643 00.332 AARE 00.0066 00.3160 CC 00.789 00.643 RMSE 16.195 24.204 E 00.615 00.140 AARE 00.0115 00.1328 CC 00.875 00.885 RMSE 18.504 27.396 E 00.763 00.480 AARE 00.0306 00.2325 CC 00.837 00.852 RMSE 20.015 19.087 E 00.695 00.723 AARE 00.0312 00.0585 Eƒ 0.574~0.899 AAREƒ 0.0004~0.0312(%) š, GRNNM l p w m CCƒ 0.643~0.903, RMSEƒ 19.087~27.396(mm), Eƒ 0.140~0.723 AAREƒ 0.0585~0.3160(%). 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 2010 7œ 405

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 11.733~16.999(mm), Eƒ 0.622~0.900 AAREƒ 0.0065~0.0509(%) š, GRNNM l p w m CCƒ 0.754~0.941, RMSEƒ 13.474~24.188(mm), Eƒ 0.300~0.868 AARE ƒ 0.0191~0.2659(%). 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 11.808~17.086(mm), Eƒ 0.618~0.899 AAREƒ 0.0003~0.0320(%) š, GRNNM l p w m CCƒ 0.746~0.950, RMSEƒ 12.472~23.834(mm), Eƒ 0.256~0.887 AARE ƒ 0.0355~0.2502(%). 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

Table 6. Statistical aalysis of the mothly PE for the testig performace (Geerated data) Statio Seoul Kagreug Icheo Statistical Idex CC 00.952 00.941 RMSE 11.733 13.474 E 00.900 00.868 AARE 00.0065 00.0191 CC 00.811 00.754 RMSE 16.999 23.117 E 00.622 00.300 AARE 00.0253 00.1581 CC 00.896 00.855 RMSE 13.762 24.188 E 00.801 00.386 AARE 00.0272 00.2659 Statio Busa Jeju Mokpo Table 6. Cotiued Statistical Idex CC 00.885 00.769 RMSE 12.314 19.064 E 00.777 00.466 AARE 00.0291 00.1092 CC 00.928 00.876 RMSE 14.134 19.182 E 00.862 00.745 AARE 00.0318 00.0334 CC 00.945 00.921 RMSE 12.550 15.410 E 00.880 00.819 AARE 00.0509 00.0562 Fig. 4 Compariso of the mothly PE for the testig performace (Geerated data) 30ƒ 4B 2010 7œ 407

Table 7. Statistical aalysis of the mothly PE for the testig performace (Mixed data) Statio Seoul Kagreug Icheo Statistical Idex CC 00.952 00.950 RMSE 11.808 12.472 E 00.899 00.887 AARE 00.0055 00.0355 CC 00.811 00.746 RMSE 17.086 23.834 E 00.618 00.256 AARE 00.0242 00.1726 CC 00.894 00.869 RMSE 13.926 22.647 E 00.797 00.462 AARE 00.0268 00.2502 Statio Busa Jeju Mokpo Table 7. Cotiued Statistical Idex CC 00.887 00.760 RMSE 12.263 19.950 E 00.779 00.416 AARE 00.0280 00.1294 CC 00.928 00.882 RMSE 14.151 18.931 E 00.861 00.752 AARE 00.032 00.0433 CC 00.940 00.924 RMSE 11.994 15.246 E 00.883 00.823 AARE 00.0003 00.0609 Fig. 5 Compariso of the mothly PE for the testig performace (Mixed data) 408 ª Œª Œ

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 0.05/0.01 1.981/2.621-0.0109 0.0117 0.0101 Accept/Accept Accept/Accept Accept/Accept Kagreug 0.05/0.01 1.981/2.621-0.0118 0.0038 0.0004 Accept/Accept Accept/Accept Accept/Accept Icheo 0.05/0.01 1.981/2.621-0.4080-0.0606-0.0661 Accept/Accept Accept/Accept Accept/Accept Busa 0.05/0.01 1.981/2.621-0.4604-0.1146-0.1327 Accept/Accept Accept/Accept Accept/Accept Jeju 0.05/0.01 1.981/2.621-0.0970-0.0074-0.0064 Accept/Accept Accept/Accept Accept/Accept Mokpo 0.05/0.01 1.981/2.621-0.3401-0.0293-0.0315 Accept/Accept Accept/Accept Accept/Accept Seoul 0.05/0.01 1.981/2.621-1.0500-0.1677-0.3138 Accept/Accept Accept/Accept Accept/Accept Kagreug 0.05/0.01 1.981/2.621-1.8711-2.1043-2.3032 Accept/Accept Reject/Accept Reject/Accept Icheo 0.05/0.01 1.981/2.621-2.9105-2.3648-2.2661 Reject/Reject Reject/Accept Reject/Accept Busa 0.05/0.01 1.981/2.621-2.2217-2.0262-2.2053 Reject/Accept Reject/Accept Reject/Accept Jeju 0.05/0.01 1.981/2.621-1.6695-0.6411-0.7221 Accept/Accept Accept/Accept Accept/Accept Mokpo 0.05/0.01 1.981/2.621-0.1871-0.9477-0.9920 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 2010 7œ 409

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 0.05/0.01 1.981/2.621 1.088 1.057 1.065 Accept/Accept Accept/Accept Accept/Accept Kagreug 0.05/0.01 1.981/2.621 1.130 1.007 1.022 Accept/Accept Accept/Accept Accept/Accept Icheo 0.05/0.01 1.981/2.621 1.012 1.146 1.141 Accept/Accept Accept/Accept Accept/Accept Busa 0.05/0.01 1.981/2.621 1.478 1.536 1.548 Accept/Accept Accept/Accept Accept/Accept Jeju 0.05/0.01 1.981/2.621 1.161 1.197 1.199 Accept/Accept Accept/Accept Accept/Accept Mokpo 0.05/0.01 1.981/2.621 1.286 1.435 1.438 Accept/Accept Accept/Accept Accept/Accept Seoul 0.05/0.01 1.981/2.621 1.394 1.133 1.114 Accept/Accept Accept/Accept Accept/Accept Kagreug 0.05/0.01 1.981/2.621 1.487 1.167 1.151 Accept/Accept Accept/Accept Accept/Accept Icheo 0.05/0.01 1.981/2.621 1.335 1.427 1.361 Accept/Accept Accept/Accept Accept/Accept Busa 0.05/0.01 1.981/2.621 1.050 1.401 1.277 Accept/Accept Accept/Accept Accept/Accept Jeju 0.05/0.01 1.981/2.621 1.701 1.057 1.051 Accept/Accept Accept/Accept Accept/Accept Mokpo 0.05/0.01 1.981/2.621 1.496 1.232 1.239 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 0.05/0.01 1.960/2.575-0.010-0.063-0.058 Accept/Accept Accept/Accept Accept/Accept Kagreug 0.05/0.01 1.960/2.575-0.016-0.100-0.068 Accept/Accept Accept/Accept Accept/Accept Icheo 0.05/0.01 1.960/2.575-0.588-0.310-0.299 Accept/Accept Accept/Accept Accept/Accept Busa 0.05/0.01 1.960/2.575-0.777-0.346-0.346 Accept/Accept Accept/Accept Accept/Accept Jeju 0.05/0.01 1.960/2.575-0.189-0.331-0.315 Accept/Accept Accept/Accept Accept/Accept Mokpo 0.05/0.01 1.960/2.575-0.357-0.210-0.205 Accept/Accept Accept/Accept Accept/Accept Seoul 0.05/0.01 1.960/2.575-1.118-0.226-0.331 Accept/Accept Accept/Accept Accept/Accept Kagreug 0.05/0.01 1.960/2.575-1.543-1.916-2.120 Accept/Accept Accept/Accept Reject/Accept Icheo 0.05/0.01 1.960/2.575-2.892-2.378-2.278 Reject/Reject Reject/Accept Reject/Accept Busa 0.05/0.01 1.960/2.575-2.199-2.157-2.315 Reject/Accept Reject/Accept Reject/Accept Jeju 0.05/0.01 1.960/2.575-1.396-0.987-1.055 Accept/Accept Accept/Accept Accept/Accept Mokpo 0.05/0.01 1.960/2.575-0.262-1.260-1.302 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

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