A Simple Method Using a Topography Correction Coefficient for Estimating Daily Distribution of Solar Irradiance in Complex Terrain

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1 w» wz, 11«1y(2009) Korean Journal of Agricultural and Forest Meteorology, Vol. 11, No. 1, (2009), pp. 13~18 x w x s * w w ( ; ; ) A Simple Method Using a Topography Correction Coefficient for Estimating Daily Distribution of Solar Irradiance in Complex Terrain Jin I. Yun* Department of Ecosystem Engineering, Kyung Hee University, Yongin , Korea (Received March 16, 2009; Revised March 17, 2009; Accepted March 19, 2009) ABSTRACT Accurate solar radiation data are critical to evaluate major physiological responses of plants. For most upland crops and orchard plants growing in complex terrain, however, it is not easy for farmers or agronomists to access solar irradiance data. Here we suggest a simple method using a sun-slope geometry based topographical coefficient to estimate daily solar irradiance on any sloping surfaces from global solar radiation measured at a nearby weather station. An hourly solar irradiance ratio (W i ) between sloping and horizontal surface is defined as multiplication of the relative solar intensity (k i ) and the slope irradiance ratio (r i ) at an hourly interval. The k i is the ratio of hourly solar radiation to the 24 hour cumulative radiation on a horizontal surface under clear sky conditions. The r i is the ratio of clear sky radiation on a given slope to that on a horizontal reference. Daily coefficient for slope correction is simply the sum of W i on each date. We calculated daily solar irradiance at 8 side slope locations circumventing a cone-shaped parasitic volcano (c.a., 570m diameter for the bottom circle and 90m bottom-to-top height) by multiplying these coefficients to the global solar radiation measured horizontally. Comparison with the measured slope irradiance from April 2007 to March 2008 resulted in the root mean square error (RMSE) of 1.61MJ m 2 for the whole period but the RMSE for April to October (i.e., major cropping season in Korea) was much lower and satisfied the 5% error tolerance for radiation measurement. The RMSE was smallest in October regardless of slope aspect, and the aspect dependent variation of RMSE was greatest in November. Annual variation in RMSE was greatest on north and south facing slopes, followed by southwest, southeast, and northwest slopes in decreasing order. Once the coefficients are prepared, global solar radiation data from nearby stations can be easily converted to the solar irradiance map at landscape scales with the operational reliability in cropping season. Key words : Solar radiation mapping, Sun-slope geometry, Topography correction I.,, x k w ƒ w. d» w ¾» d w s ƒw. w w ú» * Corresponding Author : Jin I. Yun (jiyun@khu.ac.kr )

2 14 Korean Journal of Agricultural and Forest Meteorology, Vol. 11, No. 1 yw sƒ w d w w. šƒ» d» w 5% ü ƒ w œ š w sƒƒ ƒ w š, x w ( : MJ m 2 day ) r š 1.» d w s s w 0.3~3.0 j l q, d (1 )- (1m 2 ) (J). œw» w d w 24 d wš w l MJ(=10 6 J) txw. s, m, k w. ù ƒ k w s š w s w. w,, s ew ƒ,, s Ÿ (solar irradiance) w w. ù m 30m x txw m s³ ƒ 14.3, m ƒ s 5 w 28.2% w. m 58.8% 10, %, % w. x s»»( )» w ( w) ƒ š. Ÿ yw ü ù». w y w w, ü» w» tw s w m w, ú k š ƒ w w w. m w š k š ƒ ú w yw yw w» w s w w, k e w w ww» v w.» d w s w ( w) ywš rw ý x š w x w šw. II w x i s w (W i ) wš txw. W i» k i (relative solar intensity), r i Ÿ (slope irradiance ratio) ƒ k. k i s (clear sky radiation, x i ) w w s, d w. k i (1) (2) r i s (x i ) w (y i ) d w w. r i = k i r i (2) (3) w (1) w. W i x i = x i y i = --- x i y i = x i (3) (4) w (W i ) we w ú d (W d )ƒ, s 1.0 w. W d = W i (5) ú,

3 Yun: A Simple Method Using a Topography Correction Coefficient for Estimating Daily... 15,»ƒ ƒ w s t w,» w X 0,» n w w d k š (a) (X b0 ) (X d0 ), ƒƒ w w (Gates, 1980). X b0 = X 0 τ (6) X d0 = X τ (7)» τ k»n w 0.8, l w» 80%¾ y š t w. 1/»n w k š ƒ û wì û j w. ƒ we s w. ú (y i ) y. d k š ƒ ƒ ƒƒ a, β w b š ƒ a t x (Kondratyev and Federova, 1977). { cosαcos( β b) + cosβ} Y b = X b (8) Ÿ w w (Gates, 1980). 2 α Y d = X d0 cos -- 2 (9) 2 α» cos -- 1 w œ 2 (sky view factor). Y b, Y d ƒ we Ÿ sƒ ƒ y ƒ y w» w w x sw w» d ƒ v w. p x k w y v. w Fig. 1. A satellite image of the parasitic volcano (top) and locations of 8 solar irradiance measurement points (circle) and 1 reference solar radiation site (triangle) on the elevation map of the volcano (bottom). Table 1. Slope, aspect and elevation of the 8 observation sites SITE # Slope (deg) Aspect (deg) Elevation (m) »» y w w wù ( ) x w. 570m ¾ š 90m x ƒ¾ š ƒ

4 16 Korean Journal of Agricultural and Forest Meteorology, Vol. 11, No. 1 ƒ w t (Fig. 1, Table 1). l 70m š 8 w ƒ (Model SP-100, Apogee Instruments Inc., USA) ewš»(model STL, STA, Korea) ww 1 w. w SP- 100 d ƒ 45 o ±1%, 75 o ±5%,» d» ±5% š w. x e w er w w(»» ) 3 v (Model 8-48, Eppley Laboratory Inc., USA) d w y w. x s d w» w» y s v x ewš,» (Model CR10X, Campbell Scientific, USA) w 1 d w w. m l sww 1:5,000 e x ( y ) w š l TIN(triangulated irregular network) t wš, w 1m DEM(digital elevation model) yw. DEM l ƒ e 8 w w, (4) (5) w 1 1 l ¾ (W d ) w.» ( ) d l ¾ w 8 w, ƒ SP-100 w d w w. Fig. 2. Relationship between the observed and the estimated daily solar irradiance at 8 sites for a full year from 14 April 2007 to 13 April Shaded dots indicate the data obtained from low sun angle days in winter..» w w»zt(kma, 2001) w ù 22 d» 1981 l 2000 ¾ 20 d m w, s³ 11.02MJ m ( ) MJ m 2 ( ). wr 1971 l 1980 ¾ 10 19» d d w f 16.46MJ m ( ) 2 III. š 3.1. œ p x w w 8 1 Ÿ d w 0.97 x ƒ y (Fig. 2). r s (RMSE) (3, 4, 5 ) 1.47, (6, 7, 8 ) 0.88, ƒ (9, 10, 11 ) 1.74, (12, 1, 2 ) 2.11MJ m s³ MJ m 2 Fig. 3. Seasonal variation in the root mean square error for the estimated daily solar irradiance at sloping surfaces with various aspect. Approximate aspect for each site is: N (North) =1 and 8, E (East)=2, SE (Southeast)=3, S (South) =4, SW (Southwest)=5, W (West)=6, and NW (Northwest) =7.

5 Yun: A Simple Method Using a Topography Correction Coefficient for Estimating Daily MJ m 2 ( y). x y 1.61MJ m 2 s³ 10% w w š. d» x ƒ t d»( v ) ±5% w 10% RMSE q w. w 4 l 10 RMSEƒ s³ w ƒ š ù s³ w ƒ j y w (Fig. 3). 4 l 10 ù w» w w» ƒ x w s³ w. w w w w 4 10 ¾ ƒ š 11 w 3 ¾ ƒ. w w ƒ» š û. w w 10 ƒ ƒ, 11 w s ƒ f. w û, 5 l 7 ¾» ƒ ƒw p w. w w w RMSE { j. RMSE Fig. 4. A topography corrected solar irradiance map at a 30m resolution for Doam catchment (Pyungchang, Gangwon Province). Each panel represents daily sum of solar irradiance on 4 selected days in 2008 (July 22, August 14, September 9, and October 3).

6 18 Korean Journal of Agricultural and Forest Meteorology, Vol. 11, No. 1 s ûw w ƒ j š, û -û -.,» 4 l 10 ¾ w, d ±5%. k š ƒ w û 11 l»¾ 5 ƒ j» š w w w. ƒ s k š ƒ 0 0, w y w ƒ 0. w y ƒ x e w w q.» w x yw Ÿ s ü» w» y ƒ x 5% w 5 l 10 ¾ 6 w x w s w» d w 30m yw. w w e x l 30m DEM wš, w ƒ w w, (4) (5) w 5 1 l ¾ (W d ) w.»»» dw w w. Fig. 4, 4 (7 22, 8 14, 9 9, 10 3 ) w x tx w, e w ( ) w g.» d w s m y wš rw ý x š w. s w wš,» s s w Ÿ txw. w w w ú x. ü» y š 8 Ÿ 1 dw wr, x w w w. x w r s s³ 1.61MJ m 2 ù, 4 l 10» w. w w 10 ƒ ƒ, 11 w s ƒ f. RMSE s ûw w ƒ fš, û -û x w w» dw ú w ú ü w x Ÿ s w q w. t» w, x v w ( ) w œw š, e ùy l( p w ) x w.. REFERENCES Gates, D. M., 1980: Biophysical Ecology. Springer-Verlag, New York. Kondratyev, K. Y. and M. P. Federova, 1977: Radiation Regime of Inclined Slopes. WMO Technical Note No Korea Meteorological Administration, 2001: Climatological Normals of Korea ( ). Government Publication Number