Estimation of Areal Average Rainfall in the Mountainous Kamo River Watershed, Japan

Full Paper Journal of Agricultural Meteorology 71 (2): 9-97, 215 Estimation of Areal Average Rainfall in the Mountainous Kamo River Watershed, Japan Sanz Grifrio LIMIN a, Hiroki OUE b, and Keiji TAKASE c a The United Graduate School of Agricultural Sciences, Ehime University, 3-5-7 Tarumi, Matsuyama, Ehime 79-8566, Japan b Faculty of Agriculture, Ehime University, 3-5-7 Tarumi, Matsuyama, Ehime 79-8566, Japan c Faculty of Bioresources, Ishikawa Prefecture University, 1-38 Suematsu, Nonoichi, Ishikawa 921-8836, Japan Abstract This paper evaluated the applicability of four AAR (areal average rainfall) estimation methods in the mountainous Kamo River watershed by using measured monthly rainfall at nine stations within and near this watershed between 1998 and 21. The four methods were (i) the arithmetic mean, (ii) the Thiessen polygon, (iii) the elevation regression and (iv) the combination of (ii) and (iii). Method (iv) was newly developed in this study. For methods (iii) and (iv), linear monthly relationship between elevation and monthly rainfall was applied and it was evaluated as useful for predicting rainfall even at a high elevation. Firstly, the applicability of the four AAR methods was evaluated by relationships between annual AAR (= P) and annual evapotranspiration ratio (Et/Ep). Annual evapotranspiration (Et) was obtained using the water balance equation by incorporating each AAR and measured discharge, and Ep was calculated using Penman equation. The low Et/Ep by methods (i) and (ii) was caused by the underestimation of AAR, which resulted in the underestimation of Et, mainly because these methods did not include the effect of larger rainfall in the higher elevation area. Methods (iii) and (iv) produced Et/Ep reasonably and demonstrated closer relationship to that in another mountainous watershed. Secondly, the applicability was evaluated by examining relationships between annual Ep/P and annual Et/P with a rational method of Fu (1981), where the watershed parameter w was optimized for each method. Methods (i) and (ii) produced relatively low w as a value of a mountainous watershed, which would be caused by the underestimation of annual AAR. Method (iii) produced relatively high w as a value of a mountainous watershed and R 2 was relatively low. As a result, the newly presented combination method (iv) was determined to be most applicable for AAR method in this mountainous watershed. Key words: Areal average rainfall, Combination method, Elevation regression, Evapotranspiration ratio, Mountainous watershed. 1. Introduction Determination of the areal rainfall in a watershed is a fundamental requirement for many hydrologic studies (e.g., Bayraktar et al., 25; Ly et al., 213). Rainfall has been measured at a number of sample points, and the records have been utilized to estimate areal average rainfall (AAR) for various kinds of analysis. Three classical methods of determining AAR are the arithmetic mean, the Thiessen polygon and the isohyet. However, which method offered the most satisfactory results was always debatable. The rainfall measurements at various gauging stations, especially in mountainous watersheds, have been found to differ significantly, depending on the source of rain and local topography (Martínez- Cob, 1996; Fedorovski, 1998; Şen and Habib, 2). Singh and Birsoy (1975) compared nine methods, which could be categorized as unweighted mean method or arithmetic method, area weighted method and geostatistical method for estimating AAR in five watersheds, including two mountainous watersheds. They concluded that there was no particular basis to claim that one Received; December 9, 214. Accepted; January 15, 215. Corresponding Author: oue@agr.ehime-u.ac.jp DOI: 1.248/agrmet.D-14-55 method was superior to others, although in a certain situation one method was preferable to others. Hevesi et al. (1992) and Martínez- Cob (1996) developed the multivariate geostatistic method by applying the cokriging technique, which applied annual isohyet maps as a primary attribute, with a relationship between elevation and rainfall at 42 (Hevesi et al., 1992) and 158 (Martínez-Cob, 1996) rain stations as a secondary variable in mountainous terrains. These studies suggested the necessity of rainfall observations at some points of extreme rainfall for predicting rainfall in a mountainous area and determined that the presented method could predict annual rainfall at any point successfully. In this paper, four AAR estimation methods, which do not require so many rain station data as the cokriging technique, are applied; (i) the arithmetic mean, (ii) the Thiessen polygon (Thiessen, 1911), (iii) the elevation regression and (iv) the combination of (ii) and (iii). Method (iv) is newly developed in this study. The main objective of this paper is to evaluate the applicability of AAR estimation methods in the mountainous Kamo River watershed by using monthly rainfall data at nine stations within and near this watershed from 1998 to 21. To apply methods (iii) and (iv), linear relationships between elevation and monthly rainfall are introduced and rainfall in the area of 2 m elevation with intervals up to 18 2 m elevation is predicted. To evaluate the applicability of the four methods, annual - 9 -

S. G. Limin et al. Estimation of Areal Average Rainfall in the Mountainous Watershed evapotranspiration, which is obtained as a residue in the water balance equation, is tested in two ways; evapotranspiration ratio and rational method of Fu (1981). 2. Research Area and datasets The research area is the Kamo River watershed which is located in the eastern part of Ehime Prefecture, Japan. This area is classified as a humid subtropical climate Cfa of Köppen climate classification with significant amounts of precipitation in all seasons. The Kamo River watershed area is 196.6 km2 and mostly consists of mountainous area with the elevation ranging from 12 to 192 m. The area, whose slope is greater than 2%, accounts for about 89% of total area. Topographic map of the Kamo River watershed area and nine locations of rainfall measurement are shown in Fig. 1. Among nine rain stations, six stations are located inside the watershed area and three stations are outside but near the watershed. In this study, rainfall data at eight stations except for Kamegamori from 1998 to 21 were used for analysis. At Kamegamori, data just from May to October in 29 and 21 were used for analysis, as Kamegamori station was installed in May 29 and there was snowfall during the other months. Rainfall was measured at each station by using a tipping bucket. Meteorological data from the Japan Meteorological Agency in Saijo City, about 5 km from the watershed, from 1998 to 21 were used for calculating potential evaporation by Penman s equation. Discharge in this watershed was obtained by summing discharges in the Kamo river and the Ara river, which is a tributary of the Kamo river. Discharge in the Kamo river was obtained at the Kurose Dam (established in 1972) at 12 m elevation as shown in Fig. 1. The daily discharge at this dam was calculated by subtracting daily water intake for industrial and agricultural use from daily inflow to the dam. Discharge in the Ara river was measured at the upstream of confluence of the Kamo river and the Ara river at 1 m elevation as shown in Fig. 1. The area ratios in every 2 m of elevation in this watershed are shown in Fig. 2, with the nine rain stations at their elevations. Figure 2 shows that the area ratios distribute from to 2 m uniformly with a quasi-normal distribution, which means influences of elevation on AAR should be considered in this watershed. Rainfall data at a high elevation point like Kamegamori is especially important, as Kamegamori covers about 1% of the area at 14 2 m elevation in this total watershed area as shown in Fig. 2. This was also the reason why Kamegamori station was installed for this research. But, because of insufficient data at this station, a method for predicting rainfall as a function of elevation will be presented in 3.1 and tested in 4.1. Fig. 1. Map of the Kamo River watershed surrounded by the dotted line and locations of nine rain stations (with their elevations); 1; Saijo (4 m), 2; Kurose Dam (12 m), 3; Ichinokawa (18 m), 4; Hoino (48 m), 5; Higashinokawa (56 m), 6; Ohnaru (6 (6 m), 7; Fujinoishi (7 m), 8; Jojusha (128 m) and 9; Kamegamori (162 m) and two discharge observation points ( ). - 91 -

Journal of Agricultural Meteorology 71 (2), 215 2 15 Area Ratio (%) 1 5 224 46 68 8 112 12 14 14 16 16 18 18 2 2 Elevation (m) Fig. 2. 1 2 3 4 5 6 7 8 9 The area ratios in every 2 m elevation in the Kamo River watershed and elevations of the nine rain stations. Numbers beneath the x axis correspond to those of rain stations in Fig. 1. 3. Methodology 3.1 Elevation-Rainfall Relationship Based on observational realities of a relationship between elevation and rainfall at the elevation, rainfall at a given elevation point can be written simply by the following equation; P = a H + b (1) where P is rainfall, a is a height coefficient, b is rainfall at sea level, H is the elevation of the rain station. After deciding parameters a and b, calculated P at elevations (H) of 2 m intervals, e.g. at H = 1, 3, 5 m, etc., was applied for the elevation regression method as stated in 3.2. In this paper, monthly rainfalls were applied to the analysis, considering that monthly rainfall could represent seasonal characteristics of rainfall better than annual or daily rainfall. 3.2 Methods for Estimating Areal Average Rainfall (AAR) For estimating AAR in this mountainous watershed area, (i) the arithmetic mean, (ii) the Thiessen polygon, (iii) the elevation regression and (iv) the combination of (ii) and (iii) were applied. The combination method (iv) was newly developed in this study. The arithmetic method is the simplest method for AAR calculation because it only takes the unweighted average of rainfall at all stations. This method is satisfactory if rain gauges were uniformly distributed over the area and the individual measurements would not vary largely. The Thiessen Polygon method is based on the Voronoi Diagram which is a special kind of decomposition of a given space, for example metric space, determined by distances to a specified family of object (point) in the space. The Voronoi Diagram is used to analyze spatially distributed data of rainfall measurement, and polygons within this diagram are called Thiessen Polygon. The elevation regression method or elevation area weighted method (Singh and Birsoy, 1975) calculates the areal rainfall by incorporating Eq. (1) as follows. ( A ( ah + b)) i i e = (2) Atotal P where P e is AAR by this method, A i is an area of each elevation interval, H i is the mean elevation in each elevation interval, and A total is the total area of the watershed. The parameters a and b were determined beforehand in each month by Eq. (1); the relationship between elevation and monthly rainfall at stations is stated in 3.1. In this study, 2 m was applied as the interval of elevation. In case of i = 3 in Eq. (2), for example, representative rainfall in the area between 4 and 6 m elevation was given by Eq. (1) with H i = 5 m and area between 4 and 6 m elevation was given as A i. The combination method, which is newly introduced in this paper, combines the elevation regression method and the horizontal distribution method of the Thiessen Polygon method. In this method, the effect of elevation on rainfall is represented by the elevation regression method, and the effect of spatial variation on rainfall is represented by the Thiessen Polygon method. In combining the two methods, the determination coefficient (R 2 ) of the relationship between elevation and rainfall in Eq. (1) is applied. The value of R 2 in Eq. (1) indicates a contribution rate at which the elevation can represent rainfall. A contribution rate which can t be represented by the elevation can be complemented by the effect of spatial variation on rainfall. Thus, the combination method is represented by the following equation: - 92 -

S. G. Limin et al.:estimation of Areal Average Rainfall in the Mountainous Watershed 2 2 Pc = Ph (1 R ) + Pe R (3) where P c is AAR by this method, P h is AAR by Thiessen Polygon method, P e is AAR by the elevation regression method and R 2 is the determination coefficient of the elevation regression equation (1) for each monthly rainfall. 3.3 A rational method as one evaluation method of each AAR method To evaluate applicability of each AAR method, verifying evapotranspiration (Et), which will be obtained as a residue in the water balance equation (4), is one reasonable way. In this paper, two methods were applied for verifying Et. The first compares evapotranspiration ratio Et/Ep by each method with other researcher s Et/Ep, where Ep is potential evaporation by Penman equation. The second one applies a rational method of Fu (1981) to verify the relationship between Ep/P and Et/P, where P is AAR by each method. The water balance in a watershed is written as, P = Et + Q + ΔS (4) where P is AAR, Q is total runoff and ΔS is storage change in the watershed. Over a long period, ΔS can be neglected. In this study, annual areal average Et in this watershed was estimated by applying annual AAR by each method for P and measured annual discharge for Q to Eq. (4). Fu (1981) originally developed a rational method to estimate annual average evapotranspiration. He assumed that the rate of the change in evapotranspiration with respect to rainfall in a watershed ( Et/ P) increased with residual potential evaporation (Ep -Et) but decreased with rainfall (P) over a one-year time scale. This relationship was expressed as, Et = f ( Ep Et, P) P Fu (1981) finally derived following solutions from Eq. (5). Et P 1/w w Ep Ep 1+ 1 + P P (5) = (6) where w is a parameter related to the watershed characteristic. Based on fundamental knowledge about factors, meteorological, soil water and vegetational conditions influencing on evapotranspiration; Eq. (6) represents these three influences rationally. In Eq. (6), the effect of soil water condition can be thought to be canceled by dividing Et and Ep by P. Therefore, Eq. (6) represents the effect of meteorological conditions; solar radiation, air temperature and humidity and wind speed on Et by Ep/P and represents the effect of vegetational conditions on Et by the parameter w. As a whole, w is larger in vegetational canopies which consist of larger LAI, taller plants, plants whose transpiration abilities are relatively higher, etc. Zhang et al. (24) showed w in a forest and a grass watershed fitted to 2.84 and 2.55, respectively. They presented the maximum w as 5. and the minimum as 1.7. 4. Results and Discussions 4.1 Evaluation of the relationship between elevation and monthly rainfall Examples of relationships between elevation and monthly rainfall in four months in 29 are shown in Fig. 3. Monthly rainfall data in this analysis were measured at seven stations except for Rainfall (mm/month) Rainfall (mm/month) 2 15 1 5 2 15 1 5 Jan y =.42x + 66.9 R² =.819 5 1 15 Mar y =.73x + 31. R² =.75 5 1 15 Elevation (m) 2 15 1 5 8 6 4 2 Feb y =.71x + 95.8 R² =.922 5 1 15 Dec y =.36x + 26.1 R² =.679 5 1 15 Elevation (m) Fig. 3. Examples of relationships between elevation and monthly rainfall measured at seven stations in the Kamo River watershed in 29. - 93 -

Journal of Agricultural Meteorology 71 (2), 215 Fig. 4. Examples of comparisons of monthly rainfall between measured and predicted by the elevation regression method. Hoino and Kamegamori, where data lacked in some cases. Through this analysis, parameters a and b in Eq. (1) were decided for each month in each year. Applicability of this equation was evaluated by R2 value in the relationship of monthly rainfall between that measured and that which was predicted by the equation. Examples are shown in Fig. 4. R2 values at the nine stations were.81 at Saijo,.76 at Kurose Dam,.73 at Ichinokawa,.89 at Hoino,.82 at Higashinokawa,.79 at Ohnaru,.83 at Fujinoishi,.92 at Jyojyusha and.93 at Kamegamori. It was found that Eq. (1) could successfully predict rainfall except under high monthly rainfall conditions, including at two rain stations whose rainfall data were not applied in determining the parameters. In a mountainous watershed like the Kamo River watershed, rainfall observations at a high elevation are very insufficient. Therefore, this equation is evaluated to be applicable for predicting rainfall at a high elevation and very helpful for predicting AAR in a mountainous watershed. This equation was incorporated into AAR methods (iii) and (iv). 4.2 Evaluation of the AAR Methods Reliability of the four AAR estimation methods; (i) the arithmetic mean, (ii) the Thiessen polygon, (iii) the elevation regression method and (iv) the combination method with (ii) and (iii) was evaluated in the following two ways. The first means of evaluation compared annual evapotranspira- tion ratio (Et/Ep) by each method with that in four forest watersheds by Takase and Sato (1998). In this study, annual Et was estimated as a residue in the water balance equation (4), assuming ΔS = and annual Ep was calculated by Penman equation with meteorological data at Japan Mereorological Agency in Saijo. Though areal average Ep should be applied to discuss evapotranspiration ratio (=Et/Ep) in the watershed, Ep at this meteorological station was applied as reference evaporation under the meteorological conditions in this watershed. The second method applied a rational method of Fu (1981) to verify the relationship between Ep/P and Et/P, where P is AAR by each method. Figure 5 shows relationships between annual AAR (P) and the annual evapotranspiration ratio (Et/Ep) by the four AAR methods, Arithmetic, Thiessen, Elevation and Combination, in the Kamo River watershed between 1998 and 21 and in the other four watersheds after Takase and Sato (1998) for comparison. Among the observations made by Takase and Sato (1998), the Tatsunokuchi forests and Ozu forest were noted to be densely vegetated mountainous watersheds. Utenahongawa was a sparsely vegetated watershed. As shown in Fig. 5, as a whole, Et/Ep increased with the increase of P up to some P values and decreased either slightly or largely with the increase of P under the condition of larger P. Based on fundamental knowledge about this relationship, Et/Ep in - 94 -

S. G. Limin et al.:estimation of Areal Average Rainfall in the Mountainous Watershed Fig. 5. Relationships between annual AAR (= P) and annual evapotranspiration ratio (Et/Ep) by the four AAR methods in the Kamo River watershed from 1998 to 21 and in the other four watersheds after Takase and Sato (1998) for comparison. a vegetated field should increase with the increase of P and reach around 1. due to the wet conditions. In addition, in a vegetated watershed under moderately wet conditions, Et/Ep sometimes exceeds 1. as shown in Fig. 5, mainly due to transpiration promoted by vegetation canopy over potential under fine weather with high air temperature conditions (e.g., Oue, 25). Under wetter conditions, i.e., larger P than this, however, there is the possibility of Et/Ep approaching 1. again because fewer fine days and lower air temperature cause the decrease in Et to the same level as water surface evaporation. But, the arithmetic mean and the Thiessen polygon methods produced much lower Et/Ep than others in conditions over around 28 mm/y of P. These were thought to be caused by the underestimation of AAR (= P), which resulted in the underestimation of Et using the water balance equation. An important reason for underestimating P would be the disadvantage of these two methods which do not include the effect of larger rainfall in the higher elevation area. Compared with relationships in other watersheds, the elevation regression method and the combination method also demonstrated closer relationships to that in Ozu forest among the presented four methods, although the range of P in our watershed and others differed from each other. From these discussions, the elevation regression method and the combination method could be determined to be reliable among the four methods. Applying the second method to evaluating the reliability of the AAR methods, annual scale relationships between the index of dryness (Ep/P) and Et/P by our four methods were shown in Fig. 6. For comparison with Fu s rational method (1981), calculation by Eq. (6) for each method with each fitted w was included by each dotted line. The optimized w was 1.8 (R 2 =.76) for the arithmetic mean method, 2.3 (R 2 =.95) for the Thiessen polygon method, 6.5 (R 2 =.73) for the elevation regression method and 4. (R 2 =.88) for the combination method. Lower Et/P with the lowest w of the arithmetic mean method would be caused by the underestimation of AAR (= P) for the same reasons as discussed above about the lower Et/Ep. Meanwhile, Zhang et al. (24) showed 2.84 and 2.55 of w in a forest and a grass watershed, respectively, and presented its maximum as 5. and minimum as 1.7. As discussed in 3.3, w becomes larger in vegetational canopies which consist of larger LAI, taller plants and plants whose transpiration ability is relatively high. From the viewpoint of the value of w, 2.4 of the Thiessen polygon method seems to be lower as a mountainous watershed despite the high R 2. This would be also caused by the underestimation of AAR (P) as above. Regarding the elevation regression method, w = 6.5 was relatively high compared with the value presented by Zhang et al. (24) and R 2 was not so high. Although the applicable value of w in a mountainous watershed should be investigated further, the elevation regression method was determined to be inferior to the combination method. Considering these discussions by taking w and R 2 values into account, the combination method could be evaluated as preferably - 95 -

Journal of Agricultural Meteorology 71 (2), 215 1..8.6 Et / P.4.2...2.4.6.8 1. Ep / P Observed (Arithmetic) Observed (Thiessen) Observed (Elevation) Observed (Combination) Elevation, Arithmetic, w = = 6.5, 1.8, R² R 2 = =.69.76 Combination, Thiessen, w = w 2.3, = 4., R 2 = R².95 =.86 Elevation, w = 6.5, R 2 =.73 Combination, w = 4., R 2 =.88 Fig. 6. Relationships between annual Ep/P and annual Et/P by the four AAR methods and calculated by the rational method of Fu (1981). Observational data by the four methods are shown in symbols and calculations by Eq. (6) are shown in dotted lines. applicable for AAR method in this mountainous watershed. 5. Conclusion This paper presented a new method for estimating areal average rainfall (AAR), and the applicability of four AAR methods was evaluated in the mountainous Kamo River watershed by using monthly rainfall data at nine stations within and near this watershed between 1998 and 21. The four methods were (i) the arithmetic mean, (ii) the Thiessen polygon, (iii) the elevation regression and (iv) the combination of (ii) and (iii). The combination method (iv) was newly developed in this study. To evaluate the applicability of each method, annual areal average evapotranspiration (Et), which was obtained as a residue in the water balance equation by incorporating each AAR and measured discharge at the end of two rivers in this watershed, was tested in two ways; evapotranspiration ratio (Et/Ep) and a rational method of Fu (1981). Firstly, because of the necessity of predicting rainfall at high elevation in the mountainous Kamo River watershed, the linear relationship between elevation and monthly rainfall was applied. Comparing measured and predicted monthly rainfall, this relationship was determined to be applicable for predicting rainfall even at a high elevation and very helpful for predicting AAR in a mountainous watershed. This relationship was incorporated into AAR methods (iii) and (iv). Secondly, the applicability of the four AAR estimation methods was evaluated by comparing annual Et/Ep by each method with that of Takase and Sato (1998). The arithmetic mean method and the Thiessen polygon method produced very low Et/Ep in the conditions over 28 mm/y of annual rainfall. The low Et/Ep could be caused by the underestimation of annual AAR, which resulted in the underestimation of Et. An important reason for underestimating AAR would be the disadvantage of these two methods which did not include the effect of larger rainfall in the higher elevation area. On the other hand, the elevation regression method and the combination method produced Et/Ep reasonably and offered closer relationship to that in another mountainous watershed. From these discussions, the elevation regression method and the combination method were evaluated to be the most reliable among the four methods. Thirdly, the applicability of the four AAR estimation methods was evaluated by applying a rational method of Fu (1981) to verify the relationship between annual Ep/P and annual Et/P of each method, where the parameter w was optimized for each method. Here, P was annual AAR. Considering the discussions of Zhang et al. (24) about w value, the arithmetic mean method and the Thiessen polygon method produced low Et/P with relatively low w as a value of a mountainous watershed, which would - 96 -

S. G. Limin et al.:estimation of Areal Average Rainfall in the Mountainous Watershed be caused by the underestimation of annual AAR for the same reason as above. The elevation regression method produced relatively high w as a value of a mountainous watershed, with low R 2. As a result, the combination method could be evaluated to be preferably applicable for AAR in this mountainous watershed. Finally, the newly presented combination method could be evaluated to be most applicable for AAR in a mountainous watershed such as the Kamo River watershed. References Bayraktar, H., Turalioglu, F. S., and Şen, Z., 25: The estimation of average areal rainfall by percentage weighting polygon method in Southeastern Anatolia Region, Turkey. Atmospheric Research, 73, 149 16. Fedorovski, A., 1998: Estimating areal average rainfall for an ungaged mountainous basin in the Amur Basin. Journal of Environmental Hydrology, 6, 5 15. Fu, B. P., 1981: On the calculation of the evaporation from land surface. Scientia Atmospherica Sinica, 5, 23 31 (in Chinese). Hevesi, J. A., Flint, A. L., and Istok, J. D., 1992: Precipitation estimation in mountainous terrain using multivariate geostatistics. Part II: Isohyetal maps. Journal of Applied Meteorology, 31, 677 688. Ly, S., Charles, C., and Degré, A., 213: Different methods for spatial interpolation of rainfall data for operational hydrology and hydrological modeling at watershed scale: a review. Biotechnologie, Agronomie, Société et Environement, 17, 392 46. Martínez-Cob, A., 1996: Multivariate geostatistical analysis of evapotranspiration and precipitation in mountainous terrain. Journal of Hydrology, 174, 19 35. Oue, H., 25: Influences of meteorological and vegetational factors on the partitioning of the energy of a rice paddy field. Hydrological Processes, 19, 1567 1583. Şen, Z., and Habib, Z., 2: Spatial precipitation assessment with elevation by using point cumulative semivariogram technique. Water Resources Management, 14, 311 325. Singh, V. P., and Birsoy, Y. K., 1975: Comparison of the methods of estimating mean areal rainfall. Nordic Hydrology, 6, 222 241. Takase, K., and Sato, K., 1998: Properties of annual evapotranspiration from the catchments in a semi-arid zone and in the south western part of Japan (in Japanese). Journal of Japan Sociecty of Hydrology and Water Resources, 11, 694 71. Thiessen, A. H., 1911: Precipitation averages for large areas. Monthly Weather Review, 39, 182 189. Zhang, L., Hickel, K., Dawes, W. R., Chiew, F. H., Western, A. W., and Briggs, P. R., 24: A rational function approach for estimating mean annual evapotranspiration. Water Resources Research, 4, 71 78. - 97 -