Geology and intercepts of multiple regression models as an index of baseflow

Transcription

1 Hydrology of Warm Humid Regions (Proceedings of the Yokohama Symposium, July 1993). IAHS Publ. no. 216, Geology and intercepts of multiple regression models as an index of baseflow HAJIME ANJI National Research Institute of Agricultural Engineering, sukuba, Ibaraki Prefecture, Japan 305 Abstract A statistical rainfall runoff model by multiple regression analysis was developed by Shiraishi et al. (1976). his method can separate the linear runoff component from observed discharge by the Fixed Maximum ischarge (FM) method, a high-cut filter. In this model, an intercept, a constant term, can be translated as the statistical expression of baseflow. he author applied this method to catchment areas in the one River basin. hese areas are selected mainly among dam basins and additionally among stationary observation points of discharge. In this river basin, Mushiake et al. (1981) studied the relation between geology and drought discharge. his paper makes clear the equality of this baseflow and drought discharge. An intercept of a multiple regression model with the FM method expresses drought discharge strongly dependent on geology. INROUCION A multiple regression model of rainfall runoff was developed by Shiraishi et al. (1976). heir model picks rainfall as input and runoff as output. his model can separate the linear runoff component by the FM method, a high-cut filter from observed discharge. In this formation, an intercept can be expressed as an independent term of runoff to rainfall. Shiraishi et al. (1976) suggested that an intercept of a multiple regression model could be interpreted as the baseflow value of a basin in a mathematical meaning because it expresses output under no input. Mushiake et al. (1981) studied the relation of drought discharge (355 days) and geology in the one River basin by ordinary discharge data at old water power stations. hey selected data of 50 years ago to avoid the artificial effects of baseflow. he author discusses a missing ring, the relation between an intercept and geology of a basin (Fig. 1). he author also discusses other parameters of multiple regression models. hese models represent the function between rainfall and runoff discharge when runoff discharge is low because high discharge is cut by the FM method. Parameters of models will be clusterized and control factors of runoff characteristics will be discussed is this paper. he analysis of Mushiake et al. (1981) was limited to old data before development of power resources. his paper treats newer data.

2 498 Hajitne anji drought discharge base flow Shiraishi / \ Mushiake intercept Geology? Fig. 1 Missing ring. SUIE AREAS Studied areas were set to dam basins and stationary observation points of discharge in the upstream basins of the one River (Fig. 2). ata on inflow discharge and rainfall were collected and used. he analysis period was from 1 June to 20 November, with some from 1 July to 30 November. hese periods were set to avoid the effect of snow. Analysis years were from 1976 to he geology upstream of the one River basin and studied areas is shown in Fig. 2. In this figure geology is designated as a Palaeozoic era, volcanic rocks in the ertiary period, volcanic rocks in the Quaternary period and granite. MEHO OF RAINFALL RUNOFF ANALYSIS In expressing rainfall runoff relations, Shiraishi's model of multiple regression analysis is employed in the present study (Shiraishi et al., 1976). his model is summarized as follows: the rainfall-runoff relation is expressed by Volterra series in which the present time t is taken as the start: n II^(r-r jt )dr 1 dr 2 * dr n *=i in which x(t r k ) A r - R(t r k ), where A r : area in a basin (in acres); R{t - r k ) intensity of rainfall in an area; Y(t): the value of the watershed runoff at time t; h n runoff kernel of the nth degree; r k : integral variable showing time-lag runoff; and t time. By taking the terms up to the second degree of moment and using multiple regression analysis, equation (1) can be approximated in the following discreet form: (i) m m 1=1 1=1 ]=\ \ l S X(t- t ) X(t-j) he parameters, A 0, A : and By, are determined by the method of least squares, in which the terms of the first degree, A 0, A i and the terms of the second degree By are determined separately by the Fixed Maximum ischarge (FM) method.

3 Geology and intercepts of multiple regression models 499 jra Volcanic rocks in the >^ Quaternary Period ^^j Volcanic rocks in the ertiary Period E Granite gg Paleozoic Era I I iluvium and Alluvium Boundary of a basin River - - Model basins Fig. 2 Geology and model basins. remark number shows No. in ablel For the solution of equation (2), data were arranged in a matrix form in which each /th law represents the data of the /th day. he /th law consists of the data t = / in equation (2). If equation (2) is solved by the least-square method directly, reasonable parameters of A i and B i cannot be given because of multicollinearity. In the FM method, the column with low values of y(t) is selected when the value of discharge is larger than a value of FM and only the first order of equation (2), the linear component, is solved by the least-squares method. he second order terms were solved when the target value was set as y(t) minus linear estimation. hat is called the nonlinear component. In this paper, only linear models will be discussed. he parameters A t consist of a statistical unit hydrograph. imensions of explanation parameters were decided by the method of increment. he maximum dimension was decided on the condition that all partial regression coefficients are non-negative. RESULS AN CONSIERAION Runoff characteristics in the models are expressed as (a) an intercept and partial regression coefficient, (b) FM, (c) multiple correlation coefficient, and (d) time-lag n (day). he term (c) is a criterion of fitness of estimation by a model and observed data and accuracy of observed data. If the number n (in days) was large, the influence of ft on the term (a) and the term (b) are omissible. In the experience of the authors, the cause of small lag day n is the low accuracy of the data. In this paper, many multiple regression models are identified first. Models with low multiple correlation coefficients, low variance ratios and small areas were already omitted (refer to Fig. 2). herefore the terms (c) and (d) are omissible. Multiple correlation coefficients are discussed from the viewpoint of runoff percentage and shapes of statistical unit hydrographs. Parameters of models are shown in ascending order of intercepts in able 1. he numbers in Fig. 2 show the locations of basins in able 1.

4 500 Hajime anji able 1 Parameters of runoff models of mountain area. No. River Basin Area (km 2 ) Linear runoff Intercept (mm day" 1 ) FM (mm day" 1 ) Geology" appa Karma Kinu Sekiya Usui Watarase one Kinu Karasu one Agatuma Ootani Agatuma otigi Shimokubo Ikari aimata Kirizumi Kusaki Yagisawa Kawamata Kamisatomi Iwamoto Murakami Cyuzenji Sinaki a p. Palaeozoic era; : volcanic rocks in the ertiary period; G: granite; P P P G + Q + Q Q Q Q: Quaternary period. Intercepts and linear runoff percentage Figure 3 shows relations between linear runoff percentage and intercepts. he relation between linear runoff percentage and intercepts is weak by this figure. istribution of intercepts are from 0.2 mm day" 1 to 3.2 mm day" 1. istribution of linear runoff percentage vary from 20 to 90%. remark number shows the location in Fig.2 and able"! C!» CO C~ erce Q. * r run m et IUU I3 n 1 a 6 a ri! O 10 u lntercepts(mm/day) Fig. 3 Intercepts and linear runoff percentage. FM and linear percentage runoff Figure 4 shows the correlation between FM and liner runoff percentage. If the data of points 5, 6 and 12 in the upper basin of Iwamoto were to be eliminated, the correlation of linear runoff percentage and FMs would be small. Linear runoff percentage of Yagisawa dam is large because of the location of a rainfall station at the bottom of the basin. he rainfall data used was smaller than the actual average rainfall in the basin. he linear runoff percentage is large in the upstream portion of Iwamoto. Clusterization of statistical unit hydrographs o analyse characteristics of runoff in each basin, statistical unit hydrographs were grouped together by a cluster analysis method. o avoid the effects of variance of the area of basins and data,

5 Geology and intercepts of multiple regression models 501 remark number shows the location in Fig.2 and ablel -c linear runoff percentage(%) Fig. 4 Linear runoff percentage and FM Fig. 5 endrograms of statistical unit hydrographs H I 0.05 f ^fyfc* time lag (day) '^' 20 Fig. 6 Statistical unit hydrographs. Yagisawa; -*- Aimata; -O- Shinaki; Shimokubo; Kusaki; -- Chuuzenji.

6 502 Hajime anji objects were limited to dam basins. Maximum time-lag n is written «max. he term «max is set to 20 and the values of A t (i > 20) are omitted here. If time-lag n (days) is taken as dimensions, each statistical unit hydrograph can be expressed as a point in "max space. Squared Euclidean distance is adopted as the scale of dissimilarity. Figure 5 shows a dendrogram by the furthest neighbour method. Statistical unit hydrographs of Yagisawa and Aimata dams are completely different. Shimokubo and Kirizumi dams are yet different types. Figure 6 shows statistical unit hydrographs of 20th degree (time-lag 19 (days)). Clusterization of intercepts Figure 2 shows the geology of the one River basin. It is noted and referenced in able 1. here is strong correlation between geology and intercepts. Figure 7 shows these relations, including the results of Mushiake's study. Mushiake showed the relation between geology and drought discharge (355 days). He showed drought discharge in rocks of Palaeozoic era to be 0.3 to 0.7 (mm day" 1 ), that in volcanic rocks of the ertiary period to be 1 to 3 (mm day" 1 ), that in granite to be 1.5 (mm day" 1 ) and that in volcanic rocks in the Quaternary period to be 2 to 5 (mm day" 1 ). Intercepts show values of 0.13 to 0.44 (mm day" 1 ) in Palaeozoic rocks, 0.91 to 1.42 (mm day" 1 ) in volcanic rocks of the ertiary period, 1.37 (mm day" 1 ) in granite and 2.59 to 3.13 (mm day" 1 ) in volcanic rocks of the Quaternary period. In this figure, intercepts and drought discharge were plotted as parallel. herefore, a statistical parameter, an intercept, can be interpreted as physical value of drought discharge. a> I 4 o E E 3 2 CONCLUSION aulhof's Mushjake's 1 " A i ô 0 a i i i i Paleozoic Era Granite Volcanic rocks in the Volcanic rocks Volcanic rocks Quaternary Period in the ertiary in the ertiary Penoci and Quaternary Period Fig. 7 Geology and intercepts. he physical meaning of an intercept of a multiple regression model can be translated as baseflow when the model is applied to rainfall-runoff analysis of linear runoff by the FM method. he author has shown that an intercept, as a function of geology, can express the drought discharge in the one River basin. REFERENCES Shiraishi, H., Oonishi, R. & Ito, Y. (1976) Nonlinear approach to rainfall-runoff process by multiple regression analysis. (In Japanese with English summary). rans. JSIRE 63, Mushiake, K., akahashi, Y. & Ando, Y. (1981) Effects of basin geology on river-flow regime in mountainous areas m Japan. (In Japanese with English summary). Proceedings ofjsce 309, A