A Watershed flow concentration model of applying the satellite Remote Sensing on Geomorpho - Climatic Instantaneous Unit Hydrograph

Wei Weqiu, Huang Jing
Department of river Engineering,
Wuhan University of Hydraulic and Electric Engineering,
Wuhan, China

Yang Jicheng
Centre of Remote Sensing, Ministry of water Resources, Beijing, China

Abstract
On the basis of the Geomorpho-climatic instantaneous Unit Hydrograph (G.C.IUH) Theory, a model of applying remote sensing information on G.C.JUH deduced and a concept of 0 order stream is defined . The digital image processing, interpreting and the drawing of Strahler stream ordering map are accomplished by computer. A computer program is designed to extract the geomorphic parameters from image rapidly. According to the method mentioned above, we build a model of watershed flow concentration to predict the flood processes at the busin outlet with the effective rainfall produced by runoff yield model. Moreover, it provides a useful method to hydrologic computation in the data-lack regions. The rationality of the model is proved by example calculation in Chuzhou experiment basin of Anhui province.

Introduction
Natural hydrologic phenomena respond to the properties of channel networks and precipitation in a basin . It is expected to predict the discharge processes at the outlet of the basin by solving a mathematic model which embodies varied elements that effect flow concentration mechanism. The theory of G.C.IUH, proposed by Venezuela hydrologists I. Rodriguez-Iturbe and J.B.Valdes in 1979, links the instantaneous unit hydrograph (IUH) with derived from black-box model.

The development of remote sensing technique makes it possible to extract geomorphologic characteristics form Landsat remote sensing image. Considering the advantages and peculiarities of remote sensing, we set forth a watershed flow concentration model based upon the theory of G.C.IUH in this paper. The operations of image processing, stream ordering system map drawing, parameters extracting and flood routing are accomplished by computer. Case study is in volved to verify the effect of the model proposed.

The theory of G.C.IUH
The theory of G.C.IUH considers the movement of raindrops on the basin as stochastic process, which can be described by Markovian Chains. The stream ordering system is defined by A.N.Strahler, he indicates that a certain order of stream corresponds to a certain state probability, and the movement that a raindrop goes from one stream order to any other is described by state transition probability. Assuming that the waiting time of raindrops in the stream of a certain order can be described by exponentical probability density function (pdf), we could transform the pdf of the drops at the trapping state of the basin into IUH with law of Great Numbers, i.e.

Where s = (x₁, x₂,...............,x_n) is a flow path, and S is the set of the path in the basin, P(s) represts the probability function of transition path, f_xi(t), ( i =1,2....,k ), stands for the pdf of drops waiting time at state x_i which includes hillside field state r_i and channel network state c_i .If we ignore the waiting time of the raindrop on hillside field and express the channel waiting time pdf as

Where the l_j is the inverse of the mean waiting time in streams of order j, then we could obtain the G.C.JUH expression with geographic and climatic parameters by imposting Laplace transformation and its inverse transformation on (2). As the increase of the number of stream order, the expression is getting more and more complex .The general formula induced by wen kang et al.is given by

Here W is the highest order in the basin, l_j in (3) has the same meaning given in (2) , and it is defined as

Where is the mean length of streams of order 1. Because the expression of B_ij (W) in (4) is too complicated to be generalized as a single, a program has been designed to calculate it on computer, q_jW (0) in (5) is the state probability that a drop starts its travel in the streams of or- Der j , P_ij is the probability that a drop makes its transition from a stream of order I to order j.

l_j, q_j(0) and P_ij can all be written as the function of the geomorphologic Horton numbers : R_B,R_L, R_A and the climatic parameter V_c. Here , where N_j is the number of streams of order j, L_j is the mean length of streams of order j, and A _j is the mean area of cat chment of stream j , R_B ,R_L and R_A are named the bifurcation ratio, the length ratio and the area ratio respectively, and V_c is the channel dynamic characteristic velocity.

Application of Remote Sensing Information on G.C.IUH
The characteristics of ground surface in a basin and its dynamic variability can be well reflected by the Landsat remote sensing image which has pletiful information. The geomorphic parameters of G.C.IUH can be extracted conveniently from image processed. Due to the effect of the satellite circing period, we may not obtain the image corresponding to the whole duration of a flood process in the basin. In addition to the limitation of the image resolution, the so-called first order streams, according to Stahler ordering procedure, that originate at a source may not be interpreted. The flood calculative precision would be reduced since the highest order interpreated from remote sensing image is lower than real case of the basin. In attempt to alleviate these defiency and to make use of the advantages of remote sensing, the streams which exist objectively but can't be interpreted are abstracted as streams of order 0. It is obvious that the properties of flow concentration of 0-order streams is the same as the one of any other order. Exponential pdf is also used to describe the raindrop waiting time in 0-order stream. Its expression is given by


Wherel_j is the inverse of the mean waiting time in 0-order streams draining into order j. We have reasons to believe that the flow velocity of 0-order streams is equal to V_c, and d_j can be written as


here is the mean length of 0-order streams joininng into streams of order j, it is given by


Now, we derive the expression of geomorpho-climatic instantaneous unit hydrograph applying remote sensing information (R.G.IUH) to fourth-order basin. The Analysis of flowing path in the basin is shown in Fig.1 (dotted line represents the streams of order 0). S= (s₁, s₂, s₃, s₄) is the set of drops flowing path,
where s₁ : r₁- c₁ - c₂ - c₃ - g; r₁ - c₁ - c₃ - g; s₃ : r₂ - c₂ - c₃ - g; s₄ : r₃ - c₃ - g. P_si, ( i = 1,2,3,4 ), are given by.


According to (1), we have


After letting (2) and (8) into (12) and imposing Laplace transformation according to the Theorem of Convolution, we use the Heaviside expansion to (12), the expression of R.G.IUH is now


Image Processing and prarameter calculating on computer
Digital images of Landsat TM3, 4 and 5 bands on Dec. 6, 1987 are processed around the research objective, a first, we remove the noise from the image of TM4 and enhance the stream system and large outline geonmorphic structure corresponding to low frequency by low-pass filter, and proceed to enhance the image by scaling the grey range , Secondly, the filtering of high frequency emphasis and grey scaling are imposed on TM3 to enhance the micro geomorphologic characteristics , the filtering is accomplished through the convolution between the digital image and the chosen mask . Finally false color composite image is obtained by combining the two images which have already been processed with the image or M5 enhanced by grey scaling, this color image that carries plentiful information is helpful to interpretation.

Computer program is designed to draw the map of stream ordering system interpreted from Tm image, the map Is drawn by moving the cursor by computer key board. Different grey value is given to the cursor when drawing the steams and drainage divides of different order, and then each stream order is colored differently to show the distinguishing feature of G.C.IUH (Fig.2) The number and length of streams and area surrounded by drainage divide in certain order are counted by computer, the geomorphic parameters in the expression of R.G.IUH are gained quickly. The program flow diagram of the proceeding above is shown in Fig. 3

Case Study
Flood information of Chuzhou Experiment Basin in Anhui Province is selected to test the effect of the flow concentration model of R.G.IHU proposed. After extracting the geomorphic parameters from Landsat TM image, we calculate the climatic parameter V_c Via the curve of V_c - I_r, here I_r represents the intensity of effective rainfall which produced by yield model. The expression of R.G.IUH is obtained by calculating the P_ij(0) q_j, l_j and d_j and according to formulas (5), (6), (7) and (9). And then, we transform the R.G. IUH (t) period unit hydrograph U (t)





The calculation results of those parameters are shown in Tables 1 and 2. Finally, we gain the discharge processes at the basin outlet by taking the period effective rainfall processes I_r (t) corresponding to the flood selected as the input of R.G.IUH model. It is obvious that the flood processes calculated, shown in Fig. 4, are identical with the flood processes observed. The comparison, which is made between the calculation result from R.G.IUH model and those from G.C. IUH method whose geomorphic parameters are gained from topographic map, shows that it is possible to determine the G.C. IUH by utilizing the remote sensing information.



Conclusions

1. The method of extracting geomorphic parameters of G.C.IUH quantitatively from remote sensing information opens up the way to the application of remote sensing technique to watershed flow concentration model. The calculation of geomorphic parameters can be done more quickly and conveniently from remote sensing image than from topographic map. The method can also be of great value of hydrologic computation in the data-lack-regions.
   
   
2. Methods of watershed runoff production by using remote sensing information are developing gradually. The research work on the application of remote sensing to watershed flow concentration result of G.C.IUH theory depends to a great extent on this parameter; there is much room for improving the method of determining this parameter by remote sensing information.
   
   

References

1. Rodriguez-Iturbe and J.B. Valdes: The Geomorphology Structure of Hydrologic Response. Water Resources Research, Vol. 15, No. 6, 1979.
   
   
2. Rodriguez-Iturbe et al.: A Geomorpho-climatic Theory of The Instantaneous Unit Hydrograph. Water Resources Research, Vol. 18, No. 4, 1982.