Διερεύνηση παραμέτρων του υδρολογικού σχεδιασμού με χρήση συνθετικών μοναδιαίων υδρογραφημάτων μέσω ανάλυσης χαρακτηριστικών επεισοδίων πλημμύρας στην πειραματική λεκάνη Λυκορέματος Ραφήνας

Abstract

Αντικείμενο της παρούσας εργασίας είναι η διερεύνηση μεθόδων υδρολογικού σχεδιασμού που βασίζεται στην επεξεργασία ιστορικών πλημμυρικών γεγονότων στην πειραματική λεκάνη της Ραφήνας. Αρχικά έγινε συλλογή δεδομένων βροχής και απορροής από δύο υδρομετρικούς και τέσσερις βροχομετρικούς σταθμούς στην περιοχή μελέτης και διάκριση επεισοδίων πλημμύρας βάση των μεγαλύτερων μέσων ημερησίων παροχών που έχουν παρατηρηθεί. Για κάθε επεισόδιο από τα δεδομένα βροχής έγινε αρχικά απομόνωση των συνολικών ελλειμμάτων με σκοπό την εκτίμηση του ποσού της βροχής που μετατρέπεται σε απορροή, δηλαδή της ενεργού βροχής. Για τον υπολογισμό της ενεργού βροχής χρησιμοποιήθηκε η μέθοδος εκτίμησης συνολικών ελλειμμάτων SCS με παραμέτρους τον αριθμό καμπύλης απορροής CN και τον λόγο a= haO/S όπου haO είναι το αρχικό έλλειμα και S η δυνητικά μέγιστη κατακράτηση, που εκτιμάται συναρτήσει του CN.Για τον μετασχηματισμό της βροχής σε απορροή έγινε εφαρμογή της θεωρίας του μοναδιαίου υδρογραφήματος σύμφωνα με την οποία το προσομοιωμένο πλημμυρογράφημα άμεσης απορροής της λεκάνης προκύπτει από τον πολλαπλασιασμό του ενεργού υετογράμματος με ένα συνθετικό μοναδιαίο υδρογράφημα. Στα πλαίσια της εργασίας έγινε χρήση υφιστάμενων συνθετικών μοναδιαίων υδρογραφημάτων και ενός παραμετρικού εμπειρικού μοναδιαίου υδρογραφήματος. Από το συνδυασμό του κάθε μοναδιαίου υδρογραφήματος με το ενεργό υετόγραμμα προέκυψε ένα προσομοιωμένο πλημμυρογράφημα άμεσης απορροής το οποίο συγκρίνεται με το παρατηρημένο. Για κάθε επεισόδιο έγινε αρχικά διαχωρισμός της βασικής ροής από το ολικό παρατηρημένο πλημμυρογράφημα. Για το σκοπό αυτό η αρχή της άμεσης απορροής θεωρήθηκε το σημείο όπου η ολική απορροή αυξάνει απότομα και το τέλος της άμεσης απορροής θεωρήθηκε ότι συμβαίνει σε χρόνο ίσο με τον χρόνο συγκέντρωσης μετά τη λήξη της ενεργού βροχής. Η λήξη της ενεργού βροχής θεωρήθηκε ότι ταυτίζεται με τη λήξη της ολικής βροχής. Μετά τη χρήση των συνθετικών μοναδιαίων υδρογραφημάτων του Βρετανικού Ινστιτούτου Υδρολογίας και της μεθόδου Snyder με ένα υετόγραμμα ενεργού βροχής με τιμές των παραμέτρων α και CN όπως προτείνονται από τη βιβλιογραφία και τη διαπίστωση ότι το προσομοιωμένο πλημμυρογράφημα που προκύπτει απέχει πολύ από το παρατηρημένο πλημμυρογράφημα για κάθε επεισόδιο έγινε εφαρμογή ενός εμπειρικού μοναδιαίου υδρογραφήματος, το οποίο διαθέτει έναν γραμμικό ανοδικό κλάδο, με χρόνο ανόδου tp = β* tc + d/2,έναν καθοδικό κλάδο λογαριθμικής μορφής και χρόνο βάσης ίσο με tb = tc + d (όπου d είναι η διάρκεια βροχής, tc ο χρόνος συγκέντρωσης της λεκάνης και β παράμετρος). Για κάθε επεισόδιο έγινε βελτιστοποίηση των παραμέτρων α και CN της μεθόδου SCS και της παραμέτρου β του εμπειρικού μοναδιαίου υδρογραφήματος με στόχο το προσομοιωμένο πλημμυρογράφημα να προσεγγίζει με τον καλύτερο δυνατό τρόπο το παρατηρημένο. Επίσης πραγματοποιήθηκε μία επιπλέον διερεύνηση των μελετούμενων παραμέτρων με άλλα χαρακτηριστικά μεγέθη των ιστορικών πλημμυρών προκειμένου να αποτυπωθεί η πραγματικότητα τέτοιων μεγεθών που υπεισέχονται στον υδρολογικό σχεδιασμό.

The subject of this postgraduate thesis is the investigation of parameters that present in existing methods of hydrologic design through the process of historical time series of discharge and rainfall. These parameters are used to compute the effective rainfall hyetograph and a empirical unit hydrograph that will be following presented. Specifically, data have been collected from meteorological and flow measurement stations in the area of southeast Mesogaia region of the prefecture of Attiki. Through the correlation of these data parameters for the computation of the effective rainfall and the development of the unit hydrograph will be optimised. HYDROLOGIC DESIGN ACCORDING THE THEORY OF THE UNIT HYDROGRAPH The most reliable method of hydrologic design is the application of the theory of the unit hydrograph. The unit hydrograph is the unit pulse response function of a linear hydrologic system. It is defined as a direct run off hydrograph from usually 10 mm of excess rainfall generated uniformly over the drainage area for an effective duration D. According to this method rainfalls of duration D with multiple intensity cause multiple discharge respectively. Also, the principle of stability is valid in the application of the theory of the unit hydrograph. That means that when a rainfall process of duration D ends, starts a new independent which produces a new hydrograph. As a result, the hydrographs which are produced that way are being overlapped and the final hydrograph has ordinates the sum of the ordinates of the overlapped hydrographs. The unit hydrograph is a feature of the watershed which refers to, particularly important. Once the unit hydrograph is determined, it may be applied to find the direct runoff using the selected excess rainfall hyetograph. Unit hydrographs can be developed using various procedures such as the Snyder method, the method according the British Institute of Hydrology, the triangular unit Hydrograph according to Soil Conservation Service, the SCS dimensionless hydrograph and others. The most realistic method for the estimation of the effective rainfall is the method according to Soil Conservation Service. STUDY AREA The study area is the X-Basin, which is located in the southern Athens area, is a subbasin of the basin of Rafina Stream and covers an area of 15,2 km2. The northern part with outlet the Lykorema position has been studied independently by the whole watershed with outlet the Drafi position. The raingauge data have been collected from the hydrometeorological stations which are located in Mpala, Agios Nikolaos, Drafi and Pikermi. The discharge data have been collected from the flowmeasurements stations which are located in Lykorema and Drafi. We finally chose 15 flood events for the watershed upstream Drafi and 20 flood events for the watershed upstream Lykorema. METHOLOGY The aim of the procedure is to estimate in every rainfall event the optimized value of the parameters a and CN, which are used for the calculation of the effective rainfall, and the parameter b, which is used for the development of an empirical unit hydrograph. Every flood event has been selected according to maximum mean daily discharge as they are presented in the time serie of discharge in Drafi and Lykorema. For the day of the flood and also one day before and two days after raingauge and discharge data have been recorded from every station that operated these dates. It should be mentioned that the time step of the raingauge and discharge data is 10 minutes. Then the point raingauge data have been transferred to surface data using the method of Thiessen polygons. Using the SCS method for the calculation of the effective rainfall the effective rainfall ends when the total rainfall ends. The direct runoff ends after the end of the total rainfall as long as the time concentration lasts. The time when the direct runoff starts is clear at the hyetograph since it is the time when the gradient of the chart of the streamflow grows sharply. During the flood it is supposed that the baseflow has a linear form, so it is easy to compute the amount of baseflow which will be separated from the streamflow. For the development of the simulated hydrograph the calculation of the effective rainfall and the empirical unit hydrograph is necessary. The empirical unit hydrograph which is developed through this study has an upward linear sector and a downward logarithmic sector. This hydrograph has an upward linear sector with peak time: tp=b*tc+D/2 (1) Where b is a parameter lower than one, which will be optimized, tc the time of concentration of the watershed which is calculated according to Giandotti formula, D the duration of the rainfall

For the base time we applied the equation: tb=tc+D (2) In this equation the definition of the time of concentration is reflected. Time concentration is defined as the time from the end of rainfall excess till the end of th direct runoff. The downward sector has the following form: Q(t)=Qp-k*ln(1+t-tp) (3) where : Qp the peak discharge , k parameter which is calculated according to the equation : k= Qp/ln(1+tb-tp) (4) The equation for the calculation of the peak discharge comes from the equation of the unit flood volume with the shape area of the unit hydrograph : Qp=10^4/(tp/2-1-(tb-tp)/ln(tb-tp+1)) (5)

The empirical hydrograph has the following form:

Using the unit hydrograph above in combination with the excess hyetograph the simulated hydrograph is being developed. Following, we form the error function, which is going to be used in the optimization procedure: f= SSE+l1*(Vh-Vq)^2+l2*(maxQobs-maxQsim)^2 (6)

where: SSE the sum square error,Vh the total amount of excess rainfall calculated in mm ,Vq the total amount of direct runoff calculated in mm, maxQobs the max value of discharge in the hydrograph of observed direct runoff, maxQsim the max value of discharge in the hydrograph of simulated direct runoff. At first the theory of the unit hydrograph will be applied using the Snyder method and the unit hydrograph according to the British Institute of Hydrlogy. Each one will be combined with an excess hyetograph. This hyetograph is calculated according to SCS method by setting the value 0,2 for the parameter a and the proper value for the parameter CN so that sumhe is equated with sumQe.

CONCLUSION The initial aim of the present study is to investigate the values of the parameters a, CN, b for the watersheds upstream Drafi and Lykorema. For the watershed upstream Drafi the value of the parameter CN is varied from 40 to 50 and the value of the parameter a is varied from 0 to 0,02 for most flood events.

However for both parameters it is been observed that there is a correlation with the observed peak discharge. This observation indicates that parameters a and CN probably do not have a stable value which is characteristic for the watershed. The truth probably is that depending on the peak discharge the value of the parameters vary similarly. As it has been mentioned the parameter b is presented in the development of the unit hydrograph. Thus the unit hydrograph which represents the watershed upstream Drafi has the following form: It should be mentioned that this hydrograph is refered to time concentration that is calculated using the empirical formula Giandotti. Nevertheless, through an additional investigation it is been observed that time concentration does not have a stable value but it depends on the peak discharge in a inversely proportional way. For the watershed upstream Lykorema, which as it is already been mentioned is a subbasin of the entire X-basin, the value of the parameter CN at most flood events vary from 10 to 20 and the value of the parameter a vary from 0 to 0,02. For this watershed it is observed that the parameter CN has a corresponding correlation with peak discharge as the watershed upstream Drafi. A corresponding correlation for the parameter a has not been found. However it should be mentioned that tha sample of events for this watershed does not include many cases of great values of peak discharge so that we can come to a conclusion about the correlation of peak discharge with other features. For the parameter b at most flood events its value vary from 0,35 to 0,40 after the correction of time concentration. This hydrograph refers to time concentration which is calculated using the empirical formula Giandotti. Nevertheless, through an additional investigation it is been observed that time concentration does not have a stable value but it depends on the peak discharge in a inversely proportional way. This observation about the time concentration but also the dependence of the parameters CN and probably a on the peak discharge is particularly significant since these parameters contribute to the hydrologic design through the unit hydrograph and the excess hyetograph.