RUNOFF FORECASTS BY LINEAR PREDICTIVE FILTER

ASSUMPTION OF A LINEAR STOCHASTIC PROCESS FOR THE RAINFALL AND RUNOFF SYSTEM YIELDS A WIENER-HOPF TYPE OF INTEGRAL EQUATION WHICH RELATES THE AUTOCOVARIANCE FUNCTION OF RAINFALL TO THE CROSSCOVARIANCE FUNCTION OF RAINFALL AND RUNOFF THROUGH THE SYSTEM RESPONSE FUNCTION (THE SO-CALLED UNIT HYDROGRAPH). THE ANALYTICAL SOLUTION OF THE WIENER-HOPF EQUATION IS DERIVED BY THE SPECTRUM FACTORIZATION TECHNIQUE, SHOWING THAT THE UNIT HYDROGRAPH IS NOT THE CROSSCOVARIANCE OF RAINFALL AND RUNOFF ITSELF BUT THE WEIGHTED SUM OF EACH COMPONENT WHICH CONSTITUTES THE CROSSCOVARIANCE. THE WEIGHT IS ALWAYS ZERO FOR A LAG TIME OF LESS THAN ZERO. WHILE, THE WEIGHT FOR A LAG TIME GREATER THAN OR EQUAL TO ZERO IS HEAVIER FOR A LONG PERIOD RUNOFF THAN FOR A SHORT PERIOD ONE. STATISTICAL PROPERTIES OF HYDROLOGICAL DATA SUCH AS AUTOCOVARIANCE, CROSSCOVARIANCE, SPECTRUM, COHERENCE, AND PHASE ANGLE ARE INVESTIGATED TO APPLY THE PREDICTION METHOD PRACTICALLY. IT IS SHOWN THAT THE AUTOCOVARIANCE OF DAILY RAINFALL MAY BE ROUGHLY APPROXIMATED BY THE DIRAC DELTA FUNCTION. THE CROSSCOVARIANCE OF RAINFALL AND RUNOFF ANALYZED IN THIS PAPER IS COMPOSED OF TWO RUNOFF COMPONENTS OF SHORT AND LONG PERIODS. THE COHERENCE OF RAINFALL AND RUNOFF IS NEARLY UNITY FOR LIGHT RAINFALL SUGGESTING THAT THE RAINFALL-RUNOFF PROCESS MAY BE APPROXIMATED BY A LINEAR SYSTEM. ON THE OTHER HAND, THE COHERENCE BECOMES WORSE AS THE RAINFALL INTENSITY INCREASES; THERE IS A GAP OF COHERENCE IN THE MIDDLE FREQUENCY RANGE. THE METHOD OF LINEAR PREDICTION BASED ON THE WIENER CRITERION IS APPLIED TO THE RIVER KANNAGAWA. RESULTS SHOW THAT THE AVAILABILITY IS GOOD FOR CASE OF RELATIVELY SMALL RAINFALL INTENSITY, BUT IT BECOMES WORSE AS THE RAINFALL INTENSITY INCREASES. /AUTHOR/

• Supplemental Notes:
  • Vol 96, No HY 3, PROC PAPER 7146, PP 681-702, 13 FIG, 1 TAB,
• Authors:
  • Hino, M
• Publication Date: 1970-3

Media Info

• Serial:
  • Journal of the Hydraulics Division
  • Publisher: American Society of Civil Engineers

Subject/Index Terms

• TRT Terms: Approximation (Mathematics); Covariance; Filters; Forecasting; Hydrographs; Hydrologic phenomena; Linear systems; Rainfall; Runoff; Statistical analysis; Stochastic processes; Time; Weather forecasting
• Uncontrolled Terms: Rainfall intensity; Relationships
• Old TRIS Terms: Hydrologic data; Time factor
• Subject Areas: Data and Information Technology; Highways; Hydraulics and Hydrology;

Filing Info

• Accession Number: 00204276
• Record Type: Publication
• Files: TRIS
• Created Date: May 19 1970 12:00AM