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Structural Analysis of Daily Precipitation Series

This paper explores the selection of probability distribution types for daily cumulative precipitation and introduces daily varying standard precipitation index diagrams.

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Structural Analysis of Daily Precipitation Series

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  1. Title: STRUCTURAL ANALYSIS OF DAILY PRECIPITATION SERIES Authors: Vladislava Mihailovic*, Zoran M. Radic** *Faculty of Forestry, University of Belgrade, Serbia, vmihailovic@beotel.net **Faculty of Civil Engineering, University of Belgrade, Serbia, zradic@grf.bg.ac.rs

  2. Introduction This paper is a continuation of the research presented by the same authors in the BALWOISE 2010 paper: IMPROVING METHOD FOR STRUCTURAL ANALYSIS OF DAILY RUNOFF SERIES

  3. DAILY CUM. PREC. 30,60, 90 DAYS DAILY CUMULATIVE PRECIP. STATISTICAL FUNCTIONS SERIES DAILY PRECIPITATIONDATA REFERENCE PERIOD 1961-1990 MODELING of PERIODICAL FUNCTIONS of STATISTICAL PARAMETERS RCP diagrams L-momentdiagrams PPCC, MAD&RMSE Tests CANDIDATE MARG. DISTRIBUTIONS THE BEST MARG. DISTRIBUTION Methodology DATA PREPARATION: DATA MODELING: APPLICATIONS: FLOODS STUDIES DROUGHTS STUDIES DAILY VARYING TRESHOLD SPI DERIVATION

  4. The main objectives of this paper are: THE SELECTION OF APPROPRIATE PROBABILITY DISTRIBUTION TYPE FOR MARGINAL DISTRIBUTIONS OF DAILY CUMULATIVE PRECIPITATION(30, 60 and 90 days) INTRODUCTION OF DAILY VARYING (SMOOTH) STANDARD PRECIPITATION INDEX (SPI) DIAGRAMS FOR THE REFERENT PERIOD1961-1990

  5. The appropriate probability distribution type selection - two stages: 1. PRELIMINARY SELECTION of DISTRIBUTION CANDIDATES Based on: L-moment ratio diagrams (LMR) 2. FINAL CHOICE of MARGINAL DISTRIBUTIONS TYPE Based on: (A) Goodness of fit analysis, i.e. distribution ranking bytest statistics - probability plot correlation coefficient (PPCC), meanabsolute error (MAE) and root mean square error (rRMSE) statistics, (B) Regional analysis of distribution candidates, and (C) Physical interpretation of ”best-distributions” i.e.analysis of the distribution periodical lower/upper boundary.

  6. Data Study is based on data from 25 representative stations in Serbia and for the period till 2006. Length of data: - Min. 39 years - Max. 71 years - Aver. 46 years - Reference period: 1961-1990

  7. L-Cvvs L-Ck for 2- parameter distributions 30-day precipritation 60-day precipritation 90-day precipritation W2, GAM2, GPA2 L-Csvs L-Ck for 3- parameter distributions Results PRELIMINARY SELECTION of DISTRIBUTION CANDIDATES Based onL-moment diagrams 60-day precipritation 90-day precipritation 30-day precipritation GEV, P3, W3 L-moment diagrams for 30, 60, 90-day cumulative precipitation, for the station Belgrade.

  8. The upper boundary of the marginal distribution function (if exists) should not be close to (or lower than) the line of the series of daily maxima; • The lower boundary of the marginal distribution function (if exists), should not be lower than zero; • For the application in the drought analysis (defining duration and deficit, for example) a condition was accepted that line of the 0.01 probability should be above zero over the annual cycle. Results 2.DISCRIMINATION BETWEEN DISTRIBUTION CANDIDATES ACCORDING TO THE REGIONAL APPLICABILITY IN SERBIA AND THE NATURE OF THE MODELED PHYSICAL PROCESS 2-parameter distributions: W2 (Weibull) and GAM2 (Gamma)

  9. Results 3. DISCRIMINATION BETWEEN DISTRIBUTION CANDIDATESBY TESTSTATISTICS - Results of the PPCC test for 25 representative stations from Serbia: GAM2 - average annual value of the PPCC test statistic

  10. The number of stations (of all 25) for which is better GAM2 or W2, by MAE and RMSE statistic Results 3. DISCRIMINATION BETWEEN DISTRIBUTION CANDIDATESBY TESTSTATISTICS - Ranking of distribution candidates by the RMSE and MAE statistics:

  11. FINAL CHOICE of MARGINAL DISTRIBUTIONS TYPE For Serbia GAM2 distribution should be recommended as reference model for marginal distributions ofdaily cumulative precipitation for 30, 60 and 90 days. The GAM2 marginal distribution diagram for the Belgrade station and 90-day cumulative precipitation for the drought hydrological year 1992-1993.

  12. Diagram of quantiles of the marginal distributions could be transformed into the smooth diagrams of the Standardized Precipitation Index (SPI), by an inverse SPI procedure. Those SPI diagrams represent lines of precipitation values of a certain SPI value. The SPI classes boundaries for the Belgrade station, and 90-day cumulative precipitation for the drought hydrological year 1992-1993.

  13. Conclusions For Serbia,GAM2 distribution should be recommended as a reference model for marginal distributions ofdaily cumulative precipitation of 30, 60 and 90 days Using smoothed diagrams of the marginal distributions quantiles of daily cumulative precipitations,and threshold level method, meteorological and hydrological droughts analyses would be comparable. Instead of commonly used monthly time step we used daily time step for SPI definition.In thisnew approach, the derived smoothed diagrams of the marginal distributions quantiles are the starting point in the defining of thedaily varying threshold level SPI in the drought classification (or in the analysis of dry and/or wet periods).

  14. THANK YOU FOR YOUR ATTENTION

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