HYDROLOGIC TIME SERIES ANALYSIS: THEORY AND PRACTICE
CONTENTS 1 INTRODUCTION 1 1 WATER PROBLEMS AND CHALLENGES: AN OVERVIEW 1 2 WHAT IS TIME SERIES? 1 3 TIME SERIES ANALYSIS 1 4 CLASSIFICATION OF TIME SERIES 1 4 1 DISCRETE OR CONTINUOUS TIME SERIES 1 4 2 FULL OR PARTIAL DURATION SERIES 1 4 3 UNIVARIATE OR MULTIVARIATE 1 5 STRUCTURE OF TIME SERIES 1 6 SALIENT CHARACTERISTICS OF TIME SERIES 1 7 TIME SERIES ANALYSIS VIS-A-VIS HYDROLOGY PART I: TOOLS/TECHNIQUES FOR TIME SERIES ANALYSIS 2 STATISTICAL CHARACTERISTICS OF HYDROLOGIC TIME SERIES 2 1 MEASURES OF LOCATION 2 1 1 CLASSICAL MEASURE: ARITHMETIC MEAN 2 1 2 ROBUST MEASURE: MEDIAN 2 1 3 ADDITIONAL MEASURES OF LOCATION 2 2 MEASURES OF SPREAD/DISPERSION 2 2 1 CLASSICAL MEASURES 2 2 2 ROBUST MEASURES 2 3 MEASURES OF SKEWNESS 2 3 1 CLASSICAL MEASURE OF SKEWNESS 2 3 2 ROBUST MEASURE OF SKEWNESS 2 4 ADDITIONAL ROBUST MEASURES 2 5 MEASURES OF PEAKEDNESS OR FLATNESS 2 6 STATISTICAL MEASURES FOR SYSTEM PERFORMANCE EVALUATION 2 6 1 RELIABILITY 2 6 2 RESILIENCE 2 6 3 VULNERABILITY 3 METHODS FOR TESTING NORMALITY OF HYDROLOGIC TIME SERIES 3 1 GRAPHICAL METHODS 3 1 1 FREQUENCY PLOTS/HISTOGRAM 3 1 2 STEM-AND-LEAF PLOT 3 1 3 BOX AND WHISKER PLOT 3 1 4 RANKED DATA PLOT 3 1 5 QUANTILE PLOT 3 1 6 NORMAL PROBABILITY PLOT 3 2 STATISTICAL METHODS 3 2 1 CHI-SQUARE TEST 3 2 2 KOLMOGOROV-SMIRNOV TEST 3 2 3 LILLIEFORS TEST 3 2 4 ANDERSON-DARLING TEST 3 2 5 CRAMÉR-VON-MISES TEST 3 2 6 SHAPIRO-WILK TEST 3 2 7 PROBABILITY PLOT CORRELATION COEFFICIENT 3 2 8 COEFFICIENT OF VARIATION 3 2 9 RANGE TESTS 3 2 10 JARQUE BERA TEST 3 2 11 D’AGOSTINO PEARSON OMNIBUS TEST 4 METHODS FOR TIME SERIES ANALYSIS 4 1 METHODS FOR CHECKING HOMOGENEITY 4 1 1 THE VON NEUMANN TEST 4 1 2 CUMULATIVE DEVIATIONS TEST 4 1 3 BAYESIAN TEST 4 1 4 TUKEY TEST FOR MULTIPLE COMPARISONS 4 1 5 LINK-WALLACE TEST 4 1 6 DUNNETT TEST 4 1 7 BARTLETT TEST 4 1 8 HARTLEY TEST 4 2 METHODS FOR CHECKING STATIONARITY 4 2 1 STUDENT’S T-TEST 4 2 2 SIMPLE T-TEST 4 2 3 MANN-WHITNEY TEST 4 3 METHODS FOR DETECTING TREND 4 3 1 REGRESSION TEST 4 3 2 SPEARMAN RANK ORDER CORRELATION TEST 4 3 3 TURNING POINT TEST 4 3 4 KENDALL’S PHASE TEST 4 3 5 WALD-WOLFOWITZ TOTAL NUMBER OF RUNS TEST 4 3 6 SUM OF SQUARED LENGTHS TEST 4 3 7 ADJACENCY TEST 4 3 8 DIFFERENCE SIGN TEST 4 3 9 RUN TEST ON SUCCESSIVE DIFFERENCES 4 3 10 WILCOXON-MANN-WHITNEY RANK SUM TEST 4 3 11 INVERSIONS TEST 4 3 12 KENDALL’S RANK CORRELATION TEST 4 3 13 MANN-KENDALL TEST 4 3 14 SEN’S SLOPE ESTIMATION TEST 4 3 15 TREND-HOMOGENEITY TEST 4 4 METHODS FOR CHECKING PERIODICITY 4 5 METHODS FOR PERSISTENCE TESTING 4 5 1 AUTOCORRELATION TECHNIQUE 4 5 2 SPECTRAL TECHNIQUE 4 6 MERITS AND DEMERITS OF TIME SERIES METHODS 5 STOCHASTIC MODELLING OF TIME SERIES 5 1 COMMON STOCHASTIC PROCESSES 5 1 1 PURELY RANDOM PROCESS 5 1 2 AUTOREGRESSIVE (AR) PROCESS 5 1 3 MOVING AVERAGE (MA) PROCESS 5 1 4 AUTOREGRESSIVE MOVING AVERAGE (ARMA) PROCESS 5 1 5 AUTOREGRESSIVE INTEGRATED MOVING AVERAGE (ARIMA) PROCESS 5 2 METHODOLOGY FOR ARIMA MODEL APPLICATION 5 2 1 ARIMA: IDENTIFICATION OF THE MODEL 5 2 2 ARIMA: ESTIMATION OF MODEL PARAMETERS 5 2 3 ARIMA: EVALUATION OF THE MODEL 5 2 4 ARIMA: FORECASTING 6 CURRENT STATUS OF TIME SERIES ANALYSIS IN HYDROLOGICAL SCIENCES 6 1 THEORETICAL RESEARCH ON HYDROLOGIC TIME SERIES 6 2 APPLICATION OF TIME SERIES ANALYSIS IN CLIMATOLOGY 6 2 1 PRECIPITATION/PRECIPITATION WITH OTHER CLIMATIC DATA 6 2 2 AIR AND WATER TEMPERATURE 6 2 3 EVAPOTRANSPIRATION 6 2 4 CLIMATIC CHANGE 6 3 APPLICATION OF TIME SERIES ANALYSIS IN SURFACE WATER HYDROLOGY 6 3 1 STREAMFLOW 6 3 2 SURFACE WATER QUALITY 6 4 APPLICATION OF TIME SERIES ANALYSIS IN GROUNDWATER HYDROLOGY 6 4 1 GROUNDWATER FLOW 6 4 2 GROUNDWATER QUALITY 6 5 TIME SERIES ANALYSIS OF IRRIGATION REQUIREMENT AND SOIL MOISTURE 6 6 CONCLUDING REMARKS PART II: SALIENT CASE STUDIES 7 EFFICACY OF TIME SERIES TESTS: A CRITICAL ASSESSMENT 7 1 INTRODUCTION 7 2 METHODOLOGY 7 3 GRAPHICAL INTERPRETATION 7 4 CHECKING NORMALITY 7 5 CHECKING HOMOGENEITY 7 6 CHECKING STATIONARITY 7 7 CHECKING TREND 7 7 1 APPLICATION OF TREND TESTS 7 7 2 ASSESSMENT OF TREND TESTS 7 8 INVESTIGATING PERIODICITY 7 9 INVESTIGATING PERSISTENCE 7 10 CONCLUSIONS 8 TREND AND HOMOGENEITY IN SUBSURFACE HYDROLOGIC VARIABLES: CASE STUDY IN A HARD-ROCK AQUIFER OF WESTERN INDIA 8 1 INTRODUCTION 8 2 STUDY AREA AND DATA 8 3 APPLICATION OF TIME SERIES TESTS 8 4 SPATIAL AND TEMPORAL VARIATIONS OF ANNUAL RAINFALL 8 4 1 ANNUAL RAINFALL PATTERN 8 4 2 TREND AND HOMOGENEITY IN THE ANNUAL RAINFALL TIME SERIES 8 5 TREND AND HOMOGENEITY IN SEASONAL GROUNDWATER LEVELS 8 5 1 RESULTS OF TREND TESTS 8 5 2 RESULTS OF HOMOGENEITY TESTS 8 6 TREND AND HOMOGENEITY IN ANNUAL NET RECHARGE 8 6 1 TRENDS IN ANNUAL NET RECHARGE 8 6 2 HOMOGENEITY/NON-HOMOGENEITY OF ANNUAL NET RECHARGE 8 7 CONCLUSIONS 9 ANALYSIS OF STREAMFLOW TREND IN THE SUSQUEHANNA RIVER BASIN, USA ZHENXING ZHANG, ROBERT D PODY, ANDREW D DEHOFF AND JOHN W BALAY 9 1 INTRODUCTION 9 2 STUDY AREA 9 3 METHODOLOGY 9 4 RESULTS AND DISCUSSION 9 4 1 ANNUAL STREAMFLOW TIME SERIES 9 4 2 MONTHLY STREAMFLOW TIME SERIES 9 5 CONCLUSIONS 10 ANALYSIS OF TRENDS IN LOW-FLOW TIME SERIES OF CANADIAN RIVERS M N KHALIQ AND L SUSHAMA 10 1 INTRODUCTION 10 2 COMPONENTS OF TREND ANALYSIS FRAMEWORK 10 2 1 ASSUMPTIONS ABOUT DATA DISTRIBUTION 10 2 2 TYPE OF TREND MODEL 10 2 3 ASSUMPTIONS ABOUT SERIAL STRUCTURE: INDEPENDENCE VS SHORT- AND LONG-TERM PERSISTENCE 10 2 4 FIELD SIGNIFICANCE ANALYSIS 10 3 A CASE STUDY OF TREND ANALYSIS IN TIME SERIES OF ANNUAL AND SEASONAL LOW FLOWS 10 3 1 STUDY AREA AND DATA 10 3 2 SEASONALITY OF LOW FLOWS 10 3 3 STP- AND LTP-LIKE SERIAL STRUCTURES 10 3 4 RESULTS OF TREND ANALYSIS 10 4 CONCLUDING REMARKS 11 EXPLORING TRENDS IN CLIMATOLOGICAL TIME SERIES OF ORISSA, INDIA USING NONPARAMETRIC TREND TESTS DILEEP K PANDA AND A KUMAR 11 1 INTRODUCTION 11 2 THE STUDY AREA AND CLIMATE 11 2 1 ANTHROPOGENIC ACTIVITIES 11 3 METHODOLOGY 11 4 RESULTS AND DISCUSSION 11 4 1 TREND AND VARIABILITY IN ANNUAL RAINFALL TIME SERIES 11 4 2 TRENDS IN SEASONAL RAINFALL TIME SERIES 11 4 3 TRENDS IN TEMPERATURE TIME SERIES 11 4 4 TRENDS IN TIME SERIES OF RELATIVE HUMIDITY 11 5 CONCLUSIONS 12 ANALYSIS OF TREND AND PERIODICITY IN LONG-TERM ANNUAL RAINFALL TIME SERIES OF NIGERIA PHILIP G OGUNTUNDE AND BABATUNDE J ABIODUN- 12 1 INTRODUCTION 12 2 STUDY AREA 12 3 METHODOLOGY 12 3 1 DATA COLLECTION 12 3 2 DATA ANALYSIS 12 4 RESULTS AND DISCUSSION 12 4 1 TEMPORAL ANALYSIS 12 4 2 SPATIAL ANALYSIS 12 4 3 RAINFALL CYCLES AND PERIODICITIES 12 5 CONCLUSIONS