Lecture (1) Introduction

Variables and Data in Hydrology Hydrological Variables Hydrological Series Sample and Population Hydrological Processes and Classification of Hydrology Hydrological Data

Hydrological Variables Hydrological Cycle: Evaporation: (rate of evaporation). Precipitation: (rain intensity). Runoff: (stream flow discharge). Variables can be: Discrete: measured at discrete points in scale (countable). Continuous: measured over a continuous scale.

a numerical value of a variable is usually called: an observation, a measurement, a variate, an outcome or a realization. Hydrological Variables (cont.)

Hydrological Data Classification of Hydrological data (Yevjevich, 1969): -chronological data. -field observations or survey in one or more dimensions. -experimental data gathered from laboratory and or field experiments. -simultaneous measurements of two or more random variables.

Hydrological Series Hydrological Series (Processes): A process is a description of any phenomenon that undergoes continuous change, particularly with respect to time. Time series: Sequence of values arranged in order of their occurrence and characterized by statistical properties. Space series: similar to time series but arranged in space.

Time Series Overview of topoindex of Zwalm catchment., East Flanders, Belgium

Space Series (Measurements of Hydro-geological) Mount Simon Sand Stone Aquifer, USA

Boreholes and Outcrops (Space Series)

Classification of Time (Space) Series Varying mean Varying variance Varying mean and variance

Classification of Time and (Space) series (cont.)

Why do we need Statistical Hydrology? The erratic nature of the hydrological data.The erratic nature of the hydrological data. The uncertainty due to the lack of information about the hydrological data which is known only at sparse sampled locations.The uncertainty due to the lack of information about the hydrological data which is known only at sparse sampled locations. Making Predictions of floods.Making Predictions of floods.

Stochastic versus Deterministic Hydrology A stochastic process may be defined, Bartlett [1960]:A stochastic process may be defined, Bartlett [1960]: " a physical process (series) in the real world, that has some random element involved in its structures" " a physical process (series) in the real world, that has some random element involved in its structures" If a process (series) is operating through time or space: it is considered as system comprising a particular set of states: In a classical deterministic model: the state of the system in time or space can be exactly predicted from knowledge of the functional relation specified by the governing differential equations of the system (deterministic regularity). In a classical deterministic model: the state of the system in time or space can be exactly predicted from knowledge of the functional relation specified by the governing differential equations of the system (deterministic regularity). In a stochastic model: the state of the system at any time or space is characterized by the underling fixed probabilities of the states in the system (statistical regularity).In a stochastic model: the state of the system at any time or space is characterized by the underling fixed probabilities of the states in the system (statistical regularity).

Sample and Population Sample: A set of random observations of a variable. Population: The complete set of values that the variable had taken in the past and/or can be or will take in the future. Sample

Some Terminology Event: something that happens in space and time. Sample Space (Event Space): possible outcomes of a trial or an experiment. Random Variable: It is a variable that can take a real number. Population: It represents the real world.

Simulation Simulation is mimicking reality. Simulation of an outcrop by Tree-indexed Markov chains