Lecture (1)Lecture (1)

Introduction Introduction

Variables and Data in HydrologyVariables and Data in Hydrology

Hydrological VariablesHydrological Variables

Hydrological SeriesHydrological Series

Sample and PopulationSample and Population

Hydrological Processes and Classification of Hydrological Processes and Classification of HydrologyHydrology

Hydrological Data Hydrological Data

Hydrological Variables Hydrological Variables

Hydrological Cycle: Hydrological Cycle:

Evaporation: (rate of evaporation).Evaporation: (rate of evaporation).Precipitation: (rain intensity).Precipitation: (rain intensity).Runoff: (stream flow discharge).Runoff: (stream flow discharge).

Variables can be:Variables can be:Discrete: measured at discrete points in scale Discrete: measured at discrete points in scale (countable).(countable).Continuous: measured over a continuous scale.Continuous: measured over a continuous scale.

a numerical value of a variable is usually called: a numerical value of a variable is usually called:

an observation, a measurement, a variate, an an observation, a measurement, a variate, an outcome or a realization.outcome or a realization.

Hydrological Variables (cont.)Hydrological Variables (cont.)

Hydrological Data Hydrological Data

Classification of Hydrological data (Yevjevich, Classification of Hydrological data (Yevjevich, 1969):1969):

-chronological data.-chronological data.

-field observations or survey in one or more -field observations or survey in one or more dimensions.dimensions.

-experimental data gathered from laboratory and or -experimental data gathered from laboratory and or field experiments.field experiments.

-simultaneous measurements of two or more -simultaneous measurements of two or more random variables.random variables.

Hydrological SeriesHydrological 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 SeriesTime Series

Overview of topoindex of Overview of topoindex of Zwalm catchment.,Zwalm catchment.,

East Flanders, BelgiumEast Flanders, Belgium

1995

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1996

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Space Series (Measurements of Space Series (Measurements of Hydro-geological) Hydro-geological)

Mount Simon Sand Stone Aquifer, USA

Boreholes and Outcrops (Space Boreholes and Outcrops (Space Series)Series)

Classification of Time (Space) Series Classification of Time (Space) Series

Varying mean

Varying variance

Varying mean and variance

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

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

• • Making Predictions of floods. Making Predictions of floods.

Stochastic versus Deterministic Stochastic versus Deterministic HydrologyHydrology

• 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 " a physical process (series) in the real world, that has some

random element involved in its structures"random element involved in its structures"

If a process (series) is operating through time or space: it is If a process (series) is operating through time or space: it is considered as system comprising a particular set of considered as system comprising a particular set of states:states:

• In a classical deterministic model:In a classical deterministic model: the state of the the state of the system in time or space can be exactly predicted from system in time or space can be exactly predicted from knowledge of the functional relation specified by the knowledge of the functional relation specified by the governing differential equations of the system governing differential equations of the system (deterministic regularity). (deterministic regularity).

• In a stochastic model:In a stochastic model: the state of the system at any the state of the system at any time or space is characterized by the underling fixed time or space is characterized by the underling fixed probabilities of the states in the system (statistical probabilities of the states in the system (statistical regularity).regularity).

Sample and PopulationSample 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.

1995

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1997

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Sample

Some Terminology 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.

SimulationSimulation

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Simulation is mimicking reality.

Simulation of an outcrop by Tree-indexed Markov chains