A shot noise model for the generation of soil moisture data |
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Authors: | G Tsakiris G Agrafiotis E Kiountouzis |
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Institution: | (1) National Technical University, 5 Iroon Polytechniou Str., GR-15773 Zografou, Athens, Greece;(2) Dept. of Mathematics, University of Athens, Panepistemiopolis, GR-15710 Couponia, Athens, Greece;(3) Dept. of Statistics and Information Science, Athens Graduate School of Economics and Business Studies, 76 Patission Str., GR-10434 Athens, Greece |
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Abstract: | An attempt is made to estimate the expected contribution of rainfall to soil moisture during the irrigation season. Effective rainfall and evapotranspiration are the parameters considered in the water balance carried out in the root zone. Rainfall occurrence is simulated by a Poisson process whereas evapotranspiration is described by a simple deterministic function of potential evapotranspiration and soil moisture in the root zone. Using the theory of shot noise models a closed form solution is derived from the expected soil moisture in the root zone at the end of the time interval (0,t]. For illustration purposes the proposed model is applied to a series of data from Mikra meteorological station in Greece.List of symbols x
change in water storage in the root zone during the time interval t
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X
infiltrated rainfall of thei th storm event
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ET
actual evapotranspiration during thej th day
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Poisson rate
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number of storm events in (0,t]
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t
r
duration of rainfall
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t
b
interarrival time
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h
i
rainfall depth of thei th storm event
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i
m
mean rainfall intensity
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i(t)
instantaneous rainfall intensity
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x(0),x(t)
available soil moisture in the root zone at time 0 andt, respectively
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PET
potential evapotranspiration rate
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x
F
available soil moisture in the root zone at field capacity
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soil moisture depletion rate (=PET/x
F
)
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w
impulse shape of filtered Poisson processes
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E·]
mean value
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S
i
time of thei th rainfall event
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N(t)
time of storm events in (0,t]
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estimated standard deviation
The following symbols were used in this paper |
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Keywords: | Soil moisture stochastic modelling shot noise models infiltrated rainfall evapotranspiration water balance root zone |
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