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Titel |
Model–data comparison with permutation entropy: Moving beyond summary statistics |
VerfasserIn |
Christina Bogner, Britta Aufgebauer, Bernd Huwe |
Konferenz |
EGU General Assembly 2017
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Medientyp |
Artikel
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Sprache |
en
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Digitales Dokument |
PDF |
Erschienen |
In: GRA - Volume 19 (2017) |
Datensatznummer |
250145888
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Publikation (Nr.) |
EGU/EGU2017-9865.pdf |
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Zusammenfassung |
Soil water plays an important role in the terrestrial water and energy cycles. Its movement
follows the gradient of the soil water potential and is most frequently described by the
Richards equation. The model quality is often summarized by criteria like the Nash–Sutcliffe
model efficiency coefficient that relates the model residuals to the variability of observations
or the root mean square error. However, as a summary statistics, it is unable to provide details
on the temporal behaviour of the model. We suggest to use the permutation entropy – a
complexity measure – to compare temporal patterns of modelled versus measured
data.
We modelled water fluxes in the vadose zone at a forested site (Fichtelgebirge, Germany)
with the Water Heat and Nitrogen Simulation Model (WHNSIM). The model solves the
Richards equation numerically. We characterized the temporal dynamics of soil matric
potentials measured at the study site and compared their complexity with modelled matric
potential. Natural time series can exhibit behaviours of different degrees of complexity
ranging from regular to random. The complexity of a natural time series results from the
nonlinearity of underlying processes, their different interactions and possibly measurement
noise. In our case, the measured matric potential is the result of the signal propagation from
precipitation to throughfall to infiltration and reflects the influence of the soil hydraulic
properties, evapotranspiration and possible measurement errors. In general, regular structure
like periodic signals (e.g. yearly cycle such as in evapotranspiration) is easier to model than
irregular signals. Permutation entropy values close to zero indicate that a time series is
regular and contains only few different temporal patterns. In contrast, very large
values near one result from a high number of different patterns and are typical for
noise.
The model WHNSIM reproduced the overall level of matric potentials in all modelled
depths (20, 40 and 90 cm). However, while it captured the complexity of the measurements in
the upper soil, the matrix potentials in 90 cm depth were less complex indicating a more
regular and damped signal. This result suggests that WHNSIM misses some important
processes at least in the deeper soil.
Although we used WHNSIM in our study, the permutation entropy can be calculated for
any other real-valued measured or modelled time series. It can serve as a further comparative
tool to evaluate models and uncover periods of particular match or mismatch between model
and data. |
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