commit 8f70fb0ac553546fd5cac1e7b96682213740e421
parent 56f0c34444d99fe7b8c1601324b08f5e39cfce70
Author: Ivan Gankevich <igankevich@ya.ru>
Date: Thu, 8 Jun 2017 23:13:44 +0300
Add experiment description.
Diffstat:
1 file changed, 19 insertions(+), 2 deletions(-)
diff --git a/arma-thesis.org b/arma-thesis.org
@@ -1897,8 +1897,8 @@ the formula for three-dimensional case was not derived.
:CUSTOM_ID: sec:verification
:END:
-In\nbsp{}cite:degtyarev2011modelling,degtyarev2013synoptic,boukhanovsky1997thesis AR
-model the following items are verified experimentally:
+In\nbsp{}cite:degtyarev2011modelling,degtyarev2013synoptic,boukhanovsky1997thesis
+AR model the following items are verified experimentally:
- probability distributions of different wave characteristics (wave heights,
lengths, crests, periods, slopes, three-dimensionality),
- dispersion relation,
@@ -2129,6 +2129,22 @@ arma.plot_velocity(
[[file:build/large-and-small-amplitude-velocity-field-comparison.pdf]]
*** Verification of nonlinear inertialess transformation
+In order to measure the effect of NIT on the shape of the resulting wavy
+surface, three realisations were generated:
+- realisation with Gaussian distribution (without NIT),
+- realisation with Gram---Charlier series based distribution, and
+- realisation with skew normal distribution.
+The seed of PRNG was set to be the same for all progrmme executions to make ARMA
+model produce the same values for eahc realisation. Standing wave ACF was used
+in all experiments.
+
+The results of the experiment are twofold: while the experiment showed that
+applying NIT with GCS-based distribution makes wave profiles steeper, the same
+is not true for skew normal distribution (fig.\nbsp{}[[fig-nonlinear]]. Using this
+distribution results in wavy surface each \(z\)-coordinate of which is always
+greater or equal to nought. So, skew normal distribution is unsuitable for NIT.
+
+
*** Non-physical nature of ARMA model
ARMA model, owing to its non-physical nature, does not have the notion of ocean
wave; it simulates wavy surface as a whole instead. Motions of individual waves
@@ -3525,6 +3541,7 @@ Basic Research (projects no.\nbsp{}\mbox{16-07-01111}, \mbox{16-07-00886},
- <<<LAPACK>>> :: Linear Algebra Package.
- <<<DNS>>> :: Dynamic name resolution.
- <<<HPC>>> :: High-performance computing.
+- <<<GCS>>> :: Gram---Charlier series.
- Master/slave node ::
- Principal/subordinate kernel ::
