The effect of sand nourishments on foredune sediment volume
Bachelor Thesis
N. van der Zwaag
5887712
Supervised by:
John van Boxel
&
Bas Arens
Date: 18-7-2011
Keywords: Nourishment, foredunes, sediment, volume, statistics
Table of Contents
1.
2.
3.
4.
5.
6.
7.
8.
9.
Summary ........................................................................................................................................ 2
Introduction .................................................................................................................................... 3
Goal ................................................................................................................................................ 3
Methods .......................................................................................................................................... 4
4.1. Data import profile ............................................................................................................. 6
4.2. Data import kilometer ........................................................................................................ 6
4.3. Data check .......................................................................................................................... 6
4.4. Outlier Removal ................................................................................................................. 7
4.5. Interpolation ....................................................................................................................... 7
4.6. Extrapolation ...................................................................................................................... 8
4.7. Landward Boundary ........................................................................................................... 8
4.8. Calculating total volume .................................................................................................... 9
4.9. Fitting Trend lines .............................................................................................................. 9
Results ...........................................................................................................................................11
5.1. Organize and repair Jar-Kus data ..................................................................................... 11
5.2. Finding landward boundary and creating volume data .................................................... 11
5.3. Fit trend lines to volume developments ........................................................................... 11
5.4. Determine spatial effects of a nourishment at a location downstream ............................. 13
Discussion .................................................................................................................................... 15
6.1. Organize and repair Jar-Kus data ..................................................................................... 15
6.2. Finding landward boundary and creating volume data .................................................... 15
6.3. Fit trend lines to volume developments ........................................................................... 16
6.4. Determine spatial effects of a nourishment at a location downstream ............................. 18
Conclusions .................................................................................................................................. 19
Literature ...................................................................................................................................... 20
Appendix (code) ........................................................................................................................... 21
9.1. Data import profile ........................................................................................................... 21
9.2. Data import kilometer ...................................................................................................... 25
9.3. Data check ........................................................................................................................ 29
9.4. Outlier Removal ............................................................................................................... 32
9.5. Interpolation ..................................................................................................................... 33
9.6. Extrapolation .................................................................................................................... 37
9.7. Landward boundary.......................................................................................................... 39
9.8. Calculating total volume .................................................................................................. 41
9.9. Fitting trend lines ............................................................................................................. 42
1. Summary
The Dutch dune coast has to be maintained in order to keep the inland safe. This is done by
adding sand to the system and increasing foredune sediment volume. These nourishments have
significant effects on natural values in the dunes. This report further investigates the effect of
nourishments on foredune sediment volume. New methods are developed to automate the use of
coastal height data to calculate volume developments. The best number of trend lines is added to
the developments, showing breaks in trend. These breaks in trend visualize the year of the
nourishment. This research concludes with a case study to see whether nourishments upstream
have effect on the volume development of the Groote Keeten location. There is no effect.
This thesis concludes the Earth Sciences Bachelor’s thesis course at the University of Amsterdam.
2. Introduction
Dunes are the Dutch' primary defense against water and storms from the North Sea (De Staat,
2009). A new vision on coastal appearance and natural values shows the importance of a dynamic
coastal line (Arens & Mulder, 2008). Measures to maintain the position of this coastal line should
be seen in perspective: The coastline is a part of a coastal zone: dunes, beaches, shores and
offshore areas (De Ruig, 1998). Some dunes grow naturally, others break down. Some locations
still have to be strengthened for safety of the inland. This is done by monitoring the BCL (Basic
Coastal Line) actually a coastal zone of approximately between +3m and +5m NAP (Normaal
Amsterdams Peil = Sea level reference). When the amount of sand in this zone drops below a
certain limit, the coast has to be replenished with sand nourishments.
Nourishments are an essential part of maintenance of the Dutch coastal defense system. They
strengthen the system by replenishing sand losses due to erosion. They can be applied in the
dunes, on the beach or off shore. This sand widens the beaches, increases foredune volume and,
in case of underwater nourishments, is able to break waves. The adding of sand to the coastal
system could have extensive consequences for natural habitats. A lot of these habitats are also
part of Natura 2000, a network of natural areas in the European Union. The goal of Natura 2000 is
the prevention of degradation of biodiversity (European Commission Publication Office, 2009). In
order to keep an eye on biodiversity in dune habitats, it is imperative to know what happens with
the sand that is being added.
The transportation of sand in the coastal zone has been researched. Coastal dynamics studies
(De Swart, 2006) are done and coastal sediment models (Van der Burgh et al., 2007. Van der Wal,
1999) have been developed to describe the effect of nourishments. Sand budget trends have been
calculated along the length of the Dutch coast from the foredunes to a point about 3000 m in sea
(De Ruig, Louisse, 1991). The aeolian transportation of the sediment is researched and it is shown
that grain size and composition of the sand have an effect on the dispersion (Van der Wal, 1998).
Furthermore the effect of nourishments on the sand budget is researched showing that
nourishments temporarily protect the foredunes from being eroded by waves and increase the
aeolian transport to the dunes (Van der Wal, 2004). The effect of nourishments on natural values
has also been researched. Sizeable impacts are described on several beach ecosystem
components (Speybroek et al., 2006). Arens and Wiersma (1994) classified types of foredunes to
gain further insight into the occurrence and extent of natural processes in the foredunes.
The Dutch coastal infrastructure and environment ministry are having the effects of nourishments
on dune development researched (Arens et al., 2010). The report states that there is indeed an
effect of nourishments on foredune sediment volume. However the report lacks the statistical
significance to proof this theory: The foredune sediment volumes are investigated and the dunes
are classified, volume developments for 18 locations are analyzed and trend lines are fitted and
the breakpoints of these lines are found visually and do not have statistical significance.
3. Goal
The primary goal of this research is to evaluate the (positive) effect of nourishments on foredune
sediment volume. Temporal trends in foredune volume are examined and their statistic
significance is determined. These calculations are completely automated. Methods are developed
to fit trend lines and determine their significance. Then these methods will be applied to evaluate
the spatial effect of sand nourishments at a location downstream of the nourishment.
The following research questions are formulated.
 What is the best way to organize and repair the dataset for statistical analysis?
 What is the best way to significantly proof the existence of a break in trend line?
 What is the effect of sand nourishments on foredune sediment volume?
 Is it possible to determine spatial effects of a nourishment at a location downstream?
3
4. Methods
To know how the foredunes respond to the added sand, the foredune sand volume is calculated
for every year using coastal height data. Jar-Kus data (Minneboo, 1995). Since 1997 Jar-Kus data
is measured annually by laser altimetry from a plane. Before 1997 this was done by means of
photogrammetric interpretation from air photography. A database is available which contains data
since 1964, it consists of cross profiles (height profiles from sea to land) with a mutual distance of
200-250 meters over the length of the beach. The foredune volume is calculated from the point
where the elevation first reaches +3 m NAP to a stable point landwards.The landward boundary is
calculated automatically at a location where height is stable through the years. Which means that
no sand is transported beyond this point. All the changes in foredune volume should be between
this point and the beach.
In the following paragraphs, the script used for this research is described. It consists of several
subscripts that are all put in series. Figure 1 shows a flowchart with the basic operations of the
script. A green box represents data in different states. The first state is the raw Jar-Kus dataset.
This dataset contains nearly 2000 profiles. A lot of them are too incomplete to be used and others
need to be repaired before they can be useful. In the first section of the script the dataset is
cleaned up and repaired. Incomplete profiles and outliers are deleted. The remaining profiles are
interpolated, both chronically and spatially, and extrapolated, so the data can be used effectively.
In the second section the volume is calculated. The landward boundary is found and used to
calculate the volume development. The profile data can than be averaged over a kilometer. This is
done to filter possible measurement errors. The last subscript fits the trend lines. One, two or three
lines are fitted automatically to the data, based on their Root Mean Square Error (RMSE), the
standard deviation of the residuals, a measurement of fit (Willmot et al., 1985).
A blue box represents a subscript that will be described in this chapter.
In the sections below, the script is explained section by section. For more details see the actual
commented script at the appendix. The main script is divided in two: One can be used to plot
multiple kilometers and the other can be used to plot single profiles and all the profiles from one
kilometer.
Scripts:
 Data import profile
 Data import kilometer
 Data check
 Outlier removal
 Interpolation
 Extrapolation
 Finding landward boundary
 Calculating total volume
 Fitting Trend lines
4
Figure 1: Flowchart of the functionality of the script.
5
4.1. Data import profile
This main script is used to analyze separate profiles or all profiles in one kilometer.
The script first loads the open source file 'transect.nc': the raw Jar-Kus data. Then the user is
prompted to choose between one separate profile or all profiles of one kilometer and for a grid
number and a profile or kilometer- number. The number of profiles per kilometer differs: the
mutual distance between profiles varies from 100 meters to 250 meters. One profile per kilometer
is added to correspond to the way Arens et al. (2010) averaged kilometer profiles. For example if
the profiles are 250 meters apart the kilometer will consist of (1000/250)+ 1 = 5 profiles. The
profiles are then checked to see whether they are consistent enough to use with the subscript
'data check'. Incomplete profiles are discarded. Then the data is clipped: 1965-1974 and 2010 are
removed, because those years have incomplete data. Also all cross profile coordinates that
contain height data that is lower than 0 m NAP, or do not contain any data at all, are removed. A
profile is created with on the x-axis the years and on the y-axis the cross profile coordinates. The
profile is filled with the corresponding height data. Then the script continues with all the subscripts:
Interpolation and extrapolation, calculating the landward boundary, the foredune volume and finally
fitting the trend lines.
All data is in cm.
This script is produced in 2011. Data of 2010 was not yet added to the calculations because it was
incomplete. If data for 2011 is added, 2011 is automatically discarded and 2010 is added. If data
from 2011 is good enough to use it could be added by deleting line 168. Only six profiles per
kilometer can be visualized, because of the limiting color scheme (See 'fitting trend lines' for more
information) .
This version of the script does not use the outlier script to delete outliers (see 'Outliers Removal'
for more information). Note that if only a single incomplete profile is put in, the script will fail,
because it will be removed by data check and no data are able to be used.
4.2. Data import kilometer
This script is used to analyze multiple kilometers of profiles. It develops practically the same as the
data import per profile. The separate profiles are averaged over one kilometer. Up to a maximum
of 6 kilometer profiles can be analyzed. Input is the Jar-Kus database. This script loads the data,
prompts the user for input on location, removes incomplete years and contains all the subscripts
necessary for output: A figure showing the volume development of the separate kilometer profiles,
the fitted trend lines, and the statistical significance of these lines.
Note that no outlier removal script is present (see 'Outliers Removal' for more information).
4.3. Data check
In this script the data is checked in 4 different ways to delete profiles that are too incomplete to
use. The script's input is location data of the profiles kilometers that need to be checked. The
dataset that is to be checked is loaded in the same way as the data import scripts.
First the data is checked to see if it contains 5 or more rows (Height data per coordinate) of data
that meet criteria. The first criterium is that the minimum height per row is above 200 cm NAP.
This because volume data is only calculated above 300 cm NAP. The extra meter is added
because of height jumps: extra data are needed to successfully calculate volume. The second
criterium is that every coordinate should have at least more than 5 years of height data. If those
criteria are not met, the profile is discarded.
After this a full profile is created using interpolation and extrapolation.
Then the profiles are deleted that contain more than 7 years that still consist of only NaN (Not a
6
Number = empty data cell) data. The profiles in which last year contains more than ~40 NaNs
(length of profile - 10) are also deleted. This because this would mean that the last few years are
not interpolated correctly.
Finally the first year (1975) is checked. If it contains more than ~35 (no. rows – 15) NaNs it is
deleted. The following years are also checked and deleted until a year meets the criterium. This
creates a problem, because the volume developments need to exist of the same number of years.
So a variable is created stating how many years are deleted, so the next profile (that may or may
not have incomplete first few years) is clipped the same length. This clipping happens in the import
script. Furthermore the script puts out an array of names of the profiles that are and are not
discarded.
4.4. Outlier Removal
The outlier script detects outliers and replaces them with NaNs. It calculates mean and standard
deviation of the array and compares those with the height data in the array. If the height data
minus the mean is bigger than 'x' times the standard deviation, the height data at that location is
replaced by a NaN. The 'x'-value can be changed by user. The output returns the data with all
outliers replaced as NaNs. They should be interpolated. Furthermore it shows the number of
outliers removed.
If this number is too large, too much outliers were deleted. This might happen because the outliers
deleted lower mean, creating more outliers, etc. If that is the case, it is best to raise the standard
deviation x-value or to remove the outlier script.
The outlier script is not used because in large profiles it deletes highest numbers that were still
correct.
4.5. Interpolation
The interpolation script interpolates data both chronically (during years) and spatially (at the same
x-coordinate). The interpolation is done linearly. The chronical interpolation is done first. It
interpolates over a maximum of 15 meters. The spatial interpolation is done over a maximum of
10 years. In the below figures examples of interpolation are given. The cross coordinates are
shown (x) with their corresponding heights (y). The main part of this script is from Van Puijvelde's
(2010) internship report.
Table 1: An example of chronical interpolation
7
Table 2: An example of spatial interpolation
The first columns and rows are ignored, they can't be interpolated. So the quality of the
interpolation depends on the quality of the first and last columns. In the whole year of 2002 no
measurements were done. All those data are now interpolated. It would be better if no data were
interpolated, no volume was calculated and that year was not visualized in the graph.
4.6. Extrapolation
In the extrapolation subscript height data is calculated further landward as to further fill up the
dataset. This makes it possible to find landward boundaries more landward, so the possibility of it
being more stable is bigger. The extrapolation only takes place at the most seaward ending data
columns (a column is a year) and is designed to stop when the extrapolated heights drop below
300 cm. It will extrapolate a maximum of 7 rows.
The user can choose between spline extrapolation or linear extrapolation. It will output the
enhanced profile and the number of extrapolated rows.
X
Y
X
Y
-23000 NaN
-23000 NaN
-22500 NaN
-22500 559
-22000 NaN
-22000 551
-21500 NaN
-21500 558
-21000 NaN
-->
-21000 563
-20500 NaN Extrapolation
-20500 564
-20000 NaN
-20000 556
-19500 NaN
-19500 540
-19000 611
-19000 611
-18500 553
-18500 553
-18000 542
-18000 542
-17500 547
-17500 547
-17000 608
-17000 608
Table 3: An example of extrapolation
4.7. Landward Boundary
To calculate the total foredune volume a landward boundary has to be established. The landward
boundary is a coordinate from where the dune height does not change (as much). The dunes
behind this boundary do not change in volume and are therefore not a part of the foredunes. First
8
all height data that are +300 cm NAP and do not contain any NaNs are selected. Then a trend line
is fitted through all the heights on one location through all years. This is done to find the coordinate
where the heights change the least through the years: there where the slope of the fitted trend line
is smallest. Also the RMSE of the trend line is checked. The process starts with the landward most
coordinate. If that point does not meet the criteria, say, a slope of 1 cm per year and a RMSE of 10
cm, the next coordinate seaward is fitted a trend line and checked.
If none of the points of the cross profile meets criteria the criteria are raised and the process starts
again. If the criteria are raised too high, the furthest point landward that is +300 cm NAP and does
not contain any NaNs is chosen.
Figure 2: An example of a profile through the years. The x-axis shows the distance to the sea in cm.
The y-axis shows the height in cm. The landward boundary would be found somewhere between 15000 cm and -20000 cm.
4.8. Calculating total volume
This subscript calculates the total volume per year per profile. From the dune toe to the landward
boundary, the height is multiplied with the length (500 cm). The dune toe is the maximum seaward
coordinate with heights of over 300 cm and is in this method a single cross profile location. The
height multiplied with the length is then summed and this calculation is then repeated for all years
of the profile. Because heights at the dune toe are irregular (the height drops from over 300cm to
under 300 cm) an extra 500 cm in length is added to the volume. Which might not be enough: In
some years the height might not drop under 300 cm, 1000 cm seaward from the stated dune toe.
This method differs from the way Arens et al. (2010) calculate volume. Arens et al.(2010)
interpolate the data at the 300 cm height border. This means coordinate of the dune toe differs over
the years. The coordinate of the dune toe is a static one in this report's script.
9
4.9. Fitting Trend lines
In this script the breakpoints are calculated, the trend lines are fitted and the data is visualized.
First the breakpoints are calculated. The script uses a subfunction that uses the least squares
approach to find 1, 2, or no breakpoints in the data. These breakpoints are then used to fit trend
lines (1, 2 or 3 lines, depending on the number of breakpoints). The RMSE is calculated of these
lines. The RMSE of multiple trend lines are averaged. More trend lines plotted to the data, always
means a lower statistical error, but does not always provide a logical fit.
It is imperative the correct number of trend lines is fitted to the data. To make sure of this, criteria
are formed to fit the correct number of lines. To find these criteria volume developments with clear
breakpoints are looked at. When on visual inspection of clear developments two trend lines need
to be plotted, the criteria are adapted. An example of a criteria could be that the RMSE of 2 trend
lines has to be lower than two times the RMSE of 1 trend line. For example, the RMSE of one
trend line is 30, the averaged RMSE of two trend lines is 20. if a criterium is 2 for this comparison,
then 2 * 20 is higher than 30 and a single trend line is plotted.
Finally the script puts out a figure showing the volume development, the fitted trend lines, the year
of the breakpoints and the (averaged) RMSE of the fitted lines. The second output is a table that
shows the RMSE if a different number of trend lines was plotted.
A maximum of 6 lines can be plotted to keep the figure clear.
10
5. Results
5.1. Organize and repair Jar-Kus data
As described in methods, the best way to organize the data is by deleting incomplete or false
values and adding data. The deleting is done by the script data check: It deletes incomplete
profiles and removes incomplete years. Then data is added by interpolation and extrapolation. The
complete profiles are then ready to use for calculating volume development and fitting trend lines.
5.2. Finding landward boundary and creating volume data
Landward boundaries are found as described in section 4.7. Table 4 shows the landward
boundaries found at 10 profiles at Heemskerk and Texel. The landward boundary is measured in
cm from the RSP( RijksStrandPaal = Reference line for the Dutch coast).
RSP 50: Heemskerk
RSP 50: Heemskerk
Profile
number
Profile number (km)
(km) Landward
Landward boundary
boundary (m)
(m)
50.000
-160
50.000
-160
50.250
-180
50.250
-180
50.500
-190
50.500
-190
50.750
-135
50.750
-135
51.000
-185
51.000
-185
RSP 13: Texel
Profile number (km) Landward boundary (m)
13.120
-180
13.320
-180
13.520
-180
13.720
-210
13.920
-170
13.920
-170
Table 4: Examples of landward boundaries
found.
5.3. Fit trend lines to volume developments
Figure 3 and 4 show the volume developments of multiple kilometers, with trend lines fitted. The
breakpoints and RMSE of all lines are annotated in the upper left corner. These figures are used to
calibrate the criteria, starting with Heemskerk (figure 3), kilometers 48, 49 and 50. Heemskerk was
used because of the three clearly different types of developments, all requiring a different number
of trend lines. Three numbers of trend lines are indeed fitted to the data.
Figure 4 shows the volume development of the foredunes of Texel, kilometer 11, 12, 13 and 14.
Texel was used for further calibration of the criteria because of the breakpoint around 1995 that is
clearly visible in all figures. The trend lines fitted al show a breakpoint around 1995.
After calibration the criteria found for these comparisons are:
The RMSE of three lines has to be 1.46 times smaller than that of two trend lines.
The RMSE of two lines has to be 1.50 times smaller than that of one trend line.
The RMSE of three trend lines has to be 1.67 times smaller than that of one trend lines.
These criteria are put in series. So first the RMSE of three trend lines is compared with that of the
two trend lines. If the RMSE is not smaller the second criteria is compared. Etcetera.
11
Figure 3: Volume development and trend lines of Heemskerk (RSP 48-50).
12
Figure 4: Volume development and trend lines of Texel (RSP 11-14)
13
5.4. Determine spatial effects of a nourishment at a location downstream
The volume development of Groote Keeten (RSP 8-9) is looked at. Groote Keeten is an area
downstream from large nourishments and only had a small nourishment done in 2003. The
nourishment data of the upstream location is compared with the volume development and trend
lines of Groote Keeten.
The nourishment data shows us three types of nourishments: Underwater, beach and dune
nourishments. The underwater nourishments are done in front of the beach. The effect of these
nourishments is not drastic, it takes a while before the sand gets transported into the dunes. And
they might not even be visible in the volume development (Van de Graaff et al., 1991). The beach
and dune nourishments should have a larger impact on the foredune volume development,
because they only depend on aeolian transport for dispersal.
Nourishments Upstream
Year Start profile(km) End profile (km) Nourishment size (m3/m)
1979
11.150
12.800
285
1986
10.825
13.725
428
1986
11.750
12.050
260
1991
11.000
14.000
179
1996
12.200
14.100
242
1996
10.010
12.130
217
2001
11.080
14.010
512
2003
11.100
13.750
165
2003
10.000
16.000
429
2004
11.100
13.740
82
2006
10.000
15.200
308
Nourishment at Groote Keeten
Year Start profile(km) End profile (km) Nourishment size (m3/m)
2003
9.130
9.430
41
Type of nourishment
Underwater nourishment
Beach nourishment
Beach nourishment
Underwater nourishment
Underwater nourishment
Beach nourishment
Beach nourishment
Beach nourishment
Beach nourishment
Dune nourishment
Dune nourishment
Type of nourishment
Underwater nourishment
Table 5: Nourishment data of upstream of and at the Groote Keeten location
Figure 5 shows the volume development of the dunes near Groote Keeten. When compared with
the above nourishment data, it firstly shows that the small nourishment done in 2003 in the area
itself is not visible in the volume data. But it is an underwater nourishment, so it would not make a
clear change in volume. In the kilometer figure, figure 5, no clear changes that could be correlated
to the nourishment are visible. There are some jumps in volume, but those are not in the same
year as a nourishment.
In Figure 6, kilometer 9 is split into the development data of the separate profiles. Kilometer 9 is
the kilometer of the Groote Keeten area closest to the upstream nourishments. So profile 10.000 is
the closest to the upstream nourishments and should be most influenced by them. Note that three
of the profiles show a breakpoint around 1990, although there has not been a significant
nourishment at that year, except for maybe 2 large beach nourishments in 1986. Also the large
beach nourishments of 2003 and the dune nourishment of 2006 does not seem to have a radical
influence on the volume development.
The volume developments do not on visual inspection show clear influence of the nourishments.
14
Figure 5: Volume development and trend lines of Groote Keeten (RSP 8-9).
15
Figure 6: Volume development and trend lines of all the profiles in RSP 9 of Groote Keeten.
6. Discussion
6.1. Organize and repair Jar-Kus data
The deleting of incomplete data and supplementing by means of interpolation and extrapolation
proofs to be an excellent method to get complete profiles for calculation of landward boundaries
and volume development.
The outlier script is not used in the organization of the Jar-Kus data. The script uses mean and
standard deviation values to find outliers. In big arrays, with long profiles, the mean drops so low,
that normal high height valued are seen as outliers. On visual inspection no outliers were detected
in the dataset. It is unsure whether or not an outlier removal script is required.
The database's last year, 2010, contains data that is too incomplete to use. Maybe this is because
the altitude measurements were done badly or maybe the data are not uploaded completely. Also
there is not data available for 2002. 2002 is interpolated completely. A better alternative would be
to leave 2002 empty in the volume development data and graph.
Data check deletes the first few years of a profile if they are too incomplete to work with. To make
sure the kilometer summing does not give a lower volume at those years, those years are not
added at all. This is a good thing, however, the script also deletes those first years in other
kilometer developments that are put in the same graph. In stead, these developments should show
their full data and only the incomplete one should be clipped.
6.2. Finding landward boundary and creating volume data
Tables 6 and 7 show landward boundaries found by this research and by Arens et al. (2010). It
shows us the results of the two calibration areas Heemskerk and Texel midden. The landward
boundaries do not differ very much except for Heemskerk profile 50.750 and Texel profile 13.720.
16
Closer examination of these locations shows the script finding a location that might be different
but is certainly stable. At the Heemskerk location the boundary found has a slope of 1.4 cm with a
RMSE of 13.35 cm.
The Texel boundary is further than found by Arens et al. (2010). This is probably due to excellent
extrapolation. The boundary has a slope of 0.07 cm and a RMSE of 9.08.
RSP 50: Heemskerk
Profile number (km) Landward boundary (m)
50.000
-160
50.250
-180
50.500
-190
50.750
-135
51.000
-185
RSP 13: Texel
Profile number (km) Landward boundary (m)
13.120
-180
13.320
-180
13.520
-180
13.720
-210
13.920
-170
Table 6: The landward boundaries found by
this research.
RSP 50: Heemskerk
Profile number (km) Landward boundary (m)
50.000
-180
50.250
-175
50.500
-175
50.750
-170
51.000
-165
RSP 13: Texel
Profile number (km) Landward boundary (m)
13.120
-180
13.320
-175
13.520
-175
13.720
-175
13.920
-165
Table 7: The landward boundaries found
by Arens et al. (2010).
Although the results seem to be good, a point of discussion is the fact that a point can be super
stable in height, but more landward points are not. So instead of checking only how stable one
point is, that point plus the more landward points need to be checked. In the routing of a more
seaward point is to be checked, the slope and RMSE are added to the more landward points
already checked and it is seen whether or not the slope and RMSE values improve. If these values
improve or stay the same (thus being a stable point), another point more seaward can be checked.
If the slope and RMSE values get worse significantly, that point is less stable and should be
considered as landward boundary.
6.3. Fit trend lines to volume developments
The resulting figures are compared with those of Arens et al. (2010). First the Heemskerk results
are checked (figure 7). The volumes calculated by Arens et al. (2010, figure 8) seem a bit higher
overall, but the shape of the development matches. This might be the result of different landward
boundaries: The boundaries found by this thesis are mostly lower than those found by Arens et al.
(2010), this lowers volume.
The breakpoints differ quite a lot. Arens et al. (2010) breakpoints are found by visual inspection
and probably influenced by the knowledge that a big nourishment has been done at kilometers 49
and 50 at 1996 and 1997. Note that this thesis' results don't show a breakpoint in kilometer 48,
where no nourishment has been done ever. Kilometers 49 and 50 show breakpoints before or after
1997.
While the trend lines of this research might fit better, they don't always have to make things
clearer. For example, the second breakpoint at km 50 in 1994 could be just as well moved to 1996:
1994-1996 don't show any major decline or incline. This would show a clearer effect of the
nourishment.
17
Figure 7: Volume development and trend lines of Heemskerk (RSP 48-50).
Figure 8: Volume development and trend lines of Heemskerk (RSP 48-50) by Arens et al. (2010).
18
The volume development of Texel midden (figure 9) does not seem to differ much from that of
Arens et al. (2010, figure 10). The breakpoints all are around 1994, the same year Arens et al.
(2010) found their breakpoints. However the main difference here is the major decline visible in the
Arens et al. (2010) figure of kilometer 14, the first few years. Further inspection reveals a flaw in
the results. Because this script chooses a steady seaward boundary (the point where the height
drops below 300 cm) for all years, it does not take into account that the seaward boundary could
also change per year. In this case, the seaward boundary for these results is way too far landward
for the first few years, thus showing a lower volume at those years. Seaward boundaries also need
Figure 9: Volume development and trend lines of Texel midden (RSP 11-14).
to be calculated annually.
19
Figure 10: Volume development and trend lines of Texel midden (RSP 11-14) by Arens et al.
(2010).
The criteria are found and calibrated for 7 trend lines. This might not be enough The calibration
should be done more extensively. Although the script works well on other location, more
calibration could improve the applicability of the script.
The trend line criteria should not be in series. Instead they should all be compared to one another.
This would insure an optimal choice of number of trend lines and not a by accident chosen
number, because it was first in line. Also the trend line criteria could be made user adjustable, if for
example more single trend lines have to be fitted.
Visualization could be improved: Separate tables with data, out of the graphs and names of
kilometers that are a bit more than numbers.
6.4. Determine spatial effects of a nourishment at a location downstream
There does not seem to be a lot of effect of nourishments upstream at the Groote Keeten location,
however the visual inspection done is flawed and biased. Statistical tests should be performed to
find correlation between the nourishment data and the volume developments.
20
7. Conclusions
 The Jar-Kus dataset contains a lot of faulty, incomplete profiles that have to be repaired or
removed.
 A script is developed that will remove the most badly damaged profiles and repair the
others.
 The correct coordinates of the landward boundary is found automatically by this script.
 It fits 1, 2 or 3 trend lines depending on certain criteria which are developed to make sure
the correct number of lines are fitted.
 The script has been tested on some profiles and is shown to work.
 There is no influence noticeable of upstream nourishments at a downstream location.
Recommendations:
Landward boundaries should be calculated differently: Not only a single point should be tested for
stability, but all the points landward. The test should start at the most landward point. Then the
second point, more seaward, should be tested. If stability increases or stays more or less the
same, that point is stable too. If stability decreases, that point should be seen as landward
boundary.
The error in volume calculation should be repaired: Seaward boundaries should be calculated per
year and not be a single coordinate for all years.
Input user interface could be improved. The user should be able to choose from a list of available
grid numbers, RSP and profile numbers. Also the user should be able to choose between two
options and not having to type 0 or 1. The input could furthermore be improved by giving it the
option of changing (subscript) parameters, such as the amount of data extrapolated or the criteria
for the number of trend lines fitted.
Output should be visualized better and the output tables should be added to the graph. Local
nourishment data could be added to the graph. The name of the location should be the title of the
graph.
21
8. Literature
Arens, S.M., Mulder, J.P.M., 2008. Dynamisch kustbeheer goed voor veiligheid en natuur. Land +
Water no. 9, 33-35.
Arens, S.M., Puijvelde, van, S.P., Brière, C., 2010. Effecten van suppleties op duinontwikkeling.
Bosschap, bedrijfschap voor bos en natuur, 1-98
Arens, S.M., Wiersma, J., 1994. The Dutch foredunes: Inventory and classification. Journal of
Coastal Research 10(1), 189-202.
De Staat, 2009, Samenwerkingsovereenkomst zandsuppleties natuurbeschermingsorganisaties en
Rijkswaterstaat.
De Ruig, J.H.M., Louisse, C.J., 1991. Sand budget trends and changes along the Holland coast.
Journal of Coastal Research 7(4), 1013-1026.
De Ruig, J.H.M., 1998. Coastline management of the Netherlands: Human use versus natural
dynamics. Journal of Coastal Conservation 4, 127-134.
De Swart, H., 2006. Kustdynamica, Weer, Klimaat en Kust. Meteorologica 15(4): 10-14.
European Commission Publication Office, Natura 2000, 2009, Natura 2000 factsheet.
http://ec.europa.eu/environment/nature/index_en.htm .
McLaughlan, P.F., 2001. Levenberg-Marquardt minimisation. University of Surrey.
Minneboo, F.A.J., 1995. Jaarlijkse Kustmetingen, richtlijnen voor de inwinning, bewerking en
opslag van gegevens van jaarlijkse kustmetingen. Rapport RIKZ – 95.022.
Van de Graaff, J., Niemeyer, H.D., Van Overeem, J., 1991. Beach nourishment, philosophy and
coastal protection policy. Coastal Engineering 16, 3-22.
Van der Burgh, L.M., Wijnberg, K.M., Hulsher, S.J.M.H., Mulder, J.P.M., Koningsveld, van, M,
2007. Linking coastal evolution and super storm dune erosion forecasts. Coastal
Sediments ASCE, 1-14.
Van der Wal, D., 1998. The impact of the grain-size distribution of nourishment sand on aeolian
sand transport. Journal of Coastal Research 14(2), 620-631.
Van der Wal, D., 1999. Modelling aeolian sand transport and morphological development in two
beach nourishment areas. Earth Surface Processes and Landforms 25, 77-92.
Van Puijvelde, S.P., 2010. Classification of Dutch foredunes, Internship report Deltares / Arens
bureau voor Strand en Duinonderzoek / University of Utrecht.
Speybroeck, J., Bonte, D., Courtens, W., Gheskiere, T., Grootaert, P., Maelfait, J.P., Mathys, M.,
Provoost, S., Sabbe, K., Stienen, E.W.M., Van Lancker, V., Vincx, M., Degraer, S.,
2006. Beach nourishment: an ecologically sound coastal defence alternative? A
review. Aquatic Conservation: Marine and Freshwater Ecosystems 16, 419-435
Wilmott, C.J., Ackleson, S.G., Davis, R.E., Feddema, J.J., Klink, K.M. Legates, D.R., O'Donell, J.,
Rowe, C.M., 1985. Statistics for the evaluation and comparison of models. Journal
of Geophysical Research Volume 90, No. C5, 8995-9005.
22
9. Appendix (code)
9.1. Data import profile
%
%
%
%
Main loading script to analyze loose profiles or all profiles in one
kilometer.
N.B. This Script not only gives a figure with significance, it also shows
some extra important data per profile! See Output - Data in Arrays (Below).
%
%
%
%
%
%
%
Created by: Bob van der Zwaag
Part of the BSc thesis: 'The effect of sand nourishments on foredune
sediment volume'
University of Amsterdam
Date: June 2011 ( the database was till 2010)
Contact: bobzwaag@gmail.com
Matlab Version: R2010b
% Input:
% - transect.nc:
% This file contains the raw JarKus-data. It's open source
% data from Rijkswaterstaat (Dutch Coastal maintainance office) and
% it's available at Deltares Open Earth:
http://opendap.deltares.nl:8080/thredds/catalog/opendap/rijkswaterstaat/jarkus/
catalog.html
% Files needed for operation:
% - MexCDF
% transect.nc is a database generated by MexCDf, to open it, MexCDF
% commands have to be added to Matlab system. For more information see:
% http://mexcdf.sourceforge.net/
% - Stixbox
% Stixbox functions are needed. I believe only linreg.m and llsfit.m.
% - Subscripts not native to Matlab
% These are the scripts that where created especially for this thesis.
% - Datacheck.m
% - Outliers.m
% - interpolatie.m
% - extrap.m
% - Landward_Boundary2.m
% - caltotvol.m
% - CalcTrend.m
% - User Input
% Consists of correct grid no. and RSP or Profile No. For more information
% see:
%
http://www.rijkswaterstaat.nl/geotool/geotool_kustlijnkaart.aspx?cookieload=tru
e
% and Arens et al. (2010)
%
%
%
%
%
%
%
%
%
%
%
Output
Output is decribed briefly in this section. The individual outputs
are described more thouroughly in the output sections of the subscripts.
- Figure
This script generates a figure with on the x-axis the years and on
the y-axis the volume. It is filled with the volume data and trend
lines are fitted. The Breakpoints and the siginificance of the lines
are annotated.
- Data in arrays
- idprofiles: the profiles that were used.
- idkicked: The profiles that were removed because they were
23
%
%
%
%
%
%
%
%
%
%
%
%%
incomplete.
- sumnoutliers: The number of outliers removed per run.
- sumnrextrap: the number of rows extrapolated landward
- sumboundary: All landward boundaries
- summinmax: All min & max coordinates landward boundaries
were found between
- sumslope: the slopes of landwardboundaries
- sumRMSE: the RMSEs of boundaries
- RMSE2: The RMSE of all lines(1 line per column). first row
shows the RMSE if one line was fitted, second row if two
lines where fitted and third if three lines were fitted
INITIALIZATION
clc
clear all
close all
% Creating empty arrays for concatenation
totvolsum = [] ;
sumnoutliers = [] ;
sumslope = [] ;
sumRMSE = [] ;
sumnrextrap = [] ;
summinmax = [] ;
sumboundary = [] ;
% Adding paths with neccesary files
addpath ([pwd '/mexcdf/mexnc']);
addpath ([pwd '/mexcdf/snctools']);
javaaddpath([pwd '/netcdfAll-4.2.jar']);
setpref('SNCTOOLS','USE_JAVA',true);
setpref('SNCTOOLS','USE_MEXNC',false);
addpath stixbox
% Loading RWS Data
url = 'transect.nc';
id = nc_varget(url,'id'); % Loading Profile IDs
gridlist = round(id/1000000) ; % Creating list of Grid (2-17)
Raailist = id - (gridlist*1000000) ; % Creating list of profiles
RSPlist = floor(double(Raailist)/100) ; % Creating list of kilometers
%% PROMPT USER FOR LOCATION
% Choose between 1 loose profile or all profiles in one kilometer
prompt = {'Choose profiles per km(enter 1) or loose profiles( enter 0)'} ;
dlg_title = 'Input';
num_lines = 1;
def = {'0'};
answer = inputdlg(prompt,dlg_title,num_lines,def);
Choose = str2double(answer{1}) ; % Answer
if Choose == 1 % If Answer was'1' whole kilometer is examined.
% Enter Grid And RSP(kilometer)
prompt = {'Enter GridNo. (2-13, 15-17):','Enter RSP'};
dlg_title = 'Input';
num_lines = 1;
def = {'6','11'};
answer = inputdlg(prompt,dlg_title,num_lines,def);
grid = str2double(answer{1}) ; % Answer grid
RSP = str2double(answer{2}) ; % Answer RSP
24
loc = find(gridlist == grid & RSPlist == RSP) ; % find location of id in
lists
loc(length(loc)+1) = loc(length(loc))+1 ; % Taking first of next km as well
[loc, i2, lockicked] = Datacheck(loc) ; % checking data for incomplete
profiles
else % If answer was 0, only one raai is examed
% Enter grid and profile no. (see raailist)
prompt = {'Enter GridNo. (2-13, 15-17):','Enter profile 1'};
dlg_title = 'Input';
num_lines = 1;
def = {'7','4925'};
answer = inputdlg(prompt,dlg_title,num_lines,def);
grid = str2double(answer{1}) ; % Answer grid
Raai = str2double(answer{2}) ;% Answer Profile
loc = find(gridlist == grid & Raailist == Raai) ; % find location of id in
lists
[loc, i2, lockicked] = Datacheck(loc) ; % checking data for incomplete
profiles
end
idkicked = id(lockicked(:))' ; % Summing al Profiles that were discarded
idprofiles = id(loc(:)) ;
%% CREATING PROFILE
for ID = id(loc(:))'
% Loading years
profile = [] ; % empty array to make shure everything fits :)
year = nc_varget(url,'time'); % Loading Years
year = round(year/365+1970); % Creating Years
[u,~] = size( year) ; % quantity of years
year = year(1:u-1) ; % Deleting 2010(Incomplete)
[u,~] = size( year) ; % new quantity
% Load Cross Shore Coordinates
XRSP = nc_varget(url, 'cross_shore') ;
% Create Year Numbers
for k=1:u
year_nr(1,k)= find(year == 1964+k);
end
clear k;
% Create transect number of ID
transect_nr = find(id==ID)-1;
% Load Height Data of corresponding profile
for l=1:u
z(:,l)= nc_varget(url,'altitude',[year_nr(l),transect_nr,0],[1,1,-1]);
end
clear l;
% Clear first 10 years because they're incomplete (1965-1975)
z = z(:,10:u-1) ;
year = year(11:u-1) ;
[u,~] = size( year) ;
25
year(u+1) = year(u) +1 ;
[u,~] = size( year) ;
% Multiplying heights and coordinates by 100, so they're in cm.
z= z.*100 ;
XRSP = XRSP .* 100 ;
%Heights that are -0m NAP and inComplete Data(all NaNs through all years
%on one location) are deleted
datamin = min(z,[],2) ; % Finding minimum of height on cross profile
for k = 1:u
nan(:,k) = isnan(z(:,k)) ;
nansum = sum(nan,2) ; % finding quantity of NaNs cross profile
end
com3rows = find(datamin >150 & nansum < u-5 ) ; % find rows that meet
criteria
z = z(min(com3rows):max(com3rows),:); % clip height data
XRSP = XRSP(min(com3rows):max(com3rows),:) ; % clip coordinates
%
%
[z,noutliers] = Outliers(z, 3) ; % remove outliers
sumnoutliers = [sumnoutliers,noutliers] ; % concatenate outliers
% Creating profile array
k=1;
for g=1:2:u*2
profile(:,g)=XRSP(:,1); % coordinates every uneven number
profile(:,g+1)=z(:,k); % height data every even number
k=k+1;
end
clear k g
% Clipping the profile to the smallest one(see Datacheck)
profile2(:,1:i2) = profile(:,(u*2-i2+1):(u*2)) ; % clip
profile = profile2 ;
year2 = year((length(year) - (i2/2-1)):length(year),1) ; % clipperdeclip
year = year2 ;
clear profile2 year2
%% REPAIRING PROFILE
profile = interpolatie(profile) ; %interpolation
[profile, nrextrap] = extrap(profile,1) ; %extrapolation
sumnrextrap = [sumnrextrap,nrextrap] ; %concatenating no. extrapolation
%% CALCULATING VOLUME
[BOUNDARY, slope, RMSE, minmax] = Landward_Boundary2(profile,year) ; %
finding landward boundary
sumslope = [sumslope,slope] ; % concatenate all slopes
sumRMSE = [sumRMSE,RMSE] ; % concatenate all RMSEs
summinmax = [summinmax, minmax'] ; % concatenate all min max boundaries
sumboundary = [sumboundary,BOUNDARY] ; % concatenate all found boundaries
clear z year_nr u i
totvol = caltotvol(profile, BOUNDARY) ; % calculating volume
totvolsum = [totvolsum;totvol] ; % concatenating volume developments
end
%% FITTING TRENDLINES, CALCULATING SIGNIFICANCE & VISUALIZATION
26
% Creating profilenames for visualization.
for u = 1:length(loc) % all locations
name(u) = {num2str(Raailist(loc(u)))} ; % names are number
end
% Fitting trendlines and stuff
RMSE2 = CalcTrend(totvolsum, year', name)
% Cleaning up( keeping only important data for review)
clear Choose Q RSPlist ID Raailist XRSP answer com3rows datamin def dlg_title
grid gridlist i2 i3 loc name nan nansum num_lines prompt totvol totvolsum
transect_nr u lockicked slope minmax noutliers nrextrap RMSE BOUNDARY
27
9.2. Data import kilometer
% Main loading script to analyze kilometer(s) of profiles.
% N.B. This Script does not output a lot of tables with extra information.
% For more detailed information (on RMSE of chosen boundary, the corresponding
slope, the
% minmax boundary tested, the no. outliers the no. extrapolation: please
% use dataimportraai.) please use 'dataimportraai.m'.
%
%
%
%
%
%
%
Created by: Bob van der Zwaag
Part of the BSc thesis: 'The effect of sand nourishments on foredune
sediment volume'
University of Amsterdam
Date: June 2011 ( the database was till 2010)
Contact: bobzwaag@gmail.com
Matlab Version: R2010b
% Input:
% - transect.nc:
% This file contains the raw JarKus-data. It's open source
% data from Rijkswaterstaat (Dutch Coastal maintainance office) and
% it's available at Deltares Open Earth:
http://opendap.deltares.nl:8080/thredds/catalog/opendap/rijkswaterstaat/jarkus/
catalog.html
% Files needed for operation:
% - MexCDF
% transect.nc is a database generated by MexCDf, to open it, MexCDF
% commands have to be added to Matlab system. For more information see:
% http://mexcdf.sourceforge.net/
% - Stixbox
% Stixbox functions are needed. I believe only linreg.m and llsfit.m.
% - Subscripts not native to Matlab
% These are the scripts that where created especially for this thesis.
% - Datacheck.m
% - Outliers.m
% - interpolatie.m
% - extrap.m
% - Landward_Boundary2.m
% - caltotvol.m
% - CalcTrend.m
% - User Input
% Consists of correct grid no. and RSP or Profile No. For more information
% see:
%
http://www.rijkswaterstaat.nl/geotool/geotool_kustlijnkaart.aspx?cookieload=tru
e
% and Arens et al. (2010)
%Output
% Output is decribed briefly in this section. The individual outputs
% are described more thouroughly in the output sections of the subscripts.
% - Figure
% This script generates a figure with on the x-axis the years and on
% the y-axis the volume. It is filled with the volume data and trend
% lines are fitted. The Breakpoints and the siginificance of the lines
% are annotated.
% - Data in arrays
% - idprofiles: the profiles that were used.
% - idkicked: The profiles that were removed because they were
% incomplete.
28
% - RMSE2: The RMSE of all lines(1 line per column). first row
% shows the RMSE if one line was fitted, second row if two
% lines where fitted and third if three lines were fitted
%% INITIALIZATION
clc
clear all
close all
% Creating empty arrays for concatenation
i3 = 10000000000 ; %Datacheck necessary constant
idkicked = [] ;
% Adding Paths with necessary files
addpath ([pwd '/mexcdf/mexnc']);
addpath ([pwd '/mexcdf/snctools']);
javaaddpath([pwd '/netcdfAll-4.2.jar']);
setpref('SNCTOOLS','USE_JAVA',true);
setpref('SNCTOOLS','USE_MEXNC',false);
addpath stixbox
% Loading RWS Data
url = 'transect.nc';
id = nc_varget(url,'id');
gridlist = round(id/1000000) ;
Raailist = id - (gridlist*1000000) ;
RSPlist = floor(double(Raailist)/100) ;
%% PROMPT USER FOR LOCATION OF CALCULATION
% Choose Grid no. and RSP nos.
prompt = {'Enter GridNo. (2-13, 15-17):','Enter RSP 1','Enter RSP 2','Enter RSP
3','Enter RSP 4','Enter RSP 5','Enter RSP 6'};
dlg_title = 'Input';
num_lines = 1;
def = {'6','11','12','','','',''};
answer = inputdlg(prompt,dlg_title,num_lines,def);
grid = str2num(answer{1}) ; % Answer Gridno.
% Answer RSP
for k = 2:length(answer)
if ~isempty(answer{k}) % Ignoring empty input
RSP(k-1) = str2num(answer{k}) ;
end
end
%% CREATING PROFILE
% Kilometer Loop
for a = 1: length(RSP)
nrRSP = RSP(a)
loc = find(gridlist == grid & RSPlist == nrRSP) ; % find location of id in
lists
loc(length(loc)+1) = loc(length(loc))+1 ; % Taking first of next km too
[loc, i2, lockicked] = Datacheck(loc) ; % Checking Data for incomplete
profiles
totvolsum = [] ; % (re) emptying the voulume data
idkicked = [idkicked, id(lockicked(:))'] ; % Summing all discarded profiles
29
idprofiles = id(loc(:)) ;
% Profiles per km loop
for ID = id(loc(:))'
% Loading Years
profile = [] ; % Empty array to make shure everything fits
year = nc_varget(url,'time'); % Loading years
year = round(year/365+1970); % Creating Years
[u,~] = size( year) ; % No of years
year = year(1:u-1) ; % Deleting 2010(incompete)
[u,~] = size( year) ; % New count
% Load Cross Shore Coordinates
XRSP = nc_varget(url, 'cross_shore') ;
% Create Year Numbers
for k=1:u
year_nr(1,k)= find(year == 1964+k);
end
clear k;
% Create transect number of ID
transect_nr = find(id==ID)-1;
% Load Height Data of corresponding profile
for l=1:u
z(:,l)= nc_varget(url,'altitude',[year_nr(l),transect_nr,0],[1,1,1]);
end
clear l;
% Clear first 10 years because they're incomplete
z = z(:,10:u-1) ;
year = year(11:u-1) ;
[u,~] = size( year) ;
year(u+1) = year(u) +1 ;
[u,~] = size( year) ;
% Multiplying by 100 so everything is in cm.
z= z.*100 ;
XRSP = XRSP .* 100 ;
%Heights that are -0m NAP and inComplete Data(all NaNs through all
years
%on one location) are deleted
datamin = nanmin(z,[],2) ; % Finding minimum of heght per cross profile
nan = [] ;
for k = 1:u
nan(:,k) = isnan(z(:,k)) ;
nansum = sum(nan,2) ; % Finding Quantity of NaNs per cross profile
end
com3rows = find(datamin >150 & nansum < u - 5 ) ; % Find rows that meet
criteria
z = z(min(com3rows):max(com3rows),:); % clip height data
XRSP = XRSP(min(com3rows):max(com3rows),:) ; % clip coordinates
% [z,noutliers] = Outliers(z, 3) ;
% Creating profile array
k=1;
30
for g=1:2:u*2
profile(:,g)=XRSP(:,1);
profile(:,g+1)=z(:,k);
k=k+1;
end
clear k g
% Clipping profile to the smallest dataset of all profiles
if i3 < i2 % Clipping per km
i2 = i3 ;
end
profile2(:,1:i2) = profile(:,(u*2-i2+1):(u*2)) ;
profile = profile2 ;
year2 = year((length(year) - (i2/2-1)):length(year),1) ;
year = year2 ;
clear profile2 year2
%% REPAIRING PROFILE
profile = interpolatie(profile) ; % Interpolation
[profile, nrextrap] = extrap(profile,1) ; % Extrapolation
%% CALCULATING VOLUME
[BOUNDARY, slope, RMSE, minmax] = Landward_Boundary2(profile,year) ; %
Finding Landward Boundary
clear z year_nr u i
totvol = caltotvol(profile, BOUNDARY) ; % Calculating Volume
totvolsum = [totvolsum;totvol] ; % Concatenating Volume Development
end
i3 = i2 ;
km(a,:) = nanmean(totvolsum(1:length(loc),:)) ; % Concatenaing volume data
per km
totvolsum = [] ;
name(a) = {num2str(nrRSP)} ; % concatenating names
end
%% FITTING TRENDLINES
RMSE2 = CalcTrend(km, year', name)
clear Choose Q RSPlist ID Raailist XRSP answer com3rows datamin def dlg_title
grid gridlist i2 i3 name nan nansum num_lines prompt totvol totvolsum
transect_nr u lockicked a minmax noutliers nrRSP nrextrap slope
31
9.3. Data check
function [loc2,i2, lockicked] = Datacheck(loc)
% This script check data for completeness and displays which profiles have
% to be removed
%
%
%
%
%
%
%
Created by: Bob van der Zwaag
Part of the BSc thesis: 'The effect of sand nourishments on foredune
sediment volume'
University of Amsterdam
Date: June 2011 ( the database was till 2010)
Contact: bobzwaag@gmail.com
Matlab Version: R2010b
% Input
% - Location Data (user) input from import script
% - transect.nc:
% This file contains the raw JarKus-data. It's open source
% data from Rijkswaterstaat (Dutch Coastal maintainance office) and
% it's available at Deltares Open Earth:
http://opendap.deltares.nl:8080/thredds/catalog/opendap/rijkswaterstaat/jarkus/
catalog.html
% Files needed for operation:
% - MexCDF
% transect.nc is a database generated by MexCDf, to open it, MexCDF
% commands have to be added to Matlab system. For more information see:
% http://mexcdf.sourceforge.net/
% - Stixbox
% Stixbox functions are needed. I believe only linreg.m and llsfit.m.
% - Subscripts not native to Matlab
% These are the scripts that where created especially for this thesis.
% - Outliers.m
% - interpolatie.m
% - extrap.m
%
%
%
%
%
%
Output
- loc2: the profiles that were used.
- lockicked: The profiles that were removed because they were
incomplete.
- i2: The number of remaining years after the first rows are
checked: The Years that are too incomplete are deleted.
%% INIT
% Creating Empty arrays for concatenation
a2 = [] ;
i2 = [] ;
lockicked = [] ;
% Loading RWS data
url = 'transect.nc';
id = nc_varget(url,'id');
%% CREATING PROFILE
for a = 1: length(loc) % loop all profiles
ID = id(loc(a)) ; % profile number
32
% Loading Years
profile = [] ; % Empty Array to make sure everything fits
year = nc_varget(url,'time'); % Loading years
year = round(year/365+1970); % Creating years
[u,~] = size( year) ; % Number of years
year = year(1:u-1) ; % Deleting 2010
[u,~] = size( year) ; % New Quantity
% Load Cross Shore Coordinates
XRSP = nc_varget(url, 'cross_shore') ;
% Create Year Numbers
for k=1:u
year_nr(1,k)= find(year == 1964+k);
end
clear k;
% Create transect number of ID
transect_nr = find(id==ID)-1;
clear z
% Load Height Data of corresponding profile
for l=1:u
z(:,l)= nc_varget(url,'altitude',[year_nr(l),transect_nr,0],[1,1,-1]);
end
clear l;
%Clear first 10 years because they're incomplete
z = z(:,10:u-1) ;
year = year(11:u-1) ;
[u,~] = size( year) ;
year(u+1) = year(u) +1 ;
[u,~] = size( year) ;
% Multiplying heights and coords by 100, so the data is in cm
z= z.*100 ;
XRSP = XRSP .* 100 ;
%Heights that are -0m NAP and inComplete Data(all NaNs through all years
%on one location) are deleted
datamin = min(z,[],2) ; % Finding minimum height on cross profiles
nan = [] ;
for k = 1:u
nan(:,k) = isnan(z(:,k)) ;
nansum = sum(nan,2) ; % Finding Quantity of NaNs on cross profiles
end
com3rows = find(datamin >200 & nansum < length (year)-5 ) ;% find Rows that
meet criteria
if length(com3rows) < 5 % If not enough rows (5) meet criteria, delete that
profile
a2 = [a2,a ] ;
'kicked out Raai no.:' ;
loc(a) ;
lockicked = [lockicked, loc(a)] ;
i2 = [i2,0]
;
else
z = z(min(com3rows):max(com3rows),:); % Clip height data
XRSP = XRSP(min(com3rows):max(com3rows),:) ; % Clip coordinates
33
%
[z,noutliers] = outliers(z, 3) ;
% Creating Profile Array
k=1;
for g=1:2:u*2
profile(:,g)=XRSP(:,1); % Coordinates every uneven number
profile(:,g+1)=z(:,k); % Height data every even number
k=k+1;
end
%% REPAIRING PROFILE
profile = interpolatie(profile) ; % INterpolation
[profile, nrextrap] = extrap(profile,1) ; % Extrapolation
%% MORE CHECKING
% Kick whole raai
nan = [] ;
for k = 1:u
nan(:,k) = isnan(profile(:,(k*2))) ;
nansum = sum(nan,1) ; % Find NaNs per column
end
clear i
[u,i] = size(profile) ;
% If number of columns with only NaNs is bigger than number of years /5
% or if the number of NANs in last column is bigger than columnsize -10
if (numel(find(nansum == u))) > (i/10) | nansum(i/2) > u-10
a2 = [a2,a ] ; % Profile number from list of locs
'kicked out Raai no.:' ;
loc(a) ; % profile
lockicked = [lockicked, loc(a)] ; % Add to lockicked
i2 = [i2,i]
; % add profile size to list
% kick first years
else
clear i
[u,i] = size(profile) ;
b=find(isnan(profile(:,2))) ;% calculating no. NaNs in first column
while numel(b)>u-15 % checking if no NaNs is less than size - 15
for a = 2 % if it is: check no NaNs
b = find(isnan(profile(:,a))) ;
if numel(b)>u-15
profile = profile(:,3:i) ; % CLip profile (Making
column 4 the new column 2)
year = year(2:length(year),1) ; % CLip years
end
end
clear i
[u,i] = size(profile) ; % Checking new size
end
i2 = [i2,i]
;% add i to list(clipped profile size)
end
end
end
%% FINALIZING
i2(a2) = [] ; % Delete all size data of deleted profiles
i2 = min(i2) ; % Finding min size
clear k
loc(a2) = [] ;
34
loc2 = loc ;
35
9.4. Outlier Removal
function [data, noutsum3, tel] = Outliers(data,s)
%% REMOVING OUTLIERS, s TIMES STANDARDDEVIATION OF MEAN REPLACING THEM WITH
NANS
% data is an array of data
%s = standarddeviation used to detect outliers. (if left empty it is 3).
%Nout is the number of outliers removed
%tel is the number of runs it does, in case of outlier lowers mean too much
%it finds new outliers, lowering mean etc etc.
%Data is the dataset you put in, with NaNs instead of outliers.
%The NaNs should be interpolated.
%% INIT
if isempty(s), s = 3; end
noutsum = 0 ;
noutsum2 = 2 ;
noutsum3 = 0 ;
[~,i] = size(data) ;
tel = 0 ;
%% LOOP
while noutsum2 > 0 % While there are still outliers in de data
% Calculate the mean and the standard deviation
% of each data column in the matrix
for k = 2: i
year = data(:,k) ;
%Delete first of column(year)
year(1) = [] ;
%Calculate mu and s
mu = nanmean(year);
sigma = nanstd(year) ;
[n,~] = size(year);
% Create a matrix of mean values by
% replicating the mu vector for n rows
MeanMat = repmat(mu,n,1);
% Create a matrix of standard deviation values by
% replicating the sigma vector for n rows
SigmaMat = repmat(sigma,n,1);
% Create a matrix of zeros and ones, where ones indicate
% the location of outliers
outliers = abs(year - MeanMat) > s*SigmaMat;
% Calculate the number of outliers in each column
nout = sum(outliers) ;
%Total number of outliers in data
noutsum = [noutsum, nout] ;
noutsum2 = sum(noutsum) ;
%Find outliers location
a = find(outliers == 1) ;
%Replace by NaNs(a+1 because of the deletion of year(row 1)
data(a+1,k) = NaN ;
end
tel = tel+1 ;
% Total no outliers removed
noutsum3 = noutsum3+noutsum2 ;
noutsum = [] ;
end
36
%Cleaning up
clear MeanMat SigmaMat a k mu n nout noutsum noutsum2 outliers p sigma year
37
9.5. Interpolation
function [profile] = interpolatie(profile)
% Interpolate to get rid of NaN's during years:
% Thanks to S. Van Puijvelde!
nanny=isnan(profile);
for k=2:length(nanny(1,:))
for m=2:length(nanny(:,1))-3
if nanny(m,k) == 1 && nanny(m+1,k) == 0
profile(m,k)=(profile(m-1,k)+profile(m+1,k))/2;
elseif nanny(m,k) == 1 && nanny(m+1,k) == 1 && nanny(m+2,k) == 0
profile(m,k)=(profile(m-1,k)+profile(m+2,k)-profile(m-1,k))/3;
profile(m+1,k)=profile(m,k)+nanny(m+2,k)/2;
elseif nanny(m,k) == 1 && nanny(m+1,k) == 1 && nanny(m+2,k) == 1 &&
nanny(m+3,k) == 0
profile(m,k)=(profile(m-1,k)+profile(m+3,k)-profile(m-1,k))/4;
profile(m+1,k)=(profile(m,k)+profile(m+3,k)-profile(m,k))/3;
profile(m+2,k)=profile(m+1,k)+nanny(m+3,k)/2;
else profile(m,k)=profile(m,k);
end
end
end
clear nanny k m;
% moving across length
for p=4:2:length(profile(1,:)) %Moving columns
first=isnan(profile(:,p)); %establishing NaN's of first column(column p)
if sum(first) ~=0 %If sum of NaNs first column is not 0
cellstrt=find(first==1); % Finding NaNs in column
nro=cellstrt(1);nrl=cellstrt(end); % Starting at first NaN & ending at last
findnan=isnan(profile); % Find NaNs in whole profile
for k=p:2:length(profile(1,:))-2 %moving across columns
for m=nro:nrl; %moving across rows
if findnan(m,k-2)==0 && findnan(m,k)==1 && findnan(m,k+2)==0
profile(m,k)=(profile(m,k-2)+profile(m,k+2))/2;
end
end
end
for k=p:2:length(profile(1,:))-4
for m=nro:nrl;
if findnan(m,k-2)==0 && findnan(m,k)==1 && findnan(m,k+2)==1 &&
findnan(m,k+4)==0
profile(m,k)=(profile(m,k-2))+((profile(m,k+4)-profile(m,k2))/3);
profile(m,k+2)=(profile(m,k)+profile(m,k+4))/2;
end
end
end
for k=p:2:length(profile(1,:))-6
for m=nro:nrl;
if findnan(m,k-2)==0 && findnan(m,k)==1 && findnan(m,k+2)==1 &&
findnan(m,k+4)==1 && findnan(m,k+6)==0
profile(m,k)=(profile(m,k-2))+((profile(m,k+6)-profile(m,k2))/4);
profile(m,k+2)=(profile(m,k))+((profile(m,k+6)profile(m,k))/3);
38
profile(m,k+4)=(profile(m,k+2)+profile(m,k+6))/2;
end
end
end
for k=p:2:length(profile(1,:))-8
for m=nro:nrl;
if findnan(m,k-2)==0 && findnan(m,k)==1 && findnan(m,k+2)==1 &&
findnan(m,k+4)==1 && findnan(m,k+6)==1 && findnan(m,k+8)==0
profile(m,k)=(profile(m,k-2))+((profile(m,k+8)-profile(m,k2))/5);
profile(m,k+2)=(profile(m,k))+((profile(m,k+8)profile(m,k))/4);
profile(m,k+4)=(profile(m,k+2))+((profile(m,k+8)profile(m,k+2))/3);
profile(m,k+6)=(profile(m,k+4)+profile(m,k+8))/2;
end
end
end
for k=p:2:length(profile(1,:))-10
for m=nro:nrl;
if findnan(m,k-2)==0 && findnan(m,k)==1 && findnan(m,k+2)==1 &&
findnan(m,k+4)==1 && findnan(m,k+6)==1 && findnan(m,k+8)==1 &&
findnan(m,k+10)==0
profile(m,k)=(profile(m,k-2))+((profile(m,k+10)-profile(m,k2))/6);
profile(m,k+2)=(profile(m,k))+((profile(m,k+10)profile(m,k))/5);
profile(m,k+4)=(profile(m,k+2))+((profile(m,k+10)profile(m,k+2))/4);
profile(m,k+6)=(profile(m,k+4))+((profile(m,k+10)profile(m,k+4))/3);
profile(m,k+8)=(profile(m,k+6)+profile(m,k+10))/2;
end
end
end
for k=p:2:length(profile(1,:))-12
for m=nro:nrl;
if findnan(m,k-2)==0 && findnan(m,k)==1 && findnan(m,k+2)==1 &&
findnan(m,k+4)==1 && findnan(m,k+6)==1 && findnan(m,k+8)==1 &&
findnan(m,k+10)==1 && findnan(m,k+12)==0
profile(m,k)=(profile(m,k-2))+((profile(m,k+12)profile(m,k-2))/7);
profile(m,k+2)=(profile(m,k))+((profile(m,k+12)profile(m,k))/6);
profile(m,k+4)=(profile(m,k+2))+((profile(m,k+12)profile(m,k+2))/5);
profile(m,k+6)=(profile(m,k+4))+((profile(m,k+12)profile(m,k+4))/4);
profile(m,k+8)=(profile(m,k+6))+((profile(m,k+12)profile(m,k+6))/3);
profile(m,k+10)=(profile(m,k+8)+profile(m,k+12))/2;
end
end
end
for k=p:2:length(profile(1,:))-14
for m=nro:nrl;
if findnan(m,k-2)==0 && findnan(m,k)==1 && findnan(m,k+2)==1 &&
findnan(m,k+4)==1 && findnan(m,k+6)==1 && findnan(m,k+8)==1 &&
findnan(m,k+10)==1 && findnan(m,k+12)==1 && findnan(m,k+14)==0
39
profile(m,k)=(profile(m,k-2))+((profile(m,k+14)profile(m,k-2))/8);
profile(m,k+2)=(profile(m,k))+((profile(m,k+14)profile(m,k))/7);
profile(m,k+4)=(profile(m,k+2))+((profile(m,k+14)profile(m,k+2))/6);
profile(m,k+6)=(profile(m,k+4))+((profile(m,k+14)profile(m,k+4))/5);
profile(m,k+8)=(profile(m,k+6))+((profile(m,k+14)profile(m,k+6))/4);
profile(m,k+10)=(profile(m,k+8))+((profile(m,k+14)profile(m,k+8))/3);
profile(m,k+12)=(profile(m,k+10)+profile(m,k+14))/2;
end
end
end
for k=p:2:length(profile(1,:))-16
for m=nro:nrl;
if findnan(m,k-2)==0 && findnan(m,k)==1 && findnan(m,k+2)==1 &&
findnan(m,k+4)==1 && findnan(m,k+6)==1 && findnan(m,k+8)==1 &&
findnan(m,k+10)==1 && findnan(m,k+12)==1 && findnan(m,k+14)==1 &&
findnan(m,k+16)==0
profile(m,k)=(profile(m,k-2))+((profile(m,k+16)profile(m,k-2))/9);
profile(m,k+2)=(profile(m,k))+((profile(m,k+16)profile(m,k))/8);
profile(m,k+4)=(profile(m,k+2))+((profile(m,k+16)profile(m,k+2))/7);
profile(m,k+6)=(profile(m,k+4))+((profile(m,k+16)profile(m,k+4))/6);
profile(m,k+8)=(profile(m,k+6))+((profile(m,k+16)profile(m,k+6))/5);
profile(m,k+10)=(profile(m,k+8))+((profile(m,k+16)profile(m,k+8))/4);
profile(m,k+12)=(profile(m,k+10))+((profile(m,k+16)profile(m,k+10))/3);
profile(m,k+14)=(profile(m,k+12)+profile(m,k+16))/2;
end
end
end
for k=p:2:length(profile(1,:))-18
for m=nro:nrl;
if findnan(m,k-2)==0 && findnan(m,k)==1 && findnan(m,k+2)==1 &&
findnan(m,k+4)==1 && findnan(m,k+6)==1 && findnan(m,k+8)==1 &&
findnan(m,k+10)==1 && findnan(m,k+12)==1 && findnan(m,k+14)==1 &&
findnan(m,k+16)==1 && findnan(m,k+18)==0
profile(m,k)=(profile(m,k-2))+((profile(m,k+18)profile(m,k-2))/10);
profile(m,k+2)=(profile(m,k))+((profile(m,k+18)profile(m,k))/9);
profile(m,k+4)=(profile(m,k+2))+((profile(m,k+18)profile(m,k+2))/8);
profile(m,k+6)=(profile(m,k+4))+((profile(m,k+18)profile(m,k+4))/7);
profile(m,k+8)=(profile(m,k+6))+((profile(m,k+18)profile(m,k+6))/6);
profile(m,k+10)=(profile(m,k+8))+((profile(m,k+18)profile(m,k+8))/5);
profile(m,k+12)=(profile(m,k+10))+((profile(m,k+18)profile(m,k+10))/4);
profile(m,k+14)=(profile(m,k+12))+((profile(m,k+18)-
40
profile(m,k+12))/3);
profile(m,k+16)=(profile(m,k+14)+profile(m,k+18))/2;
end
end
end
for k=p:2:length(profile(1,:))-20
for m=nro:nrl;
if findnan(m,k-2)==0 && findnan(m,k)==1 && findnan(m,k+2)==1 &&
findnan(m,k+4)==1 && findnan(m,k+6)==1 && findnan(m,k+8)==1 &&
findnan(m,k+10)==1 && findnan(m,k+12)==1 && findnan(m,k+14)==1 &&
findnan(m,k+16)==1 && findnan(m,k+18)==1 && findnan(m,k+20)==0
profile(m,k)=(profile(m,k-2))+((profile(m,k+20)profile(m,k-2))/11);
profile(m,k+2)=(profile(m,k))+((profile(m,k+20)profile(m,k))/10);
profile(m,k+4)=(profile(m,k+2))+((profile(m,k+20)profile(m,k+2))/9);
profile(m,k+6)=(profile(m,k+4))+((profile(m,k+20)profile(m,k+4))/8);
profile(m,k+8)=(profile(m,k+6))+((profile(m,k+20)profile(m,k+6))/7);
profile(m,k+10)=(profile(m,k+8))+((profile(m,k+20)profile(m,k+8))/6);
profile(m,k+12)=(profile(m,k+10))+((profile(m,k+20)profile(m,k+10))/5);
profile(m,k+14)=(profile(m,k+12))+((profile(m,k+20)profile(m,k+12))/4);
profile(m,k+16)=(profile(m,k+14))+((profile(m,k+20)profile(m,k+14))/3);
profile(m,k+18)=(profile(m,k+16)+profile(m,k+20))/2;
end
end
end
clear findnan nxt ngnxt first
end
clear nro m p k cellstrt nrl
end
41
9.6. Extrapolation
function [profile, t] = extrap(profile, z)
%profile is the profile in which extrapolation takes place. Note that the
%extrapolation only takes place at the lowest rows, landinward. it is
%extrapolated to increase the number of data points that are above 3 meters
%and doesn't contain Nan's
%z can be 1 or left empty. 1 means the extrapolation is done linearly,
%everything else meanss it is done by cubic spline method.
dataclip = profile ;
[u,i] = size(profile) ;
t = 0 ;
if isempty(z) == 1
z = 0 ;
end
for k = 1:u
nan(k,:) = isnan(dataclip(k,:)) ;
nansum = sum(nan,2) ;
end
datamin = min(dataclip(:,2:2:i),[],2) ;
com3rows = find(datamin >300 & nansum ==0 ) ;
%Furthest Coordinate Landward
minrow = min(com3rows) ;
% t = find(nansum<=5) ;
% t = min(t) ;
% q = minrow - t ;
% if q >10
%
q == 5
% end
if minrow == 1
minrow = 2 ;
end
loc5 = find(nan(minrow-1,:) == 1) ;
while dataclip(minrow,loc5) >300 & t < 7
%%
for k = 1:u
nan(k,:) = isnan(dataclip(k,:)) ;
nansum = sum(nan,2) ;
end
datamin = min(dataclip(:,2:2:i),[],2) ;
com3rows = find(datamin >300 & nansum ==0 ) ;
%Furthest Coordinate Landward
minrow = min(com3rows) ;
%%
loc5 = find(nan(minrow-1,:) == 1) ;
for l = loc5
f = minrow:minrow+5 ;
p = dataclip(minrow:minrow+5,l) ;
if z == 1
[sel,~,~,~,~] = linreg(p,f,[]) ;
y = sel(1)* minrow-1 + sel(2) ;
dataclip(minrow-1,l) = y ;
42
else
r = spline(f,p,minrow-1) ;
dataclip(minrow-1,l) = r ;
end
end
t = t+1 ;
end
profile = dataclip ;
% loc4 = find(nansum<4 & nansum>0) ; %& datamin > 300) ;
% locnan = find(isnan(data(loc4,:))) ;
% co = find(nan(86,:))
% %
% %Only Heights that are +3m NAP and Complete Data(No NaNs through all years
% %on one location)
% com3rows = find(datamin >300 & nansum == 0 ) ;
%
% %Furthest Coordinate Landward
% minrow = min(com3rows) ;
% %Furthest Coordinate Beachward
% maxrow = max(com3rows) ;
% [s1] = size(loc4)
% for j = loc4(1:s1(1))
%
co = find(nan(j,:)) ;
%
t = x(minrow:maxrow) ;
%
for l = numel(co)
%
p = dataclip(minrow:maxrow, co(l)) ;
%
[sel,~,~,~,~] = linreg(p,t,[])
%
y = sel(1)* t + sel(2)
%
%
end
% %
figure(1)
% end
43
9.7. Landward boundary
function [coord, Slope , RMSE, minmaxcoord] = Landward_Boundary2(data,year)
%% ESTABLISHING FURTHEST LANDWARD BOUNDARY
% Input 'data' includes years(even columns) and x-coordinates(uneven columns)!
% Note that the stixbox function 'linreg.m' should be in directory.
% The idea of this function is to find a stable point in the dunes where
% sand does not get blown out or in. This point will then be used as
% endpoint to calculate foredune volume from the beach (+3m NAP).
% First all data + 3 m NAP is selected and only the coordinates that have
% complete data
% A trendline is fitted through the heights of one coordinate
% Than the RMSE and slope of that line is checked.
% If those meet criteria, that point is chosen.
%% INITIATION
years = year ;
% All widths
x = data(:,1) ;
% Size
[u,i] = size(data) ;
% Some Concatenation arrays
dataclip = data ;
slrows = [] ;
rrows = [] ;
count = 0 ;
sumtest = 0 ;
ms = 0 ;
%% LANDWARD BOUNDARY
datamin = min(dataclip(:,2:2:i),[],2) ;
%Only Heights that are +3m NAP and Complete Data(No NaNs through all years
%on one location)
for k = 1:u
nan(k,:) = isnan(dataclip(k,:)) ;
nansum = sum(nan,2) ;
end
com3rows = find(datamin >300 & nansum ==0 ) ;
if isempty(com3rows) ==1
'alle data onder 300 cm of teveel NaNs in deze raai!'
end
%Furthest Coordinate Landward
minrow = min(com3rows) ;
%Furthest Coordinate Beachward
maxrow = max(com3rows) ;
% Starting testnumber for slope (0.6 cm per year)
sltestnr = 0.6 ;
% Starting testnumber for Root Mean Square Error(RMSE)(See 'rrows')
rtestnr = 6 ;
% Runs till both tests are true(2) (See ms)
while ms < 2
for d = minrow:maxrow
[sl,~,~,r,~] = linreg(dataclip(d,2:2:i)', years(:)' ) ;
%r(1) is the point estimate of y = r(1)*x + r(2) +error
44
slrows = [slrows,sl] ;
% A good measure for misfit beyond the visual interpretation
% is to consider the values of b1 (std of the residuals, also
% called the root mean squared error). The lowest value is to be
considered
% the best fit.
rrows = [rrows,r] ;
%testing to see if slope meets criteria (maximum of 1 cm incline or
%decline a year)(gives back 1 if 'true')
sltest = sl(1) < sltestnr &sl(1) >-sltestnr ;
%testing to see if root mean squared error meets criteria(lower than
%10)(gives back 1 if 'true')
rtest = r(1) < rtestnr ;
% Summing both tests to see if either of them are true or not
sumtest = [sumtest, sltest+rtest] ;
% Finding locations where they are both true(Max = 2)
ms = max(sumtest) ;
loc1 = find(sumtest == 2) ;
% finding correct row
locdata = min(loc1)+minrow ;
% Finding correct coordinate(correcting +1 for clipping)
coord = x(locdata+1) ;
end
% Making testcriteria less strict for second run
sltestnr = sltestnr + 0.2 ;
rtestnr = rtestnr + 2 ;
% adding to count to see how many times the loop has run
count = count+1 ;
% Resetting
sumtest = 0 ;
end
% if all criteria fail, choose furthest most point.
if rtestnr < 20
coord = coord
RMSE = rrows(min(loc1)+(count-1)*((maxrow-minrow)+1)-1) ;
Slope = slrows(1, min(loc1)+(count-1)*((maxrow-minrow)+1)-1) ;
else
coord = x(minrow+1)
'furthest point is chosen'
[sl,m,b,r,b2] = linreg(dataclip(maxrow,2:2:i)', years(:)' ) ;
Slope = sl(1) ;
RMSE = r ;
end
% DATA
% coordinate:
% coord = coord ;
% Slope of trendline of points on selected coordinate through years(in
% cm/y)
% Slope = Slope ;
% % % RMSE of trendline of points on selected coordinate through years(in cm)
% RMSE = RMSE ;
% The coordinate furthest away from beach that is +3 m NAP and has complete
% data
mincoordtested = x(minrow) ;
% The coordinate closest to beach that is +3 m NAP and has complete data
maxcoordtested = x(maxrow) ;
minmaxcoord = [mincoordtested,maxcoordtested] ;
%Number of runs adding RMSE and slope
45
% Runs = count - 1 ;
% toevoegen aan plot: count, RMSE - 2, Slope - 0.2, coord, min,maxrowtested
% figure(2)
% plot(yearsclip, dataclip(locdata+1,:))
% title('Chosen Coordinate ')
% xlabel(' Years')
% ylabel('Height (cm)')
% hold on
% annotation('textbox', [0.14,0.85,0.15,0.05],'string', {coord})
clear b b2 d k loc1 locdata ms r rrows rtest rtestnr sl slrows sltestnr sumtest
yearsclip
46
9.8. Calculating total volume
function [sumvolyear] = caltotvol(profile, BOUNDARY)
%This function is used to calculate total volume from dune toe to landward
%boundary. INput is the profile heights data and the landward boundary,
%calculated by the previous script.
%Output is the volume per year.
% note that dune toe is calculated for all years on the same location:
% Where there are no NaNs and all data is above 300 cm.
[u,i] = size(profile) ;
a = find (profile(:,1) == BOUNDARY) ;
sumvol = 0 ;
sumvolyear = 0 ;
datamin = min(profile(:,2:2:i),[],2) ;
for k = 1:u
nan(k,:) = isnan(profile(k,:)) ;
nansum = sum(nan,2) ;
end
com3rows = find(datamin >300 & nansum ==0 ) ; % FInd data that works
for j = 2:2:i % over all years
for l = a:max(com3rows) % from boundary to dune toe
vol= (profile(l+1,j-1)-profile(l-1,j-1))/100*0.5*((profile(l,j)300)/100) ; % Volume calculation
sumvol = [sumvol+ vol] ; % Summing
end
sumvolyear = [sumvolyear,sumvol] ; % Summing per Year
sumvol = 0 ;
end
sumvolyear = sumvolyear(1,2:length(sumvolyear)) ; % Clip (0)
47
9.9. Fitting trend lines
function [RMSE] = CalcTrend(totvol, years, name)
%% STATISTIC TOOL TO FIT TRENDLINES TO DATA
% 1 trendline, 2 trendlines or 3 trendlines are fitted to data. Th
% Parameters are in this way (visually)optimized to find how many
% trendlines can be fitted. The Parameters are Adjusted for foredune
% volumes of dunes.
%[RMSE] = VolFit(VD, Y, KM, Criteria)
%INPUT
% to a max of 6 rows of volume data (colors)
% 1 row of years
% name of kilometers
% Criteria(if you would like to change them)
% OUTPUT
%plot with lines per km in different colors
%legend with RMSE * yearbreak
% [RMSE] = table with RMSE of the other lines RMSE(1,:) is of one-line plot
% for all km. RMSE 2(,:) is of two-line plot. etc etc.
%% Init
km2 = [];
o = 'YEARBREAKS:';
p = 'RMSE:' ;
BP1conc = [] ;
BP2_1conc = [] ;
BP2_2conc = [] ;
data = totvol;
km = name ;
[u,i] = size(data) ;
colors = [ 1,0,0,1,0.6,0; ...
0,0,1,0.5,0,1; ...
0,1,0,0,0.8,1; ] ;
fullscreen = get(0,'ScreenSize');
figure('Position',[0 -50 fullscreen(3) fullscreen(4)])
%% Setting Criteria (not used)
r3r2 = 1.23 ;
r2r1 = 1.5 ;
r1r3 = 0.7 ;
%% Dissing NaNs
for j = 1:u
nan = isnan(data(j,:)) ;
[~,joc] = find(nan == 1) ;
ha = max(joc) ;
if isempty(ha) == 1
ha = 0 ;
%
else
%
ha = ha ;
end
48
startyear(j) = ha+1 ;
%% Calculating breakpoints
BP1 =
brokenstickregression(years(1,startyear(j):i),data(j,startyear(j):i),2)
BP1conc = [BP1conc, BP1(2,1)] ;
BP2 =
brokenstickregression(years(1,startyear(j):i),data(j,startyear(j):i),3)
BP2_1conc = [BP2_1conc, BP2(2,1)] ;
BP2_2conc = [BP2_2conc, BP2(3,1)] ;
;
;
%Unrounded Breaks of trendline
%
BP1conc = BP1conc ;
BP2conc = [BP2_1conc;BP2_2conc] ;
%% Calculating trendlines from breakpoints
locbreak1 = find(years == round(BP1conc(1,j))) ;
%
locbreak1 = locbreak1 - 1 ;
% locbreak2 = locbreak + 0.5 ;
locbreak2 = find(years == round(BP2conc(1,j))) ;
%
locbreak2 = locbreak2 - 1 ;
locbreak2_2 = find(years == round(BP2conc(2,j))) ;
if round(BP1(2))>= round(BP1(3))-2
locbreak1 = locbreak1-2 ;
end
if round(BP1(2))<= round(BP1(1))+2
locbreak1 = locbreak1+2 ;
end
if round(BP2(2))<= round(BP2(1))+2
locbreak2 = locbreak2+2 ;
end
if round(BP2(2))>= round(BP2(3))-2
locbreak2 = locbreak2-2 ;
end
if round(BP2(3))>= round(BP2(4))-2
locbreak2_2 = locbreak2_2 - 2 ;
end
%One trendline through data
[sl1,~,~,r1,~] = linreg(data(j,startyear(j):i)',
years(1,startyear(j):i)',[] ) ;
%Two trendlines through data
49
[sl2,~,~,r2,~] = linreg(data(j,startyear(j):locbreak1)',
years(1,startyear(j):locbreak1)',[] ) ;
[sl2_2,~,~,r2_2,~] = linreg(data(j,locbreak1:i)', years(1,locbreak1:i)',[]
) ;
% Three trendlines through data
[sl3,~,~,r3,~] = linreg(data(j,startyear(j):locbreak2)',
years(1,startyear(j):locbreak2)',[] ) ;
[sl3_2,~,~,r3_2,~] = linreg(data(j,locbreak2:locbreak2_2)',
years(1,locbreak2:locbreak2_2)',[] ) ;
[sl3_3,~,~,r3_3,~] = linreg(data(j,locbreak2_2:i)',
years(1,locbreak2_2:i)',[] ) ;
r1all(j) = r1 ;
r2mean(j) = (r2+r2_2)/2 ;
r3mean(j) = (r3+r3_2+r3_3)/3 ;
%% Comparing Criteria & plotting
if 1.46*r3mean(j)<r2mean(j)
plot(years, data(j,:),'color',colors(:,j),
'linestyle','.','markersize', 15)
y= sl3(1)*years(startyear(j):locbreak2)+sl3(2) ;
y2= sl3_2(1)*years(locbreak2:locbreak2_2)+sl3_2(2) ;
y3= sl3_3(1)*years(locbreak2_2:i)+sl3_3(2) ;
hold on
plot(years(startyear(j):locbreak2),y, 'color',colors(:,j),'linewidth',
1.5)
plot(years(1,locbreak2:locbreak2_2),y2,
'color',colors(:,j),'linewidth', 1.5)
plot(years(1,locbreak2_2:i),y3, 'color',colors(:,j),'linewidth', 1.5)
km2 = [km2, km(j), 'Trendline 1','Trendline 2', 'Trendline 3'] ;
o = [o,km(j),{BP2(2,1)},{BP2(3,1)}] ;
p = [p,km(j),{r3mean(j)}] ;
else
if 1.5*r2mean(j)< r1
plot(years, data(j,:),'color',colors(:,j),
'linestyle','.','markersize', 15)
y= sl2(1)*years(startyear(j):locbreak1)+sl2(2) ;
y2= sl2_2(1)*years(1,locbreak1:i)+sl2_2(2) ;
hold on
plot(years(startyear(j):locbreak1),y,
'color',colors(:,j),'linewidth', 1.5)
plot(years(1,locbreak1:i),y2, 'color',colors(:,j),'linewidth', 1.5)
km2 = [km2, km(j), 'Trendline 1','Trendline 2'] ;
g = {BP1(2,1)} ;
o = [o,km(j),g] ;
p = [p,km(j),{r2mean(j)}] ;
else
if 0.60* r1 <r3mean
plot(years, data(j,:),'color',colors(:,j),
'linestyle','.','markersize', 15)
y= sl1(1)*years(startyear(j):i)+sl1(2) ;
hold on
50
plot(years(startyear(j):i),y, 'color',colors(:,j),'linewidth',
1.5)
km2 = [km2, km(j),'Trendline'] ;
o = [o,km(j),'No Breakpoint'] ;
p = [p,km(j),{r1}] ;
else
plot(years, data(j,:),'color',colors(:,j),
'linestyle','.','markersize', 15)
y= sl3(1)*years(startyear(j):locbreak2)+sl3(2) ;
y2= sl3_2(1)*years(locbreak2:locbreak2_2)+sl3_2(2) ;
y3= sl3_3(1)*years(1,locbreak2_2:i)+sl3_3(2) ;
hold on
plot(years(startyear(j):locbreak2),y,
'color',colors(:,j),'linewidth', 1.5)
plot(years(1,locbreak2:locbreak2_2),y2,
'color',colors(:,j),'linewidth', 1.5)
plot(years(1,locbreak2_2:i),y3,
'color',colors(:,j),'linewidth', 1.5)
km2 = [km2, km(j), 'Trendline 1','Trendline 2', 'Trendline 3']
;
o = [o,km(j),{BP2(2,1)},{BP2(3,1)}] ;
p = [p,km(j),{r3mean(j)}] ;
end
end
end
hold on
end
%% Some plotting Visuals & Important data
RMSE = [r1all;r2mean;r3mean] ;
jo = legend(km2, 'fontsize', 16);
set(jo, 'Color', 'white', 'location','bestoutside')
set(findobj('type','axes'),'fontsize',14)
set(get(gcf,'CurrentAxes'),'FontName','Arial')
title('Best fit of Trendline(s)', 'fontsize', 24) ;
xlabel('Year', 'fontsize', 20)
ylabel('Volume (Cubic meters)', 'fontsize', 20)
annotation('textbox', [0.14,0.58,0.10,0.33],'string', o, 'fontsize', 14)
annotation('textbox', [0.25,0.58,0.10,0.33],'string', p, 'fontsize', 14)
51