The effect of sand nourishments on foredune sediment volume
N. van der Zwaag
John van Boxel
Keywords: Nourishment, foredunes, sediment, volume, statistics
Table of Contents
1. Summary...... 2
2. Introduction...... 3
3. Goal...... 3
4. 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
5. 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
6. 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
7. Conclusions...... 19
8. Literature...... 20
9. 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
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.
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.
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?
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.
Data import profile
Data import kilometer
Finding landward boundary
Calculating total volume
Fitting Trend lines
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 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.
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.
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.
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.
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 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.
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.