The bathymetric survey of Lake Vrana included a wide range of activities
that were performed in several different stages, in accordance with the
standards set by the International Hydrographic Organization. The survey was
conducted using an integrated measuring system which consisted of three main
parts: a single-beam sonar HydroStar 4300 and GPS devices; a Ashtech
ProMark 500 base, and a Thales Z-Max^{®} rover. A
total of 12 851 points were gathered.

In order to find continuous surfaces necessary for analysing the morphology of the bed of Lake Vrana, it was necessary to approximate values in certain areas that were not directly measured, by using an appropriate interpolation method. The main aims of this research were as follows: (a) to compare the efficiency of 14 different interpolation methods and discover the most appropriate interpolators for the development of a raster model; (b) to calculate the surface area and volume of Lake Vrana, and (c) to compare the differences in calculations between separate raster models. The best deterministic method of interpolation was multiquadric RBF (radio basis function), and the best geostatistical method was ordinary cokriging. The root mean square error in both methods measured less than 0.3 m.

The quality of the interpolation methods was analysed in two phases. The first phase used only points gathered by bathymetric measurement, while the second phase also included points gathered by photogrammetric restitution.

The first bathymetric map of Lake Vrana in Croatia was produced, as well as scenarios of minimum and maximum water levels. The calculation also included the percentage of flooded areas and cadastre plots in the case of a 2 m increase in the water level. The research presented new scientific and methodological data related to the bathymetric features, surface area and volume of Lake Vrana.

Bathymetric surveying has undergone many conceptual changes in the last few decades, especially since the mid 20th century due to the availability of the single-beam echo sounder. Rapid advances continued with the development of multi-beam sounders and laser systems (airborne laser sounding systems) which can gather high-density data samples and enable the development of a realistic underwater bottom model (Finkl et al., 2004; Ernstsen et al., 2006).

The process of hydrographic measurement includes measurement and
establishing the configuration of the bottom of an ocean, sea, river, lake
or any other water-related object on Earth (NOAA, 1976). The main goal of
most such hydrographic surveys is to gain data necessary to develop nautical
charts featuring special details of types of navigational hazards. Other
goals include gaining information crucial to the management and protection
of coastal areas, exploitation of resources, national spatial data
infrastructure and tourism purposes. (IHO, 2005). Contemporary bathymetry, as a
field within hydrography, is the science of measuring depths and determining
the physical properties of the underwater features on the basis of analysing
data gained from recorded profiles. There are several different methods and
techniques for bathymetric measurement, which depend on the complexity of
the project. The success of bathymetric measurement depends mostly on a
detailed planning process, which in turn enables the organization and
tracking of the measurement process from start to finish (IHO, 2005). During
this particular research, the measurement plan included a wide range of
activities and was performed in several phases according to the standards of
the International Hydrographic Organization. The area surveyed included the
whole of Lake Vrana, with a total surface area of 29.865 km

Because the Earth's landforms can be extremely complex, most scientists opt for research via the development and analysis of digital elevation models (DEM) (Dikau et al., 1995; Bishop and Shroder, 2000; Millaresis and Argialas, 2000; Wilson and Gallant, 2000; Tucker et al., 2001; Shary et al., 2002; Chaplot et al., 2006; Wilson, 2011). Most gathered data in elevation sets are point-related, regardless of rapid developments in technology (Wilson and Gallant, 2000; Li et al., 2005; Fisher and Tate, 2006; Wilson, 2011). In order to find continuous surfaces, which are necessary for the process of understanding our environment, some values need to be approximated for areas which are not measured directly. This is done using various methods of interpolation (Collins and Bolstad, 1996; Hartkamp et al., 1999; Hu et al., 2004; Naoum and Tsanis, 2004; Li and Heap, 2008; Erdogan, 2009). The final result of the interpolation is the model that approximates or simplifies the Earth's surface. Each method produces a different result, so the main challenge is to determine the characteristics of errors and variability of approximated values by comparing and testing different interpolation methods.

The bathymetric survey of Lake Vrana was performed in order to enable optimal management of the water level, to classify the lake's bottom, to create a model and bathymetric map, and to enable better management and protection of the lake's flora and fauna. This process includes all the hydro-technical measures which can determine changes of the time-and-space distribution of affected water, enabling a more efficient management of natural water resources. The water regime includes the entire dynamics of constant change: quantitative and qualitative water characteristics and the dynamics of the interchange between water and the environment (Ožanić, 2002; Kuspilić, 2008). A lack of systematic water regime management has led to extreme fluctuations in the water level, salinity, temperature and oxygen levels. This has resulted in lakes being under-exploited and under-protected in many ways, for example in terms of tourism, water resource use, biodiversity and ecology. The unsatisfactory protection culminated in a series of negative consequences in 2012, when a record number of fish died (Večernji list, 2012).

An optimal water regime can only be achieved if the amount of water in the lake is known at any moment, and if Prosika drainage canal has a regulatory water infrastructure, as well as an efficient drainage ditch used to regulate the water level, depending on the season. The canal (dimensions: 875 m length, 8 m width and 4–5 m depth) which connects Lake Vrana and the Adriatic Sea was dug through in 1770 to attain new agricultural areas in Vrana fields and protect them from seasonal flooding.

The main aims of this research are as follows: (1) to compare the efficiency of 14 methods of interpolation and determine the most appropriate interpolators for the development of a raster model of the lake (on the basis of data gained by bathymetry and by using the cross-validation method); (2) to calculate the surface area and volume of the lake and to compare the results between the raster models; (3) to develop the first bathymetric map of Lake Vrana which will enable calculation of the percentage of flooded areas in the Lake Vrana Nature Park and the flooded plots, in the case of a 2 m rise in the water level. This will serve as tool for developing a scenario for future changes in water level.

Lake Vrana in Dalmatia is the largest natural lake in Croatia, with a surface
area of 30.2 km

The surface area of the lake changes frequently. During the period from 1948 to 2008, the lowest water level was 15 cm (measured in reference to the Prosika gauge) or 0.03 m above sea level, measured in 1990 and 2008. Prosika gauge is located in the north part of the Prosika drainage canal (Fig. 1). The highest water level was 236 cm, measured with reference to the Prosika gauge (2.24 m a.s.l. measured in 1974 and 1994). The mean value was 0.81 m a.s.l. (JUPPVJ, 2010). The water level is influenced by factors such as inflow, drainage and evaporation, but also by complex hydrological and hydraulic effects such as water balance, salt and fresh water content, sea tides and other factors influencing changes in sea level (JUPPVJ, 2010).

Study area with ordinary river basin.

The characteristics of Lake Vrana water system affected the selection of
methods for the bathymetric survey. The area included Lake Vrana in its
entirety, with a surface area of 29.865 km

The lake is characterized by following characteristics:

A high percentage of shallow water – over 65% of the lake's
surface – features a water depth of

Low vertical dissection – the absolute vertical difference over the
entire area of the lake bottom – is only 3.46 m. More than 90 % of the
lake's bottom features a slope inclination of 2

Low water transparency and high turbidity, especially during even the slightest winds.

Lush vegetation (grass) on the lake's bottom and the surrounding
shoreline (

Significant seasonal oscillations in the lake's water level.

Coverage of parts of the lake's bottom by unconsolidate sediments.

Based on the characteristics of the lake, more efficient techniques, such as measuring using a multi-beam echo sonar, or laser sonar, would have been inappropriate, considering the morphology of the bottom. The percentage of the recorded bottom would increase greatly in relation to recordings from a single-beam sonar, but the cost of the survey and amount of data acquired would significantly increase as well. After consideration, it was clear that the most efficient solution was bathymetric measurement and the use of a single-beam ultrasound device.

In order to avoid frontal waves (proposed by IHO, 2005), an inflatable Hondawave boat was used (Fig. 2a). The boat was the optimal vehicle due to its small dimensions (3.85 m) and economical engine, and because it was easy to install the surveying equipment on it.

The bathymetric measurement was performed using an integrated measuring
system (Fig. 3) Installed equipment included three main components: a
HydroStar 4300 sonar, GPS devices Ashtech ProMark 500
and a Thales Z-Max^{®}. These were connected via the Real-Time Kinematic (RTK) controller
Juniper System-Allegro, which enabled real-time connection and data registration in the
FAST Survey programme. This enabled recording of the sonar coordinates and
corresponding depth. The programme automatically recalculated the
coordinates from the GPS into the local projection coordinates. The selected
projection was the universal transverse Mercator, Gauss–Krüger shape
with a central meridian of 15, a factor of scale change of 0.9999 and a
false easting of 5 500 000. The Bessel 1841 ellipsoid was used.

Integrated measuring system – combination of GPS-RTK and a sonar.

Two GPS devices were also used: a base or referential device (Fig. 2b), which was positioned according to precisely determined coordinates, and a rover device (Fig. 2c), which was used in the work area. A data-exchanging connection was established between them via a UHF radio transmitter, which would also have been possible via various GSM devices.

The distance between the base and referential devices had to be determined in advance, in order to achieve an adequate degree of precision. This was named the base line and its maximum value was 50 km. The distance between the base GPS and the UHF transmitter had to be a minimum of 10 m.

Since the UHF signal was rather weak throughout the lake, three base points
were determined using the Ashtech ProMark 500 and CROPOS system: (1)
coordinates

A dual-frequency probe was fixed to this support with a rover GPS device submerged 20 cm below the water level (Fig. 2c). This arrangement was necessary due to the shallow water of the lake and low water level at the northwest end. Since the HydroStar 4300 sonar supports depth recording simultaneously at two frequencies, the survey was conducted at two frequencies: low – 30 kHz and high – 200 kHz.

The bathymetric survey was performed according to the previously established profiles, on a geo-referential cartographic surface (digital orthophoto (DGU, 2012a) and Croatian base map (DGU, 2012b) to the scale 1 : 5000). The basic measuring profiles were planned perpendicular to the slope of the terrain, in a northeast–southwest direction. The planned profiles of the survey (basic bathymetric profiles) ensured good coverage and high resolution in the research area. The survey also included four transversal profiles which intersected with the main profiles, enabling the comparison and control of the measured depths.

Within the borders of the shoreline of Lake Vrana, 375 basic profiles were achieved. The distance between adjacent profiles was set at 200 m, which corresponds to the desired mapping resolution to the scale 1:30 000.

The time frame, and the first day of the survey were determined by the water level. The water level is important since is it impossible to register a depth of more than 0.5 m by the transducer. Weather conditions are important for navigation and the quality of data registration (Fig. 4). Wind, rain, waves and cold, for example, are usually limiting factors. Weather reports and water level oscillations were continuously observed from the production of preliminary plans in November 2010 until the beginning of the survey.

The effect of frontal

The measurement process was conducted in two phases (Fig. 5): (1) from 10 to 12 May 2012, and (2) from 7 to 9 June 2012.

The first phase took 2 days, and included a survey of 14.351 km

The data obtained from measurement were transferred to a PC via the Juniper System-Allegro controller and the FAST Survey programme package for further processing and interpolation. During measurement, the controller creates a separate file with information regarding the point coordinates, time obtained, and depth recorded. Data processing included filtering out noise, calibrating the checked depths to a common referential level and interpolation. The filtering process was implemented according to a programme which enabled the removal of errors in the data registry (Fabulić, 2012). Records of water depth were calibrated in relation to the Prosika benchmark and measuring gauge.

Since parts of Lake Vrana are quite difficult to survey, measurements taken by ultrasound showed some background noise. In simple terms, the ultrasound beam bounces off the first obstacle it encounters, so the echo sounder calculates the distance to that obstacle and represents it as a depth measurement. However, such obstacles are not always at the bottom of the lake, and indeed, random noise may be generated by floating matter, plankton, fish, or vegetation (Pribičević et al., 2007). These sounds need to be filtered and reduced in order to obtain correct, usable data. An additional caution is necessary when filtering such data. Low frequencies (30 kHz) cannot penetrate the dense, complex, “sedimentary” vegetation which forms the new bottom. As a result, the low-frequency measurement did not yield adequate results, since it could not properly determine the density of the silt or vegetation, or the boundary between the rocky and muddy bottom. Therefore it was used only during the first day of the survey. Another deficiency recorded using low frequency was significant leaps in profiles, especially in places where the frequency penetrated the vegetation and muddy deposits. This also indicated significant differences in the levels of muddy deposits. In order to perform a more detailed analysis, a sediment profiler should be used, featuring a frequency of up to 15 kHz, which could be used to gain detailed information regarding the lake's bottom (Lafferty et al., 2005; Pribičević et al., 2007). Since the lake is shallow, and water transparency during the survey was relatively good, it was relatively easy to determine the features of the lake's bottom and differentiate vegetated from non-vegetated areas.

The phases and plan of the bathymetric survey.

The spatial interpolation methods have been applied to many disciplines, where the most prominent are from the environmental sciences (Burrough and McDonnell, 1998; Webster and Oliver, 2001; Zhou et al., 2007). In comprehensive published studies, many authors (Aguilar et al., 2005; Weng, 2006; Zhou et al., 2007; Li and Heap, 2008; Heritage et al., 2009; Guarneri and Weih Jr., 2012; Tan and Xiao, 2014) compared the performance of the spatial interpolation methods. Some studies indicate that among the many existing interpolation techniques, geostatistical ones perform better than the others and vice versa (Li and Heap, 2008). Although there have been many studies on the accuracy of interpolation techniques for the generation of digital elevation models (DEMs) there is still a need to evaluate the performance of these techniques (Chaplot et al., 2006) because there are still no consistent findings about the performances of the spatial interpolators (Li and Heap, 2008; Tan and Xiao, 2014). In this paper we compared the 14 interpolation methods implemented in the Geostatistical Analyst extension (ESRI, 2013).

The most appropriate methods have been chosen, based on seven statistical parameters: minimum value, maximum value, range, sum value, mean value, variance and standard deviation. Of these, standard deviation, or root mean square error, is especially worth mentioning, since it is the most used method worldwide for determining the precision of digital elevation models (Yang and Hodler, 2000; Aguilar et al., 2005). In addition to analysing parameters, interpolation methods were compared on the basis of high-fidelity, two-dimensional and three-dimensional graphic representations of data sets. Volume comparison methods were also used, by employing various algorithms, as well as methods for calculating and comparing profiles (Pribičević et al., 2007; Medved et al., 2010).

In order to compare the accuracy of the interpolation methods, the method of cross-validation was used. Most authors suggest using this method in order to achieve a successful evaluation of accuracy (Cressie, 1993; Smith et al., 2003; Webster and Oliver, 2007; Hofierka et al., 2007).

The 14 interpolation methods were used as follows (with abbreviations):

Deterministic methods: inverse distance weighting (IDW), local polynomial function (LP),

RBF (radial basis function) – completely regularized spline (CRS), RBF – spline with tension (SWT), RBF – multiquadric function (MQ) and RBF – inverse multiquadric (IMQ).

Geostatistical methods: ordinary kriging (OK), simple kriging (SK), universal kriging (UK), disjunctive kriging (DK), ordinary cokriging (OCK), simple cokriging (SCK), universal cokriging (UCK) and disjunctive cokriging (DCK).

In order to generate continuous areas necessary for research and knowledge of the bottom of Lake Vrana, it was necessary to approximate values in areas that were not sampled directly. This was done using various interpolation methods. The effectiveness (quality) of interpolation methods was analysed in two phases. In the first phase, 12 851 points were used to develop a model of the lake and compare interpolation methods. The second phase covered 30 233 points. Using the ArcGIS extension within the Geostatistical Analyst programme, interpolation parameters were automatically optimized for each interpolation method (Table 1).

Four parameters influenced the quality of the output deterministic methods results: distance exponent, number of neighbours, distance and number of sectors. The number of neighbours which influenced an approximated point was set at 15. The criteria for distance used a circular search zone with a defined distance radius. All methods, except local polynomial methods, featured a radius of 3619.9 m (Table 1).

Parameters of interpolation methods calculated only on point data gathered by bathymetric measurement.

Geostatistical methods are more demanding to process, since they require semi-variogram modelling and the appertaining defining parameters.

Cross-validation results calculated only on point data gathered by bathymetric measurement.

The first phase showed that all methods of interpolation showed satisfying
results based on the ranges of values of the standard deviation (0.058 m),
and were adequate for developing digital elevation models of the lake, since
they had similar parameter values (Table 2). The main reason for this is the
slight difference in depth values, low vertical dissection of the lake's
bottom and minimal percentage of elements with sudden leaps in height. The
range of value for standard deviation, considering the automatically
optimized parameters, was between 0.197 and 0.255 m. According to all
parameters, the best method was simple cokriging (0.197 m). The reasons for
that were the principle of the method's process (

Since most authors point out that the quality of stochastic methods depends on the choice of criteria regarding semi-variograms, a comparison was made between the criteria automatically determined by software and those manually determined for the ordinary cokriging method. The two most common theoretical models were tested: spherical and Gauss (Table 3). The purpose of manually assigning criteria is to find out the minimum deviation and minimum value for standard deviation. In the case of the spherical model, the minimum value of standard deviation was the distance of 1800 m (0.221 m). Unlike the automated software process, finding the minimum value of standard deviation manually is more difficult and time-consuming (it requires inputting the parameters of interpolation repeatedly until the minimum value is found).

Comparison of manually and automatically determined parameters of the interpolation method (example for OCK).

Table 3 shows that the output results regarding the standard deviation do not reveal significant differences. For example, the difference between automatic and manually found standard deviation in the case of the spherical model for 12 851 points is 0.011 m. However, it is notable that the maximum error in the approximation for the same model is 0.208 m greater (2.238 m).

According to Malvić (2008), a decrease in distance also decreases the
deviation, since the values of closer points are more similar than the
values of more distant ones. The decrease in deviation should decrease the
standard deviation calculated from the differences in the measured and the
approximated values. However, the quality of approximation in other parts of
the model might be questioned. By testing using ordinary kriging, the
conclusion was that the decrease in distance affected the standard deviation
positively, and negatively in areas that were not included in the direct
measurement. The values obtained in such areas greatly surpassed the values
of the surrounding measured points. For example, a semi-variogram for Lake
Vrana was made, which was used to compare 30 233 points. The determined
distance was 1200 m, and the standard deviation for 12 851 points was 0.298
m. For the distance of 12 000 m, the standard deviation was 0.471 m. In the
case of the first distance (1200 m) the lowest value of depth for the
entire model was

Areas that were not directly measured during the survey (red squares).

Points gathered by the bathymetric survey did not include the entire surface
of the lake, since the echo sounder could not gather data in areas above

Compared visually, the methods generally show the greatest differences in the smoothness of isobaths, which is logical since the differences between the chosen parameters are essentially negligible. A more detailed analysis indicates the results of certain methods (appearance of continuous surfaces at micro levels).

In order to develop a digital model of the lake that would enable various simulations, such as changes in the water level, it is necessary to consider the data that refer to the surrounding terrain (height data, gathered by aero-photogrammetry). The combination of precisely obtained data on heights and depths enables the interpolation for the areas that were not directly included in the survey. The output results turned out well, since the lake features mostly low, flattened shores.

Due to unusual output results in the first phase, the comparison of methods
of interpolation was repeated for 30 233 points within the Lake Vrana Nature
Park (Table 4). Of those points, 12 851 were depths (bathymetrically
measured points), and 17 832 were elevations (points with

Cross-validation results calculated for elevation data from two data sets, but statistic indicators are only for points gathered by bathymetric measurement.

Digital elevation models generated from surveyed data, showing differences between deterministic and geostatistical interpolation methods.

Ordinary cokriging turned out to be the best method of interpolation according to all relevant parameters (Table 4). Figure 7 clearly shows the characteristic of the simple kriging method, when the range of elevation data set in the study area is 307.23 m, in which case the mean value for the entire area is 38.02 m. Along with the ordinary cokriging method, satisfactory results were obtained from the inverse distance weighting method, RBF – multiquadratic and ordinary kriging. The standard deviation according to all three methods was less than 0.5 m.

The differences between the four best methods of interpolation are visible in the two-dimensional (Fig. 10a–d) and three-dimensional graphic representations. Figure 8a and b show the more vertically dissected part of the lake, with an AB profile, and a length of 1500 m, which was used as a further testing sample for the four best interpolation methods. The profile line was drawn so as to cover six bathymetrically measured points.

After drawing the profile line, it was necessary to calculate the
intersection for the defined profiles based on the regular network generated
by the interpolation, i.e. to convert the two-dimensional profiles into 3-D
lines which feature

This approach enabled comparison of the profiles, a clear representation of the interpolated lake's bottom and the detection of deviation between the bathymetrically measured points and those approximated by the model. Figure 9 shows a difference in the interpolation method of deterministic (inverse distance weighting, RBF – multiquadratic) and geostatistical methods (ordinary kriging, ordinary cokriging).

Differences in profile for the four best interpolation methods.

Representation of contours in part of the lake (difference between interpolation methods).

The final result of comparing methods of interpolation using ArcGIS extension
Geostatistical Analyst is to obtain a regular spatial network or grid. Usually, the greatest
problem is deciding between greater spatial resolution or pixel size
(Hengl, 2006). In this case, the software optimized the pixel size at 40 m. The spatial resolution corresponds to McCullagh's (1988) method of
determining pixel size. The size was calculated using a grid calculator and
the method of point sample analysis (Hengl, 2006). On the basis of 12 851
points and an area of 29.865 km

The final phase of bathymetric research involved calculating the lake's surface area and volume (Diolaiuti et al., 2005; Ahmed, 2010). The output results of a certain analysis depend on the method of data gathering, dissection of the lake bottom of the lake density and distribution of points, spatial resolution (pixel size), algorithms and the interpolation method used.

The volume of a lake can be efficiently calculated by a regular grid
obtained by using a certain interpolation method. The calculation process
was relatively simple, since the number of pixels was known (18 714), as
well as the surface (40 m

In order to compare it with other algorithms, the volume was calculated for
the regular spatial grid, obtained by the ordinary cokriging interpolation
method. The volume amounted to 49 783 536 m

In order to calculate the volume, three more complex Newton–Cotes formulae
were used: (1) the extended trapezoidal rule, (2) the extended Simpson's

Volume, surface and perimeter of Lake Vrana at 0.4 m water level in reference to the Prosika gauge.

Table 5 shows calculated values for the volume derived from Newton–Cotes formulae, applied to five different methods of interpolation. Since every method displays a certain level of error in the approximation of the volume, arithmetical means for the three methods were also calculated.

The border of the lake for all the models was an isobath at 0.4 m, obtained by interpolating bathymetrically measured depth data and terrain elevation data obtained by aero-photogrammetry. The isobath was converted into a polygon, which was used to determine a raster model within the borders of the polygon. Results of the measurements of surface, perimeter and volume of the lake, regardless of the formula used, greatly depend on the model developed by interpolation (Table 5).

Perimeter and surface area of Lake Vrana at various water levels, for the most suitable (OCK) interpolation method.

The surface area of Lake Vrana, in relation to its water level (which
annually oscillates by 1.93 m) varies by almost 4 km

The total surface area of the lake is 30.815 km

The average width of the lake is 2201.4 m (minimum 262.26 and maximum 3469.31 m). The average length of the longitudinal profiles is 8765.43 m (minimum 1843.55 and maximum 13 245.34 m). These values were obtained by analysing 68 transverse (northeast–southwest) and 17 longitudinal (southeast–northwest) profiles at 200 m intervals (at the water level of 0.4 m).

The last phase of digital terrain modelling refers to the application of a model (Weibel and Heller, 1991; Hutchinson and Gallant, 2000; Hengl et al., 2003; Oksanen, 2006), therefore this research visualized the annual water level oscillation. A scenario was made for the northwestern Jasen inundation area, outside the Nature Park (Fig. 11). A section of the flooded habitats and cadastre plots within the Nature Park were also determined (Table 7), at a water level of 2 m (Fig. 12).

Annual water level oscillation in the northern part of Lake Vrana Nature Park (probable scenario in case the Jasen water pump stops working).

Percentage of flooded habitats at the water level of 2 m in reference to the Prosika gauge.

The water level map at 2 m was overlaid with the map of habitats for Lake Vrana Nature Park to the scale of 1 : 5000. The map was made in accordance with the rules of National Croatian Habitat Classification and comprises 30 classes of habitats (Jelaska, 2010). A sudden change in the water level can change the ecological features of a particular habitat, affecting the flora and fauna of Lake Vrana Nature Park. The analysis concluded that almost half the habitats are endangered if the water level rises to 2 m. The highest level of threat (100 %) relates to Illyrian-sub-Mediterranean river valley meadows and the lowest level (1 %) relates to brambles. It is worth noting that 52.7 % of the endangered areas are consolidated arable lands with monoculture crops (cereals), while 18.3 % (37.8 ha) are complex mosaics of crops.

Most field parcels in the park are used for intensive agricultural purposes.
The northern part of the park features horticultural plants with multiannual
crop rotations. Plants include mostly hybrid species. Various agrotechnical
methods are used in order to produce a better level of crop success, as well
as fertilizers and chemical components for plant protection (JUPPVJ, 2010).
In the northwestern lake area, there is a mixed culture of olive fields,
vineyards, horticulture and some cereal crops (JUPPVJ, 2010). Should the
water level rise by 2 m, it would partially or completely threaten
45.94 % of the cadastre plots. In the northern part of the park (a flatter
area), flooding would threaten the entire area. In the northwestern part,
flooding would mostly threaten areas at a lower elevation. These areas have
been more susceptible to flooding in the past, as is evident from the
specific shape of the field parcels (especially in the northwestern part).
The parcels there are narrow (10 m on average) and extremely elongated
(150 m). The inclination of these parcels (2–5

The results of this research show that the output results of the digital terrain modelling and corresponding analyses depend on the data-gathering methods, density of samples, interpolation methods, terrain features (mostly vertical dissection), pixel size and algorithms applied. In the research, 14 methods of interpolation were compared; six deterministic and eight geostatistical. Of the five most common methods for gathering elevation data and comparing interpolation methods, two sets of data were used (depth and elevation). They were obtained by various methods, techniques and procedures: bathymetry and aero-photogrammetry. The conclusion is that there is no universal method of interpolation which shows the best results in both sets of data, since the output results depend on the data-gathering method. For example, an optimal method for developing a DEM of the lake's shore was developed, but it turned out to be inadequate for developing a DEM of the lake's bottom. In addition, regardless of the fact that certain authors point out either deterministic or geostatistical methods as more advantageous, it is important to note that there is no single best interpolation method, since they are all conditioned by spatial and temporal components. This means that the result of the comparison and selection of the best method are in fact provisional and dependent on time and space components, the technology used to gather and process data and the area of research.

The fact that geostatistical methods of interpolation employ mathematical functions and the probability theory was one of the reasons for hypothesizing that geostatistical methods would be better interpolators. This was proven, but the research also showed that the differences between geostatistical and deterministic methods were negligible. The multi-quadratic function, as the globally most commonly accepted method, was proven to be the best radial basic function, but also one of the best deterministic interpolation methods in general.

In order to develop a digital model from the bathymetrically gathered data, 14 interpolation methods were compared in two phases. In the first phase (which used 12 851 bathymetrically measured points), all the methods compared showed good results, due to the low vertical dissection of the terrain. By using the method of cross-validation and analysing statistical parameters, the conclusion was that the best results were yielded by the simple cokriging method (the standard deviation was 0.197 m).

The range of the standard deviation for all 14 methods was between 0.197 and 0.255 m. Due to characteristic issues with output results and the problem of extrapolating data in the first phase, the process of comparing interpolation methods was repeated for the sample of 30 233 points within Lake Vrana Nature Park. The output results in the second phase were notably different, and the majority of methods applied showed imperfections. According to all the statistical parameters, the best method of interpolation was ordinary cokriging (Fig. 13). Along with ordinary cokriging, good results were shown by the inverse distance weighting method, RBF – multiquadratic method and ordinary kriging. The standard deviation for all three methods was less than 0.5 m. These methods were compared by graphic representation, calculation and comparison of the profiles, surface area and volume of the lake. The conclusion was that there were no significant differences between the statistical indicators in deterministic or geostatistical methods, whether the parameters were determined automatically or manually. However, by testing the ordinary kriging method, the conclusion was that the reduction in the distance positively affected standard deviation, but negatively affected approximation in the areas that were not included in the direct survey. The interpolated values in those areas turned out to be much greater than the values actually measured at the surrounding points.

Flooded agricultural parcels in the Pakoštane cadastre at a water level of 2 m (northwestern section of the park).

Bathymetric map of Lake Vrana (ordinary cokriging).

Based on the optimal method of interpolation, the lake's surface area,
perimeter and volume were calculated at the water level of 0.4 m in
reference to the Prosika gauge. The surface area of the lake is 29.865 km

All the analyses and conclusions derived can be used for further research on data-gathering methods, interpolation methods, methods of spatial resolution selection and methods of digital terrain analysis. In any future research of Lake Vrana, it would be useful to extend the profiles during the survey, if a single-beam sounder is used, so that the distance between the profiles is no greater than 50 m. In that case the relation between the profiles and the data gathered from the profiles (every 10 m) would be much more proportional. In addition, it would be useful to compare the results of the development of the lake's bottom model using single-beam, multi-beam and laser sounder techniques. It is important to note that the more efficient techniques, such as multi-beam ultrasound or laser measurement, might not yield significantly better results due to the morphology of the bottom and the relatively high percentage of dense, native vegetation. The portion of the bottom surveyed would increase in relation to the portion surveyed with the single-beam sounder, but the costs of such research would drastically increase, as well as the amount of data yielded for the processing. In that case, processing stations would have to be employed as well. A frequency of under 15 kHz is recommended for future research, in order to determine the density and volume of sediments. Since 4.6 % of the lake's surface is covered in dense vegetation, it was difficult to determine the exact borders. The dense vegetation prevents sounders from effectively reaching the surface. In order to avoid extrapolation in the bordering areas, the research employed elevation data obtained by aero-photogrammetry and stereo-restitution, where the average distance between the elevation points was 90 m. If future interpolation projects aim for a higher level of precision in the bordering areas, it will be necessary to reduce the distance between the elevation points. Recommended methods include aerolaser or aero-photogrammetry. In this case, the distance between the points should be less during stereo-restitution (maximum 10 m).

The data measured and evaluated enable the development of hydrological and hydro-technical studies which would result in an optimal water level, ensure a biological minimum and economical water minimum, and optimize the water system. In order to determine the volume of the lake, it was necessary to map the lake's bottom, gather data required for the development of the digital elevation model and make a topographic map of the lake's bottom and shoreline relative to its optimal water level, thus creating a sound basis for future activities.

We would like to thank anonymous reviewers for valuable comments on the earlier versions of the manuscript, and editor Dominic Mazvimavi who helped to improve the final version. Edited by: D. Mazvimavi