Introduction

This study is part of a broader research project in northern Namibia concerning the topics of floods and droughts and their effects on water quality in the Iishana region. Regarding floods, ongoing investigations are made to understand the hydrological system characterized by ephemeral Iishana. These net-like distributed pans may fill with water during the rainy season and inundate leading to large floods that negatively affect the Iishana region and its inhabitants. Consequences include the loss of lives and high economic losses.

Up to now, a synoptic flood forecast system is only available for the entire African continent, produced by the National Oceanic and Atmospheric Administration and its Climate Prediction Center. Detailed flood routing and prediction systems are neither available at a regional level, nor for the study area. Nevertheless, efforts have been made to prevent susceptible areas from floods: for example, the Namibian Early Flood Warning System, which was a sensor web-based pilot project starting in 2008. However, due to the large costs the project was not founded until the end (Mandl et al. 2012) and no longer exists. Further work has been done by Skakun et al. (2012), who extracted the maximum flood extents from satellite images for flood risk assessment. In addition, Awadallah and Tabet (2015) estimated flood extents via remote sensing data. Goormans et al. (2015) set up the first hydrological and hydrodynamic model for the Iihana region. They focused on the city region of Oshakati and modeled the effect of a dyke, which was planned by the Ministry of Regional and Local Government, Housing and Rural Development—Oshakati Town Council in 2012 (Bethune et al. 2012) and was in some parts realized. Nevertheless, it still does not cover the whole Iishana region. For this reason, the aim is to develop a 2D-hydrodynamic flood model covering the whole Iishana area (Fig. 1). The objective is to provide flood risk maps as well as routable flood paths. Finally, retaining-measures will be suggested and the flood model will contribute to an early warning system in the context of a broader flood risk management plan. Therefore, the model requires many input parameters like data on land use, hydrology, topography and others.

Fig. 1
figure 1

Overview of the Cuvelai Basin and the study area of the Iishana region (source: Faulstich et al. (2018), database: UN-OCHAROSA (2018) and Digital Atlas of Namibia (2002), edited by Robert Arendt)

Full size image

This paper focuses on the topography in the study area and discusses the digital elevation model and its improvement in accuracy for flood model calculations in a further step by correcting TanDEM-X elevation data via GNSS data. Therefore, this study is less about the detailed approach of GNSS physics itself and more about the application and combination of GNSS techniques for enhancing database for further flood modeling.

Today’s modern satellites provide high-resolution images and have a high vertical and horizontal accuracy. For example, the TanDEM-X mission which delivers a digital elevation model for the whole planet with a horizontal accuracy of around 12 m and in vertical up to 2 m at least (Rizzoli et al. 2017). From the hydrological point of view, this is a great improvement to former resolutions like 20 m horizontal and 16 m to 10 m vertical accuracies of the Shuttle Radar Topography Mission (Smith 2003; Mukul et al. 2017). These advancements are important for experts modelling in the field of floods, creating more exact flood risk maps and improving the results of flood models. It becomes clear that accuracy is a factor of certainty, even more so if model results are later used for flood forecasts.

To enhance the vertical accuracy of the entire DEM, different filter algorithms have been used. Moreover, water surface interferences have been corrected by masking out (Wendleder et al. 2013) and using interpolation procedures. With these methods, natural and anthropogenic hydrological obstacles, like parts of vegetation and water-induced interferences or buildings, could be equalized. Anthropogenic obstacles, in this specific case road dams (Fig. 2), have been surveyed in real time by a GNSS sensor. These road dams play a significant role in the Iishana region, which is characterized by a very low relief where almost every small sink or elevation influences the flow dynamic. Using the GNSS sensor to localize specific points precisely on the ground has been a common method used in industry and science for years (Bisnath et al. 2003; Arroyo et al. 2005; Gao et al. 2005; Knoop et al. 2017). If using a differential system an accuracy in a millimeter range is readily achieved. However, differential GNS-systems always need a base station in a certain range, otherwise the accuracy decreases dramatically up to a loss of connection. For example, the Leica GS16 System works properly up to 1 km in differential mode. If this is not wide enough for a certain use, it is possible to use the common Real-Time Kinematic (RTK) or Network-RTK mode, like other GNS-Systems. Both RTK solutions receive their correction data either from a single or even from a network of reference stations a few kilometers nearby. These systems use UHF/VHF radio signals or mobile phone networks to send their correction data to the GNSS sensor. This technique is very well known in vehicle navigation and in cases of precision farming (Knoop et al. 2017; Shrivathsa and Panjwani 2017; Skog and Handel 2009; Gebbers and Adamchuk 2010; Dixon 2006). The accuracy of (Network-) RTK generated GNSS data differs in a sub-centimeter range. In terms of precision farming, the vehicles are driving slowly with a maximum speed of 11 km/h. Even here, their work range is limited by the availability of reference stations and their application is expensive (Perez-Ruiz and Upadhyaya 2012). Moreover, potential connection losses lead to reduced accuracy up to a meter range.

Fig. 2
figure 2

High road dam crossing an Oshana in transverse direction. Water flows from north to south through the culverts. The culverts (white dotted boxes) are heavily sedimented. (Photo and editing: Robert Arendt 2018)

Full size image

To become more independent, the Satellite Based Augmentation System (SBAS) was formerly invented for the offshore industry in the early 1990s (Barboux 2000). Offshore platforms need to be constructed precisely, although they are usually located far away from the coast. In these remote areas, no reference stations are available. This method nowadays is called Real-Time Precise Point Positioning. In this case, the GNSS system receives the correction data directly from a geostationary satellite, which makes it applicable all around the world (Skog and Handel 2009; Perez-Ruiz and Upadhyaya 2012).

In this study, a Leica GS16 Sensor was installed on the roof of a car. While driving along the road dams with a maximum speed of 80 km/h, elevation surveys were automatically corrected in real time via the commercial Leica SmartLink function within a centimeter of accuracy. After the days of recording, the data were corrected by eliminating outliers and redundant measurements. In a next step, the elevation data were implemented into the post processed TanDEM-dataset for further hydrodynamic calculations.

Materials and methods

Study area

Namibia’s climate is strongly influenced by the cold Benguela current along the west coast of South Africa leading to arid and semi-arid conditions. Determined by the Intertropical Convergence Zone (ITCZ), rainy season runs from October to April and dry season from May to September.

A hydrologically diverse region therein is the transboundary Cuvelai Basin, which itself is bounded to the north by the Kunene River and Okavango River in Angola and by the Etosha Pan on the south in Namibia. The western edge is defined by the city of Ruacana and the eastern edge lies between the cities of Okongo and Mpungu Vlei. The Cuvelai Basin is divided into eight major drainage zones (Mendelsohn et al. 2013).

In this case, the study area is part of the Iishana region, consisting of the Western Oshana Zone and the Central Oshana Zone (Cunningham et al. 1992). Reduced to the Namibian state territory, it is marked to the north by the Namibian-Angolan boarder. The western edge is marked by the city of Ruacana and in the east by the city of Oshakati (Faulstich et al. 2018) (Fig. 1). The annual amount of precipitation is between 350 up to 550 mm increasing from west to east and is characterized by high rainfall variability. The potential evaporation rises in the same direction from 2.600 to 3.200 mm (Mendelsohn et al. 2013; Persendt et al. 2015). The terrain is about 1.100–1.200 m a.s.l. and has a very flat slope ranging from 0.5 to 1.0 m/km (Mendelsohn et al. 2013). The surface hydrology is featured by a large ephemeral river system and is affected by irregular floods during rainy seasons (Sakakun et al. 2012; Kuliwoye 2010; Kundzewicz et al. 2014; Shifidi 2014). These low slope, net-like troughs and sinks run in a northwesterly to southeasterly direction. The water depth during floods is about 1–7 m. Namibia gains most of its rainfall in the study area. The soils are profitable for agricultural use. These circumstances lead to the fact that around 40% of Namibia’s population lives in the northern region (Mendelsohn et al. 2013). Nevertheless, next to near-surface Aeolian and fluvial sediments of clay deposits, lime and silicate crusts, produce low infiltration capacities and high surface runoff (Hüser et al. 2001; Nguno and Angombe 2011; Goudie and Viles 2015). These facts result in widespread flooding during rainy season. While most of the surface water comes from the Angolan side of the Iishana region, floods are intensified by local convective rain events. Fatal floods in the recent past have occurred in 2008, 2009, 2010, 2011 and 2013. The large inundations affected human lives, caused huge damage to health, extensive damage to property and technical infrastructures like roads, bridges and dams (Mandl et al. 2012; Skakun et al. 2012; Awdalla and Tabet 2015; Persendt et al. 2015; Bischofberger et al. 2015; Filali-Meknassi and Ouarda 2014; Mufeti 2013).

The hydrodynamic model

In this particular study, the specific flood prediction problem is a combination of multiple factors. The large catchment of about 10.000 km2 and the TanDEM-X raster resolution of 12.5 m needs a model that is able to handle the amount of data in an adequate time. Moreover, the model needs the ability to incorporate culverts and bridges. Furthermore, the relief is very flat (slope ranging from 0.5 to 1.0 m/km), the flow speeds of floods is low (Cunningham et al. 1992) and even low obstacles can substantially change the flow behavior instantly. Nonetheless, at the same time, these areas affected by floods should be recorded as precisely as possible. Therefore, the hydrodynamic model ‘FloodArea’ will be used in a future step to calculate the runoff, flow concentration, flow velocity, backwater situations and inundation depth for variable time steps. ‘FloodArea’ is based on a simplified hydraulic approach including hydrodynamic calculations for the simulation of large areas with high spatial resolution (< 1 m) (Fritsch et al. 2016). Successful applications have been made in large-scale simulations of catchments sized up to 3.000 km2 in Germany (Assmann et al. 2013). As mentioned above, the hydrodynamic calculation itself will not be discussed in this work. Further literature regarding ‘FloodArea’ is reported in Anders et al. (2016); Assman et al. (2013) and Fritsch et al. (2016).

Road dams and culverts

According to the cited TanDEM-X accuracy, small objects like road dams are not displayed. These road dams are elongated artificial fillings of earth material or rock on which a road runs. A road dam is designed to elevate and thus overcome geomorphological and topographical obstacles and thus has a landscape-shaping effect. It must not be compared to flood protection dams, because its construction is altogether simpler and not suitable as a flood protection measure. The road embankment has no overflows or other auxiliary structures, with the exception of culverts. Its structure is not designed for the lateral pressure of large water masses and additionally hinders natural flow processes and drainage channels.

Most of the roads in the study area are almost orthogonally affected by the Iishana system (Fig. 3), and the major cities are connected by the shortest route and lowest construction costs. During most of the year (normal rainy season and dry season), this infrastructure is not negatively affected by water. In the case of an “Efundja”, a local name for a major flood, they become vulnerable to overspilling and erosion (Mendelsohn et al. 2013).

Fig. 3
figure 3

Map including the surveyed road dams and culverts (source: Faulstich et al. (2018), database: UN-OCHAROSA (2018) and Digital Atlas of Namibia (2002), edited and mapping by Robert Arendt)

Full size image

On one hand, these road dams change the flow directions and hinder flow processes, which have to be taken into account by the hydrodynamic model. There is a water build-up and settlement structures in this area are more affected by the floods. Of course, during this time, these important infrastructure facilities cannot be used. As an example for the benefit of measuring and implementing these road dams into the DEM, the divergence in elevation between the TanDEM-X raw data and the GNSS measured values shows differences ranging from 0.125 up to 1.955 m ("GNSS and TanDEM-X cross validation" section).

On the other hand, culverts and bridges have to be included and incorporated into the model. The consideration of small structures like low walls or road dams is crucial to analyze flow paths and assess the influence of flow velocity. (Fritsch et al. 2016). Therefore, over 1000 culverts and bridges were mapped via google earth satellite images and have been cross-validated during the field trip via a hand hold Garmin e-Trex GPS (Fig. 3).

A high-resolution DEM including significant obstacles is essential for the accuracy in modeling surface runoff. An accurate DEM increases the predictive capacity of the flood model in terms of a better identification of main flow paths and local sinks, the locations of high flow depths and accelerated flow velocities (Fritsch et al. 2016). The exact magnitude of the advantage cannot yet be described until the model has been run, but can be assumed as enhanced as the flow path analysis shows in the results ("Corrected TanDEM-X" section). This analysis was done three times with different pre-settings. The fist flow path calculation considered the TanDEM-X raw data set by using just the ‘Fill’ function in advance. Otherwise, there would be no flow path calculation possible. The second calculation also used the filter algorithms ("DEM pre-processing and correction" section). The third calculation included more than 1000 culverts and bridges (Fig. 3). The flow path calculations were done according to the work of Persendt and Gomez (2016) and used the D8 algorithm as a simple approach for a validation process.

GNSS and real-time kinematic precise point positioning

The surveying of positions with the Global Navigation Satellite System (GNSS) is a common method for personal navigation and is ubiquitous. It is omnipresent, whether while driving with cars or for navigation during outdoor activities, in science and industrial sectors, or for surveying and lane detection (Knoop et al. 2017). Currently, few GNS Systems are available. The most prominent and first developed GNS System is the American Global Positioning System (GPS) that emerged in the 1990s (Zumberge et al. 1997). At the same time, many different positioning systems are available. The European Space Agency (ESA) developed the Galileo Program. There is the Chinese system BeiDou and the Russian system GLONASS, which have been working parallel to GPS for many years (Skog and Handel 2009; Li et al. 2015; Liu et al. 2017). GNSS positioning is the most basic technique and founded on the measurement of pseudo-range (Shrivathsa and Paniwani 2017).

Main disturbances in positioning appear in the ionosphere and the troposphere. Therefore, different methods exist to decrease these errors. One strategies is the use of an a-priori model to estimate the residual effects from measurements (Shrivathsa and Paniwani 2017). In case of ionospheric delays, only around half of it can be deleted and errors of several meters can still occur. Another strategy to improve the accuracy is to measure the delay by collecting data with a dual-frequency receiver. These devices are more expensive (Shrivathsa and Paniwani 2017; Skog and Handel 2009).

Higher accuracies can be reached by Relative Positioning with the integration of proximate static reference stations, e.g. with Network-RTK stations. With these techniques, common mode errors for GNSS receivers in a terminated area are estimated by a nearby stationary reference station that transmits the corrected information to the rover typically via UHF radio signals (Xu 2012). The common mode error increases with distance between the rover and the base station (Skog and Handel 2009). In differential mode, a pseudo-range measurement can reach accuracies within a centimeter up to millimeter dimension (Shrivathsa and Paniwani 2017). Combining the pseudo-range measurements and carrier-phase measurements improves the accuracy even more by providing unknown carrier phase cycle ambiguities and fix them to their integer value (Knoop et al. 2017; Ge et al. 2008; Teunissen and Khodabandeh 2014). Negative aspects of differential or relative GNSS positioning are the large and costly data transfer and the need of a dense local network of reference stations in a (Network-) RTK mode (Knoop et al. 2017; Shrivathsa and Paniwani 2017).

During the last 20 years, precise point positioning (PPP) achieved powerful advancements, which significantly led to increasing accuracy. It developed from former single-frequency constellation (just GPS) to multiple GNSS constellations like GPS, GLONASS, BeiDou and Galileo (Li et al. 2015; Cai and Gao 2007; He 2015). It further enhanced from single over dual up to triple frequencies and from ambiguity-float to ambiguity-fixed solutions (Liu et al. 2018). Moreover, as a key for base station-independent work, it evolved from post-processing to real-time processing (Dixon 2006), usable in a static or even in a kinematic mode, via a globally distributed network of reference stations and geostationary satellites (Liu et al. 2018; Bisnath and Gao 2009; Kaplan and Hegarty 2005). Thus, PPP developed into a method able to measure precise point positions in a kinematic mode and correcting in real-time—real-time kinematic precise point positioning (RTKPPP) (Bisnath and Gao 2009). The main applications for RTKPPP are in the field of precision farming (Dixon 2006; Perez-Ruiz and Upadhyaya 2012) and marine constructions (Arroyo-Suarez et al. 2005).

PPP almost works like a Differential GNSS but instead of calculating the position relatively to a nearby ground or base station, it uses correction data send via a geostationary satellite. This technique provides accurate position data almost all over the globe in a decimeter, up to centimeter quality (Knoop et al. 2017; Shrivathsa and Panjwani 2017; Liu et al. 2018; Bisnath and Gao 2009; Kaplan and Hegarty 2005; Hatch et al. 2003). In a PPP system, the receiver uses the clock and orbit information of the satellite itself, and also the correction data from a relatively sparse global tracking network on the ground (Li et al. 2015). This stationary network calculates the correction for all visible satellites and the ensemble of this correction data is formatted into a binary message. This message is then sent to the Hub where it is uplinked to the geostationary satellite (Knoop et al. 2017; Shrivathsa and Panjwani 2017; Liu et al. 2018; Bisnath and Gao 2009; Kaplan and Hegarty 2005; Hatch et al. 2003). The geostationary satellite broadcasts the information to the receiving antenna on the ground (Fig. 4). The communication runs in the L-band format for GPS constellation (Skog and Handel 2009; Li et al. 2015; Kaplan and Hegarty 2005; Hatch et al. 2003). A dual-frequency receiver reduces the amount of reference stations needed to attain high accuracy (Shrivathsa and Panjwani 2017; Hatch et al. 2003). The satellite-based correction data is usually offered by commercial service providers (Liu et al. 2018; Bisnath and Gao 2009) like VERIPOS Apex/Apex2/Apex5, OmniSTAR G2, TERRASTAR-D, NavCom, Trimble CenterPoint RTX and SartFire. For open source use, the PPP-Wizard and RTKLIB are available (Jokinen 2014).

Fig. 4
figure 4

Operation of real-time-kinematic precise point positioning (source: edited after NovTel Inc. (2015), modified by Robert Arendt)

Full size image

Nowadays, different providers like the BKG (Bundesamt für Kartographie und Geodaesy), CNES (Centre National d’Etudes Spatiales), DLR (Deutsches Luft und Raumfahrtzentrum), ESA/ESOC (European Space Agency/European Space Operations Centre), GFZ (Deutsches GeoForschungsZentrum) deliver freely accessible correction data. More and detailed information regarding the topic of post-processing is discussed in Wang et al. (2018). A cutout of the globally distributed reference stations can be seen in Li et al. (2015) and are further explained in Skog and Handel (2009).

To achieve an accuracy of up to 5 cm a convergence time of 20–60 min is normally needed, depending on the actual number and geometry of visible satellites. To prevent a loss of tracking or a lock on a minimum of satellites, an open sky is needed as well as a continuously unobstructed environment (Knoop et al. 2017; Bisnath and Gao 2009). On the other hand, the use of PPP has its advantages in isolated and remote locations, expansive areas and regions where a reference station infrastructure is not generally available or is too costly (Bisnath and Gao 2009).

Sensor specifications

The Leica Viva GS16 smart antenna is a multi-frequency GNSS Sensor running together with the Leica CS20 Field Controller. Signal tracking is working with GPS (L1, L2, L2C, L5), GLONASS (L1, L2), BeiDou (B1, B2, B3 limited), Galileo (E1, E5a, E5b, Alt-BOC, E6 limited), QZSS (in future), SBAS (WAAS, EGNOS, MSAS, GAGAN) and L-band. The intern Satel M3-TR4 radio modem has 555 channels which leads to a high sensitivity and fast acquisition. The sensor can be used as a normal GNSS (absolute point positioning), in differential modus as a base station or rover as well as in a real-time-kinematic modus (RTK) with adaptive on-the-fly satellite selection (relative positioning). The RTK single baseline performance is about 8 mm + 1 ppm horizontal and 15 mm + 1 ppm in vertical. In the Network RTK mode an accuracy of 8 mm + 0.5 ppm horizontal and 15 mm + 0.5 ppm in vertical can be reached. Post-processed data measured in a static phase with long observation time can have an accuracy of about 3 mm + 0.1 ppm horizontal and 3.5 mm + 0.4 ppm vertically. The specialty of the sensor is its commercial SmartLink worldwide correction service based on the VERIPOS Apex correction service (In this study Apex2 service). The SmartLink and SmartLink fill function is a remote Precise Point Positioning system with an accuracy up to 3 cm in 2D. The measurement precision, accuracy and reliability is dependent on various factors like the number of available satellites, observation time, atmospheric conditions, multipath and others. The convergence time needed to gain full accuracy can take 20 up to 40 min. More general sensor information can be read in Leica GS 16 manual (Leica Geosystems AG 2018).

Using the SmartLink function means that permanent corrected data can be received from a geostationary satellite (RTKPPP, derived via 7 different geostationary satellites—25E, 98 W, 143.5E, AORE, AORW, IOR, POR) (Fig. 4). The accuracy in the commercial SmartLink mode is lower than in the RTK mode but it is independent of proximate reference stations and applicable all over the world. A statistical post-processing is not required because the SmartLink software automatically corrects the ionospheric and tropospheric delay as well as orbit and clock lags with help of the geostationary satellite information.

The geometric arrangement of the satellites, called Dilution of Precision (DOP), is given as GDOP (3 position coordinates plus clock offset in solution) and PDOP (Position of 3 coordinates) (Hurn 1989). A negative aspect of this commercial service is the stochastic black box, where the user has no option to look at the correct functional model and the proper intra- and inter-system weighting of observations behind (Kazmierski et al. 2018; Kazmierski 2018).

Further negative aspects of using commercial correction data instead of the free available data, for example of the CNES are its high costs and less accurate results against post-processed data.

However, depending on the task and its required accuracy it can make investigations less complex for the end-user.

Measurement setup and processing strategy

For mapping the road dams, the GS 16 Sensor was installed on the roof of a 4 × 4 car (Figs. 5, 6). The offset between the sensor and the street surface was measured with a Leica LaserDisto 8 and results in 1.93 m (Fig. 6). The sensor was connected via Bluetooth with the Leica CS20 Field-Controller in the car. This was programmed to take points automatically every 25 m or more frequently if there is an elevation change of more than 0.3 m in between that distance. The range was chosen according to the TanDEM-X digital elevation model, which has a raster resolution of 12.5 m. A higher waypoint resolution would have been possible but was not necessary because most of the time no significant elevation change was recognized in between a higher raster resolution, as previous fieldwork has shown.

Fig. 5
figure 5

Leica GS 16 Sensor installed on the roof of a car (photo: Robert Arendt 2018)

Full size image
Fig. 6
figure 6

Measurement setup—Toyota Hilux with GS 16 sensor on the car roof (photo and editing: Robert Arendt 2018)

Full size image

The coordinate reference frame used by Apex2 is ITRF2014. Due to the settings of the Field Controller CS20 it was automatically transferred into ITRF2008 and later measurements were reassigned in a geodetic format with ellipsoid and datum WGS 84, further given in Cartesian projected coordinate system UTM 33 S. Selectable satellite systems were GPS, GLONASS, Galileo and BeiDou. The Leica SmartLink option was selected by activating the Augmentation System so signals from geostationary satellites and their real-time correction data could be received. As mentioned above, the used commercial function is based on the VERIPOS Apex2 system that only allows the receiving of real-time correction data for GPS and GLONASS. That is why real-time correction data for BeiDou and Galileo could not been received. The quality of the received correction data is guaranteed by the ISO 17123-8. More information about the processing strategy can be read in Table 1. The satellite cut-off angle was set on 10°. A DOP limit was not determined in advance but verified in the post-evaluation.

Table 1 Processing strategy
Full size table

Each of the four surveying days (Fig. 3) started and ended at the campus site of the University of Namibia in Ongwediva. Before driving commenced, the GS16 was installed on the car and a convergence time of 20 to 40 min was given until the sensor achieved a 1D accuracy of lower than 10 cm.

Due to the limitation in time and parallel projects, the focus was on the main roads and required:

  1. 1.

    Transverse course to the flow direction of the Iishana and

  2. 2.

    Security for the drivers, passengers and the car.

Therefore, some remote gravel roads lacking security had to be excluded, like the part between Okahao and Outapi, which was too dangerous to drive on. The road dams east of Oshakati and Ongwediva have been excluded, because the hydrological network is different from the western system and will not be investigated further (Fig. 3). In addition, a part of short track between Tsandi and Ruacana is ignored as the system is flowing almost parallel to the road, so that the road dam will not have any important influence on the flow dynamic in this part of the study area (Fig. 3). A longer track starting west of the city of Okahao leading east of Ogongo has been omitted in consequence of its flatness.

The driving speed spanned between 0 and 80 km/h. During breaks, for example at traffic lights, the speed was 0 meanwhile the speed on long straight route sections was constantly about 80 km/h. In general, the speed was adapted to the road conditions and traffic situation. Outliers like waypoints leading to parking lots have been excluded manually. Furthermore, it has to be considered that the transverse gradient of the roads, especially in wide curves, could not always be driven along the highest positions due to road traffic regulations. To improve the process of validation, data from the Namibian Roads Authority (NRA) were utilized for cross validation. Three datasets M0092, M0133, M0123 were provided.

The NRA partly measured the same roads and their heights within a distance of 500 m with the TRIMBLE R10 GNSS receiver in 2015. Likewise using a proprietary provider for real time correction in motion, they took the Trimble Continental CenterPoint RTX data. Similar to the measuring campaign of this study, they drove along the roads with a maximum speed of 80 km/h recorded in ITRF2014 coordinate reference frame, which was later converted into a WGS 84 format. They also measured while connected to the GPS and GLONASS systems. Another part in the set up was the PDOP value. If the value rose more than 0.5 m surveying ceased. Even in this investigation, post-processing was not necessarily done because of the real-time correction. The NRA could not give information that is more detailed. Nevertheless, both datasets measured nearly the same coordinates, just with another commercial device and software but still in the same mode.

Other cross validation methods, such as double and triple measurements or single point long time static measurements, have not been executed due to the lack of time in the field campaign.

The results of the two kinematic measurement campaigns of 2015 and 2018 were later compared for cross checking and to validate their deviations and similarities giving a hint of the overall reliability of the results.

The major challenge was to find coordinates that are at an equal location for further comparison. Most of the surveyed points could not been taken for validation because both campaigns measured in opposite directions and at different distances (25–500 m). Therefore, a buffer of 3 m was set around the coordinates of the 2018 campaign and intersected with the NRA data. The setting of 3 m was chosen under the condition that every pair of points had to be as close as possible for a significant comparison. Otherwise, if the buffer was set smaller almost no pairs of points were left for comparison. Finally, 18 points were close enough to each other for further comparison imitating a double measurement at these locations.

DEM pre-processing and correction

The correction of the TanDEM-X data set took place in several steps. In step one, outliers in elevation and indifferences caused by water were sought for exclusion. Therefore, the data package of the TanDEM-X data set includes different additional information layers (Wessel 2016). In this case, the TanDEM-X Water Indication Mask was used for excluding the strong inconsistencies (Wendleder et al. 2013).

The generated holes have to be interpolated to adapt the surface to the surrounding area. This was done with the Image Analyzer in ArcGIS. Here, the mask function was used with a minimum value of 0 and a maximum value of 3034 for band 1. As a result, missing values were set to NoData. Afterwards gaps were filled with the Elevation void fill function (Short Range IDW Radius “off” and Max. Void Width “fill all”). Then, smaller sinks were filled with the standard Fill function of ArcGIS to eliminate further voids. Subsequently extreme values were reduced by a low-pass filter 3 × 3 (Pipaud et al. 2015). The last step is about the implementation of the GNSS records. Therein a 25 m buffer was set around the GNSS point data. Afterwards, a Kernel interpolation between the GNSS points was set in between the buffer area. Then, the new dataset was implemented by the ArcGIS function Mosaic to new raster.

Results

GNSS performance

The measurement setup could be applied on all road dams as planned. At the end, 16.590 points were taken and around 532 km of main road dams were tracked (Fig. 3). Nevertheless, in the post-evaluation of the recorded data, it became clear that points were not taken exactly every 25 m as was defined in the automatic mode. Most points were taken in a range between 25 and 27 m. Moreover, a large amount of points was taken in distances up to 49 m. Statistically, points have been collected within a mean of every 32.08 m.

Nevertheless, the overall GNSS performance shows PDOP and GDOP values within an excellent to ideal rating between 3.5 and 1.2 (Tables 2, 3) (Dutt et al. 2009; Langley 1999). It should be mentioned that the performance rating originally was invented for GPS only (Langley 1999).

Table 2 Overview of used satellites and accuracies of the recorded GNSS data
Full size table
Table 3 Explanation of DOP quality, after Langley (1999) in Dutt et al. (2009)
Full size table

In addition, the 1D, 2D and 3D coordinate quality (CQ) is also determined in a decimeter to a sub-decimeter range, where 1D describes the vertical accuracy, 2D the horizontal accuracy and 3D the spherical (vertical and horizontal) accuracy. As reported in Table 2, the range of total accuracy in the sector of 3D coordinate quality spans from 5.0 to 10.0 cm, where 10 cm was the cut off limit. Points with a lower accuracy were excluded in the post-evaluation process.

The calculated 3DCQ mean is about 7.1 cm with a standard deviation of 1.1 cm and a skewness of 0.544. The 1D and 2D coordinate quality is even better (Table 2).

GNSS and TanDEM-X cross validation

The cross-validation of the two surveying campaigns (Table 4) between Leica and Trimble shows differences in height between 0.006 and 0.585 m with a mean difference of 0.154 m and a median difference of 0.091 m. The standard deviation is about 0.160 m with a skewness of 1.386 and a variance of 0.026. The calculated RMSE is about 0.219.

Table 4 Cross validation of measurements with Leica, Trimble and the TanDEM-X
Full size table

Moreover, the measurements of the 2018 campaign with the Leica instrument were compared to the TanDEM-X raw data at the same positions. Obviously, the range is larger. The minimum deviation is 0.125 m and the maximum deviation is up to 1.955 m, with a mean difference of 0.418 m and a median of 0.471 m. The standard deviation is 0.973 m with a skewness of − 1.138 and a variance of 0.947. The calculated RMSE is about 1.059.

Corrected TanDEM-X

The TanDEM-X Transect Elevation Check of Fig. 7 shows two different lines and a blue plain of height along a transect, which can be found in Figs. 8, 9. The black line indicates the height of the TanDEM-X raw data set before any calculation. The red dotted line designates the same path after the correction of water interferences and the application of filtering algorithms as described before (DEM pre-processing and correction). Up to here, the topography is smoothed and represents a more realistic and natural image. Sharpe edges could be equalized and some overestimated parts (water interferences and vegetation patches) have been lowered while other underestimated parts have been raised. Until that point, the road dam is still not clearly visible.

Fig. 7
figure 7

TanDEM-X Transect Elevation Check (located in Figs. 3, 8 and 9)

Full size image
Fig. 8
figure 8

TanDEM-X scene before correction. Both scenes face in a western direction with exaggeration × 12 and the indication of the transect of Fig. 7 (also located in Fig. 3)

Full size image
Fig. 9
figure 9

TanDEM-X scene after correction. Both scenes face in a western direction with exaggeration × 12 and the indication of the transect of Fig. 7 (also located in Fig. 3)

Full size image

The plain blue specifies the final corrected DEM including the surveyed road dam, which is visible also in Fig. 9. Except for the road dam where more than a meter deviation is evident, differences in a sub-meter range could be detected. As shown in Figs. 8, 9, the application of the different filter algorithms and the correction of the water-induced interferences have been successful, so the road dam is clearly visible and the high outrage peaks are eliminated.

The value of the results becomes clearer in Fig. 10. The effect of the road dams and the modifications including culverts and bridges leads to a change in flow behavior, here emphasized in a change of flow direction. The calculated flow paths change significantly between the raw TanDEM-X model and the two edited models where additional filter algorithms were applied and culverts and bridges have been included.

Fig. 10
figure 10

Three different flow path calculations with ArcGIS illustrated in one image. Red stream definition based on the raw TanDEM-X model only used the ‘Fill’ function. Purple dotted Stream is calculated after the application of additional filter algorithms and the inclusion of the road dams. The blue Stream also includes the culverts and bridges. The road dams and culverts are influencing the flow dynamics

Full size image

Discussion

Due to left hand-traffic, data points were usually collected while driving on the left side of the roads. It has to be acknowledged, that road dams are normally transversely inclined in curves. Therefore, some of the collected point data in curves are not always representing the highest part of the road dam cross section. Nevertheless, in a few parts, the attempt was made to drive the highest profile through the curves to gain the maximum height of the road dam. These circumstances led to small differences between the left and right roadsides, which theoretically has to be added to the general vertical accuracy (1DCQ).

Airfreight costs could be saved, as just one sensor was necessary instead of two and no additional equipment. Moreover, time and work force was saved, because no differential station had to be set up every 1 km nor always had to be guarded by staff. Even the long convergence time of 30–40 min at the beginning of the measurement session was no problem at all, since this time was used to prepare the daily fieldwork.

According to Langley (1999), the GDOP and PDOP values had excellent to ideal rates. This explanation of quality was formerly developed for GPS only. Even the 1D, 2D and 3D coordinate accuracy shows a decimeter to sub-decimeter deviation. Nonetheless, coordinates could not have been detected 100% accurately every 25 m as was planned and set in the settings. It is assumed that the top speed of 80 km/h might be too high if points information were recorded every 25 m. Regarding future measurements, either the top speed has to be limited or the record span has to be widened. First estimations indicate that it is more about velocity. Some extreme outliers can be explained by an exceeding of top speed for example, due to overtaking, and others may be caused by a longer software calculation time.

It can be assumed that multipath effects were not important, due to the sparsely vegetated and very flat landscape being only rarely interrupted by trees or buildings. Multipath effects caused by the white metal roof of the car cannot be determined nor excluded. Literature did not give any hints about necessary protection measures for roof top installed GNSS sensors, nor any numbers for multipath measurement errors.

The filter algorithm used leads to a substantial improvement. The evaluation of the transect as well as Figs. 7, 8, 9 shows that most of the interferences could be eliminated successfully and the geomorphology is obviously more perceptible. Nonetheless, the delivered water mask did not cover all water surfaces, especially very small ones sometimes were not covered. As a consequence, the low-pass filter smoothed these objects but some of them still exist as small dunes. However, regarding the work of Wendleder et al. (2013), it can be assumed that around 70% of the water bodies were detected. Further statistics regarding the used water mask are pending and have to be evaluated in a next step.

The validation of the measured data was limited due to the use of commercial real-time correction data. This caused a black-box effect in which not all data quality parameters were visible. Long-term single point measurements and double and triple measurements could not have been done due to limitation of time and parallel investigations in the field. Therefore, the only chance to get an idea of the vertical accuracy was the comparison of the data with former measured data from the Namibian Roads Authority. In this case, different systems were used but with almost the same settings, measuring in motion with the same speed and the use of a commercial real-time correction service. Statistical analyses showed a sub-decimeter median value. Nonetheless, even for the data of the NRA individual quality values were missing due to the commercial real-time correction service used.

To achieve real-time correction data that is free of charge different providers like the CNES can be addressed for future measurements. In addition, post-processing would contribute to increased accuracy (Wang et al. 2018; Kazmierski et al. 2018; Kazmierski 2018). For example, with the new VERIPOS Apex5 system, receiving of correction data including BeiDou and Galileo would have been possible to increase data quality. Even with the CLK91 stream via CNES free available correction data including all 4 satellite systems could have been received (Wang et al. 2018).

To some extent, the final total estimated error in height consists of different single errors and cannot be assessed in a concluding number due to various factors: the position of the car on the street (top or down of the turn), the uncertainty of the commercial real-time correction data (partially black-box), the TanDEM-X itself (vertical/horizontal accuracy), and filter algorithms and interpolation procedures used. It becomes clear that a millimeter accuracy cannot be reached at all. Nonetheless, the aim of the work—to improve the TanDEM-X data set for further flood modelling—has been achieved.

Conclusions

The application of the different filter algorithms and the correction of the water-induced interferences have been successful, so road dams have been made clearly visible and high outrage peaks were eliminated. These modifications including culverts and bridges also lead to a change of flow directions. The automatically recoded points present excellent up to ideal GDOP and PDOP values with vertical accuracies about 4.3 cm up to 10.0 cm. The validation procedure shows huge vertical differences between GNSS measurements and the TanDEM-X raw model ranging from about 0.125 m up to 1.955 m with a median of 0.471 m. Elevation differences between two GNSS systems have shown significantly less differences in accuracy ranging between 0.006 and 0.585 m with a median of 0.091 m. These circumstances clearly illustrate the necessity of measuring smaller infrastructures for an accurate representation in the digital elevation model.

With this investigation, a scientific contribution has been made towards understanding the topographic basis of the Iishana system. Previously developed hydrological models in the Iishana region were focused on small sub-basins rather than on the entire system. The survey results reported here provide a scientific base for developing a trans-boundary flood model in the Iishana region of Angola and Namibia which would contribute towards an innovative adaptation of water management to climate change. The potential and originality of this research project is to bridge the knowledge gaps and to contribute to the scientific base for sustainable water resource management in the region.

The results underline the significance of a preprocessing of TanDEM-X data and the importance of incorporating road dams, culverts and bridges when a high quality floodwater prediction model is sought.