Dike Heights Research Articles

Raising dikes and managed realignment may be insufficient for maintaining current flood risk along the German Baltic Sea coast

Without upgrading existing adaptation, Germany is projected to be among those European countries that will suffer severe flood damages in 2100. Here we use a validated modeling framework to explore the effectiveness of two hypothetical upgrades to existing dike lines in reducing flood extent and population exposure along the German Baltic Sea coast. We perform a number of model runs where we increase the heights of existing dikes by 1.5 m, implement managed realignment as a nature-based solution, where physically plausible, and run a 200-year surge under two sea-level rise scenarios (1 and 1.5 m). We show that managed realignment is more effective in reducing future population exposure to coastal flooding compared to increasing dike heights. However, the maximum reduction in population exposure compared to a do-nothing approach amounts to only 26%, suggesting that even managed realignment is insufficient to maintain flood risk at today´s levels. The greatest potential for protecting people and property from future flooding lies in developing adaptation strategies for currently unprotected coastal sections.

Regional assessment of extreme sea levels and associated coastal flooding along the German Baltic Sea coast

Abstract. Among the Baltic Sea littoral states, Germany is anticipated to endure considerable damage as a result of increased coastal flooding due to sea-level rise (SLR). Consequently, there is a growing demand for flood risk assessments, particularly at regional scales, which will improve the understanding of the impacts of SLR and assist adaptation planning. Existing studies on coastal flooding along the German Baltic Sea coast either use state-of-the-art hydrodynamic models but cover only a small fraction of the study region or assess potential flood extents for the entire region but rely on global topographic data sources and apply the simplified bathtub approach. In addition, the validation of produced flood extents is often not provided. Here we apply a fully validated hydrodynamic modelling framework covering the German Baltic Sea coast that includes the height of natural and anthropogenic coastal protection structures in the study region. Using this modelling framework, we extrapolate spatially explicit 200-year return water levels, which align with the design standard of state embankments in the region, and simulate associated coastal flooding. Specifically, we explore (1) how flood extents may change until 2100 if dike heights are not upgraded, by applying two high-end SLR scenarios (1 and 1.5 m); (2) hotspots of coastal flooding; and (3) the use of SAR imagery for validating the simulated flood extents. Our results confirm that the German Baltic coast is exposed to coastal flooding, with flood extent varying between 217 and 1016 km2 for the 200-year event and a 200-year event with 1.5 m SLR, respectively. Most of the flooding occurs in the federal state of Mecklenburg-Western Pomerania, while extreme water levels are generally higher in Schleswig-Holstein. Our results emphasise the importance of current plans to update coastal protection schemes along the German Baltic Sea coast over the 21st century in order to prevent large-scale damage in the future.

Subsurface Geometry and Emplacement Conditions of a Giant Dike System in Elysium Fossae, Mars

AbstractElysium Fossae is a NW‐SE, 350 km‐long linear graben system located in the eastern flank of Elysium Mons, Mars. Graben widths, lengths, and topographic data were used to model the thicknesses, depths, heights, and excess pressures of a possible dike system underneath these grabens. Area balance on topographic profiles across the structures reveals dikes at depths of 241–2,330 m below the surface, with average thicknesses <60 m, and heights of 15–20 km. These heights are approximately three times larger than terrestrial dikes intruded in the shallow crust. The subsurface properties suggest a teardrop‐shape geometry for the dikes, which has been observed in many theoretical and analog dike models. Additionally, the aspect ratios (thicknesses and lengths) of the inferred dikes are consistent with sublinear scaling, characteristic of fluid‐induced fractures. The obtained critical stress intensity factors (Kic) are between 3.14 and 15.15 GPa·m1/2 and are slightly higher than those of terrestrial dikes intruded in similar lithologies. The maximum excess pressures calculated from stress intensity factors are between 31 and 276 MPa. These are also consistent with pressures calculated for terrestrial dikes despite the greater aperture and height of the Elysium dikes. Theoretical calculations of excess pressures for variable dike heights support both the values calculated from empirical observations, and that Martian dike heights may consistently be three times the heights of terrestrial dikes. In summary, this work supports: (1) the existence of a dike system underneath Elysium and (2) that dike heights in rocky planets may scale inversely with gravitational acceleration.

Numerical Study of Storm Surge Inundation in the Southwestern Hangzhou Bay Region During Typhoon Chan-Hom in 2015

Storm surge inundation is a major concern in marine hazard risk assessment during extreme weather conditions. In this study, a high-resolution coupled model (the ADVanced CIRCulation model + the Simulating WAves Nearshore model) was used to investigate the storm surge inundation in the southwestern Hangzhou Bay region during Typhoon Chan-hom in 2015. The simulated hydrodynamic processes (sea surface wave and storm tide) were validated with measured data from wave buoys and tide gauges, indicating that the overall performance of the model was satisfactory. The storm surge inundation in the coastal area was simulated for several idealized control experiments, including different wave effects (wave-enhanced wind stress, wave-enhanced bottom stress, and wave radiation stress). Dike overflowing cases with different dike heights and dike breaking cases with different dike breach lengths were considered in the simulation. The results highlight the necessity of incorporating wave effects in the accurate simulation of storm surge inundation. Dike height significantly influences the magnitude and phase of the maximum inundation area in the dike overflowing cases, and dike breach length is an important factor impacting the magnitude of the maximum inundation area in the dike breaking cases. This study may serve as a useful reference for accurate coastal inundation simulation and risk assessment.

Safe dike heights at minimal costs: An integer programming approach

Optimal dike heights are of crucial importance to the Netherlands as almost 60% of its surface is under threat of flooding from sea, lakes, or rivers. This area is protected by more than 3500 kilometres of dunes and dikes. These dunes and dikes require substantial annual investments of over 1 billion euro. In this paper we propose an integer programming model for a cost-benefit analysis to determine optimal dike heights. We improve upon the model proposed by Brekelmans, den Hertog, Roos and Eijgenraam (2012). Our model provides an alternative approach with almost complete flexibility towards input-parameters for flood probabilities, damage costs and investment costs for dike heightening. We present an easy-to-implement algorithm that provides an optimal solution to the problem. The method has been implemented and tested for the most recent data on flood probabilities, damage and investment costs, which were recently used by the government to determine the new safety standards in the Dutch Water Act.

River computations: artificial backwater from the momentum advection scheme

ABSTRACTThe established method for determining dike heights and dimensioning river training structures is to assess the resulting backwater by numerical modelling. The common consensus is that bottom friction determines the backwater and that momentum advection only has a local effect. We demonstrate that the numerical/artificial backwater contribution from the momentum advection approximation can be of the same order of magnitude as the bottom friction contribution, depending on the advection scheme. This is realized using a one-dimensional analysis and verified using a set of one- and two-dimensional test problems including a wavy bed case, flow over emerged and submerged groynes and finally an actual river. We compare first- and second-order accurate advection schemes and compute their artificial contribution to the backwater, for a range of practically-feasible grid resolutions. The tests demonstrate that the conservation/constancy properties of the scheme determine the size of this contribution, rather than the order of the scheme.

The impact of dike construction on the flow and sediment siltation in the project of Meishan Container terminal phase II

In order to avoid the adverse impact of Qinglongshan deep groove on the flow pattern of the Meishan Container terminal phase II ensuring the safety of berthing, a submarine dike is proposed along the land front direction toward the Qinglongshan Island. The influence of different dike layout schemes on the water flow in the surrounding sea area was studied through the mathematical model. In addition, the effects of different dike heights and gap width on the surrounding water flow and siltation were analysed. The results show that the crossflow in front of the terminal under the two submerged dike heights and gap widths are basically the same, which is less than that of without the construction of the dike. Appropriate reduction of dike height is conducive to improve the flow at the channel between the Qinglongshan and Meishan Island. After the dike construction, the groove will maintain a certain depth, and will not result a blocking at the top side of dike and the rear channel.

Cost‐benefit analysis of shrimp farming's flood risk reduction strategies in Thailand

Chachoengsao province is a prime shrimp producing area for domestic consumption and exports. The province, however, is often threatened by floods. Improving the effectiveness of current flood damage protection is a major challenge. This research developed a flood risk map by combining the probability of flood events and a vulnerability map based on physical characteristics of the area and socio‐economic conditions of shrimp farmers (victims). Analysis of current risk reduction measures was performed by comparing the net benefits and costs of different strategies. Damage costs to shrimp farming from flooding were also estimated for the base case (a case with no change in actions). The flood risk map shows that two‐thirds of shrimp farms are highly vulnerable to flooding when a 10‐day accumulated rainfall is greater than 250 mm which is likely to occur every 2 years. Increasing dike heights could yield higher net benefits than other flood adaptation measures. Non‐structural flood controls such as early harvesting and shifting the crop calendar are alternative measures for shrimp farmers who lack financial supports. The results show that cost‐benefit analysis based on various scenarios can help in selecting an appropriate mitigation practice especially for shrimp farms located in a high risk area.

INFLUENCE OF RETENTION AREAS ON THE PROPAGATION OF STORM SURGES IN THE WESER ESTUARY

The hydrodynamics of estuaries are forced by the tides from the open sea and the river runoff from the catchment area. The hinterland is often low-lying and densely populated and must therefore be protected by dikes. Anthropogenic climate change poses new challenges to the coastal protection. However, changes in the geometry of the estuaries can have equally severe impacts on the deformation of a storm surge wave form when it propagates through the estuary. This affects the peak water levels and hence the design water levels. This contribution focuses on the influence of retention areas or forelands seaside of the main dike lines, which are protected by summer dikes against the less severe but more frequently occurring storm surges. This is shown at the example of a retention area in the Weser estuary, which has historically been the cite of a soccer stadium and thus hosts high values which stand in sharp contrast against the low safety level against flooding. The investigation is conducted with a 3D hydrodynamic numerical model which has previously been validated for the simulation of storm surges. The results show that even very small changes in the geometry of the estuary can have effects on design levels. This is even the case when they only regard the summer dike crests heights around retention areas and not their volume. Another important finding is that the geometry changes may have their maximum impacts quite far away from the specific river reach in which they are carried out. The results underline that for designing safe and reliable storm surge infrastructure, storm events should be studied in high resolution models which are able to resolve even small scale features such as summer dike lines.

Rapid assessment of flood susceptibility in urbanized rivers using digital terrain data: Application to the Arno river case study (Firenze, northern Italy)

As a result of the recent acquisitions of detailed geographic data in fluvial environments this study proposes an analytical procedure in a GIS environment for an easy, rapid and cost-effective evaluation of flood susceptibility within urban and sub-urban areas. The method, based on data gathering in various public offices and possibly integrating missing geomorphologic information with new records, has been tested in a real case study in central Italy from which operational instructions could be extrapolated for other similar areas in the world. A long reach of the Arno river, which is currently the most important national hydraulic emergency area in terms of civil protection, was selected for this purpose. The measured dike heights, extrapolated from a geographic database previously created by the authors on behalf of the Provincia di Firenze administration, were compared with the results of hydraulic modeling conducted by the Arno River Basin Authority in which water flood levels were simulated for various return periods. This data comparison has allowed us to identify critical points for overflow hazard. In addition, the flood discharges provided by the same model were related to the freeboard typically used in river hydraulics for the major Italian watercourses (1.00 m for a 200-year flood). A deeper analysis of the flood susceptibility was subsequently carried over to the urban area of Firenze. A model of the surface hydrological flows concentrated on the historic center has provided a comprehensive response of this area to the sudden appearance of abundant surface-water flows. The behavior of the urban water circulation in terms of path and areas involved were promptly identified with great precision during normal flow conditions of the Arno in the event of river obstruction at bridges and in case of undifferentiated runoff out from the riverbed.

Optimal dike investments under uncertainty and learning about increasing water levels

AbstractWater level extremes for seas and rivers are crucial to determine optimal dike heights. Future development in extremes under climate change is, however, uncertain. In this paper, we explore impacts of uncertainty and learning about increasing water levels on dike investment. We extend previous work in which a constant rate of structural water level increase is assumed. We introduce a probability distribution for this rate and study the impact of learning about this rate. We model learning as a single stochastic event where full information becomes available. Numerical solutions are obtained with dynamic programming. We find that the expected value of information can be substantial. Before information arrives, investment size is reduced as compared with the benchmark without learning, but investment frequency may be increased. The impact of learning on the initial investment strategy, however, is small as compared with the impact of uncertainty about increasing water levels by itself.

The simultaneous occurrence of surge and discharge extremes for the Rhine delta

Abstract. The low-lying Netherlands is at risk from multiple threats of sea level rise, storm surges and extreme river discharges. Should these occur simultaneously, a catastrophe will be at hand. Knowledge about the likelihood of simultaneous occurrence or the so-called "compound effect" of such threats is essential to provide guidance on legislation for dike heights, flood barrier design and water management in general. In this study, we explore the simultaneous threats of North Sea storm surges and extreme Rhine river discharge for the current and future climate in a large 17-member global climate model ensemble. We use a simple approach, taking proxies of north-northwesterly winds over the North Sea and multiple~day precipitation averaged over the Rhine basin for storm surge and discharge respectively, so that a sensitivity analysis is straightforward to apply. By investigating soft extremes, we circumvent the need to extrapolate the data and thereby permit the model's synoptic development of the extreme events to be inspected. Our principle finding based on the climate model data is that, for the current climate, the probability of extreme surge conditions following extreme 20-day precipitation sums is around 3 times higher than that estimated from treating extreme surge and discharge probabilities as independent, as previously assumed. For the future climate (2070–2100), the assumption of independence cannot be rejected, at least not for precipitation sums exceeding 7 days.

Safe Dike Heights at Minimal Costs: The Nonhomogeneous Case

Dike height optimization is of major importance to the Netherlands because a large part of the country lies below sea level, and high water levels in rivers can cause floods. Recently impovements have been made on the cost-benefit model introduced by van Dantzig after the devastating flood in the Netherlands in 1953. We consider the extension of this model to nonhomogeneous dike rings, which may also be applicable to other deltas in the world. A nonhomogeneous dike ring consists of different segments with different characteristics with respect to flooding and investment costs. The individual segments can be heightened independently at different moments in time and by different amounts, making the problem considerably more complex than the homogeneous case. We show how the problem can be modeled as a mixed-integer nonlinear programming problem, and we present an iterative algorithm that can be used to solve the problem. Moreover, we consider a robust optimization approach to deal with uncertainty in the model parameters. The method has been implemented and integrated in software, which is used by the government to determine how the safety standards in the Dutch Water Act should be changed.

In This Issue

In This Issue

An ENO-Based Method for Second-Order Equations and Application to the Control of Dike Levels

This work aims to model the optimal control of dike heights. The control problem leads to so-called Hamilton-Jacobi-Bellman (HJB) variational inequalities, where the dike-increase and reinforcement times act as input quantities to the control problem. The HJB equations are solved numerically with an Essentially Non-Oscillatory (ENO) method. The ENO methodology is originally intended for hyperbolic conservation laws and is extended to deal with diffusion-type problems in this work. The method is applied to the dike optimisation of an island, for both deterministic and stochastic models for the economic growth.

Assessing risk of and adaptation to sea-level rise in the European Union: an application of DIVA

This paper applies the DIVA model to assess the risk of and adaptation to sea-level rise for the European Union in the 21st century under the A2 and B1 scenarios of the Intergovernmental Panel on Climate Change. For each scenario, impacts are estimated without and with adaptation in the form of increasing dike heights and nourishing beaches. Before 2050, the level of impacts is primarily determined by socio-economic development. In 2100 and assuming no adaptation, 780 × 103 people/year are estimated to be affected by coastal flooding under A2 and 200 × 103 people/year under B1. The total monetary damage caused by flooding, salinity intrusion, land erosion and migration is projected to be about US$ 17 × 109 under both scenarios in 2100; damage costs relative to GDP are highest for the Netherlands (0.3% of GDP under A2). Adaptation reduces the number of people flooded by factors of 110 to 288 and total damage costs by factors of 7 to 9. In 2100 adaptation costs are projected to be US$ 3.5 × 109 under A2 and 2.6 × 109 under B1; adaptation costs relative to GDP are highest for Estonia (0.16% under A2) and Ireland (0.05% under A2). These results suggest that adaptation measures to sea-level rise are beneficial and affordable, and will be widely applied throughout the European Union.

In-situ geotechnical experimentation and stability evaluation of an instrumented 180 m×70 m×12.5 m fill dike constructed on laminated soft ground

An instrumented trial-fill dike was constructed on soft, laminated soils of the Lisan Peninsula foreshore of the Dead Sea. The earthwork had base dimensions of 180 m by approximately 70 m wide and was raised in two stages to a maximum height of 12.5 m above original ground level. The geotechnical data of the dike were monitored in order to: assess the short- and long-term strength of the foundation, obtain and analyze the pore-pressure response of the foundation soils for potential use in construction control, obtain data on embankment settlement in order to refine end-of-construction and post-construction settlement assessments, and optimize the height of the dike to be constructed by providing information on the construction sequence for use in calculation of capital costs and alternative layouts and dike heights. The successful completion of the trial dike has demonstrated that steep-side dikes up to 12.5 m high can be constructed rapidly on soft soils. The construction of the trial dike has therefore proved a very substantial benefit to the evaluation of the likely performance of a dike constructed along the Lisan shore. The key factor which made this fast construction possible was the unexpected, very rapid consolidation of the majority of the foundation soil which has been shown to occur. The principal observations from the trial dike were: (1) end of construction settlements may be calculated using drained stiffnesses where E′/su initial has a value of around 65; (2) post-construction settlements can be calculated using a coefficient of secondary compression, Cα equal to 0.015; (3) a rapid increase in undrained shear strength occurred when loading the soil up to a value of su equal to around 30 kPa. The value of su/σv′ was as high as 0.5 at this stage. With further loading the strength increase was more modest and su/σv fell to around 0.25 for a vertical effective stress of 160 kPa; (4) for the undrained stability analyses of the trial dike, the mean vane shear-strength profile provided an appropriate assessment of the short-term factor of safety against failure, 5) For the drained stability analyses of the trial dike, lower bound effective strength parameters for the foundation and embankment fill (c′=0, φ′=30° and c′=2 kN/m2, φ′=33°, respectively), combined with field measurements of end of construction pore water pressures provided an analysis which was broadly compatible with the undrained analysis; and (6) the trial dike has been stable, pre- and post-construction, because of the well drained nature of its foundation which prevented the build up of high pore water pressures and led to rapid consolidation.

The role of rift zone storage in controlling the site and timing of eruptions and intrusions of Kilauea Volcano, Hawaii

Repeated eruptive and intrusive activity on the East Rift Zone of Kilauea volcano allows dikes to exist within the rift zone for extended periods of time. Leakage of magma from the summit storage region into the rift zone can cause inflation of a rift zone dike. Inflation raises the excess pressure at the dike centre and increases the stress intensity at the dike edges. If the inflation is sufficiently large, the stress intensity may exceed the fracture toughness of the country rocks and allow vertical or lateral dike emplacement to occur. Theoretical modelling can be used to predict the conditions under which vertical or lateral dike propagation and hence eruptive or intrusive activity may occur. Over typical ranges of dike half height and regional tension gradient, vertical propagation and hence eruption are favored by high fracture toughness, relatively low dike half heights, and low regional tension gradients. Lateral propagation can occur when the fracture toughness is low, when dike half height is higher, and when the regional tension gradient is high. The results of from the model constrain the fracture toughness within the East Rift Zone to be 100–110 MPa m½ and the regional tension gradient to be ≪ 1000 Pa/m.

A comparison of rift-zone tectonics in Iceland and Hawaii

Observations of eroded volcanic rift zones indicate that dikes in Iceland are typically several times thicker than those in Hawaii. Geodetic and seismic observations of active rifts, however, suggest that dike heights in the two regions are similar. Provided the elastic properties of the rift zones are the same, this implies that dikes are intruded with higher driving pressures (magma pressure minus compressive stress perpendicular to the dike plane) in Iceland than Hawaii. A second major difference between the two regions is the greater prevalence of large normal fault scarps in rift zones in Iceland. From this it can be infered that a lower percentage of dikes breach the surface in Iceland than in Hawaii. Thus, although dikes in Iceland are intruded with higher driving pressures, they possess lower absolute magma pressures than in Hawaii. These differences can be interpreted in terms of the tectonic settings in the two regions. In Iceland, a steady remote extension reduces the horizontal stress perpendicular to the rift zone, allowing dikes to be intruded with low absolute pressures but high driving pressures when magma becomes available. In Hawaii, a more continuous magma supply on the timescale over which the dike-induced stresses are relaxed, and perhaps a greater role for intrusions in driving long-term rift extension, ensure that the rift-compressive stress is not relaxed significantly before the next dike is intruded. Thus the magma pressure must be nearly sufficient for eruption in order for intrusion to occur. If the mechanism for relaxing the rift-compressive stress were less efficient still, then an even higher percentage of dikes would erupt, and at times the rift zone trend could become an unfavorable orientation for dike intrusion. Such might be the case at Mauna Loa, which lacks large rift-zone faults and fissures and possesses numerous radial vents outside its two main rift zones.

Efficient Reservoir Design for Playas of the Southern High Plains

ABSTRACT EVAPORATION losses from the shallow playas of the Southern High Plains can be reduced by storing the water in deep reservoirs with small surface areas. The reservoir storage is obtained most economically by con-structing a dike through the playa and diverting all runoff into the diked reservoir. For equal dike heights and reservoir areas, an efficient reservoir is obtained by maximizing the ratio of the reservoir area to the dike length. Optimality mathematics was used to maximize this ratio for sector, para-bolic and circular arc dikes within a flat-bottomed, circular playa. The maximum ratios for the three dike shapes were nearly equal; the sector dike reservoir was selected for field application because of its simplicity. Design data were developed for sector dike reservoirs covering from one-tenth to one-half of the playa bottom. The water stored per unit of earth excavated was much higher than for earlier playa modification models.