We have developed the SIND (scientific interpolation for natural disasters) model to forecast natural hazard zone for storm surge. Most previous studies have been conducted to predict hazard zone with numerical simulations based on various scenarios. It is hard to predict hazard zone for all scenarios and to respond immediately because most numerical models are requested a long simulation time and complicated postprocess, especially in coastal engineering. Thus, in this study, the SIND model was developed to overcome these limitations. The principal developing methods are the scientific interpolation for risk grades and trial and error for parameters embedded in the governing equation. Even designed with hatch files, applying disaster characteristics such as the risk propagation, the governing equation for storm surge in coastal lines was induced from the mathematical solver, COMSOL Multiphysics software that solves partial differential equations for multiple physics using FEM method. The verification process was performed through comparison with the official reference, and the accuracy was calculated with a shape similarity indicating the geometric similarity of the hazard zone. It was composed of position, shape, and area criteria. The accuracy of about 80% in terms of shape similarity was archived. The strength of the model is high accuracy and fast calculation time. It took only less than few seconds to create a hazard map for each scenario. As future works, if the characteristics of other disasters would be understood well, it would be able to present risk propagation induced from each natural disaster in a short term, which should help the decision making for EAP.

With the increasing extreme disasters including drought, heavy rain as well as ground heat, the ability to predict hazardous area affected by them has become more important. In the case of urban areas, man-made spaces were built such as impervious and underground spaces. These resulted in increasing the damage by natural disaster. Thus, many research studies have been carried out to respond to these extreme climate changes. Disaster measures to prevent extreme climate change can be divided into structural and nonstructural measures. In particular, the nonstructural measures generally include estimating the range or degree of each damage under various scenarios. Among them, a scenario-based hazard map is mainly made by governments and local public institutions to inform hazardous area to the residents.

In Korea, recently nonstructural measures have been taken to prevent natural disasters since there are many restrictions on structural measures such as land use, environmental effect, and so on. From the past, studies on countermeasures have been carried out, and the process of disaster damage to the area has been suggested by Cutter [

It has been actively carried out on past disasters and virtual disaster scenarios in order to produce a hazard map. Scenarios of coastal disasters involve earthquakes and typhoons. However, since it is difficult to predict earthquakes and typhoons, most scenarios for the global scale are constructed based on past cases. It is not realistic to consider all parameters of typhoon which occurred in the global scale. It is not realistic to consider all parameters of typhoon which occurred in the global scale because of the diversity of sizes and routes of typhoons and the lack of numerical simulation capability and DB. Thus, the studies related to numerical simulations have been carried out continuously for forecasting risk. To forecast the inundation caused by the storm surge, it is important to calculate the initial wave height. The initial tidal-wave computation studies began in the mid-1990s, with brief empirical formulas based on observations (Conner et al. [

On the other hand, in the step of disaster response, it is very important to simulate and analyze the initial wave height for making the hazard map. For this purpose, several considerations should be realized and computed in the numerical model such as the complexity of tidal, storm surge, and high waves, the effect of bottom friction in coastal submergence, and the smooth moving boundary layer calculation technique. There have been many cases related to flooding in coastal areas due to boundary and initial conditions on the outer seaside (Bates and De Roo [

In the field of weather and climate forecasting, the interpolation method has been traditionally used to estimate data for unmeasurable areas using statistical techniques such as spatial interpolation. It is meaningful in that it can provide a very good alternative method for estimating local phenomena with a small number of observational samples. However, it has a limitation that depends only on the number or values of available observed data. Many studies have been conducted to reduce the uncertainty and increase the accuracy of their estimations by using additional data that can reflect natural and physical characteristics to supplement these limitations (Yim and Lee [

For instance, representative results of cokriging, when utilizing the altitude above sea level related to temperature, are compared with the estimation results of kriging, a traditional spatial interpolation method. Ishida and Kawashima [

Fitria [

Therefore, in this study, a model was developed using the interpolation method, and a shape similarity was introduced to quantitatively verify it. It was estimated for accuracy by verifying the official hazard map and added physical meaning to the model by using additional data such as the characteristics of storm surge and the topography of the study area. Using this model, hazardous areas and risks are provided in a short time according to user-defined conditions so that a disaster situation can be determined as much as precisely for decision or policy maker.

The SIND model was developed by using the interpolation method with the governing equation expressed by a partial differential equation (PDE). Interpolation is widely used in the various fields of mathematics, economics, medicine, meteorology, and engineering. For example, it is used to perform surface modelling or numerical topography modelling and to express linearly new data points. It has been used to understand the spatial structure of the target object and to design artificial organs which implanted in the human body. Also, it is known to simulate operation plan in the medical field (Lee [

There are 3 steps to develop the SIND model as presented in Figure

Progress of the SIND model (Kim et al. [

For a storm surge, the users can input conditions such as typhoon route, wind strength, and typhoon intensity, which are already selected by users as primary input variables. If they would set these conditions, the model would start to search the prebuilt database to check if there is the same condition of the data that they want. If not, the governing equation for prediction would be loaded. And the conditions entered by the user become a reference value for selecting the governing equation set for each condition in the “Usage condition” (see Figure

Concept design of the SIND model.

The derivation of governing equations for each disaster is the most important process to develop this model. First, we must analyze the hazard maps for disaster scenarios after collecting hazard maps related to the storm surge in Korea. They were computed with numerical models and presented by government (MLTMA [

Information of hazard maps.

Hazard map | |
---|---|

Format | Shape file (.shp), AutoCad file (.dxf, .dwg) |

Agent | MLTMA (the Ministry of Land, Transport, and Maritime Affairs) |

Program | Numerical model (physical model) |

Year | 2010 |

Conditions | 50-year, 100-year, 150-year, 200-year |

The interpolation generally needed 3 reference data at least. So, we used the 3 maps to derive governing equation to predict risk grades for storm surge, 50-year, 150-year, and 200-year wave height. The other was used for verification of equation, 100-year wave height.

First, the basic form of equation was derived with physical meaning considering some assumptions. And the coefficients of the equation and boundary conditions were defined by the trial and error method. An independent variable of equation is set as the wave height frequency, and a dependent variable is the spatial distribution of the risk grades. Results from this model were put in the same conditions (50-year, 150-year, and 200-year wave height) with hazard map was compared with them to check whether this equation can exactly predict spatial distribution of risk grade. The COMSOL Multiphysics program was used to perform the trial and error method for determining the equations and comparing the results. And the shape similarity was used to estimate accuracy of prediction by comparison of inundated area with official hazard map. Finally, the governing equation for predicting the risk of storm surges was derived (see Figure

Process of derivation equation for storm surge in the SIND model.

COMSOL Multiphysics developed by COMSOL AB (Multiphysics [_{a} is the mass coefficient, _{a} is a damping coefficient or mass coefficient,

On the left-hand side of equation (

The risk grade for storm surge is based on the maximum inundation depth according to the typhoon grade. The hazard map is used as the database showing the maximum inundation depth in the coastal areas regardless of the occurrence time (MLTMA [

SIND for storm surge in coefficient form.

Parameter | Heat transfer | Risk grade for storm surge |
---|---|---|

Temperature, | Risk grade (inundation), | |

_{a} | 0 | 0 |

_{a} | 1 | |

Conductivity coef. - | Resistance coef. - | |

0 | 0 | |

Velocity | Velocity | |

0 | 0 | |

Heat flux, | Risk flux, |

The parameters of Table

The coefficient required by the basic form is the resistance coefficient _{0} for coastal areas and _{ext} for in land areas. An inundation caused by storm surge depends on the terrain characteristics. Thus, the resistance coefficient should be reflected to elevation (DEM). DEM provided by the National Geographic Information Institute in Korea was used to cover land topography with the scale of the DEM of 1 : 5000 and the grid size of 5 m. The wave height with frequency is the most important factor and boundary condition affecting inundation. The calculations of wave height can generally take into account the effects of tide, wind, and pressure fluctuations. The wave height used in the SIND model was calculated by considering the path, wind speed, and wind field of 201 typhoons for 56 years from 1951 to 2006. Wave heights were calculated according to each frequency with the KOSY. It is determined by typhoon grade and calculated as an initial risk grade on the boundaries. A regression analysis was performed to estimate the initial risk grades conditions for all scenarios, using 3 conditions of frequency (50-year, 150-year, and 200-year). The risk grades on the land boundary are defined as the distance from the coast. The assumptions for the coefficients and each boundary condition are as follows:

The resistance coefficient depends on the topographical conditions of the coastal area

Resistance constant (

The risk grade (_{0}) at the coastal boundary depends on the grade of the typhoon and the wave height

The risk grade (_{ext}) at the land boundary is lower as the distance from the coast increases

The hazard map depicts the hazardous areas and risk grades with inundation depth according to storm surge conditions. The area and location of the flooded zones are important factors and related to the shape of inundated zones. The comparison of shape of inundated area with the flooded zone in hazard map should be conducted to examine the accuracy of this SIND model. As a result, it is necessary to compare the position and shape of inundation areas to verify the result from the SIND model. It introduced the shape similarity method to quantify how much similar two figures or maps by comparing in their positions, shapes, and areas. It can express the degree of similarity using the geometrical properties of the spatial dataset. However, it does not consider the risk grades because it can just compare two-dimensional figures in terms of geometry only. To consider the risk grades, the hazardous areas for each risk grade were divided and compared again with the graded flood zone in hazard map. Thus, the shape similarity with risk grade is most efficient way to verify the results and to determine accuracy. Kim et al. [

Concept of the CRITIC method. (a) Matching coupled object. (b) Position criterion: center of gravity. (c) Shape criterion: shape index. (d) Area criterion: ratio of overlapped area.

The position criterion is evaluated as the distance between the centers of gravity of two objects. The closer the position criterion is to 1.0, the more similar the object of the SIND model is to the hazard map._{m} is _{c} is _{m} and _{m} are the center of gravity for the hazard map, and _{c} and _{c} are the center of gravity for the SIND model.

The CRITIC method is mainly used in GIS-based mapping field, and the shape of object is close to basic shape like rectangle and circle. There is a limitation to using this method because the shape of the hazardous area for storm surge shows a thin and long band shape. Thus, this method was modified by adding the RCCI index that can apply the elongated shape._{m} is _{c} is _{m} is the perimeter of the shape in hazard map. _{c} is the perimeter in the SIND model. RCCI is added shape index. Equation is _{c} and _{m} are area of each shape. CA is circumscribed circle area. _{1} and _{2} are weights of 0.4 and 0.6, respectively.

The area criterion was estimated using the ration of overlapped area between 2 maps._{m} is the inundation area in hazard map and _{c} is the inundation area in the SIND model.

The weights are calculated using the information amount and the correlation coefficient. The closer each criterion (SP, SR, and SA) is to 1.0, the overall shape similarity has higher value. That means the overall shape similarity (

Using the trial and error method, the resistance coefficient (_{ext}) at the land boundary, and the initial risk grade (_{0}) at the coast boundary were calculated. The calculated coefficient and boundary conditions are considered with the characteristics of storm surge through assumptions. According to the assumptions, the distribution of _{1} is the empirical coefficient to be 0.5 and

Coefficient and boundary conditions in the SIND model: (a) resistance coef; (b) B.C; (c) section A; (d) section B.

Results of coefficient and boundary conditions: (a) resistance coefficient with elevation; (b) land boundary conditions with d; (c) wave height with frequency; (d) coastal boundary conditions with H.

As shown in Figure _{2} is equivalent to 2.525 in sections A and B, _{3} is –1.293 in section A and –5.293 in section B, _{4} is constant, 0.25, _{2}, _{3}, and _{4} are empirical coefficients, and

The reference value is the criterion which determines similarity between the result of the equation and the hazard map. This value is 0.6, and it is used in the GIS-based mapping field. When the shape similarity is 0.6 or more, it is estimated that the results in the SIND model are implemented well. The detailed results are shown in Table

Results of overall shape similarity (

50-year | 150-year | 200-year | |
---|---|---|---|

Total matching pairs | 38 | 50 | 45 |

>0.6 | 28 | 31 | 30 |

Rate (%) | 73.7 | 62.0 | 66.7 |

Results of shape similarity for each frequency: (a) 200-year; (b) 150-year; (c) 50-year.

The SIND model can predict the hazardous area caused by storm surges in a short time with simple input conditions. Table

Overall results of the SIND model.

Grade | Distance between center of gravity | Area (km^{2}) | Perimeter (km) | Ratio of overlapped area | Shape index | |||
---|---|---|---|---|---|---|---|---|

Each | Sum | Intersect | Each value | Difference | ||||

b1RA | 19.1 | 0.056 | 0.076 | 0.018 | 0.007 | 0.611 | 8.10 | 0.39 |

b1CA | 0.038 | 0.006 | 8.49 | |||||

b2RA | 176.5 | 0.029 | 0.051 | 0.013 | 0.005 | 0.601 | 8.50 | 0.87 |

b2CA | 0.035 | 0.006 | 9.37 | |||||

b3RA | 124.7 | 0.008 | 0.021 | 0.002 | 0.003 | 0.833 | 9.05 | 2.51 |

b3CA | 0.015 | 0.003 | 6.55 | |||||

b4RA | 14.9 | 0.006 | 0.018 | 0.001 | 0.002 | 0.857 | 6.63 | 2.37 |

b4CA | 0.013 | 0.002 | 4.26 | |||||

b5RA | 47.8 | 0.003 | 0.006 | 0.001 | 0.001 | 0.126 | 6.85 | 5.02 |

b5CA | 0.034 | 0.001 | 1.84 |

A corresponding wave height with 100-year frequency was entered for a model verification, and the results were compared with the hazard map at the same conditions: 100-year frequency of wave height. Shape similarity was used to calculate the accuracy of the SIND model. The wave height of 100-year frequency was calculated by regression equation.

A threshold is needed to determine whether two shapes are similar or not. In the CRITIC method, a subjective judgment process is necessary to calculate a threshold value. The matching pairs are directly divided into exact-matching and mismatching. The shape similarity of each matching pair is analyzed to estimate the threshold (see Figure

Examples of exact-matching and mismatching objects: (a) Exact 1; (b) Exact 2; (c) Mis 1; (d) Mis 2.

Threshold of the SIND model.

It is necessary to obtain the accuracy of the area, center of gravity, and perimeter of each matching pair before calculating the overall shape similarity. Determination coefficients, root mean square error (RMSE), and Nash–Sutcliffe efficiency (NSE) were used for estimating indexes of shape characteristics. The determination coefficient is an index for evaluating the relationship between the observations and the model for the same variable. As a value is closer to 1.0 from 0.0, it indicates that the model results fit the observative values well. Nash–Sutcliffe efficiency is an index that is used as much as the determination coefficient. The Nash–Sutcliffe efficiency is a technique that evaluates the efficiency of the model using the relationship between observations and the model. Ramanarayanan et al. [

Estimation of shape parameter.

Evaluation method | Center of gravity | ^{2}) | ||
---|---|---|---|---|

^{2} | 0.9984 | 0.9986 | 0.8746 | 0.9061 |

RMSE | 0.1937 | 0.1621 | 0.0176 | 1.0528 |

NSE | 0.9962 | 0.9966 | 0.4538 | 0.8102 |

Scatter plot of (a)

The accuracy of the results was verified at the random condition by using the thresholds. The shape similarity was calculated by matching the results with the hazard map for the wave height of 100-year frequency condition (see Table

Estimation of shape similarity.

Grade | SP | SA | SR | S |
---|---|---|---|---|

b1RA | 0.987 | 0.411 | 0.986 | 0.720 |

b1CA | ||||

b2RA | 0.883 | 0.421 | 0.973 | 0.685 |

b2CA | ||||

b3RA | 0.917 | 0.198 | 0.924 | 0.584 |

b3CA | ||||

b4RA | 0.990 | 0.174 | 0.926 | 0.599 |

b4CA | ||||

b5RA | 0.968 | 0.879 | 0.847 | 0.904 |

b5CA |

Verification results.

Parallel to the hazard map made by the MLTMA [

We reflect the physical characteristics of the disaster due to storm surge into this model by selecting PDE form as governing equation and setting the simple input and boundary conditions. The wave height, which is a representative input value, appears to be simple and robust, but it is calculated by the KOSY that can take into account the effects of tide, wind, and pressure fluctuations. And we used the trial and error method to decide coefficients of governing equation for storm surge. Thus, it can predict risk grades for all disaster scenarios with high accuracy and speed. The user can find out hazardous area within a few seconds (about 5 seconds) in any condition between 50-year and 200-year frequency of wave heights. As a result, this model can make up for the limits of scenario-based disaster countermeasures. The advantages of this model can be summarized in terms of convenience, speed, and accuracy. User does not require a complicated understanding of disaster mechanism. And there is no need for cornerstone work before simulating the numerical model. Thus, they can easily yield the results in the right time and right condition for the right decision making. Although the model was performed by simple procedures, it has a physical meaning reflected the disaster characteristics including initial wave height and geographical resistance. This model also improved computation time. As mentioned, it takes approximately 5 seconds for about 720,000 km^{2} to present each hazard map while the Delft3D used commonly takes about 2 days in the same condition. And the accuracy of this model was about 80% for arbitrary condition. However, since we decided the threshold values under empirical estimations by classifying the exact-matching and mismatching, it is essential to prescribe the exact-matching and the mismatching through the clear criteria. And we would calibrate narrowly and adjust carefully multiobjects corresponding to one object so that the shape similarity will increase overall.

The SIND model shows the new approach of disaster prediction using the interpolation method with PDE representing physical characteristics of the target phenomenon. This model extenuated the complexity of the prediction for storm surge such as long simulation time and the occurrence of uncertain disasters, which were the well-known limitations in numerical modelling. Therefore, it is possible to predict disaster risk grades much quickly using this model, which should be very helpful for policy decisions to respond disaster. In fact, an early warning is very important to reduce human injury and property damage just prior to and immediately after occurrence of any event of specific disaster. Thus, the SIND model is capable of amply accurate and much rapid predicting at the early stage. Also, it is based on database like hazard maps, which can be composed of structured, semistructured, and unstructured data. Therefore, it will be applicable to various disasters if more reliable database is acquired and higher accuracy is promised in the future.

And because this model used the results from numerical simulation or observation as input data for the scientific interpolation method, it does not consider the nonstationary of historical data. However, the historical data related to topography and climate are affected by extreme events as earthquakes. For instance, the change of topography will affect the occurrence of storm surge with physical laws. Thus, future works include the method how to regenerate risk grade considering such historical data.

The data used to support the findings of this study are available from the corresponding author upon request, and some of them would be restricted because of external security issues.

The authors declare that they have no conflicts of interest regarding the publication of this paper.

This work was supported by Korea Environment Industry & Technology Institute (KEITI) through Water Management Research Program, funded by Korea Ministry of Environment (127572).