Rapid Assessment Method of Flood Damage Using Spatial-Statistical Models

Attention to damage assessment is always a priority especially in cases of natural disaster. The state of Kelantan is known to be one of a few Malaysian states with noticeable natural disaster, in particular, flood. In December 2014, an extraordinary magnitude of flood – nicknamed as yellow flood – struck the state causing hundreds of million ringgit of damage to properties. The purpose of this study is to demonstrate a spatial approach to estimating property damage incurred by flood. By selecting a badly affected area, GIS was used to map geo-referenced flood-hit location in Kuala Krai, Kelantan. Flood hazard was modelled and superimposed on estimated property damage. GIS spatial technique was then employed to estimate the flood damage incurred. This study, however, did not make a complete damage assessment of the properties but rather focusing on the methodology of damage assessment to show how it can be implemented. In conclusion, GIS spatial technique can generally be used to provide flood damage rapid assessment method.


Flood Damage Model
For any property, expected physical damage (EPD) is generally modelled as: EPD = f (SD, CD) (1) where SD is structural damage and CD is content damage. SD comprises damage to land/soil and building while CD can refer to any type and/or amount of 'content' asset. Therefore, 'content' can comprise any moveable asset inside or outside a building such furniture, radio, television, appliance, vehicle, clothes, money, etc. Damage to land/soil is difficult to ascertain. For example, the eroded soil of a land parcel may need to be replaced. Consequently, it incurs re-fill cost. However, the amount of nutrients that is being washed away from a farm as well as re-fill cost are difficult to measure. In the same manner, the number of trees/crop damaged by flood is not easy to quantify.
To overcome the above difficulty, a survey based approach is proposed adopting the model as shown in equation (1). A sample survey needs to be conducted to collect data on the quantum of damage of each property or item at a particular site. For landed properties such as residential, office, and commercial, structural as well as content damages are taken as some percentages of property value. In general, equation (1) can be re-expressed as: EPD = SD + CD = (.p1*ALV +.p2*ABV) +.p3*(ALV + ABV) where ALV = assessed land value; ABV = assessed building value; .p1, .p2, and .p3 = certain defined "proportion" or "percentage" property component's damage in decimal form. ALV, ABV, and any other 'content' asset can be estimated by replacement cost approach. Alternatively, market value (MV) of property can be used in place of ALV and ABV if sales data are available.
For agricultural properties, damage can occur to land/soil (structure) and tree/crop (content). Again, it is difficult to ascertain damage to these elements. For compensation purposes, land/soil damage can be estimated as a percentage of market value of a particular type of agricultural property but tree/crop damage is much more difficult to estimate. The general formula for damage estimation of agricultural properties with immature trees/crop is modified from equation (2) as follows: EPD = SD + CD = land/soil + tree/crop= .q1*MV + n[(c-d)(1+i) t ] where MV = market value of a particular type of agricultural property (alternatively, actual replacement cost can be used); .q1 = a defined proportion in decimal form; c = cost of replacement new of the tree/crop; i = discounting rate; t = age of immature crop; n = number of damage trees/crop.
However, this formula cannot be used directly without modification based on the type of agricultural property under view. For example, damage to annual and perennial crop such as banana, maize, rubber, oil palm, cocoa, and orchard trees need to be estimated by "individual" tree counting -a daunting, if not impossible, task in FD-RAM. As another example, the immaturity period is different for different crops. For instance, the immature period for oil palm is four years, rubber five years, while for some orchard trees, this period may be up to seven years.
A sample survey in the disaster area is needed in order to compute the reasonable figures of all the above damage components. Specifically, a priori information is needed to compute .p1, .p2, and .p3.

Rapid Damage Assessment Procedure
The whole procedure of rapid assessment of flood damage is part of the general concept of decision support system promoted by Malczewski (1997). Ideally, it should become part of national disaster management programs of any country troubled by the disaster. The actual implementation of flood damage rapid assessment method is rather complex. It has two main components, namely mapping component and spatial modelling component.
The mapping component has the following mapping activities: boundary of study area; and distribution of poor population; sampling points to compute asset value, particularly building and land value. Geographic Information System (GIS) is a standard method for flood mapping through various kinds of software such as ArcGIS, MapInfo, Idrisi, etc. One of the most widely used GIS software is Environmental System Research Institute's (ESRI) ArcGIS 10.x.
The spatial modelling process has the following modelling activities: flood inundation coverage/flood modelling based on rainfall-runoff method; spatial flood damage-estimating model; and general damage estimate. Fundamentally, we can specify flood damage-estimating model in a number of ways (Messner et al., 2007;Merz jgg.ccsenet.org Journal of Geography and Geology Vol. 8, No. 4;2016Green et al., 2011). Factors such as flood depth, velocity, duration, water contamination, precaution, and warning time can be included. However, inclusion of flood factors cannot be generalized and is very much determined by data availability.
One potential spatial flood damage-estimating model is Geographically Weighted Regression (GWR) originally developed by Fotheringham et al. (2000;. Suppose we had some location in the study area, perhaps one of the data points, where (x,y) are the coordinates of its position. We can rewrite the model, in vector form as: V(x,y)W = W(x,y)a + W(x,y)Z + W(x,y)e where V is value of damage, a is regression's intercept, Z represents hydrological, physical, environmental, and socio-economic variables/factors, W is spatial weight matrix, e is error term, and is some measure of spatial component of data points. This relationship is fitted by least squares to give an estimate of the parameters at the location (x,y) and a predicted value. This is achieved through the implementation of the geographical weighting scheme. The weighting scheme is organized such that data nearer (x,y) is given a heavier weight in the model than data further away.
Using OLS, the parameters for a linear regression model is obtained by solving: The parameter estimates for GWR are solved using a weighting scheme: The weights are chosen such that those observations near the point in space where the parameter estimates are desired have more influence on the result than observations further away. Two functions we have used for the weight calculation have been (a) bi-square and (b) Gaussian. In the case of the Gaussian scheme, the weight for the i th observation is: where d is the Euclidean distance between the location of observation i and location g, and h is a quantity known as the bandwidth. (There are similarities between GWR and kernel regression). One characteristic that is not immediately obvious, is that the locations at which parameters are estimated need not be the ones at which the data have been collected.
The resulting parameter estimates are mapped in order to examine local variations in the parameter estimates. One might also map the standard errors of the parameters estimates as well. Hypothesis tests are possible -for example one might wish to test whether or not the variations in the values of a parameter in the study area are due to chance. The bandwidth may be either supplied by the user, or estimated using a technique such as cross validation technique. The (x,y)s are typically the locations at which data are collected. This allows a separate estimate of the parameters to be made at each data point. The resulting parameter estimates can them be mapped.
Flood Loss Estimation Model for the private sector (FLEMOps) on the meso scale (Thieken et al., 2008) is applied with some adaptation to the location situations. This model calculates the damage ratio for residential buildings as a function of inundation depth classified into five classes and building characteristics, i.e. three buildings types and two building qualities. To be applicable on the meso scale, mean building composition and the mean building quality per municipality were derived and the resulting damage ratios are multiplied by total asset values disaggregated to land use units (Thieken et al., 2005).
Spatially assessed flood damage by kriging technique is used in performing data analysis. A modified Ordinary Least Squares technique, kriging adopts weights to the surrounding measured values to derive a prediction for an unmeasured location. The general formula for both interpolators is formed as a weighted sum of the data: where = weighted sum of values; = the measured value at the ith location; = an unknown weight for the measured value at the ith location; = the prediction location; N = the number of measured values.
In the kriging technique, the weights (represented by ) are based on both the distance between the measured points and the prediction location and also the overall spatial arrangement of the measured points. To use the spatial arrangement in the weights, the spatial autocorrelation must be quantified.
Journal of Geography and Geology Vol. 8, No. 4;2016 In the ordinary kriging, the weight, depends on a fitted model to the measured points, the distance to the prediction location, and the spatial relationships among the measured values around the prediction location. The following section briefly discusses how the ordinary kriging formula is used to create a map of the prediction surface and a map of the accuracy of the predictions.
There are a number of kriging techniques discussed in the literature. However, to avoid cumbersome discussion, we would only adopt ordinary kriging in this study. Ordinary kriging estimates the unknown value using weighted linear combinations of the available sample (Isaaks and Srivastava, 1989): The error of ith estimate, r i , is the difference of estimated value and true value at that same location: The average error of a set of k estimates is: The error variance is: However, we cannot use the equation because we do not know the true value V 1 ,...,V k . In order to solve this problem, we apply a stationary random function that consists of several random variables, . X i is the location of observed data for i > 0 and i ≤ n. (n is the total number of observed data). The unknown value at the location X 0 we are trying to estimate is The estimated value represented by random function is: The error variance is: (14) is the covariance of the random variable V (X0) with itself and we assume that all of our random variables have the same variance while is the Lagrange parameter.
In order to get the minimum variance of error, we calculate the partial first derivatives of the equation (11) for each w and setting the result to 0. The example of differentiation with respect to w is: All of weight w i can be represented as:  By manually using the GIS map, various types of properties were identified and listed together with their corresponding damage (see Table 2). Many places were severely inundated, more than 70% in some cases. To further illustrate the use of FD-RAM, Figure 5 took a group of hard core poor people as a case. The map indicates that the hard core poor group experienced low to severe flood damage. Most of them experienced a total flood damage of about RM 10,000/household. This a was quite small figure and was not surprising as many of them did not own high-value property. Nonetheless, this damage was about 26 times their monthly income and can be considered a huge suffering for a hard core poor family. The model, however, suffered from prediction inaccuracy and, thus, overstressing on damage figure may not be desirable due to possible over-or underestimation in the assessment process.
Not all of hard core poor in the study area were affected by flood and, thus, those hit must be identified. This was done by picking the affected hard core poor's homes from the map via clipping menu available in ArcGIS. In this case, modelled "flood polygon" layer was clipped onto "survey points" layer. The resulting clipped layer was then superimposed on another layer, namely kriged estimated total flood damage (ETFD). Figure 5 shows the locational distribution of hard core poor which was superimposed over kriged values of estimated total flood damage (ETFD) modelled using Geographically Weighted Regression based on equation (17). By this way, the hydrological and physical aspects of flood were factored into flood damage-estimating model. ighted Regress s of ETFD.

Conclusion
Although accurate estimate was not the focus of this study, being able to derive some initial figure of flood damage is an important aspect of emergency relief and recovery program by the authority. The ability of knowing the 'possible' amount of damage at a specific site is an additional useful piece of information to the government.
The usefulness of rapid damage assessment of flood disaster largely depends on the completeness of data and accuracy of damage-estimating model. The correct GWR model specification that will result in satisfactory results was rather difficult and the available body of literature was not that useful to identify all the correct variables to include. Trial and error specification and test of the candidate variables such as those of geomorphological, hydrological, physical demanded a lot of data collection that was not possible due to resource constraint.
Accurate identification of 'itemised objects' affected by flood is always a problem of flood damage estimation. In this study, only content and structural damage of certain types of property/asset were quite conveniently accounted for their respective owners their respective owners their respective owners. Moveable assets such as vehicle, machinery, agricultural tools, etc. were not easily taken into account for various technical reasons. Assignment of damages of crops and animals to their respective owners was also difficult especially for those whose properties/assets were located on different sites away from their living premise.
Estimating flood damage was very challenging particularly in choosing the most appropriate approach of valuation. Cost, market and investment approaches are legitimate bases of asset valuation but none can be suitable for all situations and for all property types. Detailed examination of the property is thus necessary before deciding on the appropriate approach to valuation. This was simply not possible in rapid damage assessment procedure.