INTRODUCTION
Flood disaster is a frequent natural calamity in China which is difficult to
control and always loses seriously. It’s essential to forecast the possibility
and intensity of flood, even more to estimate the possible loss. Obviously,
flood risk prediction and evaluation can avoid the disasters or reduce the loss.
Flood risk evaluation is to evaluate the occurrence probability of different
intensity flood and the possible loss, then judge which damage degree should
the flood disaster belong to. Now many researchers estimate flood by fuzzy method
(Kumar et al., 2011; Janal
and Stary, 2012; Zou et al., 2012), neural
network method (Pramanik and Panda, 2009; Sulaiman
et al., 2011), support vector machine (Huang
et al., 2010), genetic algorithm (Jin et
al., 2008), Monte Carlo simulation (Aronica et
al., 2012) and so on. However, all these approaches have their disadvantages
when the available data are insufficient to estimate or the data are random
and unpredictable. Considering the uncertainty and the randomness of flood disaster,
cloud model is used to estimate flood risk in this study.
THEORY OF CLOUD MODEL
Suppose U is quantitative domain expressed by accurate value, whose qualitative concept is A. If quantitative value xU and x is a random implement of A. Then the certainty degree of x on A, y = u(x) is random number which has stable tendency. The distribution of x in the domain u is called cloud and each x is called cloud droplet. The realization presents randomness and indeterminacy. Y also represents the determine degree of cloud droplet to the qualitative concept.
Shown as Fig. 1, cloud express overall qualitative concept
by three digital characters which are Expected value (Ex), Entropy(En) and Hyper
entropy(He). Expectation value (Ex) is the most typical sample which represents
qualitative concept. Entropy (En) is the uncertainty measure of the qualitative
concept. It not only measures the randomness of concept, reflecting discrete
extent of cloud droplets, but also measures the fuzziness of the concept, reflecting
the value range of acceptable could droplets in the universe of discourse. Hyper
Entropy (He) is the uncertain degree of entropy, that is, the entropy of En.
It reflects the cohesion degree of cloud droplets (Li, 2005).
The algorithm of production cloud is called cloud generator, which includes
forward cloud generator and backward cloud generator. Besides, forward cloud
generator can be divided into X condition cloud generator and Y condition cloud
generator. If the digital characteristics of cloud are inputted and the cloud
generator outputs many cloud drops (x_{i}, μ_{i}), it is
called forward cloud generator.

Fig. 1: 
Chart of normal cloud model 
On the contrary, if a group of cloud drops(x_{i}, μ_{i})
which conform to the normal cloud distributed rule are inputted into the cloud
generator while cloud’s three digital characteristics (Ex, En, He) and
the special value μ_{i} are outputted, it is named backward cloud
generator.
The forward cloud generator is widely applied. In order to discriminate the
application area, it is divided into X condition cloud generator and Y condition
cloud generator. The difference between them is input type. If cloud’s
three digital characteristics(Ex, En, He) and the special value x_{i}
are inputted, the cloud generator is called X condition cloud generator. If
cloud’s three digital characteristics (Ex, En, He) and the special value
μ_{i} are inputted, the cloud generator is called Y condition cloud
generator. X condition cloud generator and Y condition cloud generator are the
basis of doing uncertainty illation by cloud model (Hu
et al., 2007).
FLOOD RISK ESTIMATION BASED ON CLOUD MODEL
Flood risk estimation can be divided into chanciness assessment and vulnerability assessment. Flood chanciness is the possible harmful levels of flood such as the intensity and frequency, which is expressed by maximum average velocity, maximum average depth and flood duration in this study. Flood vulnerability is the possible loss levels of various types of hazardaffected bodies in specific region, which is expressed by agricultural output loss, industrial output loss and building loss in this case. Flood risk grade can be calculated after the chanciness factors and the vulnerability factors have been weighted integrated assessed. Risk is divided into four grade in this study, expressed by aggregation B = {B_{1}, B_{2}, B_{3}, B_{4}}.
Suppose there are m samples denoted as x_{1},x_{2}, … , x_{m} and n assessment factors denoted as v_{1}, v_{2}…,v_{n}. The attribute value of flood sample x_{j} for the assessment factor v_{i }is x_{ij}.
Foundation of review cloud model and score cloud model: The remark aggregation of assessment factors can be built up according to the disaster grade. It is expressed as A = {A_{1}, A_{2}, ……A_{k}} which is consistent to disaster grade. Then each remark can be quantized by the value and the fuzzy boundaries. According to a certain level review, each factor’ grade cloud model can be build as XC_{Ak}(Ex_{AK}, En_{AK}, He_{Ak}). The grade cloud model reflect the most typical value expression of each assessment factors under a certain level and reflect the fuzzy boundaries by Entropy.
In order to convert the qualitative words to quantitative value, the united score cloud model is built up. The score grades are expressed as B_{1}, B_{2}……B_{k}. Then the score model of one grade can be defined as YC_{Bk}(Ex_{BK}, En_{BK}, He_{Bk}). Hundredmark system is select in this study.
Forward reasoning by Single rule generator: The forward reasoning by
Single rule generator expresses the reasoning course from cloud’s quantitative
character to cloud’s qualitative character. The single rule generator is
combined by X condition cloud generator and Y condition cloud generator. The
reasoning rule of single rule generation can be expressed as “If A then
B” (Hu et al., 2007) which is determined
by its character. The A and B are respectively the forward parts and backward
parts.
Shown as Fig. 1, the specific algorithm is as follows:
• 
At first build X condition cloud generator by review grade
model, after inputting the three digital characteristics(Ex_{AK},
En_{AK}, He_{Ak}) and the number x_{ij} to activate
X cloud generator and then produce cloud drop to calculate each factor’s
membership u^{k}_{ij} in each grade 
• 
Secondly build Y condition cloud generator by score cloud
model, after inputting the three digital characteristics (Ex_{BK},
En_{BK}, He_{Bk}) and the membership, single factor’s
score q_{ij} can be calculated (Deng et al.,
2009) 
Shown as Fig. 2, the output of X condition cloud generator is the input of Y condition cloud generator and when connecting these two generators can found the single rule generator. It can realize the process of converting quantitative input to qualitative reasoning at first, then converting qualitative reasoning to quantitative output again.
Qualitative reasoning by X cloud generator: Calculate factors’
comprehensive evaluation score by weighting Singlefactor evaluation scores.
Comprehensive evaluation score is quantitative concept which reflects the severity
of risk by value. In fact people want to know which risk grade the samples belong,
which is the qualitative concept, so it’s necessary to qualitative infer
it by X condition cloud generator.
REVISION BASED ON CERTAINTY DEGREE
Certainty degree is an important guideline to measure the accuracy of qualitative
reasoning in cloud model. In order to make decision or evaluation people always
select the maximum degree of membership as the certainty degree to one grade.
This method is simple and unilateral, which is easy to increase evaluation error
because it only selects the maximum membership but loses the second membership.

Fig. 2: 
Forward reasoning by single generator 
Then it’s essential to analysis the result’s effectiveness and to
solve the failure of maximum membership principle. The article (Zhang,
2004) analyzes how to measure the effectiveness and the study (Liu
et al., 2010) proposes the principle of asymmetric proximity to solve
the failure of maximum membership. So the method of asymmetric proximity is
used to solve the problem in this study. The formulas are as follows:
In this formula, v^{h}_{j,t} represents the maximum value of factor j while v^{l}_{j,k} and v^{h}_{j,k}, respectively reflect the minimum and the maximum value of factor j on grade k. Formula for calculating closeness:
Then Z_{i} is the grade eigen value of sample i. The whole computation flow chart is expressed as Fig. 3.
CASE STUDY
In this study, flood risk statistics and economic statistics of JinJiang diversion area in 1998 are selected to estimate flood risk, shown as Table 1, besides, the flood risk assessment stand is shown as Table 2.

Fig. 3: 
Flow chart of assessment by improved cloud model 
Table 1: 
Flood risk sample indexes in JinJiang 

Table 2: 
Assessment standard of flood risk grade 

Table 3: 
Flood disaster assessment results by different method 

Foundation of review cloud model and score cloud model: By analyzing the risk statistics and referring the knowledge and experience of experts, build each factor’s remark cloud model. For example, according to the risk of four levels from weak to strong build remark grade cloud model of agricultural output factor, shown as (20,20/3,0.05), (50,50/3,0.05), (100,100/3,0.05), (200,200/3,0.05). The review cloud models of other factors are established by similar method.
In quantitative analysis, it is essential to analyze and quantitative express the quantity grade. So establish score cloud model to convert qualitative reasoning to quantitative expression. In this study, score cloud model is expressed by hundredmark system, shown as (30,5,0.05), (50,5,0.05), (70,5,0.05), (95,10,0.05). Reasoning by the single generator, the single factor’s score can be gotten.
Determination of weighting: In this study, Analytic hierarchy process (AHP) is applied to determine weight. The six factor’s ratio is defined as 1:0.5:0.5:.33:0.33:1. So the judgment matrix can be express as:
After it is calculated, the result is as follows: w_{i }= {0.0817, 0.1485, 0.1485, 0.2698, 0.2698, 0.0817}. The consistent ratio CR = 0.00296<0.1, so the weight is reasonable. The factor’s comprehensive assessment score can be obtained after people weighted calculate the weighted factor and the single factor’s score.
Qualitative reasoning by X cloud generator: Input the comprehensive score into the X cloud generator to infer the factor’s remark grade. In this course the same score cloud model is applied and the inference is finished by X cloud generator.
Revision of cloud model by certainty degree: After substituting the
comprehensive score into the above formula and checking calculation, the final
results are as follows. The table lists the results by cloud model before correction
and after correction by closeness; furthermore the results are also compared
with grey clustering method (Wang and Hu, 2010) and
the fuzzy method.
Shown from the Table 3, the revised results by certainty
degree is different with the results of unrevised in sample 4, 6 and 7, which
are all lower one grade than the unrevised result. It reflects the maximum membership
principle is ineffective on them because their maximum memberships are similar
with the second membership in these three samples. The asymmetric proximity
method revises the problem after comprehensively weighted calculating the distance
of each factor, which avoid the single factor’s abrupt character and more
objectively reflect the truth. Further more, the result of this method is similar
with the result by grey clustering method or the fuzzy method.
CONCLUSION
In this study, cloud model is applied to estimate flood risk. It is easy to quantitatively or qualitatively analyze risk by the transformation between them, which is the feature of cloud model. It also can provide timely foundation for policy decision. In order to make results tend to be reasonable, the certainty degree method is applied to correct the result. Compared with other two methods, the improved cloud model method is a timely possible assessment method.
ACKNOWLEDGMENTS
This work was supported by the National Key Basic Research Program of China (973 Program, Grant No. 2007CB714107), the Special Research Foundation for the Public Welfare Industry of the Ministry of Water Resources (Grant No. 201001080, 201001034) and the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20100142110012). Multidimensional geological interoperable model experiment and modeling technology support (Grant No.1212011120446).