- Email: [email protected]
Estimation of waste generation from floods
Waste Management 27 (2007) 1717–1724 www.elsevier.com/locate/wasman
Estimation of waste generation from floods Jenq-Renn Chen *, Hsiao-Yun Tsai, Ping-Chi Hsu, Chun-Cheng Shen Department of Safety, Health and Environmental Engineering, National Kaohsiung First University of Science and Technology, 1 University Road, Yenchau, Kaohsiung 824, Taiwan Accepted 26 October 2006 Available online 12 December 2006
Abstract A framework of correlation for estimating the amount of waste generation from floods is developed. Flood waste data were collected from four recent typhoons in Taiwan. Parameters affecting the flood waste are analyzed. Population density, flooded area and amount of total rainfall are chosen as the correlating parameters for the model development, and regression diagnostics are performed to check the validity of the collected data. The simple linear model is shown to be incapable of correlating the flood waste data. An exponential model is proposed and shown to give acceptable correlation with the flood waste data spanning five orders of magnitude. The model can be useful in the planning of waste cleanup after floods. 2006 Elsevier Ltd. All rights reserved.
1. Introduction Taiwan is a subtropics island located in a region where major tropic cyclones, commonly known as typhoons, have occurred almost every year. These natural disasters have endangered the communities and caused significant losses in lives and properties. They have also generated significant amounts of waste; mainly flood damaged household utilities and furniture, building debris, green waste, etc., causing considerable cleanup and disposal challenges for local public officials. In September 2001, Typhoon Nari hit central and northern Taiwan, pouring more than 1000 mm of rain and causing floods in many parts of Taiwan, including the downtown Taipei City. The removal of the flood waste in Taipei City took more than a month, caused significant burden to the local waste removal workers and raised significant pressure on the city officials. Eventually, more than 190,000 tons of waste were removed and disposed, in addition to the normal daily waste, in Taipei City alone. This
*
Corresponding author. Tel.: +886 7 6011000x2313; fax: +886 7 6011061. E-mail address: [email protected] (J.-R. Chen). 0956-053X/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.wasman.2006.10.015
amount far exceeded the normal daily waste of 2000 tons per day in Taipei City. One possible reason that the removal work took such a long time is the underestimation or lack of estimation of the possible waste generation. Without knowing the potential amount of waste generation, city environmental officials cannot correctly request the resources for waste collection and disposal. In fact, there appears to be no suitable way to estimate the amount of waste generation from floods or other natural disasters. Existing disaster plans, for example the Integrated Waste Management Disaster Plan of the California Integrated Waste Management Board (1997), calls for ‘‘best guess’’ based on the variables below: the type and severity of disaster; location and extent of the damage; building types and their age (residential, commercial, etc.); number of buildings affected; and population affected. It is, however, not a trivial task to estimate the amount of waste generation. There is generally a lack of accurate historical data on the amount of waste generated from each
1718
J.-R. Chen et al. / Waste Management 27 (2007) 1717–1724
disaster. Also, numerous parameters may affect the waste generation and precise characterization is generally difficult. Furthermore, the parameters required for the estimation must be simple and ready to collect from the disaster information to provide prompt and timely results for waste management right after the disaster. To date, there appears to be no model or method in the open literature that is capable of estimating or predicting the amount of waste generated from floods. It is necessary to resolve the following issues to estimate the flood waste: 1. What parameters have the most significant impact on the waste generation from flood? 2. To what extent can variation in the waste generation be explained or accounted for solely by variation in these parameters? 3. Can quantitative relationships be obtained between waste generation and the flood? The above questions are crucial to the management of waste following a flood. If the above questions can be resolved properly, the proposed methodology can be incorporated into the planning process for waste cleanup. In this work, a framework for estimating the amount of waste generation from floods is proposed. Contributing parameters for the estimations are proposed. Correlation models are then derived based on historical data of waste generation from several recent floods in Taiwan. The models correlate the contributing parameters with a wide range of data from different areas and different floods. 2. Flood parameters and data collection 2.1. Parameters affecting flood waste It is crucial that the parameters affecting the waste generation from the flood are well defined and properly reflect the nature of the flood. The following parameters have been considered that might affect the waste generation from flood: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
living style, country or urban; population density; type of building; amount of total rainfall; flooded area; depth of the flood; duration of flood; duration between the current and previous floods; value of the flood land; and value of flood protection measures.
Not all of the above parameters are readily accessible for use in a predictive model. For example, it is difficult to quantify the effects of living style. However, the population density may reflect part of the living style and its
source is easy to access. A high rise building will certainly be less affected by the flood compared with a typical twostory house. However, complete information on the type of building is usually not available and is thus not used in the model. Amount of rainfall usually determines whether a particular typhoon will cause flooding. Although the rainfall may not be uniformly distributed across the interested region, its variation can be obtained from locally installed weather stations. Area of the flood is probably the most important parameter that determines the amount of waste generation. The waste generation from a typhoon without flooding is much less than one with flooding; and, based on past experience in Taiwan, a typhoon without flooding does not cause a waste disposal problem. The depth of flood is certainly an important parameter that may affect the waste generation. However, the depth of flood is not uniform across the flooded region. It also requires extensive and rapid efforts to collect the depth profile, which are usually not available during the flood. Therefore, the depth of flood is also not used for the model. Duration of the flood is also another parameter that may affect the waste generation. Flood damage and therefore waste generation will be more significant if the flood persists longer. However, persistence of the flood is also not uniform across the flooded region and its utilization in the model prediction is also difficult. Finally, the duration between consecutive floods may also affect the waste generation. Flood damage will certainly be less for a consecutive flood right after the previous flood. Nevertheless, it is expected that the effects of the duration will not be directly proportional to the waste generation and would be negligible when the duration exceed a certain period of time. The value of the flood land will reflect the living standard and possibly the amount of waste generation. However, the land value is always not uniform across the flooded area. Furthermore, the total flooded area is usually the parameter known during the flood. Exact distribution of flooded area is generally unknown, which renders the utilization of land value difficult. Value of flood protection measures of a particular area will reflect the possible severity of the flood. However, these data are difficult to collect and are also not used for the model. Eventually, only population density, amount of total rainfall, and flooded area are selected and used as the parameters in the model for estimating the amount of waste generation. These parameters are more readily available before or during the flood. Population density is readily available from national statistics, while amount of total rainfall and flooded area are available from the weather stations or site visits. The use of amount of rainfall, however, implies that the model will be limited to flood caused by rain. It is possible that the flood may be caused by other factors such as a tsunami. In this case, the depth of flood may be the dominant factor of waste generation. In this work, we will limit our scope to floods caused by rainfall, which is the major cause of flooding in Taiwan where our data are collected.
J.-R. Chen et al. / Waste Management 27 (2007) 1717–1724
1719
Flooding caused by other factors should be correlated with the cause of flooding and must be empirically tested.
Table 2 The amount of waste cleaned and its contributing parameters for the Nari typhoon
2.2. Flood data collection
Data point no.
County or city
9
Yilan County Taipei City Taipei County Keelung City Taoyuan County Hsinchu County Hsinchu City Miaoli County Taichung County Taichung City Changhua County Yunlin County Chiayi County Chiayi City Tainan County Kaohsiung County Pingtung County
In 2001, two consecutive typhoons hit Taiwan in July and September. The first is Typhoon Toraji, which hit and caused flooding in central Taiwan. The second is Typhoon Nari, which caused widespread floods over all Taiwan, including the downtown Taipei city. Tables 1 and 2 give the amount of waste cleaned up for Typhoon Toraji and Nari, respectively. After the floods in 2001, Taiwan suffered drought for the following 2 years. In 2004, two major typhoons hit Taiwan again and caused floods. Typhoon Mindulle hit central Taiwan in July 2004, and Typhoon Aere hit northern Taiwan in August 2004. The amount of waste cleaned up for Typhoons Mindulle and Aere are given in Tables 3 and 4, respectively. The waste data and the flooded area are collected by the local environmental bureaus of each county or city and provided to the Environmental Protection Administration (EPA) of Executive Yuan, Taiwan. The EPA collected these data to assess the possible environmental impact and to allocate resources to the required areas. Normally, data were reported to the EPA on a daily basis during the typhoon and summarized when all waste disposal efforts were completed. It is found that some of the data was based on the actual weighing of waste trucks, while others were estimates. The data showing flood waste amounts greater than 10,000 tons were checked and found to be in consistent with the monthly increment from the monthly waste data statistics. For data with less flood waste, the monthly increment during the flood from the monthly waste data statistics were not significant and
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Amount of waste cleaned (tons)
Population density (person/km2)
Flooded area (ha)
Total rainfall (mm)
230
217
200
664.3
193,102
9960
1225
994.3
190,106
1759
2564
879.5
125,244
2945
15
566.0
15,120
1444
73
749.7
1456
313
452
788.5
2140
3586
6
768.0
5172
308
1813
725.0
45
732
59
531.5
126
6019
10
391.2
1059
1223
280
504.5
972
576
2344
559.7
7446
296
2037
524.3
884
4465
20
1065.5
15,000
549
300
816.3
97
443
22
358.8
26
328
65.1
257.2
Data on total rainfall covers 16 September 2001 to 19 September 2001.
Table 1 The amount of waste cleaned and its contributing parameters for the Toraji typhoon Data point no.
County or city
1
Miaoli County Taichung County Taichung City Nantou County Changhua County Yunlin County Chiayi County Hualien County
2 3 4 5 6 7 8
Amount of waste cleaned (tons)
Population density (person/km2)
Flooded area (ha)
Total rainfall (mm)
2159
308
2725
365.7
1952
6019
350
223.8
866
732
4186
434.5
16,496
132
1751
450.0
479
1223
131
229.5
613
576
197
231.2
2457
296
445
226.5
1861
76
101
406.0
Data on total rainfall covers 29 July 2001 to 31 July 2001.
cannot be properly compared with the flood waste. It should also be stressed that the waste data related only to the waste from the flood. Normal daily waste is not included. Mud, soil and debris flow accompanied by the flood are also not included in the waste amount as they are normally disposed separately from the household waste. The flooded area data are again reported by the local environmental officers and are usually limited to residential areas. They are at best an estimate or sometimes taken from the reported data during weather news. Uncertainties are expected to be greater than for the waste amount, and there is a lack of other comparable sources to validate these data. Regression diagnostics will be used to check the potential influences of these data. Also included are the data of the two other contributing parameters for the model, collected in this work. The population density referred to the average population in the specified county or city. Generally the population density corresponding to the flooded area should be used
1720
J.-R. Chen et al. / Waste Management 27 (2007) 1717–1724
Table 3 The amount of waste cleaned and its contributing parameters for the Mindulle typhoon Data point no.
County or city
26
Miaoli County Taichung County Changhua County Nantou County Yunlin County Chiayi City Chiayi County Tainan County Kaohsiung County Pingtung County
27 28 29 30 31 32 33 34 35
Amount of waste cleaned (tons)
Population density (person/km2)
Flooded area (ha)
Total rainfall (mm)
460
308
58
267.2
15,866
744
29,500
481.3
1070
1226
587
397.7
4007
131
486
802.8
4607
571
11,608
519.7
3525
4504
335
293
8756
496.0
424
548
56
531.2
6050
444
35
324
9.5
484.5
8.1
429.7
16
558.8
Data on total rainfall covers 30 June 2004 to 3 July 2004.
Table 4 The amount of waste cleaned and its contributing parameters for the Aere typhoon Data point no.
County or city
36
Taipei City Taipei County Hsinchu City Hsinchu County Taichung County Chiayi County
37 38 39 40 41
Amount of waste cleaned (tons)
Population density (person/km2)
Flooded area (ha)
Total rainfall (mm)
4285
9649
1
619.3
52,351
1807
1236
424.8
1014
3717
10
134.5
330
327
266
314.5
25
744
6
449.5
132
293
817
211.8
Data on total rainfall covers 23 August 2004 to 25 August 2004.
preferably instead of the total area of the county or city. However, the distribution of the flooded area is usually not known. Thus, only the county average population density is used. Department of Statistics of the Ministry of Interior, Taiwan, published the population density for every county and city in Taiwan (Department of Statistics, 2004). In the present work, the population density data at the end of the year were used for the reported typhoon. The daily rainfall data measured by the weather stations of the Central Weather Bureau of Taiwan were used in the present work (Central Weather Bureau, 2004). The total rainfall for a typhoon is defined by the summation of
rainfall of all of the consecutive days covering the typhoon period. Data and exact dates are given in Tables 1–4. The amount of rainfall in a city or a county during a typhoon is usually not uniform. The distribution is strongly affected by topology of the terrain, the path of the typhoon, and many other factors. Nevertheless, floods mostly occurred in the plain area with the highest rainfall. Thus, the first three highest rainfalls in the plain area for a city or county were averaged and used as the rainfall for the city or county. In two cases, Hsinchu City and Chiayi City, which have only one weather station, it is used directly. The choice of average of the first three highest rainfalls rather than the average of all rainfall aims to highlight the rainstorm effect, which was one the major causes of flooding. The amount of rainfall relates in part to the depth of the flood and duration of the flood whose data were lacking or more difficult to collect. Its inclusion in the model is expected to improve the waste correlation. 3. Model development and results 3.1. Linear model The easiest method to correlate the waste generation is a linear model, which assumes a linear relationship between the amount of waste generation and the contributing factors. Thus we have: y ¼ a þ bx1 þ cx2 þ dx3 ;
ð1Þ
where the dependent variable y is the amount of waste generation (metric tons), and the independent variables x1, x2, and x3 are the population density (person/km2), flooded area (ha, 102 km2), amount of rainfall (mm), respectively. a, b, c, and d are the corresponding coefficients of correlation. All of the waste data from the four typhoons are correlated directly with the three independent variables. The resulting correlation is y ¼ 31; 044:2 þ 5:52x1 þ 0:538x2 þ 73:2x3 ;
R2 ¼ 0:272: ð2Þ
The results of the correlation are shown in Fig. 1. It is apparent from Fig. 1 that the linear correlation predicts the reported waste data poorly except for the data of Taipei City in the Nari typhoon, which has the largest amount of waste. In some cases, it even predicts negative amounts of waste. Analysis of variance showed that P values are 0.0495, 0.6775, 0.0181, and 0.0601 for the three independent variables x1, x2, and x3 and the intercept coefficient a, respectively. Normally, statistical significance between the independent variable and the dependent variable can be considered to be reached when P < 0.05; thus when P < 0.05, the independent variables can be used to predict the dependent variable. The P value of 0.6775 for the parameter of flooded area indicates its poor correlation to the waste generation. This result is, however, in direct
J.-R. Chen et al. / Waste Management 27 (2007) 1717–1724
Predicted amount (tons)
a
1000000
100000
10000
1000 2001/7 Toraji 2001/9 Nari 100
2004/7 Mindulle 2004/8 Aere
10 10
100
1000
10000
100000
1000000
100000
1000000
Reported amount (tons)
b
100000 2001/7 Toraji
Predicted amount (tons)
80000
2001/9 Nari 2004/7 Mindulle
60000
2004/8 Aere
40000 20000 0 -20000 10
100
1000
10000
Reported amount (tons)
Fig. 1. Comparison of prediction from the linear correlation, Eq. (2), and the reported data. (a) Log scale. (b) Linear scale. Negative predictions did not show in log scale.
contradiction of commonly accepted knowledge where flood generated waste should be strongly correlated with flooded area. If the parameter of flooded area is removed, leaving only two independent variables x1 and x3 for correlation, the resulting correlation has an R2 of 0.269, indicating slightly larger residues compared with Eq. (2). Furthermore, P values are 0.0512, 0.0161 and 0.0626, respectively, for x1 and x3, and the intercept coefficient a. No improvements in the P values were found. Apparently, the linear model cannot properly correlate the flood data. All analyses were conducted with the statistical analysis software STATA (Release 9) from Stata Co. The linear regression model is prone to a number of possible errors other than the inclusion of irrelevant variables or the omission of relevant ones. The most likely sources of errors in the present work come from the data uncertainties, which, as noted before, exist in the reported waste amount. The data on flooded area and the amount of rainfall have smaller uncertainties, but still are subject to measurement errors. Only the population density data comes from standard statistics and would be free from measurement error during the flood incident. It is common to perform regression diagnostics to see whether one or more particular data points or variables have unusual influences on the estimated regression parameters. Among the
1721
diagnostic techniques, the Studentized residual is the residual that is obtained from each data when the regression line is estimated with that particular data omitted (Belsley et al., 1980). Studentized residuals that are greater than 1.96 in absolute value can be regarded as outliers and should receive special attention. Among the 41 data points, only four data points have Studentized residuals greater than 1.96. These are the Taipei City, Taipei County, Keelung City, and Chiayi City; all in Typhoon Nari. The first three have waste amounts greater than 100,000 tons, while the Chiayi City data point has an exceptionally high rainfall. Deleting these potential outlier data points causes the R2 of the linear model to decrease from 0.272 to 0.0665. Pvalues for x1, x2 and x3 are 0.9211, 0.2380 and 0.3732, respectively. All of them exceeded the criterion of P < 0.05. Thus, the failure of the linear model cannot be attributed to inappropriate independent variables or the data uncertainties. Nonlinearity is probably the dominant cause. Another major drawback for the linear model is its poor predictability in case of poor input data. In some cases, negative values appear, which are certainly incorrect. The reason for the appearance of negative value is attributed to the dominance of data with very large amounts of waste over the other small values. It is also possible that the negative value is a result of the nonlinear relationship. Thus, a nonlinear exponential model is proposed. 3.2. Logarithm transformation and exponential model Inasmuch as the linear model has been shown to be inappropriate to the waste prediction, the following exponential model is proposed: y ¼ axb1 xc2 xd3 ;
ð3Þ
where y is the amount of waste generation in tons, x1, x2, and x3 are the population density (person/km2), flooded area (ha, 102 km2), and amount of rainfall (mm), respectively; a is a constant of regression; and b, c, and d are the exponents for variables x1, x2, and x3. Taking logarithm on both sides of Eq. (3) gives the following linear relationship between logarithm of the amount of waste and logarithms of the three contributing parameters: log y ¼ log a þ b log x1 þ c log x2 þ d log x3 :
ð4Þ
Eq. (4) is also equivalent to perform a logarithm transformation on the dependent and independent variables. The contribution of each parameter will be reflected in the magnitude of their exponent. Should the contribution of a particular parameter be small or negligible, the correlated exponent will simply be a small value closing to zero. Furthermore, the exponential model will never give a negative prediction irrespective of the value of the contributing parameters. This is of particular importance in waste management where only positive waste amounts are rational. In fact, a similar model has been used in predicting the thermophysical properties of hydrocarbon mixtures
1722
J.-R. Chen et al. / Waste Management 27 (2007) 1717–1724
(Riazi and Daubert, 1987) and fugitive dust emission from construction sand and gravel processing plant (Lee et al., 2001). Multiple regression of Eq. (4) gives the following correlation: log y ¼ 4:064 þ 0:696 log x1 þ 0:485 log x2 þ 1:552 log x3 ð5Þ or x0:485 x1:552 ; y ¼ 8:63 105 x0:696 1 2 3 2
ð6Þ
R is 0.416, much higher than those of the linear models. Analysis of variance showed that P values are 0.0093, 0.0006, 0.0157, and 0.0243 for the three independent variables log x1, log x2, log x3, and the intercept coefficient log a, respectively. All parameters achieved statistical significance criterion of P < 0.05. This is far better than the linear model using the same dependent variables. Performing regression diagnostics again found that among the 41 data points only two data points have Studentized residuals greater than 1.96. These are Keelung City in Typhoon Nari and Kaohsiung County in Typhoon Mindulle. These two data points are both featured by the small reported flooded area but relatively large amount of waste. Kaohsiung County in Typhoon Mindulle has a reported flooded area of only 8 ha but a reported waste of more than 6000 tons. This data differs significantly from the data of Kaohsiung County in Typhoon Nari, which has a flooded area of 22 ha but a reported waste amount of only 97 tons. We traced back to the original data source and confirmed that the flooded area for Kaohsiung County must be larger than the reported 8 ha. The exact value is, however, unknown. Similar observations were also found for Keelung City, which had reported waste of more than 120,000 tons but a flood area of only 15 ha. The Keelung Bureau of Environmental Protection confirmed that flooded area was significantly larger but was unable to provide the correct value. To confirm the data error, we performed another regression diagnostics by looking at the DFBETAS for each variable. DFBETAS measures the scaled difference between the estimate and the corresponding parameter that has been estimated with a particular observation omitted. Belsley et al. (1980) suggested observations pffiffiffiffi with DFBETAS in absolute values greater than 2= N as the criterion for deserving special attention. The calculated results of DFBETAS for the 41 data points are shown in Table 5. It is clear that both influential outliers with Studentized residual greater than 1.96, Keelung City in Typhoon Nari and Kaohsiung County in Typhoon Mindulle, have DFBETAS pffiffiffiffiffi of flooded area greater than 2= 41ð¼ 0:312Þ, confirming the possibilities of error in the reported flooded area. It is interesting to note that other data points also have DFBETAS greater than 0.312. For example, Hsinchu City in Typhoon Aere and Chiayi City in Typhoon Nari both have DFBETAS of total rainfall greater than 0.312. This is
coincident with the fact that both cities have only one weather station and thus may not reflect properly the true peak rainfall in the region. The data point of Hualien County in Typhoon Toraji has an exceptionally high DFBETAS in population density. Typhoon Toraji caused not only significant rainfall but also severe debris flow in Hualien County (Cheng et al., 2005). As mentioned earlier, mud, soil and debris flow accompanied by the flood are not included in present work. The DFBETAS reflects the missing influence of debris flow in the population density. Nevertheless, these data points have acceptable residuals and it is believed that data such as more weather stations or refined parameters may help to refine the correlation. Deleting the two data points, Keelung City in Typhoon Nari and Kaohsiung County in Typhoon Mindulle, caused the R2 of the exponential model to increase from 0.416 to 0.538. P values are 0.0029, <0.0001, 0.0113, and 0.0096 for the three independent variables log x1, log x2, log x3, and the intercept coefficient log a, respectively, all smaller than 0.05. It is apparent that after deleting these two uncertain data points, both the reducing P values and increasing R2 indicate improved correlation and statistical significance. The final resulting correlation is log y ¼ 4:137 þ 0:718 log x1 þ 0:600 log x2 þ 1:422 log x3 ð7Þ or y ¼ 7:29 105 x0:718 x0:600 x1:422 : 1 2 3
ð8Þ
The results of the correlation and the residual versus predicted plot are given in Figs. 2 and 3. Although the residual plot shows that the predicted values and reported values differ significantly to a maximum of one order of magnitude, there is no pattern in the plot, suggesting that there is no violation in the regression assumptions. It is also remarkable that all three parameters are considered significant by the analysis of variance. The one order of magnitude of scatter of the residuals is still acceptable considering the wide range of waste amount spanning five orders of magnitude. For example, the predicted waste for Taipei City in Typhoon Nari is 70,652 tons. It is about one-third of the reported value but should be sufficient to raise the attention of local waste management officials about the need for more urgent help to remove and dispose of the flood waste. To improve the predictions, it will be necessary to improve the quality of the data in the amount of waste and the contributing parameters. It is also interesting to note that the exponents of x1 and x2 are of the same magnitude. In fact, the product of x1 and x2 represents an estimation of flooded population which could be another factor affecting waste generation. Thus, the data for Eqs. (7) and (8) are correlated again with two parameters: x4 = x1 · x2 and x3. The resulting correlations are log y ¼ 3:7291 þ 0:5989 log x4 þ 1:3956 log x3
ð9Þ
J.-R. Chen et al. / Waste Management 27 (2007) 1717–1724
1723
Table 5 Studentized residuals and DFBETAS of the exponential model with all data points Data point no.
Typhoon
County or city
Studentized residual
DFBETAS(log x1)
DFBETAS(log x2)
DFBETAS(log x3)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41
Toraji Toraji Toraji Toraji Toraji Toraji Toraji Toraji Nari Nari Nari Nari Nari Nari Nari Nari Nari Nari Nari Nari Nari Nari Nari Nari Nari Mindulle Mindulle Mindulle Mindulle Mindulle Mindulle Mindulle Mindulle Mindulle Mindulle Aere Aere Aere Aere Aere Aere
Miaoli County Taichung County Taichung City Nantou County Changhua County Yunlin County Chiayi County Hualien County Yilan County Taipei City Taipei County Keelung City Taoyuan County Hsinchu County Hsinchu City Miaoli County Taichung County Taichung City Changhua County Yunlin County Chiayi County Chiayi City Tainan County Kaohsiung County Pingtung County Miaoli County Taichung County Changhua County Nantou County Yunlin County Chiayi City Chiayi County Tainan County Kaohsiung County Pingtung County Taipei City Taipei County Hsinchu City Hsinchu County Taichung County Chiayi County
0.028 0.222 1.125 1.512 0.126 0.196 1.070 1.407 0.930 0.602 1.177 2.739 0.890 0.389 0.085 0.032 1.838 1.336 0.571 1.014 0.507 1.205 0.805 0.535 1.198 0.493 0.091 0.563 0.516 0.506 0.797 0.268 0.379 2.072 1.347 1.252 0.836 1.196 0.286 1.400 0.747
0.0013 0.0846 0.0914 0.2986 0.0114 0.0017 0.0877 0.5193 0.1939 0.2545 0.1900 0.2939 0.0300 0.0544 0.0081 0.0031 0.0958 0.3001 0.0390 0.0158 0.0413 0.1797 0.0571 0.0715 0.1549 0.0710 0.0129 0.0579 0.1415 0.0334 0.1325 0.0104 0.0362 0.3619 0.2911 0.2242 0.1776 0.2779 0.0280 0.1525 0.0468
0.0042 0.0456 0.2533 0.0926 0.0032 0.0024 0.0383 0.2603 0.0824 0.1645 0.2517 0.3393 0.0528 0.0056 0.0169 0.0029 0.1793 0.1325 0.0265 0.1581 0.0561 0.1340 0.0112 0.0983 0.1285 0.0597 0.0350 0.0625 0.0317 0.1433 0.1020 0.0600 0.0448 0.5584 0.3350 0.2343 0.2342 0.1054 0.0032 0.3680 0.0630
0.0023 0.0731 0.0518 0.0187 0.0320 0.0464 0.2553 0.0206 0.1483 0.1328 0.2274 0.1848 0.1490 0.0795 0.0157 0.0051 0.1152 0.1028 0.0111 0.0543 0.0236 0.3524 0.1664 0.0293 0.2120 0.0793 0.0027 0.0394 0.1218 0.0070 0.0058 0.0039 0.0263 0.0372 0.1526 0.0789 0.0877 0.5937 0.0332 0.0352 0.2019
1000000
2001/7 Toraji
Predicted amount (tons)
2001/9 Nari 100000
2004/7 Mindulle 2004/8 Aere
10000
1000
100
10 10
100
1000
10000
100000
1000000
Reported amount (tons)
Fig. 2. Comparison of prediction from Eq. (8) and the reported data.
log(Reported amount) - log(Predicted amount)
Parameters x1, x2, and x3 denote the population density, flooded area, and total rainfall, respectively.
1.5
1
0.5
2001/7 Toraji 0
2001/9 Nari 2004/7 Mindulle
-0.5
2004/8 Aere
-1
-1.5 10
100
1000
10000
Predicted amount (tons)
Fig. 3. Residual versus predicted plot for Eq. (8).
100000
1724
J.-R. Chen et al. / Waste Management 27 (2007) 1717–1724
or
4. Conclusions
x1:422 : y ¼ 1:866 104 x0:5989 4 3 2
ð10Þ
The R of the two-parameter correlation increases slightly from 0.538 of the three-parameter model to 0.541, suggesting that the overall predicted results of Eq. (10) do not differ from the three-parameter correlation. P values are 0.0127, <0.0001 and 0.0113 for the two independent variables log x4, log x3, and the intercept coefficient log a, respectively. This suggests that flooded population is a crucial parameter affecting waste generation and a two-parameter model can also correlate the data well. Unfortunately, actual data on population affected by the flood is scarce. It is recommended to use the product of flooded area and population density for correlation. Among the three contributing parameters, the P value for the amount of rainfall is highest among others, indicating less statistical significance compared with other parameters. This is attributed to two inherent causes. First, the selected rainfall may not reflect the rainfall at the flooded area. The reported highest rainfall is still restricted by the limited number of weather stations and is at best an approximation to the rainfall in the flooded area. Furthermore, not all floods are caused directly by the rainfall. For example, the flood in Taipei County during the Aere typhoon is a result of river water leaking through an underground construction site near the river dam. The river water came from various upstream sources, which collected rainfall from a much larger area. The rain at the flooded area is not the sole cause of the flood. To properly model the flood and rainfall is certainly out of the scope of the present work. The present work nevertheless gives reasonable estimation for the amount of waste generation that is useful in planning of future flood waste. It is also recommended that the proposed methodology can be used by other regions with their own flood waste data to produce their flood waste correlation.
The parameters affecting waste generation from flooding caused by typhoon are analyzed. Flood data were collected from four recent typhoons in Taiwan. Linear regression is performed and shown to be incapable of correlating the collected data. A nonlinear, exponential equation is proposed and found to correlate the collected data reasonably well. Regression diagnostics are also performed to check the validity of the collected data. The proposed correlation will be useful in the planning of waste management due to floods. Acknowledgments This work is supported by the Environmental Protection Administration, Taiwan, ROC, through the grant no. EPA-92-U1J1-02-104 and EPA-93-U1J1-02-102. All supports are gratefully acknowledged. Helpful comments from the reviewers are also greatly appreciated. References Belsley, D.A., Kuh, E., Welsch, R.E., 1980. Regression Diagnostics, Identifying Influential Data and Sources of Collinearity. Wiley, New York, USA. California Integrated Waste Management Board, 1997. Integrated Waste Management Disaster Plan – Guidance for local government on disaster, http://www.ciwmb.ca.gov/disaster/disasterplan/default.htm. Central Weather Bureau, Taiwan, 2004. Typhoon Database, http:// rdc09.cwb.gov.tw/. Cheng, J.D., Huang, Y.C., Wu, H.L., Yeh, J.L., Chang, C.H., 2005. Hydrometeorological and landuse attributes of debris flows and debris floods during typhoon Toraji, 29–30 July 2001 in central Taiwan. J. Hydrol. 306, 161–173. Department of Statistics, 2004. Monthly Bulletin of Interior Statistics, Ministry of Interior, Taiwan, ROC. http://www.moi.gov.tw/stat/ month/elist.htm. Lee, C.W., Tang, L.W., Chang, C.T., 2001. Modeling of fugitive dust emission for construction sand and gravel processing plant. Environ. Sci. Tech. 35, 2073–2077. Riazi, M.R., Daubert, T.E., 1987. Characterization parameters for petroleum fractions. Ind. Eng. Chem. Res. 26, 755–759.
Estimation of waste generation from floods Jenq-Renn Chen *, Hsiao-Yun Tsai, Ping-Chi Hsu, Chun-Cheng Shen Department of Safety, Health and Environmental Engineering, National Kaohsiung First University of Science and Technology, 1 University Road, Yenchau, Kaohsiung 824, Taiwan Accepted 26 October 2006 Available online 12 December 2006
Abstract A framework of correlation for estimating the amount of waste generation from floods is developed. Flood waste data were collected from four recent typhoons in Taiwan. Parameters affecting the flood waste are analyzed. Population density, flooded area and amount of total rainfall are chosen as the correlating parameters for the model development, and regression diagnostics are performed to check the validity of the collected data. The simple linear model is shown to be incapable of correlating the flood waste data. An exponential model is proposed and shown to give acceptable correlation with the flood waste data spanning five orders of magnitude. The model can be useful in the planning of waste cleanup after floods. 2006 Elsevier Ltd. All rights reserved.
1. Introduction Taiwan is a subtropics island located in a region where major tropic cyclones, commonly known as typhoons, have occurred almost every year. These natural disasters have endangered the communities and caused significant losses in lives and properties. They have also generated significant amounts of waste; mainly flood damaged household utilities and furniture, building debris, green waste, etc., causing considerable cleanup and disposal challenges for local public officials. In September 2001, Typhoon Nari hit central and northern Taiwan, pouring more than 1000 mm of rain and causing floods in many parts of Taiwan, including the downtown Taipei City. The removal of the flood waste in Taipei City took more than a month, caused significant burden to the local waste removal workers and raised significant pressure on the city officials. Eventually, more than 190,000 tons of waste were removed and disposed, in addition to the normal daily waste, in Taipei City alone. This
*
Corresponding author. Tel.: +886 7 6011000x2313; fax: +886 7 6011061. E-mail address: [email protected] (J.-R. Chen). 0956-053X/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.wasman.2006.10.015
amount far exceeded the normal daily waste of 2000 tons per day in Taipei City. One possible reason that the removal work took such a long time is the underestimation or lack of estimation of the possible waste generation. Without knowing the potential amount of waste generation, city environmental officials cannot correctly request the resources for waste collection and disposal. In fact, there appears to be no suitable way to estimate the amount of waste generation from floods or other natural disasters. Existing disaster plans, for example the Integrated Waste Management Disaster Plan of the California Integrated Waste Management Board (1997), calls for ‘‘best guess’’ based on the variables below: the type and severity of disaster; location and extent of the damage; building types and their age (residential, commercial, etc.); number of buildings affected; and population affected. It is, however, not a trivial task to estimate the amount of waste generation. There is generally a lack of accurate historical data on the amount of waste generated from each
1718
J.-R. Chen et al. / Waste Management 27 (2007) 1717–1724
disaster. Also, numerous parameters may affect the waste generation and precise characterization is generally difficult. Furthermore, the parameters required for the estimation must be simple and ready to collect from the disaster information to provide prompt and timely results for waste management right after the disaster. To date, there appears to be no model or method in the open literature that is capable of estimating or predicting the amount of waste generated from floods. It is necessary to resolve the following issues to estimate the flood waste: 1. What parameters have the most significant impact on the waste generation from flood? 2. To what extent can variation in the waste generation be explained or accounted for solely by variation in these parameters? 3. Can quantitative relationships be obtained between waste generation and the flood? The above questions are crucial to the management of waste following a flood. If the above questions can be resolved properly, the proposed methodology can be incorporated into the planning process for waste cleanup. In this work, a framework for estimating the amount of waste generation from floods is proposed. Contributing parameters for the estimations are proposed. Correlation models are then derived based on historical data of waste generation from several recent floods in Taiwan. The models correlate the contributing parameters with a wide range of data from different areas and different floods. 2. Flood parameters and data collection 2.1. Parameters affecting flood waste It is crucial that the parameters affecting the waste generation from the flood are well defined and properly reflect the nature of the flood. The following parameters have been considered that might affect the waste generation from flood: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
living style, country or urban; population density; type of building; amount of total rainfall; flooded area; depth of the flood; duration of flood; duration between the current and previous floods; value of the flood land; and value of flood protection measures.
Not all of the above parameters are readily accessible for use in a predictive model. For example, it is difficult to quantify the effects of living style. However, the population density may reflect part of the living style and its
source is easy to access. A high rise building will certainly be less affected by the flood compared with a typical twostory house. However, complete information on the type of building is usually not available and is thus not used in the model. Amount of rainfall usually determines whether a particular typhoon will cause flooding. Although the rainfall may not be uniformly distributed across the interested region, its variation can be obtained from locally installed weather stations. Area of the flood is probably the most important parameter that determines the amount of waste generation. The waste generation from a typhoon without flooding is much less than one with flooding; and, based on past experience in Taiwan, a typhoon without flooding does not cause a waste disposal problem. The depth of flood is certainly an important parameter that may affect the waste generation. However, the depth of flood is not uniform across the flooded region. It also requires extensive and rapid efforts to collect the depth profile, which are usually not available during the flood. Therefore, the depth of flood is also not used for the model. Duration of the flood is also another parameter that may affect the waste generation. Flood damage and therefore waste generation will be more significant if the flood persists longer. However, persistence of the flood is also not uniform across the flooded region and its utilization in the model prediction is also difficult. Finally, the duration between consecutive floods may also affect the waste generation. Flood damage will certainly be less for a consecutive flood right after the previous flood. Nevertheless, it is expected that the effects of the duration will not be directly proportional to the waste generation and would be negligible when the duration exceed a certain period of time. The value of the flood land will reflect the living standard and possibly the amount of waste generation. However, the land value is always not uniform across the flooded area. Furthermore, the total flooded area is usually the parameter known during the flood. Exact distribution of flooded area is generally unknown, which renders the utilization of land value difficult. Value of flood protection measures of a particular area will reflect the possible severity of the flood. However, these data are difficult to collect and are also not used for the model. Eventually, only population density, amount of total rainfall, and flooded area are selected and used as the parameters in the model for estimating the amount of waste generation. These parameters are more readily available before or during the flood. Population density is readily available from national statistics, while amount of total rainfall and flooded area are available from the weather stations or site visits. The use of amount of rainfall, however, implies that the model will be limited to flood caused by rain. It is possible that the flood may be caused by other factors such as a tsunami. In this case, the depth of flood may be the dominant factor of waste generation. In this work, we will limit our scope to floods caused by rainfall, which is the major cause of flooding in Taiwan where our data are collected.
J.-R. Chen et al. / Waste Management 27 (2007) 1717–1724
1719
Flooding caused by other factors should be correlated with the cause of flooding and must be empirically tested.
Table 2 The amount of waste cleaned and its contributing parameters for the Nari typhoon
2.2. Flood data collection
Data point no.
County or city
9
Yilan County Taipei City Taipei County Keelung City Taoyuan County Hsinchu County Hsinchu City Miaoli County Taichung County Taichung City Changhua County Yunlin County Chiayi County Chiayi City Tainan County Kaohsiung County Pingtung County
In 2001, two consecutive typhoons hit Taiwan in July and September. The first is Typhoon Toraji, which hit and caused flooding in central Taiwan. The second is Typhoon Nari, which caused widespread floods over all Taiwan, including the downtown Taipei city. Tables 1 and 2 give the amount of waste cleaned up for Typhoon Toraji and Nari, respectively. After the floods in 2001, Taiwan suffered drought for the following 2 years. In 2004, two major typhoons hit Taiwan again and caused floods. Typhoon Mindulle hit central Taiwan in July 2004, and Typhoon Aere hit northern Taiwan in August 2004. The amount of waste cleaned up for Typhoons Mindulle and Aere are given in Tables 3 and 4, respectively. The waste data and the flooded area are collected by the local environmental bureaus of each county or city and provided to the Environmental Protection Administration (EPA) of Executive Yuan, Taiwan. The EPA collected these data to assess the possible environmental impact and to allocate resources to the required areas. Normally, data were reported to the EPA on a daily basis during the typhoon and summarized when all waste disposal efforts were completed. It is found that some of the data was based on the actual weighing of waste trucks, while others were estimates. The data showing flood waste amounts greater than 10,000 tons were checked and found to be in consistent with the monthly increment from the monthly waste data statistics. For data with less flood waste, the monthly increment during the flood from the monthly waste data statistics were not significant and
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Amount of waste cleaned (tons)
Population density (person/km2)
Flooded area (ha)
Total rainfall (mm)
230
217
200
664.3
193,102
9960
1225
994.3
190,106
1759
2564
879.5
125,244
2945
15
566.0
15,120
1444
73
749.7
1456
313
452
788.5
2140
3586
6
768.0
5172
308
1813
725.0
45
732
59
531.5
126
6019
10
391.2
1059
1223
280
504.5
972
576
2344
559.7
7446
296
2037
524.3
884
4465
20
1065.5
15,000
549
300
816.3
97
443
22
358.8
26
328
65.1
257.2
Data on total rainfall covers 16 September 2001 to 19 September 2001.
Table 1 The amount of waste cleaned and its contributing parameters for the Toraji typhoon Data point no.
County or city
1
Miaoli County Taichung County Taichung City Nantou County Changhua County Yunlin County Chiayi County Hualien County
2 3 4 5 6 7 8
Amount of waste cleaned (tons)
Population density (person/km2)
Flooded area (ha)
Total rainfall (mm)
2159
308
2725
365.7
1952
6019
350
223.8
866
732
4186
434.5
16,496
132
1751
450.0
479
1223
131
229.5
613
576
197
231.2
2457
296
445
226.5
1861
76
101
406.0
Data on total rainfall covers 29 July 2001 to 31 July 2001.
cannot be properly compared with the flood waste. It should also be stressed that the waste data related only to the waste from the flood. Normal daily waste is not included. Mud, soil and debris flow accompanied by the flood are also not included in the waste amount as they are normally disposed separately from the household waste. The flooded area data are again reported by the local environmental officers and are usually limited to residential areas. They are at best an estimate or sometimes taken from the reported data during weather news. Uncertainties are expected to be greater than for the waste amount, and there is a lack of other comparable sources to validate these data. Regression diagnostics will be used to check the potential influences of these data. Also included are the data of the two other contributing parameters for the model, collected in this work. The population density referred to the average population in the specified county or city. Generally the population density corresponding to the flooded area should be used
1720
J.-R. Chen et al. / Waste Management 27 (2007) 1717–1724
Table 3 The amount of waste cleaned and its contributing parameters for the Mindulle typhoon Data point no.
County or city
26
Miaoli County Taichung County Changhua County Nantou County Yunlin County Chiayi City Chiayi County Tainan County Kaohsiung County Pingtung County
27 28 29 30 31 32 33 34 35
Amount of waste cleaned (tons)
Population density (person/km2)
Flooded area (ha)
Total rainfall (mm)
460
308
58
267.2
15,866
744
29,500
481.3
1070
1226
587
397.7
4007
131
486
802.8
4607
571
11,608
519.7
3525
4504
335
293
8756
496.0
424
548
56
531.2
6050
444
35
324
9.5
484.5
8.1
429.7
16
558.8
Data on total rainfall covers 30 June 2004 to 3 July 2004.
Table 4 The amount of waste cleaned and its contributing parameters for the Aere typhoon Data point no.
County or city
36
Taipei City Taipei County Hsinchu City Hsinchu County Taichung County Chiayi County
37 38 39 40 41
Amount of waste cleaned (tons)
Population density (person/km2)
Flooded area (ha)
Total rainfall (mm)
4285
9649
1
619.3
52,351
1807
1236
424.8
1014
3717
10
134.5
330
327
266
314.5
25
744
6
449.5
132
293
817
211.8
Data on total rainfall covers 23 August 2004 to 25 August 2004.
preferably instead of the total area of the county or city. However, the distribution of the flooded area is usually not known. Thus, only the county average population density is used. Department of Statistics of the Ministry of Interior, Taiwan, published the population density for every county and city in Taiwan (Department of Statistics, 2004). In the present work, the population density data at the end of the year were used for the reported typhoon. The daily rainfall data measured by the weather stations of the Central Weather Bureau of Taiwan were used in the present work (Central Weather Bureau, 2004). The total rainfall for a typhoon is defined by the summation of
rainfall of all of the consecutive days covering the typhoon period. Data and exact dates are given in Tables 1–4. The amount of rainfall in a city or a county during a typhoon is usually not uniform. The distribution is strongly affected by topology of the terrain, the path of the typhoon, and many other factors. Nevertheless, floods mostly occurred in the plain area with the highest rainfall. Thus, the first three highest rainfalls in the plain area for a city or county were averaged and used as the rainfall for the city or county. In two cases, Hsinchu City and Chiayi City, which have only one weather station, it is used directly. The choice of average of the first three highest rainfalls rather than the average of all rainfall aims to highlight the rainstorm effect, which was one the major causes of flooding. The amount of rainfall relates in part to the depth of the flood and duration of the flood whose data were lacking or more difficult to collect. Its inclusion in the model is expected to improve the waste correlation. 3. Model development and results 3.1. Linear model The easiest method to correlate the waste generation is a linear model, which assumes a linear relationship between the amount of waste generation and the contributing factors. Thus we have: y ¼ a þ bx1 þ cx2 þ dx3 ;
ð1Þ
where the dependent variable y is the amount of waste generation (metric tons), and the independent variables x1, x2, and x3 are the population density (person/km2), flooded area (ha, 102 km2), amount of rainfall (mm), respectively. a, b, c, and d are the corresponding coefficients of correlation. All of the waste data from the four typhoons are correlated directly with the three independent variables. The resulting correlation is y ¼ 31; 044:2 þ 5:52x1 þ 0:538x2 þ 73:2x3 ;
R2 ¼ 0:272: ð2Þ
The results of the correlation are shown in Fig. 1. It is apparent from Fig. 1 that the linear correlation predicts the reported waste data poorly except for the data of Taipei City in the Nari typhoon, which has the largest amount of waste. In some cases, it even predicts negative amounts of waste. Analysis of variance showed that P values are 0.0495, 0.6775, 0.0181, and 0.0601 for the three independent variables x1, x2, and x3 and the intercept coefficient a, respectively. Normally, statistical significance between the independent variable and the dependent variable can be considered to be reached when P < 0.05; thus when P < 0.05, the independent variables can be used to predict the dependent variable. The P value of 0.6775 for the parameter of flooded area indicates its poor correlation to the waste generation. This result is, however, in direct
J.-R. Chen et al. / Waste Management 27 (2007) 1717–1724
Predicted amount (tons)
a
1000000
100000
10000
1000 2001/7 Toraji 2001/9 Nari 100
2004/7 Mindulle 2004/8 Aere
10 10
100
1000
10000
100000
1000000
100000
1000000
Reported amount (tons)
b
100000 2001/7 Toraji
Predicted amount (tons)
80000
2001/9 Nari 2004/7 Mindulle
60000
2004/8 Aere
40000 20000 0 -20000 10
100
1000
10000
Reported amount (tons)
Fig. 1. Comparison of prediction from the linear correlation, Eq. (2), and the reported data. (a) Log scale. (b) Linear scale. Negative predictions did not show in log scale.
contradiction of commonly accepted knowledge where flood generated waste should be strongly correlated with flooded area. If the parameter of flooded area is removed, leaving only two independent variables x1 and x3 for correlation, the resulting correlation has an R2 of 0.269, indicating slightly larger residues compared with Eq. (2). Furthermore, P values are 0.0512, 0.0161 and 0.0626, respectively, for x1 and x3, and the intercept coefficient a. No improvements in the P values were found. Apparently, the linear model cannot properly correlate the flood data. All analyses were conducted with the statistical analysis software STATA (Release 9) from Stata Co. The linear regression model is prone to a number of possible errors other than the inclusion of irrelevant variables or the omission of relevant ones. The most likely sources of errors in the present work come from the data uncertainties, which, as noted before, exist in the reported waste amount. The data on flooded area and the amount of rainfall have smaller uncertainties, but still are subject to measurement errors. Only the population density data comes from standard statistics and would be free from measurement error during the flood incident. It is common to perform regression diagnostics to see whether one or more particular data points or variables have unusual influences on the estimated regression parameters. Among the
1721
diagnostic techniques, the Studentized residual is the residual that is obtained from each data when the regression line is estimated with that particular data omitted (Belsley et al., 1980). Studentized residuals that are greater than 1.96 in absolute value can be regarded as outliers and should receive special attention. Among the 41 data points, only four data points have Studentized residuals greater than 1.96. These are the Taipei City, Taipei County, Keelung City, and Chiayi City; all in Typhoon Nari. The first three have waste amounts greater than 100,000 tons, while the Chiayi City data point has an exceptionally high rainfall. Deleting these potential outlier data points causes the R2 of the linear model to decrease from 0.272 to 0.0665. Pvalues for x1, x2 and x3 are 0.9211, 0.2380 and 0.3732, respectively. All of them exceeded the criterion of P < 0.05. Thus, the failure of the linear model cannot be attributed to inappropriate independent variables or the data uncertainties. Nonlinearity is probably the dominant cause. Another major drawback for the linear model is its poor predictability in case of poor input data. In some cases, negative values appear, which are certainly incorrect. The reason for the appearance of negative value is attributed to the dominance of data with very large amounts of waste over the other small values. It is also possible that the negative value is a result of the nonlinear relationship. Thus, a nonlinear exponential model is proposed. 3.2. Logarithm transformation and exponential model Inasmuch as the linear model has been shown to be inappropriate to the waste prediction, the following exponential model is proposed: y ¼ axb1 xc2 xd3 ;
ð3Þ
where y is the amount of waste generation in tons, x1, x2, and x3 are the population density (person/km2), flooded area (ha, 102 km2), and amount of rainfall (mm), respectively; a is a constant of regression; and b, c, and d are the exponents for variables x1, x2, and x3. Taking logarithm on both sides of Eq. (3) gives the following linear relationship between logarithm of the amount of waste and logarithms of the three contributing parameters: log y ¼ log a þ b log x1 þ c log x2 þ d log x3 :
ð4Þ
Eq. (4) is also equivalent to perform a logarithm transformation on the dependent and independent variables. The contribution of each parameter will be reflected in the magnitude of their exponent. Should the contribution of a particular parameter be small or negligible, the correlated exponent will simply be a small value closing to zero. Furthermore, the exponential model will never give a negative prediction irrespective of the value of the contributing parameters. This is of particular importance in waste management where only positive waste amounts are rational. In fact, a similar model has been used in predicting the thermophysical properties of hydrocarbon mixtures
1722
J.-R. Chen et al. / Waste Management 27 (2007) 1717–1724
(Riazi and Daubert, 1987) and fugitive dust emission from construction sand and gravel processing plant (Lee et al., 2001). Multiple regression of Eq. (4) gives the following correlation: log y ¼ 4:064 þ 0:696 log x1 þ 0:485 log x2 þ 1:552 log x3 ð5Þ or x0:485 x1:552 ; y ¼ 8:63 105 x0:696 1 2 3 2
ð6Þ
R is 0.416, much higher than those of the linear models. Analysis of variance showed that P values are 0.0093, 0.0006, 0.0157, and 0.0243 for the three independent variables log x1, log x2, log x3, and the intercept coefficient log a, respectively. All parameters achieved statistical significance criterion of P < 0.05. This is far better than the linear model using the same dependent variables. Performing regression diagnostics again found that among the 41 data points only two data points have Studentized residuals greater than 1.96. These are Keelung City in Typhoon Nari and Kaohsiung County in Typhoon Mindulle. These two data points are both featured by the small reported flooded area but relatively large amount of waste. Kaohsiung County in Typhoon Mindulle has a reported flooded area of only 8 ha but a reported waste of more than 6000 tons. This data differs significantly from the data of Kaohsiung County in Typhoon Nari, which has a flooded area of 22 ha but a reported waste amount of only 97 tons. We traced back to the original data source and confirmed that the flooded area for Kaohsiung County must be larger than the reported 8 ha. The exact value is, however, unknown. Similar observations were also found for Keelung City, which had reported waste of more than 120,000 tons but a flood area of only 15 ha. The Keelung Bureau of Environmental Protection confirmed that flooded area was significantly larger but was unable to provide the correct value. To confirm the data error, we performed another regression diagnostics by looking at the DFBETAS for each variable. DFBETAS measures the scaled difference between the estimate and the corresponding parameter that has been estimated with a particular observation omitted. Belsley et al. (1980) suggested observations pffiffiffiffi with DFBETAS in absolute values greater than 2= N as the criterion for deserving special attention. The calculated results of DFBETAS for the 41 data points are shown in Table 5. It is clear that both influential outliers with Studentized residual greater than 1.96, Keelung City in Typhoon Nari and Kaohsiung County in Typhoon Mindulle, have DFBETAS pffiffiffiffiffi of flooded area greater than 2= 41ð¼ 0:312Þ, confirming the possibilities of error in the reported flooded area. It is interesting to note that other data points also have DFBETAS greater than 0.312. For example, Hsinchu City in Typhoon Aere and Chiayi City in Typhoon Nari both have DFBETAS of total rainfall greater than 0.312. This is
coincident with the fact that both cities have only one weather station and thus may not reflect properly the true peak rainfall in the region. The data point of Hualien County in Typhoon Toraji has an exceptionally high DFBETAS in population density. Typhoon Toraji caused not only significant rainfall but also severe debris flow in Hualien County (Cheng et al., 2005). As mentioned earlier, mud, soil and debris flow accompanied by the flood are not included in present work. The DFBETAS reflects the missing influence of debris flow in the population density. Nevertheless, these data points have acceptable residuals and it is believed that data such as more weather stations or refined parameters may help to refine the correlation. Deleting the two data points, Keelung City in Typhoon Nari and Kaohsiung County in Typhoon Mindulle, caused the R2 of the exponential model to increase from 0.416 to 0.538. P values are 0.0029, <0.0001, 0.0113, and 0.0096 for the three independent variables log x1, log x2, log x3, and the intercept coefficient log a, respectively, all smaller than 0.05. It is apparent that after deleting these two uncertain data points, both the reducing P values and increasing R2 indicate improved correlation and statistical significance. The final resulting correlation is log y ¼ 4:137 þ 0:718 log x1 þ 0:600 log x2 þ 1:422 log x3 ð7Þ or y ¼ 7:29 105 x0:718 x0:600 x1:422 : 1 2 3
ð8Þ
The results of the correlation and the residual versus predicted plot are given in Figs. 2 and 3. Although the residual plot shows that the predicted values and reported values differ significantly to a maximum of one order of magnitude, there is no pattern in the plot, suggesting that there is no violation in the regression assumptions. It is also remarkable that all three parameters are considered significant by the analysis of variance. The one order of magnitude of scatter of the residuals is still acceptable considering the wide range of waste amount spanning five orders of magnitude. For example, the predicted waste for Taipei City in Typhoon Nari is 70,652 tons. It is about one-third of the reported value but should be sufficient to raise the attention of local waste management officials about the need for more urgent help to remove and dispose of the flood waste. To improve the predictions, it will be necessary to improve the quality of the data in the amount of waste and the contributing parameters. It is also interesting to note that the exponents of x1 and x2 are of the same magnitude. In fact, the product of x1 and x2 represents an estimation of flooded population which could be another factor affecting waste generation. Thus, the data for Eqs. (7) and (8) are correlated again with two parameters: x4 = x1 · x2 and x3. The resulting correlations are log y ¼ 3:7291 þ 0:5989 log x4 þ 1:3956 log x3
ð9Þ
J.-R. Chen et al. / Waste Management 27 (2007) 1717–1724
1723
Table 5 Studentized residuals and DFBETAS of the exponential model with all data points Data point no.
Typhoon
County or city
Studentized residual
DFBETAS(log x1)
DFBETAS(log x2)
DFBETAS(log x3)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41
Toraji Toraji Toraji Toraji Toraji Toraji Toraji Toraji Nari Nari Nari Nari Nari Nari Nari Nari Nari Nari Nari Nari Nari Nari Nari Nari Nari Mindulle Mindulle Mindulle Mindulle Mindulle Mindulle Mindulle Mindulle Mindulle Mindulle Aere Aere Aere Aere Aere Aere
Miaoli County Taichung County Taichung City Nantou County Changhua County Yunlin County Chiayi County Hualien County Yilan County Taipei City Taipei County Keelung City Taoyuan County Hsinchu County Hsinchu City Miaoli County Taichung County Taichung City Changhua County Yunlin County Chiayi County Chiayi City Tainan County Kaohsiung County Pingtung County Miaoli County Taichung County Changhua County Nantou County Yunlin County Chiayi City Chiayi County Tainan County Kaohsiung County Pingtung County Taipei City Taipei County Hsinchu City Hsinchu County Taichung County Chiayi County
0.028 0.222 1.125 1.512 0.126 0.196 1.070 1.407 0.930 0.602 1.177 2.739 0.890 0.389 0.085 0.032 1.838 1.336 0.571 1.014 0.507 1.205 0.805 0.535 1.198 0.493 0.091 0.563 0.516 0.506 0.797 0.268 0.379 2.072 1.347 1.252 0.836 1.196 0.286 1.400 0.747
0.0013 0.0846 0.0914 0.2986 0.0114 0.0017 0.0877 0.5193 0.1939 0.2545 0.1900 0.2939 0.0300 0.0544 0.0081 0.0031 0.0958 0.3001 0.0390 0.0158 0.0413 0.1797 0.0571 0.0715 0.1549 0.0710 0.0129 0.0579 0.1415 0.0334 0.1325 0.0104 0.0362 0.3619 0.2911 0.2242 0.1776 0.2779 0.0280 0.1525 0.0468
0.0042 0.0456 0.2533 0.0926 0.0032 0.0024 0.0383 0.2603 0.0824 0.1645 0.2517 0.3393 0.0528 0.0056 0.0169 0.0029 0.1793 0.1325 0.0265 0.1581 0.0561 0.1340 0.0112 0.0983 0.1285 0.0597 0.0350 0.0625 0.0317 0.1433 0.1020 0.0600 0.0448 0.5584 0.3350 0.2343 0.2342 0.1054 0.0032 0.3680 0.0630
0.0023 0.0731 0.0518 0.0187 0.0320 0.0464 0.2553 0.0206 0.1483 0.1328 0.2274 0.1848 0.1490 0.0795 0.0157 0.0051 0.1152 0.1028 0.0111 0.0543 0.0236 0.3524 0.1664 0.0293 0.2120 0.0793 0.0027 0.0394 0.1218 0.0070 0.0058 0.0039 0.0263 0.0372 0.1526 0.0789 0.0877 0.5937 0.0332 0.0352 0.2019
1000000
2001/7 Toraji
Predicted amount (tons)
2001/9 Nari 100000
2004/7 Mindulle 2004/8 Aere
10000
1000
100
10 10
100
1000
10000
100000
1000000
Reported amount (tons)
Fig. 2. Comparison of prediction from Eq. (8) and the reported data.
log(Reported amount) - log(Predicted amount)
Parameters x1, x2, and x3 denote the population density, flooded area, and total rainfall, respectively.
1.5
1
0.5
2001/7 Toraji 0
2001/9 Nari 2004/7 Mindulle
-0.5
2004/8 Aere
-1
-1.5 10
100
1000
10000
Predicted amount (tons)
Fig. 3. Residual versus predicted plot for Eq. (8).
100000
1724
J.-R. Chen et al. / Waste Management 27 (2007) 1717–1724
or
4. Conclusions
x1:422 : y ¼ 1:866 104 x0:5989 4 3 2
ð10Þ
The R of the two-parameter correlation increases slightly from 0.538 of the three-parameter model to 0.541, suggesting that the overall predicted results of Eq. (10) do not differ from the three-parameter correlation. P values are 0.0127, <0.0001 and 0.0113 for the two independent variables log x4, log x3, and the intercept coefficient log a, respectively. This suggests that flooded population is a crucial parameter affecting waste generation and a two-parameter model can also correlate the data well. Unfortunately, actual data on population affected by the flood is scarce. It is recommended to use the product of flooded area and population density for correlation. Among the three contributing parameters, the P value for the amount of rainfall is highest among others, indicating less statistical significance compared with other parameters. This is attributed to two inherent causes. First, the selected rainfall may not reflect the rainfall at the flooded area. The reported highest rainfall is still restricted by the limited number of weather stations and is at best an approximation to the rainfall in the flooded area. Furthermore, not all floods are caused directly by the rainfall. For example, the flood in Taipei County during the Aere typhoon is a result of river water leaking through an underground construction site near the river dam. The river water came from various upstream sources, which collected rainfall from a much larger area. The rain at the flooded area is not the sole cause of the flood. To properly model the flood and rainfall is certainly out of the scope of the present work. The present work nevertheless gives reasonable estimation for the amount of waste generation that is useful in planning of future flood waste. It is also recommended that the proposed methodology can be used by other regions with their own flood waste data to produce their flood waste correlation.
The parameters affecting waste generation from flooding caused by typhoon are analyzed. Flood data were collected from four recent typhoons in Taiwan. Linear regression is performed and shown to be incapable of correlating the collected data. A nonlinear, exponential equation is proposed and found to correlate the collected data reasonably well. Regression diagnostics are also performed to check the validity of the collected data. The proposed correlation will be useful in the planning of waste management due to floods. Acknowledgments This work is supported by the Environmental Protection Administration, Taiwan, ROC, through the grant no. EPA-92-U1J1-02-104 and EPA-93-U1J1-02-102. All supports are gratefully acknowledged. Helpful comments from the reviewers are also greatly appreciated. References Belsley, D.A., Kuh, E., Welsch, R.E., 1980. Regression Diagnostics, Identifying Influential Data and Sources of Collinearity. Wiley, New York, USA. California Integrated Waste Management Board, 1997. Integrated Waste Management Disaster Plan – Guidance for local government on disaster, http://www.ciwmb.ca.gov/disaster/disasterplan/default.htm. Central Weather Bureau, Taiwan, 2004. Typhoon Database, http:// rdc09.cwb.gov.tw/. Cheng, J.D., Huang, Y.C., Wu, H.L., Yeh, J.L., Chang, C.H., 2005. Hydrometeorological and landuse attributes of debris flows and debris floods during typhoon Toraji, 29–30 July 2001 in central Taiwan. J. Hydrol. 306, 161–173. Department of Statistics, 2004. Monthly Bulletin of Interior Statistics, Ministry of Interior, Taiwan, ROC. http://www.moi.gov.tw/stat/ month/elist.htm. Lee, C.W., Tang, L.W., Chang, C.T., 2001. Modeling of fugitive dust emission for construction sand and gravel processing plant. Environ. Sci. Tech. 35, 2073–2077. Riazi, M.R., Daubert, T.E., 1987. Characterization parameters for petroleum fractions. Ind. Eng. Chem. Res. 26, 755–759.