(A) Influencing factors of groundwater pollution
There are many factors affecting groundwater vulnerability, which can be summarized into two categories: natural factors and human factors. Natural factors include topography, geology and hydrogeological conditions of aquifer. Man-made factors mainly refer to various behavioral factors that may cause groundwater environmental pollution [16, 17]. Table 1-2- 1 lists the natural and human factors that affect groundwater pollution.
Table 1-2- 1 Influencing factors of groundwater pollution
(B) the selection of evaluation indicators
Before the pollutants applied to the surface reach a certain position in the aquifer, they are influenced by many physical, chemical and biochemical processes above the ground, soil, vadose zone and below the groundwater level (Figure 1-2- 1), and a reasonable and scientific pollution assessment index system should reflect these main influencing processes as much as possible.
Figure 1-2- 1 Schematic diagram of pollutant migration to aquifer.
Second, the division of evaluation units
Due to the diversity and complexity of various geological factors in each local area, in order to achieve more accurate evaluation, the whole research area needs to be divided into several small pixels, that is, evaluation units. According to the different situation of each small area, different attributes are given respectively, and then regional evaluation is carried out according to these attributes. There are three commonly used division methods, namely, triangle division method, square division method and irregular polygon division method [18].
(A) triangulation method
Triangular unit division method is to divide the evaluation area on the basis of triangle. Generally speaking, it is arbitrary to divide the evaluation area units in this way, but the following three principles should be followed:
1) Any angle of the triangle shall not be greater than 90, and the lengths of the three sides shall be as close as possible.
2) The vertex of a triangle cannot fall on the edge of another triangle.
3) The character factors of each evaluation unit should be unified as much as possible.
This method is reasonable for the division of small-scale evaluation areas.
(2) Method of dividing square grid units
The division method of square grid cells is controlled by geographical coordinates and adopts square grid division; According to the specific situation, the grid size can range from 0.0 1km2 to several km2. This division method is more reasonable for the evaluation of large areas.
(3) The method of dividing irregular polygon mesh units.
The division method of irregular polygon grid elements is suitable for small-scale evaluation. Because the topographic and geological conditions change greatly and the elements are discrete when evaluating small-scale urban areas, if the square grid unit division method is still used to divide the sections with relatively uneven evaluation elements into the same evaluation unit, the sections with better uniformity may be artificially cut off, which is contrary to the requirements and objectives of small-scale urban area evaluation. Therefore, it is appropriate to evaluate a small urban area by using irregular polygon grid unit division method, and the upper limit of evaluation unit is often stipulated to be 0.5km×0.5km.
Three. Evaluation model of groundwater pollution prevention and control
(1) Overview
At present, the commonly used methods to evaluate the prevention and control of groundwater pollution at home and abroad mainly include superposition index method, process mathematical simulation method and fuzzy mathematics method. In application, these methods have their own characteristics, emphasis and scope of application (Table 1-2-2).
Table 1-2-2 Comparison of groundwater pollution research methods
1. overlap index method
The superposition index method is to superimpose the sub-indexes of the selected evaluation indexes to form a comprehensive index reflecting the degree of pollution prevention, and then evaluate the pollution prevention of groundwater with the comprehensive index. It is divided into hydrogeological background parameter method (HCS) and parameter system method (PSM) [19 ~ 22]. The former is to compare and determine the antifouling performance of the study area through a known antifouling standard area with similar conditions to the study area. This method needs to establish several groups of standard models for groundwater pollution prevention and control, and most of them are qualitative or semi-quantitative evaluation, which is generally suitable for large areas with complex hydrogeological conditions. The latter is to establish an index system for evaluating antifouling performance by selecting representative indexes, and each index has a certain range of values. This range can be divided into several intervals, each interval gives a corresponding score, the actual data of each index is compared with this standard and scored, and finally the scores obtained by each index are superimposed to get a comprehensive index.
Parametric system method is the most commonly used method in groundwater pollution assessment, which can be further subdivided into three methods: matrix system method (ms), rating system method (RS) and point counting system model method (PCSM). Among these three methods, PCSM is the most commonly used one. MS method is used to evaluate the antifouling performance of each unit in the study area qualitatively, and the latter two methods are used to evaluate quantitatively. The difference between them is that the calculation method of comprehensive index is different. The comprehensive index of RS method is formed by directly adding the scores of each index, while the comprehensive index of PCSM method is formed by superimposing the scores of each index and their respective weights, so it is also called weighted scoring method. At present, most foreign researches on groundwater pollution prevention and control are based on DRASTIC standard or pesticide DRASTIC standard, and comprehensive index or weighted index model is used to evaluate groundwater pollution prevention and control.
2. Process mathematical simulation method
Based on the migration model of water and pollutants, the process mathematical simulation method simulates the migration and transformation process of pollutants by using certain physical and chemical equations, quantifies the evaluation factors and puts them into the same mathematical model to solve them, and finally obtains a comprehensive index that can evaluate the antifouling performance [23]. The biggest advantage of this method is that it can describe the physical, chemical and biological processes that affect the prevention and control of groundwater pollution, and can estimate the temporal and spatial distribution of pollutants. Although there are many two-dimensional and three-dimensional models to describe the migration and transformation of pollutants, they have not been used in the evaluation of regional groundwater pollution prevention and control. Most of the research on pollution prevention and control focuses on the one-dimensional process model of soil and vadose zone, mostly pesticide leaching model and nitrogen cycle model.
Theoretically speaking, this method is suitable for the advanced stage of groundwater pollution prevention and evaluation, because it needs enough reliable geological data and long-term pollutant migration data. Only when people fully grasp the internal relationship between groundwater pollution prevention and its evaluation factors can they use this method. However, the evaluation of groundwater pollution prevention and control is still in its infancy, and the internal relationship between groundwater pollution prevention and its evaluation factors is still in the exploratory stage, so this method is not commonly used.
3. Statistical methods
The statistical method is to analyze the existing information and data of groundwater pollution by mathematical statistics, determine the evaluation factors of groundwater pollution prevention and control and express them with analytical equations, substitute the assigned evaluation factors into the equations for calculation, and then analyze the pollution prevention and control according to the results. Commonly used statistical methods include geological statistics, kriging, linear regression analysis, logical regression analysis, weight of evidence and other statistical methods.
At present, the application of this method in groundwater pollution prevention and evaluation is not as important as superposition index method and process mathematical model method.
4. Fuzzy comprehensive evaluation method
When there is a certain degree of pollution prevention in local sewage, its influencing factors are diverse and complicated. The prevention and control of groundwater pollution is relative and belongs to a typical fuzzy problem. Giving a scoring boundary artificially makes the original fuzzy problems artificially clear, and it is difficult for the evaluation results to accurately reflect the information provided by each evaluation index. Therefore, the best way to solve this kind of fuzzy problem is fuzzy mathematics.
Fuzzy comprehensive evaluation method is to divide the pollution degree of groundwater through fuzzy comprehensive evaluation on the basis of determining evaluation factors, grading standards of each factor and weight of factor indicators. This method fully considers the essential factors (reflecting the internal essential attributes of hydrogeology) and special factors (reflecting the influence of human activities and external environment on groundwater pollution), and does not need artificial grading, but can consider the continuous changes of various indicators and truly reflect the differences between different sample indicators. At the same time, the interaction between different evaluation indexes is considered, which makes the evaluation results more in line with the actual situation [24 ~ 27].
Among the above four methods, the index data of superposition index method is relatively easy to obtain and master, and it is the most commonly used evaluation method abroad. Its defect is that there is no unified standard for the grading standards and scores of evaluation indexes and the grading of antifouling performance, which is subjective and arbitrary, so the evaluation results of antifouling performance in different regions are difficult to compare and lack comparability. Although the process mathematical simulation method has many advantages, only by fully understanding the behavior characteristics of pollutants in groundwater environment and having enough geological data and long-sequence pollutant migration data can its potential be fully exerted. In recent years, with the popularization of GIS technology and the expansion of evaluation area, the research results of applying GIS technology combined with groundwater transport model to evaluate groundwater antifouling performance appeared abroad in the late 1990s. This research will also be the direction and development trend of groundwater pollution prevention evaluation in the future. Statistical methods rely on monitoring pollution information for a long enough time. At the same time, comparability should be considered when using. The evaluation of groundwater pollution prevention and control includes some qualitative and uncertain indicators. The comprehensive evaluation method of fuzzy mathematics based on DRASTIC, which describes uncertain parameters and their index grading boundaries through membership functions, came into being because of its great advantages.
(2) Extreme mode
1. Basic assumptions
DRASTIC method is a typical representative of parameter system method in groundwater pollution prevention evaluation [28]. At present, this method has been adopted by many countries and is the most commonly used method in groundwater pollution assessment. DRASTIC method has four main assumptions: ① pollutants exist on the surface; (2) Pollutants seep into the ground through rainfall; ③ Pollutants migrate with water; ④ Study area 100 mu (about 0.4km2) [29 ~ 30].
2. Evaluation index system
The DRASTIC method adopts seven parameters that affect and control groundwater flow and pollutant migration, and constitutes the factor system of pollution vulnerability assessment of this method. They are: groundwater depth, aquifer net recharge, aquifer lithology, soil medium, topography, vadose zone influence and aquifer hydraulic conductivity. DRASTIC is the abbreviation of English headword composed of these seven factors [3 1 ~ 33].
(1) Groundwater depth (d)
The depth of groundwater determines the various hydrogeochemical processes that surface pollutants go through before reaching the aquifer, which provides the greatest opportunity for pollutants to contact with oxygen in the atmosphere and lead to their oxidation. Generally speaking, the deeper the groundwater level, the longer it takes for surface pollutants to reach the aquifer, the greater the chance that pollutants will be diluted on the way, the smaller the possibility that pollutants will enter the groundwater, and the smaller the degree of aquifer pollution. See table 1-2-3 for specific scores.
Table 1-2-3 Table of Groundwater Depth Grades
(2) Net recharge of aquifer (R)
Pollutants can be transported vertically to the aquifer or horizontally through recharge water, so recharge water is the main tool for leaching and transporting solid and liquid pollutants to the aquifer. The greater the recharge, the higher the vulnerability of groundwater. When the amount of recharge is increased to dilute pollutants, the possibility of groundwater pollution will decrease instead of increase. Table 1-2-4 gives the net recharge score of the aquifer.
Table 1-2-4 aquifer net recharge rating table
In general, it is difficult to obtain the data of net recharge of groundwater, so precipitation recharge is often used to replace net recharge in actual evaluation. See table 1-2-5 for specific scores.
Table 1-2-5 rainfall infiltration recharge score table
(3) aquifer lithology (a)
Groundwater in aquifer is affected by aquifer medium, and the migration route and the length of migration path determine the extinction and migration process of pollutants. Generally speaking, the bigger the particles of aquifer medium or the more cracks and caves there are, the smaller the dilution capacity of medium is.
If detailed information is missing, you can choose a typical score. Typical fractional values are used to describe typical aquifers composed of related aquifer media. For bedrock aquifer, it can be classified according to the development degree of cracks and bedding in aquifer medium. For example, the water-bearing medium of metamorphic rocks or igneous rocks with moderately developed fractures scores 3 points; When the fracture is very developed, the aquifer is more likely to be polluted, and the score should be set at 5; When the fracture in metamorphic rock or igneous rock is undeveloped, the unit specific yield is low, and the aquifer is easy to be polluted, the score can be set to 2. Loose rocks can be classified according to the particle size and sorting degree of water-bearing media. For example, the typical gravel grading value is 8, but when the sediment particles are coarse and easy to be washed away, it can be assigned to 9. On the contrary, when the particle content increases and the sorting is not good, the classification value can be reduced to 6 or 7.
When assessing regional groundwater vulnerability, only one aquifer can be assessed at a time. In multi-layer aquifer system, typical and representative aquifers should be selected for evaluation. After determining the aquifer, the most important aquifer medium is taken as the evaluation factor. See table 1-2-6 for the grade of aquifer medium.
Table 1-2-6 Scoring Table of Aquifer Lithology Type
(4) Soil type
The average thickness of soil medium involved in the evaluation is 2m or
When the soil medium in a certain area is composed of multiple layers of soil, the following methods can be used to select the soil medium type: ① select the dominant and representative soil layer as the soil medium; ② Select the most unfavorable highly polluted medium for scoring; (3) Select the intermediate medium as the scoring standard, and if there are gravels, sand and clay, choose sand as the scoring medium. See table 1-2-7 for the score of soil type.
Table 1-2-7 Soil Type Scoring Table
(5) Terrain gradient (t)
Terrain controls pollutants being washed away or left in a certain surface area for a long time and seeping into the ground, which not only affects the formation of soil, but also affects the dilution degree of pollutants. For the terrain that is easy to be infiltrated by pollutants, the groundwater pollution in the corresponding section is more serious. Generally, the greater the slope, the lower the vulnerability of the aquifer. See table 1-2-8 for specific scores.
Table 1-2-8 Terrain Slope Classification and Scoring Table
(6) The influence of vadose zone (1)
The influence of vadose zone is mainly determined by the medium type of vadose zone, which determines the material reduction characteristics between soil layer and aquifer, and various physical, chemical and biological effects occur in vadose zone. The vadose zone medium also controls the length and path of seepage, thus affecting the migration time of pollutants and the degree of reaction with soil. Any crack in the vadose zone controls the seepage route.
The choice of vadose zone medium must follow the following three basic principles:
1) Select the most polluted medium.
2) When the medium has multiple layers, the relative thickness of each layer should be considered, and the layer with the largest thickness should be selected as the unsaturated zone medium.
3) The pollution sensitivity of each layer of medium must be considered. For example, when the upper limestone is covered with a layer of clay and a larger gravel layer with the same thickness, clay is the most significant control layer from the point of view of groundwater pollution, because it limits the migration of pollutants to the aquifer. At this time, it is more appropriate to choose clay layer as vadose zone medium.
Confined aquifer does not consider its overburden, and the assignment should be1; For bedrock media, the development degree of various cracks should be considered. For limestone media with well-developed karst caves, 10 can be given; For limestone media with poor karst development or poor connectivity, the score should be lower, such as 9 or 8. See table 1-2-9 for details.
Table 1-2-9 Moderate score table of vadose zone
sequential
(7) Permeability coefficient of aquifer (C)
Hydraulic conductivity coefficient reflects the permeability of aquifer medium, which controls the velocity of groundwater under a certain hydraulic gradient, and the velocity of water controls the migration rate of pollutants in aquifer. The hydraulic conductivity coefficient is determined by the size and connectivity of pores in aquifer. The greater the hydraulic conductivity, the easier it is for groundwater to be polluted. See table 1-2- 10 for the score.
Table 1-2- 10 hydraulic conductivity classification score table
Generally, the hydraulic conductivity coefficient (C) is replaced by the aquifer permeability coefficient, and the scoring conditions refer to the hydraulic conductivity coefficient scoring standard.
3. Weight determination
When applying DRASTIC method to evaluate groundwater vulnerability, each index parameter is given a relative weight, and its range is 1 ~ 5, which reflects the relative importance of each index parameter. The index weight of the most significant impact on groundwater pollution is 5, and the index weight of the least impact is 1. See table 1-2- 1 1 for the weight of each index.
Table1-2-11drastic index system parameter weights
4. Pollution index
When applying the DRASTIC method to evaluate groundwater vulnerability, on the basis of determining the scores and weights of each evaluation factor in each unit, seven factors are synthesized by vulnerability index, and the DRASTIC index, namely groundwater vulnerability index, is calculated by weighting method:
Theoretical method of urban geological environment evaluation
Where: Wi is the weight of evaluation factor; Ri is the score of evaluation factor.
Once the severe pollution index is determined, the relative pollution degree of groundwater in each hydrogeological unit can be determined. Groundwater systems in areas with high pollution index are relatively easy to be polluted.
In particular, the DRASTIC index does not represent the absolute value of groundwater pollution, but only the relative vulnerability of groundwater in different regions.
In addition, in the practical application of the DRASTIC model, it is necessary to grade (or classify) each indicator first, and give the same quota to the indicators within this level (classification), so that different levels have different quotas. When grading the same index of different evaluation units, it is possible to classify the indexes with obvious differences into the same grade and give the same quota, which can not truly reflect the differences between units, that is to say, the weighted scoring method is used to cover up the influence of the continuous change of the index values of each evaluation factor on groundwater pollution. Therefore, combined with fuzzy mathematics theory, a fuzzy comprehensive evaluation model based on DRASTIC index is proposed.
5. Evaluation and grading
The groundwater vulnerability index calculated by DRASTIC evaluation method is between 23 and 230. Because there are some problems in the separate classification of different cities, it cannot reflect the influence of the same factor on groundwater pollution in different cities. Therefore, in order to compare the evaluation results of groundwater vulnerability in different urban areas, a unified standard is adopted, and the division results are shown in table 1-2- 12.
Table 1-2- 12 groundwater vulnerability classification rules
(C) Fuzzy comprehensive evaluation model based on DRASTIC index
Based on the DRASTIC method, the model makes a fuzzy comprehensive evaluation of groundwater pollution prevention and control. The specific process is as follows.
1. Division of groundwater pollution sensitivity emotion operators
According to different hydrogeological conditions, the difficulty of aquifer pollution is different under the same pollution source or external pollution environment conditions. Therefore, the main task of groundwater vulnerability assessment is to accurately evaluate the difficulty of groundwater pollution in the assessment area. In order to correspond to this, the mood operator of 10 level can also be divided into other levels, such as level 8. According to the specific situation), as shown in table 1-2- 13.
Table 1-2- 13 Correspondence between Emotional Operator and Pollution Degree
2. Exponential standard eigenvalue matrix
See table 1-2- 14 to table 1-2-20 for the grades of the seven indicators used in the evaluation.
Table 1-2- 14 Groundwater Depth Grade and Characteristic Value
Table 1-2- 15 Net Replenishment Level and Characteristic Value
Table 1-2- 16 Terrain Slope Grade and Characteristic Value
Table 1-2- 17 aquifer permeability coefficient grade and characteristic value
Table 1-2- 18 aquifer lithology grade and characteristic value
Table 1-2- 19 Grades and Characteristic Values of Soil Types
Table 1-2-20 Influence Grade and Characteristic Value of Aerated Zone
Based on the concrete division of the levels and eigenvalues of the above seven evaluation indexes, the levels and corresponding eigenvalues of the seven indexes of the fuzzy evaluation model can be obtained. See table 1-2-2 1 for details.
Table 1-2-2 1 10 standard characteristic values of seven indicators at different levels.
If the seven indicators on which the groundwater vulnerability assessment is based are determined according to the index standard eigenvalue of 10, there is a index standard eigenvalue matrix of 7× 10:
Theoretical method of urban geological environment evaluation
Where: yih is the standard eigenvalue of H-level index I, I = 1, 2, …, 7; h= 1，2，…， 10 .
According to table 1-2-20, there are two different types of indicators: ① the standard characteristic value of indicator yih decreases with the increase of grade H; ② The standard characteristic value of indicator yih increases with the increase of grade H. ..
3. Relative membership matrix of index standard eigenvalues that are extremely difficult to pollute fuzzy concepts (1 level)
No matter for the above-mentioned ① and ② indicators, it can be determined that the relative membership degree of the standard eigenvalue of indicator 10 to extremely difficult pollution is 0, and the relative membership degree of the standard eigenvalue of indicator 1 to extremely difficult pollution is 1. For the above two kinds of indicators, if their eigenvalues are between the standard eigenvalues of 1 ~ 10, the relative membership degree that is extremely difficult to pollute can be determined according to the linear change. Then the formula of the relative membership function of the standard eigenvalue yih of the H-level index I to extremely difficult pollution is
Theoretical method of urban geological environment evaluation
Where: sih is the relative membership degree of the standard eigenvalue of H-level index I to extremely difficult pollution; Yi 1 and yi 10 are the standard values of index I, which are 1 and 10 respectively.
Using the relative membership function formula (1-2-2), the index standard eigenvalue (1-2- 1) matrix is transformed into the extremely polluted index standard eigenvalue relative membership matrix.
Theoretical method of urban geological environment evaluation
4. Eigenvalue matrix of evaluation index
According to the actual data of seven indexes of each evaluation unit in the study area, the eigenvalue matrix of each evaluation unit for evaluating groundwater vulnerability is constructed:
Theoretical method of urban geological environment evaluation
Where xij is the eigenvalue of the index i of the evaluation unit j; i= 1，2，…，7； J= 1, 2, …, n .n is the number of evaluation units.
5. Relative membership matrix of extremely difficult pollution assessment indicators
The relative membership formula of the first-class index to extremely difficult pollution is as follows
Theoretical method of urban geological environment evaluation
The relative membership formula of secondary indicators to extremely difficult pollution is as follows
Theoretical method of urban geological environment evaluation
Where: rij is the relative membership degree of the characteristic value of the index I of unit J to extremely difficult pollution. Convert matrix X into an exponential relative membership matrix by using formula (1-2-5) or formula (1-2-6):
Theoretical method of urban geological environment evaluation
Where: I = 1, 2, … 7; J= 1, 2, …n .n is the number of evaluation units.
From the matrix R, we can see that the relative membership degree of the seven indicators of unit J is
Theoretical method of urban geological environment evaluation
Now each row of the matrix S is divided into 9 intervals: [1, 2], (2, 3], (3, 4], (4, 5], (5, 6], (6, 7), (7, 8), (8, 9), (9). Comparing the relative membership degrees of the intermediate index 1, 2 with 1, 2, ..., 7 one by one in the matrix S, we can find that it falls into any of the nine intervals of the matrix S, and then compare the upper and lower levels of these seven index intervals.
6. The evaluation unit belongs to the optimal relative membership matrix of each level.
The relative membership matrix of evaluation units belonging to each level is recorded as
Theoretical method of urban geological environment evaluation
Where: uhj is the relative membership degree of evaluation unit J to H grade; j= 1，2，…，n； h= 1，2，…， 10 .
Since the relative membership degrees of the seven indicators of evaluation unit J all fall within the horizontal interval [AJ, BJ] of matrix S, matrix U should satisfy the constraint conditions:
Theoretical method of urban geological environment evaluation
As the grade interval of each evaluation unit is different, considering all evaluation units in the study area as a whole, the matrix U should satisfy:
Theoretical method of urban geological environment evaluation
Generally speaking, the grade interval [AJ, BJ] has aj≥ 1 and bj≤ 10. In order to satisfy the constraints of (1-2- 10) and (1-2-1) simultaneously, when uhj=0, H.
The difference between the evaluation unit J and the level H is expressed by the generalized Euclidean distance as follows
Theoretical method of urban geological environment evaluation
The above formula considers the weight wi of the exponent. In order to better describe the difference between the evaluation unit J and the level H, the relative membership degree uhj of the evaluation unit J belonging to the level H is taken as the weight, which is expressed by the weighted generalized Euclidean distance as follows.
Theoretical method of urban geological environment evaluation
In order to solve the optimal relative membership degree of evaluation unit J to grade H, an objective function is established:
Theoretical method of urban geological environment evaluation
According to the objective function (1-2- 14) and the constraint condition (1-2- 10), the Lagrange function is constructed, where λj is a Lagrange multiplier, then
Theoretical method of urban geological environment evaluation
Use L(uhj, λj) to take the partial derivatives of uhj and λj and make them equal to 0:
Theoretical method of urban geological environment evaluation
The optimal relative membership function formula of evaluation unit J to grade H can be obtained as follows:
Theoretical method of urban geological environment evaluation
Especially when RIJ = SIH (I = 1, 2, ..., 7), the relative membership degrees of the seven indicators of evaluation unit J are all equal to the relative membership degrees of the standard values of the seven indicators of grade H. From the formula (1-2- 12), it can be known that dhj=0 at this time, and from mathematical analysis,
It can be seen from the above that the complete form of fuzzy analysis and evaluation model of vulnerability of H-class groundwater by evaluation unit J is as follows.
Theoretical method of urban geological environment evaluation
By applying the formula (1-2- 18), we can get the optimal relative membership matrix of evaluation units belonging to each level, as shown below.
Theoretical method of urban geological environment evaluation
Where: h = 1, 2, …,10; j= 1，2，…，n .
7. Determination of evaluation results of each unit
The vector expression of the application layer eigenvalue h is
Theoretical method of urban geological environment evaluation
The quantitative evaluation information of the sensitivity of the evaluation unit to groundwater pollution is given. The greater the H, the higher the groundwater pollution sensitivity of the evaluation unit.
To sum up, the fuzzy comprehensive evaluation model based on DRASTIC index has the following advantages:
1) refers to the division standard of DRASTIC model in the index scoring system, and also considers the actual data extracted in the basin, and gives the grade and characteristic value of the new evaluation index.
2) In the classification of pollution sensitivity, the differences of hydrogeological conditions of aquifers are fully considered, and a more accurate and detailed groundwater pollution sensitivity grade (tone operator) is put forward.
3) The continuous changes of each index are fully considered in the process of fuzzy iterative operation, which can truly reflect the differences between different unit indexes.