Aggregate Indices Method in Soil Quality Evaluation Using the Relative Soil Quality Index

This paper presents a new approach to assess the soil quality by aggregate indices using the Relative Soil Quality Index (RSQI) proposed by Ho Ngoc Pham. RSQI is integrated from the individual indices into a simple formula for overall assessment of the soil quality. RSQI is different fromother approaches. Particularly, the individual indices and theweighting factors of Phamare calculated from the analytical laboratory data and the environmental standards, respectively, and not self-regulated as in methods of some other authors. In this paper, the authors applied the RSQI to assess the Soil Environmental Quality of rice intensive cultivation areas through a case study in Haiduong province in 2013. The RSQI is calculated for sampling points in 12 districts and simulated the Soil Environmental Quality on GIS map. The results show that the Soil Environmental Quality of rice intensive cultivation areas in Haiduong is predominantly divided into three levels: good, moderate, and poor. According to the report of General Statistics Office for Haiduong province, rice intensive cultivation areas in 2013 achieved a relatively high average rice yield of 5.90 tonnes per hectare; it means actual soil properties are in line with results of the research.


Introduction
The assessment of soil degradation in the world is primarily based on single criteria to build the assessment thresholds for each group of total content of bioelements, content of available forms of bioelements, heavy metals, and so forth, in which each parameter in the group of total content of bioelements and the group of content of available forms of bioelements is categorized into three levels: high, medium, and low or rich, moderate, and poor, respectively, to serve for the degradation assessment of agricultural land and forestry.The environmental quality index (EQI) approach to assess air, water, and soil was first mentioned in the work of Ott [1], and afterwards, the application of EQI to assess the soil quality (SQ) is continuously developed and widely used [2][3][4][5][6][7].
The soil degradation assessment in Vietnam has interested many scientists.Vietnamese scientists have made indepth studies on the thresholds and the assessing scale for the group of total content of bioelements, content of available forms of bioelements and heavy metals, and so forth.In which, typical studies are of Nguyen [8], Le [9], Tran [10], Nguyen [11], Le and Tran [12], and the National Technical Standards on the soil environment for the heavy metals group [13].However, the approach to assess soil degradation by aggregate indices in Vietnam is still new.Such approach was first mentioned in the dissertation of Nguyen in order to create an environmental land map at the provincial scale [14].The author applied the Total Soil Quality Index (TSQI) proposed by Pham [15] to determine the Soil Environmental Quality for agricultural land (rice cultivated areas).Nevertheless, calculating the weighting factors of each group is complicated.Therefore, Pham developed the TSQI into the Relative Soil Quality Index (RSQI) which simplifies the calculation of the weighting factors of total content of bioelements, content of available forms of bioelements, pH KCl , and heavy metals group in reality [16].Because of the paper's scope, the authors only apply RSQI into aggregate assessment of the SQ of rice intensive areas in Haiduong province.

Materials. (i)
The research used the soil sample analysis data for 12 districts with rice intensive cultivation areas in Haiduong province [17].
(ii) Research materials of Vietnamese authors [8-12] and Vietnam's environmental regulations [13] were used to convert the categorized scale of individual index into the individual assessing scale of SQ which served for the calculation of the SQ assessment by aggregate indices, using RSQI.

Method
2.2.1.Formula of Relative Soil Quality Index (RSQI).RSQI is a new approach to assess the SQ by aggregate indices.It is based on the synthesis or integration of individual index   of  surveyed parameters in order to form a formula which simplifies the SQ assessment at each monitoring point.RSQI proposed by Pham is determined by the following formula [16]: where where   is the common sum (sum of separate sums   and   );   includes  of numbers of   with values ≤1;   includes  of numbers of   with values >1;  is the number of monitored parameters.
Noting.Formula (1) clearly shows that RSQI depends on the relative ratio   /  .The higher the value of the ratio is, the smaller the value of RSQI will be.Thus, the SQ is poorer.
(i) Calculating Individual Index   (Subindex) of Each Parameter .To calculate RSQI in formula (1), we first need to calculate individual index as the following: (a) The groups below in Vietnam's environmental regulation (to the heavy metals group) are There are three cases: Case 3: (Soil with good quality-nondegraded soil) .
(ii) Calculating the Separate Sums   ,   , and the Common Sum   Using Formulas (2) to (4).From (1) to (10), is the actual monitoring value of parameter ,  *  , , and  are the permitted limit values of parameter ,  1 is the number of parameters with   = 1 (as   =  *  ),  2 is the number of parameters with   < 1,  is the number of parameters with   > 1.

Calculating the Temporary Weighting Factors 𝑊 󸀠
and the Final Weighting Factors   .  is the final weighting factors of the parameter ;   accounts for the importance which presents the relation between each parameter ; and  is the number of parameters of each examination group.The final weighting factor   is determined through the temporary weighting factor    as follows.
(a) Groups Below in Environmental Regulation (Heavy Metals Group).   is calculated by formula: where  *  is allowance limited value of parameter  and  is the number of parameters selected by the group for examination.

(b) Groups in the Interval [𝑎, 𝑏] in Environmental Regulations (Group of the Total Content of Bioelements, Group of the Content of Available Forms of Bioelements). Consider parameter groups in the intervals
The formula to calculate    of parameter  for each group is as below: where the environmental regulation value of parameter  in the interval (c) Calculate the Final Weighting Factor of Parameter  (  ).
The final weighting factor of each parameter  of each group is identified by the following formula: Obviously, where  is the number of parameters selected by the group for examination.[16].See Table 1.

Converting Hierarchy for Assessing Criterion to Hierarchy for Assessing SQ.
To apply ( 7)-( 10) formulas, first, levels and hierarchy for assessing criterion need to be converted to levels and hierarchy for assessing soil quality (SQ) for each individual criterion.The conversion Tables 2, 3, and 4 are based on the application of Vietnam research materials about criterion for assessing soil groups.

Hierarchy for
The group of the total content of bioelements (formula ( 12)): The group of the content of available forms of bioelements (formula ( 12)): The final weighting factors of other parameters of total content of bioelements group and content of available forms of bioelements group are calculated, respectively, and results are shown in Table 6.7)-( 10), calculated   and   using formulas ( 2)-( 4), and calculated the RSQI index using formula (1) for soil samples.Because of the large sample size of the rice intensive cultivation areas surveyed in Haiduong including relatively high, medium, and low plains, we present how to calculate individual index   , the separate sums  1 ,  2 , and   , and the common sum   ( = 10 parameters) in order to determine the RSQI of a particular soil sample S1 (Table 7).Thus, only result of other samples is shown in Table 8:  5) .
(20)  8, GIS technology with the spatial interpolation is applied to develop a simulated map of the SEQ assessment at the research area (Figure 1).

Discussion. (i)
From Table 8, the SQ of rice intensive cultivation areas in Haiduong is good (nondegraded soil), moderate (soil starting degradation), and poor (degraded).
(ii) From the SQ map (Figure 1), incorporation with digital land use map (Haiduong DoNRE, 2013 [18]) will calculate the area of rice intensive cultivation for 12 districts in hectare that consists of 3 groups: good (nondegraded), moderate (starting degradation), and poor (degradation) Soil Environmental Quality.Particularly, the nondegraded area of the province is 25,106.85ha (36.29%), the area which starts to degrade is 28,821.69ha (41.66%), and the degraded area is 15,254.33ha (22.05%).To districts in the provinces with the moderate and poor soil quality, the soil with moderate and poor quality needs to be monitored and fertilized properly.
(iii) According to the General Statistics Office (2013) [19], rice intensive cultivation areas in Haiduong province 2013 reached a relatively high average yield of 5.90 tonnes/ha.Because the RSQI approach shows results of the soil with good quality (nondegraded), the soil with moderate quality (start degraded), and the soil with poor quality (degraded), in which the degraded soil area accounts for only 22.05%, the soil quality of rice intensive cultivation areas is considered fairly good.Therefore, results of the research are in line with the relatively high yield in reality.

Conclusion
The research used the soil sample analysis data for twelve districts in Haiduong province to calculate individual indices for 10 parameters.The selected basic parameters are Cd, Cu, and Pb; P t , SOM, N t , and K t ; N av , P av , and K av .The separate sum   is integrated from parameters group with   ≤ 1 whereas the separate sum   is integrated from parameters group with   > 1.The common sum   equals   plus   .Using these sums, we calculated the RSQI values for 36 soil samples (16 samples in relatively high plains; 7 samples in medium plains; and 13 samples in low plains).
The results of calculations show that the soil sample with good quality (  < 1) accounts for 14/36 = 38.88%; the proportions of soil sample with medium quality (  = 1) and poor quality (  > 1) are equal; both of them account for 11/36 = 30.56%.

Figure 1 :
Figure 1: The SEQ map of rice intensive cultivation areas in Haiduong province in 2013 developed from the aggregate SQ assessment approach by using RSQI.(The map is scaled from a map with the scale of 1 : 100,000.) is the number of parameters of each group.Example.There are 2 parameters ( = 2) given in [ 1 ,  1 ], [ 2 ,  2 ].The environmental regulation values of [ 1 ,  1 ] and [ 2 ,  2 ] are ( 1 −  1 ) and ( 2 −  2 ), respectively.According to (12), we calculate (11)ssing SQ of RSQI.The hierarchical scale for aggregate assessing soil quality of RSQI corresponding to  = 10 parameters in Table1is shown in Table5.3.1.2.Calculating the Temporary Weighting Factors   and the Final Weighting Factors   .(i)Calculating the Temporary Weighting Factors    is as follows: The group of heavy metals (formula(11)):

Table 1 :
Hierarchy for assessing SQ of RSQI =  index.
(d) Very poor: hazardous SQ needs appropriate technological treatment for parameters significantly greater than acceptable standard.

Table 2 :
Converting hierarchy for assessing criterion to hierarchy for assessing SQ for the group of total content of bioelements.

Table 3 :
Converting hierarchy for assessing criterion to hierarchy for assessing SQ for the group of content of available forms of bioelements.

Table 4 :
Converting hierarchy for assessing criterion to hierarchy for assessing SQ for heavy metals (mg⋅kg −1 , top soil).

Table 5 :
Hierarchy for assessing SQ of RSQI =  with  = 10 parameters (Cd, Cu, Pb, SOM, N t , P t , K t , N av , P av , and K av ).
3.1.4.Creating the Soil Environmental Quality Map.From the Table

Table 6 :
The temporary weighting factors    and the final weighting factors   of 10 surveyed parameters.

Table 7 :
Calculating RSQI for a particular soil sample S1 with   , monitoring values.

Table 8 :
Results of calculation of RSQI based on monitoring data.