Factors, variables, and aspects Sabo Dam modelling capacity based on the Purwantoro Sabo Dam index model

Volcanic disaster risk mitigation cannot be perceived as a separating part of disaster management. Sabo Dam technology applied as lahar controller infrastructure that is part of management disaster and widely used in Indonesia. Purwantoro Sabo Dam Performance Index Model estimates the general functionality of a sabo dam in one index number. The simple calculation steps had been made which is conveniently usable and answer further practical demand such as operation and maintenance necessity, rehabilitation – newly construction prioritization decision support system, or emergency inspection aspect. Purwantoro Formula composed variables and factors that can be developed into more practical usage in the outcome approach. Capacity estimation over the Purwantoro Index is used as a disaster management approach to create capacity functions. Reviews of the actual capacity of compatibility of the three hierarchical factors, variables, and aspects are needed. It is carried out using a structural equation model with the partial least square method. The compatibility among the structures and outcome of capacity generates twenty-five grouped by nine components that are under three aspects (physical, regulative, and social) that suit the sabo dam’s potential capacity. The three hierarchical structures of aspect, component, and indicator are valid and appropriate to fulfill the t-test.


Introduction
Indonesia's characteristic as an archipelago that lies on the Pacific Ring of Fire where the three continental plates collide [1], that condition makes Indonesia a region which vulnerable to natural disasters.Volcanic and tectonic disasters and their derivatives such as volcanic eruptions, lahar floods, earthquakes, and tsunamis are continuous events that happen all the time.Within historical records, the biggest volcanic eruptions that may occurred can be found in the Indonesia Archipelago such as Toba Lake [2], Mount Tambora [3], and Krakatoa [4].Up to this moment, mountains in these volcanic lines are erupting continuously from one another and becoming sensitive during continuous continental plate collisions.
Approaches that are oriented based on the outcome of disaster mitigation infrastructure protection in managing volcanic disasters in Indonesia have become a priority.Nowadays, disaster mitigation infrastructure such as the sabo dam, is built based on acquired outcome level [5] rather than another framework.Input parameters such as budgeting will be determining factors in formulating disaster policy options.It often makes the budgeting approach and outcome approach head-to-head comparisons 2 to be chosen.However, in the face of protection urgency to settlement, national vital assets, or other important asset, then consideration of outcome level generated by the infrastructure will be put up and determines the option.
In order to describe sabo dam outcome performance, a work by Purwantoro [6], tried to solve the entire factors perceived in influencing a sabo dam performance.The purpose is to understand the factors it gathers all possible factor then tests the relationship among each other, analyzes the trend each other and conclude through multiple statistical tests.The physical aspect is stretched not limited to infrastructure but also its riparian condition covering its vegetation and river meandering including bed rocks surface and adjacent cliffs [6].Non-physical aspect covers regulative and social to explain spatial implementation and socio-human conditions influencing a sabo dam.This research works well in proportioning influence among physical, regulative, and social toward a sabo dam.The output is represented in a formula regarding three aspects and producing an index number between 0 and 5 relatively expressing a sabo dam performance.
Index numbers of Purwantoro Formula output need to be enhanced to be used in estimating actual capacity.To perform the aim of estimating actual capacity, several additional steps are needed to be conducted.The first step is checking the variable's conformability using structural mathematics equations to be added factor i.e., capacity.By this analysis, it can be defined which factor remains relevant or eliminated, thus the changing of Purwantoro Formula components to its compounding factors is inevitable.

Aspect, Component, and Indicator
The approach is conducted based on the Purwantoro Formula [6] which adapts the capacity indicator and its value following the same building samples.It consisted of three aspects.Those are physical, regulation, and social, in which capacity indicators are inserted in a physical hierarchical structure as the fourth component.The entire structure was built based on the previous studies of sabo dam and performance research.The interrelation among aspects, components, and indicators based on literature are presented in Table 1 as follows.

Scoring System and Adaptation of Capacity Indexing
Indicators as stated in Table 1 are valued based on their actual condition with scaling regarding to scoring system as mentioned in Table 2.The various quantities with specific units bound for each indicator then are converted to five (5) ranged scaling which expresses the full score five (5) for the best condition and zero (0) for the null influence toward sabo dam to perform its function.The indexing results are taken from Purwantoro [6].Table 2 describes the conversion of the capacity in actual value in m 3 into the score indexing.

Statistical Methods as Validating Approaches
Several statistical tests are used to validate the relationship among variables.It expresses validity for each relation within values of statistical parameters.However, the value limit will be used to determine the construct strength in the effort to declare variable relationship truth.

B. Composite Reliability (CR)
Composite reliability (often also called construct reliability) is a measurement of internal consistency on an indicator scale such as Cronbach alpha [49].This value is equal to the number of correct score variances to the total score variance [50].This value can also be called an indicator of shared variance between the observed variables used as latent constructs [47].The composite reliability limit value is quite widely debated, with various experts having their own opinions about the suggested value limit (most suggest > 0.6).Netemeyer et al [49] suggest that a small number of indicators that make up a construct are called reliable if they have a value of more than 0.8.The composite reliability formulation is shown as follows: where: p = indicator number λi = loading factor indicator i V(δi) = variants error indicator i

C. Cronbach Alpha (α)
This value, which is also known as τ equivalence reliability or α coefficient, is a single reliability score test against the coefficients of indicators known as Cronbach alpha.This value is the most common reliability among coefficient reliabilities and is recommended in structural equation models [40].In general, regardless of the type of research, whether pilot, applied research, or development research, a value criterion of 0.7 is used [48].Nunally and Bernstein [51] stated that a value of 0.7 could be used as a limit value for pilot studies and a value of 0.8 for more empirical studies.The composite reliability formulation is shown as follows:

Result and Discussion
Data analysis using SEM-PLS only covers two examinations: outer model examination and inner model examination.In the outer model stage, analysis is directed to examine equation structure validity and reliability while in the inner model stage, hypotheses are analyzed.

Outer Model Examination A. Validity and Reliability Test
Convergent validity is intended to look at item reliability (validity indicator) as shown by the loading factor value.The loading factor is a number that shows the correlation between the scores of a question item (indicator).A loading factor (LF) value greater than 0.7 is said to be valid.However, in the research development stage, the loading scale of 0.5 to 0.6 is still acceptable [52].
Discriminant validity means measuring what should be measured, which is indicated by the Cross Loading value.Cross-loading shows the magnitude of the correlation between each construct and its indicators and indicators from other block constructs.A measurement model has good discriminant validity if the correlation between the construct and its indicators is higher than the correlation with indicators from other block constructs.This means that latent constructs predict indicators in their block better than indicators in other blocks.The validity coefficient of a test is expressed in a coefficient number between -1.00 to 1.00.The coefficients previously stated are as follows:  ), and the coefficient is positive.The structure can be concluded as valid if there are no variables interrelation that are valued less than the conditioned limit.This means that the trial can be carried out in more than one run.The first iteration process can be seen in Figure 3 as follows.The results of each structure are tabulated in Table 5 which shows the inner model value less than 0,70 is considered not valid therefore it dropped to run the next iteration.
As stated by Ghazali [52], an inner value > 0,7 is considered valid while less than 0.7 will be not valid.This value is used to select an indicator with a lack of influence toward its superlative variable.As Table 5, several indicators are dropped and eliminated in the second run.These indicators are parapet, land cover, bedrock, meandering, roughness, width, side cliff, mining zoning, Masterplan Merapi 2001, Review Masterplan Merapi 2010, disaster vulnerability zoning, social forum, settlement, public facilities, and farming.Furthermore, the second run of the model is shown in Figure 4.The second run is carried with the remaining indicators which are valued for the inner model > 0,7.These indicators are spread out in three aspects: physical, regulative, and social within nine components of the sabo dam component, riparian vegetation, river channel properties, capacity, sand mining performance, regulative compatibility, social-culture and economic, public and private roles, and disaster loss.While valid indicators are: spillway (f 11 ), main dam (f 12 ), wings (f 13 ), drip hole (f 14 ), sub dam (f 15 ), apron (f 16 ), apron's wall (f 17 ), side dyke's heap (f 18 ), dyke's wall (f 19 ), dyke's frame (f 110 ), and dyke's top (f 111 ), vegetation type (f 22 ), depth (f 35 ), slope (f 36 ), capacity (f 41 ) under physical aspect, technical recommendation (r 23 ) and mining license (r 24 ) under regulative aspect and occupation (s 11 ), economic (s 12 ), education (s 13 ), private share (s 22 ), and livestock (s 34 ).
The result of the second run is tabulated in Table 6 as follows.All indicators are above the 0,7 inner loading threshold, so the remaining indicators considered passed the second run and need to be examined with a reliability test.The results of the reliability test above show that all research variables are fit measurements, both Average Variance Extracted (AVE) for all variables have a value of > 0.50, Composite Reliability (CR) for all variables has a value of > 0.8, and Cronbach Alpha for all variables also have a value of more than > 0.7, so that in general all the variables studied from all the question items that will be used have a good level of reliability.Disaster Loss (S 3 ) 1.000 (High reliability) 1.000 (High reliability) 1.000 (High reliability)

Inner Model and Structural Model Value
Hypothesis testing is based on the values contained in the structural model analysis, the level of significance of the path coefficient is obtained from the calculated t-value and the standardized path coefficient value.The limit value for hypothesis testing is that the calculated t-value of the factor loadings is greater than the critical value (≥1,682) level of confidence/level of significance (α) = 0.05.The following is an image of the results of processing the Smart-PLS program with Bootstrapping analysis on the inner model or structural research model (t count).Table 8 presents this calculation that is applied in three aspects.Furthermore, Figure 5  Based on the results of the structural model tests contained in the path coefficient table above, it can be concluded that the physical aspects consist of sabo dam component performance, riparian vegetation, river channel properties, and capacity, regulative aspects consist of sand mining performance and regulative compatibility), as well as social aspects consisting of (socio-cultural and economic, public and private roles and disaster losses) have a positive and significant influence on the sabo Dam Capacity Performance Model.This can be seen based on the calculated t number in the inner model analysis (Table 6), where the Physical Aspect is 15,661, the Regulative Aspect is 7,352, and the Social Aspect is 7,168, where each of these variables has a calculated t value greater than the critical value (≥1,682) level of confidence/level of significance (α) =0.05, and/or the p-value is smaller than the critical value (≤0.05).In order to determine the magnitude of the influence of each variable in the Sabo Dam Capacity Performance Model based on regression analysis, it can be seen from the Original Sample values in Table 6.The Physical Aspect variable has a regression coefficient of 0.878 (87.8%) in influencing the Sabo Dam Capacity Performance Model.The Regulative Aspect variable has a regression coefficient of 0.444 (44.4%) in influencing the model.Meanwhile, the Social Aspect variable has a regression coefficient of 0.503 (50.3%) in influencing the Sabo Dam Capacity Performance Model.
Previous studies by Purwantoro [6] and recent capacity modeling carried out in this study give clear comparisons on how an indexing model can be elaborated for more practical usage as presented in Table 8.Purwantoro [6]

Conclusions
The comparison among the established study of Purwantoro [6] with thirty-nine indicators and if it added with indicators of capacity are aimed by this study.It shows that thirteen original indicators are dropped against fifteen indicators dropped by the addition of the capacity indicator.The twelve indicators are dropped by the same indicator in both cases, while two indicators in the original case and three indicators in the capacity case are different in each case.The twenty-five indicators that suit for the capacity case are: spillway (f 11 ), main dam (f 12 ), wings (f 13 ), drip hole (f 14 ), sub dam (f 15 ), apron (f 16 ), apron's wall (f 17 ), side dyke's heap (f 18 ), dyke's wall (f 19 ), dyke's frame (f 110 ), dyke's top (f 111 ), vegetation type (f 22 ), depth (f 35 ), slope (f 36 ), capacity (f 41 ), legal mining output (r 11 ), illegal mining output (r 12 ), actual mining output (r 13 ), technical recommendation (r 23 ), mining license (r 24 ), occupation (s 11 ), economic (s 12 ), education (s 13 ), private share (s 22 ), and livestock (s 34 ).These twenty-five indicators grouped by nine components of sabo dam component performance (F 1 ), riparian vegetation (F 2 ), river channel properties (F 3 ), capacity (F 4 ), sand mining performance (R 1 ), regulative compatibility (R 2 ), social, culture and economic (S 1 ), public and private roles (S 2 ), disaster loss (S 3 ).The nine components and twenty-five indicators are grouped under three aspects Physical (F), Regulative (R), and Social (S).The three hierarchical structures of aspect, component, and indicator are valid and appropriate to fulfill the t-test.
This study of capacity modeling by including the sabo dam capacity function into Formula Purwantoro [6] shows the stability of this established formula.With the equally same approach of scoring 0-5 to express the condition of all variables, it does not change much of its variable composition with the addition of a capacity indicator.The majority of indicators are valid to be re-used while the others dropped to be compatible with the newly adopted capacity indicator.For example, an indicator of vegetation type (f 22 ), is needs to be re-used to increase accuracy in predicting actual sabo dam capacity.Furthermore, indicators of land cover (f 21 ), width (f 34 ), and public facilities (s 32 ) need to be dropped for the same reason.This result confirms that the previous study by Purwantoro [6] relatively correct and accurate by only four out of forty indicators are need to be adjusted.However general indexing as stated in Purwantoro [6] needs to be elaborated further to be beneficial usage such as capacity estimation.
Three indicators of land cover (f 21 ), river width (f 34 ), and public facilities (s 32 ) are incompatible with Sabo Dam Capacity Performance Modeling.Land cover can be understood that it has a lack of influence due to its wide covering riparian, where vegetation type directly adjacent to the river convincingly influences the capacity of a sabo dam.The same reason can be found in public facilities during disaster events since it is too far from the river.However, the non-compatibility with the river width can be a sign of data improvement necessity.It can be the failure of field measurement or the obsolete data that needs to be updated since the river morphology is changing rapidly.The usage of the appropriate topographic updated mapping device such as a robotic total station, terrestrial laser scanner, or bathymetric drone is recommended.
Several further follow up can be formulated by the result of this study.First, the next stage of the research is to determine the weight of each aspect, component, and indicator within the structure that needs to be found out.With numerous data, it can be carried out using a generalized reduced gradient method that calculates the minimum gap between sample data and the median of the scoring model.Several statistical tests also need to be attached to ensure the model output is appropriate and remains intact if compared with field findings.The second recommendation is the inevitable improvement in river width data, which needs to be derived using primary data.Another option is to use recent technology of remote sensing that will confirm the actual river width due to continuously changing morphology.
The sample data is grouped into classifications which form a structure of indicator-component-aspect so interrelationship among variables can be measured and analyzed for its compatibility among nodes and joints.It will be arranged using the structural equation modeling (SEM) variant based.Smart-PLS (Partial Least Squared) is used to solve the mathematical structural problem.The valid result among structural variables is exceed statistical boundaries of AVE (average variance extracted) > construct variance value as stated by Hair et al[46], CR (composite reliability) > 0,6 according to Fornell and Lacker[47], and Cronbach Alpha > 0,7 as recommended by Lance, Butt, and Michels[48].The steps in determining variable system is compatible with further development of the sabo dam capacity performance model are presented in Figure1as follows.

Figure 3 . 9 Table 5 .
Figure 3. First run of SEM-PLS on Sabo Dam Capacity Performance Model

Table 1 .
Aspect, Component, Indicator, and its Literature Foundation No.

Table 2 .
Scoring System Against Sabo Dam Performance Influence and Capacity Indicator Scoring

Table 4 .
Validity coefficient A. Hypotheses TestHypothesis testing is carried out to see whether a hypothesis is accepted or rejected.This is done by result consideration of the significance values between constructs (estimated values/coefficients), tstatistic values/coefficients, and p-values/coefficients for t-statistic value > 1.96, for significance pvalues < 0.05 (5%

Table 6 .
Second run of SEM-PLS result

Table 7 .
Reliability Test of SEM-PLS result h Public and private roles i Disaster loss

Table 8 .
presents bootstrapping t-test calculation in all structural equations.Path coefficient