extfieldsofstudy:
Mathematics
Computer Science

text:
A New Multivariable Grey Convolution Model Based on Simpson’s Rule and Its Applications

Accurate estimations can provide a solid basis for decision-making and policy-making that have experienced some kind of complication and uncertainty. Accordingly, a multivariable grey convolution model (GMC (1, n)) having correct solutions is put forward to deal with such complicated and uncertain issues, instead of the incorrect multivariable grey model (GM (1, n)). However, the conventional approach to computing background values of the GMC (1, n) model is inaccurate, and this model’s forecasting accuracy cannot be expected.,ereby, the drawback analysis of the GMC (1, n) model is conducted with mathematical reasoning, which can explain why this model is inaccurate in some applications. In order to eliminate the drawbacks, a new optimized GMC (1, n), shorted for OGMC (1, n), is proposed, whose background values are calculated based on Simpson’ rule that is able to efficiently approximate the integration of a function. Furthermore, its extended version that uses the Gaussian rule to discretize the convolution integral, abbreviated as OGMCG (1, n), is proposed to further enhance the model’s forecasting ability. In general, these two optimized models have such advantages as simplified structure, consistent forecasting performance, and satisfactory efficiency. ,ree empirical studies are carried out for verifying the above advantages of the optimized model, compared with the conventional GMC (1, n), GMCG (1, n), GM (1, n), and DGM (1, n) models. Results show that the new background values can effectively be calculated based on Simpson’s rule, and the optimized models significantly outperform other competing models in most cases.

Introduction
Grey system theory has gained extensive attentions from worldwide researchers and has been successfully used in many fields with favorable outcomes since it was designed by Deng in 1982 [1][2][3]. is theory is capable of addressing issues characterized by uncertainty, insufficient information, and limited data points, thereby providing strong technical support for uncertain analysis [4,5]. As the most important part of this theory, grey prediction approach and its extended versions have captured enormous attention owing to their capability to provide accurate forecasts, especially under the situation that facing sparse data and poor information [6,7]. In contrast to the intelligent techniques and traditional statistical models, which require a large amount of data for model calibration, grey models only need limited data points to estimate the system behavior.
Among the grey-model groups, the GM(1, n) model, of which 1 means one order of differential function and n stands for the number of total variables, gains its reputation and operates as a typical forecasting technique due to its capability to deal with the system prediction issues that are influenced by a range of relevant factors. Unfortunately, as the solutions to the whitening function for GM (1, n) are rough and incorrect [8], it is prone to produce large errors in applications.
ereby, since its introduction, many researchers carried out studies for further improve its prediction performance in terms of the background values [9], discrete variants [10], model structures [11], fractional model [12], and time-delayed versions [13]. Out of these, a novel grey prediction model with convolution integral, namely, GMC (1, n), was designed by Tien [14] with a view to avoiding the incorrect solutions of the GM(1, n) model. As Tien presented, a convolution integral exists in the analytic solution to the whitening function of GM (1, n), and the Trapezoid formula is used to discretize the convolution integral. Many cases have proved that the GMC(1, n) model outperforms the typical GM (1, n). Moreover, for further adapting to the sequences having various characteristics, a range of variants derived from the GMC(1, n) model is put forward, such as DGDMC (1, n) [15][16][17][18][19] IGDMC(1, n), FGMC(1, n), NGMC(1, n), GMCN(1,n), and kernel-based nonlinear GMC(1, n) [20].
ough the previous improvements in background values with the support of those heuristic intelligent techniques lead to the improvements of forecasting ability, they also result in the low-level, simply-repeated, and complicated computations of grey models. Meanwhile, it is troublesome and difficult for beginners or inexperienced users to choose a suitable heuristic intelligent algorithm for solving actual forecasting problems. erefore, proposing an accurate forecasting grey model that has a simple structure and easy-understanding computations with a focus on the background values is a very valuable work. General consensus gotten from the literature was that accurate background values are regarded as a crucial requirement to ensure the reliability and practicability of the GMC(1, n) model [23,24], and the forecasting precision is heavily dependent on their correct computations. Supporting this argument, one of the major contributions in this paper stems from the mathematical derivation of the actual background values, finding its differences from the estimated one in the conventional GMC(1, n) model. Another equally important merit of this paper is to design an optimized OGMC(1, n), whose background values are reconstructed and calculated based on Simpson's rule. Moreover, the new model's extended version is also derived by using the Gaussian rule, instead of the Trapezoidal rule, to calculate the whitening function with convolution integral, namely, OGMC G (1, n). Subsequently, three cases of diverse subjects, including tensile strength of a material, China's gross industrial output value, and electronic waste in Washington State, are utilized for verifying the efficacy and robustness of the proposed models. Empirical results, the optimized background values, based on Simpson's rule can act as a supplementary for the current estimation methods of grey models. Furthermore, the OGMC G (1, n) model having optimized background values performs best among all competitors. e detailed comparisons will be elaborated in Section 3.
is work has the following structure. e research methodology is presented in Section 2. In this section, the focus is on the previous procedures and shortcomings of the GMC(1, n) model. Subsequently, the optimized OGMC(1, n) and OGMC G (1, n) models are elaborated on. Section 3 is dedicated to three different cases for depicting the accuracy and reliability of the proposed models in comparison with a range of competitors. Conclusions and discussions are provided in the last Section 4. e nomenclature utilized in this paper is presented below and detailed explanations related to the formulas employed in each technique are given in the following sections.

Overview of the GMC (1, n) Model.
e GMC(1, n) model has gains popularity in practical applications because of its accurate estimations and simple structures. Many researchers such as Tien [14][15][16][17], Ma et al. [31,32], and Duman et al. [24], have elaborated the procedures for this model, which can currently be outlined below: Step 1: collect the original data. Assume that , r ≥ 4 is a data sequence of a system's characteristic variable, short for the system behavior sequence, and , r≥4,i�2,3,...,n are the data sequences of relevant factors, abbreviated as the relevant series. In the series, r represents the number of entries for establishing the model, rp stands for the delayed period, and n is the total number of variables. Moreover, these two categories of series are nonnegative and equally spaced over time.
Step 2: generate the X (1) by using the first-order accumulated generating operation (1 − AGO). en the accumulated sequences X (1) i , i � 1, 2, . . . , n of the original data X (0) i (i � 1, 2, . . . , n) can be produced by using 2 Complexity Accordingly, the 1 − AGO sequences of the system behavior can be obtained as And the 1 − AGO sequences of the influencing factors are Step 3: build the GMC(1, n) model. Its first-order whitening equation is presented by where β 1 and u represent the system's development coefficient and grey control parameter, respectively. Additionally, β i X (1) i (t) is known as the driving term, and β i , i � 2, 3, . . . , n are the driving coefficients corresponding to the relevant factor sequences X (0) i , i � 2, 3, . . . , n, respectively. e grey derivative in equation (5) can be approximately estimated by In addition, the background values of X (1) 1 (rp + t) and X (1) 1 (rp + t) are usually taken as However, recent studies [9,23,24] has pointed out that, the estimated values of the background value may be unequal to the actual values, explained in Section 2.2. Hence, based on the background values, the first-order grey differential equation can be formulated as Step 4: estimate the parameters by using the Ordinary Least Squares method (OLS). Substituting the values of t into equation (9), we can obtain In this matrix form, By solving the matrix Y � Bβ, the estimated values of the parameters can be calculated: Step 5: obtain the response function for projections. As introduced above, the whitening equation of the GMC(1, n) model is displayed in equation (5). By substituting the parameter values β � [β 1 , β 2 , . . . , β n , u] into equation (5) and opting the X where As Tien [14] introduced previously, the Trapezoidal rule is originally used to discretize the convolution integral in equation (13) in the traditional GMC(1, n) model, and subsequently, the response function for 1 − AGO sequences can be determined by using the following equation: where the unit step function p(t − 2) in equation (15) is formulated by Unfortunately, due to the traditional GMC(1, n) model's poor performance, the Gaussian rule gains more popularity than Trapezoidal equivalent in recent studies for discretizing the convolution integral [17,31]. Consequently, the Gaussian rule is used in this paper as well. en, the discrete response function can be presented below: where the unit step function u(t − 2) in equation (17) is formulated by For convenience, the GMC(1, n) model whose convolution integral is discretized by using the Gaussian rule is remarked as GMC G (1, n).
Step 6: generate the simulative and predictive values in the original domain. rough equation (14), we will get the fitted and predicted values of the 1 − AGO sequences, which normally are considered as intermediate sequences. Subsequently, the recursive function in the original domain can be given by utilizing the 1 − IAGO method, which is defined as where X As outlined previously, when the u and rp satisfy u � rp � 0, the GMC(1, n) is reduced to the traditional GMC(1, n) model. Moreover, when n � 1 and rp � 0, the GMC(1, n) model becomes the original GMC(1, 1) model. erefore, the GMC(1, n) model is extensions of the GM(1, n) and GM(1, 1) models, indicating that the GMC(1, n) model has wider application fields.

Drawback Analysis of the GMC (1, n) Model.
Although the popularity of GMC(1, n) has been increasing steadily, some inherent drawbacks still exist, which may generate unacceptable forecasting errors. After reviewing the procedures of the GMC(1, n) model, we can find that two core components of this model are the model establishment and parameter estimation, which refers to equations (5) and (9), respectively. Especially for the parameter estimation, the accuracy of the estimated parameters is the precondition of obtaining the response function in equation (5). Specifically, equation (5) is used for predicting the system behavior sequence on the basis of the known parameters β � [β 1 , β 2 , . . . , β n , u], which are estimated by equation (9). Hence, prior to obtaining projections, the optimal or near-optimal parameters in the GMC(1, n) and GMC G (1, n) models are essential for better forecasting precision, which are significantly influenced by the background value.
To expose the inherent weakness of the GMC(1, n) model, the actual meaning of background value needs to be further analyzed by comparing the grey differential equation in equation (9) and whitening equation in equation (5). To this end, definite integrals of equation (5) will be given on the where 4 Complexity Substituting equations (21) and (22) into equation (20), the discrete form of GMC(1, n) can be obtained as follows: In equation (23), the real background values in both sides of the equation are noted as en, comparing equation (23) with equation (9), we find that the actual background values of are approximately represented by the average values of adjacent neighbor sequences in equations (7) and (8) for the GMC(1, n) model. However, they are not always mathematically equivalent. Accordingly, the gap between the actual background values and the approximate ones produces the inaccurate parameter estimations, which exert a negative influence on the predictive performance of the whitening equation in equation (5).
To address the weakness, Wang and Hao [23] put forward a new formula to calculate the background values based on the Mean Value eorem of Integrals, which can be expressed as where λ i (i � 1, 2, . . . , n) represents the dynamic interpolation coefficients. Obviously, equations (24) and (25) are equivalent to equations (7) and (8) when λ 1 � λ 2 � · · · λ n � 0.5, which infers that the optimized GMC(1, n) model having dynamic background values in [23] has better adaptability than the original one having fixed interpolation coefficients. To determine the dynamic interpolation coefficients, metaheuristic algorithms that have complex structures and require well-versed computer skills, such as Particle Swarm Algorithm and Genetic Algorithm, are necessary for combining with the GMC(1, n) model.
Although the optimized GMC(1, n) model in [23] provides an effective solution to avoid the deviations between the actual and estimated background values, potential difficulties in using this new model may increasingly arise, especially for beginners, due to the introduction of the complex optimization algorithms. Furthermore, these metaheuristic algorithms may not generate the satisfactory parameter estimations because they can fall into the local optima stagnation, consequently failing to find the actual global optimum. erefore, to effectively and accurately estimate the parameters in the GMC(1, n) model, an alternative method based on Simpson's rule is proposed for accurately measuring the background values in this paper. is algorithm, elaborated on in Section 2.3, has merits in simple structure and is easy to understand for beginners. Furthermore, it can also significantly improve the accuracy of the GMC(1, n) and GMC G (1, n) models, which will be demonstrated by several experiments in Section 3.

A New Optimized GMC (1, n) Model Based on Simpson's
Rule. In order to overcome the shortcomings of the above approaches to estimating background values, mentioned in Section 2.2, a new method based on Simpson's rule is employed to calculate the background value in the GMC(1, n) model. e flowchart of the new optimized GMC(1, n) model is displayed in Figure 1. Furthermore, the background values in [14,23] are also presented in Figure 1 in comparison with the new model.
Simpson's rule, named after the English mathematician, omas Simpson (1710-1761), is a numerical approach to approximate the integration of a function. is method is particularly useful when integration is difficult or even impossible to do by utilizing standard techniques. e most commonly used function of Simpson's rule is provided as As introduced in Section 2.2, the actual background value can be estimated by computing the integration , instead of the average values of adjacent neighbor sequences in equations (7) and (8). In order to be consistent with the forms of Simpson's rule in equation (26), the grey differential equation that is used for parameter estimation can be obtained by considering the definite integrals of equation (5) Complexity 5 Hence, substituting equations (28) and (29) into equation (27), the grey differential equation is mathematically equivalent to According to Simpson's rule in equation (26), we can get t+1 t− 1 Substituting and simplifying, equation (30) mathematically equals to (33) Simplifying, we can get this: GMC (1, n) [23] New optimized GMC (1, n) in this paper Restored function
Equation (36) can be written into the matrix form Solving this above matrix, the estimated values of parameters will be formulated: Similar to the GMC(1, n) and GMC G (1, n) models, we can also achieve two optimized models by using the Trapezoidal and Gaussian rule to discretize the convolution integral in equation (13). Specifically, substituting the parameter values β � [β 1 , β 2 , . . . , β n , u] into equations (14) and (17), the discrete response function can be obtained: Where the unit step function u(t − 2) and function f(t) in equations (39) and (40) are formulated by For convenience, these two models in (39) and (40) are remarked as OGMC(1, n) and OGMC G (1, n) models, respectively. Subsequently, by utilizing the 1 − IAGO method, the recursive function in the original domain is defined as Where X Based on Simpson's rule, the background values of the GMC(1, n) model can be accurately calculated, which is quite different from those in [14,23]. Moreover, Figure 1 provides the detailed procedures of the optimized model, which is helpful for beginners to use this model.

Performance Evaluation.
In addition to the modeling procedures of the GMC(1, n) model, the measuring indicators are also essential for evaluating the model's performance. In this study, three different indices will be adopted to examine the performance of competing models, including APE (Absolute Percentage Error), MAPE (Mean Absolute Percentage Error), and RMSE (Root Mean Squared Error). e algorithms of the three indices are calculated using the following equations: where x (0) (t) is the actual value at time t, and the x (0) (t) is the corresponding simulative or predictive value at time t.

Experiments and Analysis
In this section, for the sake of demonstrating the practicability and efficacy of the new optimized model, three empirical studies are carried out in comparison with traditional multivariable grey prediction models.

Case One: Predicting the Tensile Strength of a Material.
e multivariable grey prediction models, such as GM(1, 2) and GMC(1, 2), can be used for the indirect measurement of the tensile strength of a material [14], the efficacy of the OGMC(1, 2) and OGMC G (1, 2) models can be revealed by comparing the experimental results of predicting tensile strength of a material in comparison with the GMC (1, 2), GMC G (1, 2), GM(1, 2), and DGM(1, 2) models. e original data are presented in Table 1, which were collected from the experimental observations in Table 117 of Samuel [33]. In addition, the tensile strength represents the system behavior sequence (X (0) 1 ), and the Brinell hardness works as the relevant series (X (0) 2 ). Moreover, six data points of X (0) 1 and X (0) 2 are utilized for model calibration, and the remaining four observations of X (0) 1 are used for checking the predictive performance, namely, setting parameters n � 2, r � 6, rp � 0, and rf � 4 [33].
As introduced in Sections 2.1 and 2.3, the procedures and flowchart of GMC(1, 2) and its extensions are presented, and the procedures of GM(1, 2) and DGM(1, 2) are similar to those of GMC(1, 2). us, according to these procedures, the estimated parameter-values of six competing models are given in Table 2.
Taking OGMC(1, 2) as an example for explanations, we can obtain the parameter values β � [β 1 , β 2 , u] � [0.15387, 0.28354, 885.67276] after substituting the original data into equations (35) and (36). Subsequently, substituting the parameter values into equation (39), we will have the discrete response function: where By using the time response function in equation (44), the forecasted results and the values of three indices measuring accuracy will be obtained, which are shown in Table 3. It is obvious that four GMC(1, 2) and its extensions are superior to the traditional GM(1, 2) and DGM(1, 2) whose MAPE values reach 24.94% and 55.91%, respectively. e reason for this phenomenon is that GM(1, 2) has an incorrect time response function and DGM(1, 2) has narrow application fields. In contrast, the GMC(1, 2) and GMC G (1, 2) models are able to provide accurate forecasts because their modeling values with convolution integral are exact theoretically [14]. However, the OGMC(1, 2) and OGMC G (1, 2) models seem to obtain a litter better forecasting performance owing to smaller MAPE values, 2.48 and 2.52, respectively. Furthermore, the RMSE values of these two models are much smaller than the other four competitors, inferring good stability and reliability of the optimized background values based on Simpson's rule.
In general, the GMC(1, 2), GMC G (1, 2), OGMC(1, 2), and OGMC G (1, 2) models share almost the similar precision in predicting the tensile strength, and they are equally applicable for further estimations. Additionally, the optimized background values based on Simpson's rule can effectively contribute to the improvements of forecasting precision.

Case Two: Estimating the Gross Industrial Output Value.
In addition to the numerical example from Tien's study [14], another actual case concerning forecasting China's industrial output value, collected from Ma and Liu [31], is selected to test the effectiveness and practicability of the proposed models. e raw observations, listed in Table 4, are collected from the National Bureau of Statistics of China, who published correct, official, and complete data. Apparently, the industrial output value is the system behavior sequence, marked as X (0) 1 . en, the total current assets and fix assets represent the relevant series, noted as X (0) 2 and X (0) 3 . e GMC (1, 3),GMC G (1, 3), OGMC(1, 3), OGMC G (1, 3), GM(1, 3), and DGM(1, 3) are employed for forecasting China's industrial output value with parameter setting m � 3, r � 10, rp � 0, and rf � 3. In other words, ten data points of the three variables are used for estimating parameters, and the last three observations of the system behavior series are selected for testing the predictive performance.
Subsequently, by using the discrete response function, the forecasted results and values of the evaluation indicators will be obtained, which are displayed in Table 6. As this table illustrates, similar conclusions can be achieved: the GMC (1, 3),GMC G (1, 3), OGMC(1, 3), and OGMC G (1, 3) models significantly outperform the GM(1, 3) and  (1, 3) model provides the highest prediction accuracy followed by GMC G (1, 3), OGMC G (1, 3), and GMC(1, 3), respectively. e reasons for such an excellent performance of this optimized model are mainly provided from two perspectives. On one hand, the Gaussian rule that discretizing the convolution interval is generally more accurate than the Trapezoid rule, which can also be verified by other studies, such as Ma and Liu [31], Tien [15], and Wang [18]. On the other hand, the improvements of the background values based on Simpson's rule are equally important to enhancing its forecasting capability, because the optimized background values are crucial requirement to ensure the reliable and accurate parameter estimations, explained in Section 2.2. Similar findings can also be obtained from the comparison of the GMC(1, 3) and OGMC(1, 3) models, of which the accuracy rate is heavily dependent on the optimization of background values.    Complexity Generally, the OGMC G (1, 3) model obtains the highest forecasting ability leading itself as the optimal technique for the projections of China's industrial output value. Moreover, Simpson's rule can be employed for calculating the background values with high precision, which is essential for parameter estimations.

Case ree: Forecasting Electronic Waste in Washington
State.
e empirical results of cases one and two demonstrate the superior forecasting performance of the OGMC(1, n) and OGMC G (1, n) models having optimized background values based on Simpson's rule, in comparison with other competitors. Furthermore, the OGMC G (1, n) model achieves a litter higher accuracy than the OGMC(1, n) model. erefore, in addition to the above two examples coming from the published papers, another new case concerning electronic waste is introduced to verify the proposed model's efficacy and reliability in the following subsections.

Data Description and Model Calibration.
As introduced in earlier work [34,35], e-waste has increasingly become one of the major contributors of municipal solid waste (MSW), whose commonly used influencing factors are the population density and median household income. In this paper, the original data sets of e-waste from 2003 to 2015 are available from the government website (ecology.wa.gov), whereas data since 2016 are unavailable. In addition, observations of these two factors are collected from the Washington State Office of Financial Management website [36,37]. All the available data of these three variables are presented in Table 7. Moreover, in Table 7, data sets from 2003 to 2012 are used for establishing six models, whereas observations from 2013 to 2015 are employed for comparison. In the GMC (1, n) and its extensions, the parameters are used as m � 3, r � 10, rp � 0, and rf � 3.

Future Projections of e-Waste via OGMC G (1, 3).
e future e-waste estimations can only be forecasted under the premise of known future values of the population density and median household income. For the future values of the population density, the Washington State Office of Financial Management has provided the trends on the website [38], which is given in Table 10. For the median household income in Table 10, its observations from 2016 to 2017 are available from the above website [36], and its future estimations from 2018 to 2020 are predicted by using the GM(1, 1) model [39], which is a reliable and practical technique for univariate predictions.
Initially, data sets of the median household income from 2003 to 2017 are used for model calibration. en we will obtain the parameters [a, b] � [− 0.02078, 48518.01491], and the corresponding time response function is given below: Subsequently, estimated values from 2018 to 2020 are given in Table 10. By the way, the MAPE value in the insample period from 2003 to 2017 reaches 3.14%, inferring excellent forecasting capability of the GM(1, 1) model.
Once we have the values of these two relevant factors from 2016 to 2020, the future projections of the e-waste amount can be forecasted by using the OGMC G (1, 3) model. following equations (1)-(4) and (27)-(36), the forecasts from 2016 to 2020 will be calculated in Table 10.
Furthermore, by using the OGMC G (1, 3) model, the visual comparison of the real observations and predicted values from 2003 to 2020 are presented in Figure 2. As it can be observed from Figure 2, the predicted values fit the real observations well in the in-sample period, and further projections are likely to remain increasing from 2016 to 2020.
us, the optimized OGMC G (1, 3) can act as an appropriate tool for e-waste forecast in this paper.

Conclusions and Discussions
In summary, accurate future estimations play an essential role for decision-makers in framing and implementing sensible plans and policies. us, a grey prediction model with convolution integral, shorted for GMC (1, n), is introduced alongside with its improved variants GMC G (1, n). ese two models have been applied to solve various prediction issues by many researchers because of their correct solutions to the whitening function. However, inaccurate methods to calculate the background values may incur large deviations of the parameter estimations, which are essential for accurate future projections. erefore, mathematical analyses of the gap between the actual and estimated background values are discussed in detail. Moreover, Simpson's rule is introduced to compute the background values. Subsequently, the OGMC(1, n) and OGMC G (1, n) models are designed by utilizing the optimized background values. en, a comparative analysis via utilizing the same data points is run to analyze the performance of the proposed models in the three case studies. rough the discussion and analysis of the experimental studies, several conclusions can be drawn:  son's rule can significantly enhance the forecasting capability of the previous GMC(1, n) models. Additionally, the reconstructed background values have merits in the simplified structure, high reliability, and wide applicability, which have been proven in three cases. Most importantly, the new method can improve the accuracy of model calibration avoiding the unsatisfactory errors generated from the discrete function to the continuous one. (iii) e OGMC G (1, n) model rises as a more viable option for future projections of e-waste amount in Washington State owing to its accurate and reliable performances in three cases. Moreover, the future e-waste amount remains increasing for the upcoming years.
A limitation of this paper is caused by the linear structure of the proposed model, which may produce errors when dealing with the nonlinear sequences. erefore, future work will be carried out by proposing a nonlinear OGMC(1, n) model with optimized background values based on Simpson's rule.

AGO:
Accumulated generating operation IAGO: Inverse accumulated generating operation GM (1, n): Grey model having one order and n variables

Data Availability
e data utilized to support the findings are available in the above context or can be obtained from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.


Spatial Metadata Usability Evaluation

Spatial metadata is a critical part of any spatial data infrastructure, which enables the organising, sharing, discovery and use of spatial data. This paper highlights a knowledge gap in the usability of the metadata systems for the end–users. It then addresses the gap by applying the User Centred Design approach to investigate the usability of metadata records. The research engages with end–users concerning efficiency and effectiveness of metadata systems, and end–users’ satisfaction and expectations. The results indicate significant gaps with the effectiveness and efficiency of metadata systems for spatial data discovery and selection. Inconsistency and irrelevant information in the metadata records were found in the title, keywords, abstracts, data quality and other elements of the metadata. Additionally, essential improvements were identified for user interfaces. Discouraging presentation of the metadata is a prominent problem found in the interface of the metadata systems.

Introduction
Spatial metadata plays an important role in promoting spatial data sharing and re-use and supporting local and global development initiatives that require spatial data to manage, monitor and measure the development. It contains information about geographic or spatial dataset descriptions, e.g., contents, structure, quality, and reference system that will help spatial data users to discover and determine the suitability of the data for their purposes through networked spatial data catalogue systems, e.g., Spatial Data Infrastructure (SDI) and geo-portals.
However, the usability of spatial metadata for data users is questioned, since the metadata is created following standards originally designed for spatial data producers for data inventory purposes. Moreover, with the limitless possible applications of the metadata, at the very least we need to know how usable the metadata for spatial data users is for discovering and selecting appropriate spatial data. With the growing number of spatial data users outside the spatial field with specific knowledge, the requirements and expectations of spatial data users should be considered.
Spatial metadata usability is a combination of the usability of the metadata records and usability of the user interface. The state of the research in spatial metadata is limited to a few broad areas. Some investigations are dedicated to creating complete and consistent metadata records [1][2][3][4][5][6][7][8][9]. These papers reveal that most challenges for automatic metadata creation and updating relate to the type of information included in spatial data characteristics. Only a few pieces of information about spatial data can be automatically extracted and stored into metadata, e.g., the reference system, projection, date of last update, and lineage statement. All other information (e.g., abstracts and data quality descriptions) still rely on manual input by humans. There are also attempts to put emphasis on the involvement of users in metadata creation. There are also quite a number of studies that improve the discovery of spatial data using semantics and ontologies [10][11][12][13][14][15][16][17][18][19][20][21][22]. The papers show that there have been attempts to involve users in the creation of metadata, both direct and indirect. For example, direct involvement has been conducted by directly engaging users to provide information for metadata creation. On the other hand, indirect or implicit user involvement is conducted by collecting and analysing users' search words and assigning the results as tags for the spatial data.
To address the current knowledge gaps in spatial metadata usability, this paper reports the results of an experiment for investigating the usability of spatial metadata by employing two User Centred Design methods, namely Think-Aloud Protocol usability testing (TAP) and semi-structured interviews. TAP records the verbal expressions of participants' thoughts during the process of task completions and researcher's notes taken while observing the process. The semi-structured interviews are used to reveal detailed information of participants' experiences by encouraging them to recall specific incidents during the task completions. Both data captured by TAP and semi-structured interviews are then analysed and extracted to determine the usability of the spatial metadata, identify the usability problems, describe the user experience and reveal the user expectations.
Section 2 starts with an explanation of the data analysis method followed by experiment design, the reasoning for material and participants selection. Section 3 of the paper provides a summary of the results. Sections 4 and 5 analyse the outcomes of the data discovery and data selection task by participants. Section 6 collects insights from the participants' opinions during the experiment. Section 7 provides a discussion on the findings of the paper, and Section 8 concludes the research.

Data Analysis Methods
The method used in the analysis process is adapted from Protocol Analysis (PA) and content analysis. PA is capable of producing deep and accurate analysis from TAP data, as these methodologies are qualitative in nature and designed to obtain rich and deep data from small quantities of samples [10][11][12]. PA consists of several progressive steps as shown in Figure 1.
descriptions) still rely on manual input by humans. There are also attempts to put emphasis on the involvement of users in metadata creation. There are also quite a number of studies that improve the discovery of spatial data using semantics and ontologies [10][11][12][13][14][15][16][17][18][19][20][21][22]. The papers show that there have been attempts to involve users in the creation of metadata, both direct and indirect. For example, direct involvement has been conducted by directly engaging users to provide information for metadata creation. On the other hand, indirect or implicit user involvement is conducted by collecting and analysing users' search words and assigning the results as tags for the spatial data.
To address the current knowledge gaps in spatial metadata usability, this paper reports the results of an experiment for investigating the usability of spatial metadata by employing two User Centred Design methods, namely Think-Aloud Protocol usability testing (TAP) and semi-structured interviews. TAP records the verbal expressions of participants' thoughts during the process of task completions and researcher's notes taken while observing the process. The semi-structured interviews are used to reveal detailed information of participants' experiences by encouraging them to recall specific incidents during the task completions. Both data captured by TAP and semistructured interviews are then analysed and extracted to determine the usability of the spatial metadata, identify the usability problems, describe the user experience and reveal the user expectations.
Section 2 starts with an explanation of the data analysis method followed by experiment design, the reasoning for material and participants selection. Section 3 of the paper provides a summary of the results. Sections 4 and 5 analyse the outcomes of the data discovery and data selection task by participants. Section 6 collects insights from the participants' opinions during the experiment. Section 7 provides a discussion on the findings of the paper, and Section 8 concludes the research.

Data Analysis Methods
The method used in the analysis process is adapted from Protocol Analysis (PA) and content analysis. PA is capable of producing deep and accurate analysis from TAP data, as these methodologies are qualitative in nature and designed to obtain rich and deep data from small quantities of samples [10][11][12]. PA consists of several progressive steps as shown in Figure 1. The analysis process begins with Transcription of Data (ToD), where recordings and researcher's notes during the testing are transformed into textual transcripts. The next step is Referring Phrase Analysis (RPA). It is done by highlighting all the nouns and noun phrases identified in each participants' verbal data and attaching codes to those phrases in accordance with code references within the spatial data search activities. Based on the provisional coding results of the RPA, the investigator then groups each code according to each relevant action during the spatial data discovery and selection. The next step is Assertions Analysis where the investigator identifies the set of assertions made by subjects to determine how relationships were being formed between concepts during problem solving. As part of the analysis, the purposes of subjects' assertions are identified. The last step is Script Analysis to identify and provide an overall description of the reasoning process during problem solving and allowing the investigator to illustrate the problems identified by the subjects during the problem-solving process.

Experiment Design
The objective of this experiment is to collect and analyse data to answer research questions based on a selected usability evaluation method as illustrated in Figure 2. The experiment was designed based on the usability evaluation framework, TAP. The TAP data collection method utilises semi-structured interviews and post-questionnaires, and spatial metadata usability is evaluated using three criteria: usefulness, effectiveness and user satisfaction (middle blocks in Figure 2). The design was based on a task-oriented activity where participants were given a set of tasks concerned with spatial metadata, following a scenario to achieve specified goals (top blocks in Figure 2). During the completion of the tasks, they were asked to actively and continuously express their thoughts and opinions verbally, as well as answering questions given by the researcher (top blocks in Figure 2). At the end of the experiment, the participants answered some questions in semi-structured interviews to provide the researcher with detailed and deeper information related to the given tasks and based on their experiences during the TAP (top blocks in Figure 2). The analysis process begins with Transcription of Data (ToD), where recordings and researcher's notes during the testing are transformed into textual transcripts. The next step is Referring Phrase Analysis (RPA). It is done by highlighting all the nouns and noun phrases identified in each participants' verbal data and attaching codes to those phrases in accordance with code references within the spatial data search activities. Based on the provisional coding results of the RPA, the investigator then groups each code according to each relevant action during the spatial data discovery and selection. The next step is Assertions Analysis where the investigator identifies the set of assertions made by subjects to determine how relationships were being formed between concepts during problem solving. As part of the analysis, the purposes of subjects' assertions are identified. The last step is Script Analysis to identify and provide an overall description of the reasoning process during problem solving and allowing the investigator to illustrate the problems identified by the subjects during the problem-solving process.

Experiment Design
The objective of this experiment is to collect and analyse data to answer research questions based on a selected usability evaluation method as illustrated in Figure 2. The experiment was designed based on the usability evaluation framework, TAP. The TAP data collection method utilises semistructured interviews and post-questionnaires, and spatial metadata usability is evaluated using three criteria: usefulness, effectiveness and user satisfaction (middle blocks in Figure 2). The design was based on a task-oriented activity where participants were given a set of tasks concerned with spatial metadata, following a scenario to achieve specified goals (top blocks in Figure 2). During the completion of the tasks, they were asked to actively and continuously express their thoughts and opinions verbally, as well as answering questions given by the researcher (top blocks in Figure 2). At the end of the experiment, the participants answered some questions in semi-structured interviews to provide the researcher with detailed and deeper information related to the given tasks and based on their experiences during the TAP (top blocks in Figure 2).

Participants
For this study, five spatial data users from different educational backgrounds were selected; civil engineering, spatial science and computer science. They were working on disaster management.
The number is optimal for usability testing method using TA protocol, since it is able to identify the most usability problems with optimum benefit-cost ratio [12]. In addition to that, the study is a qualitative and exploratory in nature, focusing on the extraction of user's insight about spatial metadata. This type of study usually needs a small number of participants with a long time of participant-researcher interaction, as opposed to a quantitative study which focuses on statistics, using a large number of participants and little if any participant-researcher interaction [10].

Materials
Spatial metadata records were selected from two data directories or portals: Victoria Data Directory (VDD) and Australian Spatial Data Directory (FIND). The portals were selected based on the following criteria. The metadata is (1) created in accordance with international metadata standards (ISO 19115); (2) available publicly and accessible via the internet; (3) the VDD represents open data platform and VDD represents spatial data catalogue. VDD is a state level portal that connects and shares spatial metadata repositories with official institutions in Victoria State, while FIND is a national level portal consisting of metadata nodes from national institutions such as Geoscience Australia and Bureau of Meteorology.
Other materials were a set of questions designed as guide questions for semi-structured interviews and written instructions for the participants containing scenarios, tasks and objectives. Another important technique for this study was the use of audio recording for collecting participants' verbal expressions and opinions during the completion of the test.

Scenario
For this experiment, the scenario was to develop an evacuation map for Greater Melbourne and the East Coast of Australia (Queensland and New South Wales). The set of spatial data required for this activity follows:

•
Elevation dataset with minimum scale of 1:25,000 • Hydrographic datasets (e.g., rivers, dams, ponds, etc.) with minimum scale of 1:25,000 • Meteorology datasets of information (e.g., rainfalls) • Road network or transportation network datasets with minimum scale 1:10,000 for urban area and 1:100,000 for rural area • Soil type maps with minimum scale of 1:100,000 To acquire the appropriate data, participants searched the Victorian Data Directory (VDD) and Australian Spatial Data Directory (FIND) websites.
Tasks-following the given scenario, the participants were allocated three main tasks, to: 1. find the required spatial data from discovery systems (VDD and FIND); 2.
determine the suitability of spatial data for the given scenario; and 3.
determine how to obtain and appropriately use the spatial data.
The first task was designed to investigate the usability of metadata, as well as discovery systems, in helping users to find and locate the required spatial data. The second was for participants to use the information from metadata records to assess the suitability of the spatial data for the given purpose. The third question targeted the utility of spatial data for the given application. They were asked to verbally express their thoughts about the tasks and spatial metadata in detail.

Procedure
The usability test was conducted in a prepared laboratory environment using the following procedures:

1.
Orientation Session-each participant attended orientation prior to performing data discovery and selection tasks. During the orientation, the participants were given an explanation about the purpose of the study, the scope and expectations of the experiment and the tasks to be performed. Written instructions were also given. In this session, participants were allowed to ask questions related to the study and the tasks, and at the end of this session participants were asked to sign a consent form. This session lasted 5 min.

2.
Task performance-each participant performed and completed three tasks as described in the task section.
• The first task was searching and locating the spatial metadata required for the given scenario from the spatial data directory. Participants were given 30 min to search and find the required spatial data from the discovery systems. They were asked to stop the task when the time was finished. At that stage, success rate was observed.

•
The second task was to decide whether the data was suitable for the given project or not, by examining the spatial metadata records obtained from the first task or, if the participant had been unable to find relevant records, the pre-selected metadata records prepared by the researcher.

3.
Interviews-after completing the tasks, participants were asked to fill out a questionnaire and to explain their answers to the researcher. The questions were designed to get participant's opinions about their experiences working with the spatial metadata during the data discovery and selection process.
During the experiment, the participants were accompanied by a representative from the research team. The representative's role was to give instructions and explanations about the test during the orientation session, answer questions raised by the participants during the performance of the tasks, and to make sure that the participants stayed focused on the objectives. The representative also asked participants the prepared questions when an interview stalled or to elicit more detailed insights from participants about the metadata.

Results
Two data sources were collected from the experiment: audio recordings and semi-structured interviews based on a set of questions. As an exploratory study, analysis methods used were mainly qualitative. TAP analysis was used to analyse the TAP data. The interview data was analysed using content analysis.

Think-Aloud Protocol (TAP)
During the spatial data discovery and selection process, participants' verbal expressions were recorded. Each record was then transcribed and analysed separately using the protocol analysis. The transcriptions were analysed by identifying referring phrases (RPA) and each phrase was given codes based on the reference codes listed in Table 1. Examples of the phrases, and the codes which resulted from this process, are presented in Table 2. Table 1. Reference codes used in Protocol Analysis [2].

Action
The manner or method or performing; a thing done Element A piece of information describing certain characteristics of spatial data Sign Objective information indicative of status of the information or tools Time A chronological reference Needs Information, tools or actions required as to discover or select data Value A rating of usefulness, importance or worth Goal A specific goal for an action From Table 2, we can see phrases and respective concepts (codes) resulted from the participants' verbal expressions during the spatial data discovery and selection. These phrases and codes identify all the vocabulary and concepts the participants' focused on during the process.
The phrases and the codes were then further analysed to determine the assertions of each phrase. These assertions were then used to understand how the relationships were being formed during the spatial data discovery and selection. Table 3 shows the phrases and their respective assertions.
The final stage of the analysis process was conducted by implementing script analysis, which assigns a set of operators to the phrases to identify the process of reasoning during spatial data discovery and selection. Three operators were used: suggest, study and conclude. These operators represent the interactions in the reasoning process of spatial data discovery and selection. Table 4 provides an explanation of the operators. Indicative 1 And maybe after half an hour or more, we can find the one you look for Causal But the efficiency of the search tools and the database should be higher than that Connotative I have to be able to find the (potential) data in one minute, otherwise, I could spend a lot of time Causal Suggest means to consider an action or information to achieve a specific goal. 2 Study means to observe or consider information or facts carefully. 3 Conclude means to decide on the significance, value or results of an action.
From the tables presented above, we can identify the participants' activities, goals and expectations, as well as relationships between them and their reasoning when they try to discover and select spatial data using the metadata via the user interfaces.
The results of script analysis were then used as the basis for identifying the effectiveness, efficiency and user satisfaction, as well as identifying usability problems and user expectations for spatial data discovery and spatial data selection.

Analysing the Outcomes of Spatial Data Discovery Tasks
In spatial data discovery users use the user interface to interact with metadata to discover the data for the given purpose according to the scenario. Effectiveness, efficiency, user satisfaction, problems and user expectations were then identified by interpreting the results.

Effectiveness
Effectiveness of the spatial metadata is a combination between the discovery systems or searching tools and the metadata records. To this end, effectiveness was measured by the successfulness of the participants in finding and discovering potential spatial data for the given scenario from the two discovery systems: VDD and FIND. From the script analysis results, we can identify the successful rate of the discovery by looking at the conclude operator, which is related to significance, value or results of an action.
To acquire a comprehensive result, conclude phrases were examined and grouped based on the tones of the phrases; positive, neutral and negative tones. Positive is when a phrase indicates a successful result and negative if it indicates otherwise. Neutral is a tone where a phrase is neither positive nor negative.
"I see some results"-Positive conclude "I cannot find exact data for Melbourne"-Negative conclude "can we assume that we are failing to discover the map?"-Neutral conclude By only analysing the conclude phrases throughout the analysis document, it is hard to make a clear statement about the effectiveness of the spatial metadata for data discovery. Nevertheless, the concludes provide indications of ineffectiveness. The example concludes phrases given above are a participant's verbalisations during the discovery process of the Melbourne Topographic Map. Meteorology data provides other examples of conclude phrases: "so, the meteorological did not respond that much" "if you look for the rain, you only get one result" Most of the conclude phrases do not provide a clear indication that the data discovery process can be successfully completed or not. In the examples above, the participant tried to finish the searching with a doubtful decision. It is interesting to investigate why this participant came to that decision. To find out, we look at other phrases, study and suggest, which, together with conclude, form the whole process of reasoning, as illustrated in Table 5. Looking at the whole reasoning process, the participants have negative concludes because they could not find the scale in the title. One participant faced 37 initial results, 1300 results after clicking the most relevant and 2000 after another click on the newest results. This participant found that the results, represented in a list of titles, should have included a scale. A scale would have greatly assisted them to locate the required spatial data, as the participant did not want to spend a lot of time searching titles by clicking on them one by one.
Another participant showed a different attitude when facing the same situation, as they just clicked on a title that they thought was the most relevant to the required data.
"There are some problems with this. I type elevation, and this one is the most related, but it does not come first" "I think the accuracy is enough, I think if we have this, the accuracy will be enough" "so, can I look for another one?" The participant ended up spending a lot of time, more than the time given to do the search, by clicking and opening each and every title in the result list to find the relevant data for the given scenario.
There were recurring groups of phrases, positive, negative and neutral, from the data during the spatial data discovery process, which indicate that spatial metadata effectiveness is subject to the quality of the metadata. The quality of the metadata is determined by the following: completeness, consistency and relevance of the information presented to users; the intuitiveness of the user interface against the user needs; detailed criteria for data search filters; and willingness of users to do further detailed search within the results.
The results indicate that spatial metadata, along with the searching tool, can be used to find and discover spatial data, but users found some obstacles that hampered them from performing the task efficiently, as explained in the next section. These obstacles might prevent users from reaching the task goal, as they tended to stop the searching right away when they found that the search was not going as they expected. They would try other ways to find the data, such as finding information about the data from an internet search engine and contacting the producer directly.

Efficiency
Spatial data users can search the required potential data from the websites, but some effort and time was necessary to find and discover the data. The following concludes indicate that the data discovery was not a straightforward process, where participants could not get the expected results in the given time: "We can spend a lot of time searching for each data" "and maybe after half an hour or more, we can find the one you look for" "But the efficiency of the search tools and the database should be higher than that" "I have to be able to find the (potential) data in one minute, otherwise, I could spend a lot of time" During the process, similar concludes were recurring to the point that most of the users did not want to continue their current data searches and asked to move to another search.
"If I cannot find it in like one minute, it means I have to move on to the next search" The researcher's notes during the process of this task also indicate that none of the participants could discover all the required data in the given time.
These results indicate that the spatial metadata is able to help users to discover spatial data from the websites, but there are efforts required to increase the efficiency of the process. What needs to be done to enhance efficiency may be determined by first revealing the problems and user expectations, as explained in the next sections, and addressing the problems by enhancing the metadata and the user interface simultaneously.

Usability Problems
Participants faced several problems in their attempts to discover the required spatial data using the websites. The problems are related to both the website (user interface) and the metadata (content). These problems can be identified by examining the results in the following examples. Figure 3 illustrates some of the problems identified during spatial data discovery as mentioned by the participants, e.g., unmatched keywords and results, tags/filters that are not easily recognised nor sufficient to participants' needs.
"No tools to choose the scale" "Some of the titles have scale in them, and some do not" "Why can we not short it based on the most relevant ones" "The title does not mention the scale" "(By applying) the most relevant, it gives me 1300. I tried to put the newest back, and it gives me 2000 results" "and when I tried to search using region (as a keyword) I cannot find exact data for Melbourne" "The system does not provide any advance search" "I think the filters (for the search) are not enough and the data are not well tagged" "Interesting part is the titles are not very accurate, I think they come from the title of database or datasets" "This tag is helpful, otherwise you see the title might not be relevant" Similar types of concludes are found in the results. From the lists the identified problems can be grouped into two types; user interface problems and metadata records problems. Table 6 summarises the problems that can be addressed to increase the usability of spatial metadata for spatial data Similar types of concludes are found in the results. From the lists the identified problems can be grouped into two types; user interface problems and metadata records problems. Table 6 summarises the problems that can be addressed to increase the usability of spatial metadata for spatial data discovery. Table 6. Identified usability problems in spatial data discovery.

User Interface Problems Metadata Records Problems
Missing important filter for data search e.g., scale is not provided (in VDD and FIND) Inconsistent information presented in titles e.g., scale, unknown abbreviations Tags are not necessarily relevant to the data (VDD) Keywords are different from the data description Inconsistency of the results when users change the newest to most relevant (FIND) Inconsistent abstracts e.g., contain superfluous information or too short and uninformative Irrelevant results with the submitted keywords (VDD and FIND) Advanced search is not available (VDD)

User Satisfactions and Expectations
User satisfaction is not a usability attribute that can be easily evaluated, since it is related to emotions, feelings and experiences of participants during the task completions. However, it could be detected by carefully observing the data (phrases) in conjunction with researcher's notes while observing the experiments. In the process of identifying the user satisfaction, user expectations on both the spatial metadata records and user interface are observed simultaneously, since the satisfaction is determined by the gap between the expectations and the reality. Following are some of the phrases that can be used to detect user satisfaction and expectations during the spatial data discovery.
"I think, I cannot find the scale, probably I need to open one by one to see what the scale is" "People should define some basic needs, and they have to face with this kind of search" Similar phrases were recurring during the spatial data discovery process that can be used to detect user satisfaction as well as identify the expectations. From the above phrases, an unsatisfactory result can be detected as the participant could not find the filter scale to narrow down the results. They expected that the searching tool would provide them with a set of basic criteria to narrow down their search.
The researcher's notes also indicate that participants were not enthusiastic when they opened the VDD website, since it only provides a simple search by submitting keywords. They did not notice the tags provided on the navigation window at the left-hand side of the web page. Even when they found out about the tags, they were not happy because when they tried to use them, the results were more irrelevant than they expected. Different reactions were given by the participants when they opened the FIND website. Participants were enthusiastic when they found the advanced search in the website. However, they started to complain about the website when they received results, especially because they could not find the way to narrow down their search using the scale. Table 7 summarises user expectations for spatial data discovery.

Analysing the Outcomes of Spatial Data Selection Tasks
Spatial data selection is a process where participants try to understand the characteristics of spatial data by reading and interpreting information presented in spatial metadata to decide whether the spatial data is suitable or fit for the given scenario or not. In their attempts to read and interpret the information, participants use their knowledge and experiences which vary between them.
The effectiveness, efficiency, usability problems, user satisfaction and expectation for spatial data selection can be identified from the protocol analysis results.

Effectiveness
Conclude phrases related to this process were observed to identify the result of participants' attempts on data selection. "So, it is not very easy to make a quick decision" "After they give you a sample then maybe you have to contact them and ask them what this data is about" "Currently from this metadata, you are not sure about data" "I am not sure of this. I think, I can say that I am in the middle" "I am confident, but I need more time to read, probably I need more experience" "You need to spend more time, and you will be more confident" "I think it is enough for me to decide whether this is what I need or not" "I think, if can have a look at the data itself, I might be confident" Again, similar phrases recurred during the experiments as thoughts from participants. As in spatial discovery, it is not easy to clearly say that spatial metadata is effective or ineffective for spatial data selection, as participants gave positive, negative and neutral concludes. Nonetheless, the phrases allow us to sense a degree of ineffectiveness. For example, a participant's verbalisations vacillated during the process. At some points, the participant would be confident in their decisions, but later, lack conviction when they had a different experience with the metadata.
Based on authors' notes during the process, at first, participants looked at the metadata page as a whole to find information that might be critical to their decisions, including abstract, production date, update, producer and accuracy, and then felt confident that they could make a decision. However, after they had a detailed look at each element, they started to have doubts. For example, when they looked at the data accuracy, they were very critical and demanded detailed information. They complained about the unclear values of the accuracy, e.g., 1-10 m, and asked for an accuracy evaluation process. Participants had similar experiences with metadata from both websites, VDD and FIND. Moreover, all participants required additional information that was not provided in the metadata, including spatial data sample (access to the data), information regarding producer's reputation and reports on spatial data quality tests.

Efficiency
Similar to spatial discovery, participants were only able to read and to evaluate half or less of the metadata from the given tasks. They spent much of their time trying to find critical information within the metadata to assess the suitability of the data, for example, accuracy, to figure out whether the information was useful or not. They spent more time trying to interpret information that was not always relevant to their knowledge. The following phrases are examples of what participants had to deal with and what cost them time locating and interpreting information in the metadata.
"the description is not so clear and too much for data source" "just have a list maybe of who are the providers" "why put this in data source? class should not be in data sources" "I think they mess (mixed up) the information (in this part of metadata)" Accordingly, efficiency of metadata needs to be increased. Moreover, participants need more time to acquire additional information from different sources, including producers and data experts, to assist them to make clear decisions on the data.

Usability Problems
Data analysis results provide us with various problems faced by participants during the spatial data selection process. These problems prevent them from making a clear decision about the suitability of the data for the given scenario, as well as hampering participants in making selections in the given amount of time. Missing important content, as in maintenance date or last update, discouraging presentation of data quality and abstracts, were also issues. However, the main problem, which all participants identified, was the irrelevance and inconsistency of information returned in abstracts and in accuracy. Figure 4 illustrates the problem found in an abstract. Participants agreed that abstract plays a crucial role in spatial data selection, as they would start the process and reasoning with it. A brief, clear, easy to understand and relevant abstract, with the terminologies they know, is essential to help them understand what the data is about and how the Participants agreed that abstract plays a crucial role in spatial data selection, as they would start the process and reasoning with it. A brief, clear, easy to understand and relevant abstract, with the terminologies they know, is essential to help them understand what the data is about and how the data would fit their purposes. A good quality abstract, according to users' perceptions, would encourage and guide them to find other information about the data within the metadata. Conversely, a messy abstract would confuse and discourage them from getting more information from the metadata. Table 8 summarises the usability problems identified from the experiment. Table 8. Identified usability problems in spatial data selection.

User Interface Metadata Records
Discouraging presentation e.g., plain textual presentation Missing metadata contents Inconsistent content between metadata records e.g., in abstract Unfamiliar terminologies e.g., in abstract and accuracy Inconsistent length of content e.g., in abstract and accuracy Lack of information in contents e.g., no validation test for accuracy Besides the above listed usability problems, the data provides us with a meta-problem, that is, a problem beyond a usability problem found by participants in metadata records and user interfaces. This meta-problem was detected from the phrases below.
"I think it's the provider, because we need to know to judge, whether we can trust the data or not" "to clearly describe the data, but I think the best way is to have a sample" "or they give you a sample then after that maybe you have to contact them" "if you can go and search one sample, not too much but to see what kind of data they have to be sure" "you can read and say -definitely I need this-but when you, download or get down, you figure out that this is not my data" The problem was related to confidence, where participants felt that information presented in metadata would only be useful to examine the information in metadata. It is not that they did not trust the metadata, but they thought that they could not base their decisions on the suitability of the spatial data solely on the information presented in the metadata. In order to make decisions, they required additional information, referred to as meta-information, including the reputation of the producers, their experiences with the data or the metadata system, that could only be obtained by live or direct interaction with the data. Similar reasoning might be found in the car sales business, where customers would look at and read the brochure or advertisements to identify potential cars that would fit their criteria. However, deciding to buy or not to buy the car is a different story and requires different information that cannot be provided by the brochures or advertisements, that is, a live experience with the car itself. Hence, test driving. The needs and expectations of this meta-information are explained in the next section.

User Satisfactions and Expectations
During the spatial data selection process, participants identify specific information in metadata records that could be useful to assess the suitability of the data for the given project. In doing so, participants start with reading the abstracts to get a brief understanding about the data before they continue the process. However, participants found that most of the abstracts were problematic and discouraged them from reading and spending more time to understand the information. This led them to go to other metadata records based on their existing knowledge to identify the important information that might be useful for them to assess the suitability. Most of them went for accuracy information and found that information presented was not necessarily clear and comprehensible. Participants went for, amongst other things, information such as production date (the date created) and the boundary (geographic coverage). During the process, they kept verbalising their thoughts, which were mainly negative, about the metadata, as they found that metadata did not meet their expectations, as summarised in Table 9. Table 9. Identified users' expectations for spatial data selection.

User Interface Metadata Records
Alternative presentation style e.g., statistical or graphical presentation for data accuracy Brief and consistent abstracts with critical information for spatial data selection Dynamic/intuitive presentation/pages Use of familiar terminology to users' knowledge and experiences Access to data sample or preview for data self-assessment Access to data producers for additional information about the data

Analysing Interviews
After completing the given tasks, participants were given a set of questions regarding the spatial data discovery and selection. The authors used these questions to explore participants' opinions and experiences about working with spatial metadata. They were encouraged to recall any critical incidents during the process and give their explanations about the incidents. Question 1: To what extent do you agree that you can find the required spatial data?
Participants gave various answers to this question as they had different experiences and problems. As can be seen in Table 10, for both spatial data discovery systems, participants' opinions vary, with no strong indications that they successfully located the required spatial data. Participants mentioned the lack of criteria as filters to narrow down their search from the earliest stage. They recalled how irritating it was when they had to look at so many listed titles and to read and check the titles one by one only to discover that the titles were inconsistently presented. When they were reminded about tags in the VDD website that could be used to filter the data, most of them were still not happy, as the tags were not easily recognised and did not provide the expected criteria, such as map scale and region (geographic coverage). They did not want to spend a lot of time searching for data that was not there. Hence, their need for complete and well-labelled filters for searching criteria to get immediate results or no results.

Question 2:
To what extent do you agree that the spatial metadata (and the user interface) meet your expectations?
As can be seen in Table 11, participants' responses to the questions were mostly negative, as were their answers to the previous question. They found serious problem during the discovery process, e.g., the inconsistency between the keywords they submitted with the titles presented in the result. A participant who had experience with the discovery websites mentioned about how to improve the system, e.g., provide tags from previous users to help him identify appropriate data as they might have different terminology for the same data and share this with other users. Another participant mentioned putting more effort into making the metadata records complete, clear and consistent, both within a record and between metadata records. They recalled a specific experience where they had encountered a title with abbreviations in it that has no explanation whatsoever in the abstract nor in the rest of the records, and they had to open the metadata because the title appeared on top of the most relevant result.

Question 3:
To what extent do you agree that you can determine spatial data fitness for use to decide whether you will use the data or not?
Participants with a spatial information background tended to leave the metadata page once they had information about the contents/features, the age of the data (last update) and the geographic coverage (region covered by the data). They would look for opportunities to download and get the data and perform their own assessment on the actual data or data sample, to find out whether the data was fit for their purpose or not. Or, they preferred to contact the data producer directly to get the information they required to make decisions about the data, instead of reading the metadata and basing their decisions on the metadata. Those from non-spatial backgrounds, like the civil engineer, would prefer to look at the data producer and get information regarding the reputation of the producers to be sure about the data. The participants' explanations, as can be seen in Table 12, were therefore mostly negative. Another participant, who was very confident with his spatial knowledge, preferred to read the report on spatial data processing, to find out information about the methodology for data collection and standards for quality validations.

Question 4:
To what extent do you agree that the spatial metadata met your expectations for spatial data suitability assessment?
As can be seen from the participants' responses in Table 13, the metadata sufficiency for assessing suitability of spatial data for a certain purpose is subject to their experience with the data and their professional backgrounds. Most of the participants gave negative responses, as the metadata barely meet their expectations. Instead, they required additional information that was not part of the metadata. The next question is, to what extent the metadata could be improved to meet their expectations? Participants' responses were unclear, as they could not articulate what they expected from the metadata. Some of them, again, asked for access to sample data. Some asked for previous usages by previous users such as in reports or reviews. Some participants said that they would not decide the suitability of the data based on the metadata. They would only use it to discover the data availability and they would try to access or obtain and check the data suitability by working with the data directly. Question 5: To what extent do you agree that you are confident to use spatial metadata again in the future for spatial data discovery and selection?
This was the last question given to participants. As Table 14 shows, the responses are, again, mostly negative. However, their explanations were not so negative. Most of the participants would still use and rely on the metadata, and data discovery systems, for searching potential spatial metadata for their future purposes. They would like to see the metadata and user interface improved by addressing identified problems and their requirements from this experiment. They still thought that metadata was important, but improvement should be made to make metadata more usable and useful to them. One participant would like to see metadata presented in different styles and presentations based on users' expertise levels, general, intermediate and experts, using different terminologies in accordance with the level of expertise. Users could choose and use the discovery system and presentation suitable for them.

Discussion
The results and findings of the usability evaluation of established spatial metadata reveals that the metadata and the user interface remain problematic for spatial data users to discover and select spatial data. Problems such as inconsistent information in most elements in the metadata records hampered spatial data users from effectively and efficiently discovering and selecting spatial data. Another problem that can be highlighted is the irrelevance of the information presented in the metadata to the users' knowledge. The problems found in the user interface add another difficulty to the discovery and selection process. Lack of searching criteria, irrelevant results from the submitted search, and discouraging textual presentation that is either too short or too long, make the discovery and selection process harder.
The fact that these metadata records were created following the same metadata standard ISO 19115 did not prevent the problems from happening. Most of the problems come from the free-text type of elements in spatial metadata standards such as title, abstract, keywords, data quality and data provenance. The information mainly comes from the metadata authors' understanding about the data. This indicates that the standard of capability remains lacking for maintaining the consistency of information presented in the metadata and the relevance of the information to the spatial data users' knowledge.
Another finding in spatial data selection reveals that spatial data users require more than just information from metadata to be able to select the data for their purposes. Access to actual spatial data or a sample is important for them so they can assess the suitability of the data themselves. They also think that experiences from other users who worked with the data are useful for the selection process. This is another indicator that the standards of the main guideline for spatial metadata creation should be improved.
The latest version of the ISO standard for geospatial metadata is the ISO 19115-1:2014, Geographic information-Metadata, Part 1: Fundamentals. According to the standard, a full metadata record is an aggregate of 12 metadata classes. There is information that can be of help for users that the standard does not currently have elements for accommodating; for example, user data rating and the number of downloads. The future research should be designed to address the problems and user expectations of spatial metadata to improve the usability of spatial metadata and recommend how spatial metadata standard ISO 19115 can be extended to provide a solution for better metadata usability.

Conclusions
This paper outlined results of a spatial metadata usability evaluation experiment. The results indicate that the spatial metadata is neither effective nor efficient for spatial data discovery and selection, and improvements are required of both the metadata records and the user interface. The experiment also revealed some usability problems in both metadata records and user interfaces (websites). Inconsistency and irrelevant information in the metadata records were found in the title, keywords, abstracts, data quality and other elements of the metadata. Lack of searching criteria, irrelevant results from the submitted search, and discouraging presentation of the metadata are some prominent problems found in the user interface. Those problems hampered the spatial data users from effectively and efficiently discovering and selecting spatial data. Moreover, the results also revealed that the information presented in metadata records does not suffice the needs of spatial data users to make a selection of spatial data. Previous user reviews and experiences and access to actual data or sample are also required by the users to make their selection.
Accordingly, spatial data users were not satisfied and expected that the websites would provide them with better searching tools and better results in terms of consistency of relevance of information regarding spatial data.
The results and findings from this evaluation will be used as the basis for usability improvements and for garnering spatial data users' needs and expectations from the wider community, as a future direction.

Patents
This section is not mandatory, but may be added if there are patents resulting from the work reported in this manuscript.