Improved Method for Estimating Construction Year of Road Bridges by Analyzing Landsat Normalized Difference Water Index 2

Abstract

The construction year of road bridges plays an important role in bridge management systems. Based on the age of road bridges and other factors, deterministic and probabilistic deterioration models can be used to calculate deterioration rates and predict the future physical condition of road bridges. Two new techniques are proposed in this manuscript for estimating the construction year of road bridges by analyzing the normalized difference water index 2 (NDWI_2). Technique 1 uses both the target bridge point (TBP) and a selected optimal reference control point, while Technique 2 uses only the TBP. Landsat 5 Thematic Mapper NDWI_2 data were analyzed at all 44 road bridges in Nago City, Japan of the bridges’ overall length ≤ 100 m and construction year between 1990 and 2006. The sequential t-test analysis of the regime shift method, at a significance level $\alpha$ = 0.05 and cutoff length l = 2 to l = 27, was used to interpret the estimated construction year from the NDWI_2 for both techniques. Both techniques successfully determined the estimated construction year, which was statistically significant with p-values < 0.05, except for seven road bridges in Technique 1 and one road bridge in Technique 2. The correlation and comparative analysis of the actual and estimated construction years yielded $R^2$ = 0.24 and $R^2$ = 0.33, as well as an average deviation of S = 5.81 years and S = 4.08 years for Technique 1 and Technique 2, respectively. The findings suggest that Technique 2 is more accurate and provides a better estimate than Technique 1. It was observed that, as the cutoff length l increased, the absolute error between the actual and estimated construction year increased. Therefore, as a measure of accuracy, the upper limit of cutoff length l was set to $l\le$ 12. It was also observed that the increase in the bridge’s overall length and forested area contributed to the accuracy of the results. By using the construction year as one of the inputs into bridge management systems, bridge managers can make more informed decisions about how best to maintain and improve road bridges to ensure user safety and road bridge preservation for the future.

1. Introduction

The construction year of road bridges plays an important role in bridge management systems (BMSs). The BMS helps extend the life of road bridges and reduce the total life-cycle cost of maintenance, repair, rehabilitation, and replacement by prioritizing road bridge rehabilitation and replacement, predicting the future deterioration of road bridges, and optimizing repair costs [1].

Road bridge managers can assess the current condition of a bridge, identify potential problems, and plan for the necessary maintenance, repair, rehabilitation, or replacement of a bridge by using the bridge’s construction year. One of the most important indicators of a bridge’s physical condition is its age. This information is used to identify priority bridges, plan and budget for future work, and develop plans for routine maintenance and inspection. The two most commonly used types of deterioration models to calculate deterioration rates and predict the future physical condition of road bridges are deterministic and probabilistic models. The deterministic deterioration model uses regression analysis to create a curve based on the relationship between the age and condition rating of road bridges and other factors such as environmental conditions. The probabilistic deterioration models, such as the Markov chain method, use the condition ratings in conjunction with the age of the road bridge to determine the deterioration rate [2]. Second, the age of the road bridge and other factors help road bridge managers determine the damage rates of bridge components, such as the corrosion rates of steel girders, and diagnose long-term damage and deterioration, such as delayed ettringite formation in concrete structures that may not become apparent for 20 years [3]. Third, the construction year is critical for budgeting and financing. One of the most important inputs into the optimal cost estimates and rehabilitation models that help road bridge managers estimate the cost of maintaining and repairing the road bridge over its expected life is the age of the road bridge. For example, older road bridges nearing the end of their expected life may require more expensive repair and replacement than newer road bridges. Fourth, legal and insurance issues are also influenced by the construction year. For example, the age of the road bridge can be used to determine who would be liable in the event of an accident and whether the road bridge was built in accordance with the safety regulations in effect at the time it was built. To effectively determine the risk associated with insuring the road bridge, insurance companies often require comprehensive information, which includes the age of the road bridge. Finally, the construction year is also important for cultural and historical reasons. The construction year can reveal important details about the people and society that built the road bridge. This is important because road bridges often have historical and cultural significance. Knowing the construction year of a road bridge can help preserve it as a historic landmark and identify past engineering achievements.

There are few known methods for estimating the construction year of road bridges, although some approaches include the following: (a) Historical document analysis is a widely used technique. This technique involves searching for contracts, construction documents, maintenance and repair records, old maps, photographs, and written records of the road bridge or road network adjacent to the road bridge. However, the feasibility of this approach depends on the availability of reliable historical records. (b) Another possibility is to ask local settlers or local bridge engineers when the road bridges were built. Unfortunately, the information obtained in this way may prove to be approximate, so it cannot be fully relied upon [4]. (c) Another method is to check the construction year on the bridge nameplate. However, this method may not provide accurate information if the construction of the road bridge was delayed or completed earlier than planned [4]. (d) Some clues to the construction year of the road bridge can be obtained by analyzing the materials and construction methods used in its construction. The era in which the road bridge was built can be inferred from the use of certain construction materials and techniques. For example, a bridge made of stone was probably built earlier than a bridge made of iron. The same is true if a bridge was built using the most modern construction methods, such as prestressed concrete, since it was most likely built after these methods were developed. However, this approach cannot provide an exact construction year of the road bridge, but only the period in which the construction methods or materials were used. (e) Analysis of the layout and architectural design of the road bridge is another alternative method. An important source of information about the period in which the road bridge was built is the design and architectural style of the structure. For example, a gothic-style bridge was probably built in the middle ages, while a modernist-style bridge was likely built in the 20th century. Again, this approach cannot provide the exact construction year of the road bridge, but only the period in which the architectural design was used. (f) Visual inspection of Landsat satellite imagery on an annual basis [4] can also be used as a technique to estimate the construction year. This method can be used provided that the road bridges have an overall length > 100 m, the surface of the road bridge is not obscured by natural or human-made cover, the region in which the road bridge is located is covered by Landsat or any related satellites, and the satellite imagery in the region is not severely attenuated by atmospheric absorption and scattering effects. (g) In the previous study [4], a method for estimating the construction year of road bridges was developed using the normalized difference water index (NDWI), a function of visible green and near-infrared (NIR), and an NDWI = (green − NIR)/(green + NIR). The previous method states that the NDWI remains the same at both the target bridge point (TBP) and two reference control points before the road bridge is built. After the road bridge is built, only the NDWI at the TBP changes, while the NDWI at the two reference control points remains the same as before. The year in which the NDWI for the TBP changes is the estimated construction year of the road bridge. The results of this method after comparing the actual construction year with the estimated construction year showed an $R^2$ = 0.31 for the road bridges with an overall length > 100 m, an $R^2$ = 0.40 for bridges with an overall length ≤ 100 m but < 20 m, and an $R^2$ = 0.41 for bridges with an overall length ≤ 20 m. The trends for the final results were not very clear, perhaps because both cloud masking and cloud cover control were not performed to reduce noise in the data. The data points were not averaged annually to reduce seasonal variation, and, finally, no method was used to interpret the estimated construction year from the NDWI plots.

Previous studies have used remote sensing techniques with an interferometric synthetic aperture radar (InSAR) and high-resolution satellites to extract features and monitor structural deformations of bridge infrastructures on the Earth’s surface. With increasing traffic loads on bridges, challenging environmental conditions such as flooding, wind loads, and other factors, and limited capital investment for bridge maintenance, repair, and rehabilitation, InSAR techniques can complement visual inspections as a source of timely information regarding early signs of bridge infrastructure damage. InSAR techniques can monitor infrastructure both day and night, penetrate cloud cover, produce accurate and high-resolution imagery, provide high-density measurements, have a relatively short satellite repetition time, and be a cost-effective and near real-time method. However, processing the collected InSAR data is time consuming and requires expertise [5,6,7,8,9,10].

In this study, two new techniques are proposed for estimating the construction year of road bridges by analyzing the normalized difference water index 2 (NDWI_2). Technique 1 uses both the target bridge point (TBP) and a selected optimal reference control point, while Technique 2 uses only the TBP. An optimal reference control point was selected from the 18 reference control points. The two techniques, in the current method, are an improvement of the previous method [4]. Technique 1 states that the NDWI_2 remains the same at both the TBP and a selected optimal reference control point before the road bridge is built. After the road bridge is built, only the NDWI_2 at the TBP changes, while the NDWI_2 at a selected optimal reference control point remains the same. Technique 2 states that the NDWI_2 differs only at the TBP before and after the road bridge is built. The year in which the NDWI_2 changes for both techniques is the estimated construction year of the road bridge. The objectives of the study are the following: (1) to analyze the 12 indices at the target bridge point using Technique 2, (2) to compare the results between Technique 1 and Technique 2, and (3) to compare the method design and results between the previous method and the current method. The current method consists of both Technique 1 and Technique 2.

The construction year plays a crucial role in the management of bridges. By incorporating the construction year of road bridges into bridge management systems, bridge managers can make more informed decisions about how best to maintain and improve road bridges to ensure user safety and bridge preservation for the future.

The remainder of this article is organized as follows. The next section presents the materials and methods. Section 3 describes the results, with the discussion covered in Section 4. Finally, the conclusions are given in Section 5.

2. Materials and Methods

2.1. Study Area

The study area is Nago City, which is located in the northern part of Okinawa Prefecture, Japan, as shown in Figure 1. The city was selected because of its diverse landscapes, forested areas, built-up areas, coastal and built-up areas, and cropland areas. This diverse environment makes the area a suitable place to test the two techniques proposed in this study. Nago City has a subtropical oceanic climate with hot and humid summers, mild winters, and temperatures that rarely reach 35 degrees celcius or more [11]. In addition to Nago City, there are 8 other major cities and 3 villages shown on the map in Figure 1. The City of Nago has a population of 63,554, or 4.3% of the total population of Okinawa Prefecture, and a surface area of 211 km${}^2$, or 9.2% of the total surface area of Okinawa Prefecture, and 330 road bridges [12,13], as shown in Figure 2a and Figure 2b, respectively.

The 330 road bridges in Nago City were filtered out of a total of about 700,000 road bridges in Japan. The 44 road bridges were filtered out of 330 road bridges based on construction year between 1990 and 2006 and each bridge’s overall length ≤ 100 m. The 44 road bridges were classified by surface cover type, which resulted in 21 road bridges in built-up areas, 16 in forested areas, and 7 in cropland areas, as shown in Figure 2f. Bridges were also classified by each bridge’s overall length, which resulted in 23 medium road bridges and 21 short bridges, as shown in Figure 2d and Figure 2e, respectively.

2.2. Landsat Mission

The Landsat mission is the longest-running space-based record of the Earth’s surface and atmosphere [14]. The mission is managed by both the National Aeronautics and Space Administration (NASA) and the United States Geological Survey (USGS). The goal of the mission is to monitor, manage, and understand the Earth’s resources that are necessary for sustaining human life and other living organisms. The mission consists of 8 successful operational Earth observation satellites that use remote sensors to collect data and images of our planet, as well as 1 failed satellite mission, as shown in Figure 3.

In the current study, the Landsat 5 Thematic Mapper was used to analyze data in Google Earth Engine.

2.3. Spectral Bands and Indices

Spectral bands in remote sensing are parts of the electromagnetic spectrum from visible radiation to optical and infrared radiation to microwave radiation that are used by various sensors to collect information from the Earth [15]. In the Landsat 5 Thematic Mapper (TM), there are 3 visible bands, 3 infrared bands, and 1 thermal infrared band, as shown in

Table 1. Band characteristics for Landsat 5 Thematic Mapper.

Band Type	Landsat 5 TM
	Wavelength (µm)
Band 1—Visible blue	0.45–0.52
Band 2—Visible green	0.52–0.60
Band 3—Visible red	0.63–0.69
Band 4—NIR	0.76–0.90
Band 5—SWIR1	1.55–1.75
Band 6—Thermal Infrared	10.40–12.50
Band 7—SWIR2	2.08–2.35

Note: TM—Thematic Mapper; NIR—near-infrared; SWIR1—shortwave infrared 1; and SWIR2—shortwave infrared 2. Spatial resolution is 30 m for bands 1 through 5 and 7, and 120 m for band 6.

.

A spectral index in remote sensing is a function of two or more spectral bands of an image per pixel, as shown in Table 2. Indices are used to enhance the observation of Earth’s features such as vegetation, water, and soil, to distinguish one feature from other features in an image and to model, predict, or infer surface processes [16]. For example, the normalized difference vegetation index (NDVI) is a function of the near-infrared (NIR) band and the visible red band, expressed mathematically as NDVI = (NIR − red)/(NIR + red), and is used as an indicator of healthy vegetation [17,18]. Additionally, normalized difference water index 2 (NDWI_2) is a function of NIR and shortwave infrared 2 (SWIR2), mathematically expressed as NDWI_2 = (NIR − SWIR2)/(NIR + SWIR2), and is used as an indicator of seasonal water dynamics in wetlands [19]. Various indices have been explored in the past, some of which are listed in Table 2, and have been used in various fields such as agriculture, water resource management, and others.

In the current study, bands 1 to 5 and band 7 in Landsat 5 TM were used to analyze data in Google Earth Engine.

2.4. Data Collection and Analysis

The United States Geological Survey (USGS) produces Landsat data in three tiers for each satellite: Tier 1, Tier 2, and Real-Time (RT) [20]. Tier 1 data meet geometric and radiometric quality requirements; Tier 2 data do not meet Tier 1 quality standards; and RT data have not yet been assessed. Based on quality and other factors, the collected data are classified into Collection 1—Level 1, Collection 1—Level 2, Collection 2—Level 1, and Collection 2—Level 2 [20,21]. The data are then processed into raw or digital numbers (DNs), top of atmosphere (ToA), and surface reflectance (SR). DN represent scaled and calibrated sensor radiance, ToA represents calibrated reflectance, and SR represents atmospheric-corrected reflectance.

In the current study, 836 image pixels were collected and analyzed using Google Earth Engine. The current study consists of both Technique 1 and Technique 2, as shown in Figure 4b, and the characteristics of the current method are shown in

Table 3. Differences between the previous method and the current method.

Characteristics	Previous Work	Current Work
		Technique 1	Technique 2
Perpendicular distance (m) from TBP	35	60	−
Number of reference control points	2	18	−
Cloud masking of data was conducted	No	Yes	Yes
The data used was annually averaged	No	Yes	Yes
It was possible to control the cloud cover from 0% to 100%	No	Yes	Yes
The p-values and variances for the reference control points were determined	No	Yes	No
Only the TBP was used to determine the estimated construction year	No	No	Yes
Both the TBP and a selected optimal reference point were used to determine the estimated construction year	No	Yes	No
Both the TBP and the two reference control points were used to determine the estimated construction year	Yes	No	No
The type of Landsat 5 Thematic Mapper data used was stated	No	Yes	Yes
The STARS method was used to interpret the estimated construction year from NDWI$\_2$	No	Yes	Yes

Note: The current method consists of both Technique 1 and Technique 2. Technique 1 uses both the target bridge point (TBP) and a selected optimal reference control point, while Technique 2 uses only the TBP, to determine the estimated construction year of the road bridge. An optimal reference control point is selected from the 18 reference control points. The previous method uses both the TBP and two reference control points to determine the estimated construction year. STARS is the sequential t-test analysis of regime shift method. NDWI$\_2$ is the normalized difference water index 2. Landsat data type is divided into raw digital numbers, top of atmosphere, bottom of atmosphere, or surface reflectance. Surface reflectance is further divided into Collection 1—Level 1, Collection 2—Level 1, and Collection 2—Level 2. Of the three, Collection 2—Level 2 has high accuracy.

. The data type used was Landsat 5 Thematic Mapper, SR—Level 2—Collection 2—Tier 1. The 836 image pixels were calculated as follows: 19 pixels per bridge × 44 road bridges × 1 Landsat satellite × 1 index = 836 image pixels. The 44 road bridges are shown in

Table 4. Characteristics and STARS results for all 44 road bridges.

					Technique 2			Technique 1
					(TBP Only)			(TBP and Sel. RP)
Bridge Name	Overall Length (m)	Width (m)	Surface Cover Type	Actual Constr. Year	Value of l	Peak RSI	Est. Constr. Year	Value of l	Peak RSI	Est. Constr. Year
Maeda	98.3	11.6	Forest	2006	6	1.83	2005	3	2.81	2006
Kuroyama	98.0	8.3	Forest	1997	5	2.00	1996	5	0.86	1996
Nagasaka	96.0	11.0	Forest	2000	9	0.91	1999	6	0.24	2000
Higashi Ebara	82.0	11.0	Forest	2003	6	1.75	2000	14	0.75	2000
Osuji	64.0	12.0	Forest	1992	5	1.22	1989	−	−	−
Mijimai	56.7	7.0	Forest	1994	3	1.82	1995	3	1.84	1995
Higashiri	51.0	11.2	Forest	1997	4	1.76	1995	3	0.78	1995
Daikan	43.0	13.3	Forest	1992	5	1.51	1989	3	0.24	1990
Nagamata	42.0	11.5	Forest	1998	3	2.22	1996	5	1.06	1997
Kamifukuchi	37.0	11.5	Forest	1992	3	1.17	1992	8	0.83	1992
Makiya No.3	24.2	16.8	Forest	1991	4	1.49	1990	3	0.14	1990
Kamiyama	23.0	11.0	Forest	1993	3	1.78	1992	6	1.41	1992
Fukushi	21.8	5.0	Forest	1992	3	1.44	1991	3	1.06	1991
Second Geya	9.5	4.0	Forest	1996	7	0.51	1991	−	−	−
Kamiyamatogawa	11.0	14.8	Forest	1992	−	−	−	−	−	−
Shitayamatogawa	11.0	14.8	Forest	1992	−	−	−	−	−	−
Blacksmith	33.9	6.5	Cropland	1992	4	1.79	1992	23	0.28	2007
Gabusoka	32.4	12.8	Cropland	1996	9	1.19	1993	25	1.19	2009
Haishi	27.9	12.5	Cropland	2002	7	0.93	1999	−	−	−
Inada	30.6	5.5	Cropland	2003	5	1.54	1999	20	0.56	2009
Fukumi	70.0	11.0	Cropland	1992	23	1.20	2008	18	1.58	2008
Hane 105-2	31.0	6.0	Cropland	1993	7	0.49	1992	−	−	−
Kayang Mata	22.3	5.0	Cropland	2001	24	0.74	2008	4	0.36	2000
Oura	77.0	15.8	Built-Up	1996	12	0.15	1997	−	−	−
Higashi Yabu	56.6	17.1	Built-Up	2000	7	1.37	1997	8	1.11	2000
Furushima	47.0	16.0	Built-Up	1999	8	1.30	1997	3	1.30	1999
Nazaki	44.6	8.0	Built-Up	1994	5	1.41	1994	−	−	−
Nakaoji	33.3	16.2	Built-Up	1993	3	0.90	1991	−	−	−
Yonagawa	31.5	22.5	Built-Up	1992	4	2.03	1991	3	1.41	1991
Makiya No 2	28.3	18.8	Built-Up	1991	4	0.85	1990	3	0.35	1990
Kado River	25.0	22.5	Built-Up	1993	3	2.01	1992	3	1.22	1992
Tamemata	23.5	15.3	Built-Up	1990	6	1.94	1991	6	1.40	1991
Anwa Minamizaki	21.5	22.5	Built-Up	1991	3	1.08	1991	3	0.68	1991
Ose	44.0	5.0	Built-Up	1993	8	0.80	1992	3	0.29	1990
Name 162-1	18.2	4.0	Built-Up	1994	4	1.04	1996	3	0.71	1987
Sugita	25.0	15.6	Built-Up	1999	3	1.43	1987	10	1.20	1997
Hanejioo	24.6	7.5	Built-Up	1990	10	1.23	1996	10	0.81	1995
Maehira	23.1	6.6	Built-Up	1992	16	0.42	2000	9	0.57	1994
Yabu	46.5	14.3	Built-Up	1991	5	0.65	1990	23	1.13	2008
Anada	15.9	22.0	Built-Up	1992	6	0.42	1995	3	1.06	1996
Apanuku	11.8	4.0	Built-Up	1996	11	0.78	1995	−	−	−
Lower River	16.0	7.0	Built-Up	1993	−	−	−	−	−	−
Makiya No. 1	11.8	20.1	Built-Up	1991	−	−	−	−	−	−
Minato	11.5	15.7	Built-Up	2000	−	−	−	−	−	−

Note: For both techniques, the significance level $\alpha$ = 0.05, Huber’s weight parameter H = 1, and cutoff length l = 2 to l = 27 were used. Est. stands for estimated, and constr. for construction. TBP is the target bridge point, and sel. RP is a selected optimal reference control point. Technique 1 uses both the target bridge point (TBP) and a selected optimal reference control point, while Technique 2 uses only the TBP, to determine the estimated construction year of the road bridge. STARS method is a sequential t-test analysis of the regime shift method. A dash (−) simply means that the STARS method did not produce any result.

and Figure 5. The applied 12 indices are shown in Figure 6 and Figure A5, for Kuroyama road bridge, and Kamiyama road bridge, respectively. The pixel satellite images for Kuroyama road bridge and Kamiyama road bridge are shown in Figure 7b and Figure A1b, respectively.

Table 2. Indices attempted in the study.

Notation	Index Name	Formula	Application
NDVI	Normalized difference vegetation index	$\frac{\mathrm{NIR}-\mathrm{Red}}{\mathrm{NIR}+\mathrm{Red}}$	The study in [17] is one of the earliest papers on the use of the NDVI. The study used NDVI using Landsat 1 data to monitor and measure vegetation conditions over wide regions. Other applications include estimating crop yields, dry biomass, and changes in surface conditions [18].
GNDVI	Green normalized difference vegetation index	$\frac{\mathrm{NIR}-\mathrm{Green}}{\mathrm{NIR}+\mathrm{Green}}$	According to the study in [22], the difference between the NDVI and GNDVI is that the latter is more chlorophyll sensitive. If you arrange the bands in GNDVI so that the index is (green − NIR)/(green + NIR), you obtain a different index; the normalized difference water index (NDWI) is an indicator of water resources [23].
BNDVI	Blue normalized difference vegetation index	$\frac{\mathrm{NIR}-\mathrm{Blue}}{\mathrm{NIR}+\mathrm{Blue}}$	BNDVI performs the same task as the NDVI and GNDVI. The only drawback is that the blue band is easily affected by the atmosphere due to its relatively short wavelength and the resulting high relative scattering effects [24].
NDMI_1	Normalized difference water index 1	$\frac{\mathrm{NIR}-\mathrm{SWIR}1}{\mathrm{NIR}+\mathrm{SWIR}1}$	NDWI_1 easily maps liquid water in vegetation and is less affected by scattering effects than the NDVI [25].
NDWI_2	Normalized difference water index 2	$\frac{\mathrm{NIR}-\mathrm{SWIR}2}{\mathrm{NIR}+\mathrm{SWIR}2}$	The index is a good indicator of the water dynamics of seasonal wetlands [19].
NDWI_3	Normalized difference water index 3	$\frac{\mathrm{Green}-\mathrm{SWIR}2}{\mathrm{Green}+\mathrm{SWIR}2}$	The index is an indicator of open water bodies [26] but is no better than the NDWI_4 [27].
NDWI_4	Normalized difference water index 4	$\frac{\mathrm{Green}-\mathrm{SWIR}1}{\mathrm{Green}+\mathrm{SWIR}1}$	The index in [27] is a good indicator of open water features, and it suppresses vegetation, soil, and the built environment noise; it is better than the NDWI in [23]. The index also serves as an indicator of snow cover [28], which is also called the normalized difference snow index.
NBR2	Normalized burn ratio 2	$\frac{\mathrm{SWIR}1-\mathrm{SWIR}2}{\mathrm{SWIR}1+\mathrm{SWIR}2}$	The index is an indicator of burned areas and also measures the severity of burned areas [29].
NDSI	Normalized difference soil index	$\frac{\mathrm{SWIR}2-\mathrm{Green}}{\mathrm{SWIR}2+\mathrm{Green}}$	The index enhances the soil information [30].
DBSI	Dry bare-soil index	$\frac{\mathrm{SWIR}1-\mathrm{Green}}{\mathrm{SWIR}1+\mathrm{Green}}-\mathrm{NDVI}$	The index maps built-up and bare areas in a dry climate [31].
NDBI	Normalized difference built-up index	$\frac{\mathrm{SWIR}1-\mathrm{NIR}}{\mathrm{SWIR}1+\mathrm{NIR}}$	The index maps urban built-up areas and, in some cases, barren, wooded, and agricultural areas [32].
BI	Built-up index	$\frac{\mathrm{SWIR}1-\mathrm{NIR}}{\mathrm{SWIR}1+\mathrm{NIR}}-\mathrm{NDVI}$	The index maps only the built-up and barren areas [33].

Note: Using Landsat 5 Thematic Mapper in Google Earth Engine, the 12 indices, which include normalized difference water index 2 (NDWI_2), were analyzed at two road bridges (Kuroyama and Kamiyama). The results for all 12 indices were accurate with a cutoff length $l\le$ 9, an absolute error ≤ 5, and statistically significant with p-values < 0.05, and the trends for all 12 indices were clear. In this study, the NDWI_2 was adopted and used to analyze all 44 road bridges. In the future, the other indices can be analyzed and compared along with the NDWI_2 to determine the most accurate index using Technique 2.

Table 2. Indices attempted in the study.

Notation	Index Name	Formula	Application
NDVI	Normalized difference vegetation index	$\frac{\mathrm{NIR}-\mathrm{Red}}{\mathrm{NIR}+\mathrm{Red}}$	The study in [17] is one of the earliest papers on the use of the NDVI. The study used NDVI using Landsat 1 data to monitor and measure vegetation conditions over wide regions. Other applications include estimating crop yields, dry biomass, and changes in surface conditions [18].
GNDVI	Green normalized difference vegetation index	$\frac{\mathrm{NIR}-\mathrm{Green}}{\mathrm{NIR}+\mathrm{Green}}$	According to the study in [22], the difference between the NDVI and GNDVI is that the latter is more chlorophyll sensitive. If you arrange the bands in GNDVI so that the index is (green − NIR)/(green + NIR), you obtain a different index; the normalized difference water index (NDWI) is an indicator of water resources [23].
BNDVI	Blue normalized difference vegetation index	$\frac{\mathrm{NIR}-\mathrm{Blue}}{\mathrm{NIR}+\mathrm{Blue}}$	BNDVI performs the same task as the NDVI and GNDVI. The only drawback is that the blue band is easily affected by the atmosphere due to its relatively short wavelength and the resulting high relative scattering effects [24].
NDMI_1	Normalized difference water index 1	$\frac{\mathrm{NIR}-\mathrm{SWIR}1}{\mathrm{NIR}+\mathrm{SWIR}1}$	NDWI_1 easily maps liquid water in vegetation and is less affected by scattering effects than the NDVI [25].
NDWI_2	Normalized difference water index 2	$\frac{\mathrm{NIR}-\mathrm{SWIR}2}{\mathrm{NIR}+\mathrm{SWIR}2}$	The index is a good indicator of the water dynamics of seasonal wetlands [19].
NDWI_3	Normalized difference water index 3	$\frac{\mathrm{Green}-\mathrm{SWIR}2}{\mathrm{Green}+\mathrm{SWIR}2}$	The index is an indicator of open water bodies [26] but is no better than the NDWI_4 [27].
NDWI_4	Normalized difference water index 4	$\frac{\mathrm{Green}-\mathrm{SWIR}1}{\mathrm{Green}+\mathrm{SWIR}1}$	The index in [27] is a good indicator of open water features, and it suppresses vegetation, soil, and the built environment noise; it is better than the NDWI in [23]. The index also serves as an indicator of snow cover [28], which is also called the normalized difference snow index.
NBR2	Normalized burn ratio 2	$\frac{\mathrm{SWIR}1-\mathrm{SWIR}2}{\mathrm{SWIR}1+\mathrm{SWIR}2}$	The index is an indicator of burned areas and also measures the severity of burned areas [29].
NDSI	Normalized difference soil index	$\frac{\mathrm{SWIR}2-\mathrm{Green}}{\mathrm{SWIR}2+\mathrm{Green}}$	The index enhances the soil information [30].
DBSI	Dry bare-soil index	$\frac{\mathrm{SWIR}1-\mathrm{Green}}{\mathrm{SWIR}1+\mathrm{Green}}-\mathrm{NDVI}$	The index maps built-up and bare areas in a dry climate [31].
NDBI	Normalized difference built-up index	$\frac{\mathrm{SWIR}1-\mathrm{NIR}}{\mathrm{SWIR}1+\mathrm{NIR}}$	The index maps urban built-up areas and, in some cases, barren, wooded, and agricultural areas [32].
BI	Built-up index	$\frac{\mathrm{SWIR}1-\mathrm{NIR}}{\mathrm{SWIR}1+\mathrm{NIR}}-\mathrm{NDVI}$	The index maps only the built-up and barren areas [33].

Note: Using Landsat 5 Thematic Mapper in Google Earth Engine, the 12 indices, which include normalized difference water index 2 (NDWI_2), were analyzed at two road bridges (Kuroyama and Kamiyama). The results for all 12 indices were accurate with a cutoff length $l\le$ 9, an absolute error ≤ 5, and statistically significant with p-values < 0.05, and the trends for all 12 indices were clear. In this study, the NDWI_2 was adopted and used to analyze all 44 road bridges. In the future, the other indices can be analyzed and compared along with the NDWI_2 to determine the most accurate index using Technique 2.

2.5. Cloud Masking and Cloud Shadow Masking

Cloud masking and cloud shadow masking are filtering techniques used in remote sensing to remove pixels contaminated with clouds and cloud shadows. Cloud masking technique uses the difference between the reflectance of the clear images and the reflectance of the cloud contaminated images to detect the clouds. The cloud shadow masking technique uses the difference between the reflectance of the clear images and the reflectance of the cloud shadow contaminated images to detect the cloud shadows. Both cloud masking and cloud shadow masking reduce the errors caused by erroneous mapping, improve the visibility, and, thus, increase the reflectivity of the Earth’s surface and objects on the Earth’s surface [34,35].

In the current study, the collected Landsat 5 Thematic Mapper (TM) data were cloud masked in Google Earth Engine using a Google Earth Engine open source code, and a cloud cover of 30% was used. Plots of Kuroyama road bridge and Kamiyama road bridge, before and after cloud masking at 100% cloud cover, are shown in Figure 7c and Figure 7d, as well as Figure A1c and Figure A1d, respectively. Due to noise in the data, the trends were not clear. Landsat satellites collect data every 16 days, so the Landsat 5 TM should have about 600 data points per bridge from 1984 to 2010. Before cloud masking at 100% cloud cover, about 52% of the data points were collected, and after cloud masking at 100% cloud cover, about 21% of the data points were collected. The 100% cloud cover was reduced to 30% cloud cover, and about 14% of the data points were collected. At 30% cloud cover and after the data points were averaged annually, the trends were clear, as shown in Figure 8a and Figure A2a for Kuroyama road bridge and Kamiyama road bridge, respectively. Both cloud masking and cloud cover control reduce noise in the data, and annual averaging of the data reduces seasonal variations.

2.6. Sequential t-Test Analysis of Regime Shift (STARS) Method

Sequential t-test analysis of regime shift (STARS) is a statistical method for detecting change points in time series data [36,37,38,39]. The method identifies the point in time when the mean of the time series data changes significantly. The change in the mean can be either a single change or multiple changes within a time series. The STARS method is based on the statistical technique of the Student’s t-test, and [38,39] describes the algorithm. The algorithm was coded in Visual Basic for use in a Microsoft Excel add-in and is available for download as freeware at www.BeringClimate.noaa.gov. The STARS method can be set to detect regimes with specific time scales and magnitudes. The inputs to the STARS Microsoft Excel add-in were the cutoff length l, the significance level $\alpha$, and the Huber weight parameter H. The cutoff length l and the significance level $\alpha$ are the main inputs that affect the magnitude of the regime shifts [40].

The STARS method uses Equations (1)–(6) to analyze and determine the regime shift of the mean in the time series data.

$$\mathit{diff}=\left|{\overline{x}}_{new}-{\overline{x}}_{cur}\right|=t\sqrt{\frac{2{\sigma }_l^2}{l}}$$

(1)

$$\mathit{dof}=2l-2$$

(2)

$$t=t(\alpha ,\mathit{dof}),$$

(3)

where $\mathit{diff}$ is the absolute difference between the mean of the current and new regime, ${\overline{x}}_{cur}$ is the mean of the current regime, ${\overline{x}}_{new}$ is the mean of the new regime, l is the cutoff length, $\mathit{dof}$ is the degree of freedom, $\alpha$ is the significance level, and t is the value of the t-distribution, which is a function of $\mathit{dof}$ and $\alpha$. It is assumed that the variance ${\sigma }_l^2$ at any given value of l is the same and equal to the average variance for the running l year intervals in the time series $x_i$. Therefore, $\mathit{diff}=constant$ for the entire session of the time series $x_i$ at each given value of l. At the current time $t_{cur}$, the mean value of the new regime ${\overline{x}}_{new}$ is unknown, but it is known that it should be equal or greater than the critical level ${\overline{x}}_{crit}^{\uparrow }$ if the shift is upward or equal or less than ${\overline{x}}_{crit}^{\downarrow }$ if the shift is downward, where

$${\overline{x}}_{crit}^{\uparrow }={\overline{x}}_{cur}+\mathit{diff}$$

(4)

$${\overline{x}}_{crit}^{\downarrow }={\overline{x}}_{cur}-\mathit{diff}.$$

(5)

If the current value $x_{cur}$ is greater than ${\overline{x}}_{crit}^{\uparrow }$ or less than ${\overline{x}}_{crit}^{\downarrow }$, the current time $t_{cur}$ is marked as a potential change point c, and subsequent data are used to reject or accept this hypothesis. The null hypothesis $H_0$ states that “there is an existence of a regime shift”. The test has three possible outcomes: accept $H_0$, reject $H_0$, or keep testing. The testing process consists of calculating the so-called regime shift index $\mathit{RSI}$ that represents a cumulative sum of the normalized anomalies relative to the critical level ${\overline{x}}_{crit}$:

$$\mathit{RSI}=\frac{1}{l{\sigma }_l^2}\sum _{i=t_{cur}}^m\left(x_i-{\overline{x}}_{crit}\right),m=t_{cur}+1,\dots ,t_{cur}+l-1.$$

(6)

If at any time during the testing period from $t_{cur}$ to $t_{cur}+l-1$, the index turns negative in the case of ${\overline{x}}_{crit}={\overline{x}}_{crit}^{\uparrow }$ or positive in the case of ${\overline{x}}_{crit}={\overline{x}}_{crit}^{\downarrow }$, the null hypothesis $H_0$ about the existence of a regime shift at the current time $t_{cur}$ is rejected, and the value $x_{cur}$ is included in the current regime ${\overline{x}}_{cur}$. Otherwise, the time $t_{cur}$ is declared a change point c.

In the current study, the STARS method was used to interpret the estimated construction year from NDWI$\_2$ for both techniques. The inputs, cutoff length l = 2 to l = 27, significance level $\alpha$ = 0.05, and Huber’s weight parameter H = 1 were used. The numbers 2 to 27 were used for l, because the total number of data points in the time series data was 27. The number 1 could not be used, because it had no value of t in the t-distribution because the $\mathit{dof}=2l-2=0$. From the cutoff length l = 2 to l = 27, the optimal absolute maximum regime shift index $\mathit{RSI}$ was determined and thus used to identify the estimated construction year. There are three possible outcomes of the STARS method test: fail to reject the null hypothesis $H_0$, reject the null hypothesis $H_0$, or keep testing. The null hypothesis $H_0$ is a regime shift in the time series data.

2.7. Flowchart and Description of the Current Method

The flowchart for the current method is shown in Figure 4b. The current method consists of both Technique 1 and Technique 2. Technique 1 uses both the TBP and a selected optimal reference control point, while Technique 2 only uses the TBP to determine the estimated construction year of the road bridge. Japan has about 700,000 road bridges. From about 700,000 road bridges, 330 road bridges in Nago City were filtered out. Nago City is located in the northern part of Okinawa Prefecture. From 330 road bridges, 44 road bridges were filtered out based on each bridge’s overall length between 0 m and 100 m and construction year between 1990 and 2006, as shown in Table 4.

In Step 1 and Step 2, we used Google Earth Engine (GEE) and global positioning system (GPS) coordinates, from the Japan bridge database [13] to locate the midspan of the bridge’s overall length for all 44 road bridges, which we called the target bridge point (TBP). After we located the TBP in Google Earth Engine (GEE), the new GPS coordinates at the midspan were collected and entered in GEE. A perpendicular line to the bridge’s overall length was drawn 60 m from the TBP, and 18 reference control points were established, with 9 points on each side of the TBP. Each reference control point and TBP occupied an independent and unique image pixel with a spatial resolution of 30 m, as shown in Figure 7a and Figure 7b, as well as Figure A1a and Figure A1b, for Kuroyama road bridge and Kamiyama road bridge, respectively. The 60 m distance was chosen, because it had less interference from the TBP image pixel. The GPS coordinates for the 18 reference control points were collected and entered into GEE. GEE is a cloud computing program for geospatial data analysis and visualization [41].

In Step 3, we analyzed the cloud unmasked data at 100% cloud cover in GEE at the TBP and 18 reference control points, as shown in Figure 7c and Figure A1c for Kuroyama road bridge and Kamiyama road bridge, respectively. Landsat 5 Thematic Mapper (TM) was used for the analysis. Cloud unmasked data are data points whose pixels are contaminated with clouds and cloud shadows and, therefore, obscure the visibility of the surface cover due to the noise in the data.

In Step 4, we used GEE to cloud mask the data at 100% cloud cover at the TBP and 18 reference control points, as shown in Figure 7d and Figure A1d for Kuroyama road bridge and Kamiyama road bridge, respectively. Landsat 5 Thematic Mapper (TM) was used for the analysis. The cloud cover was reduced from 100% to 30%, and the data were averaged annually, as shown in Figure 8a and Figure A2a for Kuroyama road bridge and Kamiyama road bridge, respectively. Both cloud masking and cloud cover control reduce noise in the data, and annual averaging of the data reduces seasonal variations.

In Step 5, we calculated the p-values and variances at the TBP and 18 reference control points. This step was performed to check the normality and variation of the data points at the TBP and the reference control points. Homogeneity of the data is assumed when the variance is minimal and the p-value > 0.05.

In Step 6 and Step 7, we selected an optimal reference control point from the 18 reference control points. The reference control point with the lowest minimum variance and p-value > 0.05 was considered an optimal reference control point. If two or more reference points had the same variance values and p-value > 0.05, the reference control point farthest from the TBP was selected as the optimal point, because it was considered to be least affected by the interference from the TBP. The TBP and a selected optimal reference control point were plotted together, as shown in Figure 8a and Figure A2a for Kuroyama road bridge and Kamiyama road bridge, respectively.

In Step 8a, Technique 1, which uses both the TBP and a selected optimal reference control point, was used to determine the estimated construction year. The sequential t-test analysis of regime shift (STARS) method [40] was used to interpret the estimated construction year from NDWI$\_2$ for the squared difference between TBP and a selected optimal reference control point, as shown in Figure 8b and Figure 8d, as well as Figure A2b and Figure A2d, for Kuroyama road bridge and Kamiyama road bridge, respectively.

In Step 8b, Technique 2, which uses only the TBP, was used to determine the estimated construction year. The STARS method [40] was used to interpret the estimated construction year from NDWI$\_2$ for the TBP only, as shown in Figure 8c and Figure 8e, as well as Figure A2c and Figure A2e, for Kuroyama road bridge and Kamiyama road bridge, respectively.

2.8. Comparison of Methods between the Previous Method and the Current Method

The current method is an improvement of the previous method [4]. The current method consists of both Technique 1 and Technique 2. Technique 1 uses both the target bridge point (TBP) and a selected optimal reference control point, while Technique 2 uses only the TBP, to determine the estimated construction year of the road bridge. The previous method uses both the TBP and two reference control points to determine the estimated construction year. The flowchart for the previous method is shown in Figure 4a, and that for the current method is shown in Figure 4b. The summary of the differences between the previous method and the current method are presented in Table 3.

Step 1 of the previous method in Figure 4a describes how the location of the TBP was determined using data from the bridge information database, which was similar to Step 1 of the current method in Figure 4b. Step 2 of the previous method in Figure 4a describes how the TBP endpoints were determined in Google Earth Engine (GEE), and this Step was included in Step 2 of the current method, as shown in Figure 4b. Step 3 of the previous method in Figure 4a describes how the midspan of the TBP was determined, and this Step was also included in Step 2 of the current method, as shown in Figure 4b. Finally, Step 4 of the previous method describes how the two reference control points were established on either side of the TBP at 35 m from the TBP perpendicular to each bridge’s overall length. This step was included in Step 2 of the current method, as shown in Figure 4b, where 60 m from the TBP and perpendicular to each bridge’s overall length was used, because it had less interference from the TBP.

The current method in Figure 4b differs from the previous method in Figure 4a in that the current method (a) performs cloud masking of the data, (b) reduces cloud cover from 100% to 30%, (c) averages the data annually, (d) selects an optimal reference control point with the lowest minimum variance and p-value > 0.05, and (e) uses the sequential t-test analysis of the regime shift method to interpret the estimated construction year from the NDWI$\_2$. Both cloud masking and cloud cover control reduce noise in the data, and annual averaging of the data reduces seasonal variations. Homogeneity of the data is assumed when the variance is minimal and p-value is >0.05.

3. Results

A total of 836 image pixels were analyzed in the Google Earth Engine, which were calculated as follows: 19 pixels per bridge × 44 road bridges in Nago City × 1 Landsat satellite × 1 index = 836 image pixels. Each analyzed road bridge was unique and had its own characteristics and behaviors. The Landsat satellite collects data on the Earth’s surface every 16 days per image pixel. For the period from 1984 to 2010, the Landsat 5 Thematic Mapper is expected to collect about 600 data points per image pixel. The average total percentage of data points collected in the Nago City for each road bridge in Landsat 5 TM was about 52% for cloud unmasked data at 100% cloud cover, about 21% for cloud masked data at 100% cloud cover, and about 14% for cloud masked data at 30% cloud cover. Summaries of the results, p-values, and absolute mean differences for all 44 road bridges are presented in Table 4, Figure 5a and Figure 5b, respectively.

3.1. Sensitivity Analysis for Sequential t-Test Analysis of Regime Shift (STARS) Method

The sequential t-test analysis of the regime shift (STARS) method was used to interpret the estimated construction year from the NDWI_2 for both Technique 1 and Technique 2. Technique 1 uses both the target bridge point (TBP) and a selected optimal reference control point, while Technique 2 uses only the TBP. The STARS method has three inputs: the Huber’s weight parameter H, the significance level $\alpha$, and the cutoff length l. The values of the Huber’s weight parameter at H = 1, 3, and 6 were tested, and the results obtained were the same, or the differences were negligible. A similar trend was observed by [42]; therefore, H = 1 was assumed for all road bridges. The inputs cutoff length l = 2 to l = 27 and significance level $\alpha$ = 0.05 were used for all road bridges. The numbers 2 to 27 were used for l because the total number of data points in the time series was 27. The number 1 could not be used because it had no value of t in the t-distribution, since $\mathit{dof}=2l-2=0$. From the cutoff length l = 2 to l = 27, the optimal absolute maximum regime shift index $\mathit{RSI}$ was determined and, thus, used to identify the estimated construction year. A time series with a downward shift results in a negative $RSI$, and an upward shift results in a positive $RSI$. An example of the cutoff length l and optimal absolute maximum regime shift index $\mathit{RSI}$ results are shown in Figure 8b and Figure 8c, as well as Figure A2b and Figure A2c for the Kuroyama road bridge and Kamiyama road bridge, respectively.

3.2. Analysis and Results of 12 Indices at 2 Road Bridges

Technique 2 was used in the analysis of 12 indices. Technique 2 uses only the target bridge point (TBP) to determine the estimated construction year of the road bridge. This analysis was performed to gain an understanding of the trends of the 12 indices in Table 2.

Two road bridges, the Kuroyama road bridge and Kamiyama road bridge, were analyzed using the 12 indices at the TBP. The trends and results for the two road bridges are shown in Figure 6 and Figure A5 for the Kuroyama road bridge and Kamiyama road bridge, respectively. The absolute errors between the actual and estimated construction year were comparable and ranged from 0 to 5 years. The cutoff length was $l\le$ 9, and the p-value was < 0.05 for all 12 indices. However, no results were recorded for the normalized difference water index 3 (NDWI_3) and the normalized difference soil index (NDSI), as shown in Figure A5f,i for the Kamiyama road bridge.

In this study, the normalized difference water index 2 (NDWI_2) was used to analyze all 44 road bridges. In the future, the other indices can be analyzed and compared along with the NDWI_2 to determine the most accurate index.

3.3. Analysis and Results of Normalized Difference Water Index 2 at All 44 Road Bridges

Technique 1 and Technique 2 were used in the analysis of all 44 road bridges. Technique 1 uses both the target bridge point (TBP) and a selected optimal reference control point, while Technique 2 only uses the TBP, to determine the estimated construction year of the road bridge.

The 44 road bridges were analyzed using the normalized difference water index 2 (NDWI$\_2$). The summarized results in terms of the p-values and absolute mean differences for all 44 road bridges are shown in Table 4, Figure 5a and Figure 5b, respectively. The absolute errors between the actual and estimated construction year ranged from 0 to 17 years, the cutoff length $l\le$ 25, and the p-value ≤ 0.23.

For brevity, only the results for three road bridges are presented. The three road bridges are the Kuroyama, Kamiyama, and Shitayamatogawa. The trends and results for the Kuroyama road bridge, Kamiyama road bridge, and Shitayamatogawa road bridge are shown in Figure 7 and Figure 8, Figure A1 and Figure A2, and Figure A3 and Figure A4, respectively.

The Kuroyama road bridge is shown in both Figure 7 and Figure 8. The Google image and satellite image of the road bridge are shown in Figure 7a and Figure 7b, respectively. The trends in Figure 7c were not clear because of noise in the data that were not cloud-masked. After cloud masking, the trends in Figure 7d were clear, because the noise in the data was reduced. The trends were even clearer when cloud cover was reduced from 100% to 30%, and the data were averaged annually, as shown in Figure 8a. Both cloud masking and cloud cover control reduce noise in the data, and annual averaging of the data reduces seasonal variations. The results for Technique 1 are shown in Figure 8b,d, and the results for Technique 2 are shown in Figure 8c,e. Both Technique 1 and Technique 2 recorded an absolute error between the actual and estimated construction year of 1 year; the cutoff length $l=$ 5, and the p-value < 0.05, as shown in Figure 5a and Figure 8d,e.

Similar trends and results were observed for the Kamiyama road bridge. Figure A1, Figure A2, Figure A3 and Figure A4 show the results for the Shitayamatogawa road bridge. Using the STARS method, no regime shift was detected for the Shitayamatogawa road bridge for both Technique 1 and Technique 2, as shown in Figure A4b, and Figure A4c, respectively. The results for the rest of the road bridges for both techniques are shown in Table 4 and Figure 5a,b.

3.4. Comparison of Results between the Previous Method and the Current Method

The previous method used both the TBP and the two reference control points to determine the estimated construction year of the road bridge. The current method consists of both Technique 1 and Technique 2. Technique 1 uses both the target bridge point (TBP) and a selected optimal reference control point, while Technique 2 only uses the TBP, to determine the the estimated construction year of the road bridge.

In the previous method, the data were contaminated with noise, because there was no cloud masking or cloud cover control; therefore, the trends were not clear. Additionally, no technique was used to interpret the estimated constructed year from the NDWI$\_2$. Figure 9a shows the trends and results for the previous method compared to the trends and results for the current method in Figure 9b. The result for the current method in Figure 9b was clear and was further analyzed using the STARS method for both Technique 1 and Technique 2, as shown in Figure 8d and Figure 8e, respectively.

Table 5. Comparative advantages between the results of the previous method and current method.

Item	Previous Method	Current Method
		Technique 1	Technique 2
Analysis time
(Figure 4a—previous method [4], and Figure 4b—current method)	Long	Longest	Longer
Interpreting the estimated construction year from NDWI$\_2$
(Figure 9a —previous method [4], and Figure 8—current method)	Difficult	Easy	Easy
Trends
(Figure 9a—previous method [4], and Figure 9b—current method)	Not clear	Clear	Clear

presents a summary of the comparative advantages between the results of the previous method and the current method.

4. Discussion

We found that the mean differences for all 44 road bridges in Table 4 were statistically significant with p-values < 0.05, except for seven road bridges in Technique 1 and one road bridge in Technique 2, as shown in Figure 5a. The absolute mean differences for Technique 1 and Technique 2 are shown in Figure 5b. Technique 1 uses both the target bridge point (TBP) and a selected optimal reference control point, while Technique 2 uses only the TBP, to determine the estimated construction year of the road bridge.

Table 6 shows the summary of the results of the correlation analysis. The correlation analysis yielded an $R^2$ = 0.24 and an $R^2$ = 0.33, as well as an average deviation of S = 5.81 years and S = 4.08 years for Technique 1 and Technique 2, respectively, as shown in Figure 10a and Figure 10b, respectively. The results suggest that Technique 2 is more accurate and provides a better estimate than Technique 1, but the $R^2$ values were low. One of the possible explanations that may have contributed to low $R^2$ values, as indicated by the gap between the actual and estimated construction year in Figure 10, is that the planned construction year recorded in the database may not have corresponded to the actual construction year due to construction delays [4].

Table 6. Summary of the coefficient of determination $R^2$ for all 44 road bridges in Table 4 according to overall length and surface cover.

	Coefficient of Determination ${\mathit{R}}^2$
	Technique 1	Technique 2
44 road bridges in Figure 10a, and Figure 10b, resp.	0.24	0.33
23 road bridges in forested and cropland areas Figure 11a, and Figure 11b, resp.	0.23	0.42
21 road bridges in the built-up areas Figure 11c, and Figure 11d, resp.	0.09	0.05
23 medium road bridges in Figure 12a, and Figure 12b, resp.	0.09	0.41
21 short road bridges Figure 12c, and Figure 12d, resp.	0.40	0.20
Mean value	0.21	0.28

Note: Resp. is respectively. Technique 1 uses both the target bridge point (TBP) and a selected optimal reference control point, while Technique 2 uses only the TBP, to determine the estimated construction year of the road bridge.

Table 6. Summary of the coefficient of determination $R^2$ for all 44 road bridges in Table 4 according to overall length and surface cover.

	Coefficient of Determination ${\mathit{R}}^2$
	Technique 1	Technique 2
44 road bridges in Figure 10a, and Figure 10b, resp.	0.24	0.33
23 road bridges in forested and cropland areas Figure 11a, and Figure 11b, resp.	0.23	0.42
21 road bridges in the built-up areas Figure 11c, and Figure 11d, resp.	0.09	0.05
23 medium road bridges in Figure 12a, and Figure 12b, resp.	0.09	0.41
21 short road bridges Figure 12c, and Figure 12d, resp.	0.40	0.20
Mean value	0.21	0.28

Note: Resp. is respectively. Technique 1 uses both the target bridge point (TBP) and a selected optimal reference control point, while Technique 2 uses only the TBP, to determine the estimated construction year of the road bridge.

Figure 10. Correlation results of the actual construction year against estimated construction year. S is standard error of the regression, which represents the average distance that the observed values fall from the regression line. (a) Technique 1 correlation results for all 44 road bridges. (b) Technique 2 correlation results for all 44 road bridges.

Figure 10. Correlation results of the actual construction year against estimated construction year. S is standard error of the regression, which represents the average distance that the observed values fall from the regression line. (a) Technique 1 correlation results for all 44 road bridges. (b) Technique 2 correlation results for all 44 road bridges.

Figure 11. Correlation results of the actual construction year against estimated construction year. S is the standard error of the regression, which represents the average distance that the observed values fall from the regression line. (a) Technique 1 correlation results for 23 road bridges in the forested and cropland areas. (b) Technique 2 correlation results for 23 road bridges in the forested and cropland areas. (c) Technique 1 correlation results for 21 road bridges in the built-up areas. (d) Technique 2 correlation results for 21 road bridges in the built-up areas.

Figure 11. Correlation results of the actual construction year against estimated construction year. S is the standard error of the regression, which represents the average distance that the observed values fall from the regression line. (a) Technique 1 correlation results for 23 road bridges in the forested and cropland areas. (b) Technique 2 correlation results for 23 road bridges in the forested and cropland areas. (c) Technique 1 correlation results for 21 road bridges in the built-up areas. (d) Technique 2 correlation results for 21 road bridges in the built-up areas.

Figure 12. Correlation results of the actual construction year against estimated construction year. S is the standard error of the regression, which represents the average distance that the observed values fall from the regression line. (a) Technique 1 correlation results for 23 medium road bridges in Figure 2d. (b) Technique 2 correlation results for 23 medium road bridges in Figure 2d. (c) Technique 1 correlation results for 21 short road bridges in Figure 2e. (d) Technique 2 correlation results for 21 short road bridges in Figure 2e.

Figure 12. Correlation results of the actual construction year against estimated construction year. S is the standard error of the regression, which represents the average distance that the observed values fall from the regression line. (a) Technique 1 correlation results for 23 medium road bridges in Figure 2d. (b) Technique 2 correlation results for 23 medium road bridges in Figure 2d. (c) Technique 1 correlation results for 21 short road bridges in Figure 2e. (d) Technique 2 correlation results for 21 short road bridges in Figure 2e.

The 44 road bridges were classified and analyzed, for both Technique 1 and Technique 2, according to each bridge’s overall length and surface cover type, as shown in Figure 2 and Table 6. For Technique 1, an $R^2$ = 0.40 was determined for the short road bridges, as shown in Figure 12c, but the number of data points was small. For Technique 2, an $R^2$ = 0.41 was higher for medium road bridges than an $R^2$ = 0.20 for short road bridges, and an $R^2$ = 0.42 was higher for road bridges in forested and cropland areas than an $R^2$ = 0.05 for road bridges in built-up areas, as shown in Table 6.

The results suggest that a greater overall length of road bridges and road bridges in forested areas contributed to accuracy. One of the possible explanations is that a road bridge with a greater overall length and a reasonable road width has a large surface area that results in a higher reflectance value, provided that the reflectance is minimally attenuated by scattering and absorption effects, and the image pixel is sufficiently covered by the road bridge surface. No analysis of the relationship between road width and accuracy was performed in this study. The normalized difference water index 2 (NDWI_2) is a function of near-infrared band (NIR) and shortwave infrared band 2 (SWIR2) values. Green healthy vegetation has a higher reflectance value in the NIR than in the SWIR2, and green healthy vegetation also has a higher reflectance value than asphalt or concrete surfaces in the NIR [43]. Therefore, the reflectance is expected to be higher before the bridge is built, assuming that the original surface cover was green healthy vegetation. After the road bridge is built, the reflectance decreases significantly, which in turn increases the mean difference between the current and new regimes in the sequential t-test analysis of the regime shift method assuming that the reflectance is minimally attenuated due to scattering and absorption effects.

The increase in the regime shift index $\mathit{RSI}$ had an insignificant effect on the absolute error between the actual and estimated construction year, as shown in Figure 13a,b. However, as the cutoff length l increased, the absolute error between the actual and estimated construction year increased, as shown in Figure 13c,d. The degree of freedom also increases as the cutoff length l increased, thus leading to a decrease in the statistically significant difference between the means of the two successive regimes [38,39], as shown in Equations (1)–(3). To increase the accuracy of the estimated construction year, we may consider setting the upper limit of the cutoff length l to $l\le$ 12 from Figure 13d. Based on the clustered results with minimum absolute errors in Figure 13d, $l\le$ 12 was selected as the working limit from the linear regression analysis between the cutoff length l and the absolute error between the actual and estimated construction year for Technique 2.

The 12 indices in Table 2 were analyzed at the two road bridges (Kuroyama, and Kamiyama), as shown in Figure 6 and Figure A5. Additionally, the following results were obtained: cutoff length ≤ 9, absolute error ≤ 5, and p-values < 0.05. Using the adopted measure of accuracy, $l\le$ 12, the results for the 12 indices were accurate and statistically significant. However, for the two indices, the normalized difference water index 3 and normalized difference soil index, no regime shifts were detected at the Kamiyama road bridge, as shown in Figure A5f,i. The lack of results could be due to seasonal variations and inadequate reflectance.

Technique 1, which uses both the TBP and a selected optimal reference control point to determine the estimated construction year, found inaccurate and statistically insignificant results for five road bridges, statistically insignificant results for two road bridges, and no results for thirteen road bridges. The five road bridges with inaccurate and statistically insignificant results were the Fukumi, Yabu, Blacksmith, Gabusoka, and Inada, and the two road bridges with statistically insignificant results were the Name 162-1 and Higashiri, which are collectively shown in Figure 5a, Figure 10a, Figure 11a,c and Figure 12a,c. Additionally, the thirteen road bridges without results were the Osuji, Second Geya, Kamiyamatogawa, Shitayamatogawa, Haishi, Hane 105-2, Oura, Nazaki, Nakaoji, Apanuku, Lower River, Makiya No. 1, and Minato, as shown in Table 4. The upper limits $l\le$ 12, and p-value ≤ 0.05 were used as measures of accurate results and statistically significant results, respectively. The Fukumi, Yabu, Blacksmith, Gabusoka, and Inada all recorded $l>$ 12 and a p-values > 0.05, and the Name 162-1 and Higashiri both recorded p-values > 0.05, as shown in Figure 5a and Table 4. The inaccurate results and the lack of results for the road bridges could be due to seasonal variations and inadequate reflectance. Excessive seasonal variations were observed at the Fukumi road bridge, which may have contributed to inaccurate results. Excessive seasonal variation at all selected optimal reference control points for five road bridges with inaccurate results may have also contributed to the inaccurate results. The Haishi Ebara road bridge was found to have l = 14 > 12, absolute error = 3, and p-value < 0.05. The absolute error was low, but l was high, which could be due to a small mean difference between successive regimes, as shown in Table 4 and Figure 5.

Technique 2, which uses only TBP to determine the estimated construction year, found inaccurate results for three road bridges, a statistically insignificant result for one road bridge, and no result for five road bridges. The three road bridges with inaccurate results were the Fukumi, Kayang Mata, and Maehira, and the one road bridge with statistically insignificant result was the Yabu, which are collectively shown in Figure 5a, Figure 10b, Figure 11b,d and Figure 12b,d. And five road bridges without results were the Kamiyamatogawa, Shitayamatogawa, Lower River, Makiya No. 1, and Minato, as shown in Table 4. The upper limits $l\le$ 12 and p-value ≤ 0.05 were used as measures of accurate results and statistically significant results, respectively. The Fukumi, Kayang Mata, and Maehira all recorded $l>$ 12, and the Yabu recorded a p-value > 0.05, as shown in Table 4 and Figure 5a. The inaccurate results and the lack of results for the road bridges could be due to seasonal variation and inadeqaute reflectance. All three road bridges with inaccurate results had seasonal variations that could have contributed to the inaccurate results. Of the three road bridges, the Fukumi had excessive seasonal variations. The overall lengths of both the Maehira road bridge and the Kayang Mata road bridge were less than 30 m and may have contributed to inaccurate results in the STARS method due to inadequate reflectance.

Table 5 shows the comparative advantages between the results for the previous method and the current method. The previous method used both the TBP and two reference control points to determine the estimated construction year. The current method consists of Technique 1 and Technique 2. Technique 1 uses both the TBP and a selected reference control point, while Technique 2 uses only the TBP, to determine the estimated construction year of the road bridge. Among the three methods in Table 5, Technique 2 is the better estimate.

The 44 road bridges in Table 4 were classified according to their surface cover and each bridge’s overall length for Technique 1 and Technique 2, and the summary of the results are shown in Table 6. For Technique 2, an $R^2$ = 0.42 was obtained for the forested and cropland areas, which was higher than the $R^2$ = 0.23 value for Technique 1. In the built-up areas, both Techniques recorded comparatively low values of $R^2$ = 0.09 and $R^2$ = 0.05 for Technique 1 and Technique 2, respectively. For Technique 2, an $R^2$ = 0.41 was obtained for medium road bridges, which was higher than the $R^2$ = 0.09 value for Technique 1. For Technique 1, an $R^2$ = 0.40 was obtained for short road bridges, which was higher than the $R^2$ = 0.20 value for Technique 2. The results indicate that an increase in the bridge’s overlength length, as well as forested and cropland areas, contributed to the accuracy of the results. All five road bridges in Technique 2 that did not produce results had bridge overall lengths of less than 30 m. Additionally, of the thirteen road bridges in Technique 2 that did not produce results, eight out of thirteen road bridges had bridge overall lengths of less than 30 m.

Nevertheless, the two proposed techniques have a number of limitations and challenges. Seasonal variations and inadequate reflectance at the TBP and the selected optimal reference control points are not easily controled. Neither technique can be readily applied in regions where the TBP is obscured by natural or artificial cover for extended periods. Neither technique can be readily applied in regions not covered by Landsat or related satellites, and neither technique can be readily applied in regions where Landsat or related satellite data are severely attenuated by atmospheric absorption and scattering effects.

In the future, the STARS method could be extended to automatically cycle through all values of a certain cutoff length l in the time series data and then produce an optimal peak $\mathit{RSI}$ at a given value of l. In future research, some correction factors could be determined using statistics or mathematical formulas to account for seasonal variations and inadequate reflectance at the TBP, as well as using all image pixels across the whole span of the TBP to increase reflectance. The cutoff length $l\le$ 12 is a working limit; therefore, in the future, there is a need to develop a robust reliability method for these proposed techniques. Finally, the generality of these two proposed techniques needs to be tested in other geographic areas.

5. Conclusions

The correlation analysis showed that increasing the cutoff length l increased the absolute error between the actual and estimated construction years. Therefore, as a measure of accuracy, the upper limit of cutoff length l was set to $l\le$ 12. Based on the clustered results with minimum absolute errors, $l\le$ 12 was selected as the working limit from the linear regression analysis between the absolute error between the actual and estimated construction year and the cutoff length l for Technique 2.

Landsat 5 Thematic Mapper (TM) in Google Earth Engine (GEE) was used for the analysis. The 12 indices, which included the normalized difference water index 2 (NDWI_2), were analyzed at two road bridges (Kuroyama and Kamiyama). The results for all 12 indices were accurate with a cutoff length $l\le$ 9, an absolute error ≤ 5, and statistically significant with p-values < 0.05. The trends for all 12 indices were clear. The NDWI_2 was adopted and used for the analysis of all 44 road bridges. In the future, the remaining indices can be analyzed and compared along with the NDWI_2 to determine the most accurate index using Technique 2. Sequential t-test analysis of regime shift (STARS) with a significance level of $\alpha$ = 0.05 and cutoff lengths of l = 2 to l = 27 was used to interpret the estimated construction year from Landsat 5 TM data generated from all 12 indices.

Landsat 5 TM in GEE was used for the analysis. The NDWI_2 data were cloud masked in GEE, the cloud cover was reduced from 100% to 30% in GEE, and the data were averaged annually for both techniques. Both cloud masking and cloud cover control reduce noise in the data, and averaging the data annually reduces seasonal variations. Technique 1 uses both the target bridge point (TBP) and a selected optimal reference control point, while Technique 2 uses only the TBP, to determine the estimated construction year of the road bridge. The STARS method was used at $\alpha$ = 0.05 and l = 2 to l = 27 to interpret the estimated construction year from Landsat 5 TM NDWI_2 data.

Both techniques successfully determined the estimated construction year, which was statistically significant with p-values < 0.05, except for seven bridges in Technique 1 and one road bridge in Technique 2. The correlation analysis of all 44 road bridges yielded an $R^2$ = 0.24 and an $R^2$ = 0.33, as well as an average deviation of S = 5.81 years and S = 4.08 years, for Technique 1 and Technique 2, respectively. The results suggest that Technique 2 is more accurate and is a better estimate than Technique 1, but the $R^2$ values were low. One of the possible explanations that may have contributed to low $R^2$ values, as indicated by the gap between the actual and estimated construction year, is that the planned construction year recorded in the database may not have corresponded to the actual construction year due to construction delays.

For Technique 1, the Haishi Ebara road bridge was found to have an l = 14 > 12, an absolute error = 3, and a p-value < 0.05. The absolute error was low, but l was high, which could be due to a small mean difference between successive regimes. The cutoff length $l\le$ 12 is a working limit; therefore, in the future, there is a need to develop a robust reliability method for these proposed techniques.

Some of the advantages of Technique 2 over Technique 1 are that (a) the analysis time was relatively shorter with Technique 2 than with Technique 1 and (b) Technique 2 did not use a selected optimal reference point, which in most cases negatively affected the final results due to seasonal variations.

A longer bridge’s overall length and road bridges in forested areas contribute to the accuracy of the results. One of the possible explanations is that a larger surface area corresponds to a higher reflectance, and the near-infrared in normalized difference water index 2 has a higher reflectance for green vegetation than for asphalt or concrete surface areas.

The comparative analysis indicated that the results for the previous technique were not clear when compared to the results of the current Technique 1 and Technique 2. Due to the lack of cloud masking and control of cloud cover, the data were contaminated with noise in the previous method.

The proposed techniques can be applied to detect any significant mean difference on the Earth’s surface, whether natural or man-made. The region must be covered by Landsat or related satellites, the features on the Earth’s surface must not be obscured by natural or human cover for extended periods, and the data from the Landsat or related satellites must not be severely attenuated by atmospheric absorption and scattering effects.

By using the construction year as one of the inputs for bridge management systems, bridge managers can make more informed decisions about how best to maintain and improve road bridges to ensure user safety and bridge preservation for the future.