Enhanced Intensity Analysis to Quantify Categorical Change and to Identify Suspicious Land Transitions: A Case Study of Nanchang, China

: Conventional methods to analyze a transition matrix do not o ﬀ er in-depth signals concerning land changes. The land change community needs an e ﬀ ective approach to visualize both the size and intensity of land transitions while considering possible map errors. We propose a framework that integrates error analysis, intensity analysis, and di ﬀ erence components, and then uses the framework to analyze land change in Nanchang, the capital city of Jiangxi province, China. We used remotely sensed data for six categories at four time points: 1989, 2000, 2008, and 2016. We had a confusion matrix for only 2016, which estimated that the map of 2016 had a 12% error, while the temporal di ﬀ erence during 2008–2016 was 22% of the spatial extent. Our tools revealed suspected errors at other years by analyzing the patterns of temporal di ﬀ erence. For example, the largest component of temporal di ﬀ erence was exchange, which could indicate map errors. Our framework identiﬁed categories that gained during one time interval then lost during the subsequent time interval, which raised the suspicion of map error. This proposed framework facilitated visualization of the size and intensity of land transitions while illustrating possible map errors that the profession routinely ignores.


Introduction
Land change measurement helps to understand the coupled human-environmental system [1,2]. The spatiotemporal pattern of land-change can reflect underlying human activities and show how humans interact with nature over time [3][4][5]. Large-scale ongoing modifications to land-use and land cover (LULC) have several environmental and socio-economic implications, including those for land productivity, biodiversity change, and urban heat island effect, all of which influence long-term environmental sustainability [6,7]. However, land change analysis relies on the data used and the methods implemented. Errors in the LULC data can propagate through change analysis. Robust methods are needed to offer in-depth signals of land change over time. As such, it remains challenging to develop a universal framework to measure land change for informing decision-makers.
Post-classification change analysis depends on the LULC data classified from remotely sensed images [8][9][10]. Some researchers mistakenly assume that data are sufficiently accurate when map accuracy is greater than 85% correct. Other authors realize the flaw of the traditional rule of thumb. For example, Quan et al. [11] suspected that data error might account for some transitions from Built to Cultivated because the data at four time-points had overall errors of 11%, 8%, 5%, and 4%. Suspicious land transitions are those transitions for which we suspect that the temporal difference Our article presents a framework that integrates error analysis, Intensity Analysis, and Difference Components, to quantify categorical changes and to identify suspicious land transitions. Two specific objectives were to give (1) an example that compared the observed errors to the errors that could explain change and (2) a method to visualize the transition pattern in terms of both the size and the intensity of the transitions. Other researchers can use this framework to identify suspicious transitions and quantify categorical changes. Figure 2 shows our proposed framework to analyze land change. The framework mainly consists of three components: (1) data pre-processing, (2) error analysis, and (3) change analysis.

Analytical Framework
Our framework is suitable for situations where researchers have a confusion matrix at one timepoint but lack information concerning errors at other time-points. Our method offers useful insights to find transitions that we suspect were caused by error, while we have no proof because we lacked the confusion matrices for three of our four time-points and we lacked information concerning errors of temporal change, as is frequently the situation in the profession. We created a method of visualization called transition pattern, which showed both the size and intensity of the transitions across multiple time intervals, in a single graphic.  Figure 2 shows our proposed framework to analyze land change. The framework mainly consists of three components: (1) data pre-processing, (2) error analysis, and (3) change analysis.

Analytical Framework
Our framework is suitable for situations where researchers have a confusion matrix at one time-point but lack information concerning errors at other time-points. Our method offers useful insights to find transitions that we suspect were caused by error, while we have no proof because we lacked the confusion matrices for three of our four time-points and we lacked information concerning errors of temporal change, as is frequently the situation in the profession. We created a method of visualization called transition pattern, which showed both the size and intensity of the transitions across multiple time intervals, in a single graphic.

Data Collection and Processing
Multi-temporal satellite images are from Landsat Thematic Mapper (TM) at 1989, 2000, and 2008, and Operational Land Imager (OLI) at 2016. Table S1 describes the satellite images that serve as the basis for the map of land categories. These Landsat images were from the United States Geological Survey. Before performing land classification, the acquired images were geo-rectified and processed for atmospheric correction. All acquired images were geo-rectified with reference to topographic maps, using at least 30 ground control points in each image, such as road intersections and stream confluences. The root mean squared errors of geometric rectification were less than half a pixel, as a result of using the first-order polynomial nearest neighbor algorithm. We performed a supervised classification to produce the map at 2016. We then used the 2016 map to help to classify each of the preceding years in sequence. The operation consisted of overlaying the map of 2016 on the 2008 image, so we could use visual interpretation to group pixels with the same characteristics. We repeated this procedure for 2000 and 1989, to produce a sequence of maps at 1989, 2000, 2008, and 2016. We assigned every cluster to one of six land categories and then compared the 2016 classification with the high-resolution image at 2016, which is available on Google Earth. We collected 1000 purely random reference samples to assess

Data Collection and Processing
Multi-temporal satellite images are from Landsat Thematic Mapper (TM) at 1989, 2000, and 2008, and Operational Land Imager (OLI) at 2016. Table S1 describes the satellite images that serve as the basis for the map of land categories. These Landsat images were from the United States Geological Survey. Before performing land classification, the acquired images were geo-rectified and processed for atmospheric correction. All acquired images were geo-rectified with reference to topographic maps, using at least 30 ground control points in each image, such as road intersections and stream confluences. The root mean squared errors of geometric rectification were less than half a pixel, as a result of using the first-order polynomial nearest neighbor algorithm. We performed a supervised classification to produce the map at 2016. We then used the 2016 map to help to classify each of the preceding years in sequence. The operation consisted of overlaying the map of 2016 on the 2008 image, so we could use visual interpretation to group pixels with the same characteristics. We repeated this procedure for 2000 and 1989, to produce a sequence of maps at 1989, 2000, 2008, and 2016. We assigned every cluster to one of six land categories and then compared the 2016 classification with the high-resolution image at 2016, which is available on Google Earth. We collected 1000 purely random reference samples to assess accuracy at 2016 and generated a confusion matrix at 2016. Each map had six categories: builtup, woodland, water, cropland, aquaculture, and bareland.

Error Analysis
We analyzed the confusion matrix at 2016, similar to how we analyzed a transition matrix of temporal difference. The loss of i corresponds to the commission error of i, the gain of j corresponds to the omission error of j, and persistence of j corresponds to the agreement of j. The supplementary

Error Analysis
We analyzed the confusion matrix at 2016, similar to how we analyzed a transition matrix of temporal difference. The loss of i corresponds to the commission error of i, the gain of j corresponds to the omission error of j, and persistence of j corresponds to the agreement of j. The supplementary materials gives the notation and equations. We also applied Equations (13) and (16) from Aldwaik and Pontius Jr [19] to assess whether the errors at 2016 could account for the deviation between the uniform change intensity and each category's gain intensity during 2008-2016.

Change Component
We budgeted the differences during each time interval into three components called Quantity, Exchange, and Shift [35]. The supplementary materials gives equations for those concepts for each category j and the extent during each time interval t, denoted as d tj , q tj , e tj , s tj , D t , Q t , E t , and S t . Table S2 defines the mathematical symbols that the equations use.

Intensity Analysis
Intensity analysis is a hierarchical framework that compares a uniform intensity to observed intensities of temporal changes among categories [12,37]. Aldwaik and Pontius Jr [29] created Intensity Analysis to dissect transition matrices at three levels of detail: time interval, category, and transition.

Transition Pattern
We coined the phrase "transition pattern" as our method to visualize both the size and intensity of the transitions. Figure 3 shows the design of the transition pattern. The rows show a category's losses. The columns show a category's gains. Diagonal entries are excluded because they indicate persistence, not change. The size of the square was proportional to the annual area of the transition. The color of the square revealed the transition intensity with which the column category gained from the row category. If the intensity for a particular transition is greater than the column's uniform transition intensity, then the square is a shade of red and we say that the gaining category targeted the row category. If the intensity for a particular transition is less than the column's uniform transition intensity, then the square is a shade of blue and we say that the gaining category avoided the row category. The intensity deviation in Figure 3 refers to the deviation between the transition intensity R tij of a particular off-diagonal entry and the column's uniform transition intensity W tj . The supplementary materials gives the equations for R tij and W tj . Readers should compare the colors within a column to see how each column's gaining category targets or avoids each row's losing category.
We budgeted the differences during each time interval into three components called Quantity, Exchange, and Shift [35]. The supplementary materials gives equations for those concepts for each category j and the extent during each time interval t, denoted as dtj, qtj, etj, stj, Dt, Qt, Et, and St. Table  S2 defines the mathematical symbols that the equations use.

Intensity Analysis
Intensity analysis is a hierarchical framework that compares a uniform intensity to observed intensities of temporal changes among categories [12,37]. Aldwaik and Pontius Jr [29] created Intensity Analysis to dissect transition matrices at three levels of detail: time interval, category, and transition.

Transition Pattern
We coined the phrase "transition pattern" as our method to visualize both the size and intensity of the transitions. Figure 3 shows the design of the transition pattern. The rows show a category's losses. The columns show a category's gains. Diagonal entries are excluded because they indicate persistence, not change. The size of the square was proportional to the annual area of the transition. The color of the square revealed the transition intensity with which the column category gained from the row category. If the intensity for a particular transition is greater than the column's uniform transition intensity, then the square is a shade of red and we say that the gaining category targeted the row category. If the intensity for a particular transition is less than the column's uniform transition intensity, then the square is a shade of blue and we say that the gaining category avoided the row category. The intensity deviation in Figure 3 refers to the deviation between the transition intensity Rtij of a particular off-diagonal entry and the column's uniform transition intensity Wtj. The supplementary materials gives the equations for Rtij and Wtj. Readers should compare the colors within a column to see how each column's gaining category targets or avoids each row's losing category.   2008-2016. Map errors might contribute to such temporal differences where a category gains during one time interval then loses during the subsequent time interval. The purpose of our framework is to call attention to possible problems with data, even when we do not have confusion matrices. Figure 4 presents the maps and percentages of the six land categories at the four time-points. All maps on the left concerning land cover looked similar because the change was less than 30% for all time intervals. The maps of Loss and Gain are essential to see the transitions. Suspicious transitions included patches in the northeast that changed from water to woodland and cropland during 2000-2008, then reverted to water during 2008-2016. In the southeast, large patches of cropland transitioned to woodland during 2000-2008, then transitioned back to cropland during 2008-2016. Additionally, many patches in the north gained builtup during 2000-2008 then lost builtup during 2008-2016. Map errors might contribute to such temporal differences where a category gains during one time interval then loses during the subsequent time interval. The purpose of our framework is to call attention to possible problems with data, even when we do not have confusion matrices.   Figure 5a is the number of observations in the Reference information for each category. The union of Commission and Agreement is the number of observations in the map for each category. If the commission error was larger than the omission error for a category, then the map overestimated the size of that category, as illustrated by the cropland. The largest Remote Sens. 2020, 12, 3323 7 of 16 component of error derived from an overestimation of cropland. If the commission error was smaller than the omission error for a category, then the map underestimated the size of that category, as all categories except the cropland illustrate. The uniform line in Figure 5b shows that the overall error in 2016 was 12% of Nanchang's spatial extent.  Figure 5a is the number of observations in the Reference information for each category. The union of Commission and Agreement is the number of observations in the map for each category. If the commission error was larger than the omission error for a category, then the map overestimated the size of that category, as illustrated by the cropland. The largest component of error derived from an overestimation of cropland. If the commission error was smaller than the omission error for a category, then the map underestimated the size of that category, as all categories except the cropland illustrate. The uniform line in figure 5b shows that the overall error in 2016 was 12% of Nanchang's spatial extent.      Figure 6b show that quantity error and exchange error constitute 39% and 46% of the overall error. Quantity error occurred because the map overestimated the size of the cropland and underestimated the size of the other categories. Exchange occurred when pairs of categories were confused with each other. The quantity component accounted for the most error within aquaculture, cropland, and water. Exchange accounted for most of the error within the other categories and most of the error overall.  Figure 5a is the number of observations in the Reference information for each category. The union of Commission and Agreement is the number of observations in the map for each category. If the commission error was larger than the omission error for a category, then the map overestimated the size of that category, as illustrated by the cropland. The largest component of error derived from an overestimation of cropland. If the commission error was smaller than the omission error for a category, then the map underestimated the size of that category, as all categories except the cropland illustrate. The uniform line in figure 5b shows that the overall error in 2016 was 12% of Nanchang's spatial extent.      Figure 7 indicates that quantity difference accounts for 6, 6, and 8 percent of Nanchang during the three time intervals. Figure 7 shows the temporal difference during 2008-2016 was 22 percent of the spatial extent. Figure 5b shows that the map at 2016 had a 12 percent error. The error at 2016 was more than half the size of the temporal difference during 2008-2016. Thus, we should not believe that all of the temporal difference was real change during 2008-2016. The left side of Figure 7 shows the size of the temporal difference during each time interval, while the intervals had different durations. The right side of Figure 7 shows the annual difference during each time interval. The annual difference accelerated then decelerated across the three time intervals. The annual difference during 1989-2000 was less than the uniform speed during the temporal extent, indicating that the annual difference during 1989-2000 was slow, relative to the temporal extent. The annual difference during the other two time intervals was faster than the uniform speed. Figure 7 combines the results from Difference Components and Intensity Analysis for the time interval level. Exchange is the largest component during all three intervals, especially during the second interval. Exchange occurs when some locations in the map experience a transition from category A to B, while the other locations experience a transition from B to A. Map error can cause exchange. The left side of Figure 7 indicates that quantity difference accounts for 6, 6, and 8 percent of Nanchang during the three time intervals. Figure 7 shows the temporal difference during 2008-2016 was 22 percent of the spatial extent. Figure 5b shows that the map at 2016 had a 12 percent error. The error at 2016 was more than half the size of the temporal difference during 2008-2016. Thus, we should not believe that all of the temporal difference was real change during 2008-2016. The left side of Figure 7 shows the size of the temporal difference during each time interval, while the intervals had different durations. The right side of Figure 7 shows the annual difference during each time interval. The annual difference accelerated then decelerated across the three time intervals. The annual difference during 1989-2000 was less than the uniform speed during the temporal extent, indicating that the annual difference during 1989-2000 was slow, relative to the temporal extent. The annual difference during the other two time intervals was faster than the uniform speed. Figures 8a,c,e show the difference components during each interval as a percentage of Nanchang. Croplands experienced the largest differences during all intervals. The largest quantity components occurred with cropland and woodland. The letter L in a quantity component denotes net loss and the letter G denotes net gain. Croplands experienced net loss, then net gain, then net loss across the three time intervals. Woodland experienced just the opposite, meaning net gain, then net loss, then net gain across the three time intervals. We suspect that confusion between Cropland and Woodland in the maps could account for this pattern, especially because cropland and woodland could be difficult to distinguish in remotely sensed images. Figure 8e indicates that cropland experienced net loss during 2008-2016, while Figure 5 shows that the map at 2016 overestimated the size of croplands. The implication was that the map at 2008 probably overestimated croplands, even more than the 2016 map overestimated cropland. Overestimation of cropland at 2008 would account for some of the substantial gain of cropland during 2000-2008, which was a major reason why the annual change was fastest during 2000-2008. This demonstrates how our analysis gives insights into  Figure 8a,c,e show the difference components during each interval as a percentage of Nanchang. Croplands experienced the largest differences during all intervals. The largest quantity components occurred with cropland and woodland. The letter L in a quantity component denotes net loss and the letter G denotes net gain. Croplands experienced net loss, then net gain, then net loss across the three time intervals. Woodland experienced just the opposite, meaning net gain, then net loss, then net gain across the three time intervals. We suspect that confusion between Cropland and Woodland in the maps could account for this pattern, especially because cropland and woodland could be difficult to distinguish in remotely sensed images. Figure 8e indicates that cropland experienced net loss during 2008-2016, while Figure 5 shows that the map at 2016 overestimated the size of croplands. The implication was that the map at 2008 probably overestimated croplands, even more than the 2016 map overestimated cropland. Overestimation of cropland at 2008 would account for some of the substantial gain of cropland during 2000-2008, which was a major reason why the annual change was fastest during 2000-2008. This demonstrates how our analysis gives insights into how the map error can influence the difference between time-points for which we do not have confusion matrices.

Change Analysis
Remote Sens. 2020, 12, x FOR PEER REVIEW 9 of 17 how the map error can influence the difference between time-points for which we do not have confusion matrices.  Figure 8b,d,f show the components of temporal difference as a percentage of the temporal difference for each category. Builtup's exchange component was larger than its quantity component during all three time intervals, which meant that the net gain of builtup was smaller than the simultaneous loss and gain of builtup. The substantial losses of builtup were suspicious. Figure 5 shows that the map at 2016 underestimated the size of the builtup, which might account for some of the apparent losses of builtup. The largest component of difference was exchange, for most of the categories, which could signal map error. The vertical lines in Figures 8b,e,f show how the overall difference derived from its three components. The Quantity component accounted for 27 percent of the overall difference during 2008-2016. The largest component of difference overall during all time intervals was exchange, shown by the difference between the red line and the blue line. When Exchange accounts for a substantial portion of the temporal difference, then we become suspicious of map errors. Figure 9a,c,e show for each category the size of gain, persistence, and loss, as a percentage of Nanchang. Cropland accounts for more than 43% of Nanchang at the four time-points, while cropland had the largest losses and gains. Figure 9b,d,f show the annual intensity of loss and gain as  Figure 8b,d,f show the components of temporal difference as a percentage of the temporal difference for each category. Builtup's exchange component was larger than its quantity component during all three time intervals, which meant that the net gain of builtup was smaller than the simultaneous loss and gain of builtup. The substantial losses of builtup were suspicious. Figure 5 shows that the map at 2016 underestimated the size of the builtup, which might account for some of the apparent losses of builtup. The largest component of difference was exchange, for most of the categories, which could signal map error. The vertical lines in Figure 8b,e,f show how the overall difference derived from its three components. The Quantity component accounted for 27 percent of the overall difference during 2008-2016. The largest component of difference overall during all time intervals was exchange, shown by the difference between the red line and the blue line. When Exchange accounts for a substantial portion of the temporal difference, then we become suspicious of map errors. Figure 9a,c,e show for each category the size of gain, persistence, and loss, as a percentage of Nanchang. Cropland accounts for more than 43% of Nanchang at the four time-points, while cropland had the largest losses and gains. Figure 9b,d,f show the annual intensity of loss and gain as a percentage of each category's size. The vertical line indicated that the annual differences were 1.6%, 3.1%, and 2.7% of Nanchang's area during the three time intervals, respectively, which were identical to the annual differences in Figure 7. If a bar stopped before the line, then the category's loss or gain was dormant, meaning the change of the category was less intensive than in Nanchang overall. If a bar exceeded the line, then the category's loss or gain was active, meaning the change of the category more intensive than that in Nanchang overall. The large sizes of cropland and water in the denominators of their intensities produced their dormant intensities.
Remote Sens. 2020, 12, x FOR PEER REVIEW 10 of 17 a percentage of each category's size. The vertical line indicated that the annual differences were 1.6%, 3.1%, and 2.7% of Nanchang's area during the three time intervals, respectively, which were identical to the annual differences in Figure 7. If a bar stopped before the line, then the category's loss or gain was dormant, meaning the change of the category was less intensive than in Nanchang overall. If a bar exceeded the line, then the category's loss or gain was active, meaning the change of the category more intensive than that in Nanchang overall. The large sizes of cropland and water in the denominators of their intensities produced their dormant intensities.  Figure 10 shows the level of error in the map at 2016, which would be necessary to explain the deviations between uniform change and the gain intensities in Figure 9f. Results from Equation (13) in Aldwaik and Pontius Jr [19] indicate that commission intensity at 2016 could not account for all of the deviations between the uniform line and the gain intensities in Figure 9f. We compared the error intensities on the right side of Figure 10 with the corresponding error intensities in Figure 5b. The errors in terms of commission intensities of builtup, woodland, and bareland on the right side of Figure 10 were larger than those in Figure 5b, therefore, commission error could account for some but not all of the deviations between uniform and observed gain intensity for those three categories. This indicated that gains of those categories were truly active. Results from Equation (16) in Aldwaik and Pontius Jr [19] indicate that omission intensity at 2016 could account for some but not all of the deviations between the uniform line and the gain intensities in Figure 9f. The omission intensities of  Figure 10 shows the level of error in the map at 2016, which would be necessary to explain the deviations between uniform change and the gain intensities in Figure 9f. Results from Equation (13) in Aldwaik and Pontius Jr [19] indicate that commission intensity at 2016 could not account for all of the deviations between the uniform line and the gain intensities in Figure 9f. We compared the error intensities on the right side of Figure 10 with the corresponding error intensities in Figure 5b. The errors in terms of commission intensities of builtup, woodland, and bareland on the right side of Figure 10 were larger than those in Figure 5b, therefore, commission error could account for some but not all of the deviations between uniform and observed gain intensity for those three categories. This indicated that gains of those categories were truly active. Results from Equation (16) in Aldwaik and Pontius Jr [19] indicate that omission intensity at 2016 could account for some but not all of the deviations between the uniform line and the gain intensities in Figure 9f. The omission intensities of water, cropland, and aquaculture on the right side of Figure 10 were larger than the corresponding omission intensities in Figure 5b. Therefore, the omission error could not account entirely for the deviation between uniform and observed gain intensity. This indicates that gains of those categories were truly dormant.
Remote Sens. 2020, 12, x FOR PEER REVIEW 11 of 17 water, cropland, and aquaculture on the right side of Figure 10 were larger than the corresponding omission intensities in Figure 5b. Therefore, the omission error could not account entirely for the deviation between uniform and observed gain intensity. This indicates that gains of those categories were truly dormant.  Figure 11 shows the transition patterns during three time intervals, which revealed both the size and intensity of transitions over time. Figure 11 immediately shows that the largest transitions were from cropland to woodland during the second time interval and from woodland to cropland during the third time interval. Confusion between woodland and cropland in the data could explain the large sizes of those transitions. Readers should look down each column to see whether the gain of the column category targets or avoids categories at the start of each time interval. A substantial portion of cropland's gain derived from bareland, as cropland's gain targeted bareland during all three time intervals. The cropland's gain targeted water during 2008-2016, which could reflect the process of converting lakes to farmland in Nanchang. The transition from woodland to cropland was large during the last time interval, but the transition avoided due to the woodland's large size. Builtup's gain derived mainly from cropland and bareland. Woodland gained most from cropland during the second time interval and targeted bareland during the first and third intervals. Bareland's gain derived mostly from its targeting of cropland during the second time interval. Water gained mostly from cropland and targeted aquaculture during all three time intervals.  Figure 11 shows the transition patterns during three time intervals, which revealed both the size and intensity of transitions over time. Figure 11 immediately shows that the largest transitions were from cropland to woodland during the second time interval and from woodland to cropland during the third time interval. Confusion between woodland and cropland in the data could explain the large sizes of those transitions. Readers should look down each column to see whether the gain of the column category targets or avoids categories at the start of each time interval. A substantial portion of cropland's gain derived from bareland, as cropland's gain targeted bareland during all three time intervals. The cropland's gain targeted water during 2008-2016, which could reflect the process of converting lakes to farmland in Nanchang. The transition from woodland to cropland was large during the last time interval, but the transition avoided due to the woodland's large size. Builtup's gain derived mainly from cropland and bareland. Woodland gained most from cropland during the second time interval and targeted bareland during the first and third intervals. Bareland's gain derived mostly from its targeting of cropland during the second time interval. Water gained mostly from cropland and targeted aquaculture during all three time intervals. Remote Sens. 2020, 12, x FOR PEER REVIEW 12 of 17

Error Analysis in the Framework Proposed for Land Change Analysis
Some investigators are under the false impression that maps are good enough to analyze change when the map at each time-point is greater than 85% correct [13,38]. The single metric of percent correct fails to convey the various types of errors. The error matrix is the most common method to summarize the various types of errors [9,39]. The matrix is sometimes referred to as a confusion matrix because it identifies the pairs of categories that are confused with each other [40]. Category level error metrics, such as overall omission and commission could be computed using the error matrix [10,41,42]. Standard accuracy assessment techniques were developed for single-date remotely sensed data, while the error matrix-based accuracy assessment method could be modified for evaluation of change detection [43][44][45]. Confusion matrices sometimes do not exist because of the difficulties in collecting reliable field-based data, especially for time-points from the distant past [8].
Our framework offered insights concerning how to identify suspicious transitions when detailed information concerning error matrices do not exist. Our proposed framework is a collection of tools to help scientists consider whether errors could explain particular temporal differences. For example, Figure 5b shows that the map at 2016 has a 12 percent error. Meanwhile, Figure 7 shows that the difference during 2008-2016 was 22 percent of the spatial extent. Thus, we should not believe that all of the temporal difference was real change. Figure 5a shows that the map at 2016 overestimated cropland, in spite of the cropland's net loss during 2008-2016. The error percentages on the right side of Figure 10 were greater than the error intensities in Figure 5b, meaning that the estimated map error could not explain all deviations between a category's gain intensity and the uniform line. We suspect data error might account for some of the apparent transition from builtup to cropland. We saw the same transition in GlobeLand30 [12], which is a global land cover data product with a 30 m spatial resolution, with 10 classes at the years 2000 and 2010 [13].
We used the framework to identify possible misclassification due to confusion between categories. Figure 7 shows that exchange was the largest component during each time interval, while Figure 8 shows that the largest component was exchange for most of the categories, which would exist when pairs of categories were confused with each other. Quan et al. [11] found similar results of land exchange in Changsha, China. Figure 9 shows that the gain intensity and loss intensity of both builtup and bareland were larger than uniform intensity during the first and third time intervals. This was consistent with other studies that used questionable data to analyze land change in an inland city of China [34,46].

Transition Pattern to Communicate Both Size and Intensity in One Graphic
Compared to traditional methods such as the land-use dynamic degree, Intensity Analysis and difference components are ways to offer in-depth signals concerning land changes [19]. This is the reason why researchers apply them widely throughout the world. Previous applications of Intensity Analysis graphically showed the sizes and the intensities of the changes at three levels of detail as lengths of bars [22]. We proposed the transition pattern as an alternative way to visualize the transition level analysis, as matrices that show both the size and intensity of the transitions. Previous research presented the intensity and size of the transitions from one gaining category at a time [11,22,47]. Yang et al. [21] proposed a table that showed all transitions and whether a transition was targeting or avoiding, but failed to show the size of each transition and failed to show how intensively the transition was targeted or avoided. Our transition pattern revealed in one graphic the sizes and intensities of all transitions during multiple time intervals.

Research Agenda
Our framework is suitable for situations where researchers have a confusion matrix for one time point, but lack information concerning errors at the other time-points, such as with the Globeland30 data [48]. Future researchers should make matrices that show errors of change during a time interval, not just errors of categories at a single time-point. It is possible that maps have small errors at their individual time-points but have larger errors concerning change. This can occur when the maps are inconsistent in some temporal respects. For example, our maps are mosaics of images that derive from various months. The seasonal inconsistency among time-points is a reason why the maps' temporal differences between years might not reflect annual change on the ground. Future methods to identify suspicious transitions should consider the entire time series of each pixel. Our method considers only pairs of sequential time-points. It would be helpful to consider all time-points simultaneously to look for suspicious transitions, such as patches that toggle between two categories across sequential time-points as Figure 4 illustrates.

Conclusions
Our article offers a framework to integrate error analysis, intensity analysis, and difference components to measure land change. We illustrated the framework with data from a growing inland city in China. The analysis provides evidence that not all temporal differences indicate real land change. The framework offers clues to identify temporal differences that map errors might have caused. The transition pattern proposed in this study presents a temporal sequence of transition matrices in graphical form. This framework facilitates visualization of the size and intensity of land transitions, while calling attention to possible map errors that the profession routinely ignores.