Application of multitemporal Landsat data to monitor land cover changes in the Eastern Nile Delta region,Egypt

Due to the progressive increase in development of desert land in Egypt, the demand for efficient and accurate land cover change information is increasing. In this study, we apply the methodology of post‐classification change detection to map and monitor land cover change patterns related to agricultural development and urban expansion in the desert fringes of the Eastern Nile Delta region. Using a hybrid classification approach, we employ multitemporal Landsat Thematic Mapper (TM)/Enhanced Thematic Mapper Plus (ETM+) images from 1984, 1990 and 2003 to produce three land cover/land‐use maps. Post‐classification comparison of these maps was used to obtain ‘from–to’ statistics and change detection maps. The change detection results show that agricultural development increased by 14% through the study period. The average annual rate of land reclamation during 1990–2003 (4511 ha a^?1) was comparable to that during 1984–1990 (4644 ha a^?1), reflecting a systematic national plan for desert reclamation that went into effect. We find that the increase in urbanization (by ca 21 300 ha) during 1990–2003 was predominantly due to encroachment into traditionally cultivated land at the fringes of urban centres. Our results accurately quantify the land cover changes and delineate their spatial patterns, demonstrating the utility of Landsat data in analysing landscape dynamics over time. Such information is critical for making efficient and sustainable policies for resource management.     

Change analysis of land surface temperature based on robust statistics in the estuarine area of Pearl River (China) from 1990 to 2000 by Landsat TM/ETM+ data

The estuarine area of Pearl River that has taken great changes in land cover since 1990 is a typical area for studying the change of land surface temperature (LST). The LST of the years 1990 and 2000 in this area was estimated from the data of Landsat TM/ETM+ band 6, respectively, and three scales, corresponding to high, normal and low temperature ranges, were divided by a robust statistical method. The results show that the area of high temperature range in 2000 has an increase of 250 km² compared with the year 1990. The urban‐used land and the bare land are the main land cover types constituting the high temperature range area.     

Identifying land cover variability distinct from land cover change: Cheatgrass in the Great Basin

An understanding of land use/land cover change at local, regional, and global scales is important in an increasingly human-dominated biosphere. Here, we report on an under-appreciated complexity in the analysis of land cover change important in arid and semi-arid environments. In these environments, some land cover types show a high degree of inter-annual variability in productivity. In this study, we show that ecosystems dominated by non-native cheatgrass (Bromus tectorum) show an inter-annual amplified response to rainfall distinct from native shrub/bunch grass in the Great Basin, US. This response is apparent in time series of Landsat and Advanced Very High Resolution Radiometer (AVHRR) that encompass enough time to include years with high and low rainfall. Based on areas showing a similar amplified response elsewhere in the Great Basin, 20,000 km², or 7% of land cover, are currently dominated by cheatgrass. Inter-annual patterns, like the high variability seen in cheatgrass-dominated areas, should be considered for more accurate land cover classification. Land cover change science should be aware that high inter-annual variability is inherent in annual dominated ecosystems and does not necessarily correspond to active land cover change.     

Analysis of land use/cover changes and urban expansion of Nairobi city using remote sensing and GIS

We used three Landsat images together with socio‐economic data in a post‐classification analysis to map the spatial dynamics of land use/cover changes and identify the urbanization process in Nairobi city. Land use/cover statistics, extracted from Landsat Multi‐spectral Scanner (MSS), Thematic Mapper (TM) and Enhanced Thematic Mapper plus (ETM+) images for 1976, 1988 and 2000 respectively, revealed that the built‐up area has expanded by about 47?km². The road network has influenced the spatial patterns and structure of urban development, so that the expansion of the built‐up areas has assumed an accretive as well as linear growth along the major roads. The urban expansion has been accompanied by loss of forests and urban sprawl. Integration of demographic and socio‐economic data with land use/cover change revealed that economic growth and proximity to transportation routes have been the major factors promoting urban expansion. Topography, geology and soils were also analysed as possible factors influencing expansion. The integration of remote sensing and Geographical Information System (GIS) was found to be effective in monitoring land use/cover changes and providing valuable information necessary for planning and research. A better understanding of the spatial and temporal dynamics of the city's growth, provided by this study, forms a basis for better planning and effective spatial organization of urban activities for future development of Nairobi city.     

Predicting the spectral information of future land cover using machine learning

Application of machine learning models to study land-cover change is typically restricted to the change detection of categorical, i.e. classified, land-cover data. In this study, our aim is to extend the utility of such models to predict the spectral band information of satellite images. A Random Forests (RF)-based machine learning model is trained using topographic and historical climatic variables as inputs to predict the spectral band values of high-resolution satellite imagery across two large sites in the western United States, New Mexico (10,570 km²), and Washington (9400 km²). The model output is used to obtain a true colour photorealistic image and an image showing the normalized difference vegetation index values. We then use the trained model to explore what the land cover might look like for a climate change scenario during the 2061–2080 period. The RF model achieves high validation accuracy for both sites during the training phase, with the coefficient of determination (R²) = 0.79 for New Mexico site and R² = 0.73 for Washington site. For the climate change scenario, prominent land-cover changes are characterized by an increase in the vegetation cover at the New Mexico site and a decrease in the perennial snow cover at the Washington site. Our results suggest that direct prediction of spectral band information is highly beneficial due to the ability it provides for deriving ecologically relevant products, which can be used to analyse land-cover change scenarios from multiple perspectives.     

Monitoring land-use change-associated land development using multitemporal Landsat data and geoinformatics in Kom Ombo area,South Egypt

Due to the progressive increase in population, sustainable development of desert land in Egypt has become a strategic priority in order to meet the increasing demands of a growing population for food and housing. Such obligations require efficient compilation of accurate land-cover information in addition to detailed analysis of archival land-use changes over an extended time span. In this study, we applied a methodology for mapping land cover and monitoring change in patterns related to agricultural development and urban expansion in the desert of the Kom Ombo area. We utilized the available records of multitemporal Landsat Thematic Mapper and Enhanced Thematic Mapper Plus images to produce three land-use/land-cover maps for 1988, 1999 and 2008.

Post-classification change detection analysis shows that agricultural development increased by 39.2% through the study period with an average annual rate of land development of 8.7 km² year^?1. We report a total increase in urbanization over the selected time span of approximately 28.0 km² with most of this urban growth concentrated to the east of the Nile and occurring through encroachment on the former old cultivated lands. The archival record of the length of irrigation canals showed that their estimated length was 341.5, 461.8 and 580.1 km in the years 1988, 1999 and 2008, respectively, with a 70% increase in canal length from 1988 to 2008. Our results not only accurately quantified the land-cover changes but also delineated their spatial patterns, showing the efficiency of Landsat data in evaluating landscape dynamics over a particular time span. Such information is critical in making effective policies for efficient and sustainable natural resource management.     

Assessing long-term variations in sagebrush habitat – characterization of spatial extents and distribution patterns using multi-temporal satellite remote-sensing data

An approach that can generate sagebrush habitat change estimates for monitoring large-area sagebrush ecosystems has been developed and tested in southwestern Wyoming, USA. This prototype method uses a satellite-based image change detection algorithm and regression models to estimate sub-pixel percentage cover for five sagebrush habitat components: bare ground, herbaceous, litter, sagebrush and shrub. Landsat images from three different months in 1988, 1996 and 2006 were selected to identify potential landscape change during these time periods using change vector (CV) analysis incorporated with an image normalization algorithm. Regression tree (RT) models were used to estimate percentage cover for five components on all change areas identified in 1988 and 1996, using unchanged 2006 baseline data as training for both estimates. Over the entire study area (24 950 km²), a net increase of 98.83 km², or 0.7%, for bare ground was measured between 1988 and 2006. Over the same period, the other four components had net losses of 20.17 km², or 0.6%, for herbaceous vegetation; 30.16 km², or 0.7%, for litter; 32.81 km², or 1.5%, for sagebrush; and 33.34 km², or 1.2%, for shrubs. The overall accuracy for shrub vegetation change between 1988 and 2006 was 89.56%. Change patterns within sagebrush habitat components differ spatially and quantitatively from each other, potentially indicating unique responses by these components to disturbances imposed upon them.     

Object-based land cover change detection for cross-sensor images

Accurate and timely land cover change detection at regional and global scales is necessary for both natural resource management and global environmental change studies. Satellite remote sensing has been widely used in land cover change detection over the past three decades. The variety of satellites which have been launched for Earth Observation (EO) and the large volume of remotely sensed data archives acquired by different sensors provide a unique opportunity for land cover change detection. This article introduces an object-based land cover change detection approach for cross-sensor images. First, two images acquired by different sensors were stacked together and principal component analysis (PCA) was applied to the stacked data. Second, based on the Eigen values of the PCA transformation, six principal bands were selected for further image segmentation. Finally, a land cover change detection classification scheme was designed based on the land cover change patterns in the study area. An image–object classification was implemented to generate a land cover change map. The experiment was carried out using images acquired by Landsat 5 TM and IRS-P6 LISS3 over Daqing, China. The overall accuracy and kappa coefficient of the change map were 83.42% and 0.82, respectively. The results indicate that this is a promising approach to produce land cover change maps using cross-sensor images.     

Evaluation of MODIS gross primary productivity and land cover products for the humid tropics using oil palm trees in Peninsular Malaysia and Google Earth imagery

Conducting quantitative studies on the carbon balance or productivity of oil palm is important in understanding the role of this ecosystem in global climate change. In this study, we evaluated the accuracy of MODIS (Moderate Resolution Imaging Spectroradiometer) annual gross primary productivity (GPP) (the product termed MOD-17) and its upstream products, especially the MODIS land cover product (the product termed MOD-12). We used high-resolution Google Earth images to classify the land cover classes and their percentage cover within each 1 km spatial resolution MODIS pixel. We used field-based annual GPP for 2006 to estimate GPP for each pixel based on percentage cover. Both land cover and GPP were then compared to MODIS land cover and GPP products. The results show that for pure pixels that are 100% covered by mature oil palm trees, the RMSE (root mean square error) between MODIS and field-based annual GPP is 18%, and that this is increased to 27% for pixels containing mostly oil palm. Overall, for an area of about 42 km² the RMSE is 26%. We conclude that land cover classification (at 1 km resolution) is one of the main factors for the discrepancy between MODIS and field-based GPP. We also conclude that the accuracy of the MODIS GPP product could be improved significantly by using higher-resolution land cover maps.     

Applying a normalized ratio scale technique to assess influences of urban expansion on land surface temperature of the semi-arid city of Erbil

The difference between surface and air temperature within a city and its surrounding area is a result of variations in surface cover, thermal capacity, and 3-dimensional geometry. This research has examined and quantified the decreasing daytime land surface temperature (LST) in Erbil, Kurdistan region of Iraq, and the influence of rapid urban expansion on urban heat/cool island effect over a 20 year period. Land-use/land-cover change across this time period is also established using pixel samples. The current study proposes the application of the normalized ratio scale (NRS) to adjust the temperature of images acquired at different dates to the same range. Eleven satellite images acquired by Landsat 4, 5, 7, and 8 during the period 1992–2013 are used to retrieve LST. The results indicate that 55.3 km² of city land cover changed from bare soil to urban; consequently, the mean LST of the new urbanized area decreased by 2.28°C. The normalized difference vegetation index (NDVI) of Sami Abdul-Rahman (S.A.) Park increased from 0.09 ± 0.01 to 0.32 ± 0.11, resulting in a decrease of the mean LST by 7.29°C. This study shows that the NRS method is appropriate for detecting temperature trends from urbanization using remote-sensing data. It also highlights that urban expansion may lead to a decrease in daytime LST in drylands.     

Surveying sandy deserts and desertified lands in north‐western China by remote sensing

Sandy deserts and desertified lands (SDDL) cover most of north‐western China, and desertification is a severe environmental issue in this region. In this study, we classify SDDL into mobile, semi‐mobile, semi‐anchored, and anchored classes, and divide the corresponding severity of desertification into four levels: extremely severe, severe, moderate, and slight. Using SDDL databases derived from Landsat TM and ETM images in 1986 and 2000, we discuss the evolution of SDDL and the processes and causes of desertification. The desertified area increased by 16 101 km² between 1986 and 2000, and most of the desertified land was classified as severely or extremely severely desertified. However, 3437 km² of SDDL were also rehabilitated during this period. The area of SDDL increased in the Qinghai and Xinjiang regions, and in the western part of Inner Mongolia, but decreased in the Shaanxi, Gansu, and Ningxia regions. The causes of desertification differed among regions, and different measures to control desertification are proposed for the different regions.     

Guidance on and comparison of machine learning classifiers for Landsat-based land cover and land use mapping

Remote sensing scientists are increasingly adopting machine learning classifiers for land cover and land use (LCLU) mapping, but model selection, a critical step of the machine learning classification, has usually been ignored in the past research. In this paper, step-by-step guidance (for classifier training, model selection, and map production) with supervised learning model selection is first provided. Then, model selection is exhaustively applied to different machine learning (e.g. Artificial Neural Network (ANN), Decision Tree (DT), Support Vector Machine (SVM), and Random Forest (RF)) classifiers to identify optimal polynomial degree of input features (d) and hyperparameters with Landsat imagery of a study region in China and Ghana. We evaluated the map accuracy and computing time associated with different versions of machine learning classification software (i.e. ArcMap, ENVI, TerrSet, and R).

The optimal classifiers and their associated polynomial degree of input features and hyperparameters vary for the two image datasets that were tested. The optimum combination of d and hyperparameters for each type of classifier was used across software packages, but some classifiers (i.e. ENVI and TerrSet ANN) were customized due to the constraints of software packages. The LCLU map derived from ENVI SVM has the highest overall accuracy (72.6%) for the Ghana dataset, while the LCLU map derived from R DT has the highest overall accuracy (48.0%) for the FNNR dataset. All LCLU maps for the Ghana dataset are more accurate compared to those from the China dataset, likely due to more limited and uncertain training data for the China (FNNR) dataset. For the Ghana dataset, LCLU maps derived from tree-based classifiers (ArcMap RF, TerrSet DT, and R RF) routines are accurate, but these maps have artefacts resulting from model overfitting problems.     

Characterizing multi-decadal,annual land cover change dynamics in Houston,TX based on automated classification of Landsat imagery

In 2017, Hurricane Harvey caused substantial loss of life and property in the swiftly urbanizing region of Houston, TX. Now in its wake, researchers are tasked with investigating how to plan for and mitigate the impact of similar events in the future, despite expectations of increased storm intensity and frequency as well as accelerating urbanization trends. Critical to this task is the development of automated workflows for producing accurate and consistent land cover maps of sufficiently fine spatio-temporal resolution over large areas and long timespans. In this study, we developed an innovative automated classification algorithm that overcomes some of the traditional trade-offs between fine spatio-temporal resolution and extent – to produce a multi-scene, 30m annual land cover time series characterizing 21 years of land cover dynamics in the 35,000 km2 Greater Houston area. The ensemble algorithm takes advantage of the synergistic value of employing all acceptable Landsat imagery in a given year, using aggregate votes from the posterior predictive distributions of multiple image composites to mitigate against misclassifications in any one image, and fill gaps due to missing and contaminated data, such as those from clouds and cloud shadows. The procedure is fully automated, combining adaptive signature generalization and spatio-temporal stabilization for consistency across sensors and scenes. The land cover time series is validated using independent, multi-temporal fine-resolution imagery, achieving crisp overall accuracies between 78–86% and fuzzy overall accuracies between 91–94%. Validated maps and corresponding areal cover estimates corroborate what census and economic data from the Greater Houston area likewise indicate: rapid growth from 1997–2017, demonstrated by the conversion of 2,040 km² (± 400 km²) to developed land cover, 14% of which resulted from the conversion of wetlands. Beyond its implications for urbanization trends in Greater Houston, this study demonstrates the potential for automated approaches to quantifying large extent, fine resolution land cover change, as well as the added value of temporally-dense time series for characterizing higher-order spatio-temporal dynamics of land cover, including periodicity, abrupt transitions, and time lags from underlying demographic and socio-economic trends.     

Landscape changes of the Ejin Delta in the Heihe River Basin in Northwest China from 1930 to 2010

The Heihe River Basin is located in the arid and semi-arid region of Northwest China; during the past 80 years, this basin has experienced water resource competition between irrigation agriculture and ecological demand in its middle and lower reaches, respectively. The land cover of the Ejin Delta in the lower reaches of the Heihe River Basin was interpreted and analysed for four different periods using a map created by Dr Sven Hedin in the 1930s, Corona satellite images taken in 1961, and Landsat Thematic Mapper (TM) images taken in 2000 and 2010. Overall, the results show that (1) the coarse resolution of the 1930s map increased the uncertainty of analysis in the study area and (2) the river area in the Ejin Delta decreased by 91.0% from the 1930s to 2000. In addition, two major terminal lakes, Gaxun Nuur Lake and Sogo Nuur Lake, dried up in 1961 and 1992, respectively, and the area of Populus euphratica decreased by 76.1% from the 1930s to 2000. Most reeds were overtaken by shrubs between the 1930s and 1961, which caused the area of reeds to decrease from 3481 to 1332 km² and the area of shrubs to increase from 805 to 2795 km². From the 1930s to 2000, the desert and alkaline land areas increased by 42.2% and 52.4%, respectively. (3) After the water transfer project was implemented in 2000, the area of Sogo Nuur Lake recovered to 40.58 km² by 2010. The areas of Populus euphratica, shrubland, and reedland showed a recovering trend, with increases of 4.5%, 6.5%, and 43.5%, respectively, by 2010. The desert and alkaline land areas decreased by 4.2% and 15.2%, respectively, by 2010. The area of cultivated land increased from 25 km² in 1961 to 85 km² in 2000 and rapidly approached 160 km² in 2010. These changes over time indicated that the ecological habitat in the Ejin Delta deteriorated between the 1930s and 2000. However, the water transfer project effectively changed the degradation trend.     

Multi-temporal and multi-source cartography of the glacial cover of Nevado Coropuna (Arequipa,Peru) between 1955 and 2003

This study reports on the glacial cover evolution of the Nevado Coropuna between 1955 and 2003, based on Peruvian topographic maps and satellite images taken from the Landsat 2 and 5 multispectral scanner (MSS), Landsat 5 Thematic Mapper (TM) and Landsat 7 (ETM+). The normalized difference snow index has been applied to these images to estimate the glacierized area of Coropuna. The satellite-based results show that the glacier area was 105 ± 16 km² in 1975 (Landsat 2 MSS), which then reduced to 96 ± 15 km² in 1985 (Landsat 5 MSS), 64 ± 8 km² in 1996 (Landsat 5 TM) and 56 ± 6 km² in 2003 (Landsat 5 TM). Altogether, between 1955 and 2003, Coropuna lost 66 km² of its glacial cover, which represents a mean retreat of 1.4 km² year^?1, that is, a loss of 54% in 48 years (11% loss per decade). The maximum rate of retreat occurred during the 1980s and 1990s, a phenomenon probably linked with the pluviometric deficit of El Niño events of 1983 and 1992.     

Assessing changes of urban vegetation cover and aboveground carbon stocks using LiDAR and Landsat imagery data in Auckland,New Zealand

ABSTRACT

Urban vegetation can help to offset carbon emissions. However, urban vegetation cover is vulnerable to urbanization. This study attempts to detect the change in vegetation cover and to quantify its impact on aboveground carbon (AGC) stocks in Auckland, New Zealand, between 1989 and 2014. Field-measured vegetation parameters were used to calculate the amount of carbon stored in plants at the plot-level. Plot-level AGC stocks were linked with vegetation spectral/structural features derived from Landsat images and Light Detection and Ranging (LiDAR) data. These data were also used to map vegetation cover and to estimate AGC stock. Vegetation cover decreased from 394.0 km² in 1989 to 379.4 km² in 2014. AGC stock in 1989 was estimated at 1,001,184 Mg C from Landsat 4 data. The total AGC in 2014 was estimated at 1,459,530 Mg C from Landsat 8 data. Thus, total AGC stock increased by 458,346 Mg C (45.8%) in spite of a 3.7% decrease in vegetation cover (14.6 km²) during the same period. The increase in AGC stock was derived partly from tree growth and tree plantings. Vegetation growth contributed more to the increase in AGC stock than its gain from non-vegetation to vegetation changes. The AGC stored in trees and shrubs estimated at 1,333,011 Mg C from the 2014 Landsat data is 5.7% lower than 1,414,607 Mg C estimated from the 2013 LiDAR data, due to the inability of optical imagery to capture the sub-canopy structure of forests and the saturation effect. Thus, LiDAR data provided a more accurate estimate of AGC stock, especially when the stock density is high (e.g. >97.9 Mg C ha^–1).     

Recent land‐cover/use change associated with land degradation in the Lake Baringo catchment,Kenya, East Africa: evidence from Landsat TM and ETM+

Many parts of East Africa are experiencing dramatic changes in land‐cover/use at a variety of spatial and temporal scales, due to both climatic variability and human activities. Information about such changes is often required for planning, management, and conservation of natural resources. Several methods for land cover/change detection using Landsat TM/ETM+ imagery were employed for Lake Baringo catchment in Kenya, East Africa. The Lake Baringo catchment presents a good example of environments experiencing remarkable land cover change due to multiple causes. Both the NDVI differencing and post‐classification comparison effectively depicted the hotspots of land degradation and land cover/use change in the Lake Baringo catchment. Change‐detection analysis showed that the forest cover was the most affected, in some sections recording reductions of over 40% in a 14‐year period. Deforestation and subsequent land degradation have increased the sediment yield in the lake resulting in reduction in lake surface area by over 10% and increased turbidity confirmed by the statistically significant increase (t = ?84.699, p<0.001) in the albedo between 1986 and 2000. Although climatic variations may account for some of the changes in the lake catchment, most of the changes in land cover are inherently linked to mounting human and livestock population in the Lake Baringo catchment.     

Mapping forest disturbance across the China–Laos border using annual Landsat time series

The China–Laos border area is one of the world’s biodiversity hotspots and has undergone unprecedented social and economic shifts related to extensive land conversion to cash plantations in recent decades. However, spatially and temporally detailed information on land conversion and forest disturbance does not exist in this area. The aim of this study is to map and analyse spatiotemporal changes in forest disturbance from 1991 to 2016 along the China–Laos border using annual Landsat time series images. Landsat-based Detection of Trends in Disturbance and Recovery (LandTrendr), based on a temporal segmentation algorithm, was used with the Atmospherically Resistant Vegetation Index (ARVI) as a disturbance index in this study. The results show that the overall accuracy of forest disturbance is 89.72% ± 0.67% and that the estimated forest disturbance area between 1991 and 2016 reaches 4366.14 km² ± 887.17 km² (at the 95% confidence interval). This accounts for 16.73% of the total area of forest cover in 1991, which is based on the error-adjusted estimator of area. The trend in the forest disturbance area increased from 1991 to 1995 and then continued downward. The forest disturbance area across the China–Laos border is closely related to global rubber prices as well as the policies and economies of the two countries and cooperation between China and Laos. Compared to Laos, the percentage of disturbed forest area is higher within China, except for some individual years (e.g., 1998–1999, 2004–2005, 2009 and 2016). The average annual disturbed forest area is 98.44 km² (0.76%) within China and 69.49 km² (0.53%) within Laos. Large disturbed patches are much more common within China than within Laos. This study highlights the merit of using dense Landsat time series for mapping the human-induced processes of forest disturbance in tropical areas, and the role of economic globalization and regional geopolitics in cross-border forest management.     

Updating the 2001 National Land Cover Database land cover classification to 2006 by using Landsat imagery change detection methods

The recent release of the U.S. Geological Survey (USGS) National Land Cover Database (NLCD) 2001, which represents the nation's land cover status based on a nominal date of 2001, is widely used as a baseline for national land cover conditions. To enable the updating of this land cover information in a consistent and continuous manner, a prototype method was developed to update land cover by an individual Landsat path and row. This method updates NLCD 2001 to a nominal date of 2006 by using both Landsat imagery and data from NLCD 2001 as the baseline. Pairs of Landsat scenes in the same season in 2001 and 2006 were acquired according to satellite paths and rows and normalized to allow calculation of change vectors between the two dates. Conservative thresholds based on Anderson Level I land cover classes were used to segregate the change vectors and determine areas of change and no-change. Once change areas had been identified, land cover classifications at the full NLCD resolution for 2006 areas of change were completed by sampling from NLCD 2001 in unchanged areas. Methods were developed and tested across five Landsat path/row study sites that contain several metropolitan areas including Seattle, Washington; San Diego, California; Sioux Falls, South Dakota; Jackson, Mississippi; and Manchester, New Hampshire. Results from the five study areas show that the vast majority of land cover change was captured and updated with overall land cover classification accuracies of 78.32%, 87.5%, 88.57%, 78.36%, and 83.33% for these areas. The method optimizes mapping efficiency and has the potential to provide users a flexible method to generate updated land cover at national and regional scales by using NLCD 2001 as the baseline.