Introduction

The Sundarbans mangrove forests of Bangladesh are a large and intricate network of small alluvial islands formed by the deposition of sediments, which were transported down through the drainage basins of the Ganges, Brahmaputra and Meghna River systems (Gopal and Chauhan 2006). Deltaic erosion, accretion and morphological changes are continuously going on in the Sundarbans region (Ghosh et al. 2003). Innumerable tidal creeks and channels with diurnal flow reversal and rapidly changing landforms make this a dynamic delta. The changes in the morphology are principally driven by the variable supply of sediments, water and sea level change (Brammer et al. 1996).

From the perspective of geomorphology, characterizing the changes in a landscape or a terrain needs an exhaustive study based on the shape of the landmass under consideration. In this regard, shape analysis is one of the most crucial components used to recognize patterns (Backes et al. 2012) along with the processes which regulate such patterns of landscape change. The process describes the distinction between regularity and irregularity of such shapes. The prime objective of the shape analysis is not only to understand the spatial pattern of a geographical phenomenon and its possible cause but also to predict a probable future pattern (Wentz 1997). Shape index (SI), in terms of the magnitude of roundness of an object, is a statistical method to quantify shape of any unit of area.

In the geographic context, shape is often characterized through a compactness indicator, which describes the form of a given region or landmass based on the degree of its deviation from a specified norm (e.g. circle, square or triangle). The method for calculating this number utilizes one or more of the geometric parameters of the region being measured, such as area or perimeter (Wentz 2000). The surface of the earth and especially landforms are always changing due to the ever dynamic exogenetic forces contributing to the transformation of landforms. Due to this dynamism, the shapes of the landforms do not remain static beyond a specific time frame and hence give rise to the irregularity of shapes during the transformation process. This problem is resolved by means of fractal analysis which is perhaps the only known approach to unambiguously recognize edge roughness (Wentz 1997), and it has been utilized in the field of soil science, oceanography, earthquake, ecology and so forth (Okubo and Aki 1987; Isichenko and Kalda 1991; MacLennan et al. 1991). Fractal dimension (FD) of an object is a fundamental component of the object’s geometry, which is used to measure its irregularity, and it tells us how much of the space the object occupies. In general, a fractal object is considered to be composed of smaller objects having similar shape and/or edge like the bigger object, and this property of fractal geometry is known as self-similarity (Backes and Bruno 2008). In other words, the concept of fractal dimension takes into account this theory of self-similarity of an object with respect to its smaller components and finally tells us how much fragmented an object is. This aspect of irregularity is quantified by measuring the fractal dimension index (FDI). In the field of coastal geomorphology, it is applied to the border of the islands or simply the coastline.

The magnitude of the two above-mentioned indices and their temporal change provides us an insight into the region-specific geomorphic processes. However, it is not always practicable to generalize that certain range of FDI and SI would indirectly indicate exclusively one type of geomorphic phenomenon and vice versa, as the relationship between fractal dimension and geometric patterns of coastlines varies widely depending upon the local environmental factors like waves, rate of erosion, altitude and so forth (Dai et al. 2004; Schwimmer 2008). It has been a general perception that higher FDI values which indicate more fragmented coastlines are always more vulnerable to erosion and those having lower values are more stable; however, the geoenvironmental attributes that influence these shapes might not always regulate these features following such over-simplified apprehensions. While surveying crenulate-bay beaches, Dai et al. (2004) found coastlines having FDI higher than a certain threshold showed accretion and vice versa. The same fundamentals are equally applicable for analysing SI values; hence apart from the magnitudes, logical understanding of the local geomorphologic processes should be kept in mind before drawing any inferences.

The present study was carried out in the tidally influenced group of islands situated in the lower deltaic plain of Ganges–Brahmaputra–Meghna (GBM) delta in Bangladesh. Remotely sensed satellite data for the study area were obtained for the years 1989 and 2010. The FDI and SI values of the individual islands were computed for these two years along with their change in magnitude within this time period. The main objective of this study was to logically correlate the changes in magnitudes of FDI and SI and their spatial variability with the ongoing geomorphological changes in this area, so that in future, the regular monitoring of these indices can give us an insight about the fate of the shapes of these islands. Available literature does not indicate existence of similar studies in other deltas. However, apart from conventional change detection studies, this type of approach might reveal a holistic scenario.

Methodology

Study area

With the exception of a few areas in north and east, much of the People’s Republic of Bangladesh is within the low-lying flood plain of the Ganges–Brahmaputra delta. This delta is formed at the confluence of Ganges–Brahmaputra–Meghna (GBM) River system and their respective distributaries. The coastal zone of Bangladesh has been classified into three main regions, namely eastern, central and western regions (Islam 2001). The present study is focussed on the islands of the western coastal regions (Fig. 1). This zone receives a large volume of silt from the GBM basin. The sediment load comprises more than 70 % of the silt with additional 10 % sand (Sarwar 2005). The morphology of this zone is very dynamic due to huge river discharge and strong currents leading to high rates of erosion and accretion. Numerous islands are located in this region. Many islands were formed due to accretion, and many have disappeared in the last few years due to erosion. The western region is mainly covered by the Sundarbans mangrove forest. The main characteristics of this zone are mangrove swamps, tidal creeks and mud flats. Majority of this region lies at an elevation of 0.9 to 2.1 m above the mean sea level (Iftekhar and Islam 2004). Soil is mainly of silt loam or alluvial type. This region is very important from the perspective of tourism.

Fig. 1
figure 1

Study area showing the location map of the Bangladesh Sundarban

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Satellite data processing

Two satellite images of different times were considered in this study. Landsat TM-5 images of the year 1989 and the year 2010 (both the images were of the month of January), having 30-m spatial resolution, of the Bangladesh Sundarbans, were downloaded from the http://glovis.usgs.gov website. All the datasets were projected in UTM projection with zone number 45 and WGS 84 datum. The raster and vector data processing and statistical analysis that were implemented in the remote sensing and GIS environment are furnished in the flow chart (Fig. 2). Both the images were carefully selected such that the tidal conditions were almost similar; otherwise, it would have led to erroneous results. Atmospheric and topographic correction (ATCOR) method was used to eliminate atmospheric and illumination effect of the images by using the plug-in in the ERDAS IMAGINE software.

Fig. 2
figure 2

Methodological flow chart diagram

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The present study was not framed in accordance with the conventional approach generally adopted for normal change detection-related studies, where researchers usually try to delineate a trend over short-term temporal scale. In this study, our main objective was to correlate a long-term change in the 2D shape complexity dynamics with the changes observed in fractal dimension index (FDI) and shape index (SI). Our image selection was based upon satellite images with the least cloud cover, similar tidal conditions and belonging to the same time of the year. Due to these reasons, we have restricted our analysis to only two images.

Analysis of morphology of islands

The raster data format was changed to vector format by three successive stages. First stage was the manual digitization of the raw images capturing island coastlines. In the second stage, topology was built to enclose lines into polygons. In the third stage, creeks and landmass were separated for the two years. The polygons representing landmass were converted to raster format in order to use it as the input for fractal dimension and shape index calculations in Fragstats (version 4.1) software. Fractal dimension and shape index were calculated using Eqs. 1 and 2 (Jorge and Garcia 1997).

$$\text{Shape}\,\text{Index} \,\left( {SI} \right) = \frac{100 \times P}{{200 \times \sqrt {\pi \times A} }}$$
(1)

where ‘P’ is the perimeter of the polygon and ‘A’ is the polygon area. If the shape index value becomes 1.0, it expresses maximum compaction, where the shape is circular. As the shape becomes more complex, the SI increases. From the perspective of our study, it could be stated that the higher the SI values of the islands under investigation, the greater their deviation from roundness or circular shape. In other words, the islands whose SI values are nearer to unity (SI = 1) are more compact having lesser perimeter compared to area and in general considered to be more stable from the viewpoint of natural phenomenon like creek bifurcation and erosion; however, as mentioned earlier, it cannot be always generalized in this way. On the other hand, those having higher SI values signify that these islands are more expanded and/or patchy and normally they are more prone to land loss due to instability of the coastline.

$${\text{Fractal Dimension Index }}\left( {\text{FDI}} \right) = \frac{\text{logN}}{{{ \log }\frac{1}{\text{r}}}}$$
(2)

where ‘r’ is the self-similarity ratio and ‘N’ is the number of step size here. Self-similarity is a typical property of fractal geometry, according to which an object can be considered self-similar, if the entire object as a whole is exactly or partially similar to a part of itself (Mandelbrot 1983). It has been established by geomorphologists long ago that coastlines are statistically self-similar in nature (Madelbrot 1967). In Eq. (2), ‘r’ actually depicts the extent to which the smaller pieces of the coastline of individual islands are similar to the entire coastline of the respective islands. The computation of FDI uses the concept of hypothetical chord lengths (i.e. steps) and measures the number of such chord lengths required to cover an entire fractal curve. In other words, it utilizes the principle of taking rulers of varying size (step) to cover the curve and ‘N’ represents the number of rulers (here step size) required in each case (Annadhason 2012). FDI of a curve may be any value ranging from 1.0 to <2.0 for lines, and from 2.0 to <3.0 for surfaces. The higher the spatial complexity of a line or surface, the higher is its fractal dimension (Nayak 2008). From a geomorphological perception, higher FDI values signify that the coastline is more and more serrated, while lower values indicate much smoother and most essentially straighter coastlines. Mathematically, FDI value of 1.0 implies the limit of a smooth curve, while a FDI of 2.0 is the limit of a plane filling curve (Mandelbrot 1975). Plane filling curves are those complex self-intersecting curves which fill the plane without holes, hence rendering a complicated shape.

The relation between FDI and SI is analysed in terms of Pearson’s correlation coefficient to identify the relation between the shape and fractal geometry of the islands. The correlation between the two is tested to see whether magnitude of FDI indicating the degree of irregularity is proportional to the shape complexity of the deltaic islands denoted by SI values.

A separate change detection study using the satellite images of the same dates was conducted to identify where erosion was occurring and quantify change in area.

Measurement of sea surface height variation

The measurement of regional mean sea level and sea level anomaly was computed from satellite altimeter data of TOPEX (NASA-built Nadir Pointing Radar Altimeter using C band, 5.3 GHz, and Ku band, 13.6 GHz) and POSEIDON (CNES-built solid State Nadir pointing Radar Altimeter using Ku band, 13.65 GHz). The datasets were analysed for measuring sea surface height from the year 1993 to 2012. Inverted barometer correction was applied to improve the data quality (Dorandeu and Traon 1999).

Measurement of elevation

A Digital Elevation Model (DEM) of the study area was estimated based on the elevation data from the Survey of Bangladesh (SOB), Institute of Water Modelling (IWM), Govt. of Bangladesh and Centre for Environmental and Geographic Information Services (CEGIS), Bangladesh. This elevation data were interpolated using the inverse distance weighting interpolation method (Mukherjee et al. 2012). The vertical datum of the DEM is mean sea level, and horizontal datum is WGS 84.

Results and discussion

Statistical analysis of change in the morphology of islands

The entire descriptive statistics of the FDI and SI analysis carried out for the years 1989 and 2010 have been tabulated comprehensively in Table 1. The spatial distribution of FDI values for the year 1989 and 2010 and the difference in FDI values within this time frame are illustrated in Figs. 3 and 4, respectively. Similarly, the spatial distribution of SI values for the year 1989 and 2010 along with their difference is illustrated in Figs. 5 and 6, respectively. The spatial distribution maps of both FDI and SI were classified into four different sectors, namely low, moderate, high and very high values. The maps illustrating the difference between the years 1989 and 2010 were classified into two classes, one portraying those areas where the respective parameters increased in the year 2010 and the other showing those areas where it decreased. It can be seen from these maps that both fractal dimension and shape index increased in the upper part, i.e. the northern end of the Bangladesh Sundarbans, while in the southern part both the indices decreased during the study period.

Table 1 Comparative analysis of fractal dimension index (FDI) and shape index (SI) of the Bangladesh Sundarbans for the year 1989 and the year 2010
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Fig. 3
figure 3

Spatial variability of FDI of all the islands of Bangladesh Sundarbans in the year a 1989 and b 2010

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Fig. 4
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Spatial distribution of the increased and decreased FDI values in the year 2010 compared to the year 1989

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Fig. 5
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Spatial variability of SI of all the islands of Bangladesh Sundarbans in the year a 1989 and b 2010

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Fig. 6
figure 6

Spatial distribution of the increased and decreased SI values in the year 2010 compared to the year 1989

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In order to quantify the change in magnitude of both FDI and SI, the Bangladesh Sundarbans were divided into northern and southern sectors at the 22°05′N latitude. In the northern sector, the mean FDI was 1.165 in 1989 and increased to 1.187 in 2010, while in the southern sector the mean FDI decreased from 1.158 to 1.145 during the same period. Similar observations were found for SI. In 1989, mean SI in the northern sector was 4.579 and increased to 4.761 in 2010. In the southern sector, it decreased from 4.078 to 3.583 during the same period. Thus, the mean value of FDI increased in the northern sector by 0.022, while in the southern sector it decreased by 0.013 (p < 0.05). Similarly, the mean SI in the northern sector increased by 0.182 and in the southern sector it decreased by 0.495 (p < 0.05).

The higher FDI values unambiguously suggest that the coastlines are elongated and more serrated, and it was observed by juxtaposing Figs. 3 and 4 that in most of the cases, the increase in FDI was found to take place in those areas that already had higher FDI values. Thus, serrated coastlines in the northern part of the Bangladesh Sundarbans became more serrated within the period of this study. On the contrary, coastlines with low-to-moderate FDI values showed a decrease in FDI and SI within the same period. This suggests that comparatively smoother coastlines in the central and southern parts of the Sundarbans are becoming more rounded. It is worth mentioning that the islands situated in the upper/northern parts of the Sundarbans and their coastlines are mainly influenced by the inner estuarine water mass where the impact of waves on the coastline is not so strong. In the southern end, the impact of sea waves on the coastline is quite pronounced. These islands in turn exhibited sharp drop in SI values as wave action, wave refraction and the corresponding erosion might have been the principal cause of smoothening their seaward faces. These southern islands suffered substantial land loss, as deciphered from the multi-temporal satellite data analysis. If we critically examine the shape of the sea facing islands, it is clearly visible that the sea facing parts of these islands are sufficiently round shaped (i.e. the SI values are attaining close to unity). On the other hand, the physical basis behind the higher FDI values in the northern part could be justified by the fact that the coastal edges of these islands experience incoming as well as receding tides daily instead of strong sea waves. In these areas, the effect of tidal water, particularly during ebb flow, is more predominant, which may give rise to more serrated features in the coastline and hence in turn increase the FDI and SI values. The daily incoming and receding tidal water rich in total suspended solid washes the coastlines and while retreating makes the coastal surface rough and serrated. It was observed that islands situated in the northern and north-eastern parts of the island system with FDI magnitudes in the range of 1.18–1.21 are more prone to becoming serrated at their edges due to intense tidal drag during the ebb flow. Islands with FDI values in the range of 1.03–1.18 in the southern part are more prone to have smoother edges due to strong wave impacts. Hence, it can be seen that 1.18 is a critical FDI value of this island system where majority of the islands having FDI more than 1.18 (in the year 1989) showed a tendency to become more serrated in the coastal boundary, while those having an FDI below 1.18 are becoming more smooth and rounded. However, some exceptions were also noted especially in the north-eastern part where islands having FDI <1.18 also showed a substantial increase in FDI. Such critical values were also observed to exist in similar studies (Dai et al. 2004; Morais et al. 2011). Similarly, Gao et al. (2011) observed different FDI values for different types of shorelines throughout China.

Correlation between FDI and SI

Scatter plots of FDI against SI for 1989 and 2010 both showed a strong positive relation. The goodness of fit of the curves (in terms of R2 values) was almost same in both the years (0.97). A logarithmic curve was found best to describe the relation between these two parameters. This strong positive response in both the years having a time gap of two decades showed that these two parameters varied hand in hand in case of all the respective islands. This means that the ongoing natural geomorphic process in this region affects the FDI and SI in the same pattern (Fig. 7). This observation might be attributed to the fact that the roundness is also lost in the places where the coastlines are more serrated due to the ebb flow (i.e. increased FDI), as the edges are incised due to either creek encroachment or inundation. Thus, the SI values in such places increased. The reverse scenario also prevailed in regions where intense wave action reshapes the coastline causing the island shapes to approach near roundness. The waves of strong but uniform thrust in these places make the coastline homogeneous, and the FDI values also get reduced. The FDI was found to have such correlation with SI due to these simultaneous events taking place.

Fig. 7
figure 7

Relation between fractal dimension index (FDI) and shape index (SI) for the year a 1989 and b 2010

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The causal factor of shape dynamics

There are several factors that can contribute to the alteration of shape complexity. In order to find the root cause of the shape dynamics of this island region, two main exogenetic factors were examined on spatio-temporal basis: one being the topographic elevation of the terrain and the other being the rate of sea level change. The elevation map of the Bangladesh Sundarbans clearly depicts that in the northern and north-eastern parts of the mangrove forest, the elevation was substantially lower with respect to the other regions (Fig. 8). Upon overlaying the maps of FDI and SI change over the two decades over this elevation map, it can be seen that places having a low elevation have undergone an increase in FDI and SI, while in the southern end and central parts where the elevation is comparatively higher, a reverse trend of decrease in FDI and SI was observed. The fractal dimension, on the contrary, marginally decreased in those areas which were comparatively more elevated amongst the islands. In contrast to the low-lying islands, where water can encroach from any direction and impart an irregular shape, relatively higher elevation seems to have restricted the ingress of water and its spread. This in turn smoothed the existing boundaries of the island coasts leading to a slight decrease in the fractal dimension. Shape and coastal configuration of islands depend upon dynamic interaction of land and sea. This can be affected by rising level of water, subsidence of islands or incursion of sea water within islands. The evaluation of the change in sea surface height from the remotely sensed data in the Bay of Bengal waters lying adjacent to the Bangladesh Sundarbans portrayed a small increase in regional sea level during the study time frame at a rate of 3.4 mm year−1 (Fig. 9). However, during the same time frame, coastal stations of Bangladesh recorded 4–8 mm/year of relative sea level rise in the inner estuarine stations (Pethick 1984; Alam 2003; Pethick and Orford 2013). Local subsidence or global warming; whatever be the reason behind such an increase, it is clear that places having lower elevation will be affected the most. As a result, a number of small islands may form in such regions of low elevation at the expense of a bigger island under intense ebb tidal action with rising sea level. It appears that with an increasing sea level, the low-lying deltaic islands of Bangladesh are becoming more complex in shape along with higher fractal dimension and shape index as well. However, the islands at a comparatively higher elevation though situated closer to the sea show an opposite trend. It was computed from the overlay of images of the study period that the mangrove island system of the Sundarbans in Bangladesh recorded a land loss of 130 km2 with accretion of 70 km2 resulting in net land loss of 60 km2 (Fig. 10).

Fig. 8
figure 8

Map showing spatial distribution of the elevation of the Bangladesh Sundarban

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Fig. 9
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Rate of change of regional sea level change between the year 1993 and 2012

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Fig. 10
figure 10

Map showing the places where erosion took place between the years 1989 and 2010

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Implications of the present findings

It has been a general perception while dealing with deltaic geomorphology that erosion activity is supposed to be highest in the sea facing end where intense wave action along with the wind driven forces collide with the land mass. Hence, it is taken into consideration that these places undergo severe habitat loss and are most susceptible to natural degradation driven by the physical forces. The present study also confirms such activity, but at the same time it indicates a reduction in fractal dimension. On the contrary, an increase in the FDI as well as in SI was found to take place in the inner estuarine parts of the Bangladesh Sundarbans compared to the ones situated close to the sea. This gives rise to a serious concern, as the present findings imply that the dense forest cover in the inner parts is likely to be most affected in the near future. Since the elevation of these regions is low, rising sea level would lead to an encroachment of saline water into these sectors which in turn would seriously affect the species composition and the overall structure of the mangrove forest. Increase in FDI and SI implies that island coastlines in these regions are becoming more complex and serrated at their edges. It is also observed that the serrated coastlines of the northern islands are becoming more uneven, which in turn would facilitate more water encroachment through creeks and channels. The mangroves which grow better in higher terrains without coming in direct contact with the highly saline water mass will be severely affected due to such water movement. Water intrusion would not only affect the forest but also the population residing in the buffer regions and the adjoining settlements. The ecosystem services of these mangrove forest regions will be severely hampered. Change in shape complexity and water encroachment could damage several temporary fringe settlements in the near future. On the other hand in the southern islands, though the FDI and SI values decreased, the main driver behind such a decrease was found to be the impact of the oceanic waves on the coastal margin, which in turn eroded the landmass in such a manner that the shape of the southern borders became compact. Change detection analysis showed that these parts underwent severe erosion which again led to loss of mangroves. Thus, it can be summed up that both the increase and decrease of FDI values in the northern and southern parts, respectively, are becoming unfavourable to mangrove stands: in the northern part due to water intrusion in the low-lying areas and in the south due to erosion.

Conclusion

From the present study, it can be concluded that the islands of the Bangladesh Sundarbans situated at the lower deltaic plain of the Ganges–Meghna–Brahmaputra Rivers showed spatially varying trends, both in terms of edge roughness and irregularity of the islands. Fractal dimension index (FDI) and shape index (SI) for these islands were computed in this study for the years 1989 and 2010. An increase in both FDI and SI was observed in the year 2010 compared to that of 1989 in the northern and north-eastern parts of the mangrove forest, while a reverse trend was observed for the rest of the area, where both decreased with time. Majority of the islands having an FDI value more than 1.18 were found to be more prone to becoming serrated in their edges due to erosion activities, and those having FDI values lower than 1.18 showed a tendency to get smoothened at their edges due to intense wave action, though there were few exceptional cases. Amongst the several possible factors behind such an increase in shape complexity, two factors, namely elevation of the terrain and regional sea level rise, might be responsible. It was observed that the elevation was substantially low in those areas where FDI and SI increased. During the same period, sea level and tidal actions increased considerably in this region resulting in a loss of more than 60 km2 land area. The physical difference in the land–water interaction occurring in the northern and southern islands might be responsible for the difference in FDI and SI values. The tidal wash is making the northern coastlines more serrated (leading to higher FDIs and SIs), while the powerful wave action is responsible for smoothening the sea faces of the southern islands accompanied by erosion (leading to lower FDIs and SIs). The altered complexity of islands along with forest area loss would imply loss of ecosystem services of the mangrove under the scenario of climate change and sea level rise. However, it is worth mentioning that results of FDI and SI computation vary over temporal scales. Hence, the observation and conclusion is valid only for the existing scale over which the study was carried out. Further studies will be required to validate the observation in various spatio-temporal scales in the deltaic islands. The present endeavour can be categorized as a new type of approach based on a well-established technique. Hence, the method described here can be applied to other tide dominated deltas like the Indian Sundarban, Ayeyarwardy, Nile, Mahakam, Mekong and so forth. The study of fractal dimensions of coastal tracts of different types of delta systems (river/wave/tide dominated) may open up new dimensions of research relating the responses of a delta system towards sea level rise and other environmental changes.