Land Change Dynamics: Insights from Intensity Analysis Applied to an African Emerging City 1 Felicia O. Akinyemia*, Robert Gilmore Pontius Jrb and Ademola K. Braimohc a School of Architecture and The Built Environment, University of Rwanda, Kigali, Rwanda; bSchool of Geography, Clark University, Worcester MA, USA rpontius@clarku.edu; cWorld Bank, Washington DC, USA abraimoh@worldbank.org *Corresponding author. Email: felicia.akinyemi@gmail.com 1 Felicia O. Akinyemi is currently based at Earth and Environmental Science Department, College of Sciences, Botswana International University of Science and Technology, Private Bag 16, Palapye, Botswana. Land Change Dynamics: Insights from Intensity Analysis Applied to an African Emerging City Land change in Kigali, Rwanda is examined using Intensity Analysis, whichmeasures the temporal stationarity of changes among categories. Maps for 1981, 2002 and 2014 were produced that show the land categories Built, Vegetated, and Other, which is comprised mainly of croplands and bare surfaces. Land change accelerated from the first time interval (1981-2002) to the second time interval (2002-2014), as increased human and economic activities drove land transformation. During the first interval, Vegetated showed net loss whereas Built showed net gain, in spite of a small transition directly from Vegetated to Built. During the second interval, Vegetated showed net gain whereas Built showed nearly equal amounts of gross loss and gross gain. The gain of Built targeted Other during both time intervals. A substantial portion of overall change during both time intervals consisted of simultaneous transitions from Vegetated to Other in some locations and from Other to Vegetated in other locations. Keywords: Land change; Intensity Analysis; transition; category; stationary; urbanization challenges, particularly the impact of 1. Introduction urbanization on the local environment The examination of land change is (Organization for Economic Cooperation increasingly important as human and Development 2011, Creutzig et al. activities modify ecosystems in urban 2015). Changes to tropical landscapes, areas (Stow and Chen 2002, Grimm et particularly changes involving al. 2008, Liu and Weng 2013, Liu and urbanization and losses of forest are Yang 2015). Urban systems worldwide increasingly of interest (Guild et al. are facing an increasing number of 2004, Liu and Yang 2015). Urbanization There is a need for greater is an important driver of economic, consideration of emerging cities in social and environmental change, in Africa, because projected growth of developing countries such as those of global urban population is expected to sub-Saharan Africa (Hall and Pfeiffer occur mostly in African cities (Mega 2000, Satterthwaite 2009, Simone and 2016, Cobbinah and Darkwah 2016). Leck 2010, Seto et al. 2012). These cities need better approaches to There is a call for research to facilitate planning for expansion, examine the environmental impact due services and sustainability (United to urbanization in Africa, where the Nations Population Fund 2007). For share of population living in urban areas many cities in Africa, the rate of is projected to grow from 36 to 54 per urbanization overwhelms the governance cent between 2010 and 2050 (Parnell capacity, resulting in substantial and Walawege 2011, Kilcullen et al. environmentally inefficient spatial 2015). With proper management, sub- configurations (Njoroge et al. 2013). Saharan Africa’s high rate of Fast growing populations, inadequate urbanization at 4.5 per cent annually, can infrastructure and weak management can result in economic development, growth, have detrimental consequences for these and poverty reduction. Otherwise, cities, depending on the pattern of inequality, poverty and slums will change (Parnell and Walawege 2011). increase (World Bank 2010). This article examines the patterns, i.e. the spatial and temporal Journal of Spatial Science configuration, of land change in an Analysis framework (Aldwaik and African urban context in order to detect Pontius 2012, 2013). This paper the principal signals of such changes. illustrates the proper application and Linking land change patterns to the interpretation of Intensity Analysis for processes underlying the change helps to an important African city. The case understand the mechanisms of change, to study is Kigali, Rwanda, which is one of aid the generation of predictions about Africa’s emerging cities with a million future rates of change, and to facilitate or more inhabitants. policy design in response to the change. 2. Study Area Understanding land use-land cover change (LULCC) patterns and processes Figure 1 shows the location of Rwanda, is fundamental in investigating the which is a landlocked country in East complex interactions between humans Africa, situated between 1o04′ - 2 o51′ S and the environment from local to global and 28 o53′ - 30 o53′ E. Rwanda shares scales (Aldwaik and Pontius 2012). borders with Uganda to the north, Mapping of LULCC reveals the relative Democratic Republic of Congo to the amounts of land under various land west, Burundi to the south and Tanzania categories. to the east . Set amongst the undulating This study takes a subsequent mountains of the Albertine branch of the step beyond mapping to quantify the East African Rift, it is referred to as the dynamics of land change during two land of a thousand hills to reflect its hilly time intervals by using the Intensity nature (National Institute of Statistics Rwanda – NISR 2008, Warnest et al. Vegetation on marginal lands is cleared 2012). to meet increasing land demand for [Insert figure 1 here.] commercial, residential and agricultural Rwanda is fast reinventing itself to uses. Originally heavily forested, Kigali becoming a regional Information and has only 77 square kilometres of forests, Communication Technology hub i.e. 10.6 per cent of total area as of 2012. (Warnest et al. 2012). The government Estimates for other land types such as has emphasized the importance of agriculture, built-up and wetlands are clarifying land rights to forestall land 60.5, 16.3 and 12.5 per cent respectively related conflicts and to promote (Surbana 2012). Forest cover in Kigali is structural transformation (Ali et al. to be increased to 30 per cent of total 2014). area by afforesting slopes greater than 60 per cent in an effort to increase forest With 10.5 million inhabitants and cover nationwide according to the 25 thousand square kilometres of land, Rwandan Vision 2020 target (City of Rwanda is densely populated, having Kigali – CoK 2012). 416 persons per square kilometre as of 2012. The capital city Kigali has a population density of 1,556 persons per 3. Methods square kilometre (NISR 2012). Data Available land is subject to land degradation because of the steep slopes Land cover was analysed at three time on the mountainous landscape. points by classifying three Landsat Journal of Spatial Science scenes from path 172 and row 61: The 33-year duration under study Landsat 3 Multispectral Scanner (MSS) includes important periods in Rwanda’s scene from 20 September 1981, Landsat history. These are pre-genocide (1981- 7 Enhanced Thematic Mapper Plus 1993), genocide (1994) and post-conflict (ETM+) scene from 17 August 2002, (1995-2014). and Landsat 8 Operational Land Imager Image processing (OLI) scene from 14 January 2014. All Landsat images were re-projected to These image scenes were selected for the Rwandan system (projection: use in this study for two main reasons. Transverse Mercator, Spheroid: Clarke First, they were mostly cloud free. 1880, Datum: Arc 1960), as was used for Secondly, they were for the same season, datasets prior to 2009. The three images i.e. dry season, in order to minimize were subset using the Kigali boundary. seasonal influence on the classification For the image classification, we results. All Landsat images were created colour infrared (CIR) composite downloaded from the United States images for each time point. The Geological Survey website supervised image classification approach (http://eros.usgs.gov/). Orthophotos of was used by applying the maximum 2008 at a resolution of 25 cm and likelihood classifier algorithm. The topographic map of 1988 were used for classification scheme has three land delimiting training sites on the satellite categories: Built, Vegetated and Other. images. Built comprises land used primarily for residential, commercial, industrial purposes as well as indicate true change, as opposed to map recreational facilities, roads and errors. government infrastructure. The Precise errors in the three maps Vegetated category comprises forests, are un-measurable, due to lack of ground savannahs, grasses and extensive information. This situation is common, wetlands such as Gikondo, and especially when the maps derive from Nyabugogo wetlands with vegetation the distant past, for which it is mostly made up of Cyperus Papyrus and impossible to obtain ground information Pennisetum. The Other category (Enaruvbe and Pontius 2015). captures mainly croplands and includes After map creation, the post- some bare surfaces. Agricultural lands classification bi-temporal change and bare surfaces were included in the detection method was used (Jonckheere Other category because their spectral et al. 2004) to compute change in land signatures are similar during some cover for two time intervals, 1981-2002 seasons. For example, farmland appears and 2002-2014. bare before germination and after Intensity Analysis harvest. We used these three broad categories, as opposed to a larger The sizes of land transitions can be seen number of more detailed categories, in in the traditional transition matrix, order to increase the likelihood that however, deeper examination is differences between the time points required to link patterns with processes (Zaehringer et al. 2015). Intensity Journal of Spatial Science Analysis is a collection of related intensity among categories within each approaches that facilitate deeper time interval. The transition level examination. Intensity Analysis is an describes the variation in intensity with accounting framework to describe the which the gain of a particular category behaviour of a categorical variable transitions from other categories within across time intervals and to measure the each time interval (Aldwaik and Pontius degree to which changes are non- 2012, 2013). uniform at various levels of detail Our analysis uses five equations (Aldwaik and Pontius 2012, Enaruvbe with notation as shown in Table 1 and Pontius 2015). Intensity Analysis is following Aldwaik and Pontius (2012). important because it is useful to know Insert Table 1 here whether an observed transition from one Equation 1 gives the speed of change category to another deviates from an during an interval, which is the size of apparently uniform process . the change divided by the duration of the Intensity Analysis has three time interval expressed as a per cent of levels: the interval level, the category the spatial extent. Equation 2 gives a level and the transition level. The category’s annual gross loss intensity interval level compares the overall during an interval, which is the size of change during one interval to the overall the category’s annual gross loss divided change during other interval(s). The by the size of the category at the initial category level describes the variation in time point of the interval. Equation 3 gross loss intensity and gross gain gives a category’s annual gross gain intensity during an interval, which is the size of the category’s annual gross gain (2) divided by the size of the category at the latter time point of the interval. The uniform hypothesis at the category level (3) for each interval is that all categories experience gross loss and gross gain with the same annual intensity, which is equal to the speed of change during the (4) interval, i.e. St. If Lti < St, then the loss of i is dormant during interval t; similarly if (5) Gtj < St, then the gain of j is dormant during interval t. If Lti > St, then the loss Equation 4 gives the transition of i is active during interval t; similarly intensity of the gain of a particular if Gtj > St, then the gain of j is active category n from another category i, during interval t. which is the size of the annual transition to the particular category n from the other category divided by the size of the (1) other category at the initial time point of the interval. The uniform hypothesis at the transition level for each interval is that the particular category n transitions Journal of Spatial Science to all other categories with the same 4. Results annual intensity, which equation 5 gives Land cover mapping as the size of the annual gain of category Figure 2 shows the maps of the three n divided by the sum of the sizes of all time points for Built, Vegetated and the other categories at the initial time Other. The pie charts in Figure 2 depict point of the interval. If Rtin < Wtn, then the share of land under each land the gain of n avoids i during interval t. If category with Other having the largest Rtin > Wtn, then the gain of n targets i share for all time points. The change during interval t. maps of losses and gains show where Aldwaik and Pontius (2012, losses and gains occurred during each 2013) and Pontius et al. (2013) give time interval. extensive description of Intensity [Insert figure 2 here] Analysis. Some case studies where Intensity Analysis was applied are Southern Nigeria (Enaruvbe and Pontius 2015), Southeast China (Zhou et al. 2014), New South Wales, Australia Change budget (Manandhar et al. 2010) and Southwest Ghana (Alo and Pontius 2008). Figure 3 shows the gain, persistence and loss for each of the land categories, for each time interval. [Insert figure 3 here.] The size of a category at the initial time area of each transition, including annual point of an interval is the union of the losses and annual gains of each category, persistence and loss for that category, including annual overall change whereas the size of a category at the (Runfola and Pontius 2013). Table 2 latter time point of an interval is the shows the flow matrix for both time union of its persistence and gain (Pontius intervals. The overall change accelerated et al. 2013). Built is a net gaining from 16.3 to 25.1 square kilometres per category during the first time interval, year from the first time interval to the and a net losing category during the second time interval. The largest annual second time interval. Vegetated is a net transitions are a pair of simultaneous losing category during the first time transitions from Vegetated to Other at interval, and a net gaining category some locations and from Other to during the second time interval. Other is Vegetated at other locations. a net losing category during both time “Exchange” is the word to describe such intervals. a pair of transitions (Pontius and Santacruz 2014). Flow matrix Insert Table 2 here A flow matrix expresses annual land transitions during a time interval, with Intensity analysis each interval’s initial time in the rows Category level intensity and each interval’s latter time in the Figure 4 shows the category level columns. A flow matrix gives the annual intensities concerning losses and gains. Journal of Spatial Science The gain intensity and loss intensity of If a bar extends beyond the uniform line, each category are compared to the then the category’s gain targets the overall intensity of change in the entire losing category, whereas if a bar stops study area, as indicated by the straight before the uniform line, then the uniform line. If a category’s bar extends category’s gain avoids the losing beyond the uniform line, then the gain or category. All transitions are stationary in loss intensity for that category is active, the respect that for both time intervals: whereas if a bar ends before the uniform 1) the gain of Built targets Other and line, then the intensity is dormant. avoids Vegetated, 2) the gain of [Insert figure 4 here.] Vegetated targets Other and avoids During the first interval, Built is Built, and 3) the gain of Other targets an active gainer and dormant loser, Vegetated and avoids Built. while Vegetated is an active loser and a [Insert figure 5 here.] dormant gainer. During the second time interval, Built and Vegetated are active 5. Discussion in terms of both gains and losses. The Other category is a dormant gainer and Time interval level loser during both time intervals. Overall land change was slower during the first time interval (1981-2002) than Transition level intensity during the second time interval (2002- Figure 5 shows the intensities of the 2014). This acceleration of land change observed transitions given the gains of is consistent with the government’s drive each category for both time intervals. for economic growth as Rwanda had a lost the social bonds needed to resettle in sustained economic growth of 7 - 8 per the countryside. Between 2006 and cent over the last decade (Warnest et al. 2011, Kigali was the destination for 58 2012). This fast paced national per cent of rural to urban migrants development drives land transformations within Rwanda (Rwanda Environment as human and economic activities Management Authority - REMA 2013). increase. Built also experienced loss during the second time interval, which Category level reflects efforts by the city to reduce During both time intervals, Built is an unplanned, informal housing by active gainer, which can be explained by relocating unplanned communities from increasing land demand for construction steep slopes (CoK 2013). About 19 per and the subsequent conversion to Built. cent of the city is built on marginal lands This pressure results from Kigali’s which are not suitable for development increasing population due to high birth (Kigali City Council 2007). Examples rates and high levels of positive net are wetlands and steep slopes, some of migration. Kigali’s population was 6 000 which are currently being restored with at independence in 1962, 765 325 vegetation. As of 2013, 62.5 per cent of by 2002 and 1 135 428 in 2012. the population of Kigali lived in Recently, Rwandans living in other informal housing (CoK 2013). Since countries started returning to the 2005, people were relocated into country. Most prefer to live in urban clustered settlements as Rwanda areas such as Kigali as some might have Journal of Spatial Science implemented Umurenge, which is impact of relative peace during the Rwanda’s programme for settlement second time interval. Ndayambaje and consolidation under its Vision 2020. Mohren (2011), Basnet and Vodacek This programme is aimed at improving (2015) note how social conflict caused living standards by service provision forest loss in this region during some (REMA 2013). years of the first time interval. Vegetated The Vegetated category losses are due mainly to the conversion experienced active gains and losses from forests to cultivated lands to meet during the second time interval. The increasing demand for agricultural gains are mainly due to ongoing efforts production. Moreover, wetlands were to restore degraded forests and wetlands converted into livestock grazing and as well as regrowth on previously crop cultivation. Crops grown are mostly cleared areas. Persistence of Vegetated is sugarcane, rice, flowers and sweet mainly attributed to the preservation of potatoes. Studies in the region existing forests, as well as improved corroborate this finding that agricultural management of existing timber lands are expanding at the expense of plantations and woodlots (Ministry of forests, savannas and wetlands (Wasige Natural Resources – MINIRENA 2014). et al. 2013, Basnet and Vodacek 2015). The flow matrix in Table 2 Since 2010, the use of wetlands shows deceleration of Vegetated loss are regulated by laws to varying degrees from the first to the second time interval, to minimise vegetation loss. The use of which can be explained partly by the each wetland can be classified as permissive unconditional exploitation, type of the large dormant category conditional exploitation, or total phenomenon (Pontius et al. 2013, Zhou protection. Irrespective of the protection et al. 2014). Gains made by Other are status, a range of activities are prohibited due partly to the conversion from in the country’s wetlands including wetlands to agriculture, which is in line construction of buildings and sewage with the findings of Kasangaki (2013). treatment plants, dumping of hazardous Agricultural activities are taking place in waste and untreated waste water. 39 per cent of wetlands in Kigali Furthermore, a 20 metre construction- (REMA (2013). This may be attributed free buffer zone is created around all to the fact that agriculture is traditionally swamps. The government’s zero-grazing the major employment sector of the city policy is also being enforced to reduce (24%), compared to financial services vegetation loss (MINIRENA 2008, (21%) and trade (20%) (REMA 2013). REMA 2011). The promotion of urban and peri-urban The Other category is dormant in agriculture is also contributing to gains gains and losses during both time of Other. The Kigali Urban and Peri- intervals and accounts for the majority of Urban Agriculture Project and the Gako the spatial extent at the three time points. Organic Farming Training Centre are Other is dormant in part because of its examples of urban farming projects. large size, while Other is still involved in Loss of Other may reflect the crop a substantial amount of change (Figure fallow cycle associated with traditional 3). The Other category illustrates one Journal of Spatial Science farming, as fallow would appear Currently, the Forest Landscape Vegetated. Restoration policy is being implemented in Rwanda with the aims of protecting Transition level existing forests and restoring degraded The transition level analysis reveals that lands through afforestation (MINIRENA all transitions are stationary, meaning 2014). The gain of Other targets that the patterns during the first time Vegetated and avoids Built, because it is interval are the same as during the easier to expand cultivation from second time interval. For example, the Vegetated than from Built. gain of Built targets Other and avoids Next steps Vegetated. This is partly explained by Our results suggests that there might be the fact that most land under Vegetated a two-step temporal transition from is protected, thus leaving Other as the Vegetated to Other to Built. This category available for conversion to transition describes a change pattern Built. The gain of Vegetated targets whereby Vegetated land transitions first Other and avoids Built perhaps because into Other before transitioning to Built. vegetation can grow easily on vacant We plan to develop methods to detect land and people are reluctant to abandon such a pattern across three time points. If the Built land. such a pattern exists, then knowledge of Two targeting transitions from its existence might be useful to project Other to Built and from Other to land change and to understand the link Vegetated are in line with policy. between pattern and process. This research agenda extends the associated with the high growth examination of the environmental impact economy that Rwanda experienced of urbanization in Africa, in line with during the early 2000s. The first time Parnell and Walawege (2011). If land interval shows net loss of Vegetated and change patterns are not adequately net gain of Built. The second time linked to processes, then research interval shows net gain of Vegetated and concerning urbanization in African cities almost zero net change in Built. The will be limited. annual loss by Vegetated was higher during the first time interval than during 6. Conclusions the second time interval perhaps because Intensity Analysis was used as a of the impacts of civil conflicts on unifying framework to analyse the forests during the 1990s and of recent dynamics of land change in Kigali, efforts at forest conservation. Rwanda. Working at three levels, i.e. the The two time intervals also have interval, category and transition levels, remarkable similarities. For example, we measured the temporal stationarity of Built is active in gains, Vegetated is changes among three land categories: active in losses, Other is dormant in both Built, Vegetated, and Other. gains and losses. The gain of Built The two time intervals have targeted Other, the gain of Vegetated important differences. Overall land targeted Other, and the gain of Other change accelerated from the first time targeted Vegetated. The largest changes interval 1981-2002 to the second time during both intervals are a transition interval 2002-2014. The acceleration is Journal of Spatial Science from Other to Built, and an exchange impacts of land tenure regularization in Africa: Pilot evidence from due to simultaneous transitions from Rwanda. Journal of Development Economics, 110, 262 - 275. Vegetated to Other in some locations Alo, C.A. and Pontius, R.G., Jr. (2008). Identifying systematic land-cover and Other to Vegetated in other transitions using remote sensing and GIS: The fate of forests inside and locations. Most of these land change outside protected areas of Southwestern Ghana. Environment patterns are stationary over the 33-year and Planning B: Planning and Design, 35, 280 - 295. temporal extent in spite of Rwanda’s doi:10.1068/b32091 Basnet, B. and Vodacek, A. (2015). tumultuous history. Tracking land use/land cover dynamics in cloud prone areas using moderate resolution satellite data: A case study in Central Africa. Remote Sensing, 7, 6683-6709. Acknowledgements Cobbinah, P.B. & Darkwah, R.M. (2016). African Urbanism: the Geography of Urban Greenery. Anonymous reviewers helped to Urban Forum DOI 10.1007/s12132- 016-9274-z improve this article. City of Kigali (2012). The City of Kigali development plan 2012/13 - 2017/18 Draft. Kigali, Rwanda: City of References Kigali. City of Kigali (2013). Kigali City Aldwaik, S. and Pontius, R.G. Jr. (2012). Master Plan Report: Task order 3 Intensity analysis to unify Concept planning. Kigali, Rwanda: measurements of size and stationarity City of Kigali. of land changes by interval, category, Creutzig, F., Baiocchi, G., Bierkandt, R., and transition. Landscape and Urban Pichler, P.P. and Seto, K.C. Planning, 106, 103 - 114. (2015). Global typology of urban doi:10.1080/13658816.2013.787618 energy use and potentials for an Aldwaik, S. and Pontius, R.G. Jr. (2013). urbanization mitigation wedge. Map errors that could account for Proceedings of the National deviations from a uniform intensity of Academy of Sciences of the United land change. International Journal of States of America (PNAS), 112(20), Geographical Information Science, 6283- 27(9), 1717 - 1739. 6288, doi:0.1073/pnas.1315545112. Ali, DA, Deininger, K., and Goldstein, Enaruvbe, G. and Pontius, R.G. Jr. M. (2014). Environmental and gender (2015). Influence of classification errors on Intensity Analysis of land https://www.gibs.co.za/about- changes in southern Nigeria. us/centres/Dynamic_Markets/Docum International Journal of Remote ents/56936_brenthurst_paper_2015- Sensing, 31(1), 244-261. 05.pdf [Accessed 02 December Grimm, N.B., Faeth, S.H., Golubiewski, 2015]. N.E., Redman, C.L., Wu, J.G., Bai, Liu, H. and Weng, Q. (2013). X. and Briggs, J.M. (2008). Global Landscape metrics for analysing change and the ecology of cities. urbanization - induced land use and Science, 319, 756-760. land cover changes. Geocarto Guild, L.S., Cohen, W.B., and International, 28(7), 582-593 doi: Kauffman, J.B. (2004). Detection of 10.1080/10106049.2012.752530. deforestation and land conversion in Liu, T. and Yang, X. (2015). Monitoring Rondonia, Brazil using change land changes in an urban area using detection techniques. International satellite imagery, GIS and landscape Journal of Remote Sensing, 25(4), metrics. Applied Geography, 56, 42- 731-750. 54. Hall, P. and Pfeiffer, U. (2000). Urban Manandhar, R., Odeh, I.O.A., and future 21: A global agenda for Pontius, R.G., Jr. (2010). Analysis of twenty-first century cities. Oxon: twenty years of categorical land Taylor and Francis. ISBN-10: transitions in the lower Hunter of 0415240751. New South Wales, Australia. Jonckheere, I., Nackaerts, K., Muys, B., Agriculture, Ecosystem and Lambin, E. (2004). Digital change Environment, 135, 336-346. detection methods in ecosystem Mega, V.P. (2016). Conscious coastal monitoring: A review. International cities: Sustainability, blue green Journal of Remote Sensing, 25, growth, and the politics of 1565-1596. imagination. Switzerland: Springer. Kasangaki, A. (2013). Status of 269p. Doi: 10.1007/978-3-319- ecosystem services in the Albertine 20218-1 Rift region. In: S. Kanyamibwa, ed. Ministry of Natural Resources (2008). Albertine Rift Conservation Status Five-year strategic plan for the Report. Albertine Rift environment and natural resources Conservation Society (ARCOS) sector (2009 –2013). Kigali, Rwanda Series No 1. Uganda and UK: - Ministry of Natural Resources. ARCOS, 25-28. Ministry of Natural Resources (2014). Kigali City Council (2007). Kigali Forest landscape restoration Conceptual Master plan. opportunity assessment for Rwanda. Kigali,Rwanda: Kigali City Council. Kigali, Rwanda: Ministry of Natural Kilcullen, D., Mills, G. and Trott, W. Resources, International Union for (2015). Poles of Prosperity or Slums Conservation of Nature Resources- of Despair? The Future of African IUCN and World Resources Cities [online]. Discussion Paper 5, Institute-WRI. ISBN 978-2-8317- South Africa: The Brenthurst 1712-8. Foundation. Available from: Journal of Spatial Science Ndayambaje, J.D., and Mohren, G.M.J. Pontius, R.G. Jr., & Santacruz, A. (2011). Fuelwood demand and (2014). Quantity, exchange and shift supply in Rwanda and the role of components of differences in a agroforestry. Agroforestry Systems, square contingency table. 83, 303-320. International Journal of Remote National Institute of statistics Rwanda Sensing, 35(21), 7543-7554. (2008). Rwanda in statistics and REMA (2011). Atlas of Rwanda’s figures. Kigali, Rwanda: National changing environment: Implications Institute of statistics Rwanda. for climate change resilience National Institute of statistics Rwanda [online]. Kigali, Rwanda: Rwanda (2012). Population housing census Environment Management provisional results. Kigali, Rwanda: Authority. Available from: National Institute of statistics https://na.unep.net/siouxfalls/publica Rwanda. tions/REMA.pdf [Accessed 26 July Njoroge, J.B., NdaNg’ang’a, P.K., and 2015]. Natuhara, Y. (2013). The pattern of REMA (2013). Kigali. State of distribution and diversity of avifauna Environment and Outlook Report over an urbanizing tropical 2013 [online]. Available from: landscape. Urban Ecosystems, 17(1), http://na.unep.net/siouxfalls/publicati 61-75. doi:10.1007/s11252–013– ons/Kigali_SOE.pdf [Accessed 07 0296–1. August 2014]. Organization for Economic Cooperation Runfola, D., and Pontius, R.G. Jr. and Development (2011). Effective (2013). Measuring the Temporal modelling of urban systems to Instability of Land Change using the address the challenges of climate Flow matrix. International Journal change and sustainability [online]. of Geographical Information Global Science Forum. Available Science, 27(9), 1696-1716. from: http://www.oecd.org/sti/sci- Satterthwaite, D. (2009). The tech/49352636.pdf [Accessed 26 implications of population growth July 2015]. and urbanization for climate change. Parnell, S. and Walawege, R. (2011). Environment and Urbanization, Sub-Saharan African urbanisation 21(2), 545-567. doi: and global environmental change. 10.1177/0956247809344361. Global Environmental Change, Seto, K.C., Guneralp, B., and Hutyra, 21(S1), S12-S20. L.R. (2012). Global forecasts of doi:10.1016/j.gloenvcha.2011.09.014 urban expansion to 2030 and direct Pontius, R.G. Jr., Gao, Y., Giner, N.M., impacts on biodiversity and carbon Kohyama, T., Osaki, M., & Hirose, pools. PNAS, 109(40), 16083-16088. K. (2013). Design and interpretation Simone, D., and Leck, H. (2010). of intensity analysis illustrated by Urbanizing the global environmental land change in Central Kalimantan, change and human security agendas. Indonesia. Land, 2, 351-369. Climate and Development, 2, 263- doi:10.3390/land2030351. 275. doi:10.3763/cdev.2010.0051. Stow, D.A. and Chen, D.M. (2002). Development Network, World Bank. Sensitivity of multitemporal NOAA Available from: AVHRR data of an urbanizing http://siteresources.worldbank.org/IN region to land-use/land-cover change TURBANDEVELOPMENT/Resour and misregistration. Remote Sensing ces/336387- of Environment, 80, 297-307. 1269651121606/FullStrategy.pdf Surbana (2012). Detailed district [Accessed 02 December 2015]. physical plans for Kicukiro and Zaehringer, J.G., Eckert, S. and Gasabo Kigali, Rwanda: vision Messerli, P. (2015). Revealing report [online]. Kigali, Rwanda: regional deforestation dynamics in Surbana International Consultants North-Eastern Madagascar-Insights PTE Ltd. Available from: from multi-temporal land cover http://www.masterplan2013.kigalicit change analysis. Land, 4, 454-474. y.gov.rw/downloads/Docs/RWF1101 Zhou, P., Huang, J., Pontius, R.G. Jr. _12_Naryugenge_Zoning%20Report and Hong, H. (2014). Land _04062013-s.pdf [Accessed 26 July classification and change Intensity 2015]. Analysis in a coastal watershed of United Nations Population Fund (2007). Southeast China. Sensors, 14, 11640- State of world population 2007: 11658. doi:10.3390/s140711640 Unleashing the Potential of Urban Growth. New York: United Nations Population Fund. Warnest, M., Sagashya, D.G. and Nkurunziza, E. (2012). Emerging in a changing climate – sustainable land use management in Rwanda. FIG Working Week proceedings, Rome, Italy, 6-10 May 2012, pp. 1-14. Wasige, J.E., Groen, T.A., Smaling, E. and Jetten, V. (2013). Monitoring basin-scale land cover changes in Kagera Basin of Lake Victoria using ancillary data and remote sensing. International Journal of Applied Earth Observation and Geoinformation, 21, 32-42. World Bank (2010). Systems of cities: Harnessing urbanization for growth and poverty alleviation, The World Bank urban and local government strategy [online]. Washington, DC: Finance, Economics and Urban Department Sustainable Journal of Spatial Science Table 1. Mathematical notation following Aldwaik and Pontius (2012). T number of time points Yt year at time point t t index for the initial time point of interval [Yt,Yt+1], where t ranges from 1 to T-1 J number of categories i index for a category at an interval’s initial time point j index for a category at an interval’s latter time point n index for the gaining category for the selected transition Ctij size of transition from category i to category j during interval [Yt,Yt+1] St annual change during interval [Yt,Yt+1] Gtj intensity of annual gain of category j during interval [Yt,Yt+1] relative to size of category j at time t+1 Lti intensity of annual loss of category i during interval [Yt,Yt+1] relative to size of category i at time t Rtin intensity of annual transition from category i to category n during interval [Yt,Yt+1] relative to size of category i at time t Wtn uniform intensity of annual transition from all non-n categories to category n during interval [Yt,Yt+1] relative to size of all non-n categories at time t Journal of Spatial Science Table 2. Flow matrix in square kilometres per year where the upper number is during the first time interval (1981-2002) and the lower number is during the second time interval (2002-2014). For Loss and Gain, superscript a means active; superscript d means dormant. For transitions, superscript τ means the gaining category in the column targets the initial category in the row; superscript α means the gaining category in the column avoids the initial category in the row. Latter Time Total 2002 or 2014 Built Vegetated Other Loss 0.0α 0.0α 0.0d 1981 or 2002 Built Initial Time 1.6α 4.1α 5.7a α τ 1.4 6.5 7.9a Vegetated 1.2α 6.2τ 7.4a τ τ 4.8 3.5 8.3d Other 4.2τ 7.9τ 12.1d a d d 6.2 3.5 6.6 16.3 Total Gain 5.4a 9.5a 10.3d 25.1 Figure caption Figure 1. Location of Kigali, Rwanda. Figure 2. Land cover at 1981, 2002, 2014 and changes during 1981-2002 and 2002-2014 Figure 3. Gain, Persistence and Loss during a) 1981-2002, and b) 2002-2014 Figure 4. Category Intensity during a) 1981-2002, and b) 2002-2014 Figure 5. Transition intensity given category gains during a) 1981-2002, and b) 2002- 2014