**3. Problems of 3D urban development studies in literature**

Nowadays the use of 3D building models focuses on visualization, which also have high "potential for supporting the 'smart city' concept" [23]. 3D city models are often managed by using CityGML that is an information model for storing, representing and exchanging of virtual 3D city models. While there are methods in CityGML that demonstrate the 3D changes to buildings [24] in urban areas, there are some problems with these methods that are listed below:


Indeed, the as-built city models derived from airborne lidar data are closer to reality than those 3D models created from cadastral layers and building height information which usually ignores detailed height information of the different parts of a building. Also, advanced remote sensing airborne lidar data captured over urban areas is an accurate source of 3D data from which to derive 3D city models. Change detection from time series airborne lidar data is a preferred approach as it does not include the above-mentioned problems. As well, advanced data collection methods such as using remote piloted aerial system (RPAS) can be used for collection of data immediately after rapid changes consequent on disaster events such as floods or earthquakes. There are several algorithms for detection of these changes from time series airborne lidar data. One of the major problems in urban change detection studies of airborne lidar data is that the pixel-based algorithms that are more appropriate for calculation of volumetric changes suffer from either lack of height change information or a high level of noise.

There are other problems relevant to 3D metrics for assessment of the sustainability of urban form. While there are 3D metrics for comparison of different urban forms or to characterize 3D cities, there is a lack of appropriate metrics for application into the assessment of the sustainability of urban form over time, as defined in the Introduction. Koziatek and Dragicevic (2019) proposed 3D indices for spatial and temporal urban analysis of 3D urban expansion, but one of the major problems of their studies is that they do not use time series 3D remote sensing data for exploration of the real changes of the buildings over time. There is a problem of uncertainty in their 3D models because various sources of building height data are used to create time series 3D city models. For example, the number of floors is one source of building height data, but as discussed before, heights between floors for buildings with different functionalities vary; therefore, estimation of building heights for an urban area with various building uses based on number of floors is very inaccurate.

All in all, a thorough review of the urban form literature and metrics [25] shows that even though urban form analysis has a long history in the literature, there are deficiencies in metrics development including (a) a lack of 3D studies using remote sensing for sustainability assessment of urban form and (b) a lack of studies on 3D urban growth assessment for sustainability.

*Sustainability in Urban Planning and Design*

structure [9] in the traditional perspective.

threshold of floor height differs from city to city.

• growth of built up areas as a 2D phenomenon [13];

time [11, 12] as shown by the following:

urban form study over time [16];

• sustainable 2D brownfield development [19];

claimed sustainable urban form [20, 21].

form over time [14];

(i.e. airborne lidar).

and factors that affect urban change over time. Indeed, the question is how a type of pattern for change in urban structures results from these processes. As shown in **Figure 1**, urban metrics are applied to remote sensing data to derive spatial and temporal patterns of urban structure and development in the bottom-up view known as modern perspective. Then the derived structure becomes the subject for analysis and investigation of the underlying processes. In contrast, it can be argued that the processes are the major drivers of the existing patterns of urban form and

While two-dimensional information on urban development patterns is typically derived from the modern approaches, they have not been applied to investigate 3D knowledge of urban patterns. This gap is noted in **Figure 1**, and the aim of this research is to fill the gap of vertical urban development pattern analysis by proposing new 3D metrics and employing 3D remote sensing data

The motivation for proposing new 3D compactness metrics in this study is the current lack of appropriate metrics. Two commonly used metrics in urban planning are building coverage ratio (BCR) and floor area ratio (FAR). BCR is defined as the building coverage area divided by the area of the land lot (plot). This metric is also known as the building–to-land ratio (BTL). FAR refers to the ratio of the combined area of building floors to the total area of the land lot. As seen, BCR and FAR are 2D and 3D, respectively. While FAR has been calculated using remote sensing data such as airborne lidar, it suffers from the problem of uncertainty, because FAR is calculated based on assumptions about each floor height. This metric is subject to uncertainty because floor height is definitely higher for a retail land use in a large shopping center than for low-density residential land use (Yu et al. [10]). Also, the

Past and current practices in urban form studies focus on themes such as the two-dimensional growth of urban form or horizontal development in space and

• using 2D landscape metrics for analysis of sustainable development of urban

• using temporal remote sensing data for assessment of urban form and mor-

• claiming to address sustainability aspects, but the study only focuses on 2D

• analysis of 2D expansion of cities using remote sensing data [17], considering compactness as a sustainable urban form and other relevant studies [18];

• change of 2D land use considering compact the urban form paradigm as a

There are also studies on the effect of urban form on energy consumption for a

phology changes over time for considering sustainability [15];

**56**

sustainable city [22].

Considering current rapid urbanization and the above-mentioned lack of studies on sustainable 3D urban development, there is an urgent need to numerically characterize how 3D urban development affect the sustainability goals of caring for the environment, including maintaining (and ideally, enhancing) vegetation.
