**2. The DART model**

### **2.1. Presentation**

technology, as well as modeling of remote sensing measurements with respect to three‐ dimensional (3D) radiative and energy budget. One of these studies is the H2020 project URBANFLUXES (http://urbanfluxes.eu), which aims to develop methods estimating the anthropogenic heat flux (QF) of urban environments by employing remote sensing data [1]. In other words, its goal is to estimate the impact of human urban activities on the energy budget of city using satellite images.Important parts ofthe surface energy balance computation are the 3Dradiativebudgetcomponentsspecificallyasurbansurfacealbedoincludingthermalexitance. However, no remote sensing model able to simulate accurately spatial distribution of urban spectral albedo and exitance has been previously available. Three conditions must be fulfilled

– The model must consider explicitly the 3D architecture of urban environments and simulate radiance images and radiative budget of urban environment. Hence, apart from physical modeling considerations, the model must be able to work with urban databases, including

– The model must work within any atmospheric conditions and possibly with air pollution of an urban environment. This requires to model radiative transfer of both the atmosphere above

– An operational methodology must allow calibrating outputs of the remote sensing model in terms of 2D distribution of albedo and exitance (i.e., to produce image outputs). This calibra‐ tion is important, because one cannot expect to have access to the optical properties of all urban surface elements, which vary in space (e.g., tiles of roofs have different reflectance values depending on their age) and time (e.g., wet and dry roofs will exhibit different anisotropy of

**Figure 1.** DART calibration with a remote sensing image (Landsat‐8) for computation of the urban surface albedo over

Here, we present a 3D radiative transfer model, DART, that fulfils these requirements and its recent improvements for studying urban and natural Earth landscapes with remote sensing acquisitions. We present also the approach that was recently designed and implemented to

in order to achieve an acceptable solution of an urban radiative budget simulation:

spatial information on vegetation and digital elevation model.

and the air among urban objects.

their reflectance).

228 Sustainable Urbanization

the city of Basel, Switzerland.

DART computes radiation propagation in the three‐dimensional (3D) Earth/atmosphere system in the entire optical domain from the visible to the thermal infrared parts of the electromagnetic spectrum (EMS) [2–6]. The Earth surfaces and the atmosphere are simulated as a three‐dimensional (3D) medium (**Figure 2**). For any urban and natural landscapes, DART simulates the 3D radiative budget and acquisitions by satellite and airborne imaging radio‐ meters and LIDAR scanners aboard of space and airborne platforms. The DART model, developed in the CESBIO Laboratory (www.cesbio.ups‐tlse.fr/fr/dart.htm) since 1992, can work with any 3D experimental landscape configuration (atmosphere, terrain geomorpholo‐ gy, forest stands, agricultural crops, angular solar illumination of any day, Earth/atmosphere curvature, etc.) and instrument specifications (spatial and spectral resolutions, sensor viewing directions, platform altitude, etc.).

**Figure 2.** DART cell matrix of the Earth/atmosphere system. The atmosphere has three vertical levels: upper (i.e., just layers), mid (i.e., cells of any size), and lower atmosphere (i.e., same cell size as the land surface). Land surface ele‐ ments are simulated as the juxtaposition of facets and turbid cells.

DART has been successfully employed in various scientific applications, including develop‐ ment of inversion techniques for airborne and satellite reflectance images [7–9], simulation of airborne sensor images of vegetation and urban landscapes [10], design of satellite sensors (e.g., NASA DESDynl, CNES Pleiades, CNES LIDAR mission project [11]), among others. DART forward simulations of vegetation reflectance were successfully verified by real measurements [12] and also cross‐compared against a number of independently designed 3D reflectance models (e.g., *FLIGHT* [13], *Sprint* [14], *Raytran* [15]) in the context of the RAdiation transfer Model Intercomparison (RAMI) experiment [16, 17].

DART creates and manages 3D landscapes independently from the RT modeling (e.g., visible and thermal infrared spectroradiometers, LIDAR, radiative budget). This multi‐sensor functionality allows users to simulate efficiently radiative transfer products of the same landscape as being captured by various sensors. Major scene elements are as follows: urban features, trees, grass and crop canopies, and water bodies. A DART simulated tree is made of a trunk, optionally with branches created with solid facets, and crown foliage that is simulated either as a set of facets or as a set of turbid cells, with specific vertical and horizontal distribu‐ tions of leaf volume density. Trees of several species with different geometric and optical properties can be located within the simulated scene of any user‐defined size randomly or based on exact coordinates. Urban objects (houses, roads, etc.) contain solid walls and roofs built from triangular facets. Finally, water bodies (rivers, lakes, etc.) are simulated as facets of appropriate optical properties. DART can use external libraries to import and to some extent also edit landscape elements, digital elevation models (DEMs), and digital surface models (DSM) produced by other software or measured in field (e.g., translation, homothetic and rotational transformations). Most importantly, the imported and DART‐created landscape objects can be combined into virtual Earth scenes of user‐defined complexity. This allows importation of whole cities from urban databases provided by city councils and urban planners. The optical properties of landscape elements and their geometry, as well as and properties of atmosphere, are specified and stored in adjacent SQL databases.

Atmospheric cells are used to simulate attenuation effects of satellite at‐sensor radiance and also to model influence of the atmosphere composition on radiative budget of Earth surfaces. The atmosphere can be treated just as an interface above the simulated Earth scene or as a light‐ propagating medium above and also within the simulated Earth scene, with cell sizes inversely proportional to the particle density. These cells are characterized by their gas and aerosol contents and spectral properties (i.e., phase functions, vertical profiles, extinction coefficients, spherical albedo). These quantities can be defined manually or obtained automatically from an atmospheric database. DART contains a database that stores the properties of major atmospheric gases and aerosol parameters for wavelengths between 0.3 and 50 μm. In addition, external databases can be imported, for instance, from the AErosol RObotic NETwork (AERONET; http://aeronet.gsfc.nasa.gov/) or from the European Centre for Medium‐Range Weather Forecasts (ECMWF; http://ecmwf.int/). Atmospheric RT modeling includes the Earth/ atmosphere radiative coupling (i.e., radiation that is emitted and/or scattered by the Earth and backscattered by the atmosphere towards the Earth). It can be simulated for any spectral band within the optical domain from the ultraviolet up to the thermal infrared part of the electro‐ magnetic spectrum. The Earth/atmosphere coupling was cross‐compared and successfully validated [18, 19] with simulations of the MODTRAN atmosphere RT model [20].

#### **2.2. Recent improvements of DART**

Set of improvements had to be recently implemented in the DART model in order to provide the optimal products required by the URBANFLUXES project.
