Towards a comprehensive city emission function (CCEF)

The comprehensive city emission function (CCEF) is developed for a heterogeneous light-emitting or blocking urban environments, embracing any combination of input parameters that characterize linear dimensions in the system (size and distances between buildings or luminaires), properties of light-emitting elements (such as luminous building façades and street lighting), ground reflectance and total uplight-fraction, all of these defined for an arbitrarily sized 2D area. The analytical formula obtained is not restricted to a single model class as it can capture any specific light-emission feature for wide range of cities. The CCEF method is numerically fast in contrast to what can be expected of other probabilistic approaches that rely on repeated random sampling. Hence the present solution has great potential in light-pollution modeling and can be included in larger numerical models. Our theoretical findings promise great progress in light-pollution modeling as this is the first time an analytical solution to city emission function (CEF) has been developed that depends on statistical mean size and height of city buildings, inter-building separation, prevailing heights of light fixtures, lighting density, and other factors such as e.g. luminaire light output and light distribution, including the amount of uplight, and representative city size. The model is validated for sensitivity and specificity pertinent to combinations of input parameters in order to test its behavior under various conditions, including those that can occur in complex urban environments. It is demonstrated that the solution model succeeds in reproducing a light emission peak at some elevated zenith angles and is consistent with reduced rather than enhanced emission in directions nearly parallel to the ground.