Research for Science Art and Technology (RFSAT) Limited

Modelling spatial-temporal distribution of weather and pollutants

Models developed by RFSAT to provide spatiotemporal distribution of weather conditions and contaminants (e.g. gasses) from sparse sensor networks over geographical areas of interest, such as pilot city areas are described below. They have developed to take into consideration the following main contributing factors:

  1. Ground\Surface elevation, including both natural ground elevation (e.g. mountains) and man-made obstacles (e.g. urban building footprints), a serious factor to accumulation of pollutants in bounded areas.
  2. Weather conditions, such as wind speed and direction, as main contributing factors in directional spread of gas contaminations. Considering that sensors only provide such information at sparse locations; geographical distribution of weather conditions has to be made at every new iteration (observation time) prior to any distribution analysis of polluting gasses can be done.
  3. Temperature and humidity as main factors contributing to vertical convection propagation of gases away from the ground, mainly during summer periods, while causing stronger accumulation during cold and humid winter periods.

Models assume that regular observations are made such that to be able to provide continuous analysis of changes to both weather conditions and gas distributions. Large irregularities are likely to negatively affect the accuracy of modelled distribution maps. Therefore, in case of longer “uncertainty” periods, linear approximation of intermediate values is made over the unknown time periods to allow models to operate in a more continuous manner.

Since there is no data available yet regarding actual pollution sources, such as road traffic or factory emissions, the developed models are based on sensor data only and attempt to perform analysis of distribution of pollutants between such monitoring stations. In this respect, such sensor monitoring stations are treated as “pollution injectors”, with detected levels of pollutions treated as constant (at any given time) gas injections.

A distribution model for air pollution assumes movement of particles from higher density areas to a lower density one, while keeping a constant amount of overall volume of pollution. The following equation defines a simple distribution model. It comprises parametrized impacts from additional effects such as wind speed and direction (WS) and ground elevation (GE):

The wind parameter WS is a distribution matrix of size N, defined and applied to each location that correlates the influence of the distributions from neighboring cells on the amount of pollutant at the current location that can be defined for any range of neighbouring cells.

In cases when there is no wind or change of elevation, the WS reduces to unity matrix. In the simplest case when we consider only the closest cells, it can be a 3x3 size, although in such a case a larger number of iterations are required per unit time since modelled propagation is much slower. On the other hand, larger matrix permits more realistic calculation of distributions, especially when accommodating for other effects like wind speed and direction, ground elevation or urban building footprint. On the other hand, this also implies larger size of the borderline undefined areas and so simulation needs to extend by N on every side of the area. Hence larger N implies larger simulation area as well as significantly longer processing times, at a benefit of more accurate simulation and less iterations per unit time.

The assumption is that WS reduces distribution by increasing impact of neighboring cells that are against the wind and increasing spread with the wind. On the contrary, the difference of elevation from a neighboring cell increases its influence, while lower elevation contributes to the easier distribution of the pollution distribution. Parameters WS and GE have a meaning of the probability and hence the total of those parameters corresponding to all neighboring cells that are expected to contribute to the new value at a given location must be equal one. Otherwise, unpredictable effects can be expected. The black background corresponds to low density while white areas indicate highly polluted areas. Certainly, colour coding can be adjusted to comply with common color code in THIS platform.

As can be noticed in the figure, with a lack of external environmental influences like wind of ground elevation, the density of pollution spreads equally in all directions. In case of sources in close vicinity, a mutual impact of distribution clouds can be observed. This clearly shows a need for dense location of sensors in order to be able to reliably model distribution of various aerial pollutants. On the other hand, as the simulation progresses (note that images come from short simulations of only 10 minutes, corresponding to more than 3600 iteration steps), the results can be expected to become smoother while areas centred around each real sensor acquisition location become more interconnected with one another.

Hypothetical distribution of the density of pollution for (left) a single source, and (b) multiple sources.

With increased wind speed distribution of pollution causes extending higher densities for a longer distance, while faster reduction shows in the direction against the wind. Certainly, different wind parameters can be defined for each location. Note that images in the figure below correspond to constant wind and same direction over a 10-minute observation period.

Hypothetical distribution of the density of pollution for (left) a single source, and (right) multiple sources, with account for wind speed and direction. In the example a strong wind comes from the South.

In order to cater for wind, the distribution matrix is no longer a unity matrix and needs to cater for reduction of the pollutions coming from cells where the wind goes to (both speed and direction) and increase from those where the wind comes from. In the simplest case a neighbourhood of N=3 (one cell) can be used that implies a 3x3 matrix:

, where

Where:

  • WSpeed is the wind speed
  • WE is the wind factor in the matrix
  • Wo is the experimental coefficient associating wind speed with its impact
  • TS is the number of simulation steps per unit of time
  • is a rotation matrix defined as:
  • α - wind angle with respect to longitude axis

A similar analysis of the distribution of air pollutions (in our case determined by the location of sensor nodes that act as reference of accurate amounts of pollution) can be done to analyse effects of changing ground elevations. In the first example shown below, a large-scale simulation for an area around Dublin was made. Areas with brighter color mark highest densities, while darker areas indicate low density. Model considers two injection data, one in central of Dublin and another one over Navan. In here a wind coming from the South causes spread of pollutant towards the North.

Example of NO2 emission distribution in the areas surrounding Dublin.

Similar distribution of NO2 pollutants in the centre of Rome, captured from over 8000 individual measurements taken over the period of more than two months from five (5) distinct air quality sensors with variable wind condition over the observation period is shown in figure below.

Example of NO2 emission distribution in the centre of Rome.

In another real-time example below, a distribution of SO2 for Bratislava is shown. As in a previous the example, data was captured from Air Quality Open Data platform over the same observation period with last one dated 15th of September 2021. To make it more interesting, a hypothetical Northern wind has been also added to nearly 1500 sensor measurements.

Real-life distribution of SO2 air pollutant in the centre of Bratislava

Real-life distribution of particulate matter PM10 in the city of Hamburg

In the next example focused on pilot cities from ARCH project, the analysis of the distribution of an important urban pollutant, the Particulate Matter and PM10 in particular has been performed, results of which are presented in Figure 14. As in previous simulations data was captured from Air Quality Open Data platform with last data from the 15th of September 2021. Over 8000 measurements have been used to produce the presented results. Note that higher density of the pollutant is marked in bright white, while lower concentrations in dark grey.

Another representative example is for the area of Valencia, which is one of those with highest density of available sensor nodes, i.e. 207 in total. Hence a simulation of distribution of the humidity has been performed for the whole municipal area of Valencia (below). It uses Netatmo weather sensors captured on the 15th of September 2021.

Real-life distribution of humidity in the municipal area of Valencia using Netatmo sensor data

In this example humidity ranges between 30% (marked as darker areas) to 100% shown in bright white shading. With high variance of the sensor values in the whole analyzed area, the model attempted to smooth those changes and provide more equivalued distribution of measurement. Note that on that day there was a very light breeze from the North that has not contributed much to the distribution of the humidity.

The ground elevation as well as high obstacles, such as buildings seriously impact convective movement and hence also the distribution of gases and other air pollutions. To model such effects additional GE i.e. Ground Elevation function has been added to equation (1) above. It is defined as the weighted slope between the point at coordinates (i,j) for which the distribution is calculated in a given iteration and its neighbouring cells. It is inverse proportional to the change between the cell at coordinates (i, j) and its adjacent ones. In the simplest approximation this can be defined as in the following equation (4), where W is a weight linking slope with real dispersion of a particular pollutant/gas in the environment. The weight values for each type of a pollutant are expected to improve as more data becomes available.

In order to illustrate the concept, a hypothetical “building” has been placed in the middle of the Valencia pilot area of an over-exaggerated size (50km across) and average height of ~50 meters, for which the same simulation as in the figure above has been performed.

As it can be seen below, this has resulted in two effects: (1) accumulation of the pollutants at the side of the “building” facing higher pollutant density and lower on the opposite side, and (2) significant lower density of the pollutant at the area where the obstacle was.

Real-life distribution of humidity in the municipal area of Valencia using Netatmo sensor data with a presence of a hypothetical “building” of an over-exaggerated size and height of ~50 meters.

In another example below, a relaxed-slope “hill” with height extruding similarly as much from the surrounding environment as the previous obstacle has replaced the “building” from the previous example to simulate smoother changes in the ground elevation. The result shows that larger amount of pollution has been “leaking” into the “hill” area causing dilution of a clear border between the hill and its base, while it still exhibits some level of resistance for air pollution to propagate over its area, visible as a slight red area at its base.

Real-life distribution of humidity in the municipal area of Valencia using Netatmo sensor data with a presence of a hypothetical large “hill” (50km across) of and a relaxed slope.

Similarly, more complicated ground elevation contours can be incorporated into the pollution distribution model alongside actual building footprints. However, at the time of writing this article, real-life evaluations of such effects were not possible due to the lack of required ground elevation and building footprint data in a format required for inclusion into the simulation alongside all sensing data captured over the period of several months.

References for Further Reading