3.1 Density heat map

The bird track density heat map is generated within a particular region and time span [Reference Chilson, Frick and Stepanian29]. The density is calculated using the kernel density algorithm.

Figure 4. A bird density heat map projected on SeaTac airport map.

Figure 5. Track altitude histogram for different radar elevation angles.

Figure 4 presents an example of a density heat map that is projected over the SeaTac airport map. It is straightforward for understanding spatial distribution characters of birds. However, density heat maps are not proper for temporal character descriptions such as migration bird situations. Technically it is not very challenging to construct density heat maps for migration birds. The problem is that dynamic characters of migration birds make density heat map variations difficult for intuitive information extraction and interpretation. Since migration routes usually cover a wide area, migration birds might distribute with prominent difference among time spans in an unpredictable manner. This makes density heat maps reflect perturbations on high density area distribution within a time span. This perturbation is presented as a random flashing in the heat map animation from consecutive time spans. This flashing provides little information for migration character interpretation, and the lack of quantitative description also confines the density heat map to the static analysis. The work presented in Ref. [Reference Kranstauber, Bouten, Leijnse, Wijers, Verlinden, Shamoun-Baranes and Dokter30] introduces a novel concept of vertically integrated reflectivity (VIR) to demonstrate the migration bird situation within the effective surveillance range of weather radar systems. One motivation of developing VIR is complementing the insufficiency of existing density heat maps in bird situation presentation and quantification. Moreover, the heat map generation principle makes it difficult for information integration with other spatial-temporal configurations.

3.2 Altitude histogram

Histogram is a representative statistical tool for data modelling and fitting [Reference Balzanella, Rivoli and Verde31–Reference Rauch and Šimůnek33]. Bird track altitude could be presented in histogram forms either. Compared with the density heat map, the altitude histogram completes bird spatial character interpretation in the altitude dimension. Figure 5 demonstrates an example of altitude histogram under different elevation angles. The dataset comes from a field experiment using the system as demonstrated in Fig. 1, which is deployed at another airport. This histogram is used to evaluate track quantities at different altitude spans and choose a proper elevation angle for monitoring the area with large bird densities. More birds at larger altitude spans are observed with increasing elevation angles, which is consistent with radar scanning characters. Like density heat maps, altitude histograms are confined to a single spatial domain. Its temporal variation characters are difficult to be interpreted effectively.

3.3 Direction histogram

Flight direction could be deduced from spatial-temporal information in track plots. Statistical characters of flight direction are valuable for bird activity analysis and identification. Figure 6 presents a representative flight direction histogram in polar form. Bird quantity and flight direction variations at different hour spans are prominent and intuitive. However, this histogram is not suitable for information integration with multiple conditional parameters. Moreover, for local birds that might fly more arbitrarily, polar histograms of flight directions might be misleading and not intuitive for activity interpretation.

Figure 6. Polar histogram of bird track directions.

Existing bird situation interpretation methods have their respective advantages and limitations. They generally provide static visualisation results with intuition but are not suitable for information integration under multiple conditional parameters. A new bird activity modelling and interpretation method for flexible temporal domain description is required.

4.1 Data filtering

The database construction is fundamental for bird activity mining. In this paper the database is constructed through radar data filtering at day scale. Radar observation data of one specific day is characterised by an hourly track count vector whose dimension is 24-by-1. The track count distribution is not only dependent on bird activities but also environments especially weather conditions. Historical works have demonstrated close relevance between bird activities and weather conditions [Reference Coates, Casazza, Halstead, Fleskes and Laughlin34, Reference Mary35]. Therefore, it is more reasonable to extract and interpret bird activity characters based on similar weather conditions.

This paper defines a conditional parameter $\boldsymbol\sigma$ which includes various weather information for data filtering. The filtered database is denoted as ${\bf{N}} = \left\{ {N\!\left( {{d_1}\!\left| {\boldsymbol{\sigma }}\! \right.} \right),N\!\left( {{d_2}\left| {\boldsymbol{\sigma }}\! \right.} \right), \ldots ,N\!\left( {{d_K}\!\left| {\boldsymbol{\sigma }}\! \right.} \right)} \right\}$. The symbol $N\!\left( {{d_k}\!\left| {\boldsymbol{\sigma }}\! \right.} \right)$ represents a track count at the date d _k with parameter $\boldsymbol\sigma$.

Table 1. Mapping relationship between normalised intensity and grade

4.2 Bird activity mining at hour scale

A novel concept of activity degree is introduced as a descriptor for quantitative bird activity interpretation. It is assumed that bird activity is characterised from intensity and uncertainty aspects. The activity degree computation is composed of intensity extraction, uncertainty extraction and their integration, which is decomposed of four steps.

STEP 1: Normalised intensity calculation. The normalised intensity is calculated from track count information at hour scale. For date d _k, its normalised intensity is denoted as ${\bf{I}} = \left\{ {I\!\left( {1\!\left| {{d_k}}\! \right.} \right),I\!\left( {2\!\left| {{d_k}\!} \right.} \right), \ldots ,I\!\left( {24\!\left| {{d_k}}\! \right.} \right)} \right\}$ with $I\!\left( {i\!\left| {{d_k}}\! \right.} \right)$ representing the hour interval between hour i-1 and i. The normalisation range is between 20 and 100. The lower bound is 20 instead of 0 as it is unreasonable to define minimum track count as no bird activity. It should be noted that this time span for normalisation is not confined to one hour but adjustable for specific problems.

STEP 2: Intensity grading. Normalised intensities from all selected dates compose a database N. A normalised intensity array is formulated as I(h _k, d) for hour h _k. The symbol d indicates all dates within N. Intensity fluctuations from slight track count variations might be misleading in activity interpretation. To solve this problem, a smoothing procedure is proposed by categorising intensity into 10 grades. The mapping relationship between grade and intensity is presented in Table 1. The new database after the mapping is denoted as G(h, d) with consistent definition of h and d as in I(h _k, d).

STEP 3: Uncertainty quantification. Large grade variations indicate higher uncertainty and corresponding bird activities are difficult to be predicted. This mechanism is realised through the entropy concept. Since the grade mapping refrains the impact from intensity fluctuations, a more sensitive entropy evaluation method is required. This paper selects the α-quadratic entropy [Reference Fauvel, Chanussot and Benediktsson36] to quantify activity uncertainty:

(1) \begin{align}E{n^\alpha }\!\left( {{\bf{G}}\!\left( {h,{\bf{d}}} \right)} \right) = \frac{1}{{{2^{ - 2\alpha }}}}\sum\limits_{j = 1}^{10} {{{\!\left( {{P^j}\!\left( {{\bf{G}}\!\left( {h,{\bf{d}}} \right)} \right)} \right)}^\alpha } \cdot {{\left( {1 - {P^j}\!\left( {{\bf{G}}\!\left( {h,{\bf{d}}} \right)} \right)} \right)}^\alpha }} \end{align}

The term ${P^j}\!\left( {{\bf{G}}\left( {h,{\bf{d}}} \right)} \right)$ indicates the probability of G(h, d) at grade j. The larger uncertainty enlargement parameter α indicates a higher uncertainty sensitivity of entropy. This paper selects α as 0.7. It is larger than recommended value of 0.5 as the grade definition limits intensity fluctuation, and the α value needs proper enlargement to maintain its entropy sensitivity [Reference Pal and Bezdek37, Reference Dai38].

The flexible definition of α makes it applicable for various scenarios. For complicated bird activities with large track count fluctuations, it does not indicate a definite higher activity uncertainty, and the α value should be small to constrain uncertainty enlargement. If bird activities have limited interference, the count fluctuation is small and a larger α value is required to enlarge the uncertainty interpretation capability. This is the dominant reason for selecting α-quadratic entropy instead of the conventional entropy.

STEP 4: Weighing factor and activity degree calculation. Intensity and uncertainty information should be integrated to interpret bird activity characters. The straightforward integration of their numerical value is improper due to their independent physical meaning and dimensions. This paper develops a weighing strategy for uncertainty characters and applies it on intensity descriptor for information integration. An uncertainty weighing factor based on α-quadratic entropy is defined as [Reference Jia, Ning, YongJun and BaoFa39]:

(2) \begin{align}w\!\left( {E{n^\alpha }\!\left( {h,{\bf{d}}} \right)} \right) = 1 + \left( {{2^{ - 2\alpha }}} \right) \cdot \exp \!\left( {E{n^\alpha }\!\left( {h,{\bf{d}}} \right) - {T_e}} \right)\end{align}

The weighing factor is larger than one, indicating its extra enlargement of intensity. The parameter T _e is the entropy threshold. Equation (2) indicates when the entropy is smaller than T _e, birds present a smooth track count variation pattern, the weighing factor provides a limited intensity enlargement. When the entropy is larger than T _e, the weighing factor presents a nonlinear increment to enlarge uncertainty contributions.

Figure 7. Relationship between entropy value and weight factors.

Figure 8. Flowchart of bird activity degree extraction at hour scale.

The current threshold selection takes a half-manual strategy. Bird activities are categorised into large and small variation groups according to track count information, and two groups of entropy information are presented in histograms. The threshold is a value which minimise the overlapping probability between large and small variations. The threshold extracted from our database is 1.63. The relationship between weighing factor and entropy in Fig. 7 indicates an exponential increment of weighing factor when the entropy is larger than the threshold.

Figure 9. Flowchart of bird activity degree extraction at minute scale.

Figure 10. Daily track count distribution and selection within the north airport region in 2018.

Figure 11. Bird activity pattern within the north airport at hour scale-August.

Figure 12. Bird activity pattern within the north airport at hour scale-September.

Figure 13. Bird activity pattern within the north airport at hour scale-October.

The activity degree at hour h is calculated by integrating intensity and weighing factor:

(3) \begin{align}C\!\left( h \right) = {I_{avg}}\!\left( {h,{\bf{d}}} \right) \times w\!\left( {E{n^\alpha }\!\left( {{\bf{G}}\!\left( {h,{\bf{d}}} \right)} \right)} \right)\end{align}

The term ${I_{avg}}\!\left( {h,{\bf{d}}} \right)$ indicates an average value of I. The bird activity degree is not confined within 100 but this does not influence its interpretation capability for bird activities. Figure 8 presents a flow chart of activity degree extraction at hour scale.

4.3 Bird activity mining at minute scale

Compared with the hour scale analysis, the mining procedure at minute scale is similar except for the selection of temporal sampling interval, which is critical in minute scale analysis. If the sampling interval is set to one minute, the track count information might not be sufficient to support statistical analysis. It is also unreasonable to interpret bird activity characters in every single minute. Track count fluctuations from small sampling intervals also influence intensity and uncertainty information quality. This paper sets the sampling interval to 10 minutes as a fundamental temporal unit. A time span distributed around a reference time is defined for intensity and uncertainty extraction.

The flow chart for minute scale analysis is presented in Fig. 9. Compared with Fig. 8, some mathematical formulas are replaced by text description. The major differences are reference time and time span definitions.