3.1 Pollen emissions framework

Pollen emission and transport has never been modelled in Australia; therefore, we trial three different emission frameworks and vary their inputs. In some instances we test parameters proven not to work elsewhere and for other pollen taxa, to investigate whether Australian ryegrass pollen characteristics are different. The first framework is a spatio-temporal decomposition of factors, the second is a pollen production–loss model and the third is a derivative of the statistical model for daily grass pollen concentrations used in the BOM's pilot forecasting system (Silver et al., 2019). The pollen emission rate E at grid-point (x,y) and time t is expressed as follows:

where I is the immediate timing (hour-by-hour variation due to changes in prevailing meteorology), G describes the gross seasonal timing (also termed the “phenology factor”) and S provides the spatial source distribution for a given season. The functions I, G and S are each dependent on other factors, which may include modelled meteorology, land use data or satellite data; these details are discussed in subsequent sections.

Table 2 gives the combinations of options for calculating E that are tested in this study. Each emission methodology is run for three months between October and December 2017 to cover the period of the pollen measurements. The modelled pollen is also averaged on a 24-hourly basis (to 09:00 AEDT each day) to be consistent with the 2017 pollen observations.

Table 2Options tested for pollen emission in this study. EVI denotes the enhanced vegetation index.

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3.1.3 Enhanced vegetation index (EVI)

Devadas et al. (2018) developed a non-linear statistical model for pollen concentrations using satellite greenness indices across areas surrounding a receptor point. The EVI is a measure of landscape greenness, which is less affected by saturation in higher biomass regions than the widely used normalised difference vegetation index (Huete et al., 2002). The EVI value typically increases rapidly with time during spring due to foliage growth in deciduous trees or grass growth. In the Victorian temperate climate, fresh grass rapidly dries (or “cures”) in late spring and early summer, causing a fall in the EVI. Given the absence of deciduous forests in Australia, most of the temporal variation in the EVI is due to grass growth and curing. Here we investigate a relationship between the timing of the pollen season and the gradient in the EVI over a region in the south-west of Victoria, spanning 37.3–38.3^∘ S and 142.0–143.3^∘ E (appearing as dashed lines in Fig. 3). This region is upwind of Melbourne, in terms of the prevailing climatological wind, and has high agricultural activity.

Figure 2(a) A 16-year climatology in EVI (black) from south-west Victoria (averaged over the region from 37.3 to 38.3^∘ S and 142.0 to 143.3^∘ E, shown in each panel of Fig. 3) and the grass pollen record in Melbourne (red); the full sequence of data is shown as circles, with a locally weighted polynomial regression overlaid (Cleveland, 1979). The EVI data are 16 d composites. (b) As in panel (a) except presenting the derivative of the 16 d EVI with respect to time. (c) The day of the year of the minimum of the $\frac{\partial \mathrm{EVI}}{\partial \mathrm{t}}$ for each year plotted against the day of the year of the maximum pollen; when assessing the timing of the grass pollen peak, the grass pollen time-series was smoothed using a cubic smoothing spline. The dashed lines in (c) represent 16 d either side of a given day, which is the width of the MODIS EVI compositing window.

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Using the Moderate Resolution Imaging Spectroradiometer (MODIS) MOD13C1 data (from the Terra satellite at 0.05^∘ resolution), Fig. 2a shows that the gradient in averaged EVI drops off rapidly, around the same time as the pollen season peaks. Fig. 2b shows that the first derivative of EVI is with the grass pollen time-series at UoM. If we examine inter-annual variation, assessing the day of the year when the EVI falls most rapidly (represented as the middle of the 16 d EVI compositing window) and the day of the year when the grass pollen peaks (having first applied a smoothing spline to the pollen time-series), a relationship between these two quantities is observed: the Pearson correlation is 0.4, the slope of the linear regression is 1.006 and the means of the two Julian dates differs by only 2.7 d (Fig. 2c). This agreement is especially notable given the uncertainty induced by the wide EVI compositing window.

Figure 3Relationship between the timing of the peak in grass pollen in Melbourne and the timing of the sharpest drop in EVI at each MODIS pixel: the correlation (a) and the root mean squared error in the timing (b). Also shown are the average timing (c) and rate (d) of the fastest fall in EVI at each point in the domain. The dashed rectangle in south-west Victoria (spanning 37.3–38.3^∘ S and 142.0–143.3^∘ E) displays the region over which the EVI time-series were averaged for Fig. 2. “argmin” refers to the minimum argument.

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Taking this one step further, we apply a similar analysis to each individual 0.05${}^{\circ }\times {\mathrm{0.05}}^{\circ }$ MODIS pixel (Fig. 3). Given the high deposition velocity of grass pollen grains (4.6 cm s⁻¹, as discussed above), the contribution of pollen emitted from the productive grassland areas in western Victoria to observations recorded in Melbourne is likely to be minimal. However, this analysis may help inform our understanding about the relationship between the remotely-sensed vegetation index and broad-scale features of the pollen season. The timing of the fall in the EVI in south-west Victoria not only correlates well with the timing of the grass pollen season experienced in Melbourne (Fig. 3a), but the differences in timing are also relatively small (Fig. 3b). The north-west of the state is generally much drier than the south-east (Fig. 1c), and the north-west area dries out earlier in the year (Fig. 3c). Areas identified as crops or pasture (Fig. 1d) demonstrate a more rapid fall in EVI (Fig. 3d).

This exploratory analysis suggests that in this bioclimate the broad parameters of the pollen season can be diagnosed from the EVI fields. On a broad temporal scale, a fall in the EVI over pollen source regions is associated with increasing pollen emissions. In light of this, we consider an EVI-based representation of the gross timing (G):

$$\begin{array}{}\text{(7)}& G(x,y,t)=max\left(\mathrm{0},-{\displaystyle \frac{\partial \mathrm{EVI}(x,y,t)}{\partial t}}\right).\end{array}$$

The $max(\cdot )$ function ensures that the emissions are strictly positive. We note that Eq. (7) incorporates both temporal and spatial information, and can thus be used to represent the spatial distribution, in which case we can set S=1.0 for all grid-points (x,y) (scenario E3). Alternatively, we can use the same spatial forcing (based on an assumed land use classification) to provide an extra spatial constraint. ∂EVI is used in scenarios E2 and E4.

3.1.6 Statistical models

In parallel to the emission–dispersion modelling presented here, statistical forecasting methods have been trialled for use in Victoria. These models are non-linear regression equations that use weather model data, derived parameters from the MODIS EVI and land use maps as predictors. These data can be decomposed into a slow-moving seasonal component (similar to the gross-timing term described above) and a second component that accounts for day-to-day variation. The models were trained on daily pollen count data, and thus cannot resolve higher-resolution temporal variation. The gross-timing function smooths out much of the day-to-day variation, and is modulated by the immediate-timing term when estimating temporal variability in the emissions module. The two statistical models are described in detail in Silver et al. (2019), and summarised here. “V1” used data from Melbourne spanning from 2000 to 2016 (scenario E9), whereas “V2” also used the 2017 data from the eight Victorian sites (scenario E10). The V1 model was developed ahead of the 2017 pollen season before counts were available at the new pollen sites, as the BOM required input for their pilot thunderstorm asthma service. The seasonal component was represented as a Cauchy distribution (which decays more slowly than a Gaussian distribution), with a fixed scale parameter (k=19 d). The magnitude of the pollen season (corresponding to the maximum of the seasonal term) was estimated by univariate linear regression on the winter-time maximum EVI. The timing of the seasonal maximum was estimated by the day of the year when the EVI falls to 0.05 below its winter-time maximum. The magnitude and timing were smoothed spatially using an inverse cubed distance weighting.

Both V1 and V2 were constructed as generalised additive models (Wood, 2006), a form of multivariate regression that allows for a non-linear influence of the predictor variable on the response variable. The response variable used was the log (x+1)-transformed pollen count. The log of the Cauchy term and a number of derived weather parameters were considered for inclusion in the model. Each model was built up via forward step-wise variable selection; starting with a “null model” (predicting nothing but the mean), terms were considered for inclusion. Each predictor was trialled as having a linear or alternatively non-linear effect on the response variable, and the out-of-sample prediction skill was tested. The combination of predictor and form (i.e., linear or non-linear) that yielded the biggest gain in predictive skill was retained. This procedure was repeated until the incremental impact of additional terms on predictive skill was negligible. The model skill was tested by leaving out entire pollen seasons, fitting the model without these data, then assessing the model using the out-of-sample subset. Model skill was quantified using the Pearson correlation between predicted and observed pollen.

The statistical models were adapted for 3-D dispersion modelling to use hourly meteorological inputs (or daily, in the case of precipitation). The adapted forms of the two models are as follows:

$$\begin{array}{ll}{\displaystyle }& {\displaystyle }\log (\mathrm{1}+{\mathrm{P}}_{\mathrm{1}}(x,y,t\left)\right)=-\mathrm{0.290}+\mathrm{0.970}\cdot {\mathrm{R}}_{\mathrm{1}}(x,y,d)\\ {\displaystyle }& {\displaystyle }-\mathrm{0.183}\cdot \log \left(\mathrm{PR}\right(x,y,d)+\mathrm{1})-\mathrm{0.117}\cdot \log \left(\mathrm{PR}\right(x,y,d\left)\right)\\ \text{(12)}& {\displaystyle }& {\displaystyle }+f_{\mathrm{TM}\mathrm{1}}(x,y,t)+f_{\mathrm{RH}\mathrm{1}}(x,y,t){\displaystyle }& {\displaystyle }\log (\mathrm{1}+{\mathrm{P}}_{\mathrm{2}}(x,y,t\left)\right)=\mathrm{1.225}+\mathrm{0.770}\cdot {\mathrm{R}}_{\mathrm{2}}(x,y,d)\\ {\displaystyle }& {\displaystyle }-\mathrm{0.033}\cdot \mathrm{WS}(x,y,t)+f_{\mathrm{RH}\mathrm{2}}(x,y,h)\\ \text{(13)}& {\displaystyle }& {\displaystyle }+f_{\mathrm{TM}\mathrm{2}}(x,y,t)+f_{\mathrm{PR}}(x,y,d),\end{array}$$

where P is the predicted pollen emission for version i at grid-point (x,y) and time t, R_i is the seasonal term based on the EVI parameters at grid-point (x,y) and for day d (outlined below), and WS is the wind speed (m s⁻¹). In both versions of the statistical model, the variable selection process assigned a non-linear response to the temperature, f_TMi (^∘C) and RH f_RHi (%). Only V2 uses a non-linear term for daily precipitation, f_PR (mm). The non-linear relationships between pollen emission and increasing temperature, RH and precipitation are shown in Fig. 4. The shaded regions correspond to plus or minus twice the standard error of the GAM term, and are greater in regions of the distribution with fewer observations. For example, there were far fewer observations at the upper tail of the temperature range considered, and the standard errors are correspondingly larger.

Figure 4The shape of the non-linear terms in the statistical models related to temperature (a and c), relative humidity (b and d) and rainfall (e) for V1 (a and b) and V2 (c, d and e). The shaded regions correspond to plus or minus twice the standard error of the GAM term.

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The statistical parameterisations were based on ambient pollen concentrations rather than emissions; thus, the non-linear terms take transport and dilution processes into account. The shapes of these relationships are similar to those described by Erbas et al. (2007) for grass pollen in Melbourne, and also by Zink et al. (2013) for birch pollen in Europe. The temperature response in both models increased until 25 to 30 ^∘C (Fig. 4a, c). The decline in pollen response at higher temperatures is likely due to dilution with higher planetary boundary layers. On days in November where the temperature is above 25 ^∘C, the maximum modelled boundary layer height is nearly double the height modelled on days below 25 ^∘C. Thus, the assumption of declining emissions with increased temperature is likely incorrect. There is relatively little non-linearity with humidity. The general trend is for increased concentrations (or emissions) in drier conditions, explained by the drying required before anther dehiscence. The rainfall term shows a sharp decline until about 2 mm d⁻¹, after which little additional pollen suppression occurs, although there is considerable uncertainty given the relative paucity of high-rainfall days. The suppression of grass pollen concentrations (or emissions) is likely due to the low potential for anther dehiscence in moist conditions, and the wet deposition of ambient pollen.

The seasonal term based on the EVI parameters is given as

$$\begin{array}{ll}\text{(14)}& {\displaystyle }& {\displaystyle }{\mathrm{R}}_i(x,y,d)=\log \left({\mathrm{SF}}_i\right(x,y)\cdot f_{\mathrm{C}}(d,{\mathit{\mu }}_i(x,y),k\left)\right),\text{where}\text{(15)}& {\displaystyle }& {\displaystyle }{f}_{\mathrm{C}}(d,\mathit{\mu },k)={\left(\mathit{\pi }\cdot k\cdot \left[\mathrm{1}+{\left({\displaystyle \frac{d-\mathit{\mu }}{k}}\right)}^{\mathrm{2}}\right]\right)}^{-\mathrm{1}}{\displaystyle }& {\displaystyle }{\mathrm{SF}}_{\mathrm{1}}(x,y)=max(-\mathrm{4355.913}+\mathrm{21490.343}\\ \text{(16)}& {\displaystyle }& {\displaystyle }\cdot E_{\max ,\mathrm{smoothed}}(x,y),{\mathrm{10}}^{-\mathrm{10}})\text{(17)}& {\displaystyle }& {\displaystyle }{\mathit{\mu }}_{\mathrm{1}}(x,y)=E_{\mathrm{drop},\mathrm{smoothed}}(x,y)\text{(18)}& {\displaystyle }& {\displaystyle }{\mathrm{SF}}_{\mathrm{2}}(x,y)=\mathrm{267.627}+\mathrm{8853.990}\cdot E_{\max ,\mathrm{smoothed}}(x,y)\text{(19)}& {\displaystyle }& {\displaystyle }{\mathit{\mu }}_{\mathrm{2}}(x,y)=\mathrm{202.478}+\mathrm{0.385}\cdot E_{\mathrm{drop},\mathrm{smoothed}}(x,y),\end{array}$$

where the scale factor parameter SF_i(x,y) is based on the smoothed value of the winter-time maximum EVI ($E_{\max ,\mathrm{smoothed}}(x,y)$), whereas the timing of the peak of the pollen season (μ_i(x,y)) is assumed to scale linearly with the smoothed field of the day of the year when the EVI drops 0.05 below its winter-time maximum (see Silver et al., 2019, for further details). The statistical approach accounts for inter-annual variation via the EVI time-series at each grid cell. Higher winter-time peak EVI values are associated with higher cumulative grass pollen counts over the following season.

3.2 Statistical evaluation

The skill of the pollen forecasts depends in part on how well the meteorology is predicted. The Pearson correlation indicates the strength of the correspondence without consideration of differences in magnitude, whereas the index of agreement (IOA, described in the Supplement) is a good indicator of model performance. The normalised mean bias (NMB) gives the relative difference between the model and observations.

To determine the best pollen emission methodology, we look for skill in the ability of VGPEM1.0 to forecast the possibility of the pollen being classed as high or extreme (>50 grains m⁻³), which is a level at which health impacts may be felt more strongly. The number and timing of predicted high pollen days is evaluated quantitatively for consistency and accuracy, by calculating the probability of detection (POD), the false alarm ratio (FAR) and the equitable threat score (ETS) from a simple table of model outcomes (Table 3). The POD is the fraction of correctly identified high model forecasts compared with the observations, between zero and one:

Table 3The 2×2 contingency table describing each model outcome. The model outcomes a, b, c and d then become the variables in Eqs. (20)–(23).

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The FAR puts a value between zero and one regarding how many of the predicted high pollen days did not correspond with an observed high pollen day:

The ETS is the fraction of modelled high pollen days that were correctly predicted and is adjusted for correctly modelled days occurring with random chance. The ETS value is between $-\mathrm{1}/\mathrm{3}$ and 1, with a score of 0 indicating no skill; this is defined as

where

As Zink et al. (2013) point out, low skill scores are given to models where the pollen concentrations are close to observed concentrations yet fall into separate “risk” categories. For example, the model predicts 48 grains m⁻³ and classes the risk category as “moderate”, whereas the observations are 52 grains m⁻³ and the risk category is “high”. Therefore, we also evaluate the modelled pollen against the observations in terms of their Pearson correlation, RMSE and Gerrity score. Statistical evaluations using categorised and non-categorised pollen counts will show how the Australian grass pollen thresholds impact our results. The Gerrity score puts a value on the accuracy of VGPEM1.0 in predicting all of the observed pollen categories, relative to that of random chance (Gerrity, 1992). Gerrity scores range between −1 and 1, with 0 indicating no skill and 1 being a perfect model. Calculation of Gerrity scores is complex and is described fully in the Supplement.

The best forecasting methodology will have a high Pearson correlation, Gerrity score, POD and ETS, and a low FAR and small RMSE.

4.1 Verification of meteorology

Meteorological variables are extracted from the ACCESS runs at the locations of the AWSs closest to the pollen observation sites (Table 1). At some pollen observation sites the AWSs are located more than 10 km away, or nearly 30 km away in the case of Dookie. A direct comparison is made of hourly temperature, wind speed, wind vectors, precipitation and RH between ACCESS and the AWS observations, using the Pearson correlation, IOA and NMB. (Fig. 5). Here the NMB is normalised by the mean of the absolute value of the observations (as opposed to the mean of the observations) because wind vectors contain negative values. Temperature and RH are both modelled with a high degree of accuracy at all sites, demonstrating a high Pearson correlation (average r=0.9), almost no bias, and high IOA (average IOA=0.8). Predicted wind speeds are biased slightly low (average $\mathrm{NMB}=-\mathrm{0.2}$). The V (north–south) component is approximately as well modelled as the U (east–west) component (average V r=0.80 compared to average U r=0.77). Precipitation has a low degree of bias (average NMB=0.17) but is not particularly well correlated with the observations (average r=0.21), and has a lower overall IOA (average IOA=0.55).

Figure 5Comparison of observed and modelled meteorological variables at automatic weather station sites nearest to the pollen observation sites. (a) Pearson correlation. (b) Index of agreement. (c) Normalised mean bias.

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4.2 Observed and modelled pollen correlations with meteorology

We assess which measured AWS meteorological variables are most strongly related to the observed pollen. Figure 6a shows that observed grass pollen is most strongly correlated with temperature at the majority of sites (average r=0.44), and most negatively correlated with RH (average $r=-\mathrm{0.34}$).

Figure 6Pearson correlations of (a) observed pollen with observed meteorological variables from the nearest automatic weather station, and (b) modelled pollen with modelled meteorological variables.

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Observed wind speed is not strongly related to observed grass pollen, except when combined with direction, specifically the U wind vector is generally a stronger predictor of pollen (average r=0.32) than the V wind vector (average r=0.22). We include a wind rose for each AWS site in the Supplement to determine the strength of the winds. The roses show a strong southerly influence, corresponding with an afternoon sea breeze at most sites apart from Churchill, located within an east–west aligned valley. Sites further west in Victoria (Hamilton and Creswick) also show a northerly influence, generally with a greater percentage of wind speeds above 4 m s⁻¹ than elsewhere. Precipitation washes pollen from the air, but shows no correlation here as rain during the 2017 season was infrequent (average r=0). Pollen observations at Dookie are the least correlated with any of the meteorological variables, perhaps because the closest AWS is 29 km away.

Figure 6b shows Pearson correlations for the modelled pollen against ACCESS meteorology, using scenario E8 as an example that uses the meteorological timing function. The strengths of the modelled correlations are broadly similar to those observed in Fig. 6a, but the model is more strongly coupled to wind speed (average r=0.25) and less correlated with the U wind vector than is observed (average $r=-\mathrm{0.07}$). However, the observed U and V correlations are not strong, and do not point to particular locations being strong pollen sources. Inverse modelling may help pinpoint productive grass pollen regions for each site. We extracted the boundary layer height from the model (unavailable in the observations), which showed that the modelled grass pollen is more strongly correlated with atmospheric dilution (average r=0.61) than it is to temperature (average r=0.44). Average modelled diurnal boundary layer evolution during November 2017 in Melbourne increases after sunrise at 05:00 AEDT to a peak of 1780 m at 13:00 AEDT. The height declines during the afternoon coincident with a southerly sea breeze, but is still above 1200 m at 17:00 AEDT. The nocturnal boundary layer is around 200 m. Over 77 % of grass pollen is found at ground level (Damialis et al., 2017) due to its size and density. The lifetime of our model pollen over 1 km is 6 h. The model RH is more negatively correlated with grass pollen levels (average $r=-\mathrm{0.52}$) than is observed. The observed relationship may be weaker, as the pollen measurements are not coincident with the AWS.

4.3 Verification of pollen source methodologies

The modelled pollen concentrations are first normalised by the observed seasonal mean across all observation sites, which is equal to 47 grains m⁻³. This normalisation allows the evaluation of trends in the daily grass pollen concentrations without considering their magnitude, as this can be corrected later. For 2017, observed individual site means range from 31 grains m⁻³ at Melbourne to 60 grains m⁻³ at Creswick. The lowest means are found in the densely populated regions of Geelong, Melbourne and Burwood (see Fig. 1f). Figure 7 shows correlations and statistical results for each pollen observation site. Numbers of observed days in the lumped high and extreme category (>50 grains m⁻³) are above 20 d for all sites.

Figure 7Results from the pollen emission methodology scenarios: (a) Pearson correlation, (b) Gerrity score, (c) POD, (d) ETS, (e) FAR and (f) RMSE. The sites are presented from west to east, and red refers to Gaussian methodologies, yellow refers to ∂EVI methodologies, green refers to the production–loss model and blue refers to statistical methodologies. A higher score is better for the Pearson correlation, Gerrity score, POD and ETS. A lower score is better for the FAR and RMSE.

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E1, E2 and E3 used wind speed as the immediate timing function, which provided poor prediction skill scores (average r=0.25, 0.18 and 0.17 respectively), similar to results by Viner et al. (2010) and Zink et al. (2013). Wind promotes pollen emissions, but the plant must flower first – a process not controlled by wind speed. Wind also correlates poorly with pollen observations due to the competing effects of strength versus increased ventilation and mixing (Sofiev et al., 2013). Subsequent method E5 used the meteorological timing function that included temperature and RH and performed better (average r=0.43). Sofiev et al. (2013) also showed that observed birch pollen in Europe was negatively correlated with RH. Widening the timing of the peak pollen emission from 2 to 4 h, as included in E6, improved results further over E5 (average r=0.44).

At most sites the Gaussian description of the season performed better than the ∂EVI, shown by improvements in the FAR of E1 over E2, both of which used wind speed as the immediate timing descriptor (average FAR=0.57 and 0.61 respectively), and E5 over E4, both of which used the meteorological timing function (average FAR=0.48 and 0.52 respectively). These results indicate that using ∂EVI data as descriptors of the pollen season results in poor skill at most of the sites. The ∂EVI data are very noisy. However, E4 using the ∂EVI data and a meteorological timing function gives a good Gerrity score (0.54) and high POD (0.92) and ETS (0.40) at Dookie. When other elements of the EVI data are used in the statistical models (E9 and E10), such as the winter maximum and the day on which the EVI falls below 0.05 of the winter maximum, the pollen prediction is much improved at most sites (average POD E9=0.67 and E10=0.69). The performance of E10 indicated improvements in forecasting skill at all sites with the exceptions of Dookie and perhaps Bendigo. E10 predicted the lowest FAR of high pollen predictions at five of the eight observation sites (average FAR=0.37). The ETS adjusts the model score for achieving high pollen predictions at random. E10 achieves higher ETS scores at four of the eight sites (average ETS=0.35). Both the statistical emission parameterisations assume an underlying Cauchy distribution, which is modulated by the effects of wind, temperature, RH and rainfall. At each model grid cell, the peak and magnitude of this bell curve is calculated from statistics inferred from the EVI gradient.

The pollen production and loss model E7 had a very high POD (0.96) at Hamilton, but the method was less effective elsewhere with high FAR and RMSE scores at the other observation sites (average FAR=0.55 and RMSE=63). E7 used the Gaussian distribution for the seasonal term which could be improved upon, but the method was superseded by the good performance of the statistical models (with the exception of E9 in Hamilton and Geelong).

The Geelong pollen observations are not well modelled by most of the emission methodologies with Gerrity scores mainly in the negative region and high FAR>0.8. E10 provides the best scores by far at Geelong with a 0.62 Pearson correlation and 0.3 Gerrity score, although, overall, results are poorer for Geelong than any other site. The wind rose for Geelong shows the strong Southern Ocean influence, and there are few grass-filled pixels between the coast and the pollen count site which the model relies upon (Supplement).

The sites vary considerably in terms of surrounding land use, whereas all of the pollen in the model comes from pasture grass. This impacts the individual site performance against the pollen observations. Hamilton, Dookie and Churchill are close to pollen source areas. Creswick is surrounded by forest. The Burwood and UoM sites are in heavily built up areas with green space, which is not included in the model pasture grass maps.

Comparing the results of the non-categorised Pearson correlation and RMSE against the categorised Gerrity score yields minor differences between 0.1 and 0.2 units, and suggests that the Australian grass pollen thresholds influence the analysis by about 15 %. If the best performing scenario for each observation site and under all scoring methods is counted from Fig. 7, shifted Gaussian methodology E8 is best 12 times, statistical representation E9 is best 4 times and E10 is best 25 times. E9, built using data prior to the 2017 season, has a stronger dependence on precipitation than E10, which is not supported by the correlation of 2017 pollen with meteorology. This suggests that the V2 statistical approach to the immediate timing combined with an EVI-based approach to the gross timing and a spatial source is likely to produce the most accurate pollen forecasts.

It is useful to plot the observed and modelled pollen as a cumulative time-series, as this indicates the timing of increased and decreased pollen counts (Fig. 8). Here we focus on the best performing scenarios from each of the seasonal emission methods, capturing the range in descriptions of the pollen season. The observations show an “S” shaped profile, with increased pollen gradients in November. By the end of the 2017 season, all modelled profiles reach a cumulative total of 4200 grains m⁻³ due to normalisation to the same observed mean value.

Figure 8Cumulative time-series for pollen across the 2017 season. Sites arranged from west to east.

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The ∂EVI method E4 tends to emit grass pollen too early in the season compared with observations at most sites. However at Dookie the shape of the season in E4 and E8 is more similar to the observations, and E4 captures the mid-November change when pollen counts decrease better than E10. The observed pollen at Dookie experienced a much larger grass pollen input from the middle of October to early November than E10 (but is represented well by E8). There is little additional observed pollen at Dookie after early November, which is at least 20 d earlier than at the other sites. At Melbourne, Bendigo and Burwood, both E8 and E10 predict the early part of the grass pollen season very well, but emitted too much modelled pollen towards the end of the season. The steeper gradient in E8 and E10 at Melbourne between the middle and the end of November shows that too much pollen was emitted during this period. In contrast, observed pollen at Churchill, Creswick, and Hamilton shows a rapid increase in emissions at the end of November that is not matched by either E8 or E10. However, the observations suggest that additional pollen continues to be emitted towards the end of December at Creswick and Churchill, prolonging the season. Scenario E8 captures the steep November gradient at Hamilton very well.

The observed and modelled pollen cumulative profiles in Melbourne, Geelong and Burwood are less smooth than the other regional sites, perhaps indicating more atmospheric variability near the coasts. It might also indicate the larger distances between the urban sites and the grass pollen production regions (more transport and less local production), compared with the monitoring sites within grass pollen production areas (less transport and more local production). Here we also note the apparent lack of an “S” shape in the modelled profiles at Geelong, which may account for the poor model performance at this site.

Table 4 splits the best model predictions from E8 and E10 into low, moderate, high and extreme categories for direct comparison with observed categories. Here data from all counting sites are combined to ensure a large sample size. The diagonal in each table highlights the number of days the model has correctly predicted the observed category. Values far from the diagonal indicate the model has under- or over-predicted the observed pollen. We want to avoid occasions where the observed pollen is extreme, but the model predicts low pollen. Table 4 shows that both E8 and E10 have good skill in predicting low observed pollen days. Both models also show high occurrences of predicting moderate pollen when the observed category is low. Siljamo et al. (2013) found difficulties in modelling moderate category days, which is not the case here. Both models are equally good at predicting the high and extreme observed categories. E10 has fewer occurrences of predicting extreme pollen on days when observations were low than E8. However, there are six cases in E8 and one in E10 that predict low pollen when the observations are extreme. These cases occur around the 10–11 November within the city at Geelong, Melbourne and Burwood. Examining the meteorology from this period (pollen counts are date-stamped at 09:00 AEDT, but represent the preceding 24 h) shows that the model has captured the observed temperature, wind speed, direction and zero rainfall. The observed wind direction is from the south and south-east, bringing mainly clean, marine air. However observed pollen is extreme on these days, suggesting a highly localised source. One explanation is that only pasture grass is considered in the model, whereas grass is usually present in most other land use categories. There is green space within most cities on both public and private land, and grass plants are efficient at colonising disturbed areas such as road verges. Correlations between observed pollen at each site are not particularly strong (average r²=0.28), suggesting that the pollen sources may not be related, or are highly localised. The modelled correlations between all sites are very strong because they share the same pollen source characteristics (average r²=0.80). Inverse modelling could highlight where other grass land use categories contribute to grass pollen. Future development of VGPEM could consider the sub-grid-scale grass fraction using high-resolution satellite data sources.

Table 4The number of days the model predicts a particular observed pollen category for E8 (left) and E10 (right). Data from all Victorian sites are combined. Bold text highlights where the model captures the correct observed category.

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