In the first step, the existing remotely sensed LST products are compared over Australia to gain a better understanding of their differences and similarities. Our analysis is focused on the temporal agreement as systematic differences may exist due to the different vertical depths that are observed; [
7] hence, coefficient of determination (R
2) and standard error (SE) are the metrics of interest. This SE was determined through Equation (1) in which
represents the variation in the MODIS LST. In order to better understand seasonal trends and interannual variability, this part of the analysis was done on both anomalies after removing the climatology as well as raw timeseries. The decomposition into anomalies was done through a standard approach that uses a 31-day moving window centered on a particular day of the year following [
4]. In the next step, the scalability of the passive microwave based product is examined and a relatively simple merging approach was proposed. Then, the various different LST products and the combined product were compared against the MERRA re-analysis LST dataset that serves as a consistent reference over the various climate zones that Australia experiences, again for anomalies and raw timeseries. Finally, the comparison against MERRA was divided over these four major climate zones to further understand their agreement.
3.1. Comparing Existing Products
A direct comparison between the LST products from MODIS and AMSR2 was presented in order to better understand their potential differences and similarities.
Figure 2 was based on the anomalies and presents both the R
2 (left) and the SE (right) for the observations that were taken during the day (top) and during the night (bottom). The raw time series were analyzed in an identical way and those spatial maps were presented in the
supplementary material (Figure S1). Furthermore, these satellite paths were explicitly separated to understand how different physical conditions during the day and the night impact these LST products. A common assumption (e.g., [
13,
14]) in applications that use LST products is that the soil and canopy temperature are equal during the night due to thermal equilibrium. During the day, this assumption introduces uncertainties due to the imposed cooling effect of transpiration which generally results in soil temperatures that are higher than canopy temperatures. This phenomenon may impact the products differently as the original spatial resolution of the MODIS LST product is 1 km; hence, this product may have better ability to represent canopy and soil temperature separately than the passive microwave LST product.
For the anomalies, it was found that the mean R
2 values over Australia were high for both the day (R
2 0.48) and night (R
2 0.56) time observations. The mean R
2 values for the raw time series from
Figure S1 were found to be even higher, for the day (R
2 0.82) and night (R
2 0.85) time observations. The spatial distribution of these R
2 values showed many similarities but also some differences for both the day and night time observations, as well as the anomalies compared to the raw time series. Generally, the products show very high agreement with R
2 ranging from 0.50 to 0.75 for the anomalies and from 0.8 to 1.0 for the raw time series over the central part of Australia. This agreement tends to drop in the tropical regions located in the north of Australia with relatively low agreement in the far north of WA and the Northern Territory (NT) for the day time observations and a relatively low agreement in the far north of Queensland (QLD) for the night time observations. Another feature that stands out in the R
2 maps is the effect that open water may have on the agreement between the products, which tends to drop significantly as shown for Lake Eyre, Lake Torrens, Lake Gairdner in SA, and Lake Mackay and Lake Argyle that border WA and the NT. Inversely, this drop in R
2 results in an increase in SE over these lakes and is evident in both the anomalies and raw time series as well as the different overpasses. Another feature that stands out in the SE maps is the contrast between the day and the night time maps which are reflected in the higher mean values over Australia for the day (SE 3.18 K for the anomalies) as compared to night (SE 1.88 K for the anomalies) time observations. This contrast is in agreement with the commonly used assumption (e.g., [
13,
14]) that was previously mentioned.
In order to further understand the comparison between both LST products, histograms that portray the relative frequency of these two metrics were also presented in a similar order as
Figure 2.
Figure 3 presents the distribution of R
2 and SE for the anomalies whereas the histograms of the raw time series were presented in in the
supplementary material (Figure S2). These histograms confirm that the vast majority of R
2 over Australia is within the high range that was indicated earlier and that only a fraction of the analyzed pixels show a weak agreement. These histograms also confirm the contrasting agreement between the day and night-time observations with significantly lower SE values for the night time LST products. The relative differences in the histograms of the anomalies and the raw time series are also in line with expectations, particularly the overall drop in R
2 shifting the entire histogram to a lower range. Again, the day and night-time contrast is in agreement with earlier findings (e.g., [
13,
14]) on thermal equilibrium.
As previously mentioned (
Section 2.2), the original passive microwave LST algorithm used a predetermined threshold to delineate frozen and unfrozen conditions. A simple analysis was conducted in order to determine the effect of such nonlinearities over our study area. The analysis as presented in
Figure 2 was repeated without the implementation of this predetermined threshold for both the anomalies and raw time series. These results confirm the nonlinear behavior below this preset threshold as R
2 drops and SE increases in absence of the masking procedure which was shown to be consistent for day- and night-time observations (
Table 1). However, this analysis also shows its marginal impact over our study area as R
2 is marginally higher and SE is marginally lower with the masking procedure applied. Finally, a note should be made that the impact of this masking procedure is expected to become rather significant in regions with more pronounced freezing seasons than that of Australia.
3.3. A Comparison against MERRA
The pixels based slope and offset presented in
Figure 4 were now used to scale AMSR2 (T
b, 37V) observations into the MODIS LST product through Equation (2). Each individual pixel in time was assessed and gaps in the MODIS LST product that were caused by clouds or aerosols were, in case AMSR2 observations were available, filled through the pixels based linear regression (Equation (2)).
These combined MODIS and AMSR2 time series were also deseasonalized resulting in anomalies from the combined LST product. Hence, the combined LST product benefits from the cloud penetrating capacity of the passive microwaves observations leading to an increased revisit frequency compared to the individual MODIS LST products. Here, both individual MODIS and AMSR2 products were compared against the MERRA re-analysis data as well as the combined LST products in which the scaled AMSR2 observations fill the cloud gaps in MODIS. The results from this comparison were presented in
Figure 5, which shows the R
2 of the three different product combinations and the percentage of observations that was gained through the addition of the passive microwaves for the night-time observations alone. This comparison against MERRA was repeated for the raw time series of which the results were presented in the
supplementary material (Figure S3).
The individual MODIS (
Figure 5a) and the AMSR2 LST products (
Figure 5c) show a very similar agreement against the independent MERRA dataset with relative high R
2 values over the vast majority of central Australia for both the anomalies and raw time series. When comparing results from the anomalies (
Figure 5) against the raw time series (
Figure S3), there is a tendency of lower R
2 values for the anomalies. This lower agreement is the result of removing seasonal trends hence representing the skills of the various products to represent the interannual variability. It should furthermore be noted that such a drop is in line with expectations [
4] as anomalies generally demonstrate lower agreement than raw time series. The agreement between the MODIS and AMSR2 LST products and the MERRA dataset breaks in the Tropical climate zone located in the north of Australia and this is more profound for AMSR2 than it is for MODIS. In this part of Australia, it is likely difficult to observe LST through passive microwaves due to rain bearing clouds and active precipitation but land surface modelling may also suffer larger uncertainties due to convection processes [
15]. Likewise, this agreement breaks for both products in Southern Victoria (VIC) and Tasmania (TAS). On the other hand, decreasing agreement between MODIS and MERRA was shown in the southern part of WA whereas AMSR2 shows moderate agreement with MERRA in these regions. Generally, the agreement between MERRA and MODIS (
Figure 5a) is highest with a country average R
2 of 0.26 for anomalies and R
2 of 0.76 for raw time series followed by the AMSR2 product (R
2 0.16 for anomalies and R
2 0.66 for raw time series) and the combined product (R
2 0.18 for anomalies and R
2 0.62 for raw time series).
Figure 6 present histograms of the results of this comparison against MERRA, again for the individual MODIS LST product (
Figure 6a), the AMSR2 LST product (
Figure 6b) and the combined LST product (
Figure 6c). This comparison was repeated for the raw timeseries of which the results were presented in the
supplementary material (Figure S4).
These results were furthermore divided in the different Köppen-Geiger climate zones [
16] that Australia experiences, the spatial distribution of these climate zones was presented in
Figure 7. These different zones are based on the original Köppen classification which was modified by [
16] and consists of 29 different climate sub categories globally and 12 sub categories for Australia. These 12 Australian sub categories were divided into four major climate zones including tropical, arid desert, arid steppe and temperate. Three sub categories were merged in the tropical (A) climate zone and they include rainforest (f), monsoon (m) and Savannah (w). Furthermore, the arid desert (BW) and arid steppe (BS) were separated into a major climate zone and both consist of two different sub categories including hot (h) and cold (k). Finally, the temperate climate zone includes five different sub categories (Csa, Csb, Cwa, Cfa and Cfb) that were categorized based on drought and temperature indicators throughout the season.
Figure 7 presents the spatial extent of these 12 Köppen-Geiger sub categories over Australia including the four major climate zones that were further used in this study.
Table 2 provides the averaged results per major climate zone and demonstrates a high degree of consistency compared to the country average results for both the anomalies and the raw time series. First, the relative agreement between MERRA and both individual and merged products is consistent with highest agreement for MODIS and the lowest agreement for the combined product, demonstrated by both R
2 and SE metrics. The lowest agreement for all products was generally found in the tropical climate zone followed by the temperate climate zone, arid steppe and the highest agreement was found over arid deserts. It should be emphasized that the agreement drops for the merged product comes with a significant increase (20% on average) in number of observations gained by adding AMSR2 to the individual MODIS based product.
Figure 5d expresses this observation gain in percentage, which is effectively a combination map between revised time of the individual sensors and cloud contamination. The central part of the country generally gains 10%–20% more observations but some regions, such as TAS, southern VIC and the Tropical regions located in the north of Australia, generally gain more than 30% more observations. Hence, it is concluded that the significant gain in observations through the MODIS-AMSR2 combinations comes at that penalty in performance.
A further example of the individual MODIS and merged LST products was provides in
Figure 8 and was, similar to
Figure 1, based on observations made on 3 April 2015. Large parts of NSW, as well as significant parts of northeastern SA, southern QLD and TAS experience cloud cover on this day, hence the MODIS LST product (
Figure 8a) presents no data values in these regions. These cloud gaps were filled by AMSR2 observations through the proposed combination approach resulting in an improved coverage over this part of Australia (
Figure 8b).
Figure 8c presents the spatial distribution of the sensors that were used in the combined LST product. Regions with gray shading are based on MODIS whereas the cyan regions are based on scaled AMSR2 observations.
A final example that demonstrates the combination approach and its potential usefulness in operational systems was presented in
Figure 9. Australia’s central coast received significant amounts of precipitation on 21 and 22 April 2015, which resulted in the Hunter Valley floods and was shown in
Figure 9. This
Figure 9c presents precipitation data for Maitland, a city located in the Lower Hunter Valley, for a five week period as obtained by the Australian Water Availability Project (AWAP; [
17]. The AWAP precipitation shows roughly three separate precipitation periods of which the first resulted in significant floods. The obvious link between precipitation and cloud obstruction resulted in the absence of MODIS data during those precipitation periods. Those gaps in MODIS were then filled by AMSR2 observations as scaled through the proposed combination approach. The periods which heavily rely on these passive microwave observations were indicated through a grey background and demonstrate the successful scaling of AMSR2 observations resulting in an increasing number of LST observations.