We propose eight signatures to quantify AET behaviour, as outlined in Fig. 1. This list is not intended to be exhaustive, but rather to seek a set that is reasonably representative of the variety of characteristics inherent to AET dynamics as a good starting point for future research. As with streamflow signatures, the metrics cover a wide range of timescales, and different metrics require different temporal aggregations of AET information (specifically daily, monthly, or annual) tailored to the metric in question.

Relative to global averages, Australia is a dry continent with annual average precipitation below 450 mmyr-1 (Isaac et al., 2017). However, the coastal areas from southeast Australia to northern Australia receive comparatively higher precipitation, exceeding 1000 mmyr-1 in many areas. This study focuses on seventeen OzFlux sites in Australia (Fig. 2). OzFlux, a part of the international FluxNET program, is a micrometeorological monitoring network in Australia and New Zealand equipped with eddy covariance measurements, providing information on carbon, energy, and water exchange. The seventeen sites constitute the majority of flux towers in Australia; while seven other active flux towers exist, they were excluded due to insufficient coverage (i.e., <7 years) and considerable percentages of negative and unavailable data. The selected study sites cover a wide range of climate and ecosystem regions in Australia, as summarised in Table 1. The time period of data availability varies at each site (typically 7–20 years). Hence, different periods of data coverage are adopted in this study to perform the analysis at each site.

To characterise the performance of AET_RS products, the signatures described in Sect. 2.1 are calculated separately for flux towers AET (AET_Fluxtower) and AET_RS. Then, we investigated the deviation of AET_RS signatures from AET_Fluxtower signatures. As mentioned above, different periods have been considered at each flux tower site depending on their data coverage. For each site, the flux tower period of record determined the period of comparison between flux tower and remotely sensed information. Finally, the traditional efficiency metrics such as NSE (Nash and Sutcliffe, 1970; Eq. 7), KGE (Gupta et al., 2009; Eq. 8), and components of KGE were calculated using monthly MODIS and CMRSET AET at each flux tower site. These metrics are often relied upon by authors to characterise quality of timeseries data but the downside is that they have limited capabilities of demonstrating what aspects of dynamics is deficient in the case of a low performance score. Here we demonstrate that the signatures can be used to contextualise low scores at some sites, where traditional metrics are deficient.

It is important to clarify that these efficiency metrics are calculated over time at individual sites. For instance, NSE is computed at each site across time, which differs from the use of NSE to assess the agreement of signature values across multiple sites between AET_RS and AET_Fluxtower. To avoid confusion, we refer to the former as NSE_{across time, single site}, and the latter as NSE_MODIS and NSE_CMRSET, which denote how well the remotely sensed AET signatures match the flux tower-derived signatures across sites. 7NSE=1-∑i=1n(AETFluxtower,i-AETRs,i)2∑i=1n(AETFluxtower,i-AETFluxtower‾)2 where, i – time step (in the case of NSE calculation across time at a single site), AETFluxtower,i – Flux tower AET at i, AETRs,i – Remotely sensed AET at i, AETFluxtower‾ – Mean of flux tower AET, n – Number of observations. 8KGE=1-(r-1)2+(α-1)2+(β-1)2 where, r – Pearson correlation coefficient between flux tower and RS AET, α – Ratio of standard deviation between RS AET and flux tower, β – Ratio of mean between RS AET and flux tower.

Figure 4a shows an increase in the long-term median (AET̃annual) values with decreasing aridity index, as expected. For example, less arid sites (shown in blues), such as Cape Tribulation and Cow Bay, have higher AET̃annual, while more arid sites (shown in reds), such as Calperum and Great Western Woodland have lower AET̃annual. The comparison of AET̃annual between flux tower and RS products shows that all sites except for three sites (i.e., Robson Creek, Cow Bay and Cape Tribulation) in the tropical northern Queensland, the RS AET̃annual aligns relatively close one to one line with flux tower AET̃annual (NSECMRSET=0.61 and NSEMODIS=0.42), although some scatter and slight underestimation are evident. In contrast, the three tropical northern Queensland sites, there is a strong overestimation of RS AET̃annual, despite differences in aridity among these sites. Figure 4b shows a higher coefficient of variation of annual AET (CVannual) at arid flux tower sites such as Calperum, Sturt Plains, and Yanco, whereas other sites show lower CVannual within the range of 0–0.2. CVannual is lower in both MODIS and CMRSET AET compared to flux towers at almost all flux towers, and the scatter is high.

Figure 5a shows periodicity (P12month) via the lag-12 autocorrelation. No clear relationship is observed in P12month with aridity. For example, weaker P12month values are observed at both the more arid flux tower sites (e.g., Great Western Woodlands, Yanco) and less arid flux tower sites (e.g., Cape Tribulation). Remotely sensed data performs more poorly in this metric than in any other. Across all sites, the P12month of CMRSET monthly AET does not systematically over- or underestimate flux tower P12month. However, there is a considerable scatter meaning some sites showing significant overestimation and others significant underestimation of CMRSET P12month to flux tower P12month. In contrast, MODIS monthly AET shows stronger periodic behaviour than ground measurements at most of the flux tower sites.

Figure 5b compares the timing of seasonal peaks (TSP) between AET_RS and AET_Fluxtower estimates. Here, CMRSET tends to show the same timing (7 out of 17 flux towers) or closer timing (e.g., one month offset – 6 out of 17 flux towers) of TSP as flux towers at many flux tower sites, whereas those calculated using MODIS AET are significantly offset with flux tower TSP.

Figure 6 quantifies and compares monthly AET signatures using AET_Fluxtower and AET_RS. Figure 6a shows a lower CVmonthly at less arid flux towers such as Cape Tribulation, Cow Bay, and Robson Creek, with most other flux towers grouping tightly between CV values of 0.3 and 0.6, while Sturt Plains is a clear outlier at 0.9. CVmonthly from CMRSET and MODIS AET do not show much overall bias relative to AET_Fluxtower, yet the match with observed is very poor, with considerable scatter due to overestimation and underestimation of CVmonthly, depending on site.

Regarding water stress (WS), Fig. 6b shows how WS increases with aridity, as expected. WS from CMRSET and MODIS AET is moderately well predicted except for wet flux towers, which are underestimated. Figure 6c shows the AET asynchronicity to PET (AAP) that incorporates differences in phases between AET and PET timeseries. Results show that both AET_Fluxtower and AET_RS are asynchronous with PET (i.e., APP>0) for all the sites. However, at wetter sites, AET is more synchronous with PET showing smaller APP values (i.e., smaller APP indicates closer synchronicity to PET), but increasing with aridity index (except at Calperum and Great Western Woodlands sites). Furthermore, the results show separation between remotely sensed products, with MODIS showing more AAP while CMRSET showing lower AAP compared to flux tower AAP for sites exhibiting higher than average asynchronicity.

Figure 7 shows the AET responsiveness to a rainfall event (R). Recall that such information is unavailable for RS data due to its longer timestep. The R of zero indicates no correlation between rainfall event and the subsequent AET, and Fig. 7 shows no discernible correlation between the magnitude of a rainfall event (i.e., >5 mmd-1 in this example) and the subsequent AET on either the rain day or thereafter (i.e., maximum of 10 d window in this example) at the majority of the flux tower sites, and even a slightly negative correlation, perhaps suggesting that rain days might be followed by cloudy weather that suppresses AET.

Figure 8 shows a range of commonly used efficiency metrics such as NSE, KGE, and the sub-components of KGE, namely, the ratio of standard deviations (α), the ratio of means (β), and the Pearson correlation coefficient (r), calculated using monthly MODIS and CMRSET AET with flux tower AET. The distribution of NSE (median: -0.11) from MODIS AET indicates a poor prediction of AET_Fluxtower on the monthly scale. In contrast, the distribution of NSE from CMRSET AET shows a positive, but still close to zero, median value of 0.14, implying better performance than MODIS but still overall poor performance.

For KGE, the median KGE values across flux tower sites for monthly MODIS and CMRSET AET are 0.45 and 0.53, respectively. The sub-components of KGE, such as α shows closer variability in MODIS AET (median α=1.07) and in CMRSET (median α=0.94) compared to flux tower estimates. The β component of KGE shows a lower mean in MODIS AET (median β=0.77) and a slightly higher mean in CMRSET (median β=1.07) compared to flux tower estimates. The r component of KGE shows a relatively similar correlation for both MODIS AET (median r=0.77) and CMRSET (median r=0.69) with AET_Fluxtower. Although these components of KGE provide valuable information about the ability of AET_RS to capture dynamics from AET_Fluxtower, this information is diluted in the final KGE value. Figure S1 in the Supplement shows the traditional efficiency metric values at each flux tower site.

AET signatures introduced in this analysis offer behavioural insights into AET to complement existing suites of indices for streamflow and, to a lesser extent, groundwater. A key benefit of these signatures is their capacity to characterise different aspects of AET dynamics, allowing the quantification of nuanced aspects that can be discerned through visual inspection but, without signatures, are not easily defined numerically. Some examples are given in Table 2.

Table 2 provides examples of how observed dynamics in AET, such as variability, seasonality, and the relationship between AET and PET, can be translated into measurable indicators using AET signatures. These signatures enable more objective comparisons between AET_RS and AET_Fluxtower, while also offering insights into the underlying processes within a given region.

This capacity for nuanced characterisation in AET signatures contrasts with traditional fit/performance metrics such as NSE and KGE. As mentioned in the introduction, these commonly used performance metrics are often applied to quantify hydrological model performances, but may obscure specific behavioural information (McMillan, 2021; Wagener and Gupta, 2005). For example, the NSE calculated using monthly MODIS and CMRSET AET at some flux tower sites showed negative values, indicating bad predictive skills, whereas the KGE calculated using both the AET_RS tended to show some predictive skills relative to flux tower observations. However, both of these conventional performance metrics fail to identify which aspects of AET in remote sensing products have led to poor prediction of AET_Fluxtower. For example, as per Table 2, at the arid Calperum site, MODIS AET exhibited an earlier seasonal peak in AET compared to the flux tower, an insight captured by the TSP signature that is unavailable using NSE or KGE. Similarly, at the wet tropical Robson Creek, AET_RS products showed slightly greater monthly variability than flux tower observations, again reflected by CV_monthly signature but not clear in conventional metrics. Even though the subcomponents of KGE, such as the ratio of standard deviation, the ratio of mean, and the Pearson correlation coefficient, provided valuable information about the ability of these two AET_RS products to capture AET dynamics compared to AET_Fluxtower, the final KGE value obscures this information.

Given that AET signatures capture more behavioural information than traditional performance metrics, they can also be used in other applications, such as hydrological modelling for more realistic outcomes, in a similar way to using other hydrological signatures. For example, Huynh et al. (2023) incorporated hydrological signatures into the calibration of a conceptual distributed hydrological model and found improved flash flood predictions, achieving higher NSE and KGE scores compared to models calibrated without signatures. Kiraz et al. (2023) developed a signature-based performance metric that strongly correlated with NSE and KGE, while also enabling calibration and evaluation of regionalised ungauged catchments. Using the AET signatures developed above, Gardiya Weligamage et al. (2025) demonstrated that incorporating AET timeseries data with streamflow information into calibration generally yields improvements in overall model performance, as indicated by NSE and KGE values. Their signature-based assessment of calibration to traditional AET metrics revealed that only the monthly variability and AET synchronicity with PET were enhanced in such calibration (relative to streamflow-only calibration).

While these signatures have many inherent strengths, challenges could remain in applying them, particularly in large sample studies, due to data errors associated with flux tower measurements, particularly in extreme climates (McMillan et al., 2023). Therefore, readers should have a prior understanding when regionalising and interpreting any hydrological behaviours using signatures.

Ozflux observations are recognised for their high quality, with minimal data gaps and errors. Isaac et al. (2017) reported that around 80 % of Ozflux sites achieved an energy balance closure ratio exceeding 0.8, indicating robust flux measurements. Moreover, these flux tower sites cover a diverse range of vegetation types, including tropical and temperate grasslands, tropical savannas, Mediterranean and temperate woodlands, and both temperate and tropical forests (Guerschman et al., 2022). Given these high-quality data and broader ecological coverage, this study confirms various anticipated AET behaviours at flux tower sites in Australia across different temporal scales. For example, the AET̃annual increased as the aridity index decreased as expected, indicating that less arid flux towers have a higher AET̃annual, whereas more arid flux towers have a lower AET̃annual. However, the CV_annual across flux tower sites was low across the majority of sites (range of 0–0.2 at 14 out of 17 sites), regardless of their aridity index. This finding is consistent with the relatively constant annual AET variability over time, as reported by Gardiya Weligamage et al. (2023). The three exceptions were flux tower sites in dry regions such as Calperum, Sturt Plains, and Ridgefield, which exhibited comparatively higher CV_annual (ranging from 0.3–0.5). This is likely driven by high interannual rainfall variability (Liu et al., 2024; Wang et al., 2017) and high PET (Pan et al., 2021) in dry regions. In such regions, evaporation from soil contributes more to AET than transpiration from vegetation in hot arid environments; moreover, vegetation tends to be opportunistic during rainfall events and remains dormant during dry periods (Ratzmann et al., 2016). Therefore, these factors collectively influence the high variability of AET in hot dry regions.

Signatures that capture short-term temporal dynamics of AET, such as CV_monthly, P12month, and TSP exhibited wide scatter across observed flux tower sites, with no clear relationship to aridity. This decoupling is likely due to the fact that AET dynamics at shorter temporal scales are strongly influenced by local geographic, biophysical, and hydroclimatic conditions such as vegetation dynamics, soil properties, soil moisture dynamics, and inter annual rainfall variability that are not well represented by broad, long-term climate classification like aridity index. van Dijke et al. (2020) reported a strong correlation between leaf area index (LAI) and latent energy (LE) in savanna and arid grassland ecosystems across FluxNet sites, including Ozflux sites. They explained that in these environments, soil water deficiency and high evaporative demand lead to a significant increase in LE even with small increases in LAI. For the evergreen broadleaf forested ecosystem, a positive correlation was also observed between LAI and energy fluxes, attributed to evaporation from canopy interception, which accounts for up to 30 % of total evapotranspiration. While their study suggests that both of these vegetation types exhibit a clear relationship with energy fluxes, our analysis indicates that AET signature patterns, especially on monthly and seasonal scales, cannot be easily explained by classifying based on vegetation cover alone.

At the event scale, most flux towers did not show a discernible correlation between rainfall events and subsequent AET events. Therefore, on first impression, the “AET responsiveness to a rainfall event” signature does not appear to add significant value in this AET signature analysis. However, we could subset event scale rainfall and AET timeseries data by climatic regions, season, or vegetation group to gain more detailed insights. Moreover, we employed this event-scale signature to evaluate commonly used conceptual rainfall-runoff model performances in a companion paper, Gardiya Weligamage et al. (2025), and the models were found to be very biased in this signature, showing simulated AET that was too responsive to precipitation. Therefore, this event-scale signature also adds value in constraining models or exploring model deficiency. Furthermore, this event-scale signature is particularly noteworthy, as it highlights a distinct aspect of AET dynamics not previously quantified. As McMillan (2020) confirmed, no signature (even an indirect AET behaviour explanation using hydrological signatures) was previously identified for assessing AET at the event scale.

The eight AET signatures proposed in this study are used to highlight the strengths and weaknesses of two AET_RS products (i.e., MODIS and CMRSET) on multiple aspects by assessing their AET signatures with those obtained from flux tower observations. Given that it is increasingly common for studies (particularly modelling studies) to adopt AET_RS products, the reported deficiencies in these AET_RS data seem particularly relevant. We emphasize the importance of investigating AET_RS data prior to use in any other applications, such as rainfall-runoff modelling.

While the plots above suggest that AET_RS is generally an unbiased estimate of AET_Fluxtower across the entire catchment sample, the problem is the wide scatter, indicating that estimates at individual sites may be subject to significant errors. This wide scatter was seen in several signatures, such as CV_monthly, AAP, P12month, and TSP.

At the seasonal scale, notable discrepancy was observed between AET_RS and AET_Fluxtower, in terms of P12month, and TSP. For example, challenges were more pronounced with the MODIS AET, which exhibited offsets in TSP (NSEMODIS=-1.44, see Fig. 5b), while being overly periodic but with scatter compared to flux tower data. This suggests that globally developed MODIS AET often failed to reflect AET dynamics at seasonal scale in diverse Australian environment. Conversely, the regionally developed CMRSET product tended to align comparatively better with the TSP observed by flux towers (NSECMRSET=0.52, see Fig. 5b) but with larger scatter. The close alignment of TSP with AET_Fluxtower is likely because the CMRSET model was calibrated only to flux tower sites in Australia (Guerschman et al., 2022), in contrast to MODIS, which is globally calibrated and thus has less Australian focus (Mu et al., 2011). Our findings concur with Guerschman et al. (2022), who reported that the calibrated CMRSET model performs better than MODIS AET (i.e., MOD16A2).

However, Guerschman et al. (2022) also noted that CMRSET captures less of seasonal variability at tropical sites and shows weaker correlation with flux tower AET in arid regions compared to temperate areas. They further explained that the seasonality in tropical and temperate regions is effectively captured by PET, which leads to higher correlation between AET_Fluxtower and CMRSET in those regions than in arid sites. Our results also agree on that higher correlation (r) between both CMRSET (median r=0.69) and MODIS AET (median r=0.77) with flux tower AET. Furthermore, our AAP signature shows that both the AET_RS and AET_Fluxtower with mostly synchronous relationship with PET at flux tower sites in temperate (i.e., flux towers at northern Australia) and tropical regions (i.e., flux towers at northern Queensland).

However, none of the information above supports explaining the differences in periodicity and offsets in seasonal peaks between AET_RS and AET_Fluxtower shown in Fig. 5. We assume that these discrepancies may be attributed to vegetation and surface water stress parameterisation in AET_RS algorithms. However, significant uncertainties related to water stress parameterisation are unlikely, as our assessment using water stress signature showed that water stress is fairly predicted by AET_RS, except for wet, tropical flux tower sites. This exception in the wet tropics could be due to uncertainties associated with the PET (recall that Morton's Wet Environment PET was used in Water Stress signature), which may not be directly comparable to AET_RS. Given this, vegetation parameterisation likely plays a vital role in these observed inconsistencies in P12month, and TSP. This could be due to uncertainties associated with Enhanced Vegetation Index (EVI) and Global Vegetation Moisture Index (GVMI) in CMRSET and in Leaf Area Index (LAI)/Fraction of Photosynthetically Active Radiation (FPAR) in MODIS. Mu et al. (2011) discussed overestimation of LAI as a potential source of overestimation in MODIS AET. Moreover, MODIS AET applies the same set of biophysical parameters for each biome type globally (Mu et al., 2011). Since Australia has distinct biome types, MODIS AET could introduce uncertainties due to differences in plant biophysics. Gan et al. (2018) also reported MODIS AET underestimates flux tower AET at non-forested sites (e.g., Dry River, Howard Springs, Sturt Plains), but overestimates at forested sites (e.g., Tumbarumba, and Wombat State Forests). Consequently, combined uncertainties and limitations could contribute to the seasonality issues in CMRSET and MODIS AET. Therefore, caution should be exercised when extracting seasonal information from both MODIS AET and CMRSET.

At the annual scale, RS AET̃annual largely matched with the flux tower AET̃annual, although some scatter and slight underestimation were observed. However, a notable overestimation of RS AET̃annual was shown at 3 tropical study sites in northern Queensland, namely Robson Creek, Cow Bay and Cape Tribulation. This discrepancy may reflect geographic and hydroclimatic influences specific to these coastal rainforest environments. This includes steep spatial gradients in wetness that may not be well characterised by gridded data, as supported by Guerschman et al. (2022) who also noted the near coast and strong orographic precipitation gradient in the Cow Bay and Cape Tribulation area. This highlights the need for caution when interpreting remotely sensed annual AET in similar settings. In the comparison of CMRSET and MODIS AET, Mohammadi et al. (2015) showed that MODIS AET tends to underestimate in arid floodplains in Australia, similar to several other studies (e.g., Kim et al., 2012; Tang et al., 2015), together suggesting that the underestimation may be due to limitations in MODIS AET in estimating land cover changes and water cover fraction. This finding is in line with our results at most flux tower sites. However, our study shows that both the AET_RS underestimate compared to flux tower AET. This could be due to the difference in spatial footprints between AET_RS and AET_Fluxtower. In addition, all CV_annual showed underestimation (negative bias) relative to flux towers, implying relatively poor year-to-year variability in MODIS AET and CMRSET compared to actual interannual variability as seen in flux tower data. This may also be due to uncertainties and limitations associated with vegetation parameterisation in AET_RS algorithms.

This study serves as a proof of concept for one potential application of the proposed AET signatures in evaluating remotely sensed AET products. Our companion study, Gardiya Weligamage et al. (2025) demonstrates another application, using AET signatures to diagnose deficiencies in hydrological models. While this study is limited to Australian sites, which geographically constrains the global applicability of the findings, it establishes a foundation for the broader development and use of AET signatures. Moreover, we consider this regional focus more appropriate for a proof of concept, particularly given the findings of McMillan et al. (2023), who reported difficulties in examining signatures and underlying behaviours across large samples that include catchments affected by unusual hydroclimate or data errors. A further limitation is that there are likely other aspects of evapotranspiration dynamics that we have not characterised, and we invite future studies to contribute ideas to broaden this initial set, in much the same way as has occurred for streamflow signatures (see Gnann et al., 2021). Our findings encourage the use and expansion of AET signatures over other regions and continents. As a starting point for the study of AET signatures, future studies could further refine or adapt these signatures to better capture AET behaviours and enhance their use in hydrological model calibration and evaluation to represent AET processes more realistically.