Finer Time Scales Research Articles

A Hybrid Bimodal LSTM Architecture for Cascading Thermal Energy Storage Modelling

Modelling of thermal energy storage (TES) systems is a complex process that requires the development of sophisticated computational tools for numerical simulation and optimization. Until recently, most modelling approaches relied on analytical methods based on equations of the physical processes that govern TES systems’ operations, producing high-accuracy and interpretable results. The present study tackles the problem of modelling the temperature dynamics of a TES plant by exploring the advantages and limitations of an alternative data-driven approach. A hybrid bimodal LSTM (H2M-LSTM) architecture is proposed to model the temperature dynamics of different TES components, by utilizing multiple temperature readings in both forward and bidirectional fashion for fine-tuning the predictions. Initially, a selection of methods was employed to model the temperature dynamics of individual components of the TES system. Subsequently, a novel cascading modelling framework was realised to provide an integrated holistic modelling solution that takes into account the results of the individual modelling components. The cascading framework was built in a hierarchical structure that considers the interrelationships between the integrated energy components leading to seamless modelling of whole operation as a single system. The performance of the proposed H2M-LSTM was compared against a variety of well-known machine learning algorithms through an extensive experimental analysis. The efficacy of the proposed energy framework was demonstrated in comparison to the modelling performance of the individual components, by utilizing three prediction performance indicators. The findings of the present study offer: (i) insights on the low-error performance of tailor-made LSTM architectures fitting the TES modelling problem, (ii) deeper knowledge of the behaviour of integral energy frameworks operating in fine timescales and (iii) an alternative approach that enables the real-time or semi-real time deployment of TES modelling tools facilitating their use in real-world settings.

Spiking Recurrent Neural Networks Represent Task-Relevant Neural Sequences in Rule-Dependent Computation.

Prefrontal cortical neurons play essential roles in performing rule-dependent tasks and working memory-based decision making. Motivated by PFG recordings of task-performing mice, we developed an excitatory-inhibitory spiking recurrent neural network (SRNN) to perform a rule-dependent two-alternative forced choice (2AFC) task. We imposed several important biological constraints onto the SRNN, and adapted spike frequency adaptation (SFA) and SuperSpike gradient methods to train the SRNN efficiently. The trained SRNN produced emergent rule-specific tunings in single-unit representations, showing rule-dependent population dynamics that resembled experimentally observed data. Under varying test conditions, we manipulated the SRNN parameters or configuration in computer simulations, and we investigated the impacts of rule-coding error, delay duration, recurrent weight connectivity and sparsity, and excitation/inhibition (E/I) balance on both task performance and neural representations. Overall, our modeling study provides a computational framework to understand neuronal representations at a fine timescale during working memory and cognitive control, and provides new experimentally testable hypotheses in future experiments.

App-Based Saccade Latency and Directional Error Determination Across the Adult Age Spectrum.

We aid in neurocognitive monitoring outside the hospital environment by enabling app-based measurements of visual reaction time (saccade latency) and directional error rate in a cohort of subjects spanning the adult age spectrum. We developed an iOS app to record subjects with the frontal camera during pro- and anti-saccade tasks. We further developed automated algorithms for measuring saccade latency and directional error rate that take into account the possibility that it might not always be possible to determine the eye movement from app-based recordings. To measure saccade latency on a tablet, we ensured that the absolute timing error between on-screen task presentation and the camera recording is within 5 ms. We collected over 235,000 eye movements in 80 subjects ranging in age from 20 to 92 years, with 96% of recorded eye movements either declared good or directional errors. Our error detection code achieved a sensitivity of 0.97 and a specificity of 0.97. Confirming prior reports, we observed a positive correlation between saccade latency and age while the relationship between directional error rate and age was not significant. Finally, we observed significant intra- and inter-subject variations in saccade latency and directional error rate distributions, which highlights the importance of individualized tracking of these visual digital biomarkers. Our system and algorithms allow ubiquitous tracking of saccade latency and directional error rate, which opens up the possibility of quantifying patient state on a finer timescale in a broader population than previously possible.

Hydrological losses and soil moisture carryover affected the relationship between evapotranspiration and rainfall in a temperate semiarid shrubland

Evapotranspiration (ET) represents a major pathway of water loss from terrestrial ecosystems. However, large uncertainty exists regarding the relationship between ET and precipitation at seasonal and interannual timescales in drylands. Using the eddy-covariance technique, we investigated temporal variations of ET in a semiarid shrubland of northern China during January 2012–December 2020. Daily ET was close to zero during winter and reached up to 2–4 mm day−1 in summer. Monthly ET was positively and linearly correlated with the normalized difference vegetation index and surface conductance (gs), and showed a saturating relationship with monthly rainfall. Analyses based on bin-averaged half-hourly values revealed increases in midday ET and gs with increasing soil water content, and decreases in midday gs and saturated ET with increasing vapor pressure deficit. Annual ET for ecohydrologic years (July 1–June 30) ranged 207–297 mm yr−1 (with a multi-year average of 242 mm yr−1), and accounted for 62%–105% of annual rainfall. Aggregated ET over the study period (2163 mm) accounted for 78% of total rainfall. Rainfall amount was a poor predictor of year-to-year differences in annual ET, wet-season (July 1–November 30) ET, and dry-season (December 1–June 30) ET. Wet-season ET (mm season−1) was generally lower than rainfall while dry-season ET tended to be higher than rainfall. Our results suggest that biotic factors played an essential role in regulating seasonal variations in ET, while air and soil dryness imposed additional constraints on ET at finer timescales. Moreover, hydrological losses (e.g., to subsurface runoff and/or deep drainage) during wet seasons and soil moisture carryover from wet to dry seasons may be nonnegligible in the studied semiarid shrubland, and thus affected seasonal and interannual relationships between ET and rainfall.

Application of Milankovitch cycles in the restoration of high-resolution deposition velocity of Neogene strata in Kutei Basin, Indonesia

Restoring the deposition velocity during evolution in basin analysis is an important aspect. The restoration of high-resolution deposition velocity—the deposition velocity over a short geological period—can improve the precision of basin analysis and research. However, the prerequisite for the restoration is to establish an accurate chronostratigraphic framework based on precise stratigraphic dating. Conventional methods for stratigraphic dating can only be used to determine the epochs of large stratigraphic intervals rather than accurate geological time. It is also difficult to establish a fine geological time scale with dating methods requiring sample testing such as isotopic dating due to their limitations in sample collection. In contrast, the Milankovich cycle-based dating possesses the advantages of high precision and high operability and can be used to restore high-resolution deposition velocity. Based on the identification and extraction of Milankovich cycles, this study restores the high-resolution deposition velocity of the Middle Miocene and later strata in the abyssal area of the Kutei Basin in Indonesia. The results show that the restored deposition velocity coincides well with lithological sections. This indicates that the Milankovitch cycle-based dating can be used to effectively restore reliable curves of high-resolution deposition velocity. Therefore, this study provides a methodological basis and data guarantee for studying the accumulation cycles and distribution patterns of oil and gas in the abyssal area of the Kutei Basin using wave analysis technology and can also serve as a reference for similar research in other basins.

Using sonobuoys and visual surveys to characterize North Atlantic right whale (Eubalaena glacialis) calling behavior in the Gulf of St. Lawrence

The appropriate use and interpretation of passive acoustic data for monitoring the Critically Endangered North Atlantic right whaleEubalaena glacialis(hereafter right whale) rely on knowledge of their calling behavior and how it varies with respect to time, space, demographics, and observed behavior. To assess such relationships in a habitat of increased management importance, sonobuoys (disposable drifting hydrophones) were deployed in the Gulf of St. Lawrence, Canada, to record sounds from aggregating right whales during visual aerial surveys in the summers (June through August) of 2017 (n = 8), 2018 (n = 13), and 2019 (n = 16). Upcalls, gunshots, and various mid-frequency (250-800 Hz) tonal calls were compared to demographics and observed behaviors of concurrently observed right whales using correlation matrices, linear regressions, and generalized linear models. Our results show that (1) call rates increased from June to August for all call types; (2) calling rates were associated negatively with observed foraging behavior and positively with observed socializing behavior; (3) upcalls were occasionally produced at higher rates (>20 calls h-1) when in association with gunshots and tonal calls; (4) acoustic monitoring did not always detect right whale presence at fine timescales (2-6 h), but presence estimates were improved when multiple calls types were considered; and (5) calling rates were too variable to provide reliable density estimates of observed right whales. These results have important implications for the interpretation of passive acoustic monitoring in this habitat and provide evidence that some whale behaviors (e.g. socializing) may be reliably inferred from acoustics alone.

Activity and Coupling to Hippocampal Oscillations of Median Raphe GABAergic Cells in Awake Mice.

Ascending serotonergic/glutamatergic projection from the median raphe region (MRR) to the hippocampal formation regulates both encoding and consolidation of memory and the oscillations associated with them. The firing of various types of MRR neurons exhibits rhythmic modulation coupled to hippocampal oscillatory activity. A possible intermediary between rhythm-generating forebrain regions and entrained ascending modulation may be the GABAergic circuit in the MRR, known to be targeted by a diverse array of top-down inputs. However, the activity of inhibitory MRR neurons in an awake animal is still largely unexplored. In this study, we utilized whole cell patch-clamp, single cell, and multichannel extracellular recordings of GABAergic and non-GABAergic MRR neurons in awake, head-fixed mice. First, we have demonstrated that glutamatergic and serotonergic neurons receive both transient, phasic, and sustained tonic inhibition. Then, we observed substantial heterogeneity of GABAergic firing patterns but a marked modulation of activity by brain states and fine timescale coupling of spiking to theta and ripple oscillations. We also uncovered a correlation between the preferred theta phase and the direction of activity change during ripples, suggesting the segregation of inhibitory neurons into functional groups. Finally, we could detect complementary alteration of non-GABAergic neurons’ ripple-coupled activity. Our findings support the assumption that the local inhibitory circuit in the MRR may synchronize ascending serotonergic/glutamatergic modulation with hippocampal activity on a subsecond timescale.

Comparative Evaluation of Simplified Surface Energy Balance Index-Based Actual ET against Lysimeter Data in a Tropical River Basin

In the past decades, multispectral and multitemporal remote sensing has been popularly used for estimating actual evapotranspiration (ETc) across the globe. It has been proven to be a cost-effective tool for understanding agricultural practices in a region. Today, because of the availability of different onboard sensors on an increasing number of different satellites, land surface activity can be captured at fine spatial and time scales. In the present study, three multi-date satellite imageries were used for the evaluation of remote sensing-based estimation of actual evapotranspiration in paddy in the command area of the tropical Kangsabati river basin. A surface energy balance model, the Simplified-Surface Energy Balance Index (S-SEBI), was applied for all three dates of the Rabi season (2014–2015) for the estimation of actual evapotranspiration. The crop coefficient was calculated using the exhaustive survey data collected from the command area and adjusted to local conditions. The ETc estimated using the S-SEBI-based model was compared with the Food and Agriculture Organization Penman–Monteith (FAO-56 PM) method multiplied by the adjusted local crop coefficient and lysimeter data in the command area. The coefficient of determination (r2) was applied to examine the accuracy of the S-SEBI model with respect to lysimeter data and the FAO-56 PM-based ETc. The results showed that the S-SEBI model performed well with the lysimeter (r2 = 0.90) in comparison with FAO-56 PM, with an r2 of 0.65. In addition to this, the S-SEBI-based ET estimates correlated well with the FAO-56 PM, with r and RMSE values of 0.06 and 1.13 mm/day (initial stage), 0.85 and 0.48 mm/day (development stage), and 0.77 and 0.52 (maturity stage) for paddy, respectively. The S-SEBI-based ETc estimate varied with different stages of crop growth and successfully captured the spatial heterogeneity within the command area. In general, this study showed that the S-SEBI method has the potential to calculate spatial evapotranspiration and provide useful information for efficient water management. The results revealed the applicability and accuracy of remote sensing-based ET for managing water resources in a command area with scarce data.

Integrated surface-subsurface water and solute modeling of a reclaimed in-pit oil sands mine: Effects of ground freezing and thawing

Study regionAthabasca Oil Sands, Alberta, Canada. Study focusThe upland and wetlands substrate in reclaimed oil sands landforms will be constructed of post-mining materials with an objective of replicating the landscape and hydrology of the surrounding boreal systems. Porewater in these materials contain elevated levels of salts and other solutes. Water quality will govern the success and sustainability of the reclaimed landscape. Tightly coupled water and heat dynamics control water and solute movement in boreal systems. We used three-dimensional integrated surface-subsurface flow and chloride transport models with and without ground freezing-thawing to compare performance of an in-pit oil sands mine currently being reclaimed. New hydrological insights for the regionTransient simulations under wet/dry climate cycles suggest that the reclaimed landform will shed water only during wet years. Annual water balance with and without coupled heat dynamics is identical. However, the three-dimensional representation of ground freeze-thaw results in reduced snowmelt infiltration, summer groundwater table, and solute release during winter. The outcome is increased spring runoff, 20% decrease in chloride mass release over simulated eight-year wet climate cycle and relatively reduced summer runoff. The model results suggest that (1) coupled heat dynamics should be considered for detailed evaluation of reclaimed in-pit landforms at finer time scales, and (2) modeling reclaimed landforms without freeze-thaw provides conservative annual solute release estimates, which is appropriate for coarse site-wide models.

A nonstationary and non‐Gaussian moving average model for solar irradiance

AbstractHistorically, power has flowed from large power plants to customers. Increasing penetration of distributed energy resources such as solar power from rooftop photovoltaic has made the distribution network a two‐way‐street with power being generated at the customer level. The incorporation of renewables introduces additional uncertainty and variability into the power grid. Distribution network operation studies are being adapted to include renewables; however, such studies require high quality solar irradiance data that adequately reflect realistic meteorological variability. Data from satellite‐based products are spatially complete, but temporally coarse, whereas solar irradiances exhibit high frequency variation at very fine timescales. We propose a new stochastic method for temporally downscaling global horizontal irradiance (GHI) to 1 min resolution, but we do not consider the spatial aspect due to limited availability of the in situ irradiance measurements. Solar irradiance's first and second‐order structures vary diurnally and seasonally, and our model adapts to such nonstationarity. Empirical irradiance data exhibits highly non‐Gaussian behavior; we develop a nonstationary and non‐Gaussian moving average model that is shown to capture realistic solar variability at multiple timescales. We also propose a new estimation scheme based on Cholesky factors of empirical autocovariance matrices, bypassing difficult and inaccessible likelihood‐based approaches. The model is demonstrated for a case study of three locations that are located in diverse climates through the United States. The model is compared against competitors from the literature and is shown to provide better uncertainty and variability quantification on testing data.

Generic Framework for Downscaling Statistical Quantities at Fine Time-Scales and Its Perspectives towards Cost-Effective Enrichment of Water Demand Records

The challenging task of generating a synthetic time series at finer temporal scales than the observed data, embeds the reconstruction of a number of essential statistical quantities at the desirable (i.e., lower) scale of interest. This paper introduces a parsimonious and general framework for the downscaling of statistical quantities based solely on available information at coarser time scales. The methodology is based on three key elements: (a) the analysis of statistics’ behaviour across multiple temporal scales; (b) the use of parametric functions to model this behaviour; and (c) the exploitation of extrapolation capabilities of the functions to downscale the associated statistical quantities at finer scales. Herein, we demonstrate the methodology using residential water demand records and focus on the downscaling of the following key quantities: variance, L-variation, L-skewness and probability of zero value (no demand; intermittency), which are typically used to parameterise a stochastic simulation model. Specifically, we downscale the above statistics down to a 1 min scale, assuming two scenarios of initial data resolution, i.e., 5 and 10 min. The evaluation of the methodology on several cases indicates that the four statistics can be well reconstructed. Going one step further, we place the downscaling methodology in a more integrated modelling framework for a cost-effective enhancement of fine-resolution records with synthetic ones, embracing the current limited availability of fine-resolution water demand measurements.

Time evolution of energies and populations in germanium perturbed by a near-infrared pulse on the atto-second scale

Implementing time-resolved spectroscopy is one of the challenging topics in solid-state physics: indeed, it can be a crucial step to unveil the early time dynamics of fundamental processes in systems such as semiconductors, metals, superconductors and topological materials. Then, it is essential to build theoretical tools in order to understand the experimental results and what actually happens in solid-state systems on a new and finer timescale: the atto-second one. Accordingly, we have developed a theoretical–numerical tool in order to study the time evolution of the electronic populations on the atto-second scale in materials perturbed by a laser pulse. After finding the ab-initio band structure of the material, we compute the maximally-localized Wannier functions and obtain the hopping terms. Then, we study the effect of the laser pulse using the Peierls substitution method and obtain the equation of motion for the electronic populations. Finally, we obtain a dynamical DOS of the system and the corresponding dynamical electronic populations. In this work, as a relevant case study, we report our results for germanium. We identify oscillations in the eigenenergies and in the populations which roughly follow either the field or its square, with some phase shifts with respect to the field.

Implicitly learning when to be ready: From instances to categories

There is growing appreciation for the role of long-term memory in guiding temporal preparation in speeded reaction time tasks. In experiments with variable foreperiods between a warning stimulus (S1) and a target stimulus (S2), preparation is affected by foreperiod distributions experienced in the past, long after the distribution has changed. These effects from memory can shape preparation largely implicitly, outside of participants’ awareness. Recent studies have demonstrated the associative nature of memory-guided preparation. When distinct S1s predict different foreperiods, they can trigger differential preparation accordingly. Here, we propose that memory-guided preparation allows for another key feature of learning: the ability to generalize across acquired associations and apply them to novel situations. Participants completed a variable foreperiod task where S1 was a unique image of either a face or a scene on each trial. Images of either category were paired with different distributions with predominantly shorter versus predominantly longer foreperiods. Participants displayed differential preparation to never-before seen images of either category, without being aware of the predictive nature of these categories. They continued doing so in a subsequent Transfer phase, after they had been informed that these contingencies no longer held. A novel rolling regression analysis revealed at a fine timescale how category-guided preparation gradually developed throughout the task, and that explicit information about these contingencies only briefly disrupted memory-guided preparation. These results offer new insights into temporal preparation as the product of a largely implicit process governed by associative learning from past experiences.

Scrutinizing proposed extensions to the Eddy Dissipation Concept (EDC) at low turbulence Reynolds numbers and low Damköhler numbers

Recent proposals to modify or extend the Eddy Dissipation Concept are investigated and compared to the standard EDC. The results with respect to the underlying principles of EDC are examined. A total of four different variants of the extended EDC are available, expressing locally determined values for two model coefficients that are constants in the standard EDC. The effects on the fine-structure region mass fraction and the fine structure time scale are demonstrated with resulting effects on the mixing and species mean reaction rate. It is found that the constraints imposed on the locally determined coefficients are more important for the results than the formulated dependencies of turbulence Reynolds number and microscale Damköhler number. Furthermore, some of the versions require a less-than-unity limitation for the fine-structure mass fraction for wide ranges of the Reynolds number. All the modified model versions maintain the EDC cascade model, and their relations to this model are investigated. A finding is that some versions maintain very high viscous effects at high turbulence Reynolds numbers. Comparison with the standard EDC shows that some of the effects motivating the extensions are already present in the standard EDC. Initially, a short cascade for low turbulence Reynolds numbers is derived from the existing EDC cascade model, which was developed for high Reynolds numbers. The resulting changes are small, and the need for a modification still remains.

Understanding marine life through long-term passive acoustic time series

Sound allows us to study the ocean on a much finer time scales than other methods of study as it is feasible to collect continuous underwater recordings over months or years at a time. My work has been focused on using such long recordings to improve our understanding of the ecology of large whales and marine fishes. However, ecological insights can only be gained from data that are truly comparable across time and space. The initial steps to achieving comparable time series from long-term recordings collected at vastly different locations include: effective detection of signals of interest, full knowledge of the characteristics of those signals and interfering noise, and normalization of those detections by appropriate recording effort across time and space. I will highlight a few things we have learned about baleen whale and fish species through long-term passive acoustic monitoring effort, such as an improved understanding of call function for some baleen whales or a better sense of animal occurrence. This, in turn, will allow us to start coupling the occurrence of these animals into the larger patterns of ecosystem dynamics, ultimately leading to a fuller understanding of their roles in the ocean.

Seasonality in aerodynamic resistance across a range of North American ecosystems

Surface roughness – a key control on land-atmosphere exchanges of heat and momentum – differs between dormant and growing seasons. However, how surface roughness shifts seasonally at fine time scales (e.g., days) in response to changing canopy conditions is not well understood. This study: (1) explores how aerodynamic resistance changes seasonally; (2) investigates what drives these seasonal shifts, including the role of vegetation phenology; and (3) quantifies the importance of including seasonal changes of aerodynamic resistance in “big leaf” models of sensible heat flux (H). We evaluated aerodynamic resistance and surface roughness lengths for momentum (z0m) and heat (z0h) using the kB−1 parameter (ln(z0m/z0h)). We used AmeriFlux data to obtain surface-roughness estimates, and PhenoCam greenness data for phenology. This analysis included 23 sites and ∼190 site years from deciduous broadleaf, evergreen needleleaf, woody savanna, cropland, grassland, and shrubland plant-functional types (PFTs). Results indicated clear seasonal patterns in aerodynamic resistance to sensible heat transfer (Rah). This seasonality tracked PhenoCam-derived start-of-season green-up transitions in PFTs displaying the most significant seasonal changes in canopy structure, with Rah decreasing near green-up transitions. Conversely, in woody savanna sites and evergreen needleleaf forests, patterns in Rah were not linked to green-up. Our findings highlight that decreases in kB−1 are an important control over Rah, explaining > 50% of seasonal variation in Rah across most sites. Decreases in kB−1 during green-up are likely caused by increasing z0h in response to higher leaf area index. Accounting for seasonal variation in kB−1 is key for predicting H as well; assuming kB−1 to be constant resulted in significant biases that also exhibited strong seasonal patterns. Overall, we found that aerodynamic resistance can be sensitive to phenology in ecosystems having strong seasonality in leaf area, and this linkage is critical for understanding land-atmosphere interactions at seasonal time scales.

Mountain biogeography coming full circle: a new '3D' floristic approach provides units for reconstructing evolutionary trajectories.

This article is a Commentary on Li et al. (2021), 232: 1424–1435.

Global consistency in response of terrestrial ecosystem respiration to temperature

Many studies have been carried out to quantify the trend of terrestrial ecosystem respiration (Re) in a warming world, but a conclusive answer has not yet been confirmed because the temperature sensitivity of Re was found inconsistent under different scales or regarding different types of respiratory flux. Aiming at reconciling the relationship between temperature and Re across different scales (i.e., short-term and site-to-site), we proposed a method to reduce noises of half-hourly Re measurements and applied nine empirical models to a 1387 site-year FLUXNET datasets. Regarding the temperature sensitivity of half-hourly Re records, we found a surprisingly consistent result that the sigmoid functions outcompeted other statistical models in 82% of site-year combinations, and on average, achieved a staggering R2 value of 0.92, indicating the positive correlation between Re and temperature on fine time scale (within one site-year dataset). Even though Re of all biomes followed sigmoid functions, the parameters of the S-curve varied strongly across sites or years. This explains why measured Q10 value (an index denote temperature sensitivity) largely depends on observation season and site. Furthermore, on the interannual variation of Re, we did not find any relationship between mean annual temperature (MAT) and mean annual Re within any site, which implies that the small year-to-year variation of the sigmoid pattern is large enough to counteract the warming effect on Re. This study brings up a conceptual framework to integrate the relationship between temperature and Re under short-term or site-to-site scales. It also provided evidence to support the argument that the relationship between MAT and mean annual Re by using data across multiple sites should not be used to interpret the response of respiration under global warming.

Multi‐Proxy, Multi‐Season Streamflow Reconstruction With Mass Balance Adjustment

AbstractDespite having offered important hydroclimatic insights, streamflow reconstructions still see limited use in water resources operations, because annual reconstructions are not suitable for decisions at finer time scales. The few attempts toward sub‐annual reconstructions have relied on statistical disaggregation, which uses none or little proxy information. Here, we develop a novel framework that optimizes proxy combinations to simultaneously produce seasonal and annual reconstructions. Importantly, the framework ensures that total seasonal flow matches annual flow closely. This mass balance criterion is necessary to avoid misguiding water management decisions, such as the allocation of water rights or dam release decisions. Using the framework, and leveraging a multi‐species network of ring width and cellulose O in Southeast Asia, we reconstruct seasonal and annual inflow to Thailand's largest reservoir. The reconstructions are statistically skillful. Furthermore, they preserve the mass balance well: the differences are mostly within 10% of the mean annual flow. As a result, the reconstructions provide more reliable estimates of the seasonal and annual surface water availability. This work is one step closer toward operational usability of streamflow reconstruction in water resources management.

Attribution of growing season evapotranspiration variability considering snowmelt and vegetation changes in the arid alpine basins

Abstract. Previous studies have successfully applied variance decomposition frameworks based on the Budyko equations to determine the relative contribution of variability in precipitation, potential evapotranspiration (E0), and total water storage changes (ΔS) to evapotranspiration variance (σET2) on different timescales; however, the effects of snowmelt (Qm) and vegetation (M) changes have not been incorporated into this framework in snow-dependent basins. Taking the arid alpine basins in the Qilian Mountains in northwest China as the study area, we extended the Budyko framework to decompose the growing season σET2 into the temporal variance and covariance of rainfall (R), E0, ΔS,Qm, and M. The results indicate that the incorporation of Qm could improve the performance of the Budyko framework on a monthly scale; σET2 was primarily controlled by the R variance with a mean contribution of 63 %, followed by the coupled R and M (24.3 %) and then the coupled R and E0 (14.1 %). The effects of M variance or Qm variance cannot be ignored because they contribute 4.3 % and 1.8 % of σET2, respectively. By contrast, the interaction of some coupled factors adversely affected σET2, and the out-of-phase seasonality between R and Qm had the largest effect (−7.6 %). Our methodology and these findings are helpful for quantitatively assessing and understanding hydrological responses to climate and vegetation changes in snow-dependent regions on a finer timescale.