Budyko Curve Research Articles

Catchment response to climatic variability: implications for root zone storage and streamflow predictions

Abstract. This paper investigates the influence of multi-decadal climatic variability on the temporal evolution of root zone storage capacities (Sr,max) and its implications for streamflow predictions in the Meuse basin. Through a comprehensive analysis of 286 catchments across Europe and the US that are hydro-climatically comparable to the Meuse basin, we construct inter-decadal distributions of past deviations in evaporative ratios (IE) from expected values based on catchment aridity (IA). These distributions of ΔIE were then used to estimate inter-decadal changes in Sr,max and to quantify the associated consequences for streamflow predictions in the Meuse basin. Our findings reveal that, while catchments do not strictly adhere to their specific parametric Budyko curves over time, the deviations in IE are generally very minor, with an average ΔIE=0.01 and an interquartile range (IQR) of −0.01 to 0.03. Consequently, these minor deviations lead to limited inter-decadal changes in Sr,max, mostly ranging between −10 and +21 mm (−5 % to +10 %). When these changes (ΔSr,max) are accounted for in hydrological models, the impact on streamflow predictions in the Meuse basin is found to be marginal, with the most significant shifts in monthly evaporation and streamflow not exceeding 4 % and 12 %, respectively. Our study underscores the utility of parametric Budyko-style equations for first-order estimates of future Sr,max in hydrological models, even in the face of climate change and variability. This research contributes to a more nuanced understanding of hydrological responses to changing climatic conditions and offers valuable insights for future climate impact studies in hydrology.

Multi-decadal fluctuations in root zone storage capacity through vegetation adaptation to hydro-climatic variability have minor effects on the hydrological response in the Neckar River basin, Germany

Abstract. Climatic variability can considerably affect catchment-scale root zone storage capacity (Sumax), which is a critical factor regulating latent heat fluxes and thus the moisture exchange between land and atmosphere as well as the hydrological response and biogeochemical processes in terrestrial hydrological systems. However, direct quantification of changes in Sumax over long time periods and the mechanistic drivers thereof at the catchment scale are missing so far. As a consequence, it remains unclear how climatic variability, such as precipitation regime or canopy water demand, affects Sumax and how fluctuations in Sumax may influence the partitioning of water fluxes and therefore also affect the hydrological response at the catchment scale. Based on long-term daily hydrological records (1953–2022) in the upper Neckar River basin in Germany, we found that variability in hydro-climatic conditions, with an aridity index IA (i.e. EP/P) ranging between ∼ 0.9 and 1.1 over multiple consecutive 20-year periods, was accompanied by deviations ΔIE between −0.02 and 0.01 from the expected IE inferred from the long-term parametric Budyko curve. Similarly, fluctuations in Sumax, ranging between ∼ 95 and 115 mm or ∼ 20 %, were observed over the same time period. While uncorrelated with long-term mean precipitation and potential evaporation, it was shown that the magnitude of Sumax is controlled by the ratio of winter precipitation to summer precipitation (p < 0.05). In other words, Sumax in the study region does not depend on the overall wetness condition as for example expressed by IA, but rather on how water supply by precipitation is distributed over the year. However, fluctuations in Sumax were found to be uncorrelated with observed changes in ΔIE. Consequently, replacing a long-term average, time-invariant estimate of Sumax with a time-variable, dynamically changing formulation of that parameter in a hydrological model did not result in an improved representation of the long-term partitioning of water fluxes, as expressed by IE (and fluctuations ΔIE thereof), or in an improved representation of the shorter-term response dynamics. Overall, this study provides quantitative mechanistic evidence that Sumax changes significantly over multiple decades, reflecting vegetation adaptation to climatic variability. However, this temporal evolution of Sumax cannot explain long-term fluctuations in the partitioning of water (and thus latent heat) fluxes as expressed by deviations ΔIE from the parametric Budyko curve over multiple time periods with different climatic conditions. Similarly, it does not have any significant effects on shorter-term hydrological response characteristics of the upper Neckar catchment. This further suggests that accounting for the temporal evolution of Sumax with a time-variable formulation of that parameter in a hydrological model does not improve its ability to reproduce the hydrological response and may therefore be of minor importance for predicting the effects of a changing climate on the hydrological response in the study region over the next decades to come.

Decreased river runoff on the Mongolian Plateau since around 2000

ContextMongolian Plateau is one of the largest contingent arid and semi-arid regions of the world. Rivers on the plateau provide vital water for millions of indigenous Mongolian people and numerous endangered wildlife, but are increasingly disturbed by climate change and human activities. Yet, long-term changes in river runoff across the plateau remain poorly studied due to data unavailability.ObjectivesThis study aimed to analyze the temporal trends in gauged river runoff on the Mongolian Plateau, identify drivers of the observed changes, and evaluate CMIP6 models' performance in simulating historical runoff changes across the plateau.MethodsWe compiled possibly the largest database of long-term (20 - 71 years) river runoff for the plateau comprising measurements over 30 major rivers. Statistical analyses were conducted to assess trends in river runoff and correlations between runoff and climatic variables. Additionally, we applied the Budyko curve framework to identify the influence of human activities on river runoff in specific basins. Furthermore, we compared ground-measured runoff data with simulations from CMIP6 models to evaluate the ability of CMIP6 models to replicate runoff dynamics in typical arid and semi-arid regions.ResultsWe observed pervasive and abrupt reduction in runoff in 21 out of the 30 rivers within 5 years before or after the year of 2000. Variations in river runoff were most significantly caused by changes in total precipitation (TP). In particular, 27 rivers experienced abrupt TP changes around 2000, and there was a significant positive correlation between annual fluctuations in TP and river runoff for 18 rivers. In addition to climate factors, the influence of human activities was identified in certain basins. The CMIP6 simulations failed to capture the abrupt changes in runoff occurred pervasively across the plateau around 2000.ConclusionsAround 2000, major rivers on the Mongolian Plateau, especially in Inner Mongolia, experienced runoff declines, primarily due to TP changes. Human activities like dam construction and water diversion further influenced local runoff. CMIP6 historical runoff simulations were inaccurate across the plateau, highlighting the difficulty of simulating river runoff in this critical region. Our study could contribute to a more comprehensive understanding of the water resource changes on the Mongolian Plateau, with direct implications for enhancing ecological conservation and management practice.

A novel partitioning of gross primary production and water use efficiency for sustaining water and food security using Budyko hypothesis

This study coupled the green water and blue water accounting with the existing standard Budyko framework and Fu's 1-parameter Budyko framework to diagnose the basin hydrological behavior. Both Budyko frameworks were employed to determine green water consumption (ETGreen) and blue water consumption (ETBlue) which, in turn, were used to map the blue water index (BWI) hotspots and green water index (GWI) bright spots. The relative contributions of green water and blue water were quantified for sustaining water and food security. A new methodology is proposed using BWI and GWI for partitioning the Gross Primary Production (GPP) and Water Use Efficiency (WUE) into GPPBlue, GPPGreen and WUEBlue and WUEGreen. The methodology was applied to five sub-basins of the Central Godavari River Basin (CGRB): Purna, Dhalegaon, GR Bridge, Yeli and Delta. Results showed that all five basins exhibited larger deviations from the theoretical Budyko curve of Fu's 1-parameter Budyko framework than did the standard Budyko framework and the Dhalegaon basin showed the largest deviations. The partitioning of GPP and WUE by the proposed methodology showed that the proportion of GPPGreen to the total GPP was much higher than that of the GPPBlue. Similarly, the proportion of WUEGreen to WUE was more than that of WUEBlue. The mapping of GPPBlue and GPPGreen, and WUEBlue and WUEGreen showed that the Delta and Yeli basins had the highest values of both GPPGreen & GPPBlue and WUEBlue and WUEGreen (bright spot basins) and the Dhalegaon and parts of GR Bridge basin had the lowest values (hot spot basins). The proposed partitioning of GPP and WUE will help identify the relative contributions of green water and blue water (for managing agricultural waters) and formulate agronomical and engineering practices for stakeholders and policy makers for increasing the overall WUE and GPP to sustain water and food security.

Examining the Water Scarcity Vulnerability in US River Basins Due To Changing Climate

AbstractAccurate assessment of changes in water availability with changing climate is vital for effective mitigation and adaptation. In this research, we employ a parsimonious Budyko curve method to evaluate changes in water availability under low‐ (SSP126) and high‐emission (SSP585) scenarios for 331 river basins in the contiguous United States. We also assess the relative role of changes in precipitation (∆P) and potential evapotranspiration (∆PET) with changing climate on the increase in water availability vulnerability. Results highlight that around 43% (28%) of basins are projected to experience increased vulnerability to changing climate in high‐emission (low‐emission) scenarios. Sub‐humid basins are most often impacted, while arid and semi‐arid basins exhibit lower sensitivity to changes. Intriguingly, ∆PET emerges as the dominant control on vulnerability, surpassing ∆P, particularly under SSP585 scenario. The analysis prompts water managers to focus on long‐term mitigation planning and scientists to further constraint climate and water budget forecasts in affected basins.

Global evapotranspiration models and their performance at different spatial scales: Contrasting a latitudinal gradient against global catchments

Actual evapotranspiration (AET) is a key variable in the global water balance, driving agricultural production and ecosystem health. It is a complex hydrologic process that depends on vegetation, climate, and available water conditions. Different moderate resolution global AET models have been developed to quantify water resources at large scales. In this work we evaluate five of these products, including MODIS, PML, SSEBop, TerraClimate, and a Synthesis AET using point and catchment-scale datasets based on flux towers. We also contrast water balance changes with total water storage (TWS) products. These comparisons cover different radiation and precipitation regimes over catchments around the world and along a strong climatic gradient in north-central Chile. We rank the models, contrast TWS datasets, and study differences related to scale in validation and the effect of rainfall and radiation on simulated values. Additionally, we use a Budyko framework to evaluate the AET products in terms of their agreement with expected water budgets. At different evaluation scales, AET estimates and observations agreed reasonably well, with the largest mean R2 of about 0.7 and errors of approximately 15% of the magnitude of the observed variables. MODIS and Synthesis AET had the highest R2 at the point (0.62) and at the catchment scales (0.71 and 0.59 for regional and global catchments), respectively, but were closely followed by PML. PML and TerraClimate led to the lowest magnitude errors at the point (RMSE = 0.78 mm day−1) and catchment scales (mean RMSE = 1.5 mm day−1), respectively. The rainfall gradient is reflected in a performance gradient. PML, MODIS, and TerraClimate gave consistent behaviour based on the Budyko curve, with a few arid catchments exceeding the water limit. The major conclusion is that remotely sensed AET outperforms flux tower AET extrapolation for water balance calculations at the catchment scale, which means that errors in satellite-based AET products tend to cancel out at larger spatial scales, which makes them viable alternatives for regional water balance studies. However, flux data integrated into AET models, such as the FluxCom model, leads to the lowest errors. The assimilation and downscaling of Gravity Recovery and Climate Experiment (GRACE) into the Global Land Data Assimilation System (GLDAS) leads to an improvement in regional results compared with other TWS products.

Runoff variation and progressive aridity during drought in catchments in southern-central Chile

Abstract Persistent drought events frequently intensify the aridity of ecosystems and cause catchment runoff depletion. Here, using large and long-term data sets of meteorological and hydrologic variables (precipitation, runoff, temperature, and potential evapotranspiration) investigated the major causes that modulated catchment runoff depletion between the years 1980 and 2020 in southern-central Chile. We identified the hydrological years where aridity index intensified, analyzed its relationship with annual runoff, and evaluated the effect of the annual evaporation index and annual aridity index on water balance of 44 catchments with different precipitation regimes located between 35° and 40°S. Our results showed that observed precipitation and runoff significantly decreased between 1980 and 2020 in 64% of the catchments in the study area. Potential evapotranspiration increased significantly in 39% of the catchments. Hydrological years in which precipitation decreased showed a decreased runoff trend. This result suggests that meteorological droughts tend to significantly decrease observed runoff. The runoff value decreased as the aridity index increased from 0.3 to 6.7, and the Budyko curve captured 98.5% of the annual variability of all catchments.

Assessment of hydrological trends and changes in hydroclimatic and land use parameters in a river basin in northeast Brazil

The hydrological effects of land use change are difficult to differentiate when changes are slow and hard to isolate when climate variability is also present. The study aims to evaluate the effects of climate variability and human activity on the flow in the Cachoeira River Basin. For this purpose, classical tests were used to identify trends and measure the strength of association between two variables, as well as the Rainfall Anomaly Index (RAI) and the Budyko Curve Decomposition were applied to the study so that it could verify the behavior of precipitation and the quantification of anthropic impacts and climate variation in the basin. In addition, the Indicators of Hydrologic Alteration (IHA) software was used to identify hydrological changes in the basin as a function of time. The results show a significantly decreasing trend for the forest and a significantly positive trend for pasture class and temperature. Correlation analysis indicated that changes in flow rate are correlated with precipitation, however, anthropic factors must be potentiating the impacts of climate variations as shown in the period 1991–1995 and 2011–2015. Finally, the hydrological indicators of the Cachoeira River Basin showed significant changes, which may compromise the flows in the long term if anthropic factors continue to enhance the climatological factors.

Climatic Control on Mean Annual Groundwater Evapotranspiration in a Three‐Stage Precipitation Partitioning Framework

AbstractA three‐stage precipitation partitioning framework is proposed to study the climate controls on mean annual groundwater evapotranspiration (GWET) for 33 gauged watersheds in west‐central Florida. Daily GWET, total evapotranspiration (ET), groundwater recharge, base flow, and total runoff are simulated by the Integrated Hydrologic Model, which dynamically couples a surface water model (HSPF) and a groundwater flow model (MODFLOW). The roles of GWET on long‐term water balance are quantified by four ratios. The ratios of GWET to total available water, watershed wetting, ET, and recharge decrease exponentially with watershed aridity index (WAI), which is defined as the ratio of potential evapotranspiration to total available water. In the one‐stage precipitation partitioning framework, the contribution of GWET to the ratio between total ET and available water for ET (i.e., the y‐axis of Budyko curve) decreases with WAI. In the two‐stage precipitation partitioning framework, the contribution of GWET to the ratio between total ET and watershed wetting (i.e., Horton index) decreases with WAI. The changes in GWET caused by intra‐monthly (IM) climate variability are the highest among the temporal scales of climate variability investigated to understand controls on GWET. The inter‐annual, intra‐annual, and IM climate variabilities lead to increase of GWET; but the sub‐daily climate variability results in decrease of GWET. For the third stage of partitioning, given the same ratio of potential GWET to available water for GWET, higher percentage of forest and wetland and lower percentage of impervious land contribute to higher ratio of GWET to available water for GWET.

Assessing future availability of water resources in Taiwan based on the Budyko framework

Assessing water resources availability in a changing climate is a determinant of promoting sustainable development in a region. Such assessment should better be inter-basin in order to unveil a region’s overall risk, so a time-varying Budyko framework is developed and adopted in this study. Gauge-based gridded precipitation and temperature, in company with runoff data, were used to derive the Budyko curves for 75 catchments over Taiwan. Downscaled precipitation and temperature data from selected global climate models and Representative Concentration Pathways (RCPs) were then used to calculate the shifts in the Budyko space of each catchment. It was found that the Budyko-related variables (e.g., evaporative and aridity indices, and catchment-specific parameter) exhibited considerable variability island-wide, with a few outliers in certain catchments being modulated by distinct landscape features and/or human activities. Under all RCPs analyzed, the majority of catchments showed the magnified movement vectors pointing at the 1st quadrant in the Budyko space in the late-21st century, suggesting a predominant and aggravating drying trend over Taiwan. Cluster analysis of the movement vectors under RCP8.5, which entailed the least inter-model differences, identified three major clusters, two of which (64 catchments included) indicated a drying trend of varied significancy. According to our findings, without effective mitigation of climate change, an increased likelihood of the worst-case scenario will substantialize the reduced availability of Taiwan’s water resources.

Climatic Asynchrony and Hydrologic Inefficiency Explain the Global Pattern of Water Availability

AbstractThe mechanisms underlying observed global patterns of partitioning precipitation () to evapotranspiration () and runoff () are controversially debated. We test the hypothesis that asynchrony between climatic water supply and demand is sufficient to explain spatio‐temporal variability of water availability. We developed a simple analytical model for that is determined by four dimensionless characteristics of intra‐annual water supply and demand asynchrony. The analytical model, populated with gridded climate data, accurately predicted global runoff patterns within 2%–4% of independent estimates from global climate models, with spatial patterns closely correlated to observations (). The supply‐demand asynchrony hypothesis provides a physically based explanation for variability of water availability using easily measurable characteristics of climate. The model revealed widespread responsiveness of water budgets to changes in climate asynchrony in almost every global region. Furthermore, the analytical model using global averages independently reproduced the Budyko curve () providing theoretical foundation for this widely used empirical relationship.

Vegetation optimality explains the convergence of catchments on the Budyko curve

Abstract. The Budyko framework puts the long-term mean annual evapotranspiration (ET) of a catchment in relation to its maximum possible value determined by the conservation of mass (ET cannot exceed mean annual precipitation) and energy (ET can not exceed mean annual net radiation) in the absence of significant storage contributions. Most catchments plot relatively close to this physical limit, which allowed the development of an empirical equation (often referred to as the Budyko curve) for estimating mean annual evaporation and runoff from observed net radiation and precipitation. Parametric forms of the curve often use a shape parameter, n, that is seen as a catchment characteristic. However, a satisfying explanation for the convergence and self-organization of catchments around such an empirical curve is still lacking. In this study, we explore if vegetation optimality can explain the convergence of catchments along a Budyko curve and in how far can n be seen as a catchment characteristic. The Vegetation Optimality Model (VOM) optimizes vegetation properties and behavior (e.g., rooting depths, vegetation cover, stomatal control) to maximize the difference between the total carbon taken up from the atmosphere and the carbon used for maintenance of plant tissues involved in its uptake, i.e., the long-term net carbon profit (NCP). This optimization is entirely independent of observed ET and hence the VOM does not require calibration for predicting ET. In a first step, the VOM was fully optimized for the observed atmospheric forcing at five flux tower sites along the North Australian Tropical Transect, as well as 36 additional locations near the transect and six Australian catchments. In addition, the VOM was run without vegetation for all sites, meaning that all precipitation was partitioned into soil evaporation and runoff. For comparison, three conceptual hydrological models (TUWmodel, GR4J, and FLEX) were calibrated for the Australian catchments using the observed precipitation and runoff. Subsequently, we emulated step changes in climate by multiplying precipitation (P) by factors ranging between 0.2 and 2 before running the VOM and hydrological models without changing the vegetation properties or model parameters, emulating invariant catchment characteristics under a changed climate. In a last step, the VOM was re-optimized for the different P amounts, allowing vegetation to adapt to the new situation. Eventually, Budyko curves were fit by adapting the parameter n to the model results. This was carried out for both multiple sites simultaneously and for each individual study site, thereby assuming that n is a site-specific characteristic. The optimized VOM runs tracked relatively close to a Budyko curve with a realistic n value and close to observations, whereas the runs without vegetation led to significantly lower evaporative fractions and unrealistically low n values compared with literature. When fitting n to individual catchments, changes in P led to changes in n (increasing n for decreasing P) in all model runs (including the three conceptual models) except if the VOM was re-optimized for each change in P, which brought the value of n back close to its value for the unperturbed P in each catchment. For the re-optimized VOM runs, the variation in n between catchments was greater than within each catchment in response to multiplications of P with a factor 0.2 to 2. These findings suggest that optimality may explain the self-organization of catchments in Budyko space, and that the accompanying parameter n does not remain constant for constant catchment and vegetation conditions as hypothesized in the literature, but in fact emerges through the adaptation of vegetation to climatic conditions in a given hydrological setting. Moreover, the results suggest that n might initially increase in response to suddenly reduced P, and only slowly returns to its original, catchment-specific value, as vegetation re-adjusts to the new climate over decades and centuries. This may constitute a new basis for the evaluation and prediction of catchment responses to climatic shifts.

Calibrating a Hydrological Model in an Ungauged Mountain Basin with the Budyko Framework

Calibrating spatially distributed hydrological models in ungauged mountain basins is complicated due to the paucity of information and the uncertainty in representing the physical characteristics of a drainage area. In this study, an innovative method is proposed that incorporates the Budyko framework and water balance equation derived water yield (WYLD) in the calibration of the Soil and Water Assessment Tool (SWAT) with a monthly temporal resolution. The impact of vegetation dynamics (i.e., vegetation coverage) on Budyko curve shape parameter ω was considered to improve the Budyko calibration. The proposed approach is applied to the upstream Lancang-Mekong River (UL-MR), which is an ungauged mountain basin and among the world’s most important transboundary rivers. We compared the differences in SWAT model results between the different calibration approaches using percent bias (PBIAS), coefficient of determination (R2), and Nash–Sutcliffe efficiency (NSE) coefficient. The results demonstrated that the Budyko calibration approach exhibited a significant improvement against an unfitted priori parameter run (the non-calibration case) though it did not perform as good as fitting of the calibration by the observed streamflow. The NSE value increased by 44.59% (from 0.46 to 0.83), the R2 value increased by 2.30% (from 0.87 to 0.89) and the PBIAS value decreased by 55.67% (from 39.7 to 17.6) during the validation period at the drainage outlet (Changdu) station. The outcomes of the analysis confirm the potential of the proposed Budyko calibration approach for runoff predictions in ungauged mountain basins.

Technical note: Do different projections matter for the Budyko framework?

Abstract. The widely used Budyko framework defines the water and energy limits of catchments. Generally, catchments plot close to these physical limits, and Budyko (1974) developed a curve that predicted the positions of catchments in this framework. Often, the independent variable is defined as an aridity index, which is used to predict the ratio of actual evaporation over precipitation (Ea/P). However, the framework can be formulated with the potential evaporation as the common denominator for the dependent and independent variables, i.e., P/Ep and Ea/Ep. It is possible to mathematically convert between these formulations, but if the parameterized Budyko curves are fit to data, the different formulations could lead to differences in the resulting parameter values. Here, we tested this for 357 catchments across the contiguous United States. In this way, we found that differences in n values due to the projection used could be ± 0.2. If robust fitting algorithms were used, the differences in n values reduced but were nonetheless still present. The distances to the curve, often used as a metric in Budyko-type analyses, systematically depended on the projection, with larger differences for the non-contracted sides of the framework (i.e., Ep/P>1 or P/Ep>1). When using the two projections for predicting Ea, we found that uncertainties due to the projections used could exceed 1.5 %. An important reason for the differences in n values, curves and resulting estimates of Ea could be found in data points that clearly appear as outliers in one projection but less so in the other projection. We argue here that the non-contracted side of the framework in the two projections should always be assessed, especially for data points that appear as outliers. At least, one should consider the additional uncertainty of the projection and assess the robustness of the results in both projections.

Fewer Basins Will Follow Their Budyko Curves Under Global Warming and Fossil-Fueled Development.

The Budyko framework consists of a curvilinear relationship between the evaporative ratio (i.e., actual evaporation over precipitation) and the aridity index (i.e., potential evaporation over precipitation) and defines evaporation's water and energy limits. A basin's movement within the Budyko space illustrates its hydroclimatic change and helps identify the main drivers of change. On the one hand, long‐term aridity changes drive evaporative ratio changes, moving basins along their Budyko curves. On the other hand, historical human development can cause river basins to deviate from their curves. The question is if basins will deviate or follow their Budyko curves under the future effects of global warming and related human developments. To answer this, we quantify the movement in the Budyko space of 405 river basins from 1901–1950 to 2051–2100 based on the outputs of seven models from the Coupled Model Intercomparison Project ‐ Phase 6 (CMIP6). We account for the implications of using different potential evaporation models and study low‐ and high‐emissions scenarios. We find considerable differences of movement in Budyko space regarding direction and intensity when using the two estimates of potential evaporation. However, regardless of the potential evaporation estimate and the scenario used, most river basins will not follow their reference Budyko curves (>72%). Furthermore, the number of basins not following their curves increases under high greenhouse gas emissions and fossil‐fueled development SP585 and across dry and wet basin groups. We elaborate on the possible explanations for a large number of basins not following their Budyko curves.

Data‐Guided Exploration of the Energy Partitioning at Land Surface in the Contiguous US

AbstractThis study explores the climatic controls of the long‐term energy partitioning of net radiation into sensible heat and latent heat at watershed scale, by following a data‐guided approach. Collected data shows that the relationship between the evaporative fraction (ratio of latent heat to net radiation) and the aridity index (ratio of energy supply to water supply), which represents the climatic conditions at watershed scale, follows a trend similar to the Budyko curve. To explore the physical basis of this relationship, we hypothesize that there are mediating factors connecting energy partitioning with climate. Two potential mediating factors are considered, namely the equilibrium root zone soil moisture and land‐air temperature difference. We extract empirical relationships between the mediating factors and the partitioning fractions of water and energy fluxes based on observational data in 219 study watersheds across the contiguous US. With the obtained empirical relationships, we analytically derive two alternate Budyko‐type equations for energy partitioning, for each of the two mediating factors separately. Both equations show similar trends as the Budyko curve. We also derive a function to relate energy partitioning to water partitioning Budyko‐type equations, suggesting a close connection between the two. The study brings out the mediating roles of soil moisture and temperature gradient that connect water/energy partitioning with climate over long timescales in watersheds. In the process, the analysis results also provide useful insights about complex watershed system behavior. The observed relationships can be used to constrain hydrological and Earth system models and thus improve modeling performance.

Predicting the flocculation kinetics of fine particles in a turbulent flow using a Budyko-type model.

Through an analogy with the Budyko curves in catchment hydrology science, this study defines the supply and demand limits for the flocculation system of cohesive particles (the supply limit can be represented by the potential floc size growth, whereas the demand limit can be represented by the steady-state floc size) and attempts to adopt Budyko-type models to estimate the temporal evolution of floc size during flocculation. Seventeen experimental datasets are collected to test the accuracy of the Budyko model with an average high correlation coefficient of 0.9784 and average low relative error and root mean squared error values of 0.1304 and 0.0605, respectively. Either the potential floc size growth or the steady-state floc size is a monotonic function of the flow shear rate, and a simple empiric power law function can be used to describe them. Other Budyko-type models are also found to show good prediction accuracies against the experimental datasets. This study indicates that Budyko-type models have potential as a good addition to existing flocculation models for predicting the temporal variation in the size population of flocs in a turbulent flow, provided that some coefficients have been calibrated by limited data points prior.

Theoretical and empirical evidence against the Budyko catchment trajectory conjecture

Abstract. The Budyko framework posits that a catchment's long-term mean evapotranspiration (ET) is primarily governed by the availabilities of water and energy, represented by long-term mean precipitation (P) and potential evapotranspiration (PET), respectively. This assertion is supported by the distinctive clustering pattern that catchments take in Budyko space. Several semi-empirical, nonparametric curves have been shown to generally represent this clustering pattern but cannot explain deviations from the central tendency. Parametric Budyko equations attempt to generalize the nonparametric framework, through the introduction of a catchment-specific parameter (n or w). Prevailing interpretations of Budyko curves suggest that the explicit functional forms represent trajectories through Budyko space for individual catchments undergoing changes in the aridity index, PETP, while the n and w values represent catchment biophysical features; however, neither of these interpretations arise from the derivation of the Budyko equations. In this study, we reexamine, reinterpret, and test these two key assumptions of the current Budyko framework both theoretically and empirically. In our theoretical test, we use a biophysical model for ET to demonstrate that n and w values can change without invoking changes in landscape biophysical features and that catchments are not required to follow Budyko curve trajectories. Our empirical test uses data from 728 reference catchments in the United Kingdom (UK) and United States (US) to illustrate that catchments rarely follow Budyko curve trajectories and that n and w are not transferable between catchments or across time for individual catchments. This nontransferability implies that n and w are proxy variables for ETP, rendering the parametric Budyko equations underdetermined and lacking predictive ability. Finally, we show that the parametric Budyko equations are nonunique, suggesting their physical interpretations are unfounded. Overall, we conclude that, while the shape of Budyko curves generally captures the global behavior of multiple catchments, their specific functional forms are arbitrary and not reflective of the dynamic behavior of individual catchments.

Application of Budyko framework to irrigation districts in China under various climatic conditions

AbstractBudyko's framework has been widely used to study basin‐scale water balance. In this study, we focus on the extended application of Fu's equation (one formulation of the Budyko‐type curves) to 371 large irrigation districts in China over a period of 2010–2017. Water balance method was used to estimate actual evapotranspiration in the irrigated areas. Considering the contribution of shallow groundwater to , the water availability in the Budyko framework defined as equivalent precipitation for irrigation areas is the sum of irrigation water , precipitation and groundwater evaporation . Results showed that the relationships between evapotranspiration , water availability and energy supply can be accurately described by the Budyko's curves. The optimal values of Budyko parameter ω for each irrigation district was obtained with multi‐annual data using least square method. The Fu's equation performed better in humid and semi‐humid regions than arid and semi‐arid regions. The comparison between and confirmed the relative effect of water availability and energy supply on according to the variation of climatic conditions. Normalized difference vegetation index (NDVI) and soil properties (denoted by the proportion of clay and sand) were selected to develop empirical equation for parameter ω using multiple linear regression analysis method. This study shows that the Budyko framework can be extended to irrigation areas and provides useful information on evapotranspiration to assist in water management in irrigation areas.

Are Brazilian catchments gaining or losing water? The effective area of tropical catchments

AbstractSimilar to most countries, the Brazilian water resources management considers topographically delineated catchment as a territorial unit for policy implementation. Yet, previous studies have shown that catchments are not hydrologically isolated, and topographic limits often neglect the groundwater boundaries. Thus, studies on effective catchment areas are promising for shedding light on inter‐catchment groundwater flow. Here, we investigated the deviation between the topographic and effective areas across Brazil. We applied the effective catchment area index (ECI) to 733 Brazilian catchments and identified the most influencing attributes on the ECI by using principal component and random forest analyses (PCA and RFA, respectively). Further analysis was carried out by contrasting the ECI values against the expected range of the Budyko curve, considering both topographic and effective catchment areas (classic and adjusted framework, respectively). We noted that nearly 32% of the Brazilian catchments presented more than 30% of difference between the effective area and its topographic boundaries. In general, the more arid biomes in Brazil—the Cerrado and Caatinga—are prone to have smaller effective areas while larger effective areas were mostly found in the Atlantic Forest biome, a humid tropical region with a higher mean elevation. Our findings indicate that the aridity index was the main driving factor and negatively correlated with ECI followed by mean slope, precipitation seasonality, and mean elevation. We highlight the potential of adopting a pooling of catchments based on their interconnectivity to minimize management costs while maximizing synergies and lessening trade‐offs between ecosystem functioning and water transfer processes. Our results contribute to a better country‐wide understanding of hydrological connectivity among catchments and highlight the need to consider the effective catchment area to overcome water‐food‐energy security challenges on multiple scales.