Hydrological Model Parameters Research Articles

Bayesian calibration of HEC-HMS model using two different algorithms

The assessment of hydrological model parameters is impacted by uncertainties that may be attributed to several sources of errors. Many methods have been developed and applied to various hydrological models in order to address these uncertainties. The present study aims to apply two uncertainty analysis methods, i.e., generalized uncertainty estimation (GLUE) and differential evolution adaptive metropolis (DREAMzs), for the purpose of evaluating the parametric and predictive uncertainty of the HEC-HMS hydrological model. The HEC-HMS model was coupled to these two approaches in order to simulate flash floods in the Mekerra watershed (Algeria) and to estimate the uncertainty of 14 model parameters which are due to be calibrated. For this, six flood events were selected for the purpose of calibrating and validating the model, two informal likelihood measures L1 and L2 were applied in GLUE and one formal likelihood measure was applied in DREAMzs. Considering the difference between the results, and not the principles of the two methods, the analysis indicated that these parameters can be better identified by DREAMzs algorithm. Indeed, the coefficients of variation of their posterior distributions are generally lower. Compared to GLUE, DREAMzs algorithm is more efficient in exploring the parametric space. With regard to the predictive uncertainty, 95% of the uncertainty intervals were estimated by both methods and then analyzed. The DREAMzs algorithm results suggested a good dynamics of the simulated floods, associated with a significant uncertainty that is due not to the parametric uncertainty but to other sources of errors. The GLUE algorithm generates similar results but does not distinguish between the total uncertainty and parametric uncertainty. Further studies would be desirable to evaluate the impact of other likelihood measures on the simulation results with both algorithms

Regionalization of a Rainfall-Runoff Model: Limitations and Potentials

Regionalized lumped rainfall-runoff (RR) models have been widely employed as a means of predicting the streamflow of an ungauged watershed because of their simple yet effective simulation strategies. Parameter regionalization techniques relate the parameter values of a model calibrated to the observations of gauged watersheds to the geohydrological characteristics of the watersheds. Thus, the accuracy of regionalized models is dependent on the calibration processes, as well as the structure of the model used and the quality of the measurements. In this study, we have discussed the potentials and limitations of hydrological model parameter regionalization to provide practical guidance for hydrological modeling of ungauged watersheds. This study used a Tank model as an example model and calibrated its parameters to streamflow observed at the outlets of 39 gauged watersheds. Multiple regression analysis identified the statistical relationships between calibrated parameter values and nine watershed characteristics. The newly developed regional models provided acceptable accuracy in predicting streamflow, demonstrating the potential of the parameter regionalization method. However, uncertainty associated with parameter calibration processes was found to be large enough to affect the accuracy of regionalization. This study demonstrated the importance of objective function selection of the RR model regionalization.

Runoff Predicting and Variation Analysis in Upper Ganjiang Basin under Projected Climate Changes

Catchment runoff is significantly affected by climate condition changes. Predicting the runoff and analyzing its variations under future climates play a vital role in water security, water resource management, and the sustainable development of the catchment. In traditional hydrological modeling, fixed model parameters are usually used to transfer the global climate models (GCMs) to runoff, while the hydrologic model parameters may be time-varying. It is more appropriate to use the time-variant parameter for runoff modeling. This is achieved by incorporating the time-variant parameter approach into a two-parameter water balance model (TWBM) through the construction of time-variant parameter functions based on the identified catchment climate indicators. Using the Ganjiang Basin with an outlet of the Dongbei Hydrological Station as the study area, we developed time-variant parameter scenarios of the TWBM model and selected the best-performed parameter functions to predict future runoff and analyze its variations under the climate model projection of the BCC-CSM1.1(m). To synthetically assess the model performance improvements using the time-variant parameter approach, an index Δ was developed by combining the Nash–Sutcliffe efficiency, the volume error, the Box–Cox transformed root-mean-square error, and the Kling–Gupta efficiency with equivalent weight. The results show that the TWBM model with time-variant C (evapotranspiration parameter) and SC (water storage capacity of catchment), where growing and non-growing seasons are considered for C, outperformed the model with constant parameters with a Δ value of approximately 5% and 10% for the calibration and validation periods, respectively. The mean annual values of runoff predictions under the four representative concentration pathways (RCPs) exhibited a decreasing trend over the future three decades (2021–2050) when compared to the runoff simulations in the baseline period (1982–2011), where the values were about −9.9%, −19.5%, −16.6%, and −11.4% for the RCP2.6, RCP4.5, RCP6.0, and RCP8.5, respectively. The decreasing trend of future precipitation exerts impacts on runoff decline. Generally, the mean monthly changes of runoff predictions showed a decreasing trend from January to August for almost all of the RCPs, while an increasing trend existed from September to November, along with fluctuations among different RCPs. This study can provide beneficial references to comprehensively understand the impacts of climate change on runoff prediction and thus improve the regional strategy for future water resource management.

Replication of ecologically relevant hydrological indicators following a modified covariance approach to hydrological model parameterization

Abstract. Hydrological models can be used to assess the impact of hydrologic alteration on the river ecosystem. However, there are considerable limitations and uncertainties associated with the replication of ecologically relevant hydrological indicators. Vogel and Sankarasubramanian's 2003 (Water Resources Research) covariance approach to model evaluation and parameterization represents a shift away from algorithmic model calibration with traditional performance measures (objective functions). Using the covariance structures of the observed input and simulated output time series, it is possible to assess whether the selected hydrological model is able to capture the relevant underlying processes. From this plausible parameter space, the region of parameter space which best captures (replicates) the characteristics of a hydrological indicator may be identified. In this study, a modified covariance approach is applied to five hydrologically diverse case study catchments with a view to replicating a suite of ecologically relevant hydrological indicators identified through catchment-specific hydroecological models. The identification of the plausible parameter space (here n≈20) is based on the statistical importance of these indicators. Evaluation is with respect to performance and consistency across each catchment, parameter set, and the 40 ecologically relevant hydrological indicators considered. Timing and rate of change indicators are the best and worst replicated respectively. Relative to previous studies, an overall improvement in consistency is observed. This study represents an important advancement towards the robust application of hydrological models for ecological flow studies.

Identifying Key Hydrological Processes in Highly Urbanized Watersheds for Flood Forecasting with a Distributed Hydrological Model

The world has experienced large-scale urbanization in the past century, and this trend is ongoing. Urbanization not only causes land use/cover (LUC) changes but also changes the flood responses of watersheds. Lumped conceptual hydrological models cannot be effectively used for flood forecasting in watersheds that lack long time series of hydrological data to calibrate model parameters. Thus, physically based distributed hydrological models are used instead in these areas, but considerable uncertainty is associated with model parameter derivation. To reduce model parameter uncertainty in physically based distributed hydrological models for flood forecasting in highly urbanized watersheds, a procedure is proposed to control parameter uncertainty. The core concept of this procedure is to identify the key hydrological and flood processes in the highly urbanized watersheds and the sensitive model parameters related to these processes. Then, the sensitive model parameters are adjusted based on local runoff coefficients to reduce the parameter uncertainty. This procedure includes these steps: collecting the latest LUC information or estimating this information using satellite remote sensing images, analyzing LUC spatial patterns and identifying dominant LUC types and their spatial structures, choosing and establishing a distributed hydrological model as the forecasting tool, and determining the initial model parameters and identifying the key hydrological processes and sensitive model parameters based on a parameter sensitivity analysis. A highly urbanized watershed called Shahe Creek in the Pearl River Delta area was selected as a case study. This study finds that the runoff production processes associated with both the ferric luvisol and acric ferralsol soil types and the runoff routing process on urban land are key hydrological processes. Additionally, the soil water content under saturated conditions, the soil water content under field conditions and the roughness of urban land are sensitive parameters.

The effects of spatial discretization on performances and parameters of urban hydrological model.

Selecting a proper spatial resolution for urban rainfall runoff modeling was not a trivial issue because it could affect the model outputs. Recently, the development of remote sensing technology and increasingly available data source had enabled rainfall runoff process to be modeled at detailed and microscales. However, the models with less complexity might have equally good performance with less model establishment and computation time. This study attempted to explore the impact of model spatial resolution on model performance and parameters. Models with different discretization degree were built up on the basis of actual drainage networks, urban parcels and specific land use. The results showed that there was very little difference in the total runoff volumes while peak flows showed obvious scale effects which could be up to 30%. Generally, model calibration could compensate the scale effect. The calibrated models with different resolution showed similar performances. The consideration of effective impervious area (EIA) as a calibration parameter marginally increased performance of the calibration period but also slightly decreased performance in the validation period which indicated the importance of detailed EIA identification.

Large ensemble flood loss modelling and uncertainty assessment for future climate conditions for a Swiss pre-alpine catchment.

Information on possible changes in future flood risk is essential for successful adaptation planning and risk management. However, various sources of uncertainty arise along the model chains used for the assessment of flood risk under climate change. Knowledge on the importance of these different sources of uncertainty can help to design future assessments of flood risk, and to identify areas of focus for further research that aims to reduce existing uncertainties. Here we investigate the role of four sources of epistemic uncertainty affecting the estimation of flood loss for changed climate conditions for a meso-scale, pre-alpine catchment. These are: the choice of a scenario-neutral method, climate projection uncertainty, hydrological model parameter sets, and the choice of the vulnerability function. To efficiently simulate a large number of loss estimates, a surrogate inundation model was used. 46,500 loss estimates were selected according to the change in annual mean precipitation and temperature of an ensemble of regional climate models, and considered for the attribution of uncertainty. Large uncertainty was found in the estimated loss for a 100-year flood event with losses ranging from a decrease of loss compared to estimations for present day climate, to more than a 7-fold increase. The choice of the vulnerability function was identified as the most important source of uncertainty explaining almost half of the variance in the estimates. However, uncertainty related to estimating floods for changed climate conditions contributed nearly as much. Hydrological model parametrisation was found to be negligible in the present setup. For our study area, these results highlight the importance of improving vulnerability function formulation even in a climate change context where additional major sources of uncertainty arise.

Reducing the uncertainty of time-varying hydrological model parameters using spatial coherence within a hierarchical Bayesian framework

Hydrological processes became non-stationary under the influences of climate change and human activities. This non-stationarity highlights the need to adopt time-varying parameters in hydrological models. The majority of existing literature quantifies time-varying parameters by incorporating real observations of single basin into a hydrological model. They are limited in their information on catchment characteristics and climatic factors to constrain time-varying parameters. Thus, models are difficult to apply for hydrological predictions outside the calibration periods. This paper formulated the time-varying parameters for a lumped hydrological model as explicit functions of physically-based covariates that captured the catchment characteristics. Then, it used a hierarchical Bayesian framework to incorporate the similarity of adjacent basins to reduce the uncertainty of the assumed functions for time-varying parameters. Four modeling scenarios were developed to explore the spatial coherence between different characteristics of adjacent basins. Five criteria were adopted to evaluate the performance of assumed functional forms. Four spatially adjacent catchments in the central United States were selected as case studies to examine the validity of the proposed method. Results showed that (1) the proposed method succeeded in reducing the uncertainty of time-varying parameters, and (2) the seasonality of the catchment storage was more coherent between adjacent basins, indicated by the largest increase in model prediction performance (i.e., 9%). This study improved the understanding of the spatial coherence of time-varying parameters, which helps improve hydrological predictions in the future.

Application Research of Parallel Optimization Technology in Hydrological Model

Hydrological model parameters are generally considered to be a simplified representation that characterizes hydrologic processes, As hydrological models continue to deepen the application of hydrological processes in the basin, they face enormous calculations. Meanwhile, in pursuit calibrating the model parameters by optimal algorithms for higher accuracy, the computation burden of optical techniques has become much heavier. Therefore, in order to solve this problem of low efficiency of hydrological model calculation, this paper uses parallel PSO algorithm to calibrate the TOPMODEL model parameters, and then uses parallel computing to process the flow generation in each sub-basin. The results show that the daily runoff simulation value of tangnaihai hydrological station fits well with the measured hydrological process; Whether PSO or sub-basin all can improve computational efficiency by using parallel optimization techniques, the former and the latter increased by 3.22 and 2.57 times, respectively. The results provide a reference for further understanding the application of parallel computing in hydrological models.

Flow Prediction in Ungauged Catchments Using Probabilistic Random Forests Regionalization and New Statistical Adequacy Tests

AbstractFlow prediction in ungauged catchments is a major unresolved challenge in scientific and engineering hydrology. This study attacks the prediction in ungauged catchment problem by exploiting advances in flow index selection and regionalization in Bayesian inference and by developing new statistical tests of model performance in ungauged catchments. First, an extensive set of available flow indices is reduced using principal component (PC) analysis to a compact orthogonal set of “flow index PCs.” These flow index PCs are regionalized under minimal assumptions using random forests regression augmented with a residual error model and used to condition hydrological model parameters using a Bayesian scheme. Second, “adequacy” tests are proposed to evaluate a priori the hydrological and regionalization model performance in the space of flow index PCs. The proposed regionalization approach is applied to 92 northern Spain catchments, with 16 catchments treated as ungauged. It is shown that (1) a small number of PCs capture approximately 87% of variability in the flow indices and (2) adequacy tests with respect to regionalized information are indicative of (but do not guarantee) the ability of a hydrological model to predict flow time series and are hence proposed as a prerequisite for flow prediction in ungauged catchments. The adequacy tests identify the regionalization of flow index PCs as adequate in 12 of 16 catchments but the hydrological model as adequate in only 1 of 16 catchments. Hence, a focus on improving hydrological model structure and input data (the effects of which are not disaggregated in this work) is recommended.

A likelihood framework for deterministic hydrological models and the importance of non-stationary autocorrelation

Abstract. The widespread application of deterministic hydrological models in research and practice calls for suitable methods to describe their uncertainty. The errors of those models are often heteroscedastic, non-Gaussian and correlated due to the memory effect of errors in state variables. Still, residual error models are usually highly simplified, often neglecting some of the mentioned characteristics. This is partly because general approaches to account for all of those characteristics are lacking, and partly because the benefits of more complex error models in terms of achieving better predictions are unclear. For example, the joint inference of autocorrelation of errors and hydrological model parameters has been shown to lead to poor predictions. This study presents a framework for likelihood functions for deterministic hydrological models that considers correlated errors and allows for an arbitrary probability distribution of observed streamflow. The choice of this distribution reflects prior knowledge about non-normality of the errors. The framework was used to evaluate increasingly complex error models with data of varying temporal resolution (daily to hourly) in two catchments. We found that (1) the joint inference of hydrological and error model parameters leads to poor predictions when conventional error models with stationary correlation are used, which confirms previous studies; (2) the quality of these predictions worsens with higher temporal resolution of the data; (3) accounting for a non-stationary autocorrelation of the errors, i.e. allowing it to vary between wet and dry periods, largely alleviates the observed problems; and (4) accounting for autocorrelation leads to more realistic model output, as shown by signatures such as the flashiness index. Overall, this study contributes to a better description of residual errors of deterministic hydrological models.

Modelling time-variant parameters of a two-parameter monthly water balance model

Parameters are usually assumed to be stationary, and regarded as constants in hydrological modelling. However, studies have shown that model parameters may vary temporally due to human activities, and climate variability and changes. This study proposes a framework for quantifying hydrological model parameters as functions of time-variant catchment properties, aiming to improve the capability of capturing hydrograph and the extrapolative ability of hydrological models under a changing environment. The framework includes four steps: (1) estimating model parameters by using an ensemble Kalman filter based on the observations; (2) analyzing correlations between estimated parameter values and catchment properties; (3) constructing a set of parameter functions based on the identified catchment properties and the proposed functional forms; and (4) selecting and testing the best-performed model. As a demonstration of the framework, the monthly water balance for Tongtianhe and Ganjiang basins in China with different climate are simulated using a two-parameter monthly water balance model. Results from the Tongtianhe Basin show that considering the time-variant evapotranspiration parameter (C) brings improvement in low flows when water storage capacity (SC) is treated as constant since there is no significant improvement in runoff simulation when SC is treated as a time-variant parameter. The application to Ganjiang Basin shows that reasonable improvements are achieved when both C and SC are treated as time-variant, especially in low and high flows. The presented framework provides a useful tool for estimating time-variant parameters of hydrological models, thereby leading to more reliable model predictions under a changing environment.

Uncertainty in hydrological analysis of climate change: multi-parameter vs. multi-GCM ensemble predictions

The quantification of uncertainty in the ensemble-based predictions of climate change and the corresponding hydrological impact is necessary for the development of robust climate adaptation plans. Although the equifinality of hydrological modeling has been discussed for a long time, its influence on the hydrological analysis of climate change has not been studied enough to provide a definite idea about the relative contributions of uncertainty contained in both multiple general circulation models (GCMs) and multi-parameter ensembles to hydrological projections. This study demonstrated that the impact of multi-GCM ensemble uncertainty on direct runoff projections for headwater watersheds could be an order of magnitude larger than that of multi-parameter ensemble uncertainty. The finding suggests that the selection of appropriate GCMs should be much more emphasized than that of a parameter set among behavioral ones. When projecting soil moisture and groundwater, on the other hand, the hydrological modeling equifinality was more influential than the multi-GCM ensemble uncertainty. Overall, the uncertainty of GCM projections was dominant for relatively rapid hydrological components while the uncertainty of hydrological model parameterization was more significant for slow components. In addition, uncertainty in hydrological projections was much more closely associated with uncertainty in the ensemble projections of precipitation than temperature, indicating a need to pay closer attention to precipitation data for improved modeling reliability. Uncertainty in hydrological component ensemble projections showed unique responses to uncertainty in the precipitation and temperature ensembles.

Hydrological modelling uncertainty analysis for different flow quantiles: a case study in two hydro-geographically different watersheds

ABSTRACTThis study focuses on analysis of hydrological model parameter uncertainty at varying sub-basin spatial scales. It was found that the variation in sub-basin spatial scale had little influence on the entire flow simulations. However, the different sub-basin spatial scales had a significant impact on the reproduction of the flow quantiles. The coarser sub-basin spatial scale provided a better coverage of most prediction uncertainty in observations. However, the finer sub-basin spatial scale produced the best single simulation output closer to the observations. In general, the optimal sub-basin spatial scales (ratio to the entire watershed size) in the two test watersheds were found to be in the ranges 14–19% and 2–4% for good simulation of high and low flows, respectively. It is therefore worthwhile to put more effort into reproducing different flow quantiles by investigating an appropriate sub-basin spatial scale.

Investigation of non-unique relationship between soil electrical conductivity and water content due to drying-wetting rate using TDR

The characterization of the relationship between volumetric soil water content (θ) and bulk electrical conductivity (EC) (or electrical resistivity) is of high interest in fields of engineering, fundamental petrophysical, hydrological model parameterization, and quantitative hydrogeophysical interpretations. Based on the relationship, for instance, the broad-area image using electrical resistivity tomography (ERT) can be transformed into θ tomograms as initial/boundary conditions of the slope stability analysis. However, the relationship is affected by the hysteresis, leading the inconsistency in drying-wetting circles. Therefore, this study focused on the factor of soil drying-wetting rate using the proposed time domain reflectometry (TDR) method and related sensors for such characterization. A modified pressure plate apparatus enhanced by TDR was first employed with a relatively low rate in which EC and θ were measured simultaneously, without evident non-unique relationship. A TDR penetrometer was then designed for acquiring the temporal variations of θ and EC in the field. On the basis of certain assumptions, observations showed an apparent dependency of the slope of the θ–EC rating curve on rates, but no hysteresis pattern. Finally, a laboratory controlled fast wetting–drying cell was used to increase the response time, proving that both the hysteresis and slopes of the θ–EC rating curves were obviously affected by the soil drying-wetting rate, as a significant finding to the related topics.

Regionalization and parameterization of a hydrologic model significantly affect the cascade of uncertainty in climate-impact projections

Climate-impact projections are subject to uncertainty arising from climate models, greenhouse gases emission scenarios, bias correction and downscaling methods (BCDS), and the impact models. We studied the effects of hydrological model parameterization and regionalization (HM-P and HM-R) on the cascade of uncertainty. We developed a new, widely-applicable approach that improves our understanding of how HM-P and HM-R along with other uncertainty drivers contribute to the overall uncertainty in climate-impact projections. We analyzed uncertainties arising from general circulation models (GCMs), representative concertation pathways, BCDS, evapotranspiration calculation methods, and specifically HM-P and HM-R. We used the Soil and Water Assessment Tool, a semi-physical process-based hydrologic model with a high capability of parameterization, to project blue and green water resources for historical (1983–2007), near future (2010–2035) and far future (2040–2065) periods in Alberta, a western province of Canada. We developed an Analysis of Variance (ANOVA)-Sequential Uncertainty Fitting Program approach, to decompose the overall uncertainty into contributions of single drivers using the projected blue and green water resources. The monthly analyses of projected water resources showed that HM-P and HM-R contribute 21–51% and 15–55% to the blue water, and 20–48% and 15–50% to the green water overall uncertainty in near future and far future, respectively. Overall, we found that in spring and summer seasons uncertainty arising from HM-P and HM-R dominates other uncertainty sources, e.g. GCMs. We also found that global climate models are another dominant source of uncertainty in future impact projections.

Constraining hydrological model parameters using water isotopic compositions in a glacierized basin, Central Asia

Water stable isotope signatures can provide valuable insights into the catchment internal runoff processes. However, the ability of the water isotope data to constrain the internal apportionments of runoff components in hydrological models for glacierized basins is not well understood. This study developed an approach to simultaneously model the water stable isotopic compositions and runoff processes in a glacierized basin in Central Asia. The fractionation and mixing processes of water stable isotopes in and from the various water sources were integrated into a glacio-hydrological model. The model parameters were calibrated on discharge, snow cover and glacier mass balance data, and additionally isotopic composition of streamflow. We investigated the value of water isotopic compositions for the calibration of model parameters, in comparison to calibration methods without using such measurements. Results indicate that: (1) The proposed isotope-hydrological integrated modeling approach was able to reproduce the isotopic composition of streamflow, and improved the model performance in the evaluation period; (2) Involving water isotopic composition for model calibration reduced the model parameter uncertainty, and helped to reduce the uncertainty in the quantification of runoff components; (3) The isotope-hydrological integrated modeling approach quantified the contributions of runoff components comparably to a three-component tracer-based end-member mixing analysis method for summer peak flows, and required less water tracer data. Our findings demonstrate the value of water isotopic compositions to improve the quantification of runoff components using hydrological models in glacierized basins.

Variation in soil hydrological properties on shady and sunny slopes in the permafrost region, Qinghai–Tibetan Plateau

Soil hydrological properties not only directly influenced soil water content, evapotranspiration, infiltration, and runoff, but also made these factors of concern in arid and semi-arid regions. Prior research has focused on the temporal and spatial variation in soil hydrological properties and the impacts of climate change, ecosystem changes over time or human activities on soil hydrological properties. However, studies conducted on the differences in soil hydrological properties between shady and sunny slopes have seldom been conducted, especially in the permafrost region of the Qinghai–Tibetan Plateau. To investigate the variation in soil hydrological properties on shady and sunny slopes, we chose the Zuomaokongqu watershed of Fenghuo Mountain, which is located on the Qinghai–Tibetan Plateau, as the study area. Three experimental sites were selected in the study area, and the distance between experimental sites was 100 m. Based on the differences in altitude and vegetation coverage, five sunny slope sample points and three shady slope sample points were selected in each experimental site. At each of these sample points, the soil water content, soil-saturated conductivity, soil water-retention curve, soil physico-chemical properties, aboveground biomass, and underground biomass were examined in the top 0–50 cm of the active layer. The results showed that the soil hydrological properties of shady slopes differed significantly from those of sunny slopes. The soil water content of sunny slopes was 20.9% less than that of shady slopes. The soil-saturated water content of sunny slopes was 12.2% less than that of shady slopes. The soil water content of sunny slopes at − 0.3 Mpa and − 0.7 Mpa matric potential was 23.5% and 21.4% less than that of shady slopes, respectively. It was indicated that the soil water-retention capacity of sunny slopes was lower than that of shady slopes. However, the soil-saturated conductivity of sunny slopes was 84.5% larger than that of shady slopes and exceeded the range of soil-saturated conductivity, which was useful for plant growth. Meanwhile, the vegetation coverage on sunny slopes was lower than that on shady slopes, but the soil sand content showed the opposite relationship. Pearson’s coefficient analysis results showed that vegetation coverage and soil desertification, which are affected by permafrost degradation, were the main factors influencing soil hydrological properties on shady and sunny slopes. These results will help determine appropriate hydraulic parameters for hydrological models in mountain areas.

GLOBAL SENSITIVITY ANALYSIS METHODS APPLIED TO HYDROLOGIC MODELING WITH THE SAC-SMA MODEL

ABSTRACT This study aimed to use global sensitivity analysis (GSA) methods to evaluate the sensitivity of the SAC-SMA hydrologic model parameters in the estimation of daily flows of the Piracicaba river basin. The study was carried out in three sections of flow monitoring of the Piracicaba river basin, with an area of 5,304.0 km2 and located in the State of Minas Gerais, Brazil. For the global sensitivity analysis of the SAC-SMA model, the Morris and Sobol methods were used. The model parameters showing high sensitivity were UZFWM, which represents the free water depth in the upper zone of the soil and interferes with the subsurface flow and groundwater aquifer recharge; ADIMP, which represents the additional impermeable area of the basin and interferes with the direct runoff generation; and LZPK, LZSK, LZFPM, and LZFSM, which are related to the base flow of the basin. The results showed that most of the SAC-SMA model parameters do not provide expressive variations in the output variable, most of the SAC-SMA model parameters with high sensitivity are the intervenient in the base flow, and the Morris method should be used as a preliminary analysis to the use of the Sobol method.

On the lower bound of Budyko curve: The influence of precipitation seasonality

As a boundary condition, the lower bound is a prerequisite for constructing the Budyko framework. However, the traditional lower bound i.e., the horizontal axis is an analytical boundary without considering realistic conditions. In fact, under real-word condition, the lower bound of Budyko curves, representing the maximum value of water yield, should be located above the horizontal axis due to complicated constraints from basin characteristics, especially the precipitation seasonality, a key driver of runoff yield and a dominant factor in constructing Budyko framework. Thus, this study focused on exploring the reasonable location of the lower bound by adequately analyzing potential influence of precipitation seasonality. To do that, multiple hydrological simulations in basins under different climate and topography conditions were developed based on various precipitation scenarios constructed by using Markov chain with full range of precipitation seasonality. To fully understand the influence from precipitation seasonality on the lower bound, the water-energy supply and the basin characteristics were fixed by aridity index and hydrological model parameters, respectively. The results reveal a positive correlation between runoff coefficient and precipitation seasonality with an obvious higher location above the horizontal axis, indicating the horizontal axis is imprecise to describe the upper bound of runoff yield under real-word condition. Furthermore, a potential location of the lower bound above the horizontal axis in Budyko space was found based on runoff yield mechanism under real basin condition, representing a more appropriate boundary condition of Budyko framework.