A coupling strategy for nonlocal and local diffusion models with mixed volume constraints and boundary conditions
Not Available
97 MATHEMATICS AND COMPUTING↗
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A Probabilistic Scheme for Semilinear Nonlocal Diffusion Equations with Volume Constraints
This work presents a probabilistic scheme for solving semilinear nonlocal diffusion equations with volume constraints and integrable kernels. The nonlocal model of interest is defined by a time-dependent semilinear partial integro-differential equation (PIDE), in which the integro-differential operator consists of both local convection-diffusion and nonlocal diffusion operators. Here, our numerical scheme is based on the direct approximation of the nonlinear Feynman–Kac formula that establishes a link between nonlinear PIDEs and stochastic differential equations. The exploitation of the Feynman–Kac representation avoids solving dense linear systems arising from nonlocal operators. Compared with existing stochastic approaches, our method can achieve first-order convergence after balancing the temporal and spatial discretization errors, which is a significant improvement of existing probabilistic/stochastic methods for nonlocal diffusion problems. Error analysis of our numerical scheme is established. The effectiveness of our approach is shown in two numerical examples. The first example considers a three-dimensional nonlocal diffusion equation to numerically verify the error analysis results. The second example presents a physics problem motivated by the study of heat transport in magnetically confined fusion plasmas.
97 MATHEMATICS AND COMPUTING↗
SU-F-T-347: An Absolute Dose-Volume Constraint Based Deterministic Optimization Framework for Multi-Co60 Source Focused Radiotherapy
Purpose: Treatment plan optimization in multi-Co60 source focused radiotherapy with multiple isocenters is challenging, because dose distribution is normalized to maximum dose during optimization and evaluation. The objective functions are traditionally defined based on relative dosimetric distribution. This study presents an alternative absolute dose-volume constraint (ADC) based deterministic optimization framework (ADC-DOF). Methods: The initial isocenters are placed on the eroded target surface. Collimator size is chosen based on the area of 2D contour on corresponding axial slice. The isocenter spacing is determined by adjacent collimator sizes. The weights are optimized by minimizing the deviation from ADCs using the steepest descent technique. An iterative procedure is developed to reduce the number of isocenters, where the isocenter with lowest weight is removed without affecting plan quality. The ADC-DOF is compared with the genetic algorithm (GA) using the same arbitrary shaped target (254cc), with a 15mm margin ring structure representing normal tissues. Results: For ADC-DOF, the ADCs imposed on target and ring are (D100>10Gy, D50,10, 0<12Gy, 15Gy and 20Gy) and (D40<10Gy). The resulting D100, 50, 10, 0 and D40 are (9.9Gy, 12.0Gy, 14.1Gy and 16.2Gy) and (10.2Gy). The objectives of GA are to maximize 50% isodose target coverage (TC) while minimize the dose delivered to the ring structure, which results in 97% TC and 47.2% average dose in ring structure. For ADC-DOF (GA) techniques, 20 out of 38 (10 out of 12) initial isocenters are used in the final plan, and the computation time is 8.7s (412.2s) on an i5 computer. Conclusion: We have developed a new optimization technique using ADC and deterministic optimization. Compared with GA, ADC-DOF uses more isocenters but is faster and more robust, and achieves a better conformity. For future work, we will focus on developing a more effective mechanism for initial isocenter determination.
60 APPLIED LIFE SCIENCES↗
Analysis of Rig Parameter Data Using Drilling Process Modeling Constraints, Volume 5: Utah FORGE Well 16B(78)-32
Drill rig parameter measurements are routinely used during deep well construction to monitor and guide drilling conditions for improved performance and reduced costs. While insightful into the drilling process, these measurements are of reduced value without a standard to aid in data evaluation and decision making. In the main body of this work (Volume 1), a method is demonstrated whereby rock reduction model constraints are used to interpret drilling response parameters; the method could be applied in real-time to improve decision-making in the field and to further discern technology performance during post-drilling evaluations. Drilling parameters are evaluated using laboratory-validated rock reduction models for predicting the phenomenological response of drag bits (Detournay and Defourny, 1992) in computational algorithms. The method presented has applicability to development of advanced analytics on future geothermal wells using real-time electronic data recording for improved performance and reduced drilling costs. A drilling cost model is also used to show the tradeoff between rate of penetration and bit life and the influence on interval drilling costs. Details of the bit specifications and performance are cataloged in an independent volume, documented under separate cover, for each of the four wells, and include Volume 2: Utah FORGE 16A(78)-32; Volume 3: Utah FORGE 56-32; Volume 4: Utah FORGE 78B-32 and Volume 5: Utah FORGE 16B(78)-32.
15 GEOTHERMAL ENERGY↗
Analysis of Rig Parameter Data Using Drilling Process Modeling Constraints, Volume 4: Utah FORGE Well 78B-32
Drill rig parameter measurements are routinely used during deep well construction to monitor and guide drilling conditions for improved performance and reduced costs. While insightful into the drilling process, these measurements are of reduced value without a standard to aid in data evaluation and decision making. In the main body of this work (Volume 1), a method is demonstrated whereby rock reduction model constraints are used to interpret drilling response parameters; the method could be applied in real-time to improve decision-making in the field and to further discern technology performance during post-drilling evaluations. Drilling parameters are evaluated using laboratory-validated rock reduction models for predicting the phenomenological response of drag bits (Detournay and Defourny, 1992) in computational algorithms. The method presented has applicability to development of advanced analytics on future geothermal wells using real-time electronic data recording for improved performance and reduced drilling costs. A drilling cost model is also used to show the tradeoff between rate of penetration and bit life and the influence on interval drilling costs. Details of the bit specifications and performance are cataloged in an independent volume, documented under separate cover, for each of the four wells, and include Volume 2: Utah FORGE 16A(78)-32; Volume 3: Utah FORGE 56-32; Volume 4: Utah FORGE 78B-32 and Volume 5: Utah FORGE 16B(78)-32.
15 GEOTHERMAL ENERGY↗
Analysis of Rig Parameter Data Using Drilling Process Modeling Constraints, Volume 3: Utah FORGE Well 56-32
Drill rig parameter measurements are routinely used during deep well construction to monitor and guide drilling conditions for improved performance and reduced costs. While insightful into the drilling process, these measurements are of reduced value without a standard to aid in data evaluation and decision making. In the main body of this work (Volume 1), a method is demonstrated whereby rock reduction model constraints are used to interpret drilling response parameters; the method could be applied in real-time to improve decision-making in the field and to further discern technology performance during post-drilling evaluations. Drilling parameters are evaluated using laboratory-validated rock reduction models for predicting the phenomenological response of drag bits (Detournay and Defourny, 1992) in computational algorithms. The method presented has applicability to development of advanced analytics on future geothermal wells using real-time electronic data recording for improved performance and reduced drilling costs. A drilling cost model is also used to show the tradeoff between rate of penetration and bit life and the influence on interval drilling costs. Details of the bit specifications and performance are cataloged in an independent volume, documented under separate cover, for each of the four wells, and include Volume 2: Utah FORGE 16A(78)-32; Volume 3: Utah FORGE 56-32; Volume 4: Utah FORGE 78B-32 and Volume 5: Utah FORGE 16B(78)-32.
15 GEOTHERMAL ENERGY↗
Analysis of Rig Parameter Data Using Drilling Process Modeling Constraints, Volume 1: Summary of Utah FORGE Wells 16A(78)-32, 56-32, 78B-32 and 16B(78)-32
Drill rig parameter measurements are routinely used during deep well construction to monitor and guide drilling conditions for improved performance and reduced costs. While insightful into the drilling process, these measurements are of reduced value without a standard to aid in data evaluation and decision making. In the main body of this work (Volume 1), a method is demonstrated whereby rock reduction model constraints are used to interpret drilling response parameters; the method could be applied in real-time to improve decision-making in the field and to further discern technology performance during post-drilling evaluations. Drilling parameters are evaluated using laboratory-validated rock reduction models for predicting the phenomenological response of drag bits (Detournay and Defourny, 1992) in computational algorithms. The method presented has applicability to development of advanced analytics on future geothermal wells using real-time electronic data recording for improved performance and reduced drilling costs. A drilling cost model is also used to show the tradeoff between rate of penetration and bit life and the influence on interval drilling costs. Details of the bit specifications and performance are cataloged in an independent volume, documented under separate cover, for each of the four wells, and include Volume 2: Utah FORGE 16A(78)-32; Volume 3: Utah FORGE 56-32; Volume 4: Utah FORGE 78B-32 and Volume 5: Utah FORGE 16B(78)-32.
15 GEOTHERMAL ENERGY↗
SU-F-T-128: Dose-Volume Constraints for Particle Therapy Treatment Planning
Purpose: Determine equivalent Organ at Risk (OAR) tolerance dose (TD) constraints for MV x-rays and particle therapy. Methods: Equivalent TD estimates for MV x-rays are determined from an isoeffect, regression-analysis of published and in-house constraints for various fractionation schedules (n fractions). The analysis yields an estimate of (α/β) for an OAR. To determine equivalent particle therapy constraints, the MV x-ray TD(n) values are divided by the RBE for DSB induction (RBE{sub DSB}) or cell survival (RBE{sub S}). Estimates of (RBE{sub DSB}) are computed using the Monte Carlo Damage Simulation, and estimates of RBES are computed using the Repair-Misrepair-Fixation (RMF) model. A research build of the RayStation™ treatment planning system implementing the above model is used to estimate (RBE{sub DSB}) for OARs of interest in 16 proton therapy patient plans (head and neck, thorax, prostate and brain). Results: The analysis gives an (α/β) estimate of about 20 Gy for the trachea and heart and 2–4 Gy for the esophagus, spine, and brachial plexus. Extrapolation of MV x-ray constraints (n = 1) to fast neutrons using RBE{sub DSB} = 2.7 are in excellent agreement with clinical experience (n = 10 to 20). When conventional (n > 30) x-ray treatments are used as the reference radiation, fast neutron RBE increased to a maximum of 6. For comparison to a constant RBE of 1.1, the RayStation™ analysis gave estimates of proton RBE{sub DSB} from 1.03 to 1.33 for OARs of interest. Conclusion: The presented system of models is a convenient formalism to synthesize from multiple sources of information a set of self-consistent plan constraints for MV x-ray and hadron therapy treatments. Estimates of RBE{sub DSB} from the RayStation™ analysis differ substantially from 1.1 and vary among patients and treatment sites. A treatment planning system that incorporates patient and anatomy-specific corrections in proton RBE would create opportunities to increase the therapeutic ratio. The research build of the RayStation used in the study was made available to the University of Washington free of charge. RaySearch Laboratories did not provide any monetary support for the reported studies.
60 APPLIED LIFE SCIENCES↗
Multi-material continuum topology optimization with arbitrary volume and mass constraints
Not Available
Sanders, Emily D.↗
PolyMat: an efficient Matlab code for multi-material topology optimization
We introduce a Matlab implementation of topology optimization for compliance minimization on unstructured polygonal finite element meshes that efficiently accommodates many materials and many volume constraints. Leveraging the modular structure of the educational code, PolyTop, we extend it to the multi-material version, PolyMat, with only a few modifications. First, a design variable for each candidate material is defined in each finite element. Next, we couple a Discrete Material Optimization interpolation with the existing penalization and introduce a new parameter such that we can employ continuation and smoothly transition from a convex problem without any penalization to a non-convex problem in which material mixing and intermediate densities are penalized. Mixing that remains due to the density filter operation is eliminated via continuation on the filter radius. To accommodate flexibility in the volume constraint definition, the constraint function is modified to compute multiple volume constraints and the design variable update is modified in accordance with the Zhang-Paulino-Ramos Jr. (ZPR) update scheme, which updates the design variables associated with each constraint independently. The formulation allows for volume constraints controlling any subset of the design variables, i.e., they can be defined globally or locally for any subset of the candidate materials. Borrowing ideas for mesh generation on complex domains from PolyMesher, we conclude which design variables are associated with each local constraint of arbitrary geometry. A number of examples are presented to demonstrate the many material capability, the flexibility of the volume constraint definition, the ease with which we can accommodate passive regions, and how we may use local constraints to break symmetries or achieve graded geometries.
79 ASTRONOMY AND ASTROPHYSICS↗
Evaluation of the Risk of Grade 3 Oral and Pharyngeal Dysphagia Using Atlas-Based Method and Multivariate Analyses of Individual Patient Dose Distributions
Purpose: The study aimed to apply the atlas of complication incidence (ACI) method to patients receiving radical treatment for head and neck squamous cell carcinomas (HNSCC), to generate constraints based on dose-volume histograms (DVHs), and to identify clinical and dosimetric parameters that predict the risk of grade 3 oral mucositis (g3OM) and pharyngeal dysphagia (g3PD). Methods and Materials: Oral and pharyngeal mucosal DVHs were generated for 253 patients who received radiation (RT) or chemoradiation (CRT). They were used to produce ACI for g3OM and g3PD. Multivariate analysis (MVA) of the effect of dosimetry, clinical, and patient-related variables was performed using logistic regression and bootstrapping. Receiver operating curve (ROC) analysis was also performed, and the Youden index was used to find volume constraints that discriminated between volumes that predicted for toxicity. Results: We derived statistically significant dose-volume constraints for g3OM over the range v28 to v70. Only 3 statistically significant constraints were derived for g3PD v67, v68, and v69. On MVA, mean dose to the oral mucosa predicted for g3OM and concomitant chemotherapy and mean dose to the inferior constrictor (IC) predicted for g3PD. Conclusions: We have used the ACI method to evaluate incidences of g3OM and g3PD and ROC analysis to generate constraints to predict g3OM and g3PD derived from entire individual patient DVHs. On MVA, the strongest predictors were radiation dose (for g3OM) and concomitant chemotherapy (for g3PD).
62 RADIOLOGY AND NUCLEAR MEDICINE↗
Semiautomated head-and-neck IMRT planning using dose warping and scaling to robustly adapt plans in a knowledge database containing potentially suboptimal plans
Purpose: Prior work by the authors and other groups has studied the creation of automated intensity modulated radiotherapy (IMRT) plans of equivalent quality to those in a patient database of manually created clinical plans; those database plans provided guidance on the achievable sparing to organs-at-risk (OARs). However, in certain sites, such as head-and-neck, the clinical plans may not be sufficiently optimized because of anatomical complexity and clinical time constraints. This could lead to automated plans that suboptimally exploit OAR sparing. This work investigates a novel dose warping and scaling scheme that attempts to reduce effects of suboptimal sparing in clinical database plans, thus improving the quality of semiautomated head-and-neck cancer (HNC) plans. Methods: Knowledge-based radiotherapy (KBRT) plans for each of ten “query” patients were semiautomatically generated by identifying the most similar “match” patient in a database of 103 clinical manually created patient plans. The match patient’s plans were adapted to the query case by: (1) deforming the match beam fluences to suit the query target volume and (2) warping the match primary/boost dose distribution to suit the query geometry and using the warped distribution to generate query primary/boost optimization dose-volume constraints. Item (2) included a distance scaling factor to improve query OAR dose sparing with respect to the possibly suboptimal clinical match plan. To further compensate for a component plan of the match case (primary/boost) not optimally sparing OARs, the query dose volume constraints were reduced using a dose scaling factor to be the minimum from either (a) the warped component plan (primary or boost) dose distribution or (b) the warped total plan dose distribution (primary + boost) scaled in proportion to the ratio of component prescription dose to total prescription dose. The dose-volume constraints were used to plan the query case with no human intervention to adjust constraints during plan optimization. Results: KBRT and original clinical plans were dosimetrically equivalent for parotid glands (mean/median doses), spinal cord, and brainstem (maximum doses). KBRT plans significantly reduced larynx median doses (21.5 ± 6.6 Gy to 17.9 ± 3.9 Gy), and oral cavity mean (32.3 ± 6.2 Gy to 28.9 ± 5.4 Gy) and median (28.7 ± 5.7 Gy to 23.2 ± 5.3 Gy) doses. Doses to ipsilateral parotid gland, larynx, oral cavity, and brainstem were lower or equivalent in the KBRT plans for the majority of cases. By contrast, KBRT plans generated without the dose warping and dose scaling steps were not significantly different from the clinical plans. Conclusions: Fast, semiautomatically generated HNC IMRT plans adapted from existing plans in a clinical database can be of equivalent or better quality than manually created plans. The reductions in OAR doses in the semiautomated plans, compared to the clinical plans, indicate that the proposed dose warping and scaling method shows promise in mitigating the impact of suboptimal clinical plans.
60 APPLIED LIFE SCIENCES↗
Integral approximations to classical diffusion and smoothed particle hydrodynamics
The contribution of the paper is the approximation of a classical diffusion operator by an integral equation with a volume constraint. A particular focus is on classical diffusion problems associated with Neumann boundary conditions. By exploiting this approximation, we can also approximate other quantities such as the flux out of a domain. Our analysis of the model equation on the continuum level is closely related to the recent work on nonlocal diffusion and peridynamic mechanics. In particular, we elucidate the role of a volumetric constraint as an approximation to a classical Neumann boundary condition in the presence of physical boundary. The volume-constrained integral equation then provides the basis for accurate and robust discretization methods. An immediate application is to the understanding and improvement of the Smoothed Particle Hydrodynamics (SPH) method.
boundary conditions, smoothed particle hydrodynami↗
The exit-time problem for a Markov jump process
The purpose of this paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Additionally, such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developed nonlocal vector calculus. Finally, this calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
SU-F-T-539: Dosimetric Comparison of Volumetric Modulated Arc Therapy and Intensity Modulated Radiation Therapy for Whole Brain Hippocampal Sparing Radiation Therapy Treatments
Purpose: To compare the treatment plan quality and dose gradient near the hippocampus between VMAT (RapidArc) and IMRT delivery techniques for whole brain radiation therapy. Methods: Fifteen patients were evaluated in this retrospective study. All treatments were planned on Varian Eclipse TPS, using 3-Arc VMAT and 9-Field IMRT, following NRG Oncology protocol NRG-CC001 guidelines evaluated by a single radiation oncologist. Prescribed doses in all plans were 30 Gy delivered over 10 fractions normalized to a minimum of 100% of the dose covering 95% of the target volume. Identical contour sets and dose-volume constraints following protocol guidelines were also applied in all plans. A paired t-test analysis was used to compare VMAT and IMRT plans. Results: NRG-CC001 protocol dose-volume constraints were met for all VMAT and IMRT plans. For the planning target volume (PTV), the average values for D2% and D98% were 6% lower and 4% higher in VMAT than in IMRT, respectively. The average mean and maximum hippocampus doses in Gy for VMAT vs IMRT plans were (11.85±0.81 vs. 12.24±0.56, p=0.10) and (16.27±0.78 vs. 16.59±0.71, p=0.24), respectively. In VMAT, the average mean and maximum chiasm doses were 3% and 1% higher than in IMRT plans, respectively. For the left optic nerve, the average mean and maximum doses were 10% and 5% higher in VMAT than in IMRT plans, respectively. These values were 12% and 3% for the right optic nerve. The average percentage of dose gradient around the hippocampus in the 0–5mm and 5–10mm abutted regions for VMAT vs. IMRT were (4.42%±2.22% /mm vs. 3.95%±2.61% /mm, p=0.43) and (4.54%±1.50% /mm vs. 4.39%±1.28% /mm, p=0.73), respectively. Conclusion: VMAT plans can achieve higher hippocampus sparing with a faster dose fall-off than IMRT plans. Though statistically insignificant, VMAT offers better PTV coverage with slightly higher doses to OARs.
60 APPLIED LIFE SCIENCES↗
SU-E-J-86: Functional Conformal Planning for Stereotactic Body Radiation Therapy with CT-Pulmonary Ventilation Imaging
Purpose: To evaluate the functional planning using CT-pulmonary ventilation imaging for conformal SBRT. Methods: The CT-pulmonary ventilation image was generated using the Jacobian metric in the in-house program with the NiftyReg software package. Using the ventilation image, the normal lung was split into three lung regions for functionality (high, moderate and low). The anatomical plan (AP) and functional plan (FP) were made for ten lung SBRT patients. For the AP, the beam angles were optimized with the dose-volume constraints for the normal lung sparing and the PTV coverage. For the FP, the gantry angles were also optimized with the additional constraint for high functional lung. The MLC aperture shapes were adjusted to the PTV with the additional 5 mm margin. The dosimetric parameters for PTV, the functional volumes, spinal cord and so on were compared in both plans. Results: Compared to the AP, the FP showed better dose sparing for high- and moderate-functional lungs with similar PTV coverage while not taking care of the low functional lung (High:−12.9±9.26% Moderate: −2.0±7.09%, Low: +4.1±12.2%). For the other normal organs, the FP and AP showed similar dose sparing in the eight patients. However, the FP showed that the maximum doses for spinal cord were increased with the significant increment of 16.4Gy and 21.0Gy in other two patients, respectively. Because the beam direction optimizer chose the unexpected directions passing through the spinal cord. Conclusion: Even the functional conformal SBRT can selectively reduce high- and moderatefunctional lung while keeping the PTV coverage. However, it would be careful that the optimizer would choose unexpected beam angles and the dose sparing for the other normal organs can be worse. Therefore, the planner needs to control the dose-volume constraints and also limit the beam angles in order to achieve the expected dose sparing and coverage.
60 APPLIED LIFE SCIENCES↗
Stereotactic Body Radiation Therapy Boost After Concurrent Chemoradiation for Locally Advanced Non-Small Cell Lung Cancer: A Phase 1 Dose Escalation Study
Purpose: Stereotactic body radiation therapy (SBRT) boost to primary and nodal disease after chemoradiation has potential to improve outcomes for advanced non-small cell lung cancer (NSCLC). A dose escalation study was initiated to evaluate the maximum tolerated dose (MTD). Methods and Materials: Eligible patients received chemoradiation to a dose of 50.4 Gy in 28 fractions and had primary and nodal volumes appropriate for SBRT boost (<120 cc and <60 cc, respectively). SBRT was delivered in 2 fractions after chemoradiation. Dose was escalated from 16 to 28 Gy in 2 Gy/fraction increments, resulting in 4 dose cohorts. MTD was defined when ≥2 of 6 patients per cohort experienced any treatment-related grade 3 to 5 toxicity within 4 weeks of treatment or the maximum dose was reached. Late toxicity, disease control, and survival were also evaluated. Results: Twelve patients (3 per dose level) underwent treatment. All treatment plans met predetermined dose-volume constraints. The mean age was 64 years. Most patients had stage III disease (92%) and were medically inoperable (92%). The maximum dose level was reached with no grade 3 to 5 acute toxicities. At a median follow-up time of 16 months, 1-year local-regional control (LRC) was 78%. LRC was 50% at <24 Gy and 100% at ≥24 Gy (P=.02). Overall survival at 1 year was 67%. Late toxicity (grade 3-5) was seen in only 1 patient who experienced fatal bronchopulmonary hemorrhage (grade 5). There were no predetermined dose constraints for the proximal bronchial-vascular tree (PBV) in this study. This patient's 4-cc PBV dose was substantially higher than that received by other patients in all 4 cohorts and was associated with the toxicity observed: 20.3 Gy (P<.05) and 73.5 Gy (P=.07) for SBRT boost and total treatment, respectively. Conclusions: SBRT boost to both primary and nodal disease after chemoradiation is feasible and well tolerated. Local control rates are encouraging, especially at doses ≥24 Gy in 2 fractions. Toxicity at the PBV is a concern but potentially can be avoided with strict dose-volume constraints.
62 RADIOLOGY AND NUCLEAR MEDICINE↗
Functional approach to exploring climatic and landscape controls of runoff generation: 1. Behavioral constraints on runoff volume
Abstract Inspired by the Dunne diagram, the climatic and landscape controls on the partitioning of annual runoff into its various components (Hortonian and Dunne overland flow and subsurface stormflow) are assessed quantitatively, from a purely theoretical perspective. A simple distributed hydrologic model has been built sufficient to simulate the effects of different combinations of climate, soil, and topography on the runoff generation processes. The model is driven by a sequence of simple hypothetical precipitation events, for a large combination of climate and landscape properties, and hydrologic responses at the catchment scale are obtained through aggregation of grid‐scale responses. It is found, first, that the water balance responses, including relative contributions of different runoff generation mechanisms, could be related to a small set of dimensionless similarity parameters. These capture the competition between the wetting, drying, storage, and drainage functions underlying the catchment responses, and in this way, provide a quantitative approximation of the conceptual Dunne diagram. Second, only a subset of all hypothetical catchment/climate combinations is found to be “behavioral,” in terms of falling sufficiently close to the Budyko curve, describing mean annual runoff as a function of climate aridity. Furthermore, these behavioral combinations are mostly consistent with the qualitative picture presented in the Dunne diagram, indicating clearly the commonality between the Budyko curve and the Dunne diagram. These analyses also suggest clear interrelationships amongst the “behavioral” climate, soil, and topography parameter combinations, implying these catchment properties may be constrained to be codependent in order to satisfy the Budyko curve.
Li, Hong‐Yi↗