Decomposition of the mean squared error and NSE performance criteria: Implications for improving hydrological modelling

Recent advances in theory and experimen- tation motivate a thorough reassessment of the physics of debris flows. Analyses of flows of dry, granular solids and solid-fluid mixtures provide a foundation for a com- prehensive debris flow theory, and experiments provide data that reveal the strengths and limitations of theoret- ical models. Both debris flow materials and dry granular materials can sustain shear stresses while remaining stat- ic; both can deform in a slow, tranquil mode character- ized by enduring, frictional grain contacts; and both can flow in a more rapid, agitated mode characterized by brief, inelastic grain collisions. In debris flows, however, pore fluid that is highly viscous and nearly incompress- ible, composed of water with suspended silt and clay, can strongly mediate intergranular friction and collisions. Grain friction, grain collisions, and viscous fluid flow may transfer significant momentum simultaneously. Both the vibrational kinetic energy of solid grains (mea- sured by a quantity termed the granular temperature) and the pressure of the intervening pore fluid facilitate motion of grains past one another, thereby enhancing debris flow mobility. Granular temperature arises from conversion of flow translational energy to grain vibra- tional energy, a process that depends on shear rates, grain properties, boundary conditions, and the ambient fluid viscosity and pressure. Pore fluid pressures that exceed static equilibrium pressures result from local or global debris contraction. Like larger, natural debris flows, experimental debris flows of ;10 m 3 of poorly sorted, water-saturated sediment invariably move as an unsteady surge or series of surges. Measurements at the base of experimental flows show that coarse-grained surge fronts have little or no pore fluid pressure. In contrast, finer-grained, thoroughly saturated debris be- hind surge fronts is nearly liquefied by high pore pres- sure, which persists owing to the great compressibility and moderate permeability of the debris. Realistic mod- els of debris flows therefore require equations that sim- ulate inertial motion of surges in which high-resistance fronts dominated by solid forces impede the motion of low-resistance tails more strongly influenced by fluid forces. Furthermore, because debris flows characteristi- cally originate as nearly rigid sediment masses, trans- form at least partly to liquefied flows, and then trans- form again to nearly rigid deposits, acceptable models must simulate an evolution of material behavior without invoking preternatural changes in material properties. A simple model that satisfies most of these criteria uses depth-averaged equations of motion patterned after those of the Savage-Hutter theory for gravity-driven flow of dry granular masses but generalized to include the effects of viscous pore fluid with varying pressure. These equations can describe a spectrum of debris flow behav- iors intermediate between those of wet rock avalanches and sediment-laden water floods. With appropriate pore pressure distributions the equations yield numerical so- lutions that successfully predict unsteady, nonuniform motion of experimental debris flows.

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The physics of debris flows

This is a review of worldwide land degradation problems. Four themes are emphasized: delineating and estimating the magnitude of soil erosion, quantifying erosion and sedimentation impacts on land productivity, establishing quantitative values for erosion-causing parameters, and implementing global and regional soil and water conservation programs. Papers deal with both developing and developed countries and illustrate how erosion control techniques used in developed countries can or cannot be applied in developing countries.

https://gendocs.ru/docs/29/28948/conv_1/file1.pdf

Soil Erosion and Conservation

Power of the Mann–Kendall and Spearman's rho tests for detecting monotonic trends in hydrological series

Performance measures (PMs) and corresponding performance evaluation criteria (PEC) are important aspects of calibrating and validating hydrologic and water quality models and should be updated with advances in modeling science. We synthesized PMs and PEC from a previous special collection, performed a meta-analysis of performance data reported in recent peer-reviewed literature for three widely published watershed-scale models (SWAT, HSPF, WARMF), and one field-scale model (ADAPT), and provided guidelines for model performance evaluation. Based on the synthesis, meta-analysis, and personal modeling experiences, we recommend coefficient of determination (R2; in conjunction with gradient and intercept of the corresponding regression line), Nash Sutcliffe efficiency (NSE), index of agreement (d), root mean square error (RMSE; alongside the ratio of RMSE and standard deviation of measured data, RSR), percent bias (PBIAS), and several graphical PMs to evaluate model performance. We recommend that model performance can be judged satisfactory for flow simulations if monthly R2 0.70 and d 0.75 for field-scale models, and daily, monthly, or annual R2 0.60, NSE 0.50, and PBIAS ≤ ±15% for watershed-scale models. Model performance at the watershed scale can be evaluated as satisfactory if monthly R2 0.40 and NSE 0.45 and daily, monthly, or annual PBIAS ≤ ±20% for sediment; monthly R20.40 and NSE 0.35 and daily, monthly, or annual PBIAS ≤ ±30% for phosphorus (P); and monthly R2 0.30 and NSE 0.35 and daily, monthly, or annual PBIAS ≤ ±30% for nitrogen (N). For RSR, we recommend that previously published PEC be used as detailed in this article. We also recommend that these PEC be used primarily for the four models for which there were adequate data, and used only with caution for other models. These PEC can be adjusted within acceptable bounds based on additional considerations, such as quality and quantity of available measured data, spatial and temporal scales, and project scope and magnitude, and updated based on the framework presented herein. This initial meta-analysis sets the stage for more comprehensive meta-analysis to revise PEC as new PMs and more data become available.

Hydrologic and Water Quality Models: Performance Measures and Evaluation Criteria

The Nash–Sutcliffe efficiency index ( Ef ) is a widely used and potentially reliable statistic for assessing the goodness of fit of hydrologic models; however, a method for estimating the statistical significance of sample values has not been documented. Also, factors that contribute to poor sample values are not well understood. This research focuses on the interpretation of sample values of Ef . Specifically, the objectives were to present an approximation of the sampling distribution of the index; provide a method for conducting hypothesis tests and computing confidence intervals for sample values; and identify the effects of factors that influence sample values of Ef including the sample size, outliers, bias in magnitude, time-offset bias of hydrograph models, and the sampling interval of hydrologic data. Actual hydrologic data and hypothetical analyses were used to show these effects. The analyses show that outliers can significantly influence sample values of Ef . Time-offset bias and bias in magnit...

Evaluation of the Nash-Sutcliffe Efficiency Index

Surface soil moisture variation on small agricultural watersheds

The role of sensitivity analysis in hydrologic modeling

Sensitivity and error analyses were used to examine the following objectives: (1) analyze the structure of commonly used evaporation models; (2) provide estimates of the effect of variation in meteorological factors on observed evaporation rates; and (3) estimate the effect of error in measurements of the meteorological factors. The results indicate error in evaporation estimates resulting from measurement error in meteorological factors is probably much less than five percent of the computer evaporation rate. Variation with both time and space of the importance of the different meteorological factors is demonstrated. The sensitivity analysis indicates that the Fractional-Evaporation Equivalent method is structurally inadequate and the Weather Bureau model is more flexible than the Penman model. However, the Penman model appears to provide more realistic estimates of the importance of the various meteorological factors.

Richard H. McCuen

Papers

Evaluation of the Nash-Sutcliffe Efficiency Index

Surface soil moisture variation on small agricultural watersheds

The role of sensitivity analysis in hydrologic modeling

A sensitivity and error analysis cf procedures used for estimating evaporation

A nonstationary flood frequency analysis method to adjust for future climate change and urbanization