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In machine learning or scientific computing, model performance is measured with an objective function. But why choose one objective over another? According to the information‐theoretic paradigm, the "best" objective function is whichever minimizes information loss. To evaluate different objectives, transform them into likelihoods. The ratios of these likelihoods represent how strongly we should prefer one objective versus another, and the log of that ratio represents the relative information loss (or gain) from one objective to another. In plain terms, minimizing information loss is equivalent to minimizing uncertainty, as well as maximizing probability and general utility. We argue that this paradigm is well‐suited to models that have many uses and no definite utility like the complex Earth system models used to understand the effects of climate change. Furthermore, the benefits of "maximizing information and general utility" extend beyond model accuracy to other important considerations including how efficiently the model calibrates, how well it generalizes, and how well it compresses data. Key Points: A basic problem in modeling is the choice of objective function (or performance metric)According to information theory, the "best" objective function minimizes information loss, which we evaluate using the AICLike friction or inefficiency in a system, information loss incurs additional cost however the model is used [ABSTRACT FROM AUTHOR]

A better understanding of modeled streamflow errors related to basin reservoir storage is needed for large regions, which normally have many ungaged basins with reservoirs. We quantified the difference between modeled and observed streamflows for one process‐based and three statistical‐transfer hydrologic models, none of which explicitly accounted for reservoir storage. Streamflow statistics representing low to high flows, seasonality, annual variability, and daily autocorrelation were examined at 1082 study basins across the conterminous USA. All models increasingly overpredict (or decreasingly underpredict) observed annual maximum flows with increasing storage. Correlations between absolute values of errors for low‐flow statistics and storage are often larger in magnitude than those for signed errors—additional storage is associated with increases in model errors in both directions even when its overall effect in one direction is weak. The rate of increase in absolute values of model errors was nonlinear for most statistics. For low flows, model errors had a change point to larger errors at 48 days of reservoir storage (relative to long‐term mean daily flow); mean and high flows had change points at 147 to 176 days. We present predicted‐to‐observed errors for nine streamflow statistics over a large range of reservoir storage to help modelers and users of modeled streamflow understand the amount of storage for which explicit reservoir modeling is needed. [ABSTRACT FROM AUTHOR]

Streamflow is one of the most important variables in hydrology, but it is difficult to measure continuously. As a result, nearly all streamflow time series are estimated from rating curves that define a mathematical relationship between streamflow and some easy-to-measure proxy like water surface elevation (stage). Despite the existence of automated methods, most rating curves are still fit manually, which can be time-consuming and subjective. Although several automated methods exist, they vary greatly in performance because of the non-convex nature of the problem. In this work, we develop a parameterization of the segmented power law that works reliably with minimal data, which could serve operationally or as a benchmark for evaluating other methods. The model, along with test data and tutorials, is available as an open-source Python package called ratingcurve. The implementation uses a modern probabilistic machine-learning framework, which is relatively easy to modify so that others can improve upon it. [ABSTRACT FROM AUTHOR]

As science becomes increasingly cross‐disciplinary and scientific models become increasingly cross‐coupled, standardized practices of model evaluation are more important than ever. For normally distributed data, mean squared error (MSE) is ideal as an objective measure of model performance, but it gives little insight into what aspects of model performance are "good" or "bad." This apparent weakness has led to a myriad of specialized error metrics, which are sometimes aggregated to form a composite score. Such scores are inherently subjective, however, and while their components may be interpretable, the composite itself is not. We contend that, a better approach to model benchmarking and interpretation is to decompose MSE into interpretable components. To demonstrate the versatility of this approach, we outline some fundamental types of decomposition and apply them to predictions at 1,021 streamgages across the conterminous United States from three streamflow models. Through this demonstration, we hope to show that each component in a decomposition represents a distinct concept, like "season" or "variability," and that simple decompositions can be combined to represent more complex concepts, like "seasonal variability," creating an expressive language through which to interrogate models and data. Plain Language Summary: Models are essential scientific tools for explaining and predicting phenomena ranging from weather and climate, to health outcomes, to economic development, to the origins of the universe, and testing competing models is one of the most basic scientific activites. Yet, how scientists evaluate and justify their models can be inconsistent or even arbitrary. Traditionally, one performance metric—such as mean squared error—is used to identify the best model, but one metric provides little insight into what aspects of a model are "good" or "bad." This paper proposes a basic language for expressing different aspects of a model's performance. On one hand, this is useful for determining which aspects of model may require revision, but it also allows the modeler to separate out the best elements among several models and combine them to form an ensemble, analogous to how an audio engineer mixes together multiple tracks to form the best rendition of a musical piece. Key Points: Mean squared error (MSE) is an objective but somewhat enigmatic measure of model performanceMSE can be decomposed into components that quantify specific aspects of model performance, such as bias and varianceMixing components among models yields a form of ensemble prediction [ABSTRACT FROM AUTHOR]

An analysis to investigate the effects of the structure of rainfall at the mesoscale varying with time according to large-scale dynamic forcing shows that the scaling properties of rainfall can be measured by a random cascade with a single parameter. The application of random cascade theory is based on the fact that rainfall fields have a scaling structure and are clustered in space, and these can be described by random cascades. There is a significant relationship between large scale atmospheric dynamics and the statistical cascade theory of mesoscale rainfall as large scale average rain rate can be diagnosed from large scale dynamics. No model with a fixed parameter can measure rainfall as it varies with time, but parameter values will vary as a function of large scale forcing.

In many simulations of historical daily streamflow distributional bias arising from the distributional properties of residuals has been noted. This bias often presents itself as an underestimation of high streamflow and an overestimation of low streamflow. Here, 1168 streamgages across the conterminous USA, having at least 14 complete water years of daily data between 1 October 1980 and 30 September 2013, are used to explore a method for rescaling simulated streamflow to correct the distributional bias. Based on an existing approach that separates the simulated streamflow into components of temporal structure and magnitude, the temporal structure is converted to simulated nonexceedance probabilities and the magnitudes are rescaled using an independently estimated flow duration curve (FDC) derived from regional regression. In this study, this method is applied to a pooled ordinary kriging simulation of daily streamflow coupled with FDCs estimated by regional regression on basin characteristics. The improvement in the representation of high and low streamflows is correlated with the accuracy and unbiasedness of the estimated FDC. The method is verified by using an idealized case; however, with the introduction of regionally regressed FDCs developed for this study, the method is only useful overall for the upper tails, which are more accurately and unbiasedly estimated than the lower tails. It remains for future work to determine how accurate the estimated FDCs need to be to be useful for bias correction without unduly reducing accuracy. In addition to its potential efficacy for distributional bias correction, this particular instance of the methodology also represents a generalization of nonlinear spatial interpolation of daily streamflow using FDCs. Rather than relying on single index stations, as is commonly done to reflect streamflow timing, this approach to simulation leverages geostatistical tools to allow a region of neighbors to reflect streamflow timing. [ABSTRACT FROM AUTHOR]

Understanding the spatial structure of daily streamflow is essential for managing freshwater resources, especially in poorly gaged regions. Spatial scaling assumptions are common in flood frequency prediction (e.g., index-flood method) and the prediction of continuous streamflow at ungaged sites (e.g. drainage-area ratio), with simple scaling by drainage area being the most common assumption. In this study, scaling analyses of daily streamflow from 173 streamgages in the southeastern United States resulted in three important findings. First, the use of only positive integer moment orders, as has been done in most previous studies, captures only the probabilistic and spatial scaling behavior of flows above an exceedance probability near the median; negative moment orders (inverse moments) are needed for lower streamflows. Second, assessing scaling by using drainage area alone is shown to result in a high degree of omitted-variable bias, masking the true spatial scaling behavior. Multiple regression is shown to mitigate this bias, controlling for regional heterogeneity of basin attributes, especially those correlated with drainage area. Previous univariate scaling analyses have neglected the scaling of low-flow events and may have produced biased estimates of the spatial scaling exponent. Third, the multiple regression results show that mean flows scale with an exponent of one, low flows scale with spatial scaling exponents greater than one, and high flows scale with exponents less than one. The relationship between scaling exponents and exceedance probabilities may be a fundamental signature of regional streamflow. This signature may improve our understanding of the physical processes generating streamflow at different exceedance probabilities. [ABSTRACT FROM AUTHOR]

This study presents the results of a detailed river flow fluctuation analysis on daily records from 14 stations in the Flint River Basin in Georgia in the southeastern United States with special focus on the effect of watershed area on long memory of river flow fluctuations. The areas of the watersheds draining to the stations range from 23 to 19,606 km2. The climatic and seasonal trends are removed using the detrended fluctuation analysis technique. Results show that (1) river flow fluctuations have two distinct scaling regimes, and the scaling break is delayed for large watershed areas; (2) large watersheds have more persistent river flow fluctuations and stronger long memory (i.e., for lag times beyond the scale break) than small watersheds do; (3) the long memory of river flow fluctuations does not come from the long memory of precipitation; (4) a linear reservoir unit hydrograph transfer function approach does not capture correctly the basin processes that convert short-memory precipitation to long-memory streamflow; and (5) the degree of multifractality of river flow fluctuations decreases with increasing watershed area. The results clearly indicate that watershed area is an important factor in the long-memory studies of streamflow such as streamflow prediction. [ABSTRACT FROM AUTHOR]

The occurrence of fire and the subsequent increase in wind erosion are known to affect vegetation dynamics in dryland landscapes. Fires act as a disturbance on shrubs and trees and expose the soil surface to the erosive action of wind, thereby affecting the loss and redistribution of soil nutrients. Despite the relevance of wind erosion and fires to the dynamics of arid ecosystems, the interactions between these two processes remain poorly understood. We have investigated how a representative water repellent organic compound released by burning biomass and absorbed in the soil may enhance soil erodibility. To this end, we carried out a series of wind tunnel experiments, laboratory tests, and theoretical analyses to assess the effect of fire-induced water repellency on the soil susceptibility to wind erosion. The experiments were carried out using clean, well-sorted sand which was artificially coated with palmitic acid, a common water repellency inducing fatty acid found in most plants. The results indicate that fire-induced water repellency enhances soil erodibility, causing a drop in wind erosion threshold velocity. The results are explained by the effect of water repellent compounds on soil-water contact angle and on the strength of interparticle wet-bonding forces. [ABSTRACT FROM AUTHOR]

Wind erosion is a dominant geomorphological process in arid and semi-arid regions with major impacts on regional climate and desertification. The erosion process occurs when the wind speed exceeds a certain threshold value, which depends on a number of factors including surface soil moisture. The understanding and modelling of aeolian erosion requires a better understanding of the soil erodibility associated with different moisture conditions. In arid regions during the dry season, the atmospheric humidity plays an important role in determining the surface moisture content and the threshold shear velocity. By a series of wind tunnel tests and theoretical analyses, this dependence of threshold velocity on near surface air humidity is shown for three soils of different textures: sand, sandy loam, and clay loam. The results show that the threshold shear velocity decreases with increasing values of relative humidity for values of relative humidity between about 40% and 65%, while above and below this range the threshold shear velocity increases with air humidity. A theoretical framework is developed to explain these dependencies assuming an equilibrium between the surface soil moisture and the humidity of the overlying atmosphere. The conditions under which soil-atmosphere equilibrium occurs were tested experimentally in the laboratory for different soils in order to determine the effect of grain surface area and texture on the time required to reach equilibrium starting from different initial conditions. [ABSTRACT FROM AUTHOR]

Presents a study of the interannual variability of rainfall erosivity due to winter precipitation in the southwestern U.S. and its relation to the El Ni ñ o-Southern Oscillation (ENSO). Observation on the erosive power of rainfall during the El Ni ñ o phase and the La Ni ñ a phase; Discussion on the dependence of rainfall erosivity on the ENSO signal; Effect of climate change to soil properties.