In this paper we present a brief overview of geomorphological instantaneous unit hydrograph (GIUH) theories and analyze their successful path without hiding their limitations. The history of the GIUH is subdivided into three major sections. The first is based on the milestone works of Rodríguez‐Iturbe and Valdés (Water Resources Research 1979; 15(6): 1409–1420) and Gupta et al. (Water Resources Research 1980; 16(5): 855–862), which recognized that a treatment of water discharges with ‘travel times’ could provide a rich interpretation of the theory of the instantaneous unit hydrograph (IUH). We show how this was possible, what assumptions were made, which of these assumptions can be relaxed, and which have become obsolete and been discarded. The second section focuses on the width‐function‐based IUH (WFIUH) approach and its achievements in assessing the interplay of the topology and geometry of the network with water dynamics. The limitations of the WFIUH approach are described, and a way to work around them is suggested. Finally, a new formal approach to estimating the water budget by ‘travel times’, which derives from a suitable use of the water budget equation and some hypotheses, has been introduced and disentangled. Copyright © 2015 John Wiley & Sons, Ltd.
Abstract. The theory of travel time and residence time distributions is reworked from the point of view of the hydrological storages and fluxes involved. The forward and backward travel time distribution functions are defined in terms of conditional probabilities. Previous approaches that used fixed travel time distributions are not consistent with our new derivation. We explain Niemi's formula and show how it can be interpreted as an expression of the Bayes theorem. Some connections between this theory and population theory are identified by introducing an expression which connects life expectancy with travel times. The theory can be applied to conservative solutes, including a method of estimating the storage selection functions. An example, based on the Nash hydrograph, illustrates some key aspects of the theory. Generalization to an arbitrary number of reservoirs is presented.
This work presents a new graphical system to represent hydrological dynamical models and their interactions. We propose an extended version of the Petri Nets mathematical modeling language, the Extended Petri Nets (EPN), which allows for an immediate translation from the graphics of the model to its mathematical representation in a clear way. We introduce the principal objects of the EPN representation (i.e., places, transitions, arcs, controllers, and splitters) and their use in hydrological systems. We show how to cast hydrological models in EPN and how to complete their mathematical description using a dictionary for the symbols and an expression table for the flux equations. Thanks to the compositional property of EPN, we show how it is possible to represent either a single hydrological response unit or a complex catchment where multiple systems of equations are solved simultaneously. Finally, EPN can be used to describe complex Earth system models that include feedback between the water, energy, and carbon budgets. The representation of hydrological dynamical systems with EPN provides a clear visualization of the relations and feedback between subsystems, which can be studied with techniques introduced in nonlinear systems theory and control theory.
Abstract. In this work 10 algorithms for estimating downwelling longwave atmospheric radiation (L↓) and 1 for upwelling longwave radiation (L↑) are integrated into the JGrass-NewAge modelling system. The algorithms are tested against energy flux measurements available for 24 sites in North America to assess their reliability. These new JGrass-NewAge model components are used (i) to evaluate the performances of simplified models (SMs) of L↓, as presented in literature formulations, and (ii) to determine by automatic calibration the site-specific parameter sets for L↓ in SMs. For locations where calibration is not possible because of a lack of measured data, we perform a multiple regression using on-site variables, i.e. mean annual air temperature, relative humidity, precipitation, and altitude. The regressions are verified through a leave-one-out cross validation, which also gathers information about the possible errors of estimation. Most of the SMs, when executed with parameters derived from the multiple regressions, give enhanced performances compared to the corresponding literature formulation. A sensitivity analysis is carried out for each SM to understand how small variations of a given parameter influence SM performance. Regarding the L↓ simulations, the Brunt (1932) and Idso (1981) SMs, in their literature formulations, provide the best performances in many of the sites. The site-specific parameter calibration improves SM performances compared to their literature formulations. Specifically, the root mean square error (RMSE) is almost halved and the Kling–Gupta efficiency is improved at all sites. Also in this case, Brunt (1932) and Idso (1981) SMs provided the best performances. The L↑ SM is tested by using three different temperatures (surface soil temperature, air temperature at 2 m elevation, and soil temperature at 4 cm depth) and model performances are then assessed. Results show that the best performances are achieved using the surface soil temperature and the air temperature.
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