scholarly journals The Budyko framework beyond stationarity

2015 ◽  
Vol 12 (7) ◽  
pp. 6799-6830 ◽  
Author(s):  
P. Greve ◽  
L. Gudmundsson ◽  
B. Orlowsky ◽  
S. I. Seneviratne
Keyword(s):  
Water Balance ◽  
Aridity Index ◽  
Additional Parameter ◽  
Economic Sectors ◽  
First Order ◽  
Wide Range ◽  
Additional Water ◽  
New Formulation ◽  
Storage Term ◽  
Land Water

Abstract. Water availability is of major importance for a wide range of socio-economic sectors. Over land, the partitioning of precipitation (P) into evapotranspiration (E) and runoff (Q) is the key process to assess hydrological conditions. For climatological averages, the Budyko framework provides a simple first order relationship to estimate the evaporative index E / P as a function of the aridity index (Ep / P, with Ep denoting potential evaporation). However, a major downside of the Budyko framework is its limitation to steady state conditions, being a result of the assumption of a closed land water balance. Nonstationary processes coming into play at other than mean annual catchment scales are thus not represented. Here we propose an analytically derived new formulation of the Budyko curve including an additional parameter being implicitly related to the nonlinear storage term of the land water balance. The new framework is comprehensively analysed, showing that the additional parameter leads to an upward rotation of the original supply limit and therefore implicitly represents the amount of additional water available for evaporation. The obtained model is further validated using standard datasets of P, E and Ep. It is shown that the model is capable to represent first-order seasonal dynamics within the hydroclimatological system.

scholarly journals A two-parameter Budyko function to represent conditions under which evapotranspiration exceeds precipitation

2016 ◽  
Vol 20 (6) ◽  
pp. 2195-2205 ◽  
Author(s):  
Peter Greve ◽  
Lukas Gudmundsson ◽  
Boris Orlowsky ◽  
Sonia I. Seneviratne
Keyword(s):  
Aridity Index ◽  
Additional Parameter ◽  
Economic Sectors ◽  
Wide Range ◽  
Terrestrial Water ◽  
Additional Water ◽  
New Formulation ◽  
Storage Change ◽  
Two Parameter ◽  
Original Water

Abstract. A comprehensive assessment of the partitioning of precipitation (P) into evapotranspiration (E) and runoff (Q) is of major importance for a wide range of socio-economic sectors. For climatological averages, the Budyko framework provides a simple first-order relationship to estimate water availability represented by the ratio E / P as a function of the aridity index (Ep∕P, with Ep denoting potential evaporation). However, the Budyko framework is limited to steady-state conditions, being a result of assuming negligible storage change in the land–water balance. Processes leading to changes in the terrestrial water storage at any spatial and/or temporal scale are hence not represented. Here we propose an analytically derived modification of the Budyko framework including a new parameter explicitly representing additional water available to evapotranspiration besides instantaneous precipitation. The modified framework is comprehensively analyzed, showing that the additional parameter leads to a rotation of the original water supply limit. We further evaluate the new formulation in an example application at mean seasonal timescales, showing that the extended framework is able to represent conditions in which monthly to annual evapotranspiration exceeds monthly to annual precipitation.

scholarly journals The Budyko functions under non-steady state conditions: new approach and comparison with previous formulations

2016 ◽  
Author(s):  
Roger Moussa ◽  
Jean-Paul Lhomme
Keyword(s):  
Steady State ◽  
Aridity Index ◽  
Soil Water Storage ◽  
Additional Parameter ◽  
Simple Relationship ◽  
Evaporation Ratio ◽  
Feasible Domain ◽  
Physically Based ◽  
New Formulation ◽  
Long Timescales

Abstract. The Budyko functions relate the evaporation ratio E / P (E is evaporation and P precipitation) to the aridity index Φ = Ep / P (Ep is potential evaporation) and are valid on long timescales under steady state conditions. A new formulation physically based (noted ML) is proposed to extend the Budyko framework under non-steady state conditions taking into account the change in soil water storage S. The ML formulation introduces an additional parameter S* = S / Ep and can be applied with all classical Budyko functions. In the standard Budyko space (Ep / P, E / P), and for the particular case where the Fu-Zhang equation is used as a Budyko function, the ML formulation yields similar results to the analytical solution of Greve et al. (2016), and a simple relationship can be established between their respective parameters. Then, the ML formulation is extended to the space [(Ep / (P + S), E / (P + S)] and compared to the formulations of Chen et al. (2013) and Du et al. (2016). We show that the ML and Greve et al. formulations have similar upper feasible domain but their lower feasible domain is different from those of Chen et al. (2103) and Du et al. (2016). Moreover, the domain of variation of Ep / (P + S) differs: it is bounded by an upper limit 1 / S* in the ML formulation, while it is bounded with a lower limit in Chen et al.'s and Du et al.'s formulations.

Location, location, location – Considering local neighborhood when analyzing large samples of UK catchments

2021 ◽  
Author(s):  
Melike Kiraz ◽  
Thorsten Wagener ◽  
Gemma Coxon
Keyword(s):  
Water Balance ◽  
Effective Means ◽  
Aridity Index ◽  
Large Samples ◽  
Local Neighborhood ◽  
Wide Range ◽  
Closed Water ◽  
Comparative Hydrology ◽  
Water Balances

<p>Studying large samples of catchments has been an effective means for comparative hydrology as it provides a wide range of hydrological conditions which can be used to learn similarities and differences between places. Such analyses typically include an attempt to organize catchments along some gradient (e.g. climate) or in clusters (e.g. geology) using catchment descriptors (e.g. an aridity index). Various past studies have pointed to the problem that available catchment descriptors are often not sufficient to capture hydrologically relevant catchment behaviours. It is further widely acknowledged that the water balance of many catchments is not closed. Several hypotheses for the causes of this lack of closed water balance are stated in literature.</p><p>If we assume that the dominant control on water balance is climate, then catchments’ water balances should change smoothly in space (since the climate varies smoothly). If they do not, then something else must be controlling this behaviour. We expect that size, location and geology might play important role in the water balances of UK catchments. We aim to study the differences in water balance between catchments to understand the role of catchment location. We test different hypotheses while considering the local neighborhood of 669 UK catchments from the CAMELS-GB dataset.</p>

Emerging Cyber-Physical Systems : An Overview

2018 ◽  
pp. 306-316
Author(s):  
Okolie S.O. ◽  
Kuyoro S.O. ◽  
Ohwo O. B
Keyword(s):  
Health Care ◽  
Economic Benefit ◽  
Physical World ◽  
Cyber Physical Systems ◽  
Cyber Physical System ◽  
Economic Sectors ◽  
Strategic Research ◽  
Physical Systems ◽  
Security Issues ◽  
Wide Range

Cyber-Physical Systems (CPS) will revolutionize how humans relate with the physical world around us. Many grand challenges await the economically vital domains of transportation, health-care, manufacturing, agriculture, energy, defence, aerospace and buildings. Exploration of these potentialities around space and time would create applications which would affect societal and economic benefit. This paper looks into the concept of emerging Cyber-Physical system, applications and security issues in sustaining development in various economic sectors; outlining a set of strategic Research and Development opportunities that should be accosted, so as to allow upgraded CPS to attain their potential and provide a wide range of societal advantages in the future.

The Use of Neural Nets for Matching Fixed or Variable Geometry Compressors With Diesel Engines

2003 ◽  
Vol 125 (2) ◽  
pp. 572-579 ◽  
Author(s):  
S. A. Nelson ◽  
Z. S. Filipi ◽  
D. N. Assanis
Keyword(s):  
Diesel Engine ◽  
System Optimization ◽  
Design Tool ◽  
Neural Nets ◽  
Additional Parameter ◽  
Mathematical Function ◽  
Neural Net ◽  
Variable Geometry ◽  
Entire Family ◽  
Wide Range

A technique which uses trained neural nets to model the compressor in the context of a turbocharged diesel engine simulation is introduced. This technique replaces the usual interpolation of compressor maps with the evaluation of a smooth mathematical function. Following presentation of the methodology, the proposed neural net technique is validated against data from a truck type, 6-cylinder 14-liter diesel engine. Furthermore, with the introduction of an additional parameter, the proposed neural net can be trained to simulate an entire family of compressors. As a demonstration, a family of compressors of different sizes is represented with a single neural net model which is subsequently used for matching calculations with intercooled and nonintercooled engine configurations at different speeds. This novel approach readily allows for evaluation of various options within a wide range of possible compressor configurations prior to prototype production. It can also be used to represent the variable geometry machine regardless of the method used to vary compressor characteristics. Hence, it is a powerful design tool for selection of the best compressor for a given diesel engine system and for broader system optimization studies.

Critical examination of various approaches used for analysing helical cables

1994 ◽  
Vol 29 (1) ◽  
pp. 43-55 ◽  
Author(s):  
M Raoof ◽  
I Kraincanic
Keyword(s):  
Large Diameter ◽  
Numerical Results ◽  
Hertzian Contact ◽  
Critical Examination ◽  
First Order ◽  
Wide Range ◽  
End Conditions ◽  
Parametric Studies ◽  
The Individual ◽  
Fixed End

Using theoretical parametric studies covering a wide range of cable (and wire) diameters and lay angles, the range of validity of various approaches used for analysing helical cables are critically examined. Numerical results strongly suggest that for multi-layered steel strands with small wire/cable diameter ratios, the bending and torsional stiffnesses of the individual wires may safely be ignored when calculating the 2 × 2 matrix for strand axial/torsional stiffnesses. However, such bending and torsional wire stiffnesses are shown to be first order parameters in analysing the overall axial and torsional stiffnesses of, say, seven wire stands, especially under free-fixed end conditions with respect to torsional movements. Interwire contact deformations are shown to be of great importance in evaluating the axial and torsional stiffnesses of large diameter multi-layered steel strands. Their importance diminishes as the number of wires associated with smaller diameter cables decreases. Using a modified version of a previously reported theoretical model for analysing multilayered instrumentation cables, the importance of allowing for the influence of contact deformations in compliant layers on cable overall characteristics such as axial or torsional stiffnesses is demonstrated by theoretical numerical results. In particular, non-Hertzian contact formulations are used to obtain the interlayer compliances in instrumentation cables in preference to a previously reported model employing Hertzian theory with its associated limitations.

scholarly journals Coping with abrupt environmental change: the impact of the coastal El Niño 2017 on artisanal fisheries and mariculture in North Peru

2018 ◽  
Vol 76 (4) ◽  
pp. 1122-1130 ◽  
Author(s):  
Lotta Clara Kluger ◽  
Sophia Kochalski ◽  
Arturo Aguirre-Velarde ◽  
Ivonne Vivar ◽  
Matthias Wolff
Keyword(s):  
El Niño ◽  
El Nino ◽  
Management Strategies ◽  
Small Scale ◽  
Artisanal Fisheries ◽  
Economic Activities ◽  
Economic Sectors ◽  
Wide Range ◽  
The Impact ◽  
Coastal El Niño

Abstract In February and March 2017, a coastal El Niño caused extraordinary heavy rains and a rise in water temperatures along the coast of northern Peru. In this work, we document the impacts of this phenomenon on the artisanal fisheries and the scallop aquaculture sector, both of which represent important socio-economic activities for the province of Sechura. Despite the perceived absence of effective disaster management and rehabilitation policies, resource users opted for a wide range of different adaptation strategies and are currently striving towards recovery. One year after the event, the artisanal fisheries fleet has returned to operating almost on a normal scale, while the aquaculture sector is still drastically impacted, with many people continuing to work in different economic sectors and even in other regions of the country. Recovery of the social-ecological system of Sechura likely depends on the occurrence of scallop seed and the financial capacity of small-scale producers to reinitiate scallop cultures. Long-term consequences of this coastal El Niño are yet to be studied, though the need to develop trans-local and trans-sectoral management strategies for coping with disturbance events of this scale is emphasized.

A Stable Mixed Element Method for the Biharmonic Equation with First-Order Function Spaces

2017 ◽  
Vol 17 (4) ◽  
pp. 601-616 ◽  
Author(s):  
Zheng Li ◽  
Shuo Zhang
Keyword(s):  
Biharmonic Equation ◽  
Two Dimensions ◽  
Zero Order ◽  
Helmholtz Decomposition ◽  
Numerical Verification ◽  
Order Function ◽  
First Order ◽  
Mixed Element ◽  
New Formulation ◽  
Element Method

AbstractThis paper studies the mixed element method for the boundary value problem of the biharmonic equation {\Delta^{2}u=f} in two dimensions. We start from a {u\sim\nabla u\sim\nabla^{2}u\sim\operatorname{div}\nabla^{2}u} formulation that is discussed in [4] and construct its stability on {H^{1}_{0}(\Omega)\times\tilde{H}^{1}_{0}(\Omega)\times\bar{L}_{\mathrm{sym}}^% {2}(\Omega)\times H^{-1}(\operatorname{div},\Omega)}. Then we utilise the Helmholtz decomposition of {H^{-1}(\operatorname{div},\Omega)} and construct a new formulation stable on first-order and zero-order Sobolev spaces. Finite element discretisations are then given with respect to the new formulation, and both theoretical analysis and numerical verification are given.

First-order autoregressive gamma sequences and point processes

1980 ◽  
Vol 12 (3) ◽  
pp. 727-745 ◽  
Author(s):  
D. P. Gaver ◽  
P. A. W. Lewis
Keyword(s):  
Parameter Estimation ◽  
Point Processes ◽  
Random Variables ◽  
Innovation Process ◽  
Sums Of Random Variables ◽  
First Order ◽  
Wide Range ◽  
Serial Correlations ◽  
Generating Sequences ◽  
Stieltjes Transforms

It is shown that there is an innovation process {∊n} such that the sequence of random variables {Xn} generated by the linear, additive first-order autoregressive scheme Xn = pXn-1 + ∊n are marginally distributed as gamma (λ, k) variables if 0 ≦p ≦ 1. This first-order autoregressive gamma sequence is useful for modelling a wide range of observed phenomena. Properties of sums of random variables from this process are studied, as well as Laplace-Stieltjes transforms of adjacent variables and joint moments of variables with different separations. The process is not time-reversible and has a zero-defect which makes parameter estimation straightforward. Other positive-valued variables generated by the first-order autoregressive scheme are studied, as well as extensions of the scheme for generating sequences with given marginal distributions and negative serial correlations.

First-order autoregressive gamma sequences and point processes

1980 ◽  
Vol 12 (03) ◽  
pp. 727-745 ◽  
Author(s):  
D. P. Gaver ◽  
P. A. W. Lewis
Keyword(s):  
Parameter Estimation ◽  
Point Processes ◽  
Random Variables ◽  
Innovation Process ◽  
Sums Of Random Variables ◽  
First Order ◽  
Wide Range ◽  
Serial Correlations ◽  
Generating Sequences ◽  
Stieltjes Transforms

It is shown that there is an innovation process {∊ n } such that the sequence of random variables {X n } generated by the linear, additive first-order autoregressive scheme X n = pXn-1 + ∊ n are marginally distributed as gamma (λ, k) variables if 0 ≦p ≦ 1. This first-order autoregressive gamma sequence is useful for modelling a wide range of observed phenomena. Properties of sums of random variables from this process are studied, as well as Laplace-Stieltjes transforms of adjacent variables and joint moments of variables with different separations. The process is not time-reversible and has a zero-defect which makes parameter estimation straightforward. Other positive-valued variables generated by the first-order autoregressive scheme are studied, as well as extensions of the scheme for generating sequences with given marginal distributions and negative serial correlations.

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