Environmental flow envelopes: quantifying ecosystem-threatening flow alterations

2021 ◽  
Author(s):  
Vili Virkki ◽  
Elina Alanärä ◽  
Miina Porkka ◽  
Lauri Ahopelto ◽  
Tom Gleeson ◽  
...  
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Human Impacts ◽  
Well Being ◽  
Environmental Flow ◽  
Freshwater Ecosystems ◽  
Low Flow ◽  
Anthropogenic Pressure ◽  
Basin Scale ◽  
Climate Forcings

<p>The benefits of harnessing rivers into human use should not come with a disproportionate expense on the Earth system. Especially, freshwater ecosystems suffer greatly from direct and indirect human impacts, such as excessive water withdrawals and climate change, which are expected to only increase in the near future. Here, we aim for quantifying the extent and degree of considerable flow alterations that threaten the well-being of freshwater ecosystems, across the world.</p><p>At the global scale, the ecological status of river systems is often assessed using global hydrological models (GHMs) and hydrological environmental flow (EF) methods. These suffer from substantial uncertainties: 1) the GHMs parameterised with variable climate forcings may give highly dispersed discharge estimates and 2) individual hydrological EF methods capture ecosystem water needs poorly. We tackle these sources of uncertainty by introducing a novel methodology: environmental flow envelopes (EFEs). The EFE is an envelope of safe discharge variability between a lower and an upper bound, defined at the sub-basin scale in monthly time resolution. It is based on pre-industrial (1801-1860) discharge and a large ensemble of EF methods, GHMs, and climate forcings, using ISI-MIP2b data. Using the EFE, we can simultaneously assess the frequency and severity of ecosystem-threatening flow alterations.</p><p>Comparing post-industrial (1976-2005) discharge to the EFEs, discharge in 32.7% of the total 3860 sub-basins, covering 28.4% of the global landmass, violates the EFE during more than 10% of all months across four GHMs. These violations are considered as severe threats to freshwater ecosystems. The most impacted regions include areas with high anthropogenic pressure, such as the Middle East, India, Eastern Asia, and Middle America. The violations clearly concentrate on the EFE lower bound during low or intermediate flow seasons. Discharge in 61.4% of sub-basins violates the EFE during more than 10% of low flow season months, average violation being 47.5% below the safe limit denoted by EFE lower bound. Indications of significantly increased flows by violations of the EFE upper bound are fewer and further apart, as well as lower bound violations during high flow season.</p><p>Although fractional discharge allocations alone cannot fully capture the ecosystem water needs, this study is a step towards less uncertainty in global EF assessments. The introduced method provides a novel, globally robust way of estimating ecosystem water needs at the sub-basin scale. The results of this study underline the importance of the low flow season, during which EFE violations are the most prevalent. While only preliminary evidence of significantly increased flows emerges in relatively few areas, the EFE upper bound would benefit from further research. The EFE methodology can be used for exploring macro-regional areas where anthropogenic flow alteration threatens freshwater ecosystems the most. However, case-specific studies incorporating factors beyond quantitative flow only are required for practical implications.</p>

scholarly journals Environmental flow envelopes: quantifying global, ecosystem–threatening streamflow alterations

2021 ◽  
Author(s):  
Vili Virkki ◽  
Elina Alanärä ◽  
Miina Porkka ◽  
Lauri Ahopelto ◽  
Tom Gleeson ◽  
...  
Keyword(s):  
Climate Change ◽  
Upper Bound ◽  
Environmental Flows ◽  
Environmental Flow ◽  
Fine Tuning ◽  
Low Flow ◽  
Practical Applications ◽  
Riverine Ecosystems ◽  
Basin Scale ◽  
The World

Abstract. Human actions and climate change have drastically altered river flows across the world, resulting in adverse effects on riverine ecosystems. Environmental flows (EFs) have emerged as a prominent tool for safeguarding riverine ecosystems. However, at the global scale, the assessment of EFs is associated with significant uncertainty. Here, we present a novel method to determine EFs by Environmental Flow Envelopes (EFE), which is an envelope of variability bounded by discharge limits within which riverine ecosystems are not seriously compromised. The EFE is defined globally in approximately 4,400 sub–basins at monthly time resolution, considering also the methodological uncertainties related with global EF studies. In addition to a lower bound of discharge, the EFE introduces an upper bound of discharge, identifying areas where streamflow has increased substantially. Further, instead of only showing whether EFs are violated, as commonly done, we quantify, for the first time, the frequency, severity, and trends of EFE violations, which can be considered as potential threats to riverine ecosystems. We use pre–industrial (1801–1860) quasi-natural discharge and a suite of hydrological EFR methods and global hydrological models to estimate EFE, applying data from the ISIMIP 2b ensemble. We then compare the EFEs to recent past (1976–2005) discharge to assess the violations of the EFE. We found that the EFE violations most commonly manifest themselves by insufficient streamflow during the low flow season, with less violations during intermediate flow season, and only few violations during high flow season. These violations are widespread: discharge in half of the sub–basins of the world has violated the EFE during more than 5 % of the months between 1976 and 2005. The trends in EFE violations have mainly been increasing during the past decades and will likely remain problematic with projected increases in anthropogenic water use and hydroclimatic changes. Indications of excessive streamflow through EFE upper bound violations are relatively scarce and spatially distributed, although signs of increasing trends can be identified and potentially attributed to climate change. While the EFE provides a quick and globally robust way of determining environmental flow allocations at the sub–basin scale, local fine–tuning is necessary for practical applications and further research on the coupling between quantitative discharge and riverine ecosystem responses is required.

scholarly journals Accounting for environmental flow requirements in global water assessments

2014 ◽  
Vol 18 (12) ◽  
pp. 5041-5059 ◽  
Author(s):  
A. V. Pastor ◽  
F. Ludwig ◽  
H. Biemans ◽  
H. Hoff ◽  
P. Kabat
Keyword(s):  
Flow Regime ◽  
Environmental Flows ◽  
Environmental Flow ◽  
Ecological Condition ◽  
Freshwater Ecosystems ◽  
Low Flow ◽  
Human Needs ◽  
High Flows ◽  
The Mean ◽  
Global Vegetation

Abstract. As the water requirement for food production and other human needs grows, quantification of environmental flow requirements (EFRs) is necessary to assess the amount of water needed to sustain freshwater ecosystems. EFRs are the result of the quantification of water necessary to sustain the riverine ecosystem, which is calculated from the mean of an environmental flow (EF) method. In this study, five EF methods for calculating EFRs were compared with 11 case studies of locally assessed EFRs. We used three existing methods (Smakhtin, Tennant, and Tessmann) and two newly developed methods (the variable monthly flow method (VMF) and the Q90_Q50 method). All methods were compared globally and validated at local scales while mimicking the natural flow regime. The VMF and the Tessmann methods use algorithms to classify the flow regime into high, intermediate, and low-flow months and they take into account intra-annual variability by allocating EFRs with a percentage of mean monthly flow (MMF). The Q90_Q50 method allocates annual flow quantiles (Q90 and Q50) depending on the flow season. The results showed that, on average, 37% of annual discharge was required to sustain environmental flow requirement. More water is needed for environmental flows during low-flow periods (46–71% of average low-flows) compared to high-flow periods (17–45% of average high-flows). Environmental flow requirements estimates from the Tennant, Q90_Q50, and Smakhtin methods were higher than the locally calculated EFRs for river systems with relatively stable flows and were lower than the locally calculated EFRs for rivers with variable flows. The VMF and Tessmann methods showed the highest correlation with the locally calculated EFRs (R2=0.91). The main difference between the Tessmann and VMF methods is that the Tessmann method allocates all water to EFRs in low-flow periods while the VMF method allocates 60% of the flow in low-flow periods. Thus, other water sectors such as irrigation can withdraw up to 40% of the flow during the low-flow season and freshwater ecosystems can still be kept in reasonable ecological condition. The global applicability of the five methods was tested using the global vegetation and the Lund-Potsdam-Jena managed land (LPJmL) hydrological model. The calculated global annual EFRs for fair ecological conditions represent between 25 and 46% of mean annual flow (MAF). Variable flow regimes, such as the Nile, have lower EFRs (ranging from 12 to 48% of MAF) than stable tropical regimes such as the Amazon (which has EFRs ranging from 30 to 67% of MAF).

scholarly journals Accounting for environmental flow requirements in global water assessments

2013 ◽  
Vol 10 (12) ◽  
pp. 14987-15032 ◽  
Author(s):  
A. V. Pastor ◽  
F. Ludwig ◽  
H. Biemans ◽  
H. Hoff ◽  
P. Kabat
Keyword(s):  
Flow Regimes ◽  
Environmental Flow ◽  
Freshwater Ecosystems ◽  
Low Flow ◽  
Variable Flow ◽  
High Flows ◽  
Natural Flow Regimes ◽  
Global Vegetation ◽  
Global And Local ◽  
First Time

Abstract. With growing water needs for food production, it is necessary to improve the quantification of "Environmental Flow Requirements (EFRs)" to secure enough water for the freshwater ecosystems. In this study, five methods for calculating EFRs were compared to 11 case studies of locally-calculated EFRs. Three of the methods already existed (Smakhtin, Tennant and Tessmann) and two were developed in this study (the Variable Monthly Flow method and the Q90_Q50 method). The Variable Monthly Flow (VFM) method mimics for the first time the natural flow regimes while being "validated" at global and local scales. The VFM uses algorithms to classify flow regime into high, intermediate and low-flow months to take into account intra-annual variability by allocating EFRs with a percentage of mean monthly flow (MMF). The Q90_Q50 method allocates annual flow quantiles (Q50 and Q90) depending on the flow season. The results showed that, over all methods, 37% of annual discharge was allocated to "Nature" with a higher pressure on low flow requirements (LFR = 46% to 71% of average low flows) than on high flow requirements (HFR = 17% to 45% of average high flows). Environmental flow methods using fixed annual thresholds such as Tennant, Q90_Q50 and Smakhtin seemed to overestimate EFRs of stable flow regimes and underestimate EFRs of variable flow regimes. VFM and Tessmann methods showed the highest correlation with the locally-calculated EFRs (R2 = 0.91). The main difference between the Tessmann and VFM methods is that Tessmann method does not allow any water withdrawals during the low-flow season. Those five methods were tested within the global vegetation and hydrological model LPJml. The calculated global annual EFRs for "fair" ecological conditions represent between 25 to 46% of mean annual flow (MAF). Variable flow regimes such as the Nile have lower EFRs (ranging from 12 to 48% of MAF) than stable tropical regimes such as the Amazon (EFRs ranging from 30 to 67% of MAF).

scholarly journals Multiple closed orbits for N-body-type problems

1998 ◽  
Vol 58 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Shiqing Zhang
Keyword(s):  
Lower Bound ◽  
Periodic Solutions ◽  
Upper Bound ◽  
Critical Value ◽  
Body Type ◽  
Fixed Energy ◽  
Closed Orbits

Using the equivariant Ljusternik-Schnirelmann theory and the estimate of the upper bound of the critical value and lower bound for the collision solutions, we obtain some new results in the large concerning multiple geometrically distinct periodic solutions of fixed energy for a class of planar N-body type problems.

Limit Cycle Bifurcations for Piecewise Smooth Hamiltonian Systems with a Generalized Eye-Figure Loop

2016 ◽  
Vol 26 (12) ◽  
pp. 1650204 ◽  
Author(s):  
Jihua Yang ◽  
Liqin Zhao
Keyword(s):  
Lower Bound ◽  
Limit Cycle ◽  
Hamiltonian Systems ◽  
Limit Cycles ◽  
Upper Bound ◽  
Melnikov Function ◽  
Piecewise Smooth ◽  
First Order ◽  
Period Annulus

This paper deals with the limit cycle bifurcations for piecewise smooth Hamiltonian systems. By using the first order Melnikov function of piecewise near-Hamiltonian systems given in [Liu & Han, 2010], we give a lower bound and an upper bound of the number of limit cycles that bifurcate from the period annulus between the center and the generalized eye-figure loop up to the first order of Melnikov function.

Isolated minima of the product of n linear forms

1953 ◽  
Vol 49 (1) ◽  
pp. 59-62 ◽  
Author(s):  
E. S. Barnes
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Linear Forms ◽  
Image Position

Letbe n linear forms with real coefficients and determinant Δ = ∥ aij∥ ≠ 0; and denote by M(X) the lower bound of | X1X2 … Xn| over all integer sets (u) ≠ (0). It is well known that γn, the upper bound of M(X)/|Δ| over all sets of forms Xi, is finite, and the value of γn has been determined when n = 2 and n = 3.

scholarly journals The Algebraic Degree of Phase-Type Distributions

2010 ◽  
Vol 47 (03) ◽  
pp. 611-629
Author(s):  
Mark Fackrell ◽  
Qi-Ming He ◽  
Peter Taylor ◽  
Hanqin Zhang
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Polynomial Algorithm ◽  
Algebraic Degree ◽  
Nonnegative Matrices ◽  
Stieltjes Transform ◽  
Special Cases ◽  
Phase Type ◽  
Phase Type Distributions ◽  
The Matrix

This paper is concerned with properties of the algebraic degree of the Laplace-Stieltjes transform of phase-type (PH) distributions. The main problem of interest is: given a PH generator, how do we find the maximum and the minimum algebraic degrees of all irreducible PH representations with that PH generator? Based on the matrix exponential (ME) order of ME distributions and the spectral polynomial algorithm, a method for computing the algebraic degree of a PH distribution is developed. The maximum algebraic degree is identified explicitly. Using Perron-Frobenius theory of nonnegative matrices, a lower bound and an upper bound on the minimum algebraic degree are found, subject to some conditions. Explicit results are obtained for special cases.

scholarly journals Encoding Two-Dimensional Range Top-k Queries

Algorithmica ◽  
2021 ◽  
Author(s):  
Seungbum Jo ◽  
Rahul Lingala ◽  
Srinivasa Rao Satti
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Upper Bound ◽  
Total Order ◽  
Two Dimensional ◽  
Information Theoretic ◽  
Cartesian Tree ◽  
Dimensional Range

AbstractWe consider the problem of encoding two-dimensional arrays, whose elements come from a total order, for answering $${\text{Top-}}{k}$$ Top- k queries. The aim is to obtain encodings that use space close to the information-theoretic lower bound, which can be constructed efficiently. For an $$m \times n$$ m × n array, with $$m \le n$$ m ≤ n , we first propose an encoding for answering 1-sided $${\textsf {Top}}{\text {-}}k{}$$ Top - k queries, whose query range is restricted to $$[1 \dots m][1 \dots a]$$ [ 1 ⋯ m ] [ 1 ⋯ a ] , for $$1 \le a \le n$$ 1 ≤ a ≤ n . Next, we propose an encoding for answering for the general (4-sided) $${\textsf {Top}}{\text {-}}k{}$$ Top - k queries that takes $$(m\lg {{(k+1)n \atopwithdelims ()n}}+2nm(m-1)+o(n))$$ ( m lg ( k + 1 ) n n + 2 n m ( m - 1 ) + o ( n ) ) bits, which generalizes the joint Cartesian tree of Golin et al. [TCS 2016]. Compared with trivial $$O(nm\lg {n})$$ O ( n m lg n ) -bit encoding, our encoding takes less space when $$m = o(\lg {n})$$ m = o ( lg n ) . In addition to the upper bound results for the encodings, we also give lower bounds on encodings for answering 1 and 4-sided $${\textsf {Top}}{\text {-}}k{}$$ Top - k queries, which show that our upper bound results are almost optimal.

On the Modal μ-Calculus Over Finite Symmetric Graphs

2015 ◽  
Vol 65 (4) ◽  
Author(s):  
Giovanna D’Agostino ◽  
Giacomo Lenzi
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Satisfiability Problem ◽  
Finite Model ◽  
Model Property ◽  
Finite Model Property ◽  
Symmetric Graphs ◽  
Trivial Consequence

AbstractIn this paper we consider the alternation hierarchy of the modal μ-calculus over finite symmetric graphs and show that in this class the hierarchy is infinite. The μ-calculus over the symmetric class does not enjoy the finite model property, hence this result is not a trivial consequence of the strictness of the hierarchy over symmetric graphs. We also find a lower bound and an upper bound for the satisfiability problem of the μ-calculus over finite symmetric graphs.

scholarly journals Polynomial Mixing of the Edge-Flip Markov Chain for Unbiased Dyadic Tilings

2018 ◽  
Vol 28 (3) ◽  
pp. 365-387
Author(s):  
S. CANNON ◽  
D. A. LEVIN ◽  
A. STAUFFER
Keyword(s):  
Markov Chain ◽  
Relaxation Time ◽  
Lower Bound ◽  
Upper Bound ◽  
Open Problem ◽  
Mixing Time ◽  
Perpendicular Bisector ◽  
Unit Square

We give the first polynomial upper bound on the mixing time of the edge-flip Markov chain for unbiased dyadic tilings, resolving an open problem originally posed by Janson, Randall and Spencer in 2002 [14]. A dyadic tiling of size n is a tiling of the unit square by n non-overlapping dyadic rectangles, each of area 1/n, where a dyadic rectangle is any rectangle that can be written in the form [a2−s, (a + 1)2−s] × [b2−t, (b + 1)2−t] for a, b, s, t ∈ ℤ⩾ 0. The edge-flip Markov chain selects a random edge of the tiling and replaces it with its perpendicular bisector if doing so yields a valid dyadic tiling. Specifically, we show that the relaxation time of the edge-flip Markov chain for dyadic tilings is at most O(n4.09), which implies that the mixing time is at most O(n5.09). We complement this by showing that the relaxation time is at least Ω(n1.38), improving upon the previously best lower bound of Ω(n log n) coming from the diameter of the chain.

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