On regionalizing the Turc‐Mezentsev water balance formula

Lebecherel, Laure; Andréassian, Vazken; Perrin, Charles

doi:10.1002/2013wr013575

Cited by 28 publications

(25 citation statements)

References 33 publications

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“…The naming convention we adopted is explained as follows: Eqs. (1) and (2) are named "Turc-Mezentsev" (TM) because Turc (1954) and Mezentsev (1955) worked independently and published the same equation almost simultaneously. Equations (3) and (4) are named "Tixeront-Fu" (TF) because although Tixeront's original publication predates Fu's by almost 20 years, both publications were independent, and the name of Fu has already gained wide international recognition.…”

Section: Presentation Of the Turc-mezentsev (Tm) Andmentioning

confidence: 99%

“…Varfolomeï Mezentsev was a Soviet geographer, working at the University of Omsk in Siberia. He published his formula in 1955, and continued working on it throughout his life (Mezentsev, 1955(Mezentsev, , 1982(Mezentsev, , 1993. Mezentsev (1955Mezentsev ( , 1982Mezentsev ( , 1993 started his analysis from a formula proposed by Bagrov (1953) (Eq.…”

Section: A2 Origin Of the Mezentsev Formulamentioning

confidence: 99%

“…The Turc-Mezentsev (Mezentsev, 1955;Turc, 1954) and Tixeront-Fu (Fu, 1981;Tixeront, 1964) formulas were introduced to model long-term water balance at the catchment scale. Both formulas are almost equivalent numerically (but differ nonetheless).…”

Section: Introductionmentioning

confidence: 99%

“…Surprisingly, comparisons are rare: Tixeront knew the work of Turc (1954), which he cites, but it seems that he did not realize that Turc's formulation was numerically equivalent to the one he proposed. Similarly, Fu knew the work of Mezentsev (1955) because he precisely starts his 1981 paper by discussing it, but it seems that he did not realize that the formulation he obtained was so close numerically.…”

Section: Introductionmentioning

confidence: 99%

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Technical Note: On the puzzling similarity of two water balance formulas – Turc–Mezentsev vs. Tixeront–Fu

Andréassian¹,

Sari

2019

Hydrol. Earth Syst. Sci.

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Abstract. This Technical Note documents and analyzes the puzzling similarity of two widely used water balance formulas: Turc–Mezentsev and Tixeront–Fu. It details their history and their hydrological and mathematical properties, and discusses the mathematical reasoning behind their slight differences. Apart from the difference in their partial differential expressions, both formulas share the same hydrological properties, and it seems impossible to recommend one over the other as more “hydrologically founded”: hydrologists should feel free to choose the one they feel more comfortable with.

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Section: Presentation Of the Turc-mezentsev (Tm) Andmentioning

confidence: 99%

Section: A2 Origin Of the Mezentsev Formulamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Technical Note: On the puzzling similarity of two water balance formulas – Turc–Mezentsev vs. Tixeront–Fu

Andréassian¹,

Sari

2019

Hydrol. Earth Syst. Sci.

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“…It originates from the well-known Turc-Mezentsev formula (Turc, 1954;Mezentsev, 1955;Lebecherel et al, 2013 are cumulated annual precipitation and PE data (computed using Oudin's formula). The model can be described using a non-linear equation:…”

Section: Mouelhi Formulamentioning

confidence: 99%

On the lack of robustness of hydrologic models regarding water balance simulation: a diagnostic approach applied to three models of increasing complexity on 20 mountainous catchments

Coron

Andréassian²,

Perrin³

et al. 2014

Hydrol. Earth Syst. Sci.

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Abstract. This paper investigates the robustness of rainfallrunoff models when their parameters are transferred in time. More specifically, we propose an approach to diagnose their ability to simulate water balance on periods with different hydroclimatic characteristics. The testing procedure consists in a series of parameter calibrations over 10 yr periods and the systematic analysis of mean flow volume errors on long records. This procedure was applied to three conceptual models of increasing structural complexity over 20 mountainous catchments in southern France. The results showed that robustness problems are common. Errors on 10 yr mean flow volume were significant for all calibration periods and model structures. Various graphical and numerical tools were used to investigate these errors and unexpectedly strong similarities were found in the temporal evolutions of these volume errors. We indeed showed that relative changes in simulated mean flow between 10 yr periods can remain similar, regardless of the calibration period or the conceptual model used. Surprisingly, using longer records for parameters optimisation or using a semi-distributed 19-parameter daily model instead of a simple 1-parameter annual formula did not provide significant improvements regarding these simulation errors on flow volumes. While the actual causes for these robustness problems can be manifold and are difficult to identify in each case, this work highlights that the transferability of water balance adjustments made during calibration can be poor, with potentially huge impacts in the case of studies in non-stationary conditions.

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Estimation of the distribution of annual runoff from climatic variables using copulas

Xiong

Gottschalk

2014

Water Resources Research

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An approach of deriving the annual runoff distribution using copulas from an annual rainfallrunoff model is proposed to provide an alternative annual runoff frequency analysis method in case of changing climatic variables. The annual rainfall-runoff model is established on the basis of the Budyko formula to estimate annual runoff, with annual precipitation and potential evapotranspiration as input variables. The model contains one single parameter k that guarantees that annual water balance is satisfied. In the derivation of the annual runoff distribution, annual precipitation, annual potential evapotranspiration, and parameter k are treated as three random variables, while the annual runoff distribution is obtained by integrating the joint probability density function of the three random variables over the domain constrained by the annual rainfall-runoff model using the canonical vine copula. This copula-based derivation approach is tested for 40 watersheds in two large basins in China. The estimated annual runoff distribution performs well in most watersheds. The performance is mainly related to the accuracy of the marginal distribution of precipitation. The copula-based derivation approach can also be used in ungauged watersheds where the distribution of k at the local site is estimated from the regional information of the k variable, and it also has acceptable performance in most watersheds, while poor performance is observed in a few watersheds with low accuracy in the Budyko formula.

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On regionalizing the Turc‐Mezentsev water balance formula

Cited by 28 publications

References 33 publications

Technical Note: On the puzzling similarity of two water balance formulas – Turc–Mezentsev vs. Tixeront–Fu

Technical Note: On the puzzling similarity of two water balance formulas – Turc–Mezentsev vs. Tixeront–Fu

On the lack of robustness of hydrologic models regarding water balance simulation: a diagnostic approach applied to three models of increasing complexity on 20 mountainous catchments

Estimation of the distribution of annual runoff from climatic variables using copulas

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