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The effect of embedding actual evapotranspiration uncertainty in water balance model: coupling of interval-based hydrologic model and METRIC method

  • Research Article - Hydrology and Hydraulics
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Abstract

The determination of actual evapotranspiration (ET) plays a crucial role in hydrological modelling; however, it is subject to multiple sources of uncertainty. Sophisticated energy-based methods, such as METRIC, may lead to varying results based on different initial and boundary conditions. In this study, the relationship between groundwater withdrawal and the uncertainty effects of ET was explored by incorporating the uncertainty of the calculated ET values through an ensemble-based implementation of the METRIC model into the comprehensive interval-based water balance model, which includes surface and groundwater modules developed in terms of gray value model. The developed interval of ET is based on 20 members with different hot/cold pixels to provide interval-based monthly ET values. The study area is the Ghorveh–Dehgolan basin, a developed and mountainous sub-basin of the Sefidrood watershed with three alluvial aquifers in Northern Iran. The paradigm shift from deterministic hydrological structure to interval-based hydrologic structure improved the statistical metrics of the model responses, such as the streamflow KGE metric of the calibration and validation datasets, which improved from (0.5, 0.18) to (0.57, 0.49), respectively. Additionally, the proposed approach decreased the uncertainty level tied to the simulated streamflow and groundwater levels. Based on the results, normalized uncertainty efficiency (NUE) values of the simulated streamflow and groundwater level values increased as well.

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Data availability

The dataset used in the current research is available online at http://doi.org/10.5281/zenodo.7549689.

Abbreviations

EO:

Earth observation (mm)

ET:

Evapotranspiration (mm)

SEB:

Surface energy balance

PM:

Penman–Monteith

MT:

Mass transfer

SEBS:

Surface energy balance system

METRIC:

Mapping Evapotranspiration at High Resolution with Internalized Calibration

SEBAL:

Surface Energy Balance Algorithm for Land

LAI:

Leaf area index

NDVI:

Normalized difference vegetation index

IRIMO:

Islamic Republic of Iran Meteorological Organization

MIDW:

Modified inverse distance weighting

MODIS:

Moderate-resolution imaging spectroradiometer

MOST:

Monin–Obukhov similarity theory

GLUE:

Generalized likelihood uncertainty estimation

GT:

Groundwater threshold (m)

IBWB:

Interval-based water balance

NSE:

Nash–Sutcliff

KGE:

Gupta efficiency

MSE:

Mean square error

R 2 :

Coefficient of determination

SCE-UA:

Shuffled Complex Evolution

ETins :

Instantaneous ET (mm/h)

R n :

Net radiation flux (W/m2)

G :

Soil heat flux (W/m2)

H :

Sensible heat flux (W/m2)

Λ :

Latent heat of vaporization (J/(kg K))

\(R_{s \downarrow }\) :

Incoming shortwave radiation (W/m2)

\(R_{l \downarrow }\) :

Incoming longwave radiation (W/m2)

\(R_{l \uparrow }\) :

Outgoing longwave radiation (W·m−2)

\(G_{{{\text{sc}}}}\) :

Solar constant (1367 W/m2)

\(\theta\) :

Solar incidence angle (rad)

\(d_{{\text{r}}}\) :

Inverse squared relative earth-sun distance (1/m2)

\({\mathcal{T}}_{{{\text{sw}}}}\) :

Atmospheric transmissivity (dimensionless)

\(\varepsilon_{{\text{a}}}\) :

Atmospheric thermal emissivity (dimensionless)

\(\sigma\) :

Stefan–Boltzmann constant (5.67 × 10–8 W/(m2K4))

T a :

Air temperature (K)

T s :

Land surface temperature (K)

\(\varepsilon_{{\text{s}}}\) :

Surface thermal emissivity (dimensionless)

Z :

Elevation (M)

\(e_{0}\) :

Water vapor pressure (kPa)

H :

Sensible heat flux

\(\rho_{a}\) :

Air density at constant pressure (kg·m−3)

\(C_{{\text{p}}}\) :

Specific heat capacity of air at constant pressure (J·kg−1·K−1)

\(r_{{\text{a}}}\) :

Aerodynamic resistance to heat transport (s·m−1)

\({\text{d}}T\) :

Temperature difference between two specific heights (K)

\(C_{{\text{H}}}\) :

Heat exchange coefficient (dimensionless)

U :

Wind speed at the reference height (m·s−1)

\(ET_{r} F\) :

Ratio of the instantaneous actual ET to the instantaneous ETr (dimensionless)

ETins :

ET obtained from standardized Penman–Monteith equation (mm/h)

\({\text{ET}}_{{{\text{month}}}}\) :

Monthly actual ET (mm/month)

\({\text{ET}}_{{r,{\text{month}}}}\) :

Reference ET at monthly temporal resolution (mm/month)

X :

Simulated and observed variables

\(\overline{X}\) :

Mean

R :

Correlation coefficient

σ :

Ratio of the mean simulated values to the mean observed ones

β :

The ratio of the standard deviation of the simulations to that of observations

\(R_{0}\) :

Maximum theoretical correlation

Sim:

Simulated values

Obs:

Observed values

ARIL:

Average Relative Interval Length. The amplitude of the uncertainty bands versus the observed values

\(P_{{{\text{level}}}}\) :

Describes how much of the observed data is grouped by the computed uncertain bands

UpLi:

Upper values of the uncertainty bands of the confidence intervals

LoLi:

Lower values of the uncertainty bands of the confidence intervals

NUE:

Normalized Uncertainty Efficiency

\(\omega\) :

Scale coefficient

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Authors and Affiliations

  1. School of Civil Engineering, College of Engineering, University of Tehran, Tehran, Iran

    Maryam Khodadadi, Tarokh Maleki Roozbahani, Mercedeh Taheri, Fatemeh Ganji & Mohsen Nasseri

  2. Department of Civil Engineering, University of Ottawa, Ottawa, ON, K1N6N5, Canada

    Mercedeh Taheri

Authors
  1. Maryam Khodadadi
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  2. Tarokh Maleki Roozbahani
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  3. Mercedeh Taheri
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  4. Fatemeh Ganji
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  5. Mohsen Nasseri
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Corresponding author

Correspondence to Mohsen Nasseri.

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All authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript.

Additional information

Edited by Dr. Michael Nones (CO-EDITOR-IN-CHIEF).

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Khodadadi, M., Maleki Roozbahani, T., Taheri, M. et al. The effect of embedding actual evapotranspiration uncertainty in water balance model: coupling of interval-based hydrologic model and METRIC method. Acta Geophys. 72, 1985–2007 (2024). https://doi.org/10.1007/s11600-023-01112-6

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  • DOI: https://doi.org/10.1007/s11600-023-01112-6

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