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Improved prediction of daily pan evaporation using Deep-LSTM model

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Abstract

Precise measurement or estimation of evaporation losses is extremely important for the development of water resource management strategies and its effective implementation, particularly in drought-prone areas for increasing agricultural productivity. Evaporation can either be measured directly using evaporimeters, or it can be estimated by means of empirical models with the help of climatic factors influencing evaporation process. In general, variations in climatic factors such as temperature, humidity, wind speed, sunshine and solar radiation influence and control the evaporation process to a great extent. Due to the highly nonlinear nature of evaporation phenomenon, it is invariably very difficult to model the evaporation process through climatic factors especially in diverse agro-climatic situations. The present investigation is carried out to examine the potential of deep neural network architecture with long short-term memory cell (Deep-LSTM) to estimate daily pan evaporation with minimum input features. Depending upon the availability of climatic data Deep-LSTM models with different input combinations are proposed to model daily evaporation losses in three agro-climatic zones of Chhattisgarh state in east-central India. The performance of the proposed Deep-LSTM models are compared with commonly used multilayer artificial neural network and empirical methods (Hargreaves and Blaney–Criddle). The results of the investigations in terms of various performance evaluation criteria reveal that the proposed Deep-LSTM structure is able to successfully model the daily evaporation losses with improved accuracy as compared to other models considered in this study.

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Abbreviations

EP:

Pan evaporation

Deep-LSTM:

Deep neural network architecture with long short-term memory cell

ACZs:

Agro-climatic zones

MLANN:

Multilayer artificial neural network

T max :

Maximum temperature

T min :

Minimum temperature

RHI :

Relative humidity morning

RHII :

Relative humidity afternoon

WS:

Wind speed

BSS:

Bright sunshine hours

SD:

Standard deviation

ET0 :

Reference evapotranspiration

CV:

Coefficient of variation

R:

Correlation coefficient

RMSE:

Root-mean-square error

R2 :

Coefficient of determination

EF:

Efficiency factor

AIC:

Akaike information criterion

g t :

Input node at time t

tanh :

Hyperbolic tangent function

x t :

Input to the memory cell at time t

W gx :

Weight matrix between input layer of the network and input node of the memory cell

h t−1 :

Hidden state input at time t − 1

W gh :

Weight matrix between hidden states at different time steps

\({\text{bias}}_{{{\text{input}}\;{\text{node}}}}\) :

Bias to the input node

i t :

Input gate at time t

σ :

Sigmoidal activation function

s t :

Internal state at time t

s t−1 :

Internal state at time t−1

\({\text{bias}}_{{{\text{input}}\;{\text{gate}}}}\) :

Bias to the input gate

f t :

Forget state at time t

\(\odot\) :

Point-wise linear operator

W fx :

Weight matrix between forget gates and input layer

W fh :

Weight matrix between forget gates and hidden states

h t :

Final output of memory cell at time t

\({\text{bias}}_{\text{forget}}\) :

Bias for the forget gate

O t :

Output gate at time t

W ox :

Weight matrix between output gates and input layers

W oh :

Weight matrix between output gates and hidden states

\({\text{bias}}_{{{\text{output}}\;{\text{gates}}}}\) :

Bias for the output gate

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Authors and Affiliations

  1. Department of Computer Science and Information Technology, Guru Ghasidas Vishwavidyalaya, Central University, Bilaspur, 495009, India

    Babita Majhi & Diwakar Naidu

  2. BRSM College of Agricultural Engineering and Technology and Research Station, Indira Gandhi Krishi Vishwavidyalaya, Mungeli, India

    Diwakar Naidu

  3. Department of CSE, ITER, Siksha ‘O’ Anusandhan University, Bhubaneswar, India

    Ambika Prasad Mishra

  4. School of Computer Engineering, KIIT University, Bhubaneswar, India

    Suresh Chandra Satapathy

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  1. Babita Majhi
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Majhi, B., Naidu, D., Mishra, A.P. et al. Improved prediction of daily pan evaporation using Deep-LSTM model. Neural Comput & Applic 32, 7823–7838 (2020). https://doi.org/10.1007/s00521-019-04127-7

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