Real-time monitoring of water requirement in protected farms by using polynomial neural networks and image processing

Abstract

The monitoring of water requirement in irrigation areas is mostly performed by on-farm methods like utilization of soil probes, tensiometers, or neutron probes. The probes are placed into the soil collected from different depths of the root zone of the crop. But such procedures are found to be time-consuming. As a result, non-portable capacitance-based probes were nowadays utilized for monitoring of soil moisture. However, the sensor-based non-portable system is expensive and out of reach of ordinary farmers. But an absence of on-time monitoring of soil moisture in the root zone of the soil often results in crop failure and incurs a substantial loss on the cultivators. In the present investigation, a real-time inexpensive water monitoring system was proposed to monitor soil moisture in the root zone of a crop such that both time and expenditure can be reduced. The present study is an attempt to develop a real-time monitoring process for crop water requirement (CWR) in protected farm irrigation systems as a function of the significant parameters such as soil porosity (SP), water availability, crop biomass equivalent (CBE), frequency of nutrient application, frequency of irrigation, and CWR. A systematic literature review was performed to identify parameters for CWR, which were then selected by a relevant group of experts on the field. A two-step methodology was followed to develop a function that can automatically estimate water requirement in the root zone of the crop. In the first step, a new probability optimization technique (POT) was proposed for the identification of the priority value of the selected parameters to generate an ideal scenario. In the second step, the index, developed from the parameters and respective priorities selected in the first step, was predicted recurring to polynomial neural network models. The implementation of the nonlinear transfer function in the development of the neural network framework ensures generation of a platform-independent model, which can be embedded to monitor watering requirement for crops cultivated in a protected farm concept. The data of SP and CBE were retrieved from two separate indices (index of soil porosity and biomass index) calculated from images captured from the root and surface areas of the crops. Here, the POT method was used followed by the z score of priority function of the selected parameters estimated by polynomial networks and was fed for the calculation of the water requirement index (WRI). The normalized relative difference of the WRI of two consecutive days provides the information about the necessity of watering and accordingly, the crops in the system are irrigated. The results from the decision-making method indicated that the most significant parameter among the compared factors is CWR. The peak pixel value of each column of the image, for retrieving information from captured images and to identify soil porosity and biomass, was found to be the most contributing factor. The polynomial neural network (PNN) model trained with the information from POT method was found to be the best predictive variant among all the considered configuration of the model having a mean absolute accuracy of 99.08% during the testing phase of the PNN model. This real-time system, when implemented in a real-life scenario, can conserve both water and energy expended in running the watering networks of protected farms.

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Correspondence to Amaresh Sarkar.

Appendices

Appendix 1

Model neurons (N) of WRI predicted from the priority value of the six parameters by POT

N2 = − 0.0037091 + N508*0.00495644 − N508*N3*0.00301011 + N3*0.999539 + N3^2*0.00164896
N3 = − 0.0039168 + N461*0.00790544 + N461*N4*0.00186553 − N461^2*0.00323974 + N4*0.996757
N4 = − 0.000361218 + N137*0.167544 − N137*N5*2.64512 + N137^2*1.27105 + N5*0.832876 + N5^2*1.37394
N5 = 0.000107192 − N77*0.145892 − N77*N6*8.01513 + N77^2*4.05907 + N6*1.14576 + N6^2*3.9561
N6 = 8.48733e − 05 − N338*0.0240165 + N338*N7*0.230432 − N338^2*0.109388 + N7*1.02395 − N7^2*0.121027
N7 = 0.000438486 − N21*0.895279 − N21*N8*13.2617 + N21^2*6.86142 + N8*1.89476 + N8^2*6.40045
N8 = − 0.000435001 + N193*0.13457 + N193*N9*0.0771467 − N193^2*0.0772959 + N9*0.865943
N9 = 0.000108749 − N353*0.0215273 − N353*N10*0.770688 + N353^2*0.392258 + N10*1.02136 + N10^2*0.378469
N10 = − 0.000593288 + N65*0.417577 + N65*N11*63.6771 − N65^2*31.9716 + N11*0.583198 − N11^2*31.7058
N11 = 0.000680251 − N386*0.00883072 − N386*N12*0.180307 + N386^2*0.0928166 + N12*1.008 + N12^2*0.0876999
N12 = − 0.00027115 + N145*0.130827 + N145*N13*12.3217 − N145^2*6.19352 + N13*0.869432 − N13^2*6.12825
N13 = − 0.000752158 − N436*N14*0.0341339 + N436^2*0.0172391 + N14*1.00074 + N14^2*0.0166723
N14 = 0.00557981 − N494*0.0126478 − N494*N15*0.0106495 + N494^2*0.00941449 + N15*1.00548 + N15^2*0.0034839
N15 = − 0.0105196 + N472*0.0129413 − N472*N16*0.0180706 + N472^2*0.00507432 + N16*0.999841 + N16^2*0.00909668
N16 = − 0.0314905 + N536*0.0539354 + N536*N21*0.0150584 − N536^2*0.0235075 + N21*0.983852 − N21^2*0.00278746
N472 = − 0.00984 + N552*N573*0.6025
N494 = 0.764551 + BI*N552*0.199409 − BI^2*0.0320372 + N552^2*0.266527
N436 = − 0.00293989 + N560*N565*0.600008
N386 = 0.264407 − BI*0.0212425 + BI*N439*0.197976 + N439*0.595578 + N439^2*0.0902778
N439 = 0.0443094 + N552*N565*0.582957
N353 = 0.0120957 + N481*0.220049 + N481*N547*0.547528 − N481^2*0.0454973 − N547*0.188109 + N547^2*0.0733046
N547 = 0.00511224 + ISP*N569*0.164629 + N569*0.916385
N481 = − 0.0476773 + BI*0.12854 + BI*N558*0.134965 − BI^2*0.045682 + N558*0.930781
N193 = 0.0699362 + N286*1.22134 − N286*N428*0.220668 + N286^2*0.0208005 − N428*0.315333 + N428^2*0.230589
N428 = 0.251899 + N521*N524*0.507865
N524 = 0.494324 + N565*N568*0.420615
N21 = − 0.000126664 + N79*N25*0.158902 − N79^2*0.158955 + N25*1.00017
N25 = 0.00186519 − FI*N30*0.00329646 + FI^2*0.00571429 + N30*0.997298 + N30^2*0.00126368
N30 = 0.000350786 + N46*0.541845 − N46*N65*41.5701 + N46^2*20.7975 + N65*0.457635 + N65^2*20.7727
N46 = − 0.00175349 − ISP*0.0173879 + ISP*N79*0.00219865 + ISP^2*0.0157769 + N79*1.006 − N79^2*0.00238992
N338 = − 0.508748 − N469*0.08218 + N469*N561*0.557738 + N469^2*0.04166 + N561*0.7197 − N561^2*0.199047
N561 = 0.794239 − ISP*0.248056 + ISP*N572*0.316633 + ISP^2*0.00759002 + N572^2*0.263134
N469 = − 0.113206 + FNA*0.270402 + FNA^2*0.0535125 + N558*0.973131
N77 = 0.0111536 − N426*0.0689968 − N426*N91*0.125064 + N426^2*0.088076 + N91*1.05385 + N91^2*0.0419257
N91 = − 0.000358474 + N135*0.634337 + N152*0.365878
N152 = − 0.0598308 + N468*0.0614455 − N468*N273*0.150855 + N468^2*0.0402472 + N273*1.03078 + N273^2*0.0767423
N273 = − 0.0216226 + N496*N532*0.539258 + N496^2*0.0181688 + N532*0.111676 − N532^2*0.0178257
N532 = 0.763437 + FI*N569*0.187531 + N569^2*0.26636
N468 = 0.76759 + FNA*N551*0.195406 + N551^2*0.261482
N135 = 0.00421704 − N456*0.056665 − N456*N200*0.0845467 + N456^2*0.0446756 + N200*1.0683 + N200^2*0.0313136
N456 = 0.0482176 + N536*N572*0.581564
N426 = − 0.171017 + N520*0.489749 + N520*N527*0.511145 − N520^2*0.143684
N527 = 0.51093 + N566*N568*0.414632
N520 = 0.0376921 − N551*0.131702 + N551*N558*0.466055 + N558*0.795413 − N558^2*0.278007
N558 = 1.39289 + FI*0.240055 + FI*CWR*0.133805 + CWR*0.174474 + CWR^2*0.0921372
N137 = − 0.0028943 + N172*0.310891 − N172*N250*0.165166 + N172^2*0.164457 + N250*0.692038
N250 = 0.0412712 + N299*1.14758 − N299*N448*0.294427 + N299^2*0.123629 − N448*0.176873 + N448^2*0.173116
N448 = 0.380812 + N521*N533*0.46132
N533 = 0.225503 + N569*N570*0.517743
N570 = 1.45457 + WA*0.0851159 + WA*CWR*0.0752131 + CWR*0.304722
N521 = 0.561037 + N552*N564*0.396441
N299 = − 0.0380339 + N486*N542*0.542782 + N486^2*0.0198416 + N542*0.114457 − N542^2*0.0187811
N542 = 0.730136 + FI*N572*0.196011 + N572^2*0.275922
N572 = 1.467 + WA*0.0978413 + WA*BI*0.0568265 + BI*0.275975
N486 = 0.762829 + ISP*N536*0.16509 + N536^2*0.275064
N172 = 0.366485 − N528*0.521139 + N528*N286*0.0360894 + N528^2*0.153862 + N286*1.05209 − N286^2*0.0413008
N286 = 0.737386 − N571*0.788406 + N571*N437*0.524843 + N571^2*0.250905 + N437^2*0.0294622
N437 = 0.935933 − N536*1.1027 + N536*N568*0.590174 + N536^2*0.331202
N528 = 0.502214 + N567*N568*0.417799
N461 = 0.0241524 + N536*N573*0.590248
N573 = 1.48446 + ISP*0.235073 + ISP*WA*0.0854765 + WA*0.0990649
N536 = 1.32542 + FNA*0.335478 + CWR*0.33977
N508 = − 0.0331815 + BI*N567*0.192263 + N567*0.922893
N35 = 0.000334684 + N47*0.682962 − N47*N65*37.1172 + N47^2*18.5291 + N65*0.316543 + N65^2*18.5883
N65 = − 0.0239747 + N522*0.0250211 − N522*N85*0.0216281 + N85*1.00903 + N85^2*0.00986259
N85 = 0.00047052 + N145*0.776536 − N145*N166*4.75125 + N145^2*2.32489 + N166*0.222677 + N166^2*2.42661
N166 = − 0.0135148 + N275*0.979491 + N275*N427*0.0363146 − N275^2*0.0352749 + N427*0.0269437
N427 = 0.25083 + N522*N525*0.508256
N525 = 0.508999 + N565*N567*0.415314
N565 = 1.37062 + ISP*0.252011 + ISP*CWR*0.0515355 + CWR*0.323582
N275 = 0.0727772 + N496*N531*0.536594 + N496^2*0.0192729 + N531^2*0.0165073
N531 = 0.772625 + FNA*N571*0.197838 + N571^2*0.259637
N571 = 1.42857 + WA*0.149311 + FI*0.324743
N496 = 0.732202 + CWR*N568*0.167415 + CWR^2*0.070277 + N568^2*0.275896
N145 = 0.0169817 + N225*1.05986 − N225*N411*0.814908 + N225^2*0.365958 − N411*0.0862089 + N411^2*0.458093
N225 = 0.10314 − N510*0.0802385 + N510*N530*0.556123 + N510^2*0.0346692 + N530*0.0313163
N530 = 0.772188 + CWR*N569*0.200386 + N569^2*0.26038
N569 = 1.43269 + WA*0.132135 + FNA*0.313848 + FNA^2*0.026408
N510 = 0.73819 + FI*N568*0.194713 + N568^2*0.272856
N522 = 0.543648 + N560*N564*0.402739
N564 = 1.34279 + BI*0.342497 − BI^2*0.0325357 + FI*0.321287
N560 = 1.35867 + BI*0.274471 + BI*FNA*0.045937 + FNA*0.310689
N47 = 0.0274057 − N411*0.214954 − N411*N79*0.652305 + N411^2*0.393446 + N79*1.18125 + N79^2*0.268809
N79 = − 0.00303813 − CWR*0.013519 − CWR*N131*0.0077796 + CWR^2*0.0315479 + N131*1.00664 − N131^2*0.00176458
N131 = 0.0281574 − N567*0.0477562 + N567^2*0.0280885 + N200*0.983737
N200 = 0.14204 − N476*0.0712366 + N476*N563*0.58679 + N476^2*0.0248736 − N563*0.077578 + N563^2*0.0250458
N563 = 0.799049 + WA*N568*0.078715 + N568^2*0.287238
N568 = 1.36661 + ISP*0.302204 − ISP^2*0.0164261 + BI*0.317799
N476 = 0.76861 + CWR*N552*0.197059 + N552^2*0.262015
N552 = 1.34021 + FNA*0.332099 + FI*0.308174
N411 = 0.12873 + N438*0.15056 + N438*N554*0.423026 + N554*0.199339 − N554^2*0.0804334
N554 = − 0.0960636 + WA*0.152139 + N567*1.01213
N567 = 1.38017 + ISP*0.275495 + ISP*FI*0.0706918 − ISP^2*0.0333733 + FI*0.288203
N438 = 0.0154782 + N551*N566*0.359349 + N551^2*0.116819 + N566^2*0.1158
N566 = 1.37524 + ISP*0.243095 + ISP*FNA*0.0578374 + FNA*0.311751
N551 = 1.35497 + BI*0.347224 − BI^2*0.038534 + CWR*0.215886 + CWR^2*0.13079

Appendix 2

Model neurons (N) of WRI predicted from the priority value of the six parameters by MAUT

N2 = 0.010134 − N531*0.0177318 − N531*N3*0.00638773 + N531^2*0.00842899 + N3*1.00563 + N3^2*0.00153705
N3 = − 6.40471e − 05 + N271*N4*1.1221 − N271^2*0.561519 + N4*1.00012 − N4^2*0.560606
N4 = − 0.00048184 + N278*0.0325854 − N278*N5*1.13395 + N278^2*0.556869 + N5*0.967964 + N5^2*0.576894
N5 = − 0.00162377 + N417*0.0212435 + N417*N6*0.048693 − N417^2*0.0302319 + N6*0.980634 − N6^2*0.0189752
N6 = − 0.000340656 − N309*N7*0.90381 + N309^2*0.453298 + N7*1.00039 + N7^2*0.450371
N7 = − 0.00664834 + N465*0.0160335 + N465*N8*0.0105284 − N465^2*0.0101837 + N8*0.992161 − N8^2*0.00282932
N8 = 2.94945e − 05 − N149*0.117832 + N149^2*0.0284731 + N9*1.1178 − N9^2*0.0284652
N9 = − 0.000205705 + N76*0.0772266 − N76*N10*2.3276 + N76^2*1.15554 + N10*0.922961 + N10^2*1.17201
N10 = − 0.00792981 + N497*0.00578878 − N497*N11*0.0161286 + N497^2*0.00665682 + N11*1.00322 + N11^2*0.00689732
N497 = − 3.36814 + N534*1.26735 + N534*N561*0.907978 − N534^2*0.564645 + N561*3.11533 − N561^2*1.15144
N76 = 0.00419861 + BI*0.0300573 − BI*N103*0.024564 − BI^2*0.00154214 + N103*0.983904 + N103^2*0.0103151
N103 = 0.323389 − N484*0.633714 − N484*N153*0.259314 + N484^2*0.321433 + N153*1.24053 + N153^2*0.0559823
N153 = 0.0489021 + N234*1.2247 − N234*N413*1.99698 + N234^2*0.899733 − N413*0.292307 + N413^2*1.11894
N413 = 0.752731 + N453*0.213862 + N453*N542*0.541658 − N453^2*0.0596105 − N542*0.856698 + N542^2*0.233882
N542 = − 0.0336089 + N557*N568*0.615665
N453 = 0.061861 + N480*N533*0.471 + N533*0.601614 − N533^2*0.253283
N234 = 1.15089 − N458*0.194501 + N458*N554*0.612767 + N458^2*0.0588612 − N554*1.26238 + N554^2*0.38955
N554 = 0.706432 + BI*0.248074 + N565^2*0.300705
N465 = − 0.0278212 + N519*N541*0.489344 + N541*0.482593 − N541^2*0.166962
N417 = − 1.17522 + N472*0.276392 + N472*N551*0.532995 − N472^2*0.0497522 + N551*1.16075 − N551^2*0.317176
N551 = − 2.51873 + N561*2.76426 − N561^2*0.587481 + N566*0.732529
N472 = 1.82096 − N539*2.08511 + N539*N556*0.561467 + N539^2*0.633307
N278 = 0.341797 − N500*0.468034 + N500*N530*0.621081 + N500^2*0.13927
N500 = − 0.0219936 + FNA*N541*0.174992 + N541*0.925741
N271 = 0.0524544 + N303*N338*95.0424 − N303^2*46.9897 + N338*0.940993 − N338^2*48.0356
N338 = 0.807218 + N470*N549*0.613098 − N549*1.02544 + N549^2*0.313626
N549 = − 0.140385 + ISP*0.310689 − ISP*N552*0.0759528 − ISP^2*0.0667124 + N552*1.04228
N303 = 0.596461 + N470*N550*0.614324 − N550*0.775477 + N550^2*0.238704
N550 = − 0.248899 + FI*0.354423 + N568*1.04177
N470 = 0.0349349 − FNA*0.0812779 + FNA*N519*0.240573 − FNA^2*0.0276961 + N519*0.888716
N11 = 0.000809303 − N26*0.820682 + N26*N12*0.476779 + N12*1.81971 − N12^2*0.47649
N12 = 0.000280056 + N113*0.379364 − N113*N13*2.78022 + N113^2*1.28635 + N13*0.62025 + N13^2*1.49398
N13 = 0.000510525 − N53*0.328795 + N53*N14*18.4806 − N53^2*9.17358 + N14*1.32811 − N14^2*9.30675
N14 = 0.00219791 − N455*0.0188856 − N455*N15*0.0611826 + N455^2*0.0361027 + N15*1.0162 + N15^2*0.0257719
N15 = 0.00141856 + N147*0.278513 − N147*N16*0.130344 + N16*0.719828 + N16^2*0.130819
N16 = 0.0064392 − N416*0.0382656 − N416*N17*0.239932 + N416^2*0.132477 + N17*1.03019 + N17^2*0.109837
N17 = 0.000319305 − N274*0.0634488 + N19*1.06326
N19 = 0.0553525 − N463*0.125622 − N463*N21*0.0654624 + N463^2*0.0697848 + N21*1.05929 + N21^2*0.0152742
N21 = 0.150601 − N531*0.22485 − N531*N25*0.0257296 + N531^2*0.0799868 + N25*1.04347
N25 = − 0.000185643 + N32*0.558015 + N47*0.442097
N47 = 0.00693562 − N430*0.0597018 − N430*N58*0.429731 + N430^2*0.238847 + N58*1.04799 + N58^2*0.194915
N58 = − 0.00268542 + N87*1.37106 + N87*N111*9.0184 − N87^2*4.74194 − N111*0.368171 − N111^2*4.27712
N111 = 0.00432513 − N359*0.448674 + N165*1.44606
N165 = 0.0166606 + N272*0.365521 + N272*N309*4.00338 − N272^2*1.94083 + N309*0.61239 − N309^2*2.05516
N309 = 1.39586 − N556*1.56744 + N556*N449*0.647717 + N556^2*0.457967 − N449*0.156712 + N449^2*0.0276558
N449 = − 1.16338 + N519*N561*0.606739 + N561*1.37527 − N561^2*0.408158
N359 = 0.32535 + N493*N526*0.608591 − N526*0.417776 + N526^2*0.127649
N526 = 0.675498 + FI*0.251464 + FI*N566*0.0596372 + N566^2*0.291986
N493 = 0.749607 + FNA*N539*0.231084 − FNA^2*0.0933153 + N539^2*0.270522
N87 = 0.151797 − N522*0.38086 − N522*N145*0.285053 + N522^2*0.247105 + N145*1.21379 + N145^2*0.0825366
N145 = 0.0707362 − N507*0.165757 − N507*N207*0.17198 + N507^2*0.151752 + N207*1.05301 + N207^2*0.0616925
N522 = − 0.00734815 + N552*N567*0.606077
N430 = − 0.266898 + N533*0.682927 + N533*N534*0.653069 − N533^2*0.22082 − N534*0.422982 + N534^2*0.112268
N32 = 0.0301788 + FI*0.0361389 − FI*N49*0.0417079 + FI^2*0.0342868 + N49*0.950485 + N49^2*0.0208526
N49 = − 0.00391871 − N490*0.072959 − N490*N80*0.301573 + N490^2*0.167148 + N80*1.08495 + N80^2*0.127859
N531 = 0.0214949 + CWR*N568*0.254534 + N568*0.861972
N463 = 0.604456 + N480*N541*0.27355 + N480^2*0.107764
N274 = 0.647776 − N534*0.405982 + N534*N491*0.634479 + N534^2*0.11198 − N491*0.409277 + N491^2*0.111434
N491 = 2.77903 + N541*N565*0.743725 − N541^2*0.063237 − N565*3.43307 + N565^2*0.98028
N416 = − 0.81295 + N452*0.850331 + N452*N540*0.363324 − N452^2*0.163203 + N540*0.417156 − N540^2*0.0638993
N540 = 0.0197661 + N561*N567*0.596179
N561 = 1.46858 + WA*FNA*0.0973923 + WA^2*0.138253 + FNA*0.240248
N452 = 0.794213 + N480*N505*0.761457 − N480^2*0.172702 − N505*0.187376 − N505^2*0.162599
N147 = − 0.00749375 + WA*0.0722731 + WA*N245*0.0199528 − WA^2*0.109779 + N245*0.994582
N245 = 0.329849 − N519*0.430333 + N519*N507*0.61346 + N519^2*0.12866
N507 = − 2.85607 + N533*N568*0.61671 + N568*3.31214 − N568^2*0.970672
N568 = 1.54295 + ISP*0.105423 + WA*0.0399154 + WA^2*0.129349
N455 = − 0.00862691 + N534*N556*0.60654
N534 = 1.38662 + WA*0.0796466 + WA*CWR*0.0435832 + WA^2*0.073648 + CWR*0.40125
N53 = 0.0448397 − N517*0.200958 − N517*N81*0.263814 + N517^2*0.188805 + N81*1.15227 + N81^2*0.0872933
N81 = 0.0097063 − FNA*0.0568162 − FNA*N198*0.0221634 + FNA^2*0.100503 + N198*0.99475 + N198^2*0.00461048
N198 = 0.00266957 + N230*1.62786 − N332*0.629466
N332 = 0.617154 − N503*0.204871 + N503*N524*0.64221 + N503^2*0.0479937 − N524*0.583773 + N524^2*0.162964
N503 = 0.0381785 + CWR*N566*0.251975 + N566*0.853119
N517 = 0.450662 + N541*N557*0.758162 − N541^2*0.142202 − N557^2*0.176459
N541 = 1.35645 + BI*0.251277 + FI*0.346121 + FI^2*0.00337906
N113 = 0.02973 − N415*0.280906 − N415*N157*0.0864398 + N415^2*0.0932358 + N157*1.25156
N157 = 0.0314636 + ISP*0.110236 + ISP*N272*0.00439145 − ISP^2*0.112535 + N272*0.938861 + N272^2*0.0173887
N272 = 0.032 + N498*N530*0.617914 − N530*0.0920599 + N530^2*0.0293031
N530 = 0.783929 + WA*N539*0.0732531 + WA^2*0.0480505 + N539^2*0.288928
N539 = 1.41113 + ISP^2*0.112254 + CWR*0.425001
N498 = − 0.00670958 + BI*N533*0.151556 + N533*0.929132
N533 = 1.35404 + FNA*0.246137 + FNA*FI*0.0840072 + FI*0.313388
N415 = 0.0703519 + N485*0.113734 + N485*N521*0.480758 + N521^2*0.027791
N521 = 0.722606 + N556*N566*0.324115 + N556^2*0.136907 − N566*0.845148 + N566^2*0.387565
N485 = 0.567556 + N505*0.14996 + N505*N519*0.30466
N26 = 0.0118997 − N490*0.0737874 − N490*N33*0.166168 + N490^2*0.101821 + N33*1.06395 + N33^2*0.0655159
N33 = 0.0231602 + FI*0.0253713 − FI*N48*0.0349155 + FI^2*0.0340755 + N48*0.962213 + N48^2*0.016264
N48 = 0.00150098 + N80*0.998155 − N80*N82*9.6047 + N80^2*4.66393 + N82^2*4.94125
N82 = 0.0265586 + CWR*0.032695 − CWR*N127*0.0600444 + CWR^2*0.0645846 + N127*0.951378 + N127^2*0.024426
N127 = 0.00149185 + N207*0.990099 − N207*N406*0.62617 + N207^2*0.279482 + N406^2*0.351743
N406 = 0.473346 − N484*0.0644604 + N484*N548*0.654684 − N548*0.566512 + N548^2*0.156409
N548 = − 0.0412003 + WA^2*0.166588 + N556*0.992259
N556 = 1.39502 + ISP*0.21217 − ISP*FI*0.0238235 − ISP^2*0.0717801 + FI*0.36678
N484 = 0.786224 + N505*N557*0.50361 − N557*0.311041
N557 = 1.39308 + BI*0.250803 + FNA*0.280123
N505 = 1.32339 + FNA*0.29649 + FNA*CWR*0.138672 − FNA^2*0.0753913 + CWR*0.359755
N207 = 0.494021 − N458*0.245804 + N458*N553*0.633514 + N458^2*0.0640245 − N553*0.412067 + N553^2*0.121856
N553 = 0.751352 + FNA*N567*0.169638 + N567^2*0.277991
N458 = − 0.00325216 + WA*N480*0.107268 + N480*0.949252
N480 = 1.29357 + FI*0.302317 + FI*CWR*0.106423 + CWR*0.374647
N80 = − 0.0049329 + WA*0.0559295 + WA*N149*0.0105945 − WA^2*0.0677293 + N149*0.994343
N149 = − 0.00105471 − FNA*0.060467 − FNA*N230*0.019219 + FNA^2*0.0989634 + N230*1.0089
N230 = 0.770646 − N502*0.41054 + N502*N524*0.633049 + N502^2*0.11449 − N524*0.567106 + N524^2*0.163263
N524 = 0.697538 + FI*N565*0.217353 + N565^2*0.282221
N502 = − 0.0213614 + WA*N519*0.0629592 + WA^2*0.0709704 + N519*0.968054
N519 = 1.34347 + BI*0.217212 + BI*CWR*0.0570127 + CWR*0.391923
N490 = 0.33899 + N537*N555*0.521238 − N555*0.0692787
N555 = 0.229304 + N565*N567*0.519697
N567 = 1.46779 + ISP*0.133019 − ISP*BI*0.0451228 + BI*0.271361
N565 = 1.44172 + ISP*0.117649 + FNA*0.37689 − FNA^2*0.0959987
N537 = − 0.938183 + N552*0.856367 + N566*0.709727
N566 = 1.47709 + WA^2*0.172986 + BI*0.251029
N552 = 1.42365 + WA^2*0.173678 + FI*0.349751

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Sarkar, A., Majumder, M. Real-time monitoring of water requirement in protected farms by using polynomial neural networks and image processing. Environ Dev Sustain 21, 1451–1483 (2019). https://doi.org/10.1007/s10668-018-0097-z

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Keywords

  • Automatic irrigation system
  • Crop yield optimization
  • High-tech irrigation system
  • Multi-story protected farms