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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Appendices
Appendix 1
1.1 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
2.1 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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DOI: https://doi.org/10.1007/s10668-018-0097-z