import numpy as np
    
def vmf3(mjd = None,lat = None,lon = None,zd = None,ah = None,aw = None): 
# =============================================================================

# (c) Department of Geodesy and Geoinformation, Vienna University of
# Technology, 2016
    
# This subroutine determines the VMF3 hydrostatic and wet mapping factors.
# The a coefficients have to be inserted from discrete data, while the b
# and c coefficients are of empirical nature containing a geographical
# and temporal dependence, represented in spherical harmonics. The
# spherical harmonics coefficients are developed to degree and order 12 and
# are based on a 5°x5° grid containing ray-tracing data from 2001-2010.
# All input quantities have to be scalars!
    
#        INPUT:
#        o ah: hydrostatic mf coefficient a (http://vmf.geo.tuwien.ac.at/trop_products/)
#        o aw: wet mf coefficient a (http://vmf.geo.tuwien.ac.at/trop_products/)
#        o mjd: modified julian date
#        o lat: latitude (radians)
#        o lon: longitude (radians)
#        o zd: zenith distance (radians)
    
#        OUTPUT:
#        o mfh: hydrostatic mapping factor
#        o mfw: wet mapping factor   
#--------------------------------------------------------------------------
  
# m-file created by Daniel Landskron
    
#--------------------------------------------------------------------------
# History:
    
# 2016-03-14: m-file created
# File Converted to python script by Zohreh Adavi zohreh.adavi@tuwien.ac.at, 2023-02-17
# =============================================================================
    
    # convert mjd to doy
    
    hour = int(np.floor((mjd - int(np.floor(mjd))) * 24))
    
    minu = int(np.floor((((mjd - int(np.floor(mjd))) * 24) - hour) * 60))
    
    sec = (((((mjd - int(np.floor(mjd))) * 24) - hour) * 60) - minu) * 60
    
    # change secs, min hour whose sec==60
    if int(sec)==60:
       minu = minu+ 1
       sec = 0
    if int(minu)==60:
       hour = hour + 1
       minu = 0
    # calc jd (yet wrong for hour==24)
    jd = mjd + 2400000.5
    # if hr==24, correct jd and set hour==0
    if int(hour)==24:
       jd = jd + 1
       hour = 0
    # integer julian date
    jd_int = int(np.floor(jd + 0.5))
    aa = jd_int + 32044
    bb = int(np.floor((4 * aa + 3) / 146097))
    cc = aa - int(np.floor((bb * 146097) / 4))
    dd = int(np.floor((4 * cc + 3) / 1461))
    ee = cc - int(np.floor((1461 * dd) / 4))
    mm = int(np.floor((5 * ee + 2) / 153))
    day = ee - int(np.floor((153 * mm + 2) / 5)) + 1
    month = mm + 3 - 12 * int(np.floor(mm / 10))
    year = bb * 100 + dd - 4800 + int(np.floor(mm / 10))
    # first check if the specified year is leap year or not (logical output)
    leapYear = (np.logical_or((np.mod(year,4) == np.logical_and(0,np.mod(year,100)) != 0),np.mod(year,400)) == 0)
    days = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]
    doy = sum(days[:month-1]) + day
    if leapYear == 1 and month > 2:
        doy = doy + 1
    
    doy = doy + mjd - int(np.floor(mjd))
    
    # determine the VMF3 coefficients
    
    # Legendre functions for bh, bw, ch and cw
    anm_bh = np.array([[0.00271285863109945,- 1.39197786008938e-06,1.34955672002719e-06,2.71686279717968e-07,1.56659301773925e-06],[9.80476624811974e-06,- 5.83922611260673e-05,- 2.07307023860417e-05,1.14628726961148e-06,4.93610283608719e-06],[- 1.03443106534268e-05,- 2.05536138785961e-06,2.09692641914244e-06,- 1.55491034130965e-08,- 1.89706404675801e-07],[- 3.00353961749658e-05,2.37284447073503e-05,2.02236885378918e-05,1.69276006349609e-06,8.72156681243892e-07],[- 7.99121077044035e-07,- 5.39048313389504e-06,- 4.21234502039861e-06,- 2.70944149806894e-06,- 6.80894455531746e-07],[7.51439609883296e-07,3.8550970886552e-07,4.41508016098164e-08,- 2.07507808307757e-08,4.95354985050743e-08],[2.21790962160087e-05,- 5.56986238775212e-05,- 1.81287885563308e-05,- 4.41076013532589e-06,4.93573223917278e-06],[- 4.47639989737328e-06,- 2.6045289307212e-06,2.56376320011189e-06,4.41600992220479e-07,2.93437730332869e-07],[8.14992682244945e-07,2.03945571424434e-07,1.11832498659806e-08,3.25756664234497e-08,3.01029040414968e-08],[- 7.96927680907488e-08,- 3.66953150925865e-08,- 6.74742632186619e-09,- 1.30315731273651e-08,- 2.00748924306947e-09],[- 2.16138375166934e-05,1.67350317962556e-05,1.93768260076821e-05,1.9959512016185e-06,- 2.42463528222014e-06],[5.34360283708044e-07,- 3.641890220406e-06,- 2.99935375194279e-06,- 2.06880962903922e-06,- 9.40815692626002e-07],[6.80235884441822e-07,1.33023436079845e-07,- 1.80349593705226e-08,2.51276252565192e-08,- 1.43240592002794e-09],[- 7.13790897253802e-08,7.81998506267559e-09,1.13826909570178e-09,- 5.89629600214654e-09,- 4.20760865522804e-09],[- 5.80109372399116e-09,1.13702284491976e-09,7.29046067602764e-10,- 9.10468988754012e-10,- 2.58814364808642e-10],[1.75558618192965e-05,- 2.85579168876063e-05,- 1.47442190284602e-05,- 6.29300414335248e-06,- 5.1220453891346e-07],[- 1.9078855829131e-06,- 1.62144845155361e-06,7.57239241641566e-07,6.93365788711348e-07,6.88855644570695e-07],[2.27050351488552e-07,1.0392579127766e-07,- 3.31105076632079e-09,2.88065761026675e-08,- 8.00256848229136e-09],[- 2.77028851807614e-08,- 5.9625113220693e-09,2.95987495527251e-10,- 5.87644249625625e-09,- 3.28803981542337e-09],[- 1.89918479865558e-08,3.54083436578857e-09,8.10617835854935e-10,4.99207055948336e-10,- 1.52691648387663e-10],[1.04022499586096e-09,- 2.36437143845013e-10,- 2.25110813484842e-10,- 7.39850069252329e-11,7.95929405440911e-11],[- 3.1157942126763e-05,- 3.43576336877494e-06,5.81663608263384e-06,8.31534700351802e-07,4.02619520312154e-06],[6.00037066879001e-07,- 1.12538760056168e-07,- 3.8674533211559e-07,- 3.88218746020826e-07,- 6.83764967176388e-07],[- 9.79583981249316e-08,9.14964449851003e-08,4.77779838549237e-09,2.44283811750703e-09,- 6.26361079345158e-09],[- 2.37742207548109e-08,- 5.53336301671633e-09,- 3.73625445257115e-09,- 1.92304189572886e-09,- 7.18681390197449e-09],[- 6.58203463929583e-09,9.28456148541896e-10,2.47218904311077e-10,1.10664919110218e-10,- 4.20390976974043e-11],[9.45857603373426e-10,- 3.29683402990254e-11,- 8.15440375865127e-11,- 1.21615589356628e-12,- 9.70713008848085e-12],[1.61377382316176e-10,6.84326027598147e-12,- 4.66898885683671e-12,2.31211355085535e-12,2.39195112937346e-12],[2.99634365075821e-07,8.14391615472128e-06,6.70458490942443e-06,- 9.92542646762e-07,- 3.0407806499275e-06],[- 6.52697933801393e-07,2.87255329776428e-07,- 1.78227609772085e-08,2.65525429849935e-07,8.60650570551813e-08],[- 1.6272716401171e-07,1.09102479325892e-07,4.97827431850001e-09,7.86649963082937e-11,- 6.67193813407656e-09],[- 2.9637000098776e-09,1.20008401576557e-09,1.75885448022883e-09,- 1.74756709684384e-09,3.21963061454248e-09],[- 9.9110169777856e-10,7.54541713140752e-10,- 2.95880967800875e-10,1.81009160501278e-10,8.31547411640954e-11],[1.21268051949609e-10,- 5.93572774509587e-11,- 5.03295034994351e-11,3.05383430975252e-11,3.56280438509939e-11],[6.92012970333794e-11,- 9.02885345797597e-12,- 3.4415183274488e-12,2.03164894681921e-12,- 5.44852265137606e-12],[5.567312636728e-12,3.57272150106101e-12,2.25885622368678e-12,- 2.44508240047675e-13,- 6.83314378535235e-13],[3.96883487797254e-06,- 4.57100506169608e-06,- 3.30208117813256e-06,3.32599719134845e-06,4.26539325549339e-06],[1.10123151770973e-06,4.58046760144882e-07,1.86831972581926e-07,- 1.60092770735081e-07,- 5.58956114867062e-07],[- 3.40344900506653e-08,2.87649741373047e-08,- 1.83929753066251e-08,- 9.74179203885847e-09,- 2.42064137485043e-09],[- 6.49731596932566e-09,- 3.07048108404447e-09,- 2.84380614669848e-09,1.55123146524283e-09,4.53694984588346e-10],[5.45175793803325e-10,- 3.73287624700125e-10,- 1.16293122618336e-10,7.2584561860269e-11,- 4.34112440021627e-11],[1.89481447552805e-10,3.67431482211078e-12,- 1.72180065021194e-11,1.47046319023226e-11,1.31920481414062e-11],[2.10125915737167e-12,- 3.08420783495975e-12,- 4.8774871236302e-12,1.1636359990249e-14,1.26698255558605e-13],[- 8.07894928696254e-12,9.19344620512607e-13,3.26929173307443e-13,2.00438149416495e-13,- 9.57035765212079e-15],[1.38737151773284e-12,1.0934017837142e-13,5.15714202449053e-14,- 5.92156438588931e-14,- 3.29586752336143e-14],[6.38137197198254e-06,4.62426300749908e-06,4.42334454191034e-06,1.15374736092349e-06,- 2.61859702227253e-06],[- 2.25320619636149e-07,3.21907705479353e-07,- 3.34834530764823e-07,- 4.8213275360181e-07,- 3.22410936343355e-07],[3.48894515496995e-09,3.49951261408458e-08,- 6.01128959281142e-09,4.78213900943443e-09,1.46012816168576e-08],[- 9.66682871952083e-11,3.75806627535317e-09,2.38984004956705e-09,2.07545049877203e-09,1.58573595632766e-09],[1.06834370693917e-09,- 4.07975055112153e-10,- 2.37598937943957e-10,5.89327007480137e-11,1.18891820437634e-10],[5.22433722695807e-11,6.02011995016293e-12,- 7.80605402956048e-12,1.50873145627341e-11,- 1.40550093106311e-12],[2.13396242187279e-13,- 1.71939313965536e-12,- 3.57625378660975e-14,- 5.01675184988446e-14,- 1.07805487368797e-12],[- 1.24352330043311e-12,8.26105883301606e-13,4.63606970128517e-13,6.39517888984486e-14,- 7.35135439920086e-14],[- 5.39023859065631e-13,2.54188315588243e-14,1.30933833278664e-14,6.06153473304781e-15,- 4.24722717533726e-14],[3.12767756884813e-14,- 2.29517847871632e-15,2.53117304424948e-16,7.07504914138118e-16,- 1.20089065310688e-15],[2.08311178819214e-06,- 1.22179185044174e-06,- 2.98842190131044e-06,3.07310218974299e-06,2.27100346036619e-06],[- 3.94601643855452e-07,- 5.44014825116083e-07,- 6.16955333162507e-08,- 2.3195482158067e-07,1.1401081300531e-07],[6.11067575043044e-08,- 3.93240193194272e-08,- 1.62979132528933e-08,1.01339204652581e-08,1.97319601566071e-08],[2.57770508710055e-09,1.87799543582899e-09,1.95407654714372e-09,1.1527641928127e-09,2.2539700540212e-09],[7.16926338026236e-10,- 3.65857693313858e-10,- 1.54864067050915e-11,6.50770211276549e-11,- 7.85160007413546e-12],[4.90007693914221e-12,3.3164939653634e-12,4.8166487116564e-13,7.26080745617085e-12,2.30960953372164e-12],[9.75489202240545e-13,- 1.68967954531421e-13,7.3838339133411e-13,- 3.58435515913239e-13,- 3.0156471002745e-13],[- 3.79533601922805e-13,2.76681830946617e-13,1.21480375553803e-13,- 1.5772907764485e-14,- 8.876649778187e-14],[- 3.96462845480288e-14,2.9415569093461e-14,6.78413205760717e-15,- 4.12135802787361e-15,- 1.46373307795619e-14],[- 8.64941937408121e-15,- 1.91822620970386e-15,- 8.01725413560744e-16,5.02941051180784e-16,- 1.07572628474344e-15],[- 4.13816294742758e-15,- 7.4360201978588e-17,- 5.54248556346072e-17,- 4.83999456005158e-17,- 1.19622559730466e-16],[- 8.34852132750364e-07,- 7.45794677612056e-06,- 6.58132648865533e-06,- 1.38608110346732e-06,5.32326534882584e-07],[- 2.7551380241415e-07,3.64713745106279e-08,- 7.12385417940442e-08,- 7.86206067228882e-08,2.28048393207161e-08],[- 4.26696415431918e-08,- 4.65599668635087e-09,7.35037936327566e-09,1.17098354115804e-08,1.44594777658035e-08],[1.12407689274199e-09,7.62142529563709e-10,- 6.72563708415472e-10,- 1.18094592485992e-10,- 1.17043815733292e-09],[1.76612225246125e-10,- 1.01188552503192e-10,7.32546072616968e-11,1.7954282180161e-11,- 2.23264859965402e-11],[- 9.35960722512375e-12,1.90894283812231e-12,- 6.3479282452576e-13,3.98597963877826e-12,- 4.47591409078971e-12],[- 3.34623858556099e-12,4.56384903915853e-14,2.72561108521416e-13,- 3.57942733300468e-15,1.99794810657713e-13],[- 6.16775522568954e-14,8.25316968328823e-14,7.19845814260518e-14,- 2.92415710855106e-14,- 5.49570017444031e-15],[- 8.50728802453217e-15,8.38161600916267e-15,3.43651657459983e-15,- 8.1942943411591e-16,- 4.089057464611e-15],[4.39042894275548e-15,- 3.69440485320477e-16,1.22249256876779e-16,- 2.09359444520984e-16,- 3.34211740264257e-16],[- 5.36054548134225e-16,3.29794204041989e-17,2.13564354374585e-17,- 1.37838993720865e-18,- 1.29188342867753e-17],[- 3.26421841529845e-17,7.38235405234126e-18,2.4929165967621e-18,8.18252735459593e-19,1.7382495227923e-20],[4.67237509268208e-06,1.93611283787239e-06,9.39035455627622e-07,- 5.84565118072823e-07,- 1.76198705802101e-07],[- 3.33739157421993e-07,4.12139555299163e-07,1.58754695700856e-07,1.37448753329669e-07,1.04722936936873e-07],[6.64200603076386e-09,1.45412222625734e-08,1.8249879611803e-08,2.86633517581614e-09,1.060669845481e-09],[5.25549696746655e-09,- 1.33677183394083e-09,7.60804375937931e-11,- 1.07918624219037e-10,8.09178898247941e-10],[1.89318454110039e-10,9.23092164791765e-11,5.5143457313118e-11,3.8669639228924e-11,- 1.15208165047149e-11],[- 1.02252706006226e-12,- 7.25921015411136e-13,- 1.9811012688762e-12,- 2.18964868282672e-13,- 7.18834476685625e-13],[- 2.69770025318548e-12,- 2.17850340796321e-14,4.73040820865871e-13,1.57947421572149e-13,1.86925164972766e-13],[1.07831718354771e-13,2.26681841611017e-14,2.56046087047783e-14,- 1.14995851659554e-14,- 2.27056907624485e-14],[6.29825154734712e-15,8.04458225889001e-16,9.53173540411138e-16,1.16892301877735e-15,- 1.04324684545047e-15],[- 5.57345639727027e-16,- 2.93949227634932e-16,7.47621406284534e-18,- 5.36416885470756e-17,- 2.87213280230513e-16],[1.73219775047208e-16,2.05017387523061e-17,9.08873886345587e-18,- 2.86881547225742e-18,- 1.25303645304992e-17],[- 7.30829109684568e-18,2.03711261415353e-18,7.62162636124024e-19,- 7.54847922012517e-19,- 8.8510509819503e-19],[5.62039968280587e-18,- 1.38144206573507e-19,1.68028711767211e-20,1.81223858251981e-19,- 8.50245194985878e-20]])
    anm_bw = np.array([[0.00136127467401223,- 6.83476317823061e-07,- 1.37211986707674e-06,7.02561866200582e-07,- 2.16342338010651e-07],[- 9.53197486400299e-06,6.58703762338336e-06,2.42000663952044e-06,- 6.04283463108935e-07,2.0214442467699e-07],[- 6.76728911259359e-06,6.03830755085583e-07,- 8.72568628835897e-08,2.21750344140938e-06,1.0514603293102e-06],[- 3.21102832397338e-05,- 7.88685357568093e-06,- 2.55495673641049e-06,- 1.99601934456719e-06,- 4.62005252198027e-07],[- 7.8463926352325e-07,3.11624739733849e-06,9.02170019697389e-07,6.37066632506008e-07,- 9.44485038780872e-09],[2.19476873575507e-06,- 2.20580510638233e-07,6.94761415598378e-07,4.80770865279717e-07,- 1.34357837196401e-07],[2.18469215148328e-05,- 1.80674174262038e-06,- 1.5275428560506e-06,- 3.51212288219241e-07,2.73741237656351e-06],[2.85579058479116e-06,1.57201369332361e-07,- 2.80599072875081e-07,- 4.91267304946072e-07,- 2.11648188821805e-07],[2.8172925559477e-06,3.02487362536122e-07,- 1.64836481475431e-07,- 2.11607615408593e-07,- 6.47817762225366e-08],[1.31809947620223e-07,- 1.58289524114549e-07,- 7.05580919885505e-08,5.56781440550867e-08,1.23403290710365e-08],[- 1.29252282695869e-05,- 1.0724707203759e-05,- 3.31109519638196e-06,2.13776673779736e-06,- 1.49519398373391e-07],[1.81685152305722e-06,- 1.17362204417861e-06,- 3.1920527713637e-08,4.09166457255416e-07,1.53286667406152e-07],[1.63477723125362e-06,- 2.68584775517243e-08,4.94662064805191e-09,- 7.09027987928288e-08,4.44353430574937e-08],[- 2.13090618917978e-07,4.05836983493219e-08,2.94495876336549e-08,- 1.75005469063176e-08,- 3.03015988647002e-09],[- 2.16074435298006e-09,9.37631708987675e-09,- 2.05996036369828e-08,6.97068002894092e-09,- 8.90988987979604e-09],[1.38047798906967e-05,2.05528261553901e-05,1.59072148872708e-05,7.34088731264443e-07,1.2822671038358e-06],[7.08175753966264e-07,- 9.27988276636505e-07,1.60535820026081e-07,- 3.27296675122065e-07,- 2.20518321170684e-07],[1.90932483086199e-07,- 7.44215272759193e-08,1.81330673333187e-08,4.37149649043616e-08,4.18884335594172e-08],[- 5.37009063880924e-08,2.22870057779431e-08,1.73740123037651e-08,- 4.45137302235032e-09,9.44721910524571e-09],[- 6.83406949047909e-08,- 1.95046676795923e-10,2.57535903049686e-09,4.8264316408302e-09,3.37657333705158e-09],[3.96128688448981e-09,- 6.63809403270686e-10,2.44781464212534e-10,5.92280853590699e-11,- 4.78502591970721e-10],[1.75859399041414e-05,- 2.81238050668481e-06,- 2.43670534594848e-06,3.58244562699714e-06,- 1.76547446732691e-06],[- 1.06451311473304e-07,1.54336689617184e-06,- 2.00690000442673e-07,1.3879004791188e-09,- 1.62490619890017e-07],[- 2.72757421686155e-07,1.71139266205398e-07,- 2.55080309401917e-08,- 8.40793079489831e-09,- 1.01129447760167e-08],[2.92966025844079e-08,- 2.07556718857313e-08,5.45985315647905e-09,8.7685769027415e-09,1.06785510440474e-08],[- 1.22059608941331e-08,6.52491630264276e-09,- 1.79332492326928e-10,3.75921793745396e-10,- 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1.22214298993313e-15,1.69928513019657e-15,1.93593051311405e-16],[1.68528879784841e-05,3.57144412031081e-05,- 1.65999910125077e-05,5.40370336805755e-05,0.000118138122851376],[- 3.28151779115881e-05,1.04231790790798e-05,- 2.8076186289064e-06,2.98996152515593e-06,- 2.67641158709985e-06],[- 2.08664816151978e-06,- 1.64463884697475e-06,6.79099429284834e-08,7.23955842946495e-07,- 6.86378427465657e-07],[- 2.88205823027255e-09,2.38319699493291e-09,1.14169347509045e-07,8.12981074994402e-08,- 1.56957943666988e-07],[- 7.09711403570189e-09,6.29470515502988e-09,3.50833306577579e-09,8.31289199649054e-09,- 2.14221463168338e-09],[- 8.11910123910038e-10,3.34047829618955e-10,3.7061937744649e-10,3.30426088213373e-10,4.86297305597865e-11],[1.98628160424161e-11,- 4.98557831380098e-12,- 5.90523187802174e-12,- 1.27027116925122e-12,1.49982368570355e-11],[2.62289263262748e-12,3.91242360693861e-12,6.56035499387192e-12,- 1.17412941089401e-12,- 9.40878197853394e-13],[- 3.37805010124487e-13,5.39454874299593e-13,- 2.41569839991525e-13,- 2.41572016820792e-13,- 3.01983673057198e-13],[- 1.85034053857964e-13,4.31132161871815e-14,4.13497222026824e-15,- 4.6007551459598e-14,- 1.92454846400146e-14],[2.96113888929854e-15,- 1.11688534391626e-14,3.76275373238932e-15,- 3.72593295948136e-15,1.98205490249604e-16],[1.40074667864629e-15,- 5.15564234798333e-16,3.56287382196512e-16,5.07242777691587e-16,- 2.30405782826134e-17],[2.96822530176851e-16,- 4.77029898301223e-17,1.12782285532775e-16,1.58443229778573e-18,8.22141904662969e-17]])
    bnm_bh = np.array([[0,0,0,0,0],[0,0,0,0,0],[- 2.29210587053658e-06,- 2.33805004374529e-06,- 7.49312880102168e-07,- 5.12022747852006e-07,5.88926055066172e-07],[0,0,0,0,0],[- 4.6338275484369e-06,- 2.23853015662938e-06,8.14830531656518e-07,1.15453269407116e-06,- 4.53555450927571e-07],[- 6.92432096320778e-07,- 2.98734455136141e-07,1.48085153955641e-08,1.37881746148773e-07,- 6.92492118460215e-09],[0,0,0,0,0],[- 1.9150797985031e-06,- 1.83614825459598e-06,- 7.46807436870647e-07,- 1.28329122348007e-06,5.04937180063059e-07],[- 8.07527103916713e-07,2.8399784057457e-08,- 6.01890498063025e-08,- 2.48339507554546e-08,2.46284627824308e-08],[- 2.82995069303093e-07,1.38818274596408e-09,3.22731214161408e-09,2.87731153972404e-10,1.53895537278496e-08],[0,0,0,0,0],[- 6.682102709568e-07,- 2.19104833297845e-06,1.30116691657253e-07,4.7844573043345e-07,- 4.40344300914051e-07],[- 2.36946755740436e-07,- 1.32730991878204e-07,1.8366959369386e-08,7.90218931983569e-08,- 4.70161979232584e-08],[1.07746083292179e-07,- 4.1708863776033e-09,- 1.83296035841109e-09,- 5.80243971371211e-09,- 2.11682361167439e-09],[- 5.44712355496109e-08,1.89717032256923e-09,2.27327316287804e-10,7.78400728280038e-10,8.82380487618991e-12],[0,0,0,0,0],[- 5.61707049615673e-08,- 1.09066447089585e-06,- 2.25742250174119e-07,- 8.64367795924377e-07,1.0641127524068e-08],[2.41782935157918e-08,- 3.65762298303819e-08,- 6.93420659586875e-08,- 3.97316214341991e-08,- 2.0876781648639e-08],[6.38293030383436e-08,1.1137793633447e-08,6.91424941454782e-09,1.39887159955004e-09,5.25428749022906e-09],[1.09291268489958e-08,1.23935926756516e-10,3.92917259954515e-10,- 1.79144682483562e-10,- 9.11802874917597e-10],[- 4.40957607823325e-09,1.45751390560667e-10,1.24641258165301e-10,- 6.45810339804674e-11,- 8.92894658893326e-12],[0,0,0,0,0],[1.54754294162102e-08,- 1.60154742388847e-06,- 4.08425188394881e-07,6.18170290113531e-09,- 2.58919765162122e-07],[1.37130642286873e-08,- 6.67813955828458e-08,- 7.01410996605609e-09,3.82732572660461e-08,- 2.73381870915135e-08],[2.19113155379218e-08,4.11027496396868e-09,6.33816020485226e-09,- 1.49242411327524e-09,- 6.14224941851705e-10],[6.26573021218961e-09,5.17137416480052e-10,- 3.49784328298676e-10,1.13578756343208e-10,2.80414613398411e-10],[1.65048133258794e-11,1.00047239417239e-10,1.05124654878499e-10,- 3.03826002621926e-11,4.57155388334682e-11],[6.20221691418381e-11,9.75852610098156e-12,- 5.46716005756984e-12,1.31643349569537e-11,3.6161877571547e-12],[0,0,0,0,0],[- 1.03938913012708e-06,- 1.78417431315664e-07,2.86040141364439e-07,1.83508599345952e-08,- 1.34452220464346e-07],[- 4.36557481393662e-08,7.49780206868834e-09,- 8.62829428674082e-09,5.50577793039009e-09,- 9.46897502333254e-09],[3.43193738406672e-10,1.13545447306468e-08,1.25242388852214e-09,6.0322150195962e-10,1.5717207036118e-09],[- 4.73307591021391e-10,1.70855824051391e-10,- 2.62470421477037e-11,2.04525835988874e-10,- 1.17859695928164e-10],[- 3.36185995299839e-10,3.19243054562183e-11,1.17589412418126e-10,- 1.35478747434514e-12,5.11192214558542e-11],[3.19640547592136e-11,2.94297823804643e-12,- 1.0065152627699e-11,- 1.67028733953153e-12,3.03938833625503e-12],[1.68928641118173e-11,- 7.90032886682002e-13,- 1.40899773539137e-12,7.76937592393354e-13,7.32539820298651e-13],[0,0,0,0,0],[2.32949756055277e-07,1.46237594908093e-07,- 1.07770884952484e-07,1.26824870644476e-07,- 2.36345735961108e-08],[8.89572676497766e-08,7.24810004121931e-08,2.67583556180119e-08,2.48434796111361e-08,- 3.55004782858686e-09],[- 1.00823909773603e-08,8.84433929029076e-10,- 2.55502517594511e-10,- 5.48034274059119e-10,- 8.50241938494079e-10],[1.13259819566467e-09,5.55186945221216e-10,7.63679807785295e-11,- 1.70067998092043e-11,1.57081965572493e-10],[- 2.37748192185353e-10,2.45463764948e-11,3.2320841480286e-11,- 2.72624834520723e-12,8.144491836665e-12],[- 1.54977633126025e-11,4.58754903157884e-12,- 1.25864665839074e-12,2.44139868157872e-12,- 1.82827441958193e-12],[3.28285563794513e-12,- 1.10072329225465e-12,- 7.23470501810935e-13,5.85309745620389e-13,4.11317589687125e-13],[4.5759697438417e-13,9.84198128213558e-14,3.3450381770283e-14,7.08431086558307e-15,2.79891177268807e-14],[0,0,0,0,0],[- 3.6782071915558e-07,6.98497901205902e-07,1.833973887503e-07,2.39730262495372e-07,- 2.58441984368194e-07],[5.17793954077994e-08,5.54614175977835e-08,1.75026214305232e-09,- 2.55518450411346e-09,- 6.12272723006537e-09],[- 7.94292648157198e-09,- 1.01709107852895e-09,- 1.4925124181231e-09,9.32827213605682e-10,- 8.24490722043118e-10],[1.36410408475679e-11,2.16390220454971e-10,1.24934806872235e-10,- 6.82507825145903e-11,- 4.01575177719668e-11],[- 1.41619917600555e-11,- 1.54733230409082e-11,1.36792829351538e-11,1.11157862104733e-12,2.08548465892268e-11],[- 3.56521723755846e-12,4.47877185884557e-12,- 6.34096209274637e-16,- 1.13010624512348e-12,- 2.82018136861041e-13],[2.22758955943441e-12,- 4.6387646555938e-13,- 5.80688019272507e-13,2.45878690598655e-13,1.49997666808106e-13],[- 6.26833903786958e-14,2.73416335780807e-14,1.91842340758425e-14,1.6740506112901e-14,- 2.45268543953704e-17],[1.81972870222228e-14,5.43036245069085e-15,1.92476637107321e-15,8.78498602508626e-17,- 1.42581647227657e-15],[0,0,0,0,0],[9.74322164613392e-07,- 5.23101820582724e-07,- 2.81997898176227e-07,4.54762451707384e-08,- 3.34645078118827e-08],[- 6.75813194549663e-09,3.49744702199583e-08,- 5.09170419895883e-09,5.24359476874755e-09,4.96664262534662e-09],[4.53858847892396e-10,- 1.49347392165963e-09,- 2.00939511362154e-09,9.30987163387955e-10,9.74450200826854e-11],[- 4.92900885858693e-10,5.34223033225688e-12,1.08501839729368e-10,- 6.43526142089173e-11,- 3.11063319142619e-11],[1.3846924638669e-11,- 7.91180584906922e-12,2.26641656746936e-13,4.55251515177956e-12,6.05270575117769e-12],[4.02247935664225e-12,1.82776657951829e-12,- 1.28348801405445e-13,- 2.1625730130035e-13,- 5.54363979435025e-14],[4.15005914461687e-13,- 2.00647573581168e-13,- 1.67278251942946e-13,1.30332398257985e-13,1.52742363652434e-13],[6.36376500056974e-14,1.65794532815776e-14,- 3.80832559052662e-15,- 6.40262894005341e-16,2.42577181848072e-15],[- 5.55273521249151e-15,3.69725182221479e-15,2.02114207545759e-15,- 4.50870833392161e-16,9.62950493696677e-17],[1.00935904205024e-17,6.54751873609395e-17,- 1.09138810997186e-16,- 8.62396750098759e-17,- 3.82788257844306e-17],[0,0,0,0,0],[4.21958510903678e-07,- 8.30678271007705e-08,- 3.47006439555247e-07,- 3.36442823712421e-08,9.90739768222027e-08],[2.64389033612742e-08,2.65825090066479e-09,- 1.28895513428522e-08,- 7.07182694980098e-10,7.1090716530118e-09],[6.31203524153492e-09,- 1.67038260990134e-09,1.33104703539822e-09,8.34376495185149e-10,- 2.52478613522612e-10],[1.18414896299279e-10,- 2.57745052288455e-11,2.88295935685818e-11,- 3.27782977418354e-11,- 1.05705000036156e-11],[- 4.20826459055091e-12,- 6.97430607432268e-12,- 3.90660545970607e-12,- 3.90449239948755e-13,- 4.60384797517466e-13],[- 9.476683565582e-13,6.53305025354881e-13,2.6324018543496e-13,1.40129115015734e-13,3.85788887132074e-14],[2.23947810407291e-13,7.35262771548253e-15,- 3.83348211931292e-14,4.20376514344176e-14,4.26445836468461e-14],[- 3.88008154470596e-16,2.2856142466775e-15,- 8.73599966653373e-16,2.14321147947665e-15,6.3863182507192e-16],[- 8.62165565535721e-15,1.7974291214981e-15,1.01541125038661e-15,- 7.91027655831866e-17,- 4.0650513282523e-16],[- 2.35355054392189e-16,- 6.13997759731013e-17,- 2.73490528665965e-17,2.63895177155121e-17,- 4.47531057245187e-18],[6.0190970682353e-17,5.35520010856833e-18,- 2.15530106132531e-18,- 2.46778496746231e-18,- 7.09947296442799e-19],[0,0,0,0,0],[- 3.75005956318736e-07,- 5.39872297906819e-07,- 1.19929654883034e-07,4.52771083775007e-08,1.82790552943564e-07],[7.82606642505646e-09,- 1.68890832383153e-08,- 8.45995188378997e-09,1.42958730598502e-09,3.21075754133531e-09],[4.28818421913782e-09,- 1.07501469928219e-09,8.84086350297418e-10,9.74171228764155e-10,8.59877149602304e-12],[1.28983712172521e-10,- 6.96375160373676e-11,- 2.13481436408896e-11,1.33516375568179e-11,- 1.65864626508258e-11],[- 4.48914384622368e-12,9.68953616831263e-13,- 1.61372463422897e-12,- 2.09683563440448e-12,- 1.90096826314068e-12],[- 1.12626619779175e-13,3.34903159106509e-14,- 1.21721528343657e-13,7.46246339290354e-14,3.68424909859186e-13],[5.0829427436779e-14,2.8303615997709e-14,1.48074873486387e-14,- 9.59633528834945e-15,- 1.262310609511e-14],[- 4.01464098583541e-16,1.97047929526674e-15,- 5.29967950447497e-16,- 3.59120406619931e-16,1.69690933982683e-16],[- 1.73919209873841e-15,7.52792462841274e-16,3.65589287101147e-16,- 7.79247612043812e-17,- 8.24599670368999e-17],[- 4.61555616150128e-17,4.94529746019753e-19,- 1.0985815721227e-17,3.95550811124928e-18,3.239723998841e-18],[- 2.27040686655766e-17,- 3.27855689001215e-18,- 3.30649011116861e-19,9.08748546536849e-19,8.92197599890994e-19],[5.67241944733762e-18,3.84449400209976e-19,1.77668058015537e-19,2.00432838283455e-20,- 2.00801461564767e-19]])
    bnm_bw = np.array([[0,0,0,0,0],[0,0,0,0,0],[- 9.56715196386889e-06,- 3.6804063302042e-08,1.27846786489883e-07,1.32525487755973e-06,1.53075361125066e-06],[0,0,0,0,0],[- 7.17682617983607e-06,2.89994188119445e-06,- 2.97763578173405e-07,8.95742089134942e-07,3.44416325304006e-07],[- 8.0266113228521e-07,3.66738692077244e-07,- 3.0288096572328e-07,3.54144282036103e-07,- 1.68873066391463e-07],[0,0,0,0,0],[- 2.89640569283461e-06,- 7.83566373343614e-07,- 8.36667214682577e-07,- 7.41891843549121e-07,- 9.23922655636489e-08],[- 1.06144662284862e-06,1.57709930505924e-07,1.04203025714319e-07,1.20783300488461e-07,- 1.38726055821134e-07],[- 4.16549018672265e-07,- 1.35220897698872e-07,- 6.40269964829901e-08,1.63258283210837e-08,- 2.57958025095959e-08],[0,0,0,0,0],[3.52324885892419e-06,- 2.26705543513814e-07,1.53835589488292e-06,- 3.75263061267433e-07,3.69384057396017e-07],[- 2.06569149157664e-07,- 9.36260183227175e-08,- 3.55985284353048e-08,- 9.13671163891094e-08,6.931562565626e-09],[1.32437594740782e-07,4.44349887272663e-08,- 3.38192451721674e-08,- 3.97263855781102e-08,- 1.930878229958e-09],[- 1.29595244818942e-07,- 1.40852985547683e-08,1.4258759293976e-09,7.05779876554001e-09,- 1.00996269264535e-08],[0,0,0,0,0],[4.06960756215938e-06,- 1.97898540226986e-06,7.21905857553588e-08,- 1.19908881538755e-06,- 5.67561861536903e-08],[6.53369660286999e-08,- 2.42818687866392e-07,- 1.66203004559493e-08,- 2.41512414151897e-08,4.45426333411018e-08],[1.44650670663281e-07,8.50666367433859e-09,- 4.61165612004307e-09,4.88527987491045e-09,1.06277326713172e-08],[1.86770937103513e-08,- 6.4419794028893e-10,- 7.60456736846174e-09,- 9.97186468682689e-10,8.73229752697716e-10],[- 1.00206566229113e-08,1.33934372663121e-09,1.4169150343922e-09,8.72352590578753e-10,- 8.04561626629829e-10],[0,0,0,0,0],[3.07161843116618e-06,1.8296208565647e-06,1.87728623016069e-07,7.10611617623261e-07,2.26499092250481e-07],[4.50766403064905e-08,- 1.67752393078256e-07,2.4784472363907e-08,- 3.56484348424869e-09,- 1.56634836636584e-08],[3.7701165188109e-08,- 7.23045828480496e-09,5.22995988863761e-09,- 1.03740320341306e-09,4.57839777217789e-09],[8.09495635883121e-09,- 3.01977244420529e-10,- 2.30104544933093e-09,3.63658580939428e-10,4.39320811714867e-10],[9.37087629961269e-11,1.00780920426635e-09,1.2814053991335e-10,- 6.65795285522138e-12,4.71732796198631e-11],[- 8.88504487069155e-11,- 1.63253810435461e-10,7.22669710644299e-11,5.64715132584527e-11,- 1.08949308197617e-12],[0,0,0,0,0],[- 2.64054293284174e-07,- 2.37611606117256e-06,- 1.83671059706264e-06,- 3.12199354841993e-07,- 1.05598289276114e-07],[7.41706968747147e-08,- 1.64359098062646e-08,- 3.09750224040234e-08,- 9.68640079410317e-09,- 7.90399057863403e-08],[- 1.00254376564271e-08,1.12528248631191e-08,- 2.678415491741e-09,- 2.69481819323647e-09,1.56550607475331e-09],[- 2.18568129350729e-09,6.2642205697745e-10,1.95007291427316e-09,3.14226463591125e-10,- 3.62000388344482e-10],[- 9.30451291747549e-10,5.62175549482704e-11,1.01022849902012e-10,5.18675856498499e-11,5.37561696283235e-11],[5.33151334468794e-11,1.07571307336725e-10,- 1.31714567944652e-11,- 4.17524405900018e-11,- 2.16737797893502e-12],[4.69916869001309e-11,- 4.34516364859583e-12,- 6.61054225868897e-12,- 5.75845818545368e-12,- 2.32180293529175e-12],[0,0,0,0,0],[- 3.50305843086926e-06,1.76085131953403e-06,8.16661224478572e-07,4.09111042640801e-07,- 9.85414469804995e-08],[1.44670876127274e-07,- 1.41331228923029e-08,- 3.06530152369269e-08,- 1.46732098927996e-08,- 2.30660839364244e-08],[- 2.00043052422933e-08,1.72145861031776e-09,2.13714615094209e-09,1.02982676689194e-09,- 1.64945224692217e-10],[1.23552540016991e-09,1.42028470911613e-09,8.79622616627508e-10,- 7.44465600265154e-10,- 7.17124672589442e-11],[- 6.67749524914644e-10,- 5.7772287493405e-11,3.40077806879472e-11,4.2617607654184e-11,8.23189659748212e-11],[- 4.62771648935992e-11,- 7.24005305716782e-13,1.18233730497485e-12,5.18156973532267e-12,- 1.53329687155297e-12],[4.75581699468619e-12,- 3.79782291469732e-12,1.33077109836853e-12,- 1.0242602010712e-12,3.1038501924913e-13],[1.66486090578792e-12,1.08573672403649e-12,1.26268044166279e-13,- 1.23509297742757e-13,- 1.81842007284038e-13],[0,0,0,0,0],[9.93870680202303e-08,- 1.85264736035628e-06,- 5.58942734710854e-07,- 5.5418344831627e-07,- 3.95581289689398e-08],[7.88329069002365e-08,2.04810091451078e-08,3.74588851000076e-09,3.42429296613803e-08,- 2.00840228416712e-08],[- 5.93700447329696e-10,- 6.57499436973459e-10,- 6.90560448220751e-09,3.56586371051089e-09,7.33310245621566e-11],[- 6.38101662363634e-11,4.23668020216529e-10,- 2.43764895979202e-10,- 9.31466610703172e-11,- 3.17491457845975e-10],[1.5094372538247e-11,- 6.11641188685078e-11,- 4.37018785685645e-11,- 2.32871158949602e-11,4.19757251950526e-11],[- 1.18165328825853e-11,- 9.91299557532438e-13,6.40908678055865e-14,2.41049422936434e-12,- 8.20746054454953e-14],[6.01892101914838e-12,- 8.7848712287345e-13,- 1.58887481332294e-12,- 3.13556902469604e-13,5.14523727801645e-14],[- 1.50791729401891e-13,- 1.45234807159695e-13,1.65302377570887e-13,- 5.77094211651483e-15,9.22218953528393e-14],[- 1.85618902787381e-14,5.64333811864051e-14,- 9.9431137794557e-15,- 2.40992156199999e-15,- 2.19196760659665e-14],[0,0,0,0,0],[- 8.16252352075899e-08,1.61725487723444e-06,9.55522506715921e-07,4.02436267433511e-07,- 2.80682052597712e-07],[7.6868479032863e-09,- 5.00940723761353e-09,- 2.43640127974386e-08,- 2.59119930503129e-08,3.35015169182094e-08],[7.97903115186673e-09,3.73803883416618e-09,3.27888334636662e-09,1.37481300578804e-09,- 1.10677168734482e-10],[- 1.67853012769912e-09,- 1.61405252173139e-10,- 1.98841576520056e-10,- 1.46591506832192e-11,9.3571048780466e-11],[4.08807084343221e-11,- 3.74514169689568e-11,- 3.0363849332391e-11,- 5.02332555734577e-12,- 8.03417498408344e-12],[6.48922619024579e-12,1.96166891023817e-12,- 1.96968755122868e-12,- 5.20970156382361e-12,- 1.62656885103402e-12],[1.28603518902875e-12,- 4.88146958435109e-13,- 3.3703488699184e-13,1.37393696103e-14,4.41398325716943e-14],[1.48670014793021e-13,4.41636026364555e-14,2.06210477976005e-14,- 3.4371758358539e-14,- 1.21693704024213e-14],[- 1.67624180330244e-14,6.59317111144238e-15,2.57238525440646e-15,- 3.21568425020512e-17,5.29659568026553e-15],[7.85453466393227e-16,6.91252183915939e-16,- 1.20540764178454e-15,- 3.85803892583301e-16,3.46606994632006e-16],[0,0,0,0,0],[2.86710087625579e-06,- 1.68179842305865e-06,- 8.4830677201687e-07,- 7.08798062479598e-07,- 1.27469453733635e-07],[2.11824305734993e-09,2.02274279084379e-08,1.61862253091554e-08,3.25597167111807e-08,3.40868964045822e-09],[1.21757111431438e-08,1.68405530472906e-09,1.55379338018638e-09,- 3.81467795805531e-10,2.53316405545058e-09],[- 9.98413758659768e-11,5.38382145421318e-10,3.92629628330704e-10,- 1.43067134097778e-10,3.74959329667113e-12],[- 1.57270407028909e-11,- 9.02797202317592e-12,8.4599705988769e-12,4.71474382524218e-12,5.41880986596427e-12],[- 1.20658618702054e-12,7.12940685593433e-13,1.02148613026937e-12,1.63063852348169e-13,1.74048793197708e-13],[3.80559390991789e-13,1.19678271353485e-13,9.72859455604188e-14,5.42642400031729e-14,8.18796710714586e-14],[- 4.69629218656902e-14,5.59889038686206e-15,2.05363292795059e-15,5.38599403288686e-15,- 2.68929559474202e-15],[- 1.88759348081742e-14,5.20975954705924e-15,- 4.43585653096395e-16,5.57436617793556e-16,- 3.95922805817677e-16],[- 9.80871456373282e-16,2.50857658461759e-17,- 1.24253000050963e-16,6.00857065211394e-17,3.537996353115e-18],[2.49370713054872e-16,- 1.49119714269816e-17,- 3.12276052640583e-17,- 2.42001662334001e-17,- 1.69766504318143e-17],[0,0,0,0,0],[- 1.69222102455713e-06,1.64277906173064e-06,5.28855114364096e-07,4.2815985326865e-07,- 1.57362445882665e-07],[1.67656782413678e-08,- 3.77746114074055e-08,- 2.21564555842165e-08,- 3.37071806992217e-08,1.474540087398e-08],[1.06080499491408e-08,3.21990403709678e-09,3.87301757435359e-09,2.92241827834347e-10,- 1.86619473655742e-11],[1.62399669665839e-10,3.51322865845172e-10,2.67086377702958e-11,- 1.31596563625491e-10,3.14164569507034e-11],[- 2.02180016657259e-11,2.03305178342732e-11,6.34969032565839e-12,5.99522296668787e-12,- 4.46275273451008e-12],[- 9.88409290158885e-13,- 1.47692750858224e-13,3.1465555073053e-13,- 2.41857189187879e-13,4.47727504501486e-13],[1.71430777754854e-13,1.73950835042486e-13,5.92323956541558e-14,8.06625710171825e-15,2.33252485755634e-14],[- 1.74184545690134e-15,- 8.18003353124179e-16,- 6.62369006497819e-16,4.16303374396147e-15,7.06513748014024e-15],[- 6.02936238677014e-15,1.89241084885229e-15,1.9909788194427e-17,- 6.9997429069664e-16,- 2.69504942597709e-17],[- 4.65632962602379e-16,3.70281995445114e-18,- 9.04232973763345e-17,2.20847370761932e-17,7.62909453726566e-17],[- 6.25921477907943e-17,- 2.10532795609842e-17,- 1.03808073867183e-17,1.15091380049019e-18,4.66794445408388e-19],[9.39427013576903e-18,9.17044662931859e-19,2.04132745117549e-18,- 1.72364063154625e-19,- 1.18098896532163e-18]])
    bnm_ch = np.array([[0,0,0,0,0],[0,0,0,0,0],[3.44092035729033e-05,- 1.21876825440561e-05,- 1.87490665238967e-05,- 2.60980336247863e-05,4.31639313264615e-06],[0,0,0,0,0],[- 2.60125613000133e-05,1.70570295762269e-05,3.08331896996832e-05,1.66256596588688e-05,- 1.07841055501996e-05],[8.74011641844073e-06,- 2.25874169896607e-06,6.50985196673747e-07,1.30424765493752e-06,- 1.85081244549542e-07],[0,0,0,0,0],[3.77496505484964e-05,- 1.08198973553337e-05,- 1.67717574544937e-05,- 3.22476096673598e-05,1.12281888201134e-05],[- 7.68623378647958e-07,- 4.01400837153063e-06,- 2.16390246700835e-06,- 1.76912959937924e-06,- 1.12740084951955e-06],[- 2.37092815818895e-06,- 9.52317223759653e-07,- 2.22722065579131e-07,- 6.2515761977253e-08,1.86582003894639e-08],[0,0,0,0,0],[- 6.10254317785872e-05,- 2.51815503068494e-05,2.01046207874667e-05,7.21107723367308e-06,- 1.30692058660457e-05],[- 9.60655417241537e-06,- 7.31381721742373e-06,- 2.52767927589636e-06,9.09039973214621e-07,- 6.76454911344246e-07],[- 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9.41515631694254e-11],[7.4719602264413e-12,- 2.51369898528782e-11,- 2.121966878092e-11,1.55282119505201e-11,9.99224438231805e-12],[- 7.90534019004874e-13,3.55824506982589e-12,8.00835777767281e-13,8.73460019069655e-13,1.34176126600106e-12],[0,0,0,0,0],[3.12855262465316e-05,1.31629386003608e-05,2.65598119437581e-06,8.68923340949135e-06,- 7.51164082949678e-06],[1.56870792650533e-06,1.8922730168537e-06,4.15620385341985e-07,- 2.74253787880603e-07,- 4.288262101192e-07],[- 9.99176994565587e-08,- 1.10785129426286e-07,- 1.10318125091182e-07,6.22726507350764e-09,- 3.3921456638625e-08],[1.24872975018433e-08,1.10663206077249e-08,5.40658975901469e-09,- 2.79119137105115e-09,- 2.47500096192502e-09],[1.1151891715406e-10,- 4.21965763244849e-10,3.26786005211229e-10,1.93488254914545e-10,7.00774679999972e-10],[1.50889220040757e-10,1.03130002661366e-10,- 3.09481760816903e-11,- 4.47656630703759e-11,- 7.362450218038e-12],[- 1.91144562110285e-12,- 1.11355583995978e-11,- 1.76207323352556e-11,8.15289793192265e-12,3.45078925412654e-12],[- 2.73248710476019e-12,- 1.65089342283056e-13,- 2.20125355220819e-13,5.32589191504356e-13,5.70008982140874e-13],[8.06636928368811e-13,1.30893069976672e-13,9.72079137767479e-14,3.87410156264322e-14,- 5.56410013263563e-14],[0,0,0,0,0],[2.02454485403216e-05,- 9.77720471118669e-06,- 4.35467548126223e-06,2.19599868869063e-06,- 3.2667081904369e-06],[- 3.2183925631054e-08,8.38760368015005e-07,- 5.0805883572406e-07,4.16177282491396e-08,1.5384259276212e-07],[- 1.57377633165313e-07,- 7.86803586842404e-08,- 7.40444711426898e-08,3.15259864117954e-08,5.60536231567172e-09],[- 3.26080428920229e-10,- 3.14576780695439e-09,8.46796096612981e-10,- 2.59329379174262e-09,- 8.01054756588382e-10],[- 4.58725236153576e-11,- 6.87847958546571e-11,8.18226480126754e-12,1.81082075625897e-10,1.74510532938256e-10],[7.60233505328792e-11,4.76463939581321e-11,- 2.47198455442033e-11,- 8.83439688929965e-12,5.93967446277316e-13],[- 8.92919292558887e-12,- 4.38524572312029e-12,- 4.02709146060896e-12,4.84344426425295e-12,5.1286904278152e-12],[1.91518361809952e-12,3.06846255371817e-13,- 2.44830265306345e-13,7.86297493099244e-14,2.7234780580198e-13],[9.09936624159538e-14,7.20650818861447e-15,2.45383991578283e-14,- 4.79580974186462e-15,3.64604724046944e-14],[- 4.63611142770709e-14,1.73908246420636e-15,- 4.41651410674801e-15,- 6.61409045306922e-16,- 1.60016049099639e-15],[0,0,0,0,0],[6.17105245892845e-06,- 1.04342983738457e-05,- 1.72711741097994e-05,- 8.16815967888426e-07,3.42789959967593e-06],[- 2.44014060833825e-07,2.06991837444652e-07,- 3.85805819475679e-07,1.67162359832166e-08,4.15139610402483e-07],[8.1819900680402e-08,- 3.20013409049159e-08,5.94000906771151e-08,2.24122167188946e-08,- 1.33796186160409e-08],[7.66269294674338e-11,- 6.07862178874828e-10,4.95795757186248e-10,- 3.07589245481422e-10,3.44456287710689e-10],[- 1.84076250254929e-10,- 1.30985312312781e-10,- 1.52547325533276e-10,- 2.51000125929512e-11,- 1.93924012590455e-11],[- 2.93307452197665e-11,2.88627386757582e-11,5.58812021182217e-12,- 1.68692874069187e-13,1.80464313900575e-12],[- 9.59053874473003e-13,6.04803122874761e-13,- 9.80015608958536e-13,1.70530372034214e-12,1.70458664160775e-12],[2.80169588226043e-13,9.09573148053551e-14,2.16449186617004e-14,1.15550091496353e-13,4.97772796761321e-14],[- 3.04524400761371e-14,3.42845631349694e-14,2.44230630602064e-14,5.76017546103056e-16,- 9.74409465961093e-15],[5.98765340844291e-15,- 2.63942474859535e-15,- 1.80204805804437e-15,- 1.84981819321183e-16,- 5.8507339216366e-16],[- 2.37069441910133e-15,2.87429226086856e-16,- 1.67055963193389e-16,2.7211068491409e-18,8.46646962667892e-17],[0,0,0,0,0],[- 2.71386164105722e-05,- 1.41834938338454e-05,- 2.00777928859929e-07,5.94329804681196e-07,8.61856994375586e-06],[- 3.93656495458664e-08,- 6.36432821807576e-07,- 2.47887475106438e-07,- 2.64906446204966e-08,1.10689794197004e-07],[5.25319489188562e-08,9.00866357158695e-09,5.00693379572512e-08,2.47269011056404e-08,- 7.27648556194598e-09],[1.87207107149043e-09,- 1.46428282396138e-09,- 2.71812237167257e-10,8.44902265891466e-10,- 5.62683870906027e-10],[- 1.08295119666184e-10,4.75553388543793e-11,- 5.49429386495686e-11,- 6.60907871731611e-11,- 5.97347322824822e-11],[- 4.95118306815571e-12,5.3108373523497e-13,- 1.93679746327378e-12,- 1.6177052184051e-12,1.2327672720251e-11],[6.685826829099e-13,7.38288575160449e-13,5.47630483499201e-13,- 1.00770258118914e-13,- 1.65564928475981e-13],[5.80963409268471e-14,6.93474288078737e-14,6.60728092794315e-15,- 5.21029056725202e-15,- 1.11283532854883e-16],[- 4.10567742688903e-15,1.62252646805882e-14,1.00774699865989e-14,- 2.44793214897877e-16,- 1.59283906414563e-15],[1.84669506619904e-17,8.28473337813919e-17,- 1.53400662078899e-16,- 5.01060672199689e-17,- 2.20727935766132e-16],[2.65355116203636e-16,- 3.70233146147684e-17,3.52689394451586e-18,- 8.62215942516328e-18,9.26909361974526e-18],[9.94266950643135e-17,4.17028699663441e-18,- 7.65153491125819e-21,- 5.62131270981041e-18,- 3.03732817297438e-18]])
    bnm_cw = np.array([[0,0,0,0,0],[0,0,0,0,0],[- 0.000209104872912563,- 1.4153027497354e-05,3.00318745764815e-05,- 1.82864291318284e-05,- 7.62965409959238e-06],[0,0,0,0,0],[- 0.000186336519900275,0.000191256553935638,7.28356195304996e-05,3.59637869639906e-05,- 2.53927226167388e-05],[0.000108195343799485,- 6.97050977217619e-05,- 6.68037133871099e-05,2.30387653190503e-05,- 1.22735483925784e-05],[0,0,0,0,0],[0.000119941091277039,- 7.70547844186875e-05,- 8.15376297964528e-05,1.06005789545203e-05,2.3117723226872e-05],[- 1.77494760217164e-05,- 1.37061385686605e-05,- 1.74805936475816e-05,- 6.91745900867532e-07,- 7.10231790947787e-06],[- 1.47564103733219e-05,2.0889078548526e-06,3.19876879447867e-06,9.43984664503715e-07,- 4.90480527577521e-06],[0,0,0,0,0],[4.93300138389457e-05,- 6.77641298460617e-05,- 3.25043347246397e-05,8.33226714911921e-06,8.11499972792905e-06],[- 2.80449863471272e-05,- 1.04367606414606e-05,1.64473584641163e-07,- 3.57420965807816e-06,2.95887156564038e-06],[1.88835280111533e-06,5.69125761193702e-07,- 2.22757382799409e-06,- 1.96699131032252e-07,- 2.91861219283659e-07],[- 4.6991897143668e-06,- 7.00778948636735e-07,2.97544157334673e-09,3.8610051254441e-07,2.30939653701027e-07],[0,0,0,0,0],[1.77050610394149e-05,- 3.18353071311574e-05,3.04232260950316e-05,- 6.26821316488169e-05,- 1.75094810002378e-06],[9.25605901565775e-06,- 8.25179123302247e-06,6.74032752408358e-06,3.22192289084524e-06,6.09414500075259e-06],[4.282338252422e-06,2.10470570087927e-07,- 4.75050074985668e-07,- 4.89382663470592e-07,8.75232347469207e-07],[8.50393520366934e-07,1.58764911467186e-07,- 2.1626763832121e-07,- 7.43341300487416e-10,1.7513172981323e-07],[- 2.87064111623119e-07,4.5039389310283e-08,6.6331504441669e-08,7.61199387418853e-08,- 6.05694385243652e-09],[0,0,0,0,0],[- 1.95692079507947e-05,5.15486098887851e-05,3.00852761598173e-05,1.21485028343416e-05,- 6.72450521493428e-06],[5.34496867088158e-06,3.90973451680699e-06,3.70148924718425e-06,5.73731499938212e-08,5.5225822028878e-07],[3.39950838185315e-07,- 5.63443976772634e-07,4.52082211980595e-07,- 2.57094645806243e-07,- 6.84885762924729e-08],[2.15793276880684e-07,2.05911354090873e-07,1.33747872341142e-08,- 2.07997626478952e-08,- 3.69812938736019e-08],[2.11952749403224e-09,4.04317822544732e-08,2.4097202488365e-09,8.56289126938059e-09,2.310352834902e-08],[- 2.08402298813248e-09,- 8.50243600879112e-09,2.60895410117768e-09,- 6.69156841738591e-10,- 5.16280278087006e-09],[0,0,0,0,0],[0.000124901291436683,- 5.70770326719086e-05,- 8.44887248105015e-05,- 3.11442665354698e-05,- 1.12982893252046e-05],[- 8.38934444233944e-06,1.56860091415414e-06,- 1.77704563531825e-06,- 5.70219068898717e-08,- 4.30377735031244e-06],[3.72965318017681e-07,6.98175439446187e-07,1.75760544807919e-08,1.59731284857151e-07,3.62363848767891e-07],[- 2.32148850787091e-07,- 4.21888751852973e-08,8.35926113952108e-08,- 2.24572480575674e-08,- 6.92114100904503e-08],[- 2.92635642210745e-09,3.38086229163415e-09,4.72186694662901e-09,- 8.32354437305758e-11,4.19673890995627e-09],[- 1.264528876929e-09,1.91309690886864e-09,1.54755631983655e-09,- 1.09865169400249e-09,1.83645326319994e-10],[9.92539437011905e-10,- 2.963182034883e-10,1.17466020823486e-10,- 5.00185957995526e-10,- 8.54777591408537e-11],[0,0,0,0,0],[- 0.000182885335404854,7.27424724520089e-05,3.05286278023427e-05,2.55324463432562e-05,- 6.39859510763234e-06],[- 5.21449265232557e-06,- 6.70572386081398e-06,- 3.95473351292738e-06,- 6.41023334372861e-07,- 3.11616331059009e-06],[2.37090789071727e-07,3.58427517014705e-07,2.55709192777007e-07,8.44593804408541e-08,9.27243162355359e-09],[7.24370898432057e-08,- 7.4394512033771e-09,8.61751911975683e-10,- 2.34651212610623e-08,2.94052921681456e-09],[- 1.22127317934425e-08,- 3.89758984276768e-09,4.12890383904924e-11,2.06528068002723e-09,1.7348869697227e-09],[- 5.4413740690762e-10,- 4.81034553189921e-10,- 2.56101759039694e-11,3.21880564410154e-10,- 2.7019534316525e-11],[1.08394225300546e-10,- 7.99525492688661e-11,1.73850287030654e-10,- 8.06390014426271e-11,- 7.6314336429116e-13],[- 3.41446959267441e-11,2.72675729042792e-11,5.69674704865345e-12,- 3.38402998344892e-12,- 2.96732381931007e-12],[0,0,0,0,0],[2.9116131598725e-05,- 7.24641166590735e-05,- 8.58323519857884e-06,- 1.1403744425582e-05,1.32244819451517e-05],[1.24266748259826e-06,- 4.13127038469802e-06,- 8.47496394492885e-07,5.48722958754267e-07,- 1.98288551821205e-06],[- 1.70671245196917e-08,1.3689112708354e-08,- 2.8090197224987e-07,- 5.45369793946222e-09,- 9.58796303763498e-08],[1.14115335901746e-08,2.79308166429178e-08,- 1.71144803132413e-08,4.8611624356538e-09,- 8.1306145995228e-09],[- 1.19144311035824e-09,- 1.28197815211763e-09,- 1.22313592972373e-09,6.23116336753674e-10,2.11527825898689e-09],[4.94618645030426e-10,- 1.01554483531252e-10,- 3.58808808952276e-10,1.23499783028794e-10,- 1.21017599361833e-10],[1.33959569836451e-10,- 1.87140898812283e-11,- 3.04265350158941e-11,- 1.42907553051431e-11,- 1.09873858099638e-11],[1.30277419203512e-11,- 4.95312627777245e-12,2.23070215544358e-12,1.66450226016423e-12,6.26222944728474e-12],[- 4.40721204874728e-12,2.99575133064885e-12,- 1.54917262009097e-12,8.9001566452706e-14,- 1.59135267012937e-12],[0,0,0,0,0],[- 4.1766721132316e-05,1.39005215116294e-05,1.46521361817829e-05,3.23485458024416e-05,- 8.57936261085263e-06],[9.4849102652445e-07,1.67749735481991e-06,6.80159475477603e-07,- 1.34558044496631e-06,1.62108231492249e-06],[- 2.67545753355631e-07,- 3.31848493018159e-08,1.05837219557465e-07,1.555876554794e-07,- 2.84996014386667e-08],[- 5.15113778734878e-08,8.83630725241303e-09,3.36579455982772e-09,- 6.22350102096402e-09,5.03959133095369e-09],[2.04635880823035e-11,- 1.07923589059151e-09,- 6.96482137669712e-10,- 4.70238500452793e-10,- 6.60277903598297e-10],[- 2.41897168749189e-11,1.33547763615216e-10,- 5.13534673658908e-11,- 8.32767177662817e-11,5.72614717082428e-11],[7.5517056235994e-12,- 1.57123461699055e-11,- 1.48874069619124e-11,- 7.10529462981252e-13,- 7.99006335025107e-12],[2.4188315673896e-12,2.97346980183361e-12,1.2871997773145e-12,- 2.49240876894143e-12,6.71155595793198e-13],[4.16995565336914e-13,- 1.71584521275288e-13,- 7.23064067359978e-14,2.45405880599037e-13,4.4353293490583e-13],[3.56937508828997e-14,2.430125112603e-14,- 7.96090778289326e-14,- 1.59548529636358e-14,8.99103763000507e-15],[0,0,0,0,0],[0.000117579258399489,- 4.52648448635772e-05,- 2.69130037097862e-05,- 3.82266335794366e-05,- 4.36549257701084e-06],[- 1.43270371215502e-06,1.21565440183855e-06,8.53701136074284e-07,1.52709810023665e-06,1.22382663462904e-06],[3.06089147519664e-07,9.79084123751975e-08,7.96524661441178e-08,4.54770947973458e-08,2.22842369458882e-07],[- 9.94254707745127e-09,1.43251376378012e-08,1.9391175368516e-08,- 6.52214645690987e-09,- 1.97114016452408e-09],[- 9.20751919828404e-10,- 9.44312829629076e-10,7.24196738163952e-11,- 6.71801072324561e-11,2.33146774065873e-10],[- 1.4354429895641e-11,1.78464235318769e-10,7.69950023012326e-11,- 4.22390057304453e-12,3.05176324574816e-11],[- 7.8805375397399e-12,- 3.20207793051003e-12,1.01527407317625e-12,6.02788185858449e-12,1.14919530900453e-11],[- 1.21558899266069e-12,5.31300597882986e-13,3.44023865079264e-13,- 6.22598216726224e-14,- 5.47031650765402e-14],[- 4.15627948750943e-13,2.77620907292721e-13,- 8.99784134364011e-14,1.07254247320864e-13,6.85990080564196e-14],[- 3.91837863922901e-14,9.7471497681618e-15,6.79982450963903e-15,- 2.41420876658572e-15,- 2.20889384455344e-15],[9.25912068402776e-15,- 4.02621719248224e-15,- 2.43952036351187e-15,- 1.97006876049866e-15,1.03065621527869e-16],[0,0,0,0,0],[- 0.000103762036940193,4.38145356960292e-05,2.43406920349913e-05,7.89103527673736e-06,- 1.6684146533916e-05],[- 1.18428449371744e-06,- 1.30188721737259e-06,- 1.8801355711665e-06,- 1.01342046295303e-06,9.21813037802502e-07],[1.5183606871246e-07,1.11362553803933e-07,1.55375052233052e-07,1.94450910788747e-09,- 1.73093755828342e-08],[- 3.77758211813121e-09,1.2332396958361e-08,1.72510045250302e-09,- 1.88609789458597e-09,1.28937597985937e-09],[- 1.07947760393523e-09,5.26051570105365e-10,- 3.67657536332496e-11,3.1611012352384e-10,- 3.2427319824217e-10],[- 2.0038564920982e-12,2.5470386968239e-11,4.08563622440851e-12,- 4.83350348928636e-11,- 3.98153443845079e-13],[2.73094467727215e-12,5.08900664114903e-12,- 7.66669089075134e-13,2.50015592643012e-12,4.29763262853853e-12],[6.5394648753789e-13,- 2.24958413781008e-13,6.74638861781238e-15,3.28537647613903e-14,2.54199700290116e-13],[- 1.09122051193505e-13,8.36362392931501e-14,- 3.907501539123e-14,- 5.4491591074195e-14,2.43816947219217e-14],[- 1.41882561550134e-14,1.00455397812713e-14,2.63347255121581e-15,1.53043256823601e-15,2.49081021428095e-15],[- 1.17256193152654e-15,1.05648985031971e-16,1.31778372453016e-16,1.44815198666577e-16,- 3.7253276861848e-16],[2.66203457773766e-16,- 7.67224608659658e-17,3.51487351031864e-18,4.10287131339291e-17,- 6.72171711728514e-17]])
    # read the respective lines from the matrices
    anm_bh_A0 = anm_bh[:,0]
    anm_bh_A1 = anm_bh[:,1]
    anm_bh_B1 = anm_bh[:,2]
    anm_bh_A2 = anm_bh[:,3]
    anm_bh_B2 = anm_bh[:,4]
    
    anm_bw_A0 = anm_bw[:,0]
    anm_bw_A1 = anm_bw[:,1]
    anm_bw_B1 = anm_bw[:,2]
    anm_bw_A2 = anm_bw[:,3]
    anm_bw_B2 = anm_bw[:,4]
    
    anm_ch_A0 = anm_ch[:,0]
    anm_ch_A1 = anm_ch[:,1]
    anm_ch_B1 = anm_ch[:,2]
    anm_ch_A2 = anm_ch[:,3]
    anm_ch_B2 = anm_ch[:,4]
    
    anm_cw_A0 = anm_cw[:,0]
    anm_cw_A1 = anm_cw[:,1]
    anm_cw_B1 = anm_cw[:,2]
    anm_cw_A2 = anm_cw[:,3]
    anm_cw_B2 = anm_cw[:,4]
    
    bnm_bh_A0 = bnm_bh[:,0]
    bnm_bh_A1 = bnm_bh[:,1]
    bnm_bh_B1 = bnm_bh[:,2]
    bnm_bh_A2 = bnm_bh[:,3]
    bnm_bh_B2 = bnm_bh[:,4]
    
    bnm_bw_A0 = bnm_bw[:,0]
    bnm_bw_A1 = bnm_bw[:,1]
    bnm_bw_B1 = bnm_bw[:,2]
    bnm_bw_A2 = bnm_bw[:,3]
    bnm_bw_B2 = bnm_bw[:,4]
    
    bnm_ch_A0 = bnm_ch[:,0]
    bnm_ch_A1 = bnm_ch[:,1]
    bnm_ch_B1 = bnm_ch[:,2]
    bnm_ch_A2 = bnm_ch[:,3]
    bnm_ch_B2 = bnm_ch[:,4]
    
    bnm_cw_A0 = bnm_cw[:,0]
    bnm_cw_A1 = bnm_cw[:,1]
    bnm_cw_B1 = bnm_cw[:,2]
    bnm_cw_A2 = bnm_cw[:,3]
    bnm_cw_B2 = bnm_cw[:,4]
    # conversions
    el = np.pi / 2 - zd
    polDist = np.pi / 2 - lat
    # a.) calculate Legendre polynomials
    
    # degree n and order m
    nmax = 12
    # unit vector
    x = np.sin(polDist) * np.cos(lon)
    y = np.sin(polDist) * np.sin(lon)
    z = np.cos(polDist)
    # Legendre polynomials
    V = np.zeros((nmax+1, nmax+1))
    W = np.zeros((nmax+1, nmax+1))

    V[0,0] = 1
    W[0,0] = 0
    V[1,0] = z * V[0,0]
    W[1,0] = 0

    for n in range(2, nmax+1):
      V[n,0] = ((2*n-1) * z * V[n-1,0] - (n-1) * V[n-2,0]) / n
      W[n,0] = 0

    for m in range(1, nmax+1):
      V[m,m] = (2*m-1) * (x*V[m-1,m-1] - y*W[m-1,m-1])
      W[m,m] = (2*m-1) * (x*W[m-1,m-1] + y*V[m-1,m-1])
      if m < nmax:
        V[m+1,m] = (2*m+1) * z * V[m,m]
        W[m+1,m] = (2*m+1) * z * W[m,m]
      for n in range(m+2, nmax+1):
        V[n,m] = ((2*n-1)*z*V[n-1,m] - (n+m-1)*V[n-2,m]) / (n-m)
        W[n,m] = ((2*n-1)*z*W[n-1,m] - (n+m-1)*W[n-2,m]) / (n-m)
    
    # b.) determine the coefficients bh, bw, ch and cw
    
    # initialize
    bh_A0 = 0
    bh_A1 = 0
    bh_B1 = 0
    bh_A2 = 0
    bh_B2 = 0
    bw_A0 = 0
    bw_A1 = 0
    bw_B1 = 0
    bw_A2 = 0
    bw_B2 = 0
    ch_A0 = 0
    ch_A1 = 0
    ch_B1 = 0
    ch_A2 = 0
    ch_B2 = 0
    cw_A0 = 0
    cw_A1 = 0
    cw_B1 = 0
    cw_A2 = 0
    cw_B2 = 0
    i = 0
    for n in np.arange(0,nmax+1).reshape(-1):
        for m in np.arange(0,n+1).reshape(-1):
            
            bh_A0 = bh_A0 + (anm_bh_A0[i] * V[n,m] + bnm_bh_A0[i] * W[n,m])
            bh_A1 = bh_A1 + (anm_bh_A1[i] * V[n,m] + bnm_bh_A1[i] * W[n,m])
            bh_B1 = bh_B1 + (anm_bh_B1[i] * V[n,m] + bnm_bh_B1[i] * W[n,m])
            bh_A2 = bh_A2 + (anm_bh_A2[i] * V[n,m] + bnm_bh_A2[i] * W[n,m])
            bh_B2 = bh_B2 + (anm_bh_B2[i] * V[n,m] + bnm_bh_B2[i] * W[n,m])
            bw_A0 = bw_A0 + (anm_bw_A0[i] * V[n,m] + bnm_bw_A0[i] * W[n,m])
            bw_A1 = bw_A1 + (anm_bw_A1[i] * V[n,m] + bnm_bw_A1[i] * W[n,m])
            bw_B1 = bw_B1 + (anm_bw_B1[i] * V[n,m] + bnm_bw_B1[i] * W[n,m])
            bw_A2 = bw_A2 + (anm_bw_A2[i] * V[n,m] + bnm_bw_A2[i] * W[n,m])
            bw_B2 = bw_B2 + (anm_bw_B2[i] * V[n,m] + bnm_bw_B2[i] * W[n,m])
            ch_A0 = ch_A0 + (anm_ch_A0[i] * V[n,m] + bnm_ch_A0[i] * W[n,m])
            ch_A1 = ch_A1 + (anm_ch_A1[i] * V[n,m] + bnm_ch_A1[i] * W[n,m])
            ch_B1 = ch_B1 + (anm_ch_B1[i] * V[n,m] + bnm_ch_B1[i] * W[n,m])
            ch_A2 = ch_A2 + (anm_ch_A2[i] * V[n,m] + bnm_ch_A2[i] * W[n,m])
            ch_B2 = ch_B2 + (anm_ch_B2[i] * V[n,m] + bnm_ch_B2[i] * W[n,m])
            cw_A0 = cw_A0 + (anm_cw_A0[i] * V[n,m] + bnm_cw_A0[i] * W[n,m])
            cw_A1 = cw_A1 + (anm_cw_A1[i] * V[n,m] + bnm_cw_A1[i] * W[n,m])
            cw_B1 = cw_B1 + (anm_cw_B1[i] * V[n,m] + bnm_cw_B1[i] * W[n,m])
            cw_A2 = cw_A2 + (anm_cw_A2[i] * V[n,m] + bnm_cw_A2[i] * W[n,m])
            cw_B2 = cw_B2 + (anm_cw_B2[i] * V[n,m] + bnm_cw_B2[i] * W[n,m])
            i = i + 1
    
    # adding the seasonal amplitudes for the specified doy to the mean values
    bh = bh_A0 + bh_A1 * np.cos(doy / 365.25 * 2 * np.pi) + bh_B1 * np.sin(doy / 365.25 * 2 * np.pi) + bh_A2 * np.cos(doy / 365.25 * 4 * np.pi) + bh_B2 * np.sin(doy / 365.25 * 4 * np.pi)
    bw = bw_A0 + bw_A1 * np.cos(doy / 365.25 * 2 * np.pi) + bw_B1 * np.sin(doy / 365.25 * 2 * np.pi) + bw_A2 * np.cos(doy / 365.25 * 4 * np.pi) + bw_B2 * np.sin(doy / 365.25 * 4 * np.pi)
    ch = ch_A0 + ch_A1 * np.cos(doy / 365.25 * 2 * np.pi) + ch_B1 * np.sin(doy / 365.25 * 2 * np.pi) + ch_A2 * np.cos(doy / 365.25 * 4 * np.pi) + ch_B2 * np.sin(doy / 365.25 * 4 * np.pi)
    cw = cw_A0 + cw_A1 * np.cos(doy / 365.25 * 2 * np.pi) + cw_B1 * np.sin(doy / 365.25 * 2 * np.pi) + cw_A2 * np.cos(doy / 365.25 * 4 * np.pi) + cw_B2 * np.sin(doy / 365.25 * 4 * np.pi)
    # calculating the hydrostatic and wet mapping factors
    mfh = (1 + (ah / (1 + bh / (1 + ch)))) / (np.sin(el) + (ah / (np.sin(el) + bh / (np.sin(el) + ch))))
    mfw = (1 + (aw / (1 + bw / (1 + cw)))) / (np.sin(el) + (aw / (np.sin(el) + bw / (np.sin(el) + cw))))
    return mfh,mfw