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+ return jdate + +jday = np.array([]) +for i in range(len(data_mld)): + jday = np.append(jday, datestdtojd(data_mld['date'][i])) +data_mld.insert(1, 'Julian day', pd.DataFrame(jday)) # phychem data + +#--------------------------------------------------------------------- +""" +Mixed Layer Depth (MLD) +1. taking the mean for each julian day +2. taking the mean for each month +3. interpolate a function based on 12-month data points +""" +mld_GR = data_mld.groupby('Julian day', as_index=False)['thermocl'].median().to_numpy() + +condlist = [0., 32., 70., 90., 121., 152., 182., 213., 244., 274., 305., 330., 345, 365] + +# there are noise in MLD data, so we did some manipulation from visual inspection +extrct_GR_mld = np.zeros((len(condlist), 2)) +extrct_GR_mld[:, 0] = condlist +extrct_GR_mld[0:2, 1] = np.repeat(30, 2) +extrct_GR_mld[2:, 1] = np.array([12, 3, 4, 5, 6, 7, 8, 9, 12, 18, 30, 30]) + + +## Quick plot +fig, axs = plt.subplots(1, 1, figsize=(7, 4), sharex='all') +fig.subplots_adjust(wspace=0.3, hspace=0.12, left=0.1, right=0.96, top=0.9, bottom=0.2) +axs.scatter(mld_GR[:, 0], mld_GR[:, 1], s=15, color='gray') +axs.scatter(extrct_GR_mld[:, 0], extrct_GR_mld[:, 1], s=25, color='r') +axs.axis([0, 365, 35, -1]) +axs.set_xlabel('day', labelpad=10) +axs.set_ylabel('MLD', labelpad=10) + +from scipy.interpolate import PchipInterpolator +MLD_pchip_GR = PchipInterpolator(extrct_GR_mld[:, 0], extrct_GR_mld[:, 1], axis=0) +MLD_pchip_GR_spl = MLD_pchip_GR(np.arange(365)) + +# Detailed plot +fig, axs = plt.subplots(figsize=(8, 4)) +fig.subplots_adjust(wspace=0.2, hspace=0.1, left=0.1, right=0.95, top=0.95, bottom=0.15) + +axs.plot(np.arange(365), MLD_pchip_GR_spl, color='r', lw=2.5, zorder=2, label='forcing') +axs.scatter(mld_GR[:, 0], mld_GR[:, 1], s=15, facecolor='steelblue', edgecolor='k', lw=0.25, zorder=1, label='data') +# axs.scatter(extrct_GR_mld[:, 0], extrct_GR_mld[:, 1], s=50, color='r', lw=1, edgecolor='k', zorder=3, +# label='Extracted lake median') +axs.axis([0, 365, 35, -1]) +axs.set_ylabel('Mixed layer depth, MLD (m)\nGreifen', fontsize=12, labelpad=10) +axs.set_xlabel('Month', fontsize=12, labelpad=10) +axs.legend(loc=4, fontsize=9, ncol=1, bbox_to_anchor=(0.9, 0)) +axs.set_xticks([1., 32., 60., 91., 121., 152., 182., 213., 244., 274., 305., 335]) +axs.set_xticklabels(['J', 'F', 'M', 'A', 'M', 'J', 'J', 'A', 'S', 'O', 'N', 'D'], fontsize=12) + +plt.savefig(fname=wd + '/MLD_final.png', dpi=800) + +## save csv, save points and interpolate again in the run script +MLD_pt = np.vstack((extrct_GR_mld[:, 0], extrct_GR_mld[:, 1])).T +np.savetxt(wd+"/MLD_final.csv", MLD_pt, delimiter=",") diff --git a/LakeData/TSM_PARForcing.py b/LakeData/TSM_PARForcing.py new file mode 100644 index 0000000..dee785a --- /dev/null +++ b/LakeData/TSM_PARForcing.py @@ -0,0 +1,97 @@ +""" +Generate PAR (irradiance) forcing from observation data of Greifensee +irradiance is measured by the unit of W m-2 +""" +import seaborn as sns +import matplotlib.pyplot as plt +import numpy as np +import pandas as pd + +wd = 'your wd' + +data = pd.read_csv(wd+'/RawData_Temp+PAR.csv') +data_nSSI = data[['date', 'global_radiation']] + + +# convert real data to julian day (0-365) +import datetime + +def datestdtojd(stddate): + """ + source: https://rafatieppo.github.io/post/2018_12_01_juliandate/ + :param stddate: standard date for input + :return: + """ + fmt = '%Y-%m-%d' + sdtdate = datetime.datetime.strptime(stddate, fmt) + sdtdate = sdtdate.timetuple() + jdate = sdtdate.tm_yday + return jdate + +jday = np.array([]) +for i in range(len(data_nSSI)): + jday = np.append(jday, datestdtojd(data_nSSI['date'][i])) +data_nSSI.insert(1, 'Julian day', pd.DataFrame(jday)) # phychem data + + +#--------------------------------------------------------------------- +data['month'] = pd.DatetimeIndex(data['date']).month +dayno = np.array([1., 32., 60., 91., 121., 152., 182., 213., 244., 274., 305., 335]) +dayno_used = np.array([16, 47, 75, 106, 136, 167, 197, 228, 259, 289, 320, 350]) + + +""" +Irradiance +1. taking the interquartile range at 75% for each julian day +2. taking the monthly mean of the daily interquantile +3. calculating PAR +5. interpolate a function based on 12-month data points +""" +nSSI_quart = data.groupby(['Julian day'], as_index=False)['global_radiation'].quantile(0.75) + +# adding the column month from julian day +nSSI_quart.insert(1, 'year_fool', np.repeat(2000, len(nSSI_quart))) +nSSI_quart['date_fool'] = pd.to_datetime(nSSI_quart['year_fool'], format='%Y') + pd.to_timedelta(nSSI_quart['Julian day'], unit='D') - pd.Timedelta('1D') +nSSI_quart['month'] = pd.DatetimeIndex(nSSI_quart['date_fool']).month +nSSI_quart_month = nSSI_quart.groupby(['month'], as_index=False)['global_radiation'].mean().to_numpy() + + +def nSSI2PAR(netSSI): + """ + This function is to convert nSSI (W m-2) into PAR (E m-2 d-1) + Procedure: + 1. extr = extraction factor (only about 45% of the nSSI is in the 400-700nm range, Howell et al. 1983) + 2. conv = conversion factor from W m-2 to Ein m-2 d-1 (Lampert and Sommer, 2007, pp.20)** + ** further details please see PAR_UnitConversion.docx + """ + extr = 0.45 + conv = 0.432 + return netSSI * extr * conv + +#### Interpolation #### +from scipy.interpolate import make_interp_spline +PAR_pchip = make_interp_spline(dayno+15, nSSI2PAR(nSSI_quart_month[:, 1]), k=3) +PAR_pchip_spl = PAR_pchip(np.arange(365)) +################### + +fig, axs = plt.subplots(figsize=(8, 4)) +fig.subplots_adjust(wspace=0.2, hspace=0.1, left=0.1, right=0.95, top=0.95, bottom=0.15) + +axs.scatter(x=data_nSSI['Julian day'], y=nSSI2PAR(data_nSSI['global_radiation']), s=15, color='steelblue', lw=0.25, ec='k') +axs.set_ylabel('PAR (Ein m$^{-2}$ d$^{-1}$)', fontsize=12) +axs.plot(np.arange(365), PAR_pchip_spl, color='r', lw=2.5, label='forcing') +axs.set_xlim(0, 365) +axs.set_ylim(0, 80) +axs.set_xticks([1., 32., 60., 91., 121., 152., 182., 213., 244., 274., 305., 335]) +axs.set_xticklabels(['J', 'F', 'M', 'A', 'M', 'J', 'J', 'A', 'S', 'O', 'N', 'D']) +axs.set_xlabel('Month', fontsize=12, labelpad=10) +axs.legend(loc=1, fontsize=12) + +plt.savefig(fname=wd + '/PAR_final.png', dpi=800) + +## save csv, save points and interpolate again in the run script +PAR_pt = np.vstack((dayno+15, nSSI2PAR(nSSI_quart_month[:, 1]))).T +np.savetxt(wd+"TempSizeMod_TSM/Forcing/Final/PAR_final.csv", PAR_pt, delimiter=",") + + + diff --git a/LakeData/TSM_TempForcing.py b/LakeData/TSM_TempForcing.py new file mode 100644 index 0000000..1d44ce4 --- /dev/null +++ b/LakeData/TSM_TempForcing.py @@ -0,0 +1,85 @@ +""" +Generate temperature forcing from observation data of Greifensee +""" +import matplotlib.pyplot as plt +import numpy as np +import pandas as pd + +wd = 'your wd' + +data = pd.read_csv(wd+'/RawData_Temp+PAR.csv') +data_temp = data[['date', 'water_temp']] + + +# convert real data to julian day (0-365) +import datetime + +def datestdtojd(stddate): + """ + source: https://rafatieppo.github.io/post/2018_12_01_juliandate/ + :param stddate: standard date for input + :return: + """ + fmt = '%Y-%m-%d' + sdtdate = datetime.datetime.strptime(stddate, fmt) + sdtdate = sdtdate.timetuple() + jdate = sdtdate.tm_yday + return jdate + +jday = np.array([]) +for i in range(len(data_temp)): + jday = np.append(jday, datestdtojd(data_temp['date'][i])) +data_temp.insert(1, 'Julian day', pd.DataFrame(jday)) + +#--------------------------------------------------------------------- +data['month'] = pd.DatetimeIndex(data['date']).month +dayno = np.array([1., 32., 60., 91., 121., 152., 182., 213., 244., 274., 305., 335]) +dayno_used = np.array([16, 47, 75, 106, 136, 167, 197, 228, 259, 289, 320, 350]) + +""" +Temperature +1. taking the mean from each julian day +2. taking the mean from each month +3. interpolate a function based on 12-month data points +""" + +temp = data_temp.groupby(['Julian day'], as_index=False)['water_temp'].mean() + +# adding the column month from julian day +temp.insert(1, 'year_fool', np.repeat(2000, len(temp))) +temp['date_fool'] = pd.to_datetime(temp['year_fool'], format='%Y') + pd.to_timedelta(temp['Julian day'], unit='D') - pd.Timedelta('1D') +temp['month'] = pd.DatetimeIndex(temp['date_fool']).month + +temp_mean = temp.groupby(['month'], as_index=False)['water_temp'].mean().to_numpy() + +#### Interpolation #### +from scipy.interpolate import make_interp_spline +ext_time = np.append(np.append(dayno+15, 365+dayno+15), 365*2+dayno+15) +Temp_pchip = make_interp_spline(ext_time, np.tile(temp_mean[:, 1], 3), k=3) +Temp_pchip_spl = Temp_pchip(np.arange(365*3)) +Temp_pchip_spl = Temp_pchip_spl[365:730] # we select the middle year for a smoother forcing + +temp_val = [] +for i in range(len(dayno_used)): + temp_val = np.append(temp_val, Temp_pchip_spl[dayno_used[i]]) + +################### +fig, axs = plt.subplots(figsize=(8, 4)) +fig.subplots_adjust(wspace=0.2, hspace=0.1, left=0.1, right=0.95, top=0.95, bottom=0.15) + +axs.scatter(x=data_temp['Julian day'], y=data_temp['water_temp'], s=15, color='steelblue', lw=0.25, ec='k', label='data') +axs.plot(np.arange(365), Temp_pchip_spl, color='r', lw=2.5, label='forcing') +# axs.plot(dayno+15, temp_mean[:, 1], color='r', lw=2) +axs.set_ylabel('Photic zone water temperature', fontsize=12) +axs.set_xlim(0, 365) +axs.set_ylim(0, 25) +axs.set_xticks([1., 32., 60., 91., 121., 152., 182., 213., 244., 274., 305., 335]) +axs.set_xticklabels(['J', 'F', 'M', 'A', 'M', 'J', 'J', 'A', 'S', 'O', 'N', 'D']) +axs.set_xlabel('Month', fontsize=12, labelpad=10) +axs.legend(loc=2) + +plt.savefig(fname=wd + '/Temp_final.png', dpi=800) + +## save csv, save points and interpolate again in the run script +Temp_pt = np.vstack((dayno_used, temp_val)).T +np.savetxt(wd+"/Temp_final.csv", Temp_pt, delimiter=",") diff --git a/LakeData/TempForc_CTD.csv b/LakeData/TempForc_CTD.csv deleted file mode 100644 index a81abbc..0000000 --- a/LakeData/TempForc_CTD.csv +++ /dev/null @@ -1,365 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-310.0884956,306.3519414,301.4370075,261.3613932,212.4528302,166.4150943,114.7169811,65.66037736,40,228.164 -341.1780973,299.8603142,293.0550212,236.3442461,173.9622642,115.0943396,67.54716981,29.81132075,14.33962264,228.162 -364,296.4083176,285.8223062,221.5500945,153.9622642,92.83018868,50.18867925,20.37735849,7.547169811,228.160 diff --git a/LakeData/note b/LakeData/note deleted file mode 100644 index d94ed02..0000000 --- a/LakeData/note +++ /dev/null @@ -1,4 +0,0 @@ -This is the supplementary lake data (https://zenodo.org/record/3582838#.YzQzuexBwc8) from Pomati et al. (2020) and is used for comparison in this theoretical temperature size-based model. - -There are in total 8 lakes: Walensee (WA); Upper Lake Zurich (UZ); Lake Lucerne (LU); Lower Lake Zurich (LZ); Sempachersee (SE); Hallwilersee (HA); Baldeggersee (BA); Greifensee (GR). -Further information on data format please refer to the readme.txt diff --git a/LakePlankData/PlanktData4Calibr.csv b/LakePlankData/PlanktData4Calibr.csv new file mode 100644 index 0000000..5db7164 --- /dev/null +++ b/LakePlankData/PlanktData4Calibr.csv @@ -0,0 +1,1391 @@ +,Julian day,PhyBiom,Sw,ZooBiom +0,72.0,0.0,,0.0 +1,73.0,0.0,,0.0 +2,74.0,0.0,,0.0 +3,75.0,0.0,,0.0 +4,76.0,0.0,,0.0 +5,77.0,0.0,,0.0 +6,78.0,0.0,,0.0 +7,79.0,0.0,,0.0 +8,80.0,0.0,,0.0 +9,81.0,0.0,,0.0 +10,82.0,0.0,,0.0 +11,83.0,0.0,,0.0 +12,84.0,0.0,,0.0 +13,85.0,0.08829921885768073,5388.677645798787,0.10717580038692659 +14,86.0,0.12613880966830002,6194.996465048912,0.09709739400494749 +15,87.0,0.05829723002845536,5391.605711868365,0.08509229182368419 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The raw plankton data ('GRE_raw_plankton_ab_size.csv') +2. The script used to produce a time-averaged plankton data for calibrating the model ('TSM_PlanktonData.py') +3. The time-averaged plankton data ('PlanktData4Calibr.csv') + +

+### A brief description: +We used the averaged (3-year) lake nutrient and plankton data to calibrate the model, based on four results: 1.) total phytoplankton biomass(µM P); 2.) total zooplankton biomass(µM P) ; and 3.) community mean phytoplankton size(µm ESD). For the data transformation, please refer to the supporting information of the related publication of this work. +The common unit considered for the model outputs and the data are: biomass concentration(µM P) and biovolume(µm3) + + +


+*For more detailed descriptions and indications of the symbols herein, please refer to the related publication of this model. + + diff --git a/LakePlankData/TSM_PlanktonData.py b/LakePlankData/TSM_PlanktonData.py new file mode 100644 index 0000000..cf256f1 --- /dev/null +++ b/LakePlankData/TSM_PlanktonData.py @@ -0,0 +1,278 @@ +""" +[Include colonial large species] +Plotting selected plankton data in Greifensee (data source: Eawag) +- annual composite +""" +import seaborn as sns +import matplotlib.pyplot as plt +import numpy as np +import pandas as pd +from matplotlib import cm + +wd = 'your wd' + +#### Selection of zooplantkon data #### +# We chose the more abundant zooplantkon species that are +# 1. mostly herbivores (non-carnivores and consume autotrophs) +# 2. non-predatory species +# p.s. The model does not consider intra-guild predation; there are certain trophic links unable to capture. + +## For phytoplankton, we use only the ROIs and the bio-area data (see flow chart) +phydata = pd.read_csv(wd + '/raw_NPdata.csv', sep=',', + usecols=['date', + 'dinobryon_ROIs', 'dinobryon_area_log10_mm2', + 'uroglena_ROIs', 'uroglena_area_log10_mm2', + 'centric_diatom_ROIs', 'centric_diatom_area_log10_mm2', + 'cryptophyceae_ROIs', 'cryptophyceae_area_log10_mm2', + 'rhodomonas_ROIs', 'rhodomonas_area_log10_mm2', + 'chlorophytes_ROIs', 'chlorophytes_area_log10_mm2']) + +## For zooplankton, we use major axis length and minor axis length for ciliates and major axis length for daphnia +zoodata_used = pd.read_csv(wd + '/raw_NPdata.csv', sep=',', + usecols=['date', 'daphnia_ROIs', 'daphnia_area_log10_mm2', 'daphnia_MaL_mm', 'daphnia_MiL_mm', + 'ciliates_ROIs', 'ciliates_area_log10_mm2', 'ciliates_MaL_mm', 'ciliates_MiL_mm']) + +## set name +physpecies = ['dinobryon', 'uroglena', 'centric_diatom', 'cryptophyceae', 'rhodomonas', 'chlorophytes'] +zoospecies_used = ['daphnia', 'ciliates'] + + +## bio-area unit conversion +def logArea2μmArea(LnArea): + """ + The conversion of raw data from the underwater camera to μm ESD + :param LnArea: log10 cell area (mm2) + :return: μm2 bio-area + """ + mm_sq2μm_sq = 1e6 + return (10 ** LnArea) * mm_sq2μm_sq + + +# adjusting the data units +for i in range(len(physpecies)): + phydata.insert(1 + i, physpecies[i] + '_area_μm2', logArea2μmArea(phydata[physpecies[i] + '_area_log10_mm2'])) + +for i in range(len(zoospecies_used)): + zoodata_used.insert(1 + i, zoospecies_used[i] + '_area_μm2', logArea2μmArea(zoodata_used[zoospecies_used[i] + '_area_log10_mm2'])) + +for i in range(len(zoospecies_used)): + zoodata_used.insert(1+len(zoospecies_used) + i, zoospecies_used[i] + '_MaL_μm', zoodata_used[zoospecies_used[i] + '_MaL_mm'] * 1e3) + +for i in range(len(zoospecies_used)): + zoodata_used.insert(1+len(zoospecies_used)*2 + i, zoospecies_used[i] + '_MiL_μm', zoodata_used[zoospecies_used[i] + '_MiL_mm'] * 1e3) + + + +# The ROIs data refers to region of interest (ROI), it is taken by the underwater imaging camera, and the unit is objects capture or +# detected per second [For details please refer to Merz et al. (2021)] +def ROI_0p5x(roi): + """ + 0p5x is for cells or individuals that are in large size (100μm-7mm). + All phytoplankton >100μm ESD, dinobryon and uroglena, and large zooplankton e.g. daphnia are measured in this magnification. + This linear log-log relationship of transforming ROI to count/mL is verified by field measurement data in Merz et al. (2021). + :param roi: region of interest; basically refer to counts/identification by the camera + :return: count per mL per day + """ + x = 10 ** (0.91 / 1.3) * roi ** (1 / 1.3) + return x + +def ROI_5p0x(roi): + """ + 5p0x is for cells or individuals that are in sMaLler size (~10-150μm). + All phytoplankton <100μm ESD and ciliates are measured in this magnification. + This linear log-log relationship of transforming ROI to count/mL is verified by field measurement data in Merz et al. (2021). + :param roi: region of interest; basically refer to counts/identification by the camera + :return: count per mL per day + """ + x = 10 ** (2.9 / 0.71) * roi ** (1 / 0.71) + return x + + +### converting to phyto abundance +phydata.insert(2, 'dinobryon_count/mL', ROI_0p5x(phydata['dinobryon_ROIs'])) # large phyto +phydata.insert(3, 'uroglena_count/mL', ROI_0p5x(phydata['uroglena_ROIs'])) # large phyto +phydata.insert(4, 'centric_diatom_count/mL', ROI_5p0x(phydata['centric_diatom_ROIs'])) # small cells +phydata.insert(5, 'cryptophyceae_count/mL', ROI_5p0x(phydata['cryptophyceae_ROIs'])) # small cells +phydata.insert(6, 'rhodomonas_count/mL', ROI_5p0x(phydata['rhodomonas_ROIs'])) # small cells +phydata.insert(7, 'chlorophytes_count/mL', ROI_5p0x(phydata['chlorophytes_ROIs'])) # small cells + +zoodata_used.insert(2, 'daphnia_count/mL', ROI_0p5x(zoodata_used['daphnia_ROIs'])) +zoodata_used.insert(4, 'ciliates_count/mL', ROI_5p0x(zoodata_used['ciliates_ROIs'])) + + +### Bio-area to biovolume +def bioArea2Vol(Area): + """ + Based on the scaling provided in Ryabov et al. (2021) + :param Area: + :return: Biovolume (μm3) + """ + v = ((1 / (10**0.25)) * Area) ** (1/0.68) # calibrated + return v + +### Ellipsoidal ciliates +def Length2Vol(aa, bb, cc): + """ + Calculting biovolume assuming ellipsoidal ciliates, following Hillebrand et al. (1999) + :param aa: minor axis length (μm) + :param bb: depth (μm) + :param cc: major axis length (μm) + :return: biovolume (μm3) + """ + v = (np.pi/6) * aa * bb * cc + return v + + +### Deriving phytoplankton biomass +# calculating the biovolume from area using the scaling function from Ryabov et al. (2021) +for i in range(len(physpecies)): + phydata.insert(1 + i, physpecies[i] + '_biov', bioArea2Vol(phydata[physpecies[i] + '_area_μm2'])) + +def mwP_Ind(biov): + """ + This function uses the allometric relationship on P content for each size class (Hillebrand et al. 2022) Fig. 5C + :param biov: input ESD (µm) + :return: µg P count-1 + """ + slope, intercept = 0.88, -2.95 # slope and intercept regressed from P content data of Hillebrand et al. (2022) + # 1. picogram phosphate per cell at a certain cell size + pgPcount = (10 ** intercept) * (biov ** slope) + # 2. microgram phosphorus per cell at a certain cell size + µgP_count = pgPcount * 1e-6 + return µgP_count + + +def Phy_abun2biomass(biov, abun): + """ + Converting phytoplankton abundance of specific size classes to biomass (count mL-1 to µmol P L-1) + :param biov: input biovolume (µm3) + :param abun: abundance (count mL-1) + :return: µmol P L-1 + """ + mwP = 30.973762 # µg/L 1 µg P/l = 1/MW P = 0.032285 µmol/l (https://www.ices.dk/data/tools/Pages/Unit-conversions.aspx) + mL2L = 1e3 + µgP_ind = mwP_Ind(biov) + µmolP_ind = µgP_ind / mwP # from g to mol + µmolP_L = µmolP_ind * (abun * mL2L) + return µmolP_L + +### Deriving zooplankton biomass + +# calculating the biovolume of ciliates +zoodata_used.insert(1, 'ciliates_biov2', Length2Vol(zoodata_used['ciliates_MiL_μm'], zoodata_used['ciliates_MiL_μm']*(2/3), zoodata_used['ciliates_MaL_μm'])) + +def CiliatePcontent_Putt(biov): + """ + Scaling function for ciliate body size and carbon content (Putt and Stoecker 1989) + #(10**0.12) * (v**0.19) + :param biov: input biovolume (µm3) + :return: µmol P ind-1 + """ + Cfactor = 0.19 # pg C um-3 + pg2µg = 1e-6 + mwC = 12.011 + µgC_ind = ((10**0.12) * biov * Cfactor) * pg2µg + µmolC_ind = µgC_ind / mwC + C2P_ratio = 100 # a mean from 80-120 of Golz et al. (2015) - assuming redfield ratio for carbon to phosphate transformation - but the range can vary between 80-300 for daphnia + µmolP_ind = µmolC_ind / C2P_ratio + return µmolP_ind + +def Daph_L_W_Schalau(MaL_mm): + """ + Length-weight ratio for daphnia used in the model of Schalau et al. (2008) and sourced from Urabe and Watanabe (1991) & Lynch et al. (1986) + :param MaL_mm: Maximum Axis Length (mm) + :return: µmol P ind-1 + """ + mwC = 12.011 + L = MaL_mm * 0.75 # ref: Ranta et al. (1993); Karpowicz et al. (2020) + µgC_ind = 1.6 * (L**3) + µmolC_ind = µgC_ind / mwC # convert to molar + C2P_ratio = 350 # the mean threshold elemental ratio (to maintain Daphnia growth - good reference for C:P) + # a mean from Hessen (2006) - assuming redfield ratio for carbon to phosphate transformation - + # but the range can vary between 80-385 for daphnia + µmolP_ind = µmolC_ind / C2P_ratio + return µmolP_ind + + + +## phytoplankton total biomasses +for i in range(len(physpecies)): + phydata.insert(1 + i, physpecies[i] + '_biomass', Phy_abun2biomass(phydata[physpecies[i] + '_biov'], phydata[physpecies[i] + '_count/mL'])) +phydata.insert(1, 'Phy_TB', phydata.loc[:, ['dinobryon_biomass', 'uroglena_biomass', 'centric_diatom_biomass', 'cryptophyceae_biomass', + 'rhodomonas_biomass', 'chlorophytes_biomass']].sum(axis=1)) + +## zooplankton total biomasses +zoodata_used.insert(1, 'daphnia_biomass', Daph_L_W_Schalau(zoodata_used['daphnia_MaL_mm']) * zoodata_used['daphnia_count/mL'] * 1e3) +zoodata_used.insert(2, 'ciliates_biomass', CiliatePcontent_Putt(zoodata_used['ciliates_biov2']) * zoodata_used['ciliates_count/mL'] * 1e3) + +zoodata_used.insert(1, 'Zoo_TB', zoodata_used.loc[:, ['daphnia_biomass', 'ciliates_biomass']].sum(axis=1)) + + + +### biomass weighted-mean biovolume +def WMeanSize(biom, biov): + """ + ab = abundance of a specific size class; s = that size class (i.e. size array) + axis=1 because the result data array is in the size of array[days, size groups, nut, mix] + """ + return np.nansum(biom * biov, axis=1) / np.nansum(biom, axis=1) + # return np.nansum(biom * np.log10(biov), axis=1) / np.nansum(biom, axis=1) + +npBiom = phydata.loc[:, ['dinobryon_biomass', 'uroglena_biomass', 'centric_diatom_biomass', 'cryptophyceae_biomass', + 'rhodomonas_biomass', 'chlorophytes_biomass']].to_numpy() +npBiov = phydata.loc[:, ['dinobryon_biov', 'uroglena_biov', 'centric_diatom_biov', 'cryptophyceae_biov', 'rhodomonas_biov', + 'chlorophytes_biov']].to_numpy() + +Sw_df = pd.DataFrame(WMeanSize(npBiom, npBiov), columns=['Sw']) + + +### Add julian date stamps +import datetime + +def datestdtojd(stddate): + """ + source: https://rafatieppo.github.io/post/2018_12_01_juliandate/ + :param stddate: standard date for input + :return: + """ + fmt = '%Y-%m-%d' + sdtdate = datetime.datetime.strptime(stddate, fmt) + sdtdate = sdtdate.timetuple() + jdate = sdtdate.tm_yday + return jdate + + +jday = np.array([]) +for i in range(len(phydata)): + jday = np.append(jday, datestdtojd(phydata['date'][i])) + +phydata.insert(1, 'Julian day', pd.DataFrame(jday)) +zoodata_used.insert(1, 'Julian day', pd.DataFrame(jday)) +Sw_df.insert(1, 'Julian day', pd.DataFrame(jday)) + + +phydata['year'] = pd.DatetimeIndex(phydata['date']).year +phy_median = phydata.groupby(['Julian day'], as_index=False)['Phy_TB'].median().to_numpy() +phy_mean = phydata.groupby(['Julian day'], as_index=False)['Phy_TB'].mean().to_numpy() + + +Sw_df['year'] = pd.DatetimeIndex(phydata['date']).year +Sw_median = Sw_df.groupby(['Julian day'], as_index=False)['Sw'].median().to_numpy() +Sw_mean = Sw_df.groupby(['Julian day'], as_index=False)['Sw'].mean().to_numpy() + + +## export to csv +PhyTB_arr = phydata.loc[:, ['dinobryon_biomass', 'uroglena_biomass', 'centric_diatom_biomass', 'cryptophyceae_biomass', + 'rhodomonas_biomass', 'chlorophytes_biomass']].to_numpy() +PhyBiov_arr = phydata.loc[:, ['dinobryon_biov', 'uroglena_biov', 'centric_diatom_biov', 'cryptophyceae_biov', 'rhodomonas_biov', + 'chlorophytes_biov']].to_numpy() + + +plankdata = np.column_stack((Sw_df['Julian day'].to_numpy(), phydata['Phy_TB'].to_numpy(), Sw_df['Sw'].to_numpy(), + zoodata_used['Zoo_TB'].to_numpy())) +plankdata = pd.DataFrame(plankdata) +plankdata.columns = ['Julian day', 'PhyBiom', 'Sw', 'ZooBiom'] + + +plankdata.to_csv(wd + "/PlankData4Calibr.csv") + diff --git a/LakePlankData/raw_NPdata.csv b/LakePlankData/raw_NPdata.csv new file mode 100644 index 0000000..811ffe1 --- /dev/null +++ b/LakePlankData/raw_NPdata.csv @@ -0,0 +1,1391 @@ +,date,Julian day,phosphate_ug,dinobryon_ROIs,dinobryon_area_log10_mm2,uroglena_ROIs,uroglena_area_log10_mm2,centric_diatom_ROIs,centric_diatom_area_log10_mm2,cryptophyceae_ROIs,cryptophyceae_area_log10_mm2,rhodomonas_ROIs,rhodomonas_area_log10_mm2,chlorophytes_ROIs,chlorophytes_area_log10_mm2,daphnia_ROIs,daphnia_area_log10_mm2,daphnia_MaL_mm,daphnia_MiL_mm,ciliates_ROIs,ciliates_area_log10_mm2,ciliates_MaL_mm,ciliates_MiL_mm +0,2019-03-13,72.0,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA +1,2019-03-14,73.0,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA +2,2019-03-15,74.0,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA +3,2019-03-16,75.0,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA +4,2019-03-17,76.0,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA +5,2019-03-18,77.0,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA 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+1389,2022-12-31,365.0,10.7195225,0.0025,-3.04686775886764,0.00625,-1.42746100426497,0.01784722,-2.95776520569826,0.020277774,-3.3634594558677,0.01229167,-3.81793674889522,0.001736111,-3.72487876289943,0.13875,-0.656255437076182,0.870542839781374,0.446985506933019,0.0024305556,-2.93733927712455,0.0528326871140166,0.0358469266686687 diff --git a/Models/FinalMod/FinalMod_Sbm.py b/Models/FinalMod/FinalMod_Sbm.py new file mode 100644 index 0000000..a3c1bc2 --- /dev/null +++ b/Models/FinalMod/FinalMod_Sbm.py @@ -0,0 +1,294 @@ +import pdb + +import numpy as np +from scipy.integrate import odeint + + +class SizeModLogspace: + """ + Size-based model + Model has multiple groups of phytoplankton, two groups of zooplankton in different sizes, one nutrient source, + and a detritus community. + + Model assumption: + - thermal response of the phytoplankton follows a unimodal curve adapted from Norberg (2004) + - the maximum growth of phytoplankton follows an allometric relationship taken from data compilations of Edwards et al. (2012) + - phytoplankton nutrient uptake follows Michelis-Menton kinetics + - the half-saturation constant of the uptake kinetics derived from a community mean value and is not size-dependent + - phytoplankton are grazed by size-selective zooplankton, small phytoplankton are grazed more intensively + - zooplankton graze on a wide size-feeding range; small zooplankton has a narrower range than large zooplankton in absolute values + - zooplankton grazing is scaled by a Q10 factor + ------- + Flexible parameters: + - n0 + - prey tolerance + - P size range + - Z size range + - no. of P size classes + - no. of years for model running + + Fixed parameters: + - Community mean Kn + - Allometric parameters for Mu + - Allometric parameters for Topt + - Allometric parameters for Imax + - Allometric parameters for grazing size preference + - Model params + """ + + def __init__(self, mld, par, sst, dmdt, N0, minP=0, maxP=np.log10(200), numP=15, minZ=20, maxZ=600, numZ=2, numYears=5, + Zsmall0=6.25e-4, Zlarge0=6.25e-4, D0=6.25e-4, Mz2S0=0, Mz2L0=0, + Pmax=1.1, Kpar=0.1, alpha=0.02, Mz=0.1, Mp=0.1, Mz2=0.34, + Ieff=0.75, beta=0.69, Kp=0.19, Rem=0.15, k=0.1, + mu_alpha=-0.36, mu_beta=10 ** 0.69, Kn=0.06, + sig_T=12.5, topt=13, graz_Q10=2.8, #sig_T=12.5, topt=16.5 + graz_alpha=-0.28, graz_beta=23, ops_alpha=0.7, ops_beta=0.45, + SizeTol=[0.435, 0.6]): + self.mld = mld + self.par = par # photosynethically activated radiation (E*m^-2*d^-1) + self.sst = sst # sea surface temperature/lake surface water temperature (LSWT) + self.dmdt = dmdt # dmdt + self.N0 = N0 # Initial nutrient concentrations (µmol P*L^-1) + self.minP = minP # min. size of P size range + self.maxP = maxP # max. size of P size range + self.numP = numP # number of phytoplankton size class + self.minZ = minZ # min. size of Z size range + self.maxZ = maxZ # max. size of Z size range + self.numZ = numZ # number of zooplankton size class + self.numYears = numYears # Number of years for model run + self.Zsmall0 = Zsmall0 # Initial Zsmall concentration (µmol P*L^-1) + self.Zlarge0 = Zlarge0 # Initial Zlarge concentration (µmol P*L^-1) + self.D0 = D0 # Initial detritus concentration (µmol P*L^-1) + self.Ps0 = np.repeat(6.25e-4, self.numP, axis=0) # Initial P concentration (µmol P*L^-1) + self.muP0 = np.repeat(0, self.numP, axis=0) # Initial concentration for growth fluxes (µmol P*L^-1) + self._2ZS0 = np.repeat(0, self.numP, axis=0) # Initial concentration for Z1 grazing fluxes (µmol P*L^-1) + self._2ZL0 = np.repeat(0, self.numP, axis=0) # Initial concentration for Z2 grazing fluxes (µmol P*L^-1) + self.Mz2S0 = Mz2S0 + self.Mz2L0 = Mz2L0 + self.Pmax = Pmax # Max photosynthesis rate + self.Kpar = Kpar # Water attenuation coefficient + self.alpha = alpha # Initial slope of P-I curve + self.Mz = Mz # Natural mortality - Zooplankton + self.Mp = Mp # Natural mortality - Phytoplankton + self.Mz2 = Mz2 # Mortality from upper predators + self.Ieff = Ieff # Ingestion efficiency + self.beta = beta # Assimlation efficiency + self.Kp = Kp # Phytoplankton half-saturation constant (µmol P*L^-1) + self.Rem = Rem # Remineralization rate (day^-1) + self.k = k # Cross thermocline mixing factor (m/day) + self.mu_alpha = mu_alpha # Slope of allometric max. uptk rate + self.mu_beta = mu_beta # Intercept of allometric max. uptk rate + self.Kn = Kn # nutrient half-saturation constant for phytoplankton + self.sig_T = sig_T # community mean thermal tolerance breadth width as per Thomas et al. (2015) + self.topt = topt # optimal growth temperature + self.graz_alpha = graz_alpha # Slope of allometric max. grazing rate (day^-1) + self.graz_beta = graz_beta # Intercept of allometric max.grazing rate (day^-1) + self.ops_alpha = ops_alpha # Slope of allometric optimum prey size + self.ops_beta = ops_beta # Intercept of allometric optimum prey size + self.SizeTol = SizeTol # Prey size tolerance (should be an array) + self.graz_Q10 = graz_Q10 # Q10 temperature for grazing + self.init_con = np.concatenate(([self.N0[0]], # N0 + [self.Zsmall0], # Zsmall0 + [self.Zlarge0], # Zlarge0 + [self.D0], # D0 + [self.Ps0], # Ps0 + [self.muP0], + [self._2ZS0], + [self._2ZL0], + [self.Mz2S0], + [self.Mz2L0]), axis=None) + self.t_array = np.arange(0, 365 * self.numYears) # Time array + self.Psize_array = np.logspace(self.minP, self.maxP, num=self.numP, base=10) # Size array for phytoplankton + self.Zsize_array = np.linspace(self.minZ, self.maxZ, self.numZ) # Size array for zooplankton + self.solution = odeint(self.AlloNPsZD, self.init_con, self.t_array, rtol=1.e-10, atol=1.e-10) #, hmax=1, hmin=1) + + def Vol2ESD(self, v): # Vol2ESD(1) = 1.2407 + esd = ((v * 6) / np.pi) ** (1 / 3) + return esd + + def Allo_mumax(self, PhySize): + return self.mu_beta * ((PhySize / self.Vol2ESD(1)) ** self.mu_alpha) + + def NU(self, nut): + """ + Michelis-Menton uptake + :param nut: + :return: + """ + return nut / (nut + self.Kn) + + def temp_dependence(self, time): + """ + Eppley-Norberg formulation + :param time: timestep to derive temperature + :return: + """ + b_eppley = 0.0633 + thermtol = (1 - ((time - self.topt) / self.sig_T) ** 2) * np.exp(b_eppley * time) + return thermtol + + def LightLim(self, I, Z): + """ + Light limitation function on photosynthesis based on Smith's function, + illustrated by a P-I curve + """ + I0 = I + Iz = I0 * np.exp(-self.Kpar * Z) + LL = (((self.Pmax / (self.Kpar * Z)) * np.log((self.alpha * I0 + np.sqrt((self.Pmax ** 2) + + (self.alpha * I0) ** 2)) / ((self.alpha * Iz) + + np.sqrt(self.Pmax ** 2 + (self.alpha * Iz) ** 2))))) + return LL + + def Imax_Q10(self, time): + """ + Q10 method based on Sherman et al. (2016) Global Biogeochemical Cycles, 30(4) + ----------------------------------------------------------------------------------- + T0: reference temperature, adopted as 303.15K (30 degree Celcius) + Q10: the factor change in growth rate for a 10 degree change in temperature + :param time: timestep + :return: size- and temperature- dependent grazing rates + """ + ref_temp = 15 # reference temperature + # G0 = 0.57 # (marine zooplankton: Sherman et al., 2016):: we use size-dependent grazing rates + # Q10 = 1.47 # (marine zooplankton: Sherman et al., 2016) + # Q10 = 2.4 # Durbin and Durbin (1992) + # Q10 = 3.9 # Kiørboe et al. (1982) + # Q10 = 2.8 # Hansen et al. (1997) & Gosselain et al. (1996) + return self.graz_Q10 ** ((time - ref_temp) / 10) + + def AlloImax(self, ZooSize, time): + """ + Max. ingestion rate also depends on the size of the zooplankton + ---------- + graz_alpha = -0.4 # Hansen et al. 1994, Banas, 2011 + graz_beta = 26 # Hansen et al. 1994, Banas, 2011 [day^-1] + """ + imax = self.graz_beta * ((ZooSize / 1) ** self.graz_alpha) + return self.Imax_Q10(time) * imax + + def AllogpP(self, PhySize, ZooSize, SizeTol): + """ + Selected zooplankton size class of 10 & 200[µm] + """ + OPS = self.ops_beta * ((ZooSize / 1) ** self.ops_alpha) # µm ESD + gpP = np.exp(-((np.log10(PhySize) - np.log10(OPS)) / SizeTol) ** 2) + return gpP + + def AlloGraz(self, PhySize, ZooSize, Pi, SizeTol, denom, time): + """ + PhySize = Size class/array of phytoplankton population; + ZooSize = Size class/array of zooplankton population; + Pi = Phytoplankton biomass + """ + graz = self.AlloImax(ZooSize, time) * ((self.AllogpP(PhySize, ZooSize, SizeTol) * Pi) / (self.Kp + denom)) + return graz + + def mixing(self, time): + """k refers to the cross thermocline mixing factor""" + return (self.k + max(self.dmdt[time], 0.)) / self.mld[time] + + def AlloNPsZD(self, y, t): + """ + A size-based trophic model with multiple phytoplankton and zooplankton size class + ---------- + y: array of initial conditions of state variables (var) + t: time array + """ + # Initialization + N = y[0] + Zsmall = y[1] + Zlarge = y[2] + D = y[3] + Ps = y[4:4+self.numP*1] + flux_muP = y[4+self.numP*1:4+self.numP*2] + flux_2ZS = y[4+self.numP*2:4+self.numP*3] + flux_2ZL = y[4 + self.numP * 3:4 + self.numP * 4] + Mz2_ZS = y[4 + self.numP * 4 + 0] + Mz2_ZL = y[4 + self.numP * 4 + 1] + var = np.zeros(len(y)) + t = int(t) + + # non-P dependent equations + """ + Zsmall = specialist, narrower size tolerance factor; + Zlarge = generalist, wider size tolerance factor. + """ + Graz_denomZsmall = np.sum(self.AllogpP(self.Psize_array, self.Zsize_array[0], self.SizeTol[0]) * Ps) + Graz_denomZlarge = np.sum(self.AllogpP(self.Psize_array, self.Zsize_array[1], self.SizeTol[1]) * Ps) + Mz2_ZS = self.Mz2 * (Zsmall ** 2) + Mz2_ZL = self.Mz2 * (Zlarge ** 2) + + # [dNdt] + var[0] = (self.Rem * D # Remineration + + self.mixing(t) * (self.N0[t] - N)) # MixingN + + # [dZ1dt] + var[1] = (- self.Mz * Zsmall # Natural mortality Z1 + - Mz2_ZS # density-dependent top predator grazing Z1 + - (self.dmdt[t] / self.mld[t]) * Zsmall) # Mixing loss Z1 + + # [dZ2dt] + var[2] = (- self.Mz * Zlarge # Natural mortality Z2 + - Mz2_ZL # Top predator grazing Z2 + - (self.dmdt[t] / self.mld[t]) * Zlarge) # Mixing loss Z2 + + # [dDdt] + var[3] = (self.Mz * (Zsmall + Zlarge) # MortalityZsmall+Zlarge + - self.Rem * D # Remineration + - self.mixing(t) * D) # Mixing loss D + + # P-dependent (loop) + for i in range(len(Ps)): + """ + Psize = Size class/array of phytoplankton population; + """ + P = Ps[i] # define P in the loop + Psize = self.Psize_array[i] # define Psize in the loop + flux_muP = (self.Allo_mumax(Psize) * self.temp_dependence(self.sst[t])) * self.NU(N) * self.LightLim(self.par[t], self.mld[t]) * P + # flux_mu_temp = self.temp_dependence(self.sst[t]) + # flux_mu_nut = self.NU(N) + flux_2ZS = self.beta * self.Ieff * self.AlloGraz(Psize, self.Zsize_array[0], P, self.SizeTol[0], Graz_denomZsmall, self.sst[t]) * Zsmall + flux_2ZL = self.beta * self.Ieff * self.AlloGraz(Psize, self.Zsize_array[1], P, self.SizeTol[1], Graz_denomZlarge, self.sst[t]) * Zlarge + + # [dNdt] + var[0] = (var[0] + - flux_muP + + (self.beta * (1. - self.Ieff) * self.AlloGraz(Psize, self.Zsize_array[0], P, self.SizeTol[0], Graz_denomZsmall, self.sst[t])) * Zsmall + # Excretion from grazing(Zsmall)) + + (self.beta * (1. - self.Ieff) * self.AlloGraz(Psize, self.Zsize_array[1], P, self.SizeTol[1], Graz_denomZlarge, self.sst[t])) * Zlarge) + # Excretion from grazing(Zlarge)) + + # [dZ1dt] + var[1] = (var[1] + + flux_2ZS) # GrazingP from Zsmall + + # [dZ2dt] + var[2] = (var[2] + + flux_2ZL) # GrazingP from Zlarge + + # [dDdt] + var[3] = (var[3] + + ((1. - self.beta) * self.AlloGraz(Psize, self.Zsize_array[0], P, self.SizeTol[0], Graz_denomZsmall, self.sst[t])) * Zsmall # SloppyfeedP - Zsmall + + ((1. - self.beta) * self.AlloGraz(Psize, self.Zsize_array[1], P, self.SizeTol[1], Graz_denomZlarge, self.sst[t])) * Zlarge # SloppyfeedP - Zlarge + + self.Mp * P) + + # [dPsdt] + var[4 + i] = (var[4 + i] + + flux_muP # Uptk + - self.Mp * P # MortalityP + - self.AlloGraz(Psize, self.Zsize_array[0], P, self.SizeTol[0], Graz_denomZsmall, self.sst[t]) * Zsmall # GrazingP from Zsmall + - self.AlloGraz(Psize, self.Zsize_array[1], P, self.SizeTol[1], Graz_denomZlarge, self.sst[t]) * Zlarge # GrazingP from Zlarge + - self.mixing(t) * P) # Mixing + + # growth fluxes + var[4 + self.numP*1 + i] = var[4 + self.numP*1 + i] + flux_muP + + # grazing fluxes + var[4 + self.numP*2 + i] = var[4 + self.numP*2 + i] + flux_2ZS + var[4 + self.numP*3 + i] = var[4 + self.numP*3 + i] + flux_2ZL + + # predatory fluxes + var[4 + self.numP*4 + 0] = Mz2_ZS + var[4 + self.numP * 4 + 1] = Mz2_ZL + #pdb.set_trace() + return var diff --git a/Models/FinalMod/FinalMod_proj.py b/Models/FinalMod/FinalMod_proj.py new file mode 100644 index 0000000..bda8489 --- /dev/null +++ b/Models/FinalMod/FinalMod_proj.py @@ -0,0 +1,103 @@ +import numpy as np +import time + +import pandas as pd +import xarray as xr +from scipy.interpolate import make_interp_spline + +Pnum = 10 # specify the nos of phytoplankton size groups +Ynum = 10 # no. of modeling year +mod_name = 'Mod_proj' + +# Import forcing data +wd = 'wd' + +LWST = np.genfromtxt(wd+'ForcData_Temp.csv', delimiter=',') +PAR = np.genfromtxt(wd+'ForcData_PAR.csv', delimiter=',') +MLD = np.genfromtxt(wd+'ForcData_MLD.csv', delimiter=',') + +""" +Interpolation +""" +LWST_spl = make_interp_spline(LWST[:, 0], LWST[:, 1], k=3) +LWST_spl = LWST_spl(np.arange(365)) + +PAR_spl = make_interp_spline(PAR[:, 0], PAR[:, 1], k=3) +PAR_spl = PAR_spl(np.arange(365)) + +from scipy.interpolate import PchipInterpolator +MLD_pchip_spl = PchipInterpolator(MLD[:, 0], MLD[:, 1], axis=0) +MLD_pchip_spl = MLD_pchip_spl(np.arange(365)) +MLD_pchip_spl[364] = MLD_pchip_spl[0] + + +""" +dmdt +""" +dmdt = np.zeros((365)) +dmdt[0:364] = np.diff(MLD_pchip_spl) # dmdt (364,) +dmdt[364] = dmdt[0] + +####### +## Setting up temperature increase for different RCP scenarios +temp_incr = [0, 1.4, 2.5, 4.2] +LWST_rcp = np.zeros((365, len(temp_incr))) + +for i in range(len(temp_incr)): + LWST_rcp[:, i] = LWST_spl + temp_incr[i] + + +####### + +LWST_run = np.tile(LWST_rcp, (Ynum, 1)) # change this line for RCP scenarios +PAR_run = np.tile(PAR_spl, Ynum) +mld_run = np.tile(MLD_pchip_spl, Ynum) # multiplicating physical forcing arrays +dmdt_run = np.tile(dmdt, Ynum) + +N0 = np.repeat(0.75, Ynum*365) + +sol = np.zeros((Ynum*365, Pnum + 4, len(temp_incr))) # time; no. var; RCP scenarios + + +from FinalMod_Sbm import SizeModLogspace + +# Run solution +starttime = time.ctime() # save it for documentation purposes +print(mod_name, str(Pnum), "start:", starttime) +start = time.time() # start the timer + +for i in range(len(temp_incr)): + sol[:, :, i] = SizeModLogspace(mld=mld_run, par=PAR_run, sst=LWST_run[:, i], dmdt=dmdt_run, N0=N0, numP=Pnum, + numYears=Ynum).solution + +# Complete +end = time.time() # stop the timer +endtime = time.ctime() # save it for documentation purposes +print(mod_name, str(Pnum), "complete:", endtime) +runtime = (end - start) / 3600 # calculate run time (hour) +print(mod_name, str(Pnum), "run time(hour):", runtime) +print(mod_name, str(Pnum), "run time(day):", runtime/24) + + +# Storing output +out = xr.Dataset( + {'Nut': (['time', 'RCP'], sol[:, 0, :]), + 'Zoo': (['time', 'ZooSize', 'RCP'], sol[:, 1:3, :]), + 'Phy': (['time', 'PhySize', 'RCP'], sol[:, 4:4+Pnum*1, :])}, + coords={'time': np.arange(Ynum*365), + 'ZooSize': [20, 600], + 'PhySize': np.logspace(0, np.log10(150), Pnum), + 'RCP': [0, 1.4, 2.5, 4.2]}, + attrs={'Title': 'This file contains sol output with different nutrient and mixing regimes', + 'No. phytoplankton size group': Pnum, + 'LWST units': 'Degree celcius', + 'PAR units': 'Ein m$^{-2}$ d$^{-1}$', + 'MLD units': 'Meters', + 'Variable units': 'µmol P L$^{-1}$', + 'Size units': 'µm ESD', + 'Phyto size range': '1 - 200', + 'Zoo size range': '20 - 600'}) +out.to_netcdf(wd + 'output_proj.nc') # export + + + diff --git a/Models/FinalMod/FinalMod_run.py b/Models/FinalMod/FinalMod_run.py new file mode 100644 index 0000000..498c021 --- /dev/null +++ b/Models/FinalMod/FinalMod_run.py @@ -0,0 +1,87 @@ +import numpy as np +import time + +import pandas as pd +import xarray as xr +from scipy.interpolate import make_interp_spline + +Pnum = 10 # specify the nos of phytoplankton size groups +Ynum = 10 # no. of modelling year +mod_name = 'Mod' + +# Import forcing data +wd = 'wd' + +LWST = np.genfromtxt(wd+'/ForcData_Temp.csv', delimiter=',') +PAR = np.genfromtxt(wd+'/ForcData_PAR.csv', delimiter=',') +MLD = np.genfromtxt(wd+'/ForcData_MLD.csv', delimiter=',') + +""" +Interpolation +""" +LWST_spl = make_interp_spline(LWST[:, 0], LWST[:, 1], k=3) +LWST_spl = LWST_spl(np.arange(365)) + +PAR_spl = make_interp_spline(PAR[:, 0], PAR[:, 1], k=3) +PAR_spl = PAR_spl(np.arange(365)) + +from scipy.interpolate import PchipInterpolator +MLD_pchip_spl = PchipInterpolator(MLD[:, 0], MLD[:, 1], axis=0) +MLD_pchip_spl = MLD_pchip_spl(np.arange(365)) +MLD_pchip_spl[364] = MLD_pchip_spl[0] + + +""" +dmdt +""" +dmdt = np.zeros((365)) +dmdt[0:364] = np.diff(MLD_pchip_spl) # dmdt (364,) +dmdt[364] = dmdt[0] + + +LWST_run = np.tile(LWST_spl, Ynum) # change this line for RCP scenarios +PAR_run = np.tile(PAR_spl, Ynum) +mld_run = np.tile(MLD_pchip_spl, Ynum) # multiplicating physical forcing arrays +dmdt_run = np.tile(dmdt, Ynum) + +N0 = np.repeat(0.75, Ynum*365) + +from FinalMod_Sbm import SizeModLogspace + +# Run solution +starttime = time.ctime() # save it for documentation purposes +print(mod_name, str(Pnum), "start:", starttime) +start = time.time() # start the timer + +sol = SizeModLogspace(mld=mld_run, par=PAR_run, sst=LWST_run, dmdt=dmdt_run, N0=N0, numP=Pnum, numYears=Ynum).solution #, graz_beta=23, + +# Complete +end = time.time() # stop the timer +endtime = time.ctime() # save it for documentation purposes +print(mod_name, str(Pnum), "complete:", endtime) +runtime = (end - start) / 3600 # calculate run time (hour) +print(mod_name, str(Pnum), "run time(hour):", runtime) +print(mod_name, str(Pnum), "run time(day):", runtime/24) + + +# Storing output +out = xr.Dataset( + {'Nut': (['time'], sol[:, 0]), + 'Zoo': (['time', 'ZooSize'], sol[:, 1:3]), + 'Phy': (['time', 'PhySize'], sol[:, 4+Pnum*0:4+Pnum*1]), + 'mu': (['time', 'PhySize'], sol[:, 4+Pnum*1:4+Pnum*2]), + 'grazS': (['time', 'PhySize'], sol[:, 4+Pnum*2:4+Pnum*3]), + 'grazL': (['time', 'PhySize'], sol[:, 4 + Pnum * 3:4 + Pnum * 4])}, + coords={'time': np.arange(Ynum*365), + 'ZooSize': [20, 600], + 'PhySize': np.logspace(0, np.log10(200), Pnum)}, + attrs={'Title': 'This file contains sol output with different nutrient and mixing regimes', + 'No. phytoplankton size group': Pnum, + 'LWST units': 'Degree celcius', + 'PAR units': 'Ein m$^{-2}$ d$^{-1}$', + 'MLD units': 'Meters', + 'Variable units': 'µmol P L$^{-1}$', + 'Size units': 'µm ESD', + 'Phyto size range': '1 - 200', + 'Zoo size range': '20 - 600'}) +out.to_netcdf(wd + 'output.nc') # export diff --git a/Models/FinalMod/README.md b/Models/FinalMod/README.md new file mode 100644 index 0000000..c9f9476 --- /dev/null +++ b/Models/FinalMod/README.md @@ -0,0 +1,47 @@ +To run the model, one needs the model script 'FinalMod_Sbm.py' and the model run script 'FinalMod_run.py'. +

+ +#### FinalMod_Sbm.py +This is the file containing the size-based NPZD model. The default parameter values are coded in the model. + + +

+#### FinalMod_run.py +In the run script, one could adjust the number of year and of phytoplankton size classes according to their own preferences. +```` +Pnum = 10 # specify the nos of phytoplankton size groups +Ynum = 10 # no. of modelling year +```` + +To change model parameter values from the default values, one enters their preferred values in below lines. +```` +sol = SizeModLogspace(mld=mld_run, par=PAR_run, sst=LWST_run, dmdt=dmdt_run, N0=N0, numP=Pnum, numYears=Ynum).solution +```` +For example, if one wants to change remineralization rate to 0.5, please input it as +```` +sol = SizeModLogspace(mld=mld_run, par=PAR_run, sst=LWST_run, dmdt=dmdt_run, N0=N0, numP=Pnum, numYears=Ynum, Rem=0.5).solution +```` +or if one wants to change the parameters that determine the allometric relationships for $\mu_{max}$ i.e. $\alpha_{\mu_{max}}$ to 0.25, +```` +sol = SizeModLogspace(mld=mld_run, par=PAR_run, sst=LWST_run, dmdt=dmdt_run, N0=N0, numP=Pnum, numYears=Ynum, mu_alpha=0.25).solution +```` + +The coding name for the parameters can be found in FinalMod_Sbm.py. + + + +

+#### FinalMod_proj.py +In this script one can run a number of projection sceanrios, i.e. linear (or, non-linear depending on the input forcing) increase in temperature. +If one wants to configure the increase in temperature by their own preferred values, or adjust the number of scenarios, please change at the below line: +```` +temp_incr = [0, 1.4, 2.5, 4.2] +```` + +




+* Shall there be any queries or difficulties in conducting the runs, please feel free to reach out at: sto@constructor.university + + + + + diff --git a/Models/TheoMod/README.md b/Models/TheoMod/README.md deleted file mode 100644 index 8e672fb..0000000 --- a/Models/TheoMod/README.md +++ /dev/null @@ -1,17 +0,0 @@ -Theoretical model is set up with constant nutrient input, similar to a chemostat type model with other environmental forcing like the irradiance and the temperature. Nutrient is required to input with a forcing array in the model. - -The model output is a multi-dimensional array, containing the solutions for every time step. The model solution includes the below variables: -1. One nutrient; -2. Two zooplankton of different sizes; -3. One detritus; -4. _N_ classes of phytoplankton in different sizes; -5. Total growth from phytoplankton; -6. Grazing from small zooplankton; -7. Grazing from large zooplankton; -8. Temperature dependence for phytoplankton growth; and -9. Nutrient limitation for phytoplankton growth. - -The model solution contains all variable fluxes for environmental conditions as below: -- Nutrient levels (oligotrophic, eutrophic, and hypertrophic) -- Grazing regimes (nanoflagellate+daphnia, ciliates+daphnia, and copepods+daphnia) -- Grazing strategies (non-daphnia zooplankton as a specialist or as a generalist) diff --git a/Models/TheoMod/TheoMod_run.py b/Models/TheoMod/TheoMod_run.py deleted file mode 100644 index ffb61ab..0000000 --- a/Models/TheoMod/TheoMod_run.py +++ /dev/null @@ -1,81 +0,0 @@ -import os -import numpy as np -import time -import xarray as xr -from scipy.interpolate import make_interp_spline - -Pnum = 30 # specify the nos of phytoplankton size groups -Ynum = 10 # no. of modeling year - -# Import forcing data -wd = '/Users/szewing/Desktop/PhD_work/3. ThermalTrait/TempSizeMod_TSM' # '/people/home/sto/SizeMod' -os.chdir(wd) - -# Temperature and PAR data -LWST_CTD = np.genfromtxt('Forcing/TempForc_CTD.csv', delimiter=',') -# LWST_8 = np.genfromtxt('Forcing/TempForc.csv', delimiter=',') -nSSI = np.genfromtxt('Forcing/nSSI_13p_syn.csv', delimiter=',') -MLD = np.genfromtxt('Forcing/MLDForc_Theoretical.csv', delimiter=',') - -for a in range(8): # To synchonized the initial and end forcing value - nSSI[0, a + 1] = nSSI[12, a + 1] - - -# Converting nSSI into PAR -def nSSI2PAR(netSSI): - """ - This function is to convert nSSI (W m-2) into PAR (Ein m-2 d-1) - PAR is a term used to describle radiation in wavelengths usedful for photosynthesis [1] - PAR is generally accepted to be wavelengths between 400 and 700 nm [1] - Procedure: - 1. extr = extraction factor (only about 45% of the nSSI is in the 400-700nm range, Howell et al. 1983) - 2. conv = conversion factor from W m-2 to Ein m-2 d-1 (Lampert and Sommer, 2007, pp.20)** - ** see PAR_UnitConversion.docx - """ - extr = 0.45 - conv = 0.432 - return netSSI * extr * conv - - -PAR = nSSI2PAR(nSSI) -PAR[:, 0] = nSSI[:, 0] - -# Creating forcing curves -PAR_spl = make_interp_spline(PAR[:, 0], PAR[:, 5], k=2) -PAR_spl = PAR_spl(np.arange(365)) -PAR_spl[364] = PAR_spl[0] - -# generate dmdt arrays -dmdt = np.zeros(365) -dmdt[0:364] = np.diff(MLD[:]) -dmdt[364] = dmdt[0] - -MLD_run = np.tile(MLD, Ynum) -dmdt_run = np.tile(dmdt, Ynum) -LWST_CTD_spl = np.tile(LWST_CTD, Ynum) -PAR_spl = np.tile(PAR_spl, Ynum) - -# Runs - loop -N0_list = np.array([0.01, 0.1, 1]) # equivalent to 0.03, 0.3, 3 µmol PO4 L-1 ( x 95 to convert to µg) -Z1_size = np.array([5, 20, 150]) -Z1_GrazStrtgy = np.array([0.2, 0.5]) # specialist or generalist -######################################################## -sol = np.zeros((Ynum*365, 4 + Pnum + (5*Pnum), len(N0_list), len(Z1_size), len(Z1_GrazStrtgy))) - -mod_name = 'TSM_flux_theor' + str(Ynum) + 'yr' - -from TheoMod import SizeModLogspace - -# Run solution -starttime = time.ctime() # save it for documentation purposes -print(mod_name, "start:", starttime) -start = time.time() # start the timer -for i in range(len(N0_list)): # nutrient level - for j in range(len(Z1_size)): - for k in range(len(Z1_GrazStrtgy)): - sol[:, :, i, j, k] = SizeModLogspace(mld=MLD_run, par=PAR_spl, sst=LWST_CTD_spl, dmdt=dmdt_run, N0=N0_list[i], - numP=Pnum, numYears=Ynum, minZ=Z1_size[j], SizeTol=[Z1_GrazStrtgy[k], 0.5]).solution - -end = time.time() # stop the timer -endtime = time.ctime() # save it for documentation purposes -print(mod_name, "complete:", endtime) diff --git a/Models/TheoMod/TheoMod_v1.0.py b/Models/TheoMod/TheoMod_v1.0.py deleted file mode 100644 index edd3902..0000000 --- a/Models/TheoMod/TheoMod_v1.0.py +++ /dev/null @@ -1,317 +0,0 @@ -import numpy as np -from scipy.integrate import odeint - - -class SizeModLogspace: - """ - Size-based model under the assumption of allometric relationships on growth and grazing. - ------- - Model has multiple groups of phytoplankton, 2 groups of zooplankton in different sizes, - one nutrient source and a detritus state variable. - ------- - Flexible parameters: - - n0 - - prey tolerance - - P size range - - Z size range - - no. of P size classes - - no. of years for model running - - Fixed parameters: - - Allometric parameters for Kn - - Allometric parameters for Mu - - Allometric parameters for Topt - - Allometric parameters for Imax - - Allometric parameters for Popt - - Model params - """ - - def __init__(self, mld, par, sst, dmdt, minP=0., maxP=np.log10(200), numP=3, minZ=5, maxZ=400, numZ=2, numYears=5, - N0=0.1, Zsmall0=0.01, Zlarge0=0.01, D0=0.01, - Pmax=1.1, Kpar=0.1, alpha=0.15*0.432, Mz=0.1, Mp=0.15, Mz2=0.34, immigration=1e-4, - Ieff=0.75, beta=0.69, Kp=3, Rem=0.6, k=0.1, - mu_alpha=-0.36, mu_beta=10 ** 0.69, Kpo4_alpha=0.53, Kpo4_beta=10 ** -1.5, - graz_alpha=-0.4, graz_beta=26, ops_alpha=0.56, ops_beta=0.65, topt_alpha=-0.11, topt_beta=34.5, - SizeTol=[0.2, 0.5], graz_Q10=3, sig_T=15, vectorize=True): # graz_Q10=2, - self.mld = mld - self.par = par # photosynethically activated radiation (E*m^-2*d^-1) - self.sst = sst # sea surface temperature/lake surface water temperature (LSWT) - self.dmdt = dmdt # dmdt - self.minP = minP # min. size of P size range - self.maxP = maxP # max. size of P size range - self.numP = numP # number of phytoplankton size class - self.minZ = minZ # min. size of Z size range - self.maxZ = maxZ # max. size of Z size range - self.numZ = numZ # number of zooplankton size class - self.numYears = numYears # Number of years for model run - self.N0 = N0 # Initial nutrient concentrations (mmol N*m^-3) - self.Zsmall0 = Zsmall0 # Initial Zsmall concentration (mmol N*m^-3) - self.Zlarge0 = Zlarge0 # Initial Zlarge concentration (mmol N*m^-3) - self.D0 = D0 # Initial detritus concentration (mmol N*m^-3) - self.Ps0 = np.repeat(0.01, self.numP, axis=0) # Initial P concentration (mmol N*m^-3) - self.Pmax = Pmax # Max photosynthesis rate - self.Kpar = Kpar # Water attenuation coefficient - self.alpha = alpha # Initial slope of P-I curve - self.Mz = Mz # Natural mortality - Zooplankton - self.Mp = Mp # Natural mortality - Phytoplankton - self.Mz2 = Mz2 # Mortality from upper predators - self.immigration = immigration # exogeneous - self.Ieff = Ieff # Ingestion efficiency - self.beta = beta # Assimlation efficiency - self.Kp = Kp # Phytoplankton half-saturation constant (mmol*m^-3) - self.Rem = Rem # Remineralization rate (day^-1) - self.k = k # Cross thermocline mixing factor (m/day) - self.mu_alpha = mu_alpha # Slope of allometric max. uptk rate - self.mu_beta = mu_beta # Intercept of allometric max. uptk rate - self.Kpo4_alpha = Kpo4_alpha # Slope of allometric half-saturation constant - self.Kpo4_beta = Kpo4_beta # Intercept of allometric half-saturation constant - self.graz_alpha = graz_alpha # Slope of allometric max. grazing rate (day^-1) - self.graz_beta = graz_beta # Intercept of allometric max.grazing rate (day^-1) - self.ops_alpha = ops_alpha # Slope of allometric optimum prey size - self.ops_beta = ops_beta # Intercept of allometric optimum prey size - self.SizeTol = SizeTol # Prey size tolerance (should be an array) - self.sig_T = sig_T # community mean thermal tolerance breadth width as per Thomas et al. (2015) - self.topt_alpha = topt_alpha # Slope of allometric optimal growth temperature - self.topt_beta = topt_beta # Intercept of allometric optimal growth temperature - self.graz_Q10 = graz_Q10 # Q10 temperature for grazing - self._vectorize = vectorize - self.Fluxes0 = np.zeros(self.numP * 5) - self.init_con = np.concatenate(([self.N0], # N0 - [self.Zsmall0], # Zsmall0 - [self.Zlarge0], # Zlarge0 - [self.D0], # D0 - [self.Ps0], # Ps0 - [self.Fluxes0]), # Growth and grazing fluxes - axis=None) # Ps0 - self.t_array = np.arange(0, 365 * self.numYears) # Time array - self.Psize_array = np.logspace(self.minP, self.maxP, num=self.numP, base=10) # Size array for phytoplankton - self.Zsize_array = np.linspace(self.minZ, self.maxZ, self.numZ) # Size array for zooplankton - self.solution = odeint(self.AlloNPsZD, self.init_con, self.t_array, rtol=1.e-10, atol=1.e-10, hmax=1.e16, hmin=1.e-16) - - def Vol2ESD(self, v): # Vol2ESD(1) = 1.2407 - esd = ((v * 6) / np.pi) ** (1 / 3) - return esd - - def Allo_mumax(self, PhySize): - return self.mu_beta * ((PhySize / self.Vol2ESD(1)) ** self.mu_alpha) - - def Allo_NU(self, nut, PhySize): - Kpo4_scal = self.Kpo4_beta * ((PhySize / self.Vol2ESD(1)) ** self.Kpo4_alpha) # allometric function for half-saturation - return nut / (nut + Kpo4_scal) - - def Allo_Topt(self, PhySize): - return self.topt_beta * ((PhySize / 1) ** self.topt_alpha) - - def temp_dependence(self, time, topt): - """ - Eppley-Norberg formulation - :param topt: optimal growth temperature obtained from Allo_Topt - :param time: timestep to derive temperature - :return: - """ - thermtol = 1 - ((time - topt) / self.sig_T) ** 2 - return thermtol - - def LightLim(self, I, Z): - """ - Light limitation function on photosynthesis based on Smith's function, - illustrated by a P-I curve - """ - I0 = I - Iz = I0 * np.exp(-self.Kpar * Z) - LL = (((self.Pmax / (self.Kpar * Z)) * - np.log((self.alpha * I0 + np.sqrt((self.Pmax ** 2) + (self.alpha * I0) ** 2)) / - ((self.alpha * Iz) + np.sqrt(self.Pmax ** 2 + (self.alpha * Iz) ** 2))))) - return LL - - def Imax_Q10(self, time): - """ - Q10 method based on Sherman et al. (2016) Global Biogeochemical Cycles, 30(4) - ----------------------------------------------------------------------------------- - T0: reference temperature, adopted as 303.15K (30 degree Celcius) - Q10: the factor change in growth rate for a 10 degree change in temperature - :param time: timestep - :return: size- and temperature- dependent grazing rates - """ - ref_temp = 10 # reference temperature - # G0 = 0.57 # (marine zooplankton: Sherman et al., 2016):: we use size-dependent grazing rates - # Q10 = 1.47 # (marine zooplankton: Sherman et al., 2016) - # Q10 = 2.4 # Durbin and Durbin (1992) - # Q10 = 3.9 # Kiørboe et al. (1982) - # Q10 = 2.8 # Hansen et al. (1997) & Gosselain et al. (1996) - return self.graz_Q10 ** ((time - ref_temp) / 10) - - def AlloImax(self, ZooSize, time): - """ - Max. ingestion rate also depends on the size of the zooplankton - ---------- - graz_alpha = -0.4 # Hansen et al. 1994, Banas, 2011 - graz_beta = 26 # Hansen et al. 1994, Banas, 2011 [day^-1] - """ - return self.graz_beta * ((ZooSize / 1) ** self.graz_alpha) * self.Imax_Q10(time) - - def AllogpP(self, PhySize, ZooSize, SizeTol): - """ - Selected zooplankton size class of 10 & 200[µm] - """ - OPS = self.ops_beta * ((ZooSize / 1) ** self.ops_alpha) # µm ESD - gpP = np.exp(-((np.log10(PhySize) - np.log10(OPS)) / SizeTol) ** 2) - return gpP - - def AlloGraz(self, PhySize, ZooSize, Pi, SizeTol, denom, time): - """ - PhySize = Size class/array of phytoplankton population; - ZooSize = Size class/array of zooplankton population; - Pi = Phytoplankton biomass - """ - graz = self.AlloImax(ZooSize, time) * ((self.AllogpP(PhySize, ZooSize, SizeTol) * Pi) / (self.Kp + denom)) - return graz - - def mixing(self, time): - """k refers to the cross thermocline mixing factor""" - return (self.k + max(self.dmdt[time], 0.)) / self.mld[time] - - def AlloNPsZD(self, y, t): - """ - A size-based trophic model with multiple phytoplankton and zooplankton size class - ---------- - y: array of initial conditions of state variables (var) - t: time array - """ - # Initialization - N = y[0] - Zsmall = y[1] # copepod nauplii or - Zlarge = y[2] # cladocerans or rotifera - D = y[3] - Ps = y[4:4 + self.numP] - var = np.zeros(len(y)) - t = int(t) - - # non-P dependent equations - """ - Zsmall = specialist, narrower size tolerance factor; - Zlarge = generalist, wider size tolerance factor. - """ - Graz_denomZsmall = np.sum(self.AllogpP(self.Psize_array, self.Zsize_array[0], self.SizeTol[0]) * Ps) - Graz_denomZlarge = np.sum(self.AllogpP(self.Psize_array, self.Zsize_array[1], self.SizeTol[1]) * Ps) - - if self._vectorize: - Pgrowth = self.Allo_mumax(self.Psize_array) * (self.temp_dependence(self.sst[t], self.Allo_Topt(self.Psize_array)) * - self.Allo_NU(N, self.Psize_array) * self.LightLim(self.par[t], self.mld[t])) * Ps - Pmortality = self.Mp * Ps - grossGraz_S = (self.AlloGraz(self.Psize_array, self.Zsize_array[0], Ps, self.SizeTol[0], Graz_denomZsmall, self.sst[t]) * Zsmall) - grossGraz_L = (self.AlloGraz(self.Psize_array, self.Zsize_array[1], Ps, self.SizeTol[1], Graz_denomZlarge, self.sst[t]) * Zlarge) - PgrowthTemp = self.temp_dependence(self.sst[t], self.Allo_Topt(self.Psize_array)) * Ps - PgrowthNut = self.Allo_NU(N, self.Psize_array) * Ps - - # [dNdt] - var[0] = (self.Rem * D # Remineralization - + self.mixing(t) * (self.N0 - N) # MixingN - - np.sum(Pgrowth) # Phytoplankton growth - + self.beta * (1. - self.Ieff) * np.sum(grossGraz_S) # Excretion from grazing(Zsmall)) - + self.beta * (1. - self.Ieff) * np.sum(grossGraz_L) # Excretion from grazing(Zlarge)) - ) - - # [dZ1dt] - var[1] = (- self.Mz * Zsmall # Natural mortality Z1 - - self.Mz2 * (Zsmall ** 2) # density-dependent top predator grazing Z1 - - (self.dmdt[t] / self.mld[t]) * Zsmall # Mixing loss Z1 - + self.beta * self.Ieff * np.sum(grossGraz_S) - ) - - # [dZ2dt] - var[1] = (- self.Mz * Zsmall # Natural mortality Z1 - - self.Mz2 * (Zsmall ** 2) # density-dependent top predator grazing Z1 - - (self.dmdt[t] / self.mld[t]) * Zsmall # Mixing loss Z1 - + self.beta * self.Ieff * np.sum(grossGraz_L) - ) - - # [dDdt] - var[3] = (self.Mz * (Zsmall + Zlarge) # MortalityZsmall+Zlarge - + np.sum(Pmortality) - - self.Rem * D # Remineration - - self.mixing(t) * D # Mixing loss D - + (1. - self.beta) * np.sum(grossGraz_S) - + (1. - self.beta) * np.sum(grossGraz_L) - ) - - # [dPsdt] - var[4:4 + self.numP * 1] = (Pgrowth - Pmortality - grossGraz_S - grossGraz_L - self.mixing(t) * Ps) + self.immigration - - # [growth] - var[4 + self.numP * 1: 4 + self.numP * 2] = Pgrowth - - # [grazingS] - var[4 + self.numP * 2: 4 + self.numP * 3] = grossGraz_S - - # [grazingL] - var[4 + self.numP * 3: 4 + self.numP * 4] = grossGraz_L - - var[4 + self.numP * 4: 4 + self.numP * 5] = PgrowthTemp - var[4 + self.numP * 5: 4 + self.numP * 6] = PgrowthNut - - else: - # [dNdt] - var[0] = (self.Rem * D # Remineration - + self.mixing(t) * (self.N0 - N)) # MixingN - - # [dZ1dt] - var[1] = (- self.Mz * Zsmall # Natural mortality Z1 - - self.Mz2 * (Zsmall ** 2) # density-dependent top predator grazing Z1 - - (self.dmdt[t] / self.mld[t]) * Zsmall) # Mixing loss Z1 - - # [dZ2dt] - var[2] = (- self.Mz * Zlarge # Natural mortality Z2 - - self.Mz2 * (Zlarge ** 2) # Top predator grazing Z2 - - (self.dmdt[t] / self.mld[t]) * Zlarge) # Mixing loss Z2 - - # [dDdt] - var[3] = (self.Mz * (Zsmall + Zlarge) # MortalityZsmall+Zlarge - - self.Rem * D # Remineration - - self.mixing(t) * D) # Mixing loss D - - # P-dependent (loop) - for i in range(len(Ps)): # for each P size class - P = Ps[i] # define P in the loop - Psize = self.Psize_array[i] # Size class/array of phytoplankton population - - # [dNdt] - var[0] = (var[0] - - self.Allo_mumax(Psize) * (self.temp_dependence(self.sst[t], self.Allo_Topt(Psize)) * self.Allo_NU(N, Psize) * - self.LightLim(self.par[t], self.mld[t])) * P - + (self.beta * (1. - self.Ieff) * - self.AlloGraz(Psize, self.Zsize_array[0], P, self.SizeTol[0], Graz_denomZsmall, self.sst[t])) * Zsmall # Excretion from grazing(Zsmall)) - + (self.beta * (1. - self.Ieff) * - self.AlloGraz(Psize, self.Zsize_array[1], P, self.SizeTol[1], Graz_denomZlarge, self.sst[t])) * Zlarge) # Excretion from grazing(Zlarge)) - - # [dZ1dt] - var[1] = (var[1] - + (self.beta * self.Ieff * self.AlloGraz(Psize, self.Zsize_array[0], P, self.SizeTol[0], - Graz_denomZsmall, self.sst[t])) * Zsmall) # GrazingP from Zsmall - - # [dZ2dt] - var[2] = (var[2] - + (self.beta * self.Ieff * self.AlloGraz(Psize, self.Zsize_array[1], P, self.SizeTol[1], - Graz_denomZlarge, self.sst[t])) * Zlarge) # GrazingP from Zlarge - - # [dDdt] - var[3] = (var[3] - + ((1. - self.beta) * self.AlloGraz(Psize, self.Zsize_array[0], P, self.SizeTol[0], - Graz_denomZsmall, self.sst[t])) * Zsmall # SloppyfeedP - Zsmall - + ((1. - self.beta) * self.AlloGraz(Psize, self.Zsize_array[1], P, self.SizeTol[1], - Graz_denomZlarge, self.sst[t])) * Zlarge # SloppyfeedP - Zlarge - + self.Mp * P) - - # [dPsdt] - var[4 + i] = (var[4 + i] - + self.Allo_mumax(Psize) * (self.temp_dependence(self.sst[t], self.Allo_Topt(Psize)) * self.Allo_NU(N, Psize) - * self.LightLim(self.par[t], self.mld[t])) * P # Uptk - - self.Mp * P # MortalityP - - self.AlloGraz(Psize, self.Zsize_array[0], P, self.SizeTol[0], - Graz_denomZsmall, self.sst[t]) * Zsmall # GrazingP from Zsmall - - self.AlloGraz(Psize, self.Zsize_array[1], P, self.SizeTol[1], - Graz_denomZlarge, self.sst[t]) * Zlarge # GrazingP from Zlarge - - self.mixing(t) * P # Mixing - + self.immigration) # exogeneous - - return var diff --git a/README.md b/README.md index ef82fa5..a0fa34e 100644 --- a/README.md +++ b/README.md @@ -1,65 +1,102 @@ # TempSizeMod - Temperature-size Model ## Background -Over half of the global freshwater bodies are reporting threats of anthropogenic eutrophication (Ho et al. 2019). Anthropogenic eutrophication has become a major environmental problem since the mid-20th century. It is characterized by excessive input of nutrient in lakes that facilitates an overgrowth of algae in the aquatic ecosystem (Carpenter 2005). Such overabundance of phytoplantkon population can cause multiple harmful effects to the ecosystem like degradation in water quality, harmful algae blooms, and trophic disorganization such as mass fish kills due to the deprivation of oxygen by large-scale degradations of dead algae (Huisman et al. 2018). +Over half of the global lakes are recording increases in lake temperature and reporting rising bloom events (O'Reilley et al. 2015; Ho et al. 2019; Dokulil et al. 2021). Climate warming is increasingly threatening freshwater ecosystem biodiversity (Paerl et al. 2016; Dudgeon 2019; Reid et al. 2019). Temperature change leads to alterations in the temporal dynamics (also known as phenological shifts) and community compositions of phytoplankton (Winder and Sommer 2012; Zohary et al. 2021). It is crucial to understand how temperature drives changes to the assembly and the dynamics of the phytoplankton community (Petchey et al. 1999; Yvon-Durocher et al. 2011; Shurin et al. 2012; Striebel et al. 2016). -Climate warming is another factor increasingly threatening freshwater ecosystem biodiversity (Paerl et al. 2016; Dudgeon 2019; Reid et al. 2019). Phytoplankton is one of the groups at the forefront of rising water temperautures. Temperature change has led to alterations in the temporal dynamics of phytoplankton (i.e. phenological shifts), the community compositions and even the trophic structures. It is crucial to understand how temperature drives changes to the assembly and the dynamics of the phytoplankton community (Petchey et al. 1999; Yvon-Durocher et al. 2011; Striebel et al. 2016). +In the current realm of global environmental change, understanding the effects of temperature on the phytoplankton community is highly important for ecosystem management (Paerl et al. 2016). Nevertheless, in a multi-stressor system, disentangling the effects of temperature on phytoplankton is not easy (Dudgeon 2019). Temperature often interacts with other environmental factors like lake mixing and stratification, lights, and zooplankton grazer (Pomati et al. 2020), thus affecting phytoplankton communities both directly and indirectly (Zohary et al. 2021). This makes predicting plankton dynamics difficult. For instance, the occurrence of phytoplankton blooms is becoming more unpredictable as blooms are found in both cold and warm waters (e.g. Sterner et al. 2020; Reinl et al. 2021, 2023). -In the current realm of global environmental change, understanding the effects of temperature and eutrophication on phytoplankton community is highly important for ecosystem management (Paerl et al. 2016). Nevertheless, in a multi-stressor system, disentangling the effects of temperature on phytoplankotn is not easy (Dudgeon 2019). Temperature often interacts with other environmental factors like nutrient and zooplankton grazer (Pomati et al. 2020), thus contributing to various nonlinear feedbacks to the phytoplankton community and making predictions on community dynamics difficult. For example, the occurrence of phytoplankton blooms is becoming more unpredictable (e.g. Reinl et al. 2021, 2023). +Trait-based models are valuable tools to disentangle possible effects and test the possible mechanisms that water temperature has on phytoplankton (Litchman 2023). Phytoplankton cell size is a master trait and has been widely used in modelling work (Litchman and Klausmeier 2008). Size-based models allow explorations of aggregated community properties such as total biomass and community mean cell size of phytoplankton (e.g. Ward et al. 2012; Acevedo-Trejos et al. 2018; To et al. 2024). They are useful for understanding changes in the macroecological patterns of the phytoplankton community size compositions in response to changes in environmental conditions. +

+## Model description +The model is adapted from the well-established Nutrient-Phytoplankton-Zooplankton-Detritus (NPZD) model (_sensu_ Fasham et al., 1990; Post et al. 2024) incorporated into a size-based framework (e.g., Armstrong 1994; To et al. 2024). The model is differential equation-based and includes one nutrient source, phosphorus $N$, available for uptake by different phytoplankton size classes ($A_i$). The phytoplankton are subject to grazing by two zooplankton of different size groups ($Z_1$, $Z_2$). The growth of phytoplankton is limited by light and nutrients, and is scaled by temperature dependence. The detritus pool, $D$, collects the dead and ungrazed matters, followed by recharging the nutrient pool through remineralization processes. +Phytoplankton growth and zooplankton grazing are size-dependent. The depth of the epilimnion is known as the mixed layer depth (MLD) and is seasonally varying. The blue arrows indicate ecological and biogeochemical processes (solid lines) and physical processes (dashed lines). Environmental forcing to this model is provided by in-situ observations of photosynthetically active radiations (PAR), mixed layer depth (MLD – an indicator of lake mixing), and water temperature (LWST) from Greifensee, Switzerland. To approximate real-world grazing, the grazed material is split into (1) a portion that is not ingested (due to sloppy feeding) and is immediately lost into detritus, (2) a portion that is ingested and assimilated by zooplankton, and (3) an additional portion that is not assimilated after being ingested and quickly excreted into nutrient. The loss of zooplankton to higher order predation is density-dependent and formulated as a quadratic function. We assume that the loss of nutrients from the epilimnion is recharged through changes in MLD by a constant nutrient source, $N_0$, from the hypolimnion. The value of $N_0$ is determined by adjusting the modelled nutrient dynamics with observations and is also prescribed as forcing to the model. -Trait-based models have been applied to investigate the effects of environmental conditions on phytoplankton population dynamics (Litchman 2023). Phytoplantkon cell size is a master trait and has been used widely in modelling works (Litchman and Klausmeier 2008). Size-based models allow explorations on aggregated community properties such as total biomass, community mean cell size, and size variances (e.g. Ward et al. 2012; Acevedo-Trejos et al. 2018). They are useful for understanding changes in the macroecological patterns of the phytoplankton community size compositions (Merico et al. 2009). +

+ Figure1_v3 + + +The model focuses on capturing size-dependent bottom-up and top-down interactions through data-driven allometric relationships between phytoplankton growth and zooplankton grazing. In this study, the allometric parameters are calibrated against lake-specific data within the reported ranges (Hansen et al. 1994, 1997; Edwards et al. 2012). For this study, the model aims at capturing nutrient and plankton dynamics in a Swiss lake, Greifensee, followed by projecting changes to these dynamics based on IPCC reported climate change scenarios (RCPs). Alternatively, the model can be used to study changes in the size compositions of lake phytoplankton communities under varying temperature and nutrient conditions. + +
+## Temperature dependence in the model +The temperature dependence for phytoplankton growth follows a bell-shaped thermal tolerance curve, given by, -## Model description -The model is adapted from the well-established Nutrient-Phytoplankton-Zooplankton-Detritus (NPZD) model (_sensu_ Fasham et al., 1990) incorporated to a size-based framework (e.g. Moloney and Field 1991; Armstrong 1994; Stock et al. 2008). The model (differential equation-based) includes one nutrient source, phosphorus $PO_4^{3-}$, available for uptake by different phytoplankton size classes ($P_i$). The phytoplankton are subject to grazing by two zooplankton of different sizes ($Z_1$, $Z_2$). The phytoplankton growth is limited by light and nutrient, and is scaled by temperature dependence. The detritus pool, $D$, collects the dead and ungrazed matters, follows by recharging the nutrient pool through remineralization processes. -Figure1_v2 +$$E(T) = e^{0.063T} \left[1- \left(\frac{T-T_{opt}}{\sigma_T}\right)^2 \right] $$, +
+where $T$ is the ambient lake water surface temperature (LWST), $T_{opt}$ is the thermal optima that determines the median of the curve, and $\sigma_T$ is the thermal tolerance that determines the width of the curve. In this study, we assume a community mean thermal tolerance curve to all phytoplankton size classes. -The model focuses on capturing size-dependent bottom-up and top-down interactions through data-driven allometric relationships of phytoplankton growth and zooaplankton grazing (Hansen et al. 1994, 1997; Edwards et al. 2012). The model aims at studying changes in the size compositions of lake phytoplankton communities. +The maximum ingestion rates of zooplankton follows a Q10 model such that, the maximum grazing increases with temperature. The equation for the dependence is, +$$I_{max}(S_j^Z) \cdot Q_{10}^{\frac{T-T_{ref}}{10}}$$. +
+The Q10 temperature coefficient here specifies the amount of maximum ingestion rate increases with a 10 $^{\circ}$ C temperature increase. It describes the sensitivity of zooplankton response to a higher temperature. $T$ refers to the lake temperature, while $T_{ref}$ refers to the reference temperature when the rate is equal to the baseline rate (i.e. no effects from temperature). + +

## Allometric relationships in the model -Based on multiple allometric equations, the model produce an ecological trade-off that favour a certain phytoplantkon size classes at different environmental conditions. +The model comprises of three allometric equations. These allometries allow an ecological trade-off to arise in the model based on water temperature throughout the year. The small phytoplantkon can grow faster than the large phytoplankton, but are subject to stronger grazing from the smaller zooplankton, who will selectively graze on the small cells. The allometric relationships considered in the model are: $$\mu_{max}(S_i^P) = \beta_{\mu_{max}}\cdot (S_i^P)^{\alpha_{\mu_{max}}}$$ -$$K_n(S_i^P) = \beta_{K_n}\cdot (S_i^P)^{\alpha_{K_n}}$$ +$$\psi_{max}(S_j^Z) = \beta_{I_{max}}\cdot (S_j^Z)^{\alpha_{\psi_{max}}}$$ + +$$P_{opt}(S_i^P, S_j^Z) = \beta_{P_{opt}}\cdot (S_j^Z)^{\alpha_{P_{opt}}}$$ -$$T_{opt}(S_i^P) = \beta_{T_{opt}}\cdot (S_i^P)^{\alpha_{T_{opt}}}$$ +
+representing, respectively, maximum growth rate, $\mu_{max}(S_i^P)$, for phytoplankton size class $i$, and maximum ingestion rate, $I_{max}(S_j^Z)$, and optimal prey size, $P_{opt}(S_i^P, S_j^Z)$, for zooplankton size class $j$. -$$I_{max}(S_j^Z) = \beta_{I_{max}}\cdot (S_j^Z)^{\alpha_{I_{max}}}$$ +

+## Model calibration +We fine-tuned selected parameters against the time-averaged plankton data collected from lake Greifensee, consisting plankton size (bio-area) and abundance (ROI/sec). For details, please refer to the related publication of this model (under review). After calibrating the parameter values, we obtained a best-fit model that reflect the current average state of the lake. -$$P_{opt}(S_i^P, S_j^Z) = \beta_{P_{opt}}\cdot (S_j^Z)^{\alpha_{P_{opt}}}$$ -representing, respectively, maximum growth rate, $\mu_{max}(S_i^P)$, half-saturation for nutrient uptake, $K_n(S_i^P)$, and thermal optima, $T_{opt}(S_i^P)$, for phytoplankton size class $i$, and maximum ingestion rate, $I_{max}(S_j^Z)$, and optimal prey size, $P_{opt}(S_i^P, S_j^Z)$, for zooplankton size class $j$. +

+## Experiments +Using the standard model, we conduct two numerical experiments:
+1. a projection based on Representative Climate Pathways (RCPs) issued by IPCC +2. a sensitivity analysis for the two thermal traits, $T_{opt}$ and $\sigma_T$ in different warming (i.e., RCP by IPCC) scenarios +## Supplementary tests +- a sensitivity test for the model parameters for the standard model run +- a sensitivity run for varying lake mixing parameters for the worst warming scenario +For details, please refer to the related publication of this model (under review). +





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Hydrobiologia, 848(1), 143–155. https://doi.org/10.1007/s10750-020-04246-6 diff --git a/Results/Proj.nc b/Results/Proj.nc new file mode 100644 index 0000000..6c91157 Binary files /dev/null and b/Results/Proj.nc differ diff --git a/Results/Readme.md b/Results/Readme.md new file mode 100644 index 0000000..4d72ddc --- /dev/null +++ b/Results/Readme.md @@ -0,0 +1,63 @@ +Here contains two sets of model results, one for the projection of future RCP scenarios ('Proj.nc') and one for sensitivity test ('Sensit.nc') over thermal traits (i.e. thermal optima and thermal tolerance) in the standard and RCP scenarios. + + +----------------------- Proj.nc -----------------------\ +This file stores the output data from the projection, and is saved as a multi-dimensional dataset in a netCDF file. +The dataset contains nutrient fluxes ('Nut'), phytoplankton biomass ('Phy'; $P_i$, $i$=1,2,..,10) and zooplankton biomass ('Zoo'; $Z_j$, $j$=1,2) data of each size class from day 3285 to day 3650, on the 10th year of the simulation. This is a time range after the spin-up stage of the model. + +To extract the data, one could use the netCDF4 library in python (https://unidata.github.io/netcdf4-python/) + +```` +wd = '/YourWorkingDirectory' + +import netCDF4 +out = netCDF4.Dataset(wd+'/Proj.nc') # output file +Phy = out.variables['Phy'][:] +Zoo = out.variables['Zoo'][:] +Nut = out.variables['Nut'][:] +```` + +The coordinates (dimensions) of the 'Phy' dataset are as below:\ +'time': '365 days',\ +'PhySize': '10 phytoplankton size classes ranged from 1 to 200µm ESD',\ +'RCP': '4 different climate change scenarios considered by IPCC: RCP 2.6; RCP 6.0; and RCP 8.5'\ +\ +The coordinates (dimensions) of the 'Zoo' dataset are as below:\ +'time': '365 days',\ +'ZooSize': '2 zooplankton size classes at 20 and 600µm ESD',\ +'RCP': '4 different climate change scenarios considered by IPCC: RCP 2.6; RCP 6.0; and RCP 8.5'\ +\ +The coordinates (dimensions) of the 'Nut' dataset are as below:\ +'time': '365 days',\ +'RCP': '4 different climate change scenarios considered by IPCC: RCP 2.6; RCP 6.0; and RCP 8.5'\ + +\ +\ +----------------------- Sensit.nc -----------------------\ +This file stores the output data from the sensitivity test, and is saved as a multi-dimensional dataset in a netCDF file. +The dataset contains nutrient fluxes ('Nut'), phytoplankton biomass ('Phy'; $P_i$, $i$=1,2,..,10) and zooplankton biomass ('Zoo'; $Z_j$, $j$=1,2) data of each size class from day 0 to day 3650. For analyses, we used data from the last year, after the model is spinned-up, hence, day 3285 to 3650. +```` +wd = '/YourWorkingDirectory' + +import netCDF4 +out = netCDF4.Dataset(wd+'/Sensit.nc') # output file +Phy = out.variables['Phy'][:] +Zoo = out.variables['Zoo'][:] +Nut = out.variables['Nut'][:] +```` +The coordinates (dimensions) of the 'Phy' dataset are as below:\ +'time': '365 days',\ +'PhySize': '10 phytoplankton size classes ranged from 1 to 200µm ESD',\ +'RCP': '4 different climate change scenarios considered by IPCC: RCP 2.6; RCP 6.0; and RCP 8.5',\ +'Sensit': '4 different configurations on thermal traits to test their sensitivities in climate change scenarios considered by IPCC: RCP 2.6; RCP 6.0; and RCP 8.5'\ +\ +The coordinates (dimensions) of the 'Zoo' dataset are as below:\ +'time': '365 days',\ +'ZooSize': '2 zooplankton size classes at 20 and 600µm ESD',\ +'RCP': '4 different climate change scenarios considered by IPCC: RCP 2.6; RCP 6.0; and RCP 8.5',\ +'Sensit': '4 different configurations on thermal traits to test their sensitivities in climate change scenarios considered by IPCC: RCP 2.6; RCP 6.0; and RCP 8.5'\ +\ +The coordinates (dimensions) of the 'Nut' dataset are as below:\ +'time': '365 days',\ +'RCP': '4 different climate change scenarios considered by IPCC: RCP 2.6; RCP 6.0; and RCP 8.5',\ +'Sensit': '4 different configurations on thermal traits to test their sensitivities in climate change scenarios considered by IPCC: RCP 2.6; RCP 6.0; and RCP 8.5'\ diff --git a/Results/Sensit.nc b/Results/Sensit.nc new file mode 100644 index 0000000..d62287d Binary files /dev/null and b/Results/Sensit.nc differ diff --git a/SensitivityRun/LakeMix_futMLD.nc b/SensitivityRun/LakeMix_futMLD.nc new file mode 100644 index 0000000..ba5b416 Binary files /dev/null and b/SensitivityRun/LakeMix_futMLD.nc differ diff --git a/SensitivityRun/LakeMix_k=0.05.nc b/SensitivityRun/LakeMix_k=0.05.nc new file mode 100644 index 0000000..61cde1e Binary files /dev/null and b/SensitivityRun/LakeMix_k=0.05.nc differ diff --git a/SensitivityRun/README.md b/SensitivityRun/README.md new file mode 100644 index 0000000..ef2c928 --- /dev/null +++ b/SensitivityRun/README.md @@ -0,0 +1,28 @@ +This is a sensitivity run for examining how sensitive are the model variables to the changes in lake stratification. This model has a simplified lake stratification dyanmics between the epilimnion and the hypolimnion. It is regulated by two components, the temporal change in mixed layer depth (a forcing function for one year) and the vertical diffusive mixing coefficient (a parameter with a unit of day-1). + +We vary the lake mixing dynamics for the worst climate change scenario of our projection, RCP 8.5, in which the lake water temperature increases by 4.2 ℃ throughout the year. This number is based on literature data that are supplemented in the related publication of this work. Based on the estimation of the median change in stratification period by Woolway et al. (2021), we created a prolonged lake stratification that starts 22 days earlier and ends 11 days later (see below figure). This leads to a longer stratified period of the lake by 33 days. In another case, we reduced the diffusive mixing coefficient by 50%. This parameter determines the strength of nutrient mixing from the hypolimnion into the epilimnion, which is a realistic approximation of nutrient transportations in a lake water column (Peeters et al. 2007). + +Sensit_mix + +


+The future MLD profile can be found in the 'LakeData' named under 'ForcData_futMLD.csv'. +To run this experiment, please import the future MLD profile (1): + +``` +futMLD = np.genfromtxt(wd+'/ForcData_futMLD.csv', delimiter=',') +``` + +or modify the diffusive mixing parameter, $k$ (2) in the line of the model run: + +``` +sol = SizeModLogspace(mld=mld_run, par=PAR_run, sst=LWST_run, dmdt=dmdt_run, N0=N0, numP=Pnum, numYears=Ynum, k=0.05).solution +``` + +
+The results are attached in this folder. More details can be found in the related publication of this work (See front page). + + +







++ Peeters, F., D. Straile, A. Lorke, and D. M. Livingstone. 2007. Earlier onset of the spring phytoplankton bloom in lakes of the temperate zone in a warmer climate. Global Change Biology 13: 1898–1909. doi:10.1111/j.1365-2486.2007.01412.x + ++ Woolway, R. I., S. Sharma, G. A. Weyhenmeyer, and others. 2021. Phenological shifts in lake stratification under climate change. Nat Commun 12: 2318. doi:10.1038/s41467-021-22657-4 diff --git a/SensitivityTest/README.md b/SensitivityTest/README.md new file mode 100644 index 0000000..ad13f9c --- /dev/null +++ b/SensitivityTest/README.md @@ -0,0 +1,50 @@ +The sensitivity test is conducted to estimate the uncertainty of different model parameters on the model results. I selected 14 model parameters, which are neither examined by the sensitivty analysis (i.e., the thermal traits) nor the sensitivty run (i.e., the lake mixing parameters). +For these 14 parameters, I tested ±25% the default parameter values and examined the changes in the model results, i.e., total nutrient concentration (μM P), community biomass of phytoplankton and zooplankton (μM P), and community-weighted mean phytoplankton biovolume (μm3). + +To run this test, we first define a dictionary of the parameters with their default values. +``` +Param = { # these are all default parameter values + 'alpha': 0.02, # Initial slope of P-I curve + 'Pmax': 1.1, # Max photosynthesis rate + 'Kpar': 0.1, # Attenuation-phytoplankton self-shading + 'Mz': 0.1, # Mortality - zooplankton + 'Mp': 0.1, # Mortality - phytoplankton + 'Mz2': 0.34, # Mortality - zooplankton from higher predators + 'Ieff': 0.75, # Ingestion efficiency (sloppy feeding) + 'beta': 0.69, # Assimilation effiency + 'Kp': 0.19, # Phytoplankton half-saturation constant (mmol*m^-3) + 'Rem': 0.15, # Remineralization rate [time lagged for nutrient recharge] + 'k': 0.1, # Cross thermocline mixing factor + 'mu_alpha': -0.36, + 'mu_beta': 10 ** 0.69, + 'Kn': 0.06, + 'graz_Q10': 2.8, + 'graz_alpha': -0.28, + 'graz_beta': 23, + 'ops_alpha': 0.7, + 'ops_beta': 0.45} +``` + +We followed by creating the output arrays + +``` +numParam = len(Param.keys()) +outM25 = np.zeros((365*Ynum, Pnum*4 + 2 + 4, numParam)) #-25% +outP25 = np.zeros((365*Ynum, Pnum*4 + 2 + 4, numParam)) #+25% +``` + +To run the solution, we loop over the parameter values via the dictionary. + +``` +for k, v in enumerate(Param.keys()): + Param[v] = Param[v]*0.75 # change value (+/- 25%) + print('test value', k, v, Param[v]) # check value before run + solM25 = SizeModLogspace(mld=mld_run, par=PAR_run, sst=LWST_run, dmdt=dmdt_run, N0=N0, numP=Pnum, + numYears=Ynum, **Param) + outM25[:, :, k] = solM25.solution[:, :] # store results + Param[v] = Param[v]/0.75 # recover the value in the dictionary + print('default value', k, v, Param[v]) # check value after restoring the value +print(Param.items()) # check the whole dictionary after run +``` + +The results are attached in this folder. More details can be found in the related publication of this work (See front page). diff --git a/SensitivityTest/Sensit_+25%.nc b/SensitivityTest/Sensit_+25%.nc new file mode 100644 index 0000000..851e514 Binary files /dev/null and b/SensitivityTest/Sensit_+25%.nc differ diff --git a/SensitivityTest/Sensit_-25%.nc b/SensitivityTest/Sensit_-25%.nc new file mode 100644 index 0000000..5024424 Binary files /dev/null and b/SensitivityTest/Sensit_-25%.nc differ