# Modelling Surface Energy Balance at an AmeriFlux Site Using SuPy¶

This tutorial aims to demonstrate how to use an advanced land surface model (SuPy, SUEWS in Python) to better understand the surface energy balance (SEB) features by conducting a simulation at an AmeriFlux site. This would be particularly useful after building your own model: as you will learn how sophisticated models could be developed from those simpler ones.

SuPy is a Python-enhanced urban climate model with SUEWS, *Surface Urban Energy and Water Balance Scheme*, as its computation core. More SuPy tutorials are available here.

In this tutorial the workflow to model the surface energy balance (SEB) at a chosen AmeriFlux (AMF) site using SuPy/SUEWS is undertaken. The steps, consist of

[1]:

import matplotlib.pyplot as plt
import supy as sp
import pandas as pd
import numpy as np
from pathlib import Path
%matplotlib inline


## Prepare input data¶

### Site-specific configuration of surface parameters¶

Given pandas.DataFrame as the core data structure of SuPy, all operations, including modification, output, demonstration, etc., on SuPy inputs (df_state_init and df_forcing) can be done using pandas-based functions/methods. Please see SuPy quickstart for methods to do so.

Below we will modify several key properties of the chosen site with appropriate values to run SuPy. First, we copy the df_state_init to have a new DataFrame for manipulation.

[2]:

df_state_init,df_forcing=sp.load_SampleData()
df_state_amf = df_state_init.copy()

2020-07-06 11:24:40,102 - SuPy - INFO - All cache cleared.

[3]:

# site identifier
name_site = 'US-AR1'


Details for determining the proper values of selected physical parameters can be found here.

#### location¶

[4]:

# latitude
df_state_amf.loc[:, 'lat'] = 41.37
# longitude
df_state_amf.loc[:, 'lng'] = -106.24
# altitude
df_state_amf.loc[:, 'alt'] = 611.


#### land cover fraction¶

Land covers in SUEWS

[5]:

# view the surface fraction variable: sfr
df_state_amf.loc[:, 'sfr'] = 0
df_state_amf.loc[:, ('sfr', '(4,)')] = 1
df_state_amf.loc[:, 'sfr']

[5]:

ind_dim (0,) (1,) (2,) (3,) (4,) (5,) (6,)
grid
1 0.0 0.0 0.0 0.0 1.0 0.0 0.0

#### albedo¶

[6]:

# we only set values for grass as the modelled site has a single land cover type: grass.
df_state_amf.albmax_grass = 0.19
df_state_amf.albmin_grass = 0.14

[7]:

# initial albedo value
df_state_amf.loc[:, 'albgrass_id'] = 0.14


#### LAI/phenology¶

[8]:

df_state_amf.filter(like='lai')

[8]:

var laimax laimin laipower laitype laicalcyes lai_id
ind_dim (0,) (1,) (2,) (0,) (1,) (2,) (0, 0) (0, 1) (0, 2) (1, 0) ... (3, 0) (3, 1) (3, 2) (0,) (1,) (2,) 0 (0,) (1,) (2,)
grid
1 5.1 5.5 5.9 4.0 1.0 1.6 0.04 0.04 0.04 0.001 ... 0.0015 0.0015 0.0015 1.0 1.0 1.0 1 4.0 1.0 1.6

1 rows × 25 columns

[9]:

# properties to control vegetation phenology
# you can skip the details for and just set them as provided below

# LAI paramters
df_state_amf.loc[:, ('laimax', '(2,)')] = 1
df_state_amf.loc[:, ('laimin', '(2,)')] = 0.2
# initial LAI
df_state_amf.loc[:, ('lai_id', '(2,)')] = 0.2

# BaseT
df_state_amf.loc[:, ('baset', '(2,)')] = 5
# BaseTe
df_state_amf.loc[:, ('basete', '(2,)')] = 20

# SDDFull
df_state_amf.loc[:, ('sddfull', '(2,)')] = -1000
# GDDFull
df_state_amf.loc[:, ('gddfull', '(2,)')] = 1000


#### surface resistance¶

[10]:

# parameters to model surface resistance
df_state_amf.maxconductance = 18.7
df_state_amf.g1 = 1
df_state_amf.g2 = 104.215
df_state_amf.g3 = 0.424
df_state_amf.g4 = 0.814
df_state_amf.g5 = 36.945
df_state_amf.g6 = 0.025


#### measurement height¶

[11]:

# height where forcing variables are measured/collected
df_state_amf.z = 2.84


#### urban feature¶

[12]:

# disable anthropogenic heat by setting zero population
df_state_amf.popdensdaytime = 0
df_state_amf.popdensnighttime = 0


#### check df_state¶

[13]:

# this procedure is to double-check proper values are set in df_state_amf
sp.check_state(df_state_amf)

2020-07-06 11:24:43,372 - SuPy - INFO - SuPy is validating df_state...
2020-07-06 11:24:43,574 - SuPy - INFO - All checks for df_state passed!


### prepare forcing conditions¶

Here we use the SuPy utility function read_forcing to read in forcing data from an external file in the format of SUEWS input. Also note, this read_forcing utility will also resample the forcing data to a proper temporal resolution to run SuPy/SUEWS, which is usually 5 min (300 s).

#### load and resample forcing data¶

[15]:

# load forcing data from an external file and resample to a resolution of 300 s.
# Note this dataset has been gap-filled.

# this procedure is to double-check proper forcing values are set in df_forcing_amf
_ = sp.check_forcing(df_forcing_amf)

2020-07-06 11:24:44,453 - SuPy - INFO - SuPy is validating df_forcing...
2020-07-06 11:24:46,299 - SuPy - ERROR - Issues found in df_forcing:
kdown should be between [0, 1400] but -1.298 is found at 2010-01-01 00:05:00


The checker detected invalid values in variable kdown: negative incoming solar radiation is found. We then need to fix this as follows:

[16]:

# modify invalid values
df_forcing_amf.kdown = df_forcing_amf.kdown.where(df_forcing_amf.kdown > 0, 0)

[17]:

# check df_forcing again
_ = sp.check_forcing(df_forcing_amf)

2020-07-06 11:24:46,312 - SuPy - INFO - SuPy is validating df_forcing...
2020-07-06 11:24:48,523 - SuPy - INFO - All checks for df_forcing passed!


#### examine forcing data¶

We can examine the forcing data:

[18]:

list_var_forcing = [
"kdown",
"Tair",
"RH",
"pres",
"U",
"rain",
]
dict_var_label = {
"kdown": "Incoming Solar\n Radiation ($\mathrm{W \ m^{-2}}$)",
"Tair": "Air Temperature ($^{\circ}}$C)",
"RH": r"Relative Humidity (%)",
"pres": "Air Pressure (hPa)",
"rain": "Rainfall (mm)",
"U": "Wind Speed (m $\mathrm{s^{-1}}$)",
}
df_plot_forcing_x = (
df_forcing_amf.loc[:, list_var_forcing].copy().shift(-1).dropna(how="any")
)
df_plot_forcing = df_plot_forcing_x.resample("1h").mean()
df_plot_forcing["rain"] = df_plot_forcing_x["rain"].resample("1h").sum()

axes = df_plot_forcing.plot(subplots=True, figsize=(8, 12), legend=False,)
fig = axes[0].figure
fig.tight_layout()
fig.autofmt_xdate(bottom=0.2, rotation=0, ha="center")
for ax, var in zip(axes, list_var_forcing):
_ = ax.set_ylabel(dict_var_label[var])


## Run simulations¶

Once met-forcing (via df_forcing_amf) and initial conditions (via df_state_amf) are loaded in, we call sp.run_supy to conduct a SUEWS simulation, which will return two pandas DataFrames: df_output and df_state_final.

[19]:

df_output, df_state_final = sp.run_supy(df_forcing_amf, df_state_amf)

2020-07-06 11:24:51,973 - SuPy - INFO - ====================
2020-07-06 11:24:51,974 - SuPy - INFO - Simulation period:
2020-07-06 11:24:51,975 - SuPy - INFO -   Start: 2010-01-01 00:05:00
2020-07-06 11:24:51,975 - SuPy - INFO -   End: 2011-01-01 00:00:00
2020-07-06 11:24:51,976 - SuPy - INFO -
2020-07-06 11:24:51,977 - SuPy - INFO - No. of grids: 1
2020-07-06 11:24:51,977 - SuPy - INFO - SuPy is running in serial mode
2020-07-06 11:25:01,975 - SuPy - INFO - Execution time: 10.0 s
2020-07-06 11:25:01,976 - SuPy - INFO - ====================



### df_output¶

df_output is an ensemble output collection of major SUEWS output groups, including:

• SUEWS: the essential SUEWS output variables
• DailyState: variables of daily state information
• snow: snow output variables (effective when snowuse = 1 set in df_state_init)
• RSL: profile of air temperature, humidity and wind speed within roughness sub-layer.

Detailed description of variables in df_output refers to SuPy output

[20]:

df_output.columns.levels[0]

[20]:

Index(['SUEWS', 'snow', 'RSL', 'SOLWEIG', 'DailyState'], dtype='object', name='group')


### df_state_final¶

df_state_final is a DataFrame for holding:

1. all model states if save_state is set to True when calling sp.run_supy (supy may run significantly slower for a large simulations);
2. or, only the final state if save_state is set to False (the default setting) in which mode supy has a similar performance as the standalone compiled SUEWS executable.

Entries in df_state_final have the same data structure as df_state_init and can thus be used for other SUEWS simulations staring at the timestamp as in df_state_final.

Detailed description of variables in df_state_final refers to SuPy output

[21]:

df_state_final.T.head()

[21]:

datetime 2010-01-01 00:05:00 2011-01-01 00:05:00
grid 1 1
var ind_dim
ah_min (0,) 15.0 15.0
(1,) 15.0 15.0
ah_slope_cooling (0,) 2.7 2.7
(1,) 2.7 2.7
ah_slope_heating (0,) 2.7 2.7

## Examine results¶

Thanks to the functionality inherited from pandas and other packages under the PyData stack, compared with the standard SUEWS simulation workflow, supy enables more convenient examination of SUEWS results by statistics calculation, resampling, plotting (and many more).

### Ouptut structure¶

df_output is organised with MultiIndex (grid,timestamp) and (group,varaible) as index and columns, respectively.

[22]:

df_output.head()

[22]:

group SUEWS ... DailyState
var Kdown Kup Ldown Lup Tsurf QN QF QS QH QE ... DensSnow_Paved DensSnow_Bldgs DensSnow_EveTr DensSnow_DecTr DensSnow_Grass DensSnow_BSoil DensSnow_Water a1 a2 a3
grid datetime
1 2010-01-01 00:05:00 0.0 0.0 265.492652 305.638434 -1.593 -40.145783 0.0 -9.668746 -24.387976 1.284400 ... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
2010-01-01 00:10:00 0.0 0.0 265.492652 305.638434 -1.593 -40.145783 0.0 -9.424108 -6.676973 1.618190 ... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
2010-01-01 00:15:00 0.0 0.0 265.492652 307.825865 -1.593 -42.333213 0.0 -0.545992 16.458627 11.833592 ... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
2010-01-01 00:20:00 0.0 0.0 265.492652 307.825865 -1.593 -42.333213 0.0 -0.536225 15.988621 11.830741 ... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
2010-01-01 00:25:00 0.0 0.0 265.492652 307.825865 -1.593 -42.333213 0.0 -0.525680 15.537087 11.827934 ... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN

5 rows × 371 columns

Here we demonstrate several typical scenarios for SUEWS results examination.

The essential SUEWS output collection is extracted as a separate variable for easier processing in the following sections. More advanced slicing techniques are available in pandas documentation.

[23]:

grid = df_state_amf.index[0]
df_output_suews = df_output.loc[grid, 'SUEWS']


### Statistics Calculation¶

We can use .describe() method for a quick overview of the key surface energy balance budgets.

[24]:

df_output_suews.loc[:, ['QN', 'QS', 'QH', 'QE', 'QF']].describe()

[24]:

var QN QS QH QE QF
count 105120.000000 105120.000000 105120.000000 105120.000000 105120.0
mean 118.207887 19.047648 38.349672 62.790798 0.0
std 214.335328 61.955598 85.050755 112.585643 0.0
min -104.566267 -81.170768 -212.925432 -15.483971 0.0
25% -33.437969 -23.174678 -15.992876 0.341017 0.0
50% -1.894385 -2.603727 9.862241 3.042328 0.0
75% 248.960723 52.299898 68.130871 65.272384 0.0
max 749.868243 218.450452 414.514498 559.472107 0.0

### Plotting¶

#### Basic example¶

Plotting is very straightforward via the .plot method bounded with pandas.DataFrame. Note the usage of loc for to slices of the output DataFrame.

[25]:

# a dict for better display variable names
dict_var_disp = {
"QN": "$Q^*$",
"QS": r"$\Delta Q_S$",
"QE": "$Q_E$",
"QH": "$Q_H$",
"QF": "$Q_F$",
"Kdown": r"$K_{\downarrow}$",
"Kup": r"$K_{\uparrow}$",
"Ldown": r"$L_{\downarrow}$",
"Lup": r"$L_{\uparrow}$",
"Rain": "$P$",
"Irr": "$I$",
"Evap": "$E$",
"RO": "$R$",
"TotCh": "$\Delta S$",
}


Peek at the simulation results:

[26]:

grid = df_state_init.index[0]

[27]:

ax_output = (
df_output_suews.loc["2010-06-01":"2010-06-07", ["QN", "QS", "QE", "QH", "QF"]]
.rename(columns=dict_var_disp)
.plot()
)
_ = ax_output.set_xlabel("Date")
_ = ax_output.set_ylabel("Flux ($\mathrm{W \ m^{-2}}$)")
_ = ax_output.legend()


#### Plotting after resampling¶

The suggested runtime/simulation frequency of SUEWS is 300 s, which usually results in a large output and may be over-weighted for storage and analysis. Also, you may feel an apparent slowdown in producing the above figure as a large amount of data were used for the plotting. To slim down the result size for analysis and output, we can resample the default output very easily.

[28]:

rsmp_1d = df_output_suews.resample("1d")
# daily mean values
df_1d_mean = rsmp_1d.mean()
# daily sum values
df_1d_sum = rsmp_1d.sum()


We can then re-examine the above energy balance at hourly scale and plotting will be significantly faster.

[29]:

# energy balance
ax_output = (
df_1d_mean.loc[:, ["QN", "QS", "QE", "QH", "QF"]]
.rename(columns=dict_var_disp)
.plot(figsize=(10, 3), title="Surface Energy Balance",)
)
_ = ax_output.set_xlabel("Date")
_ = ax_output.set_ylabel("Flux ($\mathrm{W \ m^{-2}}$)")
_ = ax_output.legend()


Then we use the hourly results for other analyses.

[30]:

# radiation balance
ax_output = (
df_1d_mean.loc[:, ["QN", "Kdown", "Kup", "Ldown", "Lup"]]
.rename(columns=dict_var_disp)
)
_ = ax_output.set_xlabel("Date")
_ = ax_output.set_ylabel("Flux ($\mathrm{W \ m^{-2}}$)")
_ = ax_output.legend()

[31]:

# water balance
ax_output = (
df_1d_sum.loc[:, ["Rain", "Irr", "Evap", "RO", "TotCh"]]
.rename(columns=dict_var_disp)
.plot(figsize=(10, 3), title="Surface Water Balance",)
)
_ = ax_output.set_xlabel("Date")
_ = ax_output.set_ylabel("Water amount (mm)")
_ = ax_output.legend()


Get an overview of partitioning in energy and water balance at monthly scales:

[32]:

# get a monthly Resampler
df_plot = df_output_suews.copy()
df_plot.index = df_plot.index.set_names("Month")
rsmp_1M = df_plot.shift(-1).dropna(how="all").resample("1M", kind="period")
# mean values
df_1M_mean = rsmp_1M.mean()
# sum values
df_1M_sum = rsmp_1M.sum()

[33]:

# month names
name_mon = [x.strftime("%b") for x in rsmp_1M.groups]
# create subplots showing two panels together
fig, axes = plt.subplots(2, 1, sharex=True)
# surface energy balance
_ = (
df_1M_mean.loc[:, ["QN", "QS", "QE", "QH", "QF"]]
.rename(columns=dict_var_disp)
.plot(
ax=axes[0],  # specify the axis for plotting
figsize=(10, 6),  # specify figure size
title="Surface Energy Balance",
kind="bar",
)
)
# surface water balance
_ = (
df_1M_sum.loc[:, ["Rain", "Irr", "Evap", "RO", "TotCh"]]
.rename(columns=dict_var_disp)
.plot(
ax=axes[1],  # specify the axis for plotting
title="Surface Water Balance",
kind="bar",
)
)

# annotations
_ = axes[0].set_ylabel("Mean Flux ($\mathrm{W \ m^{-2}}$)")
_ = axes[0].legend()
_ = axes[1].set_xlabel("Month")
_ = axes[1].set_ylabel("Total Water Amount (mm)")
_ = axes[1].xaxis.set_ticklabels(name_mon, rotation=0)
_ = axes[1].legend()


### Save results to external files¶

The supy output can be saved as txt files for further analysis using supy function save_supy.

[34]:

list_path_save = sp.save_supy(df_output, df_state_final)

[35]:

for file_out in list_path_save:
print(file_out.name)

1_2010_DailyState.txt
1_2010_SUEWS_60.txt
1_2010_snow_60.txt
1_2010_RSL_60.txt
1_2010_SOLWEIG_60.txt
df_state.csv


## More explorations into simulation results¶

In this section, we will use the simulation results to explore more features revealed by SuPy/SUEWS simulations but unavailable in your simple model.

### Dynamics in rainfall and soil moisture deficit (SMD)¶

[36]:

df_dailystate = (
df_output.loc[grid, "DailyState"].dropna(how="all").resample("1d").mean()
)

[37]:

# daily rainfall
ser_p = df_dailystate.P_day.rename("Rainfall")
ser_smd = df_output_suews.SMD
ser_smd_dmax = ser_smd.resample("1d").max().rename("SMD")

ax = pd.concat([ser_p, ser_smd_dmax], axis=1).plot(secondary_y="SMD", figsize=(9, 4))
_ = ax.set_xlabel("Time (month)")


### Variability in albedo¶

#### How does albedo change over time?¶

[38]:

ser_alb = df_dailystate.AlbGrass
ax = ser_alb.plot()
_ = ax.set_xlabel("Time (month)")


#### How is albedo associated with vegetation phenology?¶

[39]:

ser_lai = df_dailystate.LAI_Grass
pd.concat([ser_lai, ser_alb], axis=1).plot(secondary_y="AlbGrass", figsize=(9, 4))
ax = ser_lai.plot()
_ = ax.set_xlabel("Time (month)")

[39]:

<matplotlib.axes._subplots.AxesSubplot at 0x7f8969449978>

[40]:

ax_alb_lai = df_dailystate[["LAI_Grass", "AlbGrass"]].plot.scatter(
x="LAI_Grass", y="AlbGrass",
)
ax_alb_lai.set_aspect("auto")


### Variability in surface resistance¶

#### How does surface resistance vary over time?¶

[41]:

ser_rs = df_output_suews.RS

• intra-annual
[42]:

ax = ser_rs.resample("1d").median().plot()
_ = ax.set_xlabel("Time (month)")

• intra-daily
[43]:

# a winter day
ax = ser_rs.loc["2010-01-22"].between_time("0830", "1600").plot()
_ = ax.set_xlabel("Time")

[44]:

# a summer day
ax = ser_rs.loc["2010-07-01"].between_time("0530", "1900").plot()
_ = ax.set_xlabel("Time")


#### How is surface resistance associated with other surface properties?¶

[45]:

# SMD
ser_smd = df_output_suews.SMD
df_x = (
pd.concat([ser_smd, ser_rs], axis=1)
.between_time("1000", "1600")
.resample("1d")
.mean()
)
df_x = df_x.loc[df_x.RS < 500]
_ = df_x.plot.scatter(x="SMD", y="RS",)

[46]:

# LAI
df_x = pd.concat(
[ser_lai, ser_rs.between_time("1000", "1600").resample("1d").mean()], axis=1
)
df_x = df_x.loc[df_x.RS < 500]
_ = df_x.plot.scatter(x="LAI_Grass", y="RS",)


#### How is surface resistance dependent on meteorological conditions?¶

[47]:

cmap_sel = plt.cm.get_cmap('RdBu', 12)

[48]:

# solar radiation
# colour by season
ser_kdown = df_forcing_amf.kdown
df_x = pd.concat([ser_kdown, ser_rs], axis=1).between_time('1000', '1600')
df_x = df_x.loc[df_x.RS < 1500]
df_plot = df_x.iloc[::20]
ax = df_plot.plot.scatter(x='kdown',
y='RS',
c=df_plot.index.month,
cmap=cmap_sel,
sharex=False)
fig = ax.figure
_ = fig.axes[1].set_title('month')
fig.tight_layout()

[49]:

# air temperature
ser_ta = df_forcing_amf.Tair
df_x = pd.concat([ser_ta, ser_rs], axis=1).between_time('1000', '1600')
df_x = df_x.loc[df_x.RS < 1500]
df_plot = df_x.iloc[::15]
ax = df_plot.plot.scatter(x='Tair',
y='RS',
c=df_plot.index.month,
cmap=cmap_sel,
sharex=False)
fig = ax.figure
_ = fig.axes[1].set_title('month')
fig.tight_layout()

[50]:

# air humidity
ser_rh = df_forcing_amf.RH
df_x = pd.concat([ser_rh, ser_rs], axis=1).between_time('1000', '1600')
df_x = df_x.loc[df_x.RS < 1500]
df_plot = df_x.iloc[::15]
ax = df_plot.plot.scatter(x='RH',
y='RS',
c=df_plot.index.month,
cmap=cmap_sel,
sharex=False)
fig = ax.figure
_ = fig.axes[1].set_title('month')
fig.tight_layout()

Based on the above plots showing RS vs. met. conditions, explore these relationships again at the intra-daily scales.