64  Soil moisture drydowns

Keywords

soil moisture, drydown, exponential decay

Soil moisture drydowns refer to the rate at which soil loses its moisture content over time, typically following a rainfall event. The initial rate of moisture loss is typically rapid, slowing down as the soil reaches a lower moisture content. Thus, this process is often described by an exponential decay model.

In this exercise we will extract drydown events from a time series of rootzone soil moisture. Basically, a drydown represents the period of moisture loss between precipitation events. Since in this region small rainfall events don’t usually contribute to appreciable soil moisture recharge, we will set a tolerance level to ignore small rainfall events.

Model description

SWC = A \ e^{-t/\tau} + \theta_{res}

SWC = Soil water content in m^{3}/m^{3}
A = The initial soil water content above \theta_{res} in m^{3}/m^{3} (i.e., SWC = A + \theta_{res} at time t=0)
t = Days since rainfall event
\tau = Constant that modulates the rate at which the soil dries
\theta_{res} = Residual soil water content m^{3}/m^{3}.

# Import modules
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
from pprint import pprint

# Define model using an anonymous lambda function
model = lambda t,tau,A,S_min: A * np.exp(-t/tau) + S_min
xrange = np.arange(30)

# Create figure with example drydowns
plt.figure(figsize=(5,4))

# Rapid decay. Typical of summer, coarse soils, and actively growing vegetation
plt.plot(xrange, model(xrange,5,70,50), color='green')     

# Drydowns during moderate atmospheric demand (spring and fall)
plt.plot(xrange, model(xrange,20,70,50), color='tomato')

# Drydown during low atmospheric demand (winter)
plt.plot(xrange, model(xrange,100,70,50), color='navy')

plt.xlabel('Days since last rainfall')
plt.ylabel('Storage (mm)')
plt.show()

Load dataset

# Load data
df = pd.read_csv('../datasets/kings_creek_2022_2023_daily.csv',parse_dates=['datetime'])
df.head()

	datetime	pressure	tmin	tmax	tavg	rmin	rmax	prcp	srad	wspd	wdir	vpd	vwc_5cm	vwc_20cm	vwc_40cm	soiltemp_5cm	soiltemp_20cm	soiltemp_40cm	battv	discharge
0	2022-01-01	96.838	-14.8	-4.4	-9.60	78.475	98.012	0.25	2.098	5.483	0.969	0.028	0.257	0.307	0.359	2.996	5.392	7.425	8714.833	0.0
1	2022-01-02	97.995	-20.4	-7.2	-13.80	50.543	84.936	0.25	9.756	2.216	2.023	0.072	0.256	0.307	0.358	2.562	4.250	6.692	8890.042	0.0
2	2022-01-03	97.844	-9.4	8.8	-0.30	40.622	82.662	0.50	9.681	2.749	5.667	0.262	0.255	0.307	0.358	2.454	3.917	6.208	8924.833	0.0
3	2022-01-04	96.419	0.1	8.6	4.35	48.326	69.402	0.25	8.379	5.806	2.627	0.363	0.289	0.319	0.357	2.496	3.754	5.842	8838.292	0.0
4	2022-01-05	97.462	-11.1	-2.2	-6.65	50.341	76.828	0.00	5.717	4.207	1.251	0.126	0.313	0.337	0.357	1.688	3.429	5.567	8848.083	0.0

# Add day of the year column
df.insert(1, 'doy', df['datetime'].dt.dayofyear)

# Compute soil water storage in top 50 cm
df['storage'] = df['vwc_5cm']*100 + df['vwc_20cm']*200 + df['vwc_40cm']*200

# Plot timeseries of soil moisture and precipitation
plt.figure(figsize=(8,3))

plt.plot(df['datetime'], df['storage'], color='k', linewidth=1.0)
plt.ylabel('Soil water storage (mm)')

plt.twinx()

plt.plot(df['datetime'], df['prcp'], color='tomato', linewidth=0.5)
plt.ylabel('Precipitation (mm)', color='tomato')

plt.show()

# Find residual soil water storage
storage_min = df['storage'].min()
print(storage_min)

# Define model by forcing minimum storage
model = lambda t,tau,A: A * np.exp(-t/tau) + storage_min

90.80000000000001

Extract drydowns

The loop below scans the storage time series one day at a time:

• Compute the change in storage relative to the previous day.
• If storage decreased (or increased by less than the tolerance, which we treat as a negligible rainfall event), the drydown continues, so we add the day to the current event.
• If storage increased by more than the tolerance, the drydown ends. Events shorter than drydown_min_length days are discarded; longer events are fitted with the exponential model and saved.
• Reset the variables and start looking for the next drydown.

# Iterate over soil moisture timeseries to retrieve drydowns
day_counter = 0
drydown_min_length = 7 # days
tolerance = 1 # mm. Ignore storage increases smaller than this value (small rainfall events)
all_drydowns = []
drydown_event = {'date':[],'storage':[],'doy':[],
                 'days':[],'length':[], 'par':[]}

# We start the loop on the second day
for i in range(1,len(df)):
    delta = df["storage"][i] - df["storage"][i-1]
    
    if delta < tolerance:
        day_counter += 1
        drydown_event['date'].append(df.loc[i,'datetime'])
        drydown_event['storage'].append(df.loc[i,'storage'])
        drydown_event['doy'].append(df.loc[i,'doy'])
        drydown_event['days'].append(day_counter)
        drydown_event['length'] = day_counter

    else:
        # Avoid saving data for short drydowns
        if day_counter < drydown_min_length:
            
            # Reset variables
            day_counter = 0
            drydown_event = {'date':[],'storage':[],'doy':[],
                             'days':[],'length':[], 'par':[]}
            continue
        else:
            
            # Fit model to drydown event
            par_opt, par_cov = curve_fit(model, 
                                         drydown_event['days'], 
                                         drydown_event['storage'])
            drydown_event['par'] = par_opt
            
            # Append current event
            all_drydowns.append(drydown_event)
            
            # Reset variables
            day_counter = 0
            drydown_event = {'date':[],'storage':[],'doy':[],
                             'days':[],'length':[], 'par':[]}

        
print('There are a total of',len(all_drydowns),'drydowns')   

There are a total of 35 drydowns

# Inspect one drydown event
drydown = all_drydowns[8]
print('Start date:', drydown['date'][0].date())
print('Length:', drydown['length'], 'days')
print('Initial storage:', round(drydown['storage'][0], 1), 'mm')
print('Final storage:', round(drydown['storage'][-1], 1), 'mm')
print('Fitted parameters (tau, A):', np.round(drydown['par'], 2))

Start date: 2022-07-03
Length: 22 days
Initial storage: 184.7 mm
Final storage: 104.7 mm
Fitted parameters (tau, A): [ 11.07 107.7 ]

Overlay soil moisture timeseries and extracted drydowns

plt.figure(figsize=(8,3))
plt.plot(df['datetime'], df['storage'], color='k', linewidth=1.0)
for event in all_drydowns:
    plt.plot(event['date'], model(np.asarray(event['days']), *event['par']), '-r')

plt.ylabel('Soil water storage (mm)')
plt.show()