Snow model¶
R.A. Collenteur, University of Graz / Eawag, November 2021
In this notebook it is shown how to account for snowfall and smowmelt on groundwater recharge and groundwater levels, using a degree-day snow model. This notebook is work in progress and will be extended in the future.
[1]:
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from scipy.signal import fftconvolve
import pastas as ps
ps.set_log_level("ERROR")
ps.show_versions(numba=True)
Python version: 3.8.2 (default, Mar 25 2020, 11:22:43)
[Clang 4.0.1 (tags/RELEASE_401/final)]
Numpy version: 1.21.2
Scipy version: 1.7.1
Pandas version: 1.3.3
Pastas version: 0.19.0b
Matplotlib version: 3.4.3
numba version: 0.51.2
1. Load data¶
In this notebook we will look at some data for a well near Heby, Sweden. All the meteorological data is taken from the E-OBS database. As can be observed from the temperature time series, the temparature regularly drops below zero in winter. Given this observation, we may expect precipitation to (partially) fall as snow during these periods.
[2]:
head = pd.read_csv("../data/heby_head.csv", index_col=0, parse_dates=True,
squeeze=True)
evap = pd.read_csv("../data/heby_evap.csv", index_col=0, parse_dates=True,
squeeze=True)
prec = pd.read_csv("../data/heby_prec.csv", index_col=0, parse_dates=True,
squeeze=True)
temp = pd.read_csv("../data/heby_temp.csv", index_col=0, parse_dates=True,
squeeze=True)
ps.plots.series(head=head, stresses=[prec, evap, temp]);
2. Make a simple model¶
First we create a simple model with precipitation and potential evaporation as input, using the non-linear FlexModel to compute the recharge flux. We not not yet take snowfall into account, and thus assume all precipitation occurs as snowfall. The model is calibrated and the results are visualized for inspection.
[3]:
# Settings
tmin = "1985" # Needs warmup
tmax = "2010"
[4]:
ml1 = ps.Model(head)
sm1 = ps.RechargeModel(prec, evap, recharge=ps.rch.FlexModel(),
rfunc=ps.Gamma, name="rch")
ml1.add_stressmodel(sm1)
# As the evaporation used is a very rough estimation, vary k_v
ml1.set_parameter("rch_kv", vary=True)
# Solve the Pastas model in two steps
ml1.solve(tmin=tmin, tmax=tmax, noise=False, fit_constant=False, report=False)
ml1.set_parameter("rch_srmax", vary=False)
ml1.solve(tmin=tmin, tmax=tmax, noise=True, fit_constant=False, initial=False)
ml1.plot(figsize=(10,3));
Fit report Head Fit Statistics
=================================================
nfev 39 EVP 45.86
nobs 590 R2 0.46
noise True RMSE 0.13
tmin 1985-01-01 00:00:00 AIC -3259.99
tmax 2010-01-01 00:00:00 BIC -3229.33
freq D Obj 1.15
warmup 3650 days 00:00:00 ___
solver LeastSquares Interp. No
Parameters (7 optimized)
=================================================
optimal stderr initial vary
rch_A 1.087756 ±8.65% 0.767453 True
rch_n 1.295260 ±1.97% 2.214778 True
rch_a 216.934067 ±9.62% 80.852758 True
rch_srmax 14.695434 ±nan% 14.695434 False
rch_lp 0.250000 ±nan% 0.250000 False
rch_ks 14.360124 ±0.40% 20.398394 True
rch_gamma 11.877105 ±1.54% 12.944031 True
rch_kv 1.397010 ±1.00% 1.898142 True
rch_simax 2.000000 ±nan% 2.000000 False
constant_d 77.975073 ±nan% 0.000000 False
noise_alpha 100.761258 ±6.34% 1.000000 True
The model fit with the data is not too bad, but we are clearly missing the highs and lows of the observed groundwater levels. This could have many causes, but in this case we may suspect that the occurence of snowfall and melt impacts the results.
3. Account for snowfall and snow melt¶
A second model is now created that accounts for snowfall and melt through a degree-day snow model (see e.g., Kavetski & Kuczera (2007). To run the model we add the keyword snow=True to the FlexModel and provide a time series of mean daily temperature to the RechargeModel. The temperature time series is used to split the precipitation into snowfall and rainfall.
[5]:
ml2 = ps.Model(head)
sm2 = ps.RechargeModel(prec, evap, recharge=ps.rch.FlexModel(snow=True),
rfunc=ps.Gamma, name="rch", temp=temp)
ml2.add_stressmodel(sm2)
# As the evaporation used is a very rough estimation, vary k_v
ml2.set_parameter("rch_kv", vary=True)
# Solve the Pastas model in two steps
ml2.solve(tmin=tmin, tmax=tmax, noise=False, fit_constant=False, report=False)
ml2.set_parameter("rch_srmax", vary=False)
ml2.solve(tmin=tmin, tmax=tmax, noise=True, fit_constant=False, initial=False)
Fit report Head Fit Statistics
===================================================
nfev 34 EVP 73.24
nobs 590 R2 0.73
noise True RMSE 0.09
tmin 1985-01-01 00:00:00 AIC -3398.34
tmax 2010-01-01 00:00:00 BIC -3358.92
freq D Obj 0.90
warmup 3650 days 00:00:00 ___
solver LeastSquares Interp. No
Parameters (9 optimized)
===================================================
optimal stderr initial vary
rch_A 0.606753 ±4.61% 0.577787 True
rch_n 1.165620 ±1.29% 1.359219 True
rch_a 153.926064 ±5.79% 106.644772 True
rch_srmax 164.065206 ±nan% 164.065206 False
rch_lp 0.250000 ±nan% 0.250000 False
rch_ks 371.272542 ±35.03% 508.921991 True
rch_gamma 17.818537 ±2.97% 18.839531 True
rch_kv 0.697501 ±1.31% 0.724236 True
rch_simax 2.000000 ±nan% 2.000000 False
rch_tt 2.100000 ±3.19% 1.984374 True
rch_k 3.620893 ±3.60% 3.410441 True
constant_d 78.374355 ±nan% 0.000000 False
noise_alpha 56.662416 ±5.12% 1.000000 True
Compare results¶
From the fit_report we can already observe that the model fit improved quite a bit. We can also visualize the results to see how the model improved.
[6]:
ax = ml2.plot(figsize=(10,3));
ml1.simulate().plot(ax=ax)
plt.legend(["Observations", "Model w Snow NSE={:.2f}".format(ml2.stats.nse()),
"Model w/o Snow NSE={:.2f}".format(ml1.stats.nse())], ncol=3)
[6]:
<matplotlib.legend.Legend at 0x7f8a74c18d60>
Extract the water balance (States & Fluxes)¶
[7]:
df = ml2.stressmodels["rch"].get_water_balance(ml2.get_parameters("rch"), tmin=tmin, tmax=tmax)
df.plot(subplots=True, figsize=(10, 10));
References¶
Kavetski, D. and Kuczera, G. (2007). Model smoothing strategies to remove microscale discontinuities and spurious secondary optima in objective functions in hydrological calibration. Water Resources Research, 43(3).