Modeling snow#
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.
import matplotlib.pyplot as plt
import pandas as pd
import pastas as ps
ps.set_log_level("ERROR")
ps.show_versions()
Pastas : 2.0.0
Python : 3.14.6
Numpy : 2.4.6
Pandas : 3.0.3
Scipy : 1.18.0
Matplotlib : 3.11.0
Numba : 0.65.1
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 temperature regularly drops below zero in winter. Given this observation, we may expect precipitation to (partially) fall as snow during these periods.
head = pd.read_csv("data/heby_head.csv", index_col=0, parse_dates=True).squeeze()
evap = pd.read_csv("data/heby_evap.csv", index_col=0, parse_dates=True).squeeze()
prec = pd.read_csv("data/heby_prec.csv", index_col=0, parse_dates=True).squeeze()
temp = pd.read_csv("data/heby_temp.csv", index_col=0, parse_dates=True).squeeze()
ps.plots.series(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.
# Settings
tmin = "1985" # Needs warmup
tmax = "2010"
ml1 = ps.Model(head)
sm1 = ps.RechargeModel(
prec, evap, recharge=ps.rch.FlexModel(), rfunc=ps.Gamma(), name="rch"
)
ml1.add_stressmodel(sm1)
# Solve the Pastas model in two steps
ml1.solve(tmin=tmin, tmax=tmax, fit_constant=False, report=False)
ml1.add_noisemodel(ps.ArNoiseModel())
ml1.set_parameter("rch_srmax", vary=False)
ml1.solve(tmin=tmin, tmax=tmax, fit_constant=False, initial=False)
ml1.plot(figsize=(10, 3));
Fit report solver Fit Statistics
==================================================
nfev 33 EVP 38.97
nobs 590 R2 0.39
noise True RMSE 0.13
tmin 1985-01-01 00:00:00 AICc -3230.94
tmax 2010-01-01 00:00:00 BIC -3200.47
freq D Obj nan
freq_obs None ___
warmup 3650 days 00:00:00 Interp. No
Parameters (7 optimized)
==================================================
optimal initial vary
rch_A 1.776658 1.084025 True
rch_n 1.317593 3.104068 True
rch_a 207.152841 53.437882 True
rch_srmax 3.641957 3.641957 False
rch_lp 0.250000 0.250000 False
rch_ks 125.342107 111.823796 True
rch_gamma 15.942870 1.121171 True
rch_kv 1.988227 1.998688 True
rch_simax 2.000000 2.000000 False
constant_d 77.818734 0.000000 False
noise_alpha 109.152141 15.000000 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 occurrence 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.
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)
# Solve the Pastas model in two steps
ml2.solve(tmin=tmin, tmax=tmax, fit_constant=False, report=False)
ml2.add_noisemodel(ps.ArNoiseModel())
ml2.set_parameter("rch_srmax", vary=False)
ml2.solve(tmin=tmin, tmax=tmax, fit_constant=False, initial=False)
Fit report solver Fit Statistics
==================================================
nfev 30 EVP 67.27
nobs 590 R2 0.67
noise True RMSE 0.10
tmin 1985-01-01 00:00:00 AICc -3374.81
tmax 2010-01-01 00:00:00 BIC -3340.02
freq D Obj nan
freq_obs None ___
warmup 3650 days 00:00:00 Interp. No
Parameters (8 optimized)
==================================================
optimal initial vary
rch_A 0.738472 0.577197 True
rch_n 1.125325 1.453819 True
rch_a 203.139985 107.144788 True
rch_srmax 154.512306 154.512306 False
rch_lp 0.250000 0.250000 False
rch_ks 346.746314 183.893295 True
rch_gamma 13.494362 18.173118 True
rch_kv 0.633731 0.705266 True
rch_simax 2.000000 2.000000 False
rch_tt 0.000000 0.000000 False
rch_k 1.000000 1.000034 True
constant_d 78.218979 0.000000 False
noise_alpha 69.999457 15.000000 True
Warnings! (1)
==================================================
Parameter 'rch_k' on lower bound: 1.00e+00
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.
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,
)
<matplotlib.legend.Legend at 0x785aa7fe4980>
Extract the water balance (States & Fluxes)#
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).