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 version: 1.13.2
Python version: 3.11.12
NumPy version: 2.3.5
Pandas version: 2.3.3
SciPy version: 1.17.0
Matplotlib version: 3.10.8
Numba version: 0.63.1
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=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 Head Fit Statistics
==================================================
nfev 47 EVP 41.95
nobs 590 R2 0.42
noise True RMSE 0.13
tmin 1985-01-01 00:00:00 AICc -3231.61
tmax 2010-01-01 00:00:00 BIC -3201.14
freq D Obj 1.20
freq_obs None ___
warmup 3650 days 00:00:00 Interp. No
solver LeastSquares weights Yes
Parameters (7 optimized)
==================================================
optimal initial vary
rch_A 2.242098 1.358609 True
rch_n 1.364099 3.129693 True
rch_a 192.051364 52.727898 True
rch_srmax 2.620060 2.620060 False
rch_lp 0.250000 0.250000 False
rch_ks 11.529277 102.662189 True
rch_gamma 19.629712 1.121165 True
rch_kv 1.556400 1.999999 True
rch_simax 2.000000 2.000000 False
constant_d 77.792153 0.000000 False
noise_alpha 100.176827 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 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 Head Fit Statistics
==================================================
nfev 41 EVP 67.51
nobs 590 R2 0.68
noise True RMSE 0.10
tmin 1985-01-01 00:00:00 AICc -3388.14
tmax 2010-01-01 00:00:00 BIC -3353.35
freq D Obj 0.92
freq_obs None ___
warmup 3650 days 00:00:00 Interp. No
solver LeastSquares weights Yes
Parameters (8 optimized)
==================================================
optimal initial vary
rch_A 0.733596 0.573522 True
rch_n 1.080971 1.398730 True
rch_a 212.931919 108.625483 True
rch_srmax 159.889166 159.889166 False
rch_lp 0.250000 0.250000 False
rch_ks 527.336423 358.381607 True
rch_gamma 13.413341 18.461413 True
rch_kv 0.647128 0.713615 True
rch_simax 2.000000 2.000000 False
rch_tt 0.000000 0.000000 False
rch_k 0.660382 0.793974 True
constant_d 78.233831 0.000000 False
noise_alpha 71.536749 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.
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 0x70f0ee612590>
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).