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: 1.8.0b
Python version: 3.11.10
NumPy version: 2.0.2
Pandas version: 2.2.3
SciPy version: 1.15.0
Matplotlib version: 3.10.0
Numba version: 0.60.0
DeprecationWarning: As of Pastas 1.5, no noisemodel is added to the pastas Model class by default anymore. To solve your model using a noisemodel, you have to explicitly add a noisemodel to your model before solving. For more information, and how to adapt your code, please see this issue on GitHub: https://github.com/pastas/pastas/issues/735
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 50 EVP 50.15
nobs 590 R2 0.50
noise True RMSE 0.12
tmin 1985-01-01 00:00:00 AICc -3292.15
tmax 2010-01-01 00:00:00 BIC -3261.69
freq D Obj 1.09
warmup 3650 days 00:00:00 ___
solver LeastSquares Interp. No
Parameters (7 optimized)
================================================
optimal initial vary
rch_A 0.793930 0.577011 True
rch_n 1.145045 2.444868 True
rch_a 254.082093 82.680615 True
rch_srmax 123.797696 123.797696 False
rch_lp 0.250000 0.250000 False
rch_ks 1004.502717 207.261970 True
rch_gamma 7.810098 0.404507 True
rch_kv 0.589192 0.893974 True
rch_simax 2.000000 2.000000 False
constant_d 78.069882 0.000000 False
noise_alpha 98.168961 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 32 EVP 54.86
nobs 590 R2 0.55
noise True RMSE 0.11
tmin 1985-01-01 00:00:00 AICc -3339.37
tmax 2010-01-01 00:00:00 BIC -3300.26
freq D Obj 1.00
warmup 3650 days 00:00:00 ___
solver LeastSquares Interp. No
Parameters (9 optimized)
================================================
optimal initial vary
rch_A 0.917927 0.783740 True
rch_n 1.355545 1.553572 True
rch_a 152.613437 110.816491 True
rch_srmax 16.437531 16.437531 False
rch_lp 0.250000 0.250000 False
rch_ks 123.901919 123.314886 True
rch_gamma 8.453966 6.887808 True
rch_kv 1.520016 1.118175 True
rch_simax 2.000000 2.000000 False
rch_tt 1.526904 1.641662 True
rch_k 2.702180 2.990550 True
constant_d 78.013451 0.000000 False
noise_alpha 82.601675 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 0x7f1b254d8550>
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).