Adding river levels

Developed by R.A. Collenteur & D. Brakenhoff

In this example it is shown how to create a Pastas model that not only includes precipitation and evaporation, but also observed river levels. We will consider observed heads that are strongly influenced by river level, based on a visual interpretation of the raw data.

import pandas as pd
import pastas as ps
import matplotlib.pyplot as plt

%matplotlib notebook

ps.show_versions()
ps.set_log_level("INFO")

Python version: 3.7.8 | packaged by conda-forge | (default, Jul 31 2020, 02:37:09)
[Clang 10.0.1 ]
Numpy version: 1.18.5
Scipy version: 1.4.0
Pandas version: 1.1.2
Pastas version: 0.16.0b
Matplotlib version: 3.1.3

1. import and plot data

Before a model is created, it is generally a good idea to try and visually interpret the raw data and think about possible relationship between the time series and hydrological variables. Below the different time series are plotted.

The top plot shows the observed heads, with different observation frequencies and some gaps in the data. Below that the observed river levels, precipitation and evaporation are shown. Especially the river level show a clear relationship with the observed heads. Note however how the range in the river levels is about twice the range in the heads. Based on these observations, we would expect the the final step response of the head to the river level to be around 0.5 [m/m].

oseries = pd.read_csv("../data/nb5_head.csv", parse_dates=True,
                      squeeze=True, index_col=0)
rain = pd.read_csv("../data/nb5_prec.csv", parse_dates=True, squeeze=True,
                   index_col=0)
evap = pd.read_csv("../data/nb5_evap.csv", parse_dates=True, squeeze=True,
                   index_col=0)
waterlevel = pd.read_csv("../data/nb5_riv.csv", parse_dates=True,
                         squeeze=True, index_col=0)

fig, axes = plt.subplots(4,1, figsize=(10, 5), sharex=True)
oseries.plot(ax=axes[0], x_compat=True, legend=True, marker=".", linestyle=" ")
waterlevel.plot(ax=axes[1], x_compat=True, legend=True)
rain.plot(ax=axes[2], x_compat=True, legend=True)
evap.plot(ax=axes[3], x_compat=True, legend=True)
plt.xlim("2000", "2020");

2. Create a timeseries model

First we create a model with precipitation and evaporation as explanatory time series. The results show that precipitation and evaporation can explain part of the fluctuations in the observed heads, but not all of them.

ml = ps.Model(oseries.resample("D").mean().dropna(), name="River")

sm = ps.RechargeModel(rain, evap, rfunc=ps.Exponential, name="recharge")
ml.add_stressmodel(sm)

ml.solve(tmin="2000", tmax="2019-10-29")
ml.plots.results(figsize=(12, 8));

INFO: Cannot determine frequency of series Head: freq=None. The time series is irregular.
INFO: Inferred frequency for time series Prec: freq=D
INFO: Inferred frequency for time series Evap: freq=D

Fit report River                 Fit Statistics
==================================================
nfev     17                     EVP          38.60
nobs     5963                   R2            0.39
noise    True                   RMSE          0.46
tmin     2000-01-27 00:00:00    AIC          -4.31
tmax     2019-10-29 00:00:00    BIC          29.16
freq     D                      Obj          18.34
warmup   3650 days 00:00:00     ___
solver   LeastSquares           Interpolated    No

Parameters (5 were optimized)
==================================================
                optimal   stderr     initial  vary
recharge_A   516.665718  ±39.48%  183.785267  True
recharge_a   217.825010  ±38.80%   10.000000  True
recharge_f    -1.594862  ±19.43%   -1.000000  True
constant_d     8.536652   ±3.12%    8.547142  True
noise_alpha   66.997992  ±14.22%    1.000000  True

Parameter correlations |rho| > 0.5
==================================================
recharge_A recharge_a  0.98
recharge_f constant_d -0.97

3. Adding river water levels

Based on the analysis of the raw data, we expect that the river levels can help to explain the fluctuations in the observed heads. Here, we add a stress model (ps.StressModel) to add the rivers level as an explanatory time series to the model. The model fit is greatly improved, showing that the rivers help in explaining the observed fluctuations in the observed heads. It can also be observed how the response of the head to the river levels is a lot faster than the response to precipitation and evaporation.

w = ps.StressModel(waterlevel, rfunc=ps.One,  name="waterlevel",
                   settings="waterlevel")
ml.add_stressmodel(w)
ml.solve(tmin="2000", tmax="2019-10-29")
axes = ml.plots.results(figsize=(12, 8));
axes[-1].set_xlim(0,10);  # By default, the axes between responses are shared.

INFO: Inferred frequency for time series River: freq=D

Fit report River                  Fit Statistics
===================================================
nfev     20                     EVP           93.39
nobs     5963                   R2             0.93
noise    True                   RMSE           0.15
tmin     2000-01-27 00:00:00    AIC            2.15
tmax     2019-10-29 00:00:00    BIC           42.31
freq     D                      Obj            4.24
warmup   3650 days 00:00:00     ___
solver   LeastSquares           Interpolated     No

Parameters (6 were optimized)
===================================================
                 optimal   stderr     initial  vary
recharge_A    206.754929  ±23.04%  183.785267  True
recharge_a    167.139827  ±22.57%   10.000000  True
recharge_f     -1.264738  ±16.38%   -1.000000  True
waterlevel_d    0.422350   ±0.73%    1.000000  True
constant_d      8.476929   ±1.00%    8.547142  True
noise_alpha    32.222936  ±10.56%    1.000000  True

Parameter correlations |rho| > 0.5
===================================================
recharge_A recharge_a  0.95
           constant_d -0.67
recharge_a constant_d -0.51
recharge_f constant_d -0.94

Model Diagnostic Checking Adding groundwater pumping