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Groundwater signatures#

R.A. Collenteur, Eawag, 2023

In this notebook we introduce the groundwater signatures module available in Pastas. The signatures methods can be accessed through the signatures module in the pastas.stats sub-package.

Groundwater signatures are quantitative metrics that characterize different aspects of a groundwater time series. They are commonly subdivided in different categories: shape, distribution, and structure. Groundwater signatures are also referred to as ‘indices’ or ‘quantitative’ metrics. In Pastas, ‘signatures’ is adopted to avoid any confusion with time indices and goodness-of-fit metrics. For an introduction to the signatures concept in groundwater studies we refer to Heudorfer and Haaf et al. (2019).

The signatures can be used to objectively characterize different groundwater systems, for example, distinguishing between fast and slow groundwater systems. The use of signatures is common in other parts of hydrology (e.g., rainfall-runoff modeling) and can be applied in all phases of modeling (see, for example, McMillan, 2021 for an overview).

Note: The `signatures` module is under active development and any help is welcome. Please report any issues and bugs on the Pastas GitHub repository!
import numpy as np
import pandas as pd
import pastas as ps

import matplotlib.pyplot as plt
from matplotlib.gridspec import GridSpec

ps.show_versions()
Python version: 3.11.6
NumPy version: 1.26.4
Pandas version: 2.2.2
SciPy version: 1.13.0
Matplotlib version: 3.8.4
Numba version: 0.59.1
LMfit version: 1.3.1
Latexify version: Not Installed
Pastas version: 1.5.0

1. Load two time series with different characteristics#

To illustrate the use of groundwater signatures we load two time series of hydraulic heads with visually different characteristics.

head1 = pd.read_csv(
    "data_notebook_20/head_threshold.csv", index_col=0, parse_dates=True
).squeeze()
head2 = pd.read_csv(
    "data_wagna/head_wagna.csv", index_col=0, parse_dates=True, skiprows=2
).squeeze()
head2 = head2.resample("D").mean().loc["2012":]

fig, [ax1, ax2] = plt.subplots(2, 1, figsize=(10, 4), sharex=True)

head1.plot(ax=ax1)
head2.plot(ax=ax2)
<Axes: xlabel='Date'>
../_images/dbc763026dfb1e65062944ba09aad3401f911d77794b71387ffd92c90067978e.png

2. Compute signatures#

To compute all available signatures at once, we can use the stats method from the signatures module. This is shown below. Alternatively, each signature can be computed with a separate method (e.g., ps.stats.signatures.baseflow_index).

sigs1 = ps.stats.signatures.summary(head1)
sigs2 = ps.stats.signatures.summary(head2)

# Create a dataframe for easy comparison and plotting
df = pd.concat([sigs1, sigs2], axis=1)
df
WARNING: The estimated recession constant (1000.0) is close to the boundary. This may lead to incorrect results.
B28H1804_2 GWL
cv_period_mean 0.015684 0.001481
cv_date_min 0.119447 0.361901
cv_date_max 1.577802 118.358253
cv_fall_rate -0.970657 -0.705874
cv_rise_rate 1.171908 1.079511
parde_seasonality 0.662627 0.389114
avg_seasonal_fluctuation 0.839583 0.873115
interannual_variation 0.469333 0.908889
low_pulse_count 2.125000 0.875000
high_pulse_count 2.250000 1.125000
low_pulse_duration 31.294118 83.428571
high_pulse_duration 29.555556 65.000000
bimodality_coefficient 0.701896 0.426865
mean_annual_maximum 0.964633 0.752266
rise_rate 0.010977 0.012369
fall_rate -0.008958 -0.005853
reversals_avg 123.250000 32.875000
reversals_cv 0.183372 0.251066
colwell_contingency 0.379523 0.271618
colwell_constancy 0.138205 0.063745
recession_constant 5.623457 NaN
recovery_constant NaN 22.397220
duration_curve_slope -0.661123 -0.957628
duration_curve_ratio 0.357271 0.197775
richards_pathlength 1.258451 2.513411
baselevel_index 0.851327 0.754928
baselevel_stability 0.308739 0.355291
magnitude 0.072510 0.007240
autocorr_time 32.000000 33.000000
date_min 231.811299 255.267674
date_max 17.737988 0.765875

3. Plot the results#

Depending on the signature, different ranges of parameters can be expected. We therefore normalize the signatures values by the mean value of each signature. This way we can easily compare the two groundwater systems.

_, ax = plt.subplots(1, 1, figsize=(10, 4))
df.div(df.mean(axis=1), axis=0).mul(100).plot(ax=ax)
ax.set_xticks(
    np.arange(len(df.index)),
    df.index,
    rotation=90,
)
ax.set_ylabel("% Change from the mean\n signature  value")
ax.grid()
../_images/212e45eb4ce16a2d00a65bd07456e583b1223dfccb4141392f8e166c9bace81d.png

4. Interpretation of signatures#

The different signatures can be used to compare the different systems or characterize a single system. For example, the first head time series has a high bimodality coefficient (>0.7), indicating a bimodal distribution of the data. This makes sense, as this time series is used as an example for the non-linear threshold model (see notebook). Rather than (naively) testing all model structures, this is an example where we can potentially use a groundwater signature to identify a ‘best’ model structure beforehand.

Another example. The second time series is observed in a much slower groundwater system than the first. This is, for example, clearly visible and quantified by the different values for the ‘pulse_duration’, the ‘recession and recovery constants’, and the ‘slope of the duration curves’. We could use this type of information to determine whether we should use a ‘fast’ or ‘slow’ response function (e.g., an Exponential or Gamma function). These are just some examples of how groundwater signatures can be used to improve groundwater modeling, more research on this topic is required. Please contact us if interested!

A little disclaimer: from the data above, it is actually not that straightforward to compare the signature values because the range in values is large. For example, the rise and fall rate show small differences in absolute values, but their numbers vary by over 200%. Thus, interpretation requires some more work.

References#

The following references are helpful in learning about the groundwater signatures: