13  Data Visualization

Visualizing time series data is a critical step in any MIKE+ modelling workflow. Effective plots can help understand data quality, model behavior, the agreement between simulations and observations, as well as communicating key findings.

Note

Module 4 will delve deeper into creating plots and calculating statistics for model calibration and validation using the ModelSkill package.

13.1 Why Visualize Data?

Visual inspection of data serves several key purposes in the modelling process:

• Validate input data: Quickly identify anomalies, gaps, or questionable patterns in input time series like rainfall, flow, or water levels.
• Grasp system behavior: Understand underlying trends, seasonality, and extreme events within your datasets.
• Calibrate/validate: Graphically compare simulated results against observed data to assess model performance.
• Diagnose model errors: Pinpoint discrepancies in timing, magnitude, or overall patterns between model output and reality.
• Communicate results: Create clear visuals to share modelling outcomes, impacts of different scenarios, or model performance metrics with stakeholders.

13.2 Simple Statistics

Before diving into plots, it’s often useful to get a quick numerical summary of your data.

Assuming you have a DataFrame df containing your time series with both observed and model data:

df.head()

	Model	Observed
1993-12-02 00:00:00	-0.2689	-0.219229
1993-12-02 00:30:00	-0.2847	-0.298526
1993-12-02 01:00:00	-0.3020	-0.237231
1993-12-02 01:30:00	-0.3223	-0.169997
1993-12-02 02:00:00	-0.3483	-0.371715

The describe() method provides useful statistics of each column in the DataFrame.

df.describe()

	Model	Observed
count	577.000000	577.000000
mean	-0.005975	-0.007724
std	0.219331	0.247389
min	-0.501200	-0.671723
25%	-0.136900	-0.162345
50%	-0.000200	-0.009162
75%	0.124900	0.154040
max	0.510600	0.699579

13.3 Useful Time Series Plots

This section showcases a few useful plot types for time series data in MIKE+ modelling.

13.3.1 Line Plots

Line plots are essential for visualizing temporal patterns in hydraulic data like flows, water levels, or rainfall. They are also the primary way to compare simulated versus observed time series.

You can plot a single series directly from a DataFrame column:

df['Observed'].plot(
    title='Observed Flow Over Time',
    xlabel='Time',
    ylabel='Flow (m$^3$/s)'
)

Compare two time series, such as observed and modelled flow:

df[['Observed', 'Model']].plot(
    title='Flow Comparison: Observed vs. Model',
    ylabel='Flow (m$^3$/s)'
)

13.3.2 Rolling Mean / Moving Average Plot

This plot helps smooth out noisy time series data, such as high-frequency sensor readings for flow or water level. This smoothing can make it easier to visualize underlying trends or long-term patterns.

df['Observed_Rolling_Mean'] = df['Observed'].rolling(window=6).mean()

df[['Observed', 'Observed_Rolling_Mean']].plot(
    title='Observed 6-Hour Rolling Mean',
    ylabel='Flow (m$^3$/s)'
)

Tip

Adjust the window size in the .rolling() method to control the amount of smoothing. Larger windows result in smoother trends but might obscure shorter-term variations.

13.3.3 Scatter Plots

Scatter plots are particularly useful for model calibration. By plotting paired observed values against simulated values, you can assess point-by-point agreement.

ax = df.plot.scatter(
    x='Observed',
    y='Model',
    alpha=0.5, # so we can see overlapping points better
    title='Observed vs. Model'
)

# plot 1:1 line
max_val = max(df['Observed'].max(), df['Model'].max())
min_val = min(df['Observed'].min(), df['Model'].min())
ax.plot([min_val, max_val], [min_val, max_val], 'k--', label='1:1 Line')  # black dashed line
ax.legend()

Note

Points clustering around the 1:1 line (the dashed line in the example) indicate good agreement.

13.3.4 Box Plots

To understand seasonal variability in your data (e.g. diurnal or seasonal flow patterns), box plots can be effective.

df['Day'] = df.index.day_name()
ax = df.boxplot(column='Observed', by='Day')
ax.get_figure().suptitle("") # remove figure title, just use axes title
ax.set_title("Flows by Day of Week")
ax.set_ylabel("Water level (m)")

Text(0, 0.5, 'Water level (m)')

13.3.5 Cumulative Sum Plots

Cumulative sum plots are excellent for assessing overall water balance or comparing total accumulated volumes (e.g., rainfall, runoff) between observed and simulated data over a period.

df_discharge.cumsum().plot(ylabel="Cumulative Discharge (m$^3$/s)")

Note

Cumulative sums for mass balance require calculating volume differentials. The example below is a simplified approach, recognizing they time series share the same time axis.

13.3.6 Distribution Plots

Histograms help you examine the frequency distribution of variables, such as water levels or flows. This can be useful for comparing the overall statistical profile of observed versus simulated data or understanding the prevalence of certain magnitudes.

df.plot.hist(bins=15, alpha=0.5)

Similarly, review frequency distribution with KDE plots:

df.plot.kde()

13.4 Saving Plots

Easily save plots for inclusion in reports via plt.savefig().

import matplotlib.pyplot as plt

ax = df['Observed'].plot(title='Daily Average Flow', ylabel="Flow ($m^3/s$)")
plt.savefig("my_plot.png")