AxisUtilities 19.11.20.334

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What is AxisUtilities

Axis Utilities was originally developed to manages Time Axis and different operations related to time with the main focus on Earth & Atmospheric Science Community. For example, you might have a daily 3D spatially distributed temperature and you want to calculate the monthly average of this data. This result in the same spatial coordinate, however, with a different time axis/coordinate.

However, similar operations could be performed on any one-dimensional axis. Let's say your data is distributed along the z-coordinate in certain way, and now you want to average them in a different vertical distribution. Although, your source axis is not time anymore, the mathematical operation that is being performed is the same. For this reason, it was decided to rename the package from TimeAxis to AxisUtilities.

During the axis conversion (conversion from source axis to destination axis), for example computing the monthly mean from the daily data, there are a lot of computations that needs to be done which does not involve the data itself. This means that we could cache these computations and reuse them to achieve a better performance. As long as the source and the destination axis have not changed, we could use the cached computation to perform the axis conversion. One of the features that AxisUtilities provide is caching these computations and allowing you to reuse it to achieve better performance. The same concept is being used in other packages such as ESMF, SCRIP, and 2D and 3D Remapping. In those packages, the cached computation is referred as Remapping Weights.

How To Install?

using pip

As usual, you could use pip installation as follows:

pip install axisutilities

How to use AxisUtilities?

The general procedure is:

1. Create a source axis, i.e. the axis that your original data is on,
2. Create a destination axis, i.e. the axis that you want to convert your data to,
3. Create an AxisConverter object by passing the source and destination axis you created previously,
4. Finally, convert your data from the source axis to the destination axis, using the AxisConverter object you created in previous step.

You could repeat step (4) as many time as you want, as long as the source and destination axis are the same. The true benefit of this approach is in the reuse of the same computations, a.k.a. remapping weights.

For some examples refer to the following examples or the API documentations.

Documentation

For AxisUtilities documentation click here.

Examples:

Daily data averaged to weekly

Step 1: Create a source Axis

In this example, first we create a daily time-axis of length 14 days, i.e. we just have 14 data points along the time axis:

from axisutilities import DailyTimeAxisBuilder
from datetime import date
from_axis = DailyTimeAxisBuilder(
    start_date=date(2019, 1, 1),
    n_interval=14
).build()

Step 2: Create a destination Axis

Now we create a weekly time-axis of length 3, i.e. the time axis would have three elements with span of 3 weeks:

from axisutilities import WeeklyTimeAxisBuilder
from datetime import date
to_axis = WeeklyTimeAxisBuilder(
    start_date=date(2019, 1, 1),
    n_interval=3
).build()

Step 3: Create a AxisConverter object

now we create a time axis converter object, as follows:

from axisutilities import AxisConverter
tc = AxisConverter(
    from_axis=from_axis, 
    to_axis=to_axis
)

Step 4: Converting data from source axis to destination axis

Now we can use tc to convert data from the from_axis to to_axis, as follows:

to_data = tc.average(from_data)

the resulting to_data is the weekly average of the from_data. By default, we are assuming that the first dimension is the time dimension. If the time dimension (source axis) is not the first dimension, you could define it as follows:

to_data = tc.average(from_data, dimension=n)

where n is the time dimension (or source axis if the axis you have created is not time).

Repeating Step 4: as many time as needed

If we have other data sources that are on the same source axis (in this case the same time axis), you could use the same tc or AxisConverter object that you created before to convert them to your new destination axis:

to_data = tc.average(another_data_field)

NOTE: Please do note that only the 1D axis that you are converting from needs to be the same along all these different data sources. Their other dimensions could be completely different.

Rolling/moving weekly avarage

You could easily calculate a rolling or moving average of your data. Here is an example:

from axisutilities import DailyTimeAxisBuilder, RollingWindowTimeAxisBuilder, AxisConverter
from_axis = DailyTimeAxisBuilder(
    start_date=date(2019, 1, 1),
    n_interval=14
).build()

to_axis = RollingWindowTimeAxisBuilder(
    start_date=date(2019, 1, 1),
    end_date=date(2019, 1, 15),
    window_size=7
).build()

tc = AxisConverter(from_axis=from_axis, to_axis=to_axis)

to_data = tc.average(from_data)

as you can see, the only difference is the construction og the to_axis. In this example, we are building a rolling time axis that starts on Jan. 1st, 2019 and ends on Jan. 15th, 2019 with a window size of 7. Since the base time delta, if not provided, is one day, our window is one week (7 * 1 day). However, this is a rolling time axis, meaning that the next element on time axis is shifted only one day. Yes, the intervals in the time-axis are overlapping each other.

Daily Averaged to Monthly

# Daily time axis spanning ten years.
from axisutilities import DailyTimeAxisBuilder, MonthlyTimeAxisBuilder, AxisConverter
from_axis = DailyTimeAxisBuilder(
    start_date=date(2010, 1, 1),
    end_date=date(2020, 1, 1)
).build()

# Monthly Time Axis spanning 10 years.
to_axis = MonthlyTimeAxisBuilder(
    start_year=2010,
    end_year=2019,
).build()

tc = AxisConverter(from_axis=from_axis, to_axis=to_axis)
monthly_avg = tc.average(daily_data)

if you do not provide any month, the start month is assumed to be the January and the end month is assumed to be the December. If you want to control that you could pass the start_month and/or end_month to change this behavior:

from axisutilities import MonthlyTimeAxisBuilder
to_axis = MonthlyTimeAxisBuilder(
    start_year=2010,
    start_monnth=4,
    end_year=2019,
    end_month=10
).build()

Min and Max

The same way that you could calculate average, you could calculate the min and max.

tc = AxisConverter(from_axis=from_axis, to_axis= to_axis)

tc.min(data)
tc.max(data)

for example, if the form axis is a daily axis, and to_axis is a monthly axis, tc.min(data) calculates the minimum daily data within the month.

User-defined functions

The users are able to define their own function to apply. All you need to do is to pass the data along with the function that you want to apply. Let's say the user is interested to calculate the standard deviation:

tc = AxisConverter(from_axis=daily_axis, to_axis=monthly_axis)

to_data = tc.apply_function(from_data, np.nanstd)

NOTES:

• Pay attention that there is no parenthesis after np.nanstd. You need to pass the function object itself. Any thing that is conisdered Callable within Python.
• Note that instead of passing np.std, we are passing the version of the function that handles the NaN. The function that you pass must handle the NaN and missing values properly. If you pass the regular standard deviation and your source data contains NaN your converted results would become also NaN. Also note that the function is forced to performed the operation along axis=0; These are the requirements. You could pass any function that you want:

tc = AxisConverter(from_axis=daily_axis, to_axis=monthly_axis)

def myfunction(data):
    return np.nansum(data, axis=0) * 42

to_data = tc.apply_function(from_data, myfunction)

Again, pay attention that when passing myfunction there is no parenthesis and we are handling the NaN inside the function by using np.nansum instead of np.sum. Also, pay attention to the axis=0; The user-defined function must perform it's operation along this axis only.

Authors:

• Abouali, Mohammad ([e-mail]; [e-mail])
• Banihirwe, Anderson ([e-mail])
• Long, Matthew ([e-mail])