Working With Units

Early in our scientific careers we all learn about the importance of paying attention to units in our calculations. Unit conversions can still get the best of us and have caused more than one major technical disaster, including the crash and complete loss of the $327 million Mars Climate Orbiter.

In MetPy, we use the pint library and a custom unit registry to help prevent unit mistakes in calculations. That means that every quantity you pass to MetPy should have units attached, just like if you were doing the calculation on paper! This simplifies the MetPy API by eliminating the need to specify units various functions. Instead, only the final results need to be converted to desired units. For more information on unit support, see the documentation for Pint. Particular attention should be paid to the support for temperature units.

In this tutorial we’ll show some examples of working with units and get you on your way to utilizing the computation functions in MetPy.

Getting Started

To use units, the first step is to import the default MetPy units registry from the units module:

import numpy as np

import metpy.calc as mpcalc
from metpy.units import units

The unit registry encapsulates all of the available units, as well as any pertinent settings. The registry also understands unit prefixes and suffixes; this allows the registry to understand 'kilometer' and 'meters' in addition to the base 'meter' unit.

In general, using units is only a small step on top of using the numpy.ndarray object.

Adding Units to Data

The easiest way to attach units to an array (or integer, float, etc.) is to multiply by the units:

distance = np.arange(1, 5) * units.meters

It is also possible to directly construct a pint.Quantity, with a full units string:

time = units.Quantity(np.arange(2, 10, 2), 'sec')

Compound units can be constructed by the direct mathematical operations necessary:

9.81 * units.meter / (units.second * units.second)

9.81 meter/second²

This verbose syntax can be reduced by using the unit registry’s support for parsing units:

9.81 * units('m/s^2')

9.81 meter/second²

Operations With Units

With units attached, it is possible to perform mathematical operations, resulting in the proper units:

print(distance / time)

[0.5 0.5 0.5 0.5] meter / second

For multiplication and division, units can combine and cancel. For addition and subtraction, instead the operands must have compatible units. For instance, this works:

print(distance + distance)

[2 4 6 8] meter

But for instance, distance + time would not work; instead it gives an error:

DimensionalityError: Cannot convert from ‘meter’ ([length]) to ‘second’ ([time])

Even if the units are not identical, as long as they are dimensionally equivalent, the operation can be performed:

print(3 * units.inch + 5 * units.cm)

4.968503937007874 inch

pint by default will print full unit names for Quantity.

print(f'{20 * units.meter ** 2}')

20 meter ** 2

This can be reduced to symbolic by specifying a compact (~) formatter:

print(f'{20 * units.meter ** 2:~}')

20 m ** 2

A compact (~), pretty (P) formatter:

print(f'{20 * units.meter ** 2:~P}')

20 m²

Place formatters following other print specifications:

print(f'{20 * units.meter ** 2:0.3f~P}')

20.000 m²

Other string formatting options are available, see the Pint string formatting specification.

Converting Units

Converting a Quantity between units can be accomplished by using the to() method call, which constructs a new Quantity in the desired units:

print((1 * units.inch).to(units.mm))

25.4 millimeter

There is also the ito() method which performs the same operation in-place:

a = np.arange(5.) * units.meter
a.ito('feet')
print(a)

[0.0 3.2808398950131235 6.561679790026247 9.84251968503937 13.123359580052494] foot

To simplify units, there is also the to_base_units() method, which converts a quantity to SI units, performing any needed cancellation:

Lf = 3.34e6 * units('J/kg')
print(Lf, Lf.to_base_units(), sep='\n')

3340000.0 joule / kilogram
3340000.0 meter ** 2 / second ** 2

to_base_units() can also be done in-place via the ito_base_units() method.

By default Pint does not do any more than simple unit simplification, so when you perform operations you could get some seemingly odd results:

length = 10.4 * units.inch
width = 5 * units.cm
area = length * width
print(area)

52.0 centimeter * inch

This is another place where to() comes in handy:

print(area.to('m^2'))

0.013208 meter ** 2

Temperature

Temperature units are actually relatively tricky (more like absolutely tricky as you’ll see). Temperature is a non-multiplicative unit - they are in a system with a reference point. That means that not only is there a scaling factor, but also an offset. This makes the math and unit book-keeping a little more complex. Imagine adding 10 degrees Celsius to 100 degrees Celsius. Is the answer 110 degrees Celsius or 383.15 degrees Celsius (283.15 K + 373.15 K)? That’s why there are delta degrees units in the unit registry for offset units. For more examples and explanation you can watch MetPy Monday #13: https://www.youtube.com/watch?v=iveJCqxe3Z4.

Let’s take a look at how this works and fails:

We would expect this to fail because we cannot add two offset units (and it does fail as an “Ambiguous operation with offset unit”).

10 * units.degC + 5 * units.degC

On the other hand, we can subtract two offset quantities and get a delta. A delta unit is pint’s way of representing a relative change in two offset units, indicating that this is not an absolute value of 5 degrees Celsius, but a relative change of 5 degrees Celsius.

print(10 * units.degC - 5 * units.degC)

5 delta_degree_Celsius

We can add a delta to an offset unit as well since it is a relative change.

print(25 * units.degC + 5 * units.delta_degF)

27.77777777777778 degree_Celsius

Absolute temperature scales like Kelvin and Rankine do not have an offset and therefore can be used in addition/subtraction without the need for a delta version of the unit.

print(273 * units.kelvin + 10 * units.kelvin)

283 kelvin

print(273 * units.kelvin - 10 * units.kelvin)

263 kelvin

MetPy Calculations

All MetPy calculations are unit-aware and rely on this information to ensure that the calculations operate correctly. For example, we can use units to take an observation in whatever units are most convenient and let MetPy handle everything under the hood. Below we calculate dewpoint from the temperature and relative humidity:

temperature = 73.2 * units.degF
rh = 64 * units.percent
dewpoint = mpcalc.dewpoint_from_relative_humidity(temperature, rh)

print(dewpoint)

15.726236381245258 degree_Celsius

or back to Fahrenheit:

print(dewpoint.to('degF'))

60.3072254862414 degree_Fahrenheit

Dropping Units

While units are part of the MetPy ecosystem, they can be a headache after we have computed the desired quantities with MetPy and would like to move on. For example, we might have computed the dewpoint temperature for two points, say A and B, and would like to compute the average:

temperature_a = 73.2 * units.degF
rh_a = 64 * units.percent
dewpoint_a = mpcalc.dewpoint_from_relative_humidity(temperature_a, rh_a)

temperature_b = 71.1 * units.degF
rh_b = 52 * units.percent
dewpoint_b = mpcalc.dewpoint_from_relative_humidity(temperature_b, rh_b)

Per our previous discussion on temperature units, adding two temperatures together won’t work. In this case, the easiest way to add two quantities and compute an average is by dropping the units attached to the values via .magnitude:

print(dewpoint_b.magnitude)

11.445590005179099

dewpoint_mean = (dewpoint_a.magnitude + dewpoint_b.magnitude) / 2.
print(dewpoint_mean)

13.585913193212178

Common Mistakes

There are a few common mistakes the new users often make. Be sure to check these when you’re having issues.

• Pressure units are mbar or hPa for common atmospheric measurements. The unit mb is actually millibarns–a unit used in particle physics.

• When using masked arrays, units must be multiplied on the left side. This will be addressed in the future, but is a current limitation in the ecosystem. The expected error will be AttributeError: ‘MaskedArray’ object has no attribute ‘units’ or calculation functions complaining about expecting a units and getting “dimensionless”.