Mathematical operations
Creating new variables
Variable creation in nctoolkit can be done using the assign
method,
which works in a similar way to the method available in pandas.
The assign
method works using lambda functions. Let’s say we have a
dataset with a variable ‘var’ and we simply want to add 10 to it and call
the new variable ‘new’. We would do the following:
ds.assign(new = lambda x: x.var + 10)
If you are unfamilar with lambda functions, note that the x after lambda signifies that x represents the dataset in whatever comes after ‘:’, which is the actual equation to evaluate. The x.var term is var from the dataset.
By default assign keeps the original variables in the dataset. However, we may only want the new variable or variables. In that case you can use the drop argument:
ds.assign(new = lambda x: x.var+ 10, drop = True)
This results in only one variable.
Note that the assign
method uses kwargs for the lambda functions, so
drop can be positioned anywhere. So the following will do the same thing
ds.assign(new = lambda x: x.var+ 10, drop = True)
ds.assign(drop = True, new = lambda x: x.var+ 10)
At present, assign
requires that it is written on a single line. So avoid doing something
like the following:
ds.assign(new = lambda x: x.var+ 10,
drop = True)
The assign method will evaluate the lambda functions sent to it for each dataset grid cell for each time step. So every part of the lambda function must evaluate to a number. So the following will work:
k = 273.15
ds.assign(drop = True, sst_k = lambda x: x.sst + k)
However, if you set k
to a string or anything other than a number it
will throw an error. For example, this will throw an error:
k = "273.15"
ds.assign(drop = True, sst_k = lambda x: x.sst + k)
Applying mathematical functions to dataset variables
As part of your lambda function you can use a number of standard
mathematical functions. These all have the same names as those in numpy:
abs
, floor
, ceil
, sqrt
, exp
, log10
, sin
,
cos
, tan
, arcsin
, arccos
and arctan
.
For example if you wanted to calculate the ceiling of a variable you could do the following:
ds.assign(new = lambda x: ceil(x.old))
An example of using logs would be the following:
ds.assign(new = lambda x: log10(x.old+1))
Using spatial statistics
The assign
method carries out its calculations in each time step,
and you can access spatial statistics for each time step when generating
new variables. A series of functions are available that have the same
names as nctoolkit methods for spatial statistics: spatial_mean
,
spatial_max
, spatial_min
, spatial_sum
, vertical_mean
,
vertical_max
, vertical_min
, vertical_sum
, zonal_mean
,
zonal_max
, zonal_min
and zonal_sum
.
An example of the usefulness of these functions would be if you were working with global temperature data and you wanted to map regions that are warmer than average. You could do this by working out the difference between temperature in one location and the global mean:
ds.assign(temp_comp = lambda x: x.temperature  spatial_mean(x.temperature), drop = True)
You can also do comparisons. In the above case, we instead might simply want to identify regions that are hotter than the global average. In that case we can simply do this:
ds.assign(temp_comp = lambda x: x.temperature > spatial_mean(x.temperature), drop = True)
Let’s say we wanted to map regions which are 3 degrees hotter than average. We could that as follows:
ds.assign(temp_comp = lambda x: x.temperature > spatial_mean(x.temperature + 3), drop = True)
or like this:
ds.assign(temp_comp = lambda x: x.temperature > (spatial_mean(x.temperature)+3), drop = True)
Logical operators work in the standard Python way. So if we had a dataset with a variable called ‘var’ and we wanted to find cells with values between 1 and 10, we could do this:
ds.assign(one2ten = lambda x: x.var > 1 & x.var < 10)
You can process multiple variables at once using assign
. Variables
will be created in the order given, and variables created by the first
lambda function can be used by the next one, and so on. The simple
example below shows how this works. First we create a var1, which is
temperature plus 1. Then var2, which is var1 plus 1. Finally, we
calculate the difference between var1 and var2, and this should be 1
everywhere:
ds.assign(var1 = lambda x: x.var + 1, var2 = lambda x: x.var1 + 1, diff = lambda x: x.var2  x.var1)
Functions that work with nctoolkit variables
The following functions can be used on nctoolkit variables as part of lambda functions.
Function 
Description 
Example 


Absolute value 


Ceiling of variable 


Area of gridcell (m2) 


Trigonometric cosine of variable 


Day of the month of the variable 


Exponential of variable 


Floor of variable 


Hour of the day of the variable 


Is variable a missing value/NA? 


Latitude of the grid cell 


Vertical level of variable. 


Natural log of variable 


Base log10 of variable 


Longitude of the grid cell 


Month of the variable 


Trigonometric sine of variable 


Spatial max of variable at timestep 


Spatial mean of variable at timestep 


Spatial min of variable at timestep 


Spatial sum of variable at timestep 


Square root of variable 


Trigonometric tangent of variable 


Time step of variable. Using Python indexing. 


Year of the variable 


Zonal max of variable at timestep 


Zonal mean of variable at timestep 


Zonal min of variable at timestep 


Zonal sum of variable at timestep 

Simple mathematical operations on variables
If you want to do simple operations like adding or subtracting numbers from the variables in datasets you can use
the add
, subtract
, divide
and multiply
methods. For example if you wanted to add 10 to every variable
in a dataset, you would do the following:
ds.add(10)
If you wanted to multiply everything by 10, you would do this:
ds.multiply(10)
These methods will also let you use other datasets or netCDF files. So, you could add the values in a dataset data2 to a dataset called data1 as follows:
ds1.add(ds2)
Please note that this will require that the datasets are structured in a way that the operation makes sense. So each dimension in the datasets will either have to be identical, with the exception of when one dataset has a single value for a dimension. So for example if ds2 above has data covering only 1 timestep, but ds1 has multiple timesteps the data from that single time step will be added to all timesteps in ds1. But if the time steps match, then the data from the first time step in ds2 will be added to the data in the first time step in ds1, and the same will happen with the following time steps.
Simple numerical comparisons
If you want to do something as simple as working out whether the values of the variables in a dataset are greater than zero, you can use the
compare
method. This method accepts a simple comparison formula, which follows Python conventions. For example, if you wanted to figure
out if the values in a dataset were greater than zero, you would do the following:
ds.compare(">0")
If you wanted to know if they were equal to zero you would do this:
ds.compare("==0")