**The issue**

I have a contourf plot I made with a pandas dataframe that plots some 2-dimensional value with time on the x-axis and vertical pressure level on the y-axis. The field, time, and pressure data I’m pulling is all from a netCDF file. I can plot it fine, but I’d like to scale the y-axis to better represent the real atmosphere. (The default scaling is linear, but the pressure levels in the file imply a different king of scaling.) Basically, it should look something like the plot below on the y-axis. It’s like a log scale, but compressing the bottom part of the axis instead of the top. (I don’t know the term for this… like a log scale but inverted?) It doesn’t need to be exact.

**Working example (written in Jupyter notebook)**

#modules import numpy as np import pandas as pd import matplotlib.pyplot as plt from matplotlib import ticker, colors #data time = np.arange(0,10) lev = np.array([900,800,650,400,100]) df = pd.DataFrame(np.arange(50).reshape(5,10),index=lev,columns=time) df.index.name = 'Level' print(df)

0 1 2 3 4 5 6 7 8 9 Level 900 0 1 2 3 4 5 6 7 8 9 800 10 11 12 13 14 15 16 17 18 19 650 20 21 22 23 24 25 26 27 28 29 400 30 31 32 33 34 35 36 37 38 39 100 40 41 42 43 44 45 46 47 48 49

#lists for plotting levtick = np.arange(len(lev)) clevels = np.arange(0,55,5) #Main plot fig, ax = plt.subplots(figsize=(10, 5)) im = ax.contourf(df,levels=clevels,cmap='RdBu_r') #x-axis customization plt.xticks(time) ax.set_xticklabels(time) ax.set_xlabel('Time') #y-axis customization plt.yticks(levtick) ax.set_yticklabels(lev) ax.set_ylabel('Pressure') #title and colorbar ax.set_title('Some mean time series') cbar = plt.colorbar(im,values=clevels,pad=0.01) tick_locator = ticker.MaxNLocator(nbins=11) cbar.locator = tick_locator cbar.update_ticks()

**The Question**

How can I scale the y-axis such that values near the bottom (900, 800) are compressed while values near the top (200) are expanded and given more plot space, like in the sample above my code? I tried using `ax.set_yscale('function', functions=(forward, inverse))`

but didn’t understand how it works. I also tried simply `ax.set_yscale('log')`

, but log isn’t what I need.

You can use a custom scale transformation with `ax.set_yscale('function', functions=(forward, inverse))`

as you suggested. From the documentation:

`forward`

and`inverse`

are callables that return the scale transform and its inverse.

In this case, define in `forward()`

the function you want, such as the inverse of the log function, or a more custom one for your need. Call this function before your y-axis customization.

def forward(x): return 2**x def inverse(x): return np.log2(x) ax.set_yscale('function', functions=(forward,inverse))

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