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I've used a quick very rough approximation of the drop of atmospheric density with altitude in this answer and in this answer by using a single exponential and scale height parameter, but that's not what happens in reality. I've typed in some numbers from the U.S. Standard Atmosphere 1976 for $\rho(Z)/\rho_0$ and plotted it below.

The Standard Atmosphere document contains a thorough introduction, and I will try to read it, but in the mean time I'd still like to know if there is a very simple way to understand what changes in the atmospheric physics in the neighborhood 100 km that makes the density fall off so much more slowly beyond this region? Why the giant knee?

Is there a way to write a nice, smooth, analytic function that better approximates the density that reproduces the general behavior of this knee?

note: the three thin lines are simple scale-height plots with $h_{scale}$ of 6.5, 7, and 7.5 km, bottom to top, just for reference.

enter image description here


Python for plot:

info = """80, 1.5068E-05, 85, 6.7099E-06, 90, 2.789E-06, 
95, 1.137E-06, 100, 4.575E-07, 105, 1.898E-07,
110, 7.925E-08, 115, 3.501E-08, 120, 1.814E-08, 
125, 1.054E-08, 130, 6.655E-09, 135, 4.461E-09, 
140, 3.128E-09, 145, 2.270E-09, 150, 1.694E-09, 
155, 1.294E-09, 160, 1.007E-09, 165, 7.959E-10,
170, 6.380E-10, 175, 5.174E-10, 180, 4.240E-10,
190, 2.924E-10, 200, 2.047E-10, 210, 1.507E-10,
220, 1.116E-10, 230, 8.402E-11, 240, 6.415E-11,
250, 4.957E-11, 260, 3.871E-11, 280, 2.425E-11,
300, 1.564E-11, 320, 1.032E-11, 340, 6.941E-12, 
360, 4.739E-12, 380, 3.276E-12, 400, 2.288E-12,
420, 1.612E-12, 440, 1.144E-12, 460, 8.180E-13,
480, 5.844E-13, 500, 4.257E-13"""

import numpy as np
import matplotlib.pyplot as plt

alti, ratio = [info.strip('/n').split(',')[i::2] for i in range(2)]

alti, ratio = [np.array([float(x) for x in thing]) for thing in [alti, ratio]]

alts = alti[:15]

rats = [np.exp(-alts/hs) for hs in [6.5, 7, 7.5]]

# https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770009539.pdf
# U.S. Standard Atmosphere, 1976, NOAA, NASA, USAF
# Altitude (Z, Geometric Height) is in kilometers above sea level.
# Data is from Table 4.
# Here ratio is rho(Z) / rho_0, and rho_0 seems to be 1.225 kg/m^3

plt.figure()
plt.yscale('log')
for rat in rats:
    plt.plot(alts, rat, linewidth=0.6)
plt.plot(alti, ratio, '-k', linewidth=2)
plt.show()
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