Calculation of diode switching losses
You will struggle to find a datasheet that explicitly states the turnon information. TurnOn switching losses of a diode are typically quite small &amp; unlike the TurnOff characteristics, ONLY affect the diode

The reason for this is the turn-off characteristics have bigger ramifications. 

The key information with regards to turn-off are


Reverse recovery time \$t_{rr}\$
Reverse recovery charge \$Q_{rrm} \$
Peak reverse recovery current \$I_{rr}\$
Peak rate of fall of recovery current \$dI_{rr}/dt\$


The turn-off of the DIODE characteristic have an immediate knock on effect on the associated commutating device (eg IGBT). The reverse recovery current is additive to the turn-on switching current of the associated device and thus that devices turn-on (the IGBT). Switching 600A through an inductive load can easily have 50A of additional current 

This however is turn-off of the DIODE &amp; this information is provided in the datasheet &amp; equally the question was associated with turn-on

Turn-OFF characteristics (for minority carriers) is dominated by die,package, installation: resistance AND inductance. As the current is rising at the \$dI_{rr}/dt\$ rate, an additional voltage is generated on-die. In practice however due to application specific installation stray inductance the \$dI_{rr}/dt\$ will be lower.

To ESTIMATE the turn-OFF switching losses of a power Diode requires three things


Reverse Recovery Charge
blocking Voltage 
switching frequency.


Depending on the size of the diode, you may or may not be provided with \$Q_R\$  against \$dI_f/dt\$ graphs.

If you are provided these graphs, the 1st step is to determine the \$Q_R\$ for your operating case: external inductance limiting the \$dI_f/dt\$ and your operating current.

The switching power can then be estimated by

\$P_s = Q_R V_r f_s\$

if you are interested in W.s/pulse (\$J_R\$) This can be estimated via:
\$J_R = V_R Q_R\$

As mentioned: TurnON losses are not only tricky (due to the complex nature of interacting strays) but equally is a small contributor