I've been to Beijing a few times and I seriously don't think you should jog outside or perform any form of exercise for that matter. If you really want to do it then I suggest you bring along some breathing apparatus so that you won't pass out along the way. I'd suggest you thread rubber unless you want to get lungfuls of fumes each time. 

My late 'pop' was an avid long distance (20km and longer) runner. He was doing long runs as 65 Y old man.

When outside was bad weather (snow and freezing), he would 'jog' inside the house.

He stepped into the doors frame, and hold frame with both hands. He wouldn't raise his feet of the ground, like in outside run, but both of his feet toes would be on the ground, raising his heels, mimicking 'running'.

He could stay in between the doors frame longer than an hour, practicing several times a day.

Dentist by profession! Once somebody told me, dentists and psychiatrist are weird, because one looks into other people's mouth/teeth 8 hours a day, and other one gets into the insane brain in all his working period.

I don't live in Beijing... In Suzhou, the pollution is not as bad as in Beijing, yet it's high enough to be a worry. If I run outside when the AQI PM2.5 is at 200, after one hour my lungs will burn, a smell of ashes and ozone will persist. The day after, I will cough and spit green slime. At a level of 400, simply biking from home to work is enough to be a problem. Soooo, just don't run the days it's polluted, even if it means not much running. Yup, it's very sad :(

We have bright sun in my city with POUR of rain at 3:30pm.

I've never seen this before.

Sun is so bright, shades are a must, and rain is pouring so hard some 10' already, you can't go out not even with umbrella.

Running water in the city is closed, because of some repairs. Is this OIC?