Tying it to vehicles isn't a bad idea. Just make sure it doesn't fall onto vehicles.
This calculator is useful. The area of an 8x8 is about six square metres (since (8x12x25.4/1000)2 = 5.945) which in a 20-knot (10.2m/s) wind will apply a force of 375N, equal to about 38 kilos or 83lb. 20 knots is not much of a breeze. Calculating the tension applied to a tie-down is unfortunately not straightforward but it may significantly exceed the wind force. Assuming the frame is upright and square on to the wind and the tie-downs are at a 45 degree angle to both the ground and the frame, and the tie-downs are pointing directly into the wind, the tie down system overall might experience a load of up to 1.41 times the wind load. The more vertical the ropes become or the greater the angle between the tie-downs and the oncoming wind, the worse it gets.
Even quite basic synthetic ropes can have a breaking strain of around a metric ton (2200lb) at 8mm diameter so you are unlikely to break any reasonable rope but it's easy to drag or uproot an anchor. Calculating the force required to drag an object along a complex surface is extremely un-straightforward.
Can't say I'd reach for jute or any other natural fibre rope for this.