PWM probably won't work with an LED light bar. These things usually have a built-in constant-current power supply and it will "fight" the PWM as it tries to hold the current constant.You'd have to completely re-build (or replace) the internal power supply. If you can take it apart and "see" how it's wired you could get a dimmable constant current (technically variable controlled current) LED power supply/driver. The "industry standard" for dimming is 10V PWM or 0-10VDC, so you'd need a small (low current) transistor or MOSFET driver circuit to "boost" the Arduino's 5V PWM. You'll need to know the required current through the LEDs and but it's easier to measure voltage than current so you can measure the voltage across the LED string/array and calculate the required current as Current = Wattage/Voltage.
Choose the right module, so that the strips don't die for a too high current. Without a signal the control provides the maximum current.Eventually you can connect the Uno PWM output directly to the PWM input. The data sheet is not clear with that input.Next time buy dimmable LED strips.