So, can you extend the neighbor's dry creek bed to the other side of your property, to where ever it naturally drains off?? Is that going to be in another neighbor's yard? If it involves someone else you would need to give them a heads up if it is legal to do this in your area. Not a good surprise. Especially when we get toad-strangler rains from hurricanes from down south.

Working link to OP's photo:
http://www.flickr.com/photos/32311231@N06/sets/72157625998997739/

From your photos it appears the water "sheets" across your yard rather than via a defined channel. If so I would not attempt to make a 6' wide channel as you may wind up with an ugly ditch. A four foot deep channel will eventually fill in with fines, debris etc, and you may get lateral erosion as well. If you can mow the area now (can't tell from photos) I'd leave it alone.

What happens when the 4' deep trench meets the property line? The water in the ditch will have nowhere to go until the ditch is completely full. Then it will continue on the way it used to onto the neighboring property. As soon as it has lowered enough it will stop flowing and you'll have a 4' deep puddle in your yard. How is that beneficial?

SquireJohn is right that when you slow down water that is carrying suspended material, the material drops out and will eventually fill your ditch.

You are limited by how the water leaves your property.If there is a deeper narrower area that the water exits by when it crosses the property line, you have more options. If it leaves in a wide sheet, there is not much benefit to making a channel. Right now, it appears that it exits your property and is not a problem of sitting water.

You will find that the pro's on this Forum have a healthy respect for moving water and also the reaction of a local municipality when a water course is altered without permission. Don't go there! Call your local building department and request that its civil engineer meet with you to discuss the situation. There should be no charge for this. It appears that you are willing to foot the bill for remediation so you should find your cash strapped government helpful with the design. Or, due to downstream considerations, permission may be denied.

This is a new age in municipal water management; collecting, detaining and releasing storm water in 'rain gardens' slowly on private properties. Technically your backyard could be classified as a rain garden. Your problem may fall on deaf ears. Whatever...get permission and an approved plan before putting blade to soil.

Thank you all for the replies. I failed to mention that as the water departs my yard, the neighbors downstream have a defined ditch/creek and further downstream in the neighborhood the creek is approximately 10-15' wide.

Since this photo was taken 2 years ago, I've used a shovel to help channel the water down stream. Now there is no grass where the water is in the pictures, just a muddy mess.

Do any of you know how to find maps of the city's intentions on moving the storm water from the neighborhood behind mine that is causing this problem?

I'll take more pictures upstream and downstream to give a better sense of what I'm dealing with.

If the upland neighborhood is a more recent subdivision, the builders are sometimes required to include stormwater runoff plans as part of their submittals. If this was required in your case, you could find the plan at the permit office.

Does the city have a stormwater plan? You could ask at the zoning office. In a lot of places, they don't, especially if it goes from one private residence to another.

Although it looks like a lot of water, it doesn't look very deep. A 6' wide, 4-5' deep trench seems like it would be overkill and really break up your yard. How big is the upland neighbor's dry creek bed? It might make sense to have a smaller dry bed along with perhaps a rain garden/ rain swale to deal with some overflow.

I have never actually measured the depth, since it does come thru rather fast...the girls next door did try (unsuccessfully) to intertube down the rapids last summer.

I had a similar problem and the county was very helpful. They sent a guy out who had lots of storm water experience - the free consult was very worthwhile. Legally I cannot keep water from flowing onto my land that is supposed to flow there according to the subdivision plan. But I built a mini berm to guide it around the house. It's just two garden timbers with some soil behind it, that goes diagonally across the hillside. It was the storm guy's idea and it helps a lot. I'm going to put a dry stream bed about two foot across by six inches deep along one side of the house and across the front yard, because I need to channel a lot of water through without muddy spots, and I have the vertical drop to keep it flowing. HTH

Perhaps your town Planning Dept. has maps of your development with elevations showing. From those you could see how rain water naturally finds a creek or stream to be carried away. I have one for my development in NY State and successfully required a developer behind my backyard to drain his drain water correctly. This is also important for large rains in early spring with ground still frozen.

As suggested, consider making a shallow dry creek bed, like pooring a few bags of gravel to form a low dam to channel any of neighbor's water across your yard to the natural low spot at your property line. But your own rain water probably also wants to run to a low spot.

Not sure if you've resolved this or not but there are some good solutions out there. Take a look at Rain Gardening in the South. Here's the publisher's link but it's available at the library and local book stores. http://www.blairpub.com/educational%20titles/Rain_Gardening.html. There's also a good link on the NC Cooperative Extension website - http://www.bae.ncsu.edu/topic/raingarden/
Rain gardens really work. Hope this helps!