When a homeowner is granted permission to erect a higher fence than what is normally permitted, this is known as a:

When a homeowner receives permission to build a higher fence than what local zoning regulations typically allow, this is referred to as a variance. A variance provides an exception to existing zoning ordinances, permitting the property owner to undertake uses of their property that are not typically allowed under those regulations. This is often necessary when a unique circumstance regarding the property necessitates deviation from the standard zoning restrictions.

In addition to allowing for variations in construction, variances often require a formal process, including public notification and a hearing to consider impacts on surrounding properties and the community. This mechanism ensures that while individual property rights are respected, they do not infringe upon the rights or welfare of neighboring property owners.

The other options, like convenience or special exception, do not specifically apply to the adjustment of height restrictions in this context, and nonconforming use relates more to existing uses of a property that were legal when established but do not comply with current zoning laws. Therefore, the concept of a variance best encapsulates the situation described.