California's ambient ozone concentrations have two principal contributions: U.S. background ozone and enhancements produced from anthropogenic precursor emissions; only the latter effectively respond to California emission controls. From 1980 to 2015 ozone has been monitored in eight air basins in Southern California. The temporal evolution of the largest measured concentrations, i.e., those that define the ozone design value (ODV) upon which the National Ambient Air Quality Standard (NAAQS) is based, is described very well by an exponential decrease on top of a positive offset. We identify this offset as the ODV due to the U.S. background ozone (i.e., the concentration that would be present if U.S. anthropogenic precursor emissions were reduced to zero) and is estimated to be 62.0 +/- 1.9 ppb in six of the basins. California's emission control efforts have reduced the anthropogenic ozone enhancements by a factor of similar to 5 since 1980. However, assuming that the current rate of exponential decrease is maintained and that U.S. background ODV remains constant, projections of the past decrease suggest that similar to 35 years of additional emission control efforts will be required to reach the new NAAQS of 70 ppb in the Los Angeles area. The growing predominance of U.S. background ozone contributions has shifted the maximum ozone concentrations in all air basins from later to earlier in the summer. Comparisons indicate that currently accepted model estimates of U.S. background ozone concentrations in Southern California are somewhat underestimated; thus, reducing ozone in this region to the 2015 NAAQS may be more difficult than currently expected. Plain Language Summary Over the past decades, ozone air quality in Southern California has been greatly improved, but the National Ambient Air Quality Standard (NAAQS) has not yet been achieved in much of the region. The ozone standard is based on the rare, highest recorded concentrations (similar to 98th percentile). A simple mathematical function is shown to provide an excellent description of the decrease in these ozone concentrations, which allows some implications to be inferred. Since 1980 the anthropogenic contribution to these concentrations has been reduced by a factor of similar to 5. However, the contribution of background ozone is estimated as similar to 89% of the NAAQS. Since this background contribution is so large, projection of the past rate of decrease of the anthropogenic contribution into the future suggests that similar to 35 years of additional emission control efforts will be required to reach the new NAAQS of 70 ppb in the Los Angeles region. The model calculations of the background ozone contribution that were considered in the formulation of the new NAAQS underestimate the background contribution. Thus, reducing Southern California ozone concentrations to the NAAQS may be more difficult than currently expected.