The effects of solar variability on regional climate time series were examined using a sequence of physical connections between total solar irradiance (TSI) modulated by galactic cosmic rays (GCRs), and ocean and atmospheric patterns that affect precipitation and streamflow. The solar energy reaching the Earth's surface and its oceans is thought to be controlled through an interaction between TSI and GCRs, which are theorized to ionize the atmosphere and increase cloud formation and its resultant albedo. High (low) GCR flux may promote cloudiness (clear skies) and higher (lower) albedo at the same time that TSI is lowest (highest) in the solar cycle which in turn creates cooler (warmer) ocean temperature anomalies. These anomalies have been shown to affect atmospheric flow patterns and ultimately affect precipitation over the Midwestern United States. This investigation identified a relation among TSI and geomagnetic index aa (GI-AA), and streamflow in the Mississippi River Basin for the period 1878-2004. The GI-AA was used as a proxy for GCRs. The lag time between the solar signal and streamflow in the Mississippi River at St. Louis, Missouri is approximately 34 years. The current drought (1999-2007) in the Mississippi River Basin appears to be caused by a period of lower solar activity that occurred between 1963 and 1977. There appears to be a solar "fingerprint" that can be detected in climatic time series in other regions of the world, with each series having a unique lag time between the solar signal and the hydroclimatic response. A progression of increasing lag times can be spatially linked to the ocean conveyor belt, which may transport the solar signal over a time span of several decades. The lag times for any one region vary slightly and may be linked to the fluctuations in the velocity of the ocean conveyor belt.