A Regression Model for Annual Streamflow in the Upper Mississippi River Basin Based on Solar Irradiance

Annual streamflow in the upper Mississippi River Basin demonstrates an apparent connection to annual solar-irradiance variations. The relation is associated with the amount of solar energy available for absorption by the tropical Pacific Ocean and the subsequent effects this stored energy has on mid-latitude atmospheric circulation and precipitation occurrence. The suggested physical mechanism for this relation includes varying solar-energy input that creates ocean-temperature anomalies in the tropical ocean. The temperature anomalies are transported northward by ocean currents to locations where ocean and atmospheric processes can modify jet-stream patterns. These patterns affect jet-stream location and characteristics downwind over North America, which affect the occurrence of precipitation and, ultimately, the amount of streamflow in the upper Mississippi River Basin. The relation provides an opportunity to estimate the annual streamflow of the upper Mississippi River. A multivariate model using solar-irradiance variations and the previous year's basin precipitation explains nearly one-half of the annual streamflow variability. When data for only La Nina years are considered, the model explains more than two-thirds of the variability since 1950.

In the past solar/climate connections have been considered tenuous at best, with apparent significant correlations (Brooks 1926) having phase changes (Clayton 1940) or complete correlation breakdowns (Eddy 1983). Solar/climate correlations that pass significance tests lack physical explanations. At the decadal and interdecadal scales, there is growing evidence that long-term changes in the Sun's radiation output do have an effect on global air temperature (Hoyt 1979; Friis-Christensen and Lassen 1991) and on global sea-surface temperatures (White and others 1997), even though the observed change in solar irradiance during the average 11-year solar cycle is small and amounts to only 0.15% variation. However, mean irradiance can differ by 0.25% from month to month and by as much as 0.50% day to day (Hoyt and Schatten, 1997).

Solar irradiance has been measured in space by sensors on several spacecraft including the Nimbus-7 satellite (ERB 1978-93), the Earth Radiation Budget Satellite (ERBS 1984-96), and two Active Cavity Radiometers (ACRIM 1980-89) that flew on the Solar Maximum Mission (SMM), and an Active Cavity Radiometer (ACRIMII 1991-present) that is aboard the Upper Atmospheric Research Satellite (UARS). Currently (1999), these measurements account for more than 20 years of overlapping data. However, the time series of direct irradiance observations is of insufficient length for adequate comparison with climatic data.

Fortunately, several solar-irradiance investigators have developed empirical models for estimating total solar irradiance before 1978 (Foukal and Lean 1990; Hoyt and Schatten 1993, 1997). The Hoyt and Schatten model of solar irradiance (1993, 1997) includes relations between solar irradiance and solar-cycle length, cycle decay rate, mean level of solar activity, solar rotation rate, and fraction of penumbral spots. Using these five solar indices, estimates of total solar irradiance have been made back to 1874. Estimates of total solar irradiance also were made from 1700 to 1873 and are based on cycle length, cycle decay rate, and mean level of solar activity.

A mechanism proposed for the coupling of global total solar irradiance with short-term regional hydroclimatology was suggested by Perry (1994) and entails four major linkages.

1. Solar-irradiance variations create ocean-temperature anomalies by absorption of solar energy into a deep surface layer.
2. Major currents of the Pacific Ocean transport ocean-temperature anomalies around the Pacific Ocean gyre to temperate regions.
3. Persistent ocean-temperature anomalies affect characteristics of the upper level jet stream.
4. Jet-stream characteristics downwind (troughs and ridges) yield regional climatic factors such as precipitation, temperature, and evaporation that in turn control streamflow throughout North America.

Climate for a region can be defined as the prevailing or average weather conditions over a period of many years. Short-term climate variations are seasonal to multiyear deviations from the average conditions of precipitation, temperature, and evapotranspiration. The interaction of these meteorological variables and their seasonal and annual fluctuations constitute climate variability. Measuring the variability of climate can be quite challenging as precipitation and temperature data are obtained at specific sites and times and can be subject to various sampling errors. Evapotranspiration at a single site is difficult to measure, and areal observations are virtually nonexistent.

Given these difficulties, streamflow records can be excellent indicators of regional climates, for both the short and long terms. The total volume of water flowing out of a hydrologic basin is the net sum of the water budget for that basin. It is an integration of climatic conditions including precipitation, evapotranspiration, and storage over a continuous area and period of time.

Mean annual streamflow in the upper Mississippi River Basin is the hydrologic variable examined in this paper. The upper Mississippi River Basin occupies about one-fourth of the total area of the contiguous 48 States, and extends roughly from the Rocky Mountains of Montana, Wyoming, and Colorado, eastward almost to Lake Superior and Lake Michigan, and southward to St. Louis, Missouri. The general climatology of the 1,800,000-km² basin varies from semiarid in the west to humid in the east. The long-term (1934-98) mean annual streamflow of the Mississippi River at St. Louis, Missouri, is 5,350 m³/s. Water storage within the upper Mississippi River Basin includes a vast and complex groundwater component, a riverine component, and an artificial impoundment component. The integrated effect of these components moderate the short-term variability of streamflow. The variance of the mean annual streamflow is 1,820 m³/s.

Variations in solar irradiance may yield significant ocean-temperature anomalies that, in turn, affect the regional climate and streamflow of the upper Mississippi River Basin and its outflow. Because it is the relative difference in the temperature between the anomalies in various parts of the ocean that may affect the upper atmospheric patterns, annual changes in total solar irradiance are assumed to be the climatic-forcing mechanism. A slightly varying solar irradiance over several years time would result in ocean-temperature anomalies that are nearly the same temperature, whereas a strongly varying solar irradiance could generate anomalies with contrasting temperatures.

The detection of the solar signal in streamflow data allows development of a predictive model for streamflow in the upper Mississippi River Basin. Using only annual solar-irradiance variations, almost 40 percent of the annual variability of streamflow is explained by the weighted, moving-averaged irradiance lagged 5 years. However, other atmospheric and climatic variables can be used in conjunction with solar irradiance in developing a multivariate model.

The fundamental conclusion of this paper is that short-term changes in total solar irradiance from the Sun may have an effect on the short-term regional climate of North America through global oceanic and atmospheric processes. Annual solar-irradiance variations may create warm and cool ocean water anomalies in the tropical Pacific Ocean, which can affect streamflow in the Mississippi 5 years later through induced position of ridges and troughs in the jet stream.

The relation between solar irradiance and streamflow in the upper Mississippi River Basin allows the development of a model to predict annual mean streamflow. A stepwise multivariate regression analysis using the previous year's average basin precipitation and changes in weighted solar irradiance lagged 5 years produces a model that explains nearly one-half of the variability in annual streamflow. When data for only La Niña years (cold phase) are considered, the model explains more than two-thirds of the variability since 1950.

Brooks, C.E.P., 1926, The relations of solar and meteorological phenomena: A summary of the literature from 1914 to 1924 inclusive. First report, Commission for the Study of Solar and Terrestrial Relationships. Brussels: International Council of Scientific Unions. p 66-100.

Clayton, H.H., 1940, The 11-year and 27-day solar periods in meteorology: Smithsonian Miscellaneous Collections 39 (5), 20 p.

Eddy, J.A., 1983, Keynote address: A historical review of solar variability, weather, and climate, in McCormac, B.M., editor. Weather and Climate Responses to Solar Variations: Boulder, CO, Colorado Associated University Press. p. 1-15.

Foukal P., and Lean, J., 1990, An empirical model of total solar irradiance variation between 1874 and 1988: Science v. 247, p. 556-9.

Friis-Christiensen, E., and Lassen, K., 1991, Length of solar cycle: An indicator of solar activity closely associated with climate: Science v. 254, p. 698-700.

Hoyt, D.V., 1979, Variations in sunspot structure and climate: Climatic Change 2, p. 79-92.

Hoyt, D.V., and Schatten, K.H., 1993, A discussion of plausible solar irradiance variations, 1700-1992: Journal of Geophysical Research, v. 98A, p. 18,895-906.

Hoyt, D.V., and Schatten, K.H., 1997, The Role of the Sun in Climate Change: Oxford, NY, Oxford University Press, 279 p.

Perry, C.A., 1994, Solar-irradiance variations and regional precipitation fluctuations in the western USA: International Journal of Climatology v. 14, p. 969-84.

White, W.B., Lean, J., Cayan, D.R., and Dettinger, M.D., 1997, Response of global upper ocean temperature to changing solar irradiance: Journal of Geophysical Research v. 102(c2), p. 3255-66.