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

By Charles A. Perry

Proceedings of the Sixteenth Annual Pacific Climate Workshop
The Wrigley Institute for Environmental Studies
Two Harbors, Santa Catalina Island, California
May 24-27, 1999

Edited by G.James West and Lauren Buffaloe





    Figure 1. Solar-Irradiance/Ocean-Atmosphere Climate Mechanism
    Figure 2. Solar cycle maxima and annual solar-irradiance changes, 1940-97, computed from Hoyt and Schatten (1997) model
    Figure 3. Comparison of annual solar-irradiance changes computed from Hoyt and Schatten (1997) model lagged 5 years and annual mean streamflow in the Mississippi River at St. Louis, Missouri, 1950-97
    Figure 4. Relation between previous year's mean precipitation in the upper Mississippi River Basin and annual mean streamflow in the Mississippi River at St. Louis, Missoui, 1950-97
    Figure 5. Comparison of observed annual mean streamflow in the Mississippi River at St. Louis, Missouri, and streamflow generated from the multivariate model for 1950-97
    Figure 6. Relation between observed annual mean streamflow in the Mississippi River at St. Louis, Missouri, and streamflow generated from the multivariate model using La Niña years only


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.

Solar/Hydroclimate Mechanism

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.

Upper Mississippi River Streamflow Relation to Solar Irradiance

The four major components of the physical connection between solar irradiance and hydroclimatology of the upper Mississippi River Basin are illustrated by the diagrams in figure 1. A period of increased total solar irradiance heats the Pacific Warm Pool (the western tropical Pacific Ocean) to an anomalously warm temperature forming a warm ocean water (WOW) anomaly (figure 1A). Two years later the WOW has been transported northward by the ocean currents and is east of Japan (figure 1B). The atmosphere responds to the warmer ocean surface by moving the jet stream farther north forming a high-pressure ridge. This ridge causes the atmosphere to have anticyclonic curvature that results in dynamically sinking air, which inhibits development of precipitation and causes dry conditions to prevail beneath the ridge. Downwind, east of the ridge, the perturbed jet stream must turn back to the left, and a trough is induced. To the east of the trough's axis, the atmosphere is dynamically lifted and precipitation occurrence is enhanced. Five years after its formation, the WOW is in the eastern North Pacific Ocean along with its accompanying upper level ridge. A trailing cool ocean water (COW) anomaly, formed during a period of decreased irradiance 2 to 3 years after the strong increase, has moved northward and has pulled the jet stream southward forming a trough. These two areas of ocean-temperature anomalies together result in a vigorous jet-stream pattern that places a strong persistent trough over western North America. This could have been the case in 1993 when a strong persistent trough over the Rocky Mountains helped to create very persistent rains over the upper Mississippi River Basin and historic flooding. This persistent trough may have originated from a very strong increase in solar irradiance that occurred in 1988-89, which then was followed by a sharp irradiance decrease in 1990.

Hydrologic Data as a Climate Indicator

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.

Solar Irradiance, Climatic Factors, and Streamflow

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.

Annual changes in solar irradiance were computed from Hoyt and Schatten's model of solar irradiance (Hoyt and Schatten 1997). The annual differences from 1940 to 1997 are shown in figure 2. Maximum differences precede slightly or coincide with the solar cycle maxima (which occurred in 1947, 1957, 1968, 1979, and 1989). Annual mean streamflow for the years 1950-97 from the Mississippi River at St. Louis, Missouri, is compared with the irradiance variations in figure 3. Here, the best fit between irradiance variations and streamflow occurs with a lag time of 5 years. The simple linear correlation coefficient between these two data sets is R=0.55. Peaks do not always coincide; the lag times for graphical comparison for different peaks actually range from 4 to 6 years, reflecting the variations in ocean-current patterns and velocities. Therefore, a weighted, moving average (1-2-1) of solar irradiance changes lagged 5 years was used in the correlation with streamflow, and the correlation coefficient increased to R=0.63. Other variables, including the El Niño/Southern Oscillation effects and the Quasi-Biennial Oscillation (QBO) of the tropical stratosphere, may be involved in the delay, early arrival, or dispersal of the solar-irradiance/streamflow relation in the upper Mississippi River Basin.

Mississippi River Streamflow Model

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.

Because storage is an important component of the streamflow from an area as large as the upper Mississippi River Basin, the previous water year's (October to September) mean basin precipitation was included as a variable in the model. Mean basin precipitation was computed by averaging the 75 National Oceanic and Atmospheric Administration (NOAA) meteorological divisions that are in the upper Mississippi River Basin. The relation between the previous year's mean basin precipitation and streamflow in the Mississippi River at St. Louis, Missouri for 1950-97 is shown in figure 4.. The correlation coefficient between these data is R=0.55; the previous year's mean basin precipitation explains slightly more than 30 percent of the annual variability of streamflow. There is some interdependence between weighted solar-irradiance change and the previous year's precipitation as they are weakly correlated (R=0.38, which is just significant at the 5-percent level).

When irradiance change and basin precipitation are included together in a stepwise, multivariate regression analysis, nearly 50 percent of the streamflow variability is explained. The multivariate model for streamflow in cubic meters per second becomes:


Annual streamflow = 225(prec-1) + 5,540(average irradiance change) + 2020     (1)



    prec-1 = previous year's mean precipitation over the upper Mississippi Basin in centimeters;


    average irradiance change = 0.25(4-yr irrad) + 0.5(5-yr irrad) + 0.25(6-yr irrad) in watts per square meter; and


    4-yr irrad = irradiance difference lagged 4 years; 5-yr irrad = irradiance difference lagged 5 years;
    and 6-yr irrad = irradiance difference lagged 6 years.



Figure 5 shows the time series of the observed and modeled annual mean streamflow in the Mississippi River at St. Louis, Missouri. The greatest error of the multivariate model results in underestimating the extreme high streamflows such as those occurring in 1973, 1986 and 1993. These were all warm-phase El Niño years. Years for which the model overestimates the streamflow were 1961 and 1971, which were both cold-phase La Niña years.

When the streamflow data are grouped according to warm or cold phases of the tropical Pacific Ocean, the relation between upper Mississippi River Basin streamflow and solar irradiance change and the previous year's basin precipitation shows some improvement. Warm- or cold- phase years were determined from NOAA's NINO3 index, obtained from the Climate Analysis Center (http://nic.fb4.noaa.gov/data/cddb/cddb/sstoi.indices). NINO3 is an index computed from the sea surface temperature (SST) anomalies in the eastern tropical Pacific Ocean from 5°S to 5°N and 150°W to 90°W. Figure 6 shows the relation between modeled and observed annual mean streamflow for years when the NINO3 index averaged less than 0 for the year (La Niña). Using data for the La Niña years only, two-thirds of the annual streamflow variability is explained (adjusted multiple R²=0.66) by solar-irradiance variations and the previous year's precipitation. The multivariate model for streamflow in cubic meters per second with mean basin precipitation in centimeters and irradiance change in watts per square meter becomes:


Annual Streamflow = 355(prec-1) + 4,933(average irradiance change) - 6,388     (2)


Comparison of observed and modeled annual mean streamflow for the Mississippi River at St. Louis, Missouri using only La Niña years is shown in figure 6. There was no improvement in the model using data for only El Niño years.


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.


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