Empirical Relationships Between Runoff, and Climate Parameters: An Analysis for Minnesota

Abstract

Correlations between past climate and streamflow in 5 streams in the state of Minnesota are investigated. The rivers are the Straight, Baptism, Zumbro, Clearwater, and Mississippi Rivers. Runoff measured over periods of up to 37 years are correlated with precipitation, air temperature, wind, and dew point temperature. The overall objective is to obtain relationships which can be used in long-term water budget estimates and which use only readily available input parameters without calibration. A seasonal (3 month) time frame produced the closest fit for the linear regressions without time lag. Although the watershed sizes varied greatly, the 3 month period seemed sufficiently long to average long term processes such as infiltration, evaporation, and groundwater flow. An equation was found for each season (3 months) separately for each of the final river records chosen. Winter (December, January, February) regressions utilize only the precipitation data; the spring regressions use air temperature and precipitation; summer and fall regressions are found with precipitation and an evaporation term which used a combination of air temperature, dew point temperature, and wind. The coefficients in the regresssion equations are related to watershed characteristics. Statistics for the seasonal linear regression equations include a root mean square error (RMSE) between observed and predicted runoff values and a coefficient of variability (CV). The RMSE error values, found from the sum of the squares of the errors (SSE), range from 0.111 in/mo to 0.692 in/mo. The coefficients of variability (CV), a measure of the relative error of the fitted runoff values, range from 0.237 to 0.529. The seasonal regression equations are used to project future runoff averages if a climate change occurs. For this purpose the Goddard Institute for Space Studies (GISS) values for the "2xC02 climate scenario", i.e. the climate projected after a doubling of atmospheric CO2, are applied to the linear runoff regression equations. The projections are that the spring runoff values will decrease by 16 % to 35 % while the other seasons will experience an increase in streamflow between 3 % and 50 %. Annual runoff will not change dramatically; decreases (3 to 4 %) are projected for the Baptism and Mississippi River basins, while an increase (9 %) is projected for the Zumbro River. The results are in the range of changes predicted by other investigations using very different techniques. Since predictions are based on equations found with past records, it is implied that the land cover will remain unchanged in the 2xC02 environment. This may be unrealistic and needs further investigation.