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<br />001077 <br /> <br />low runoff years are overforecast; (2) the error in this month's <br />seasonal forecast is strongly correlated with the error in the pre- <br />ceding month's forecast. Since these established patterns are <br />inherent in the equations used by the CRSM, the forecast errors com- <br />puted by the CRSM will also tend to produce these same patterns. <br /> <br />A regression model has been developed to aid in determining the error <br />to be incorporated into the seasonal forecast for each month from <br />January to June. The error is the sum of a deterministic and a ran- <br />dom component. The determi ni sti c component is computed from the <br />regression equation. The random component is computed by multiplying <br />the standard error of the regression equation by a random Inean <br />deviation selected from the standard normal distribution (mean = 0, <br />variance = 1). <br /> <br />The forecast error equation has the following form (all runoff units <br />are million acre-feet): <br /> <br />Ei = ai Xi + biE(i -1) + Ci + Zrdi <br /> <br />Where: <br /> <br />i <br />Ei <br />Xi <br />ai <br />E(i -1) <br />bi <br />Ci <br />Zr <br /> <br />di <br /> <br />= month <br />= error in the forecast for month "i. II <br />= natural runoff into Lake Powell from month "i" through July. <br />= linear regression coefficient for Xi. <br />= previous month's forecast error <br />= linear regression coefficient for E(i-l). <br />= constant term in regression equation for month "i." <br />= randomly determined mean deviation taken from the standard <br />normal distribution <br />= standard error of estimate for regression equation for <br />month "i." <br /> <br />The following table summari zes the regression equation coefficients <br />for each month: <br /> Standard <br /> Runoff Error error of <br /> coefficient coefficient Constant estimate <br />Month ill (ai) (bi) (Ci) (di) <br />Jan. 1 0.70 0.00 -8.195 1.270 <br />Feb. 2 0.00 0.80 -0.278 0.977 <br />Mar. 3 0.00 0.90 0.237 0.794 <br />Apr. 4 0.00 0.76 0.027 0.631 <br />May 5 0.00 0.85 0.132 0.377 <br />Jun. 6 0.24 0.79 0.150 0.460 <br /> <br />Once the above forecast error is determined, the runoff forecast for <br />the current month through the end of the water year is computed by <br />adding or subtracting the forecast error from the sum of the natural <br /> <br />29 <br />