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I have managed to successfully run the model below in Google earth engine, however the parameters α and β are unknown coefficients that need to be determined through optimization based on the conditions below:

var Q = ee.Image(-1) // Value to use when none of the conditions match 
  .where(
    evaluate('(Vo) <= ((Sa) - P)'),
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  )
  .where(
    evaluate('((Sa) - P) < (Vo) < (Sa)'),
    evaluate('(((P - (Sa) + (Vo)) * (P - (Sa) + (2*(Vo)))) / (P - (Sa) + (2*(Vo)) + S))')
  )

  .where(
    evaluate('(Sa) <= (Vo) <= ((Sa) + S)'),
    evaluate('( P * ( 1 - ( ( ( ( (Sa) + (S) - (Vo) ) **2) ) / ( (P * ( (Sa) + (S) - (Vo))) + ( S * (S + (Vo)) ) ) ) ) )')
  )

To compute the initial soil moisture Vo and the threshold soil moisture, Sa the following equations were used:

where Vo = α√(P5*S)

and Sa = βS

P5 is the 5-day antecedent rainfall and P is the precipitation for the day.

Is there a way to achieve this in GEE?

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