Fix terms of quadratic equation in Modified Puls Approach

The inflow and outflow variables for the lake module are defined for dt, so the terms (Qin1 (t1) + Qin2 (t2))/2  and (Qout1 (t1) + Qout2 (t2))/2 as in the original mass balance equation of the Modified Puls Approach are not required. Because of this the terms of the quadratic equation were fixed (the solution of the quadratic equation based on the original mass balance equation was implemented.

src/reservoir_lake.jl

@@ -513,7 +513,8 @@ function update(lake::Lake, i, inflow, doy, timestepsecs)
 
         if si_factor_adj > 0.0
             outflow = pow(
-                -lakefactor + pow((pow(lakefactor, 2.0) + 2.0 * si_factor_adj), 0.5),
+                0.5 *
+                (-lakefactor + pow((pow(lakefactor, 2.0) + 4.0 * si_factor_adj), 0.5)),
                 2.0,
             )
         else

test/reservoir_lake.jl

@@ -50,10 +50,10 @@ end
     )
 
     Wflow.update(lake, 1, 2500.0, 181, 86400.0)
-    @test lake.outflow[1] ≈ 85.31903276150577
-    @test lake.totaloutflow[1] ≈ 7.371564430594098e6
-    @test lake.storage[1] ≈ 3.551103576940606e9
-    @test lake.waterlevel[1] ≈ 19.672569557695734
+    @test lake.outflow[1] ≈ 85.14292808113598
+    @test lake.totaloutflow[1] ≈ 7.356348986210149e6
+    @test lake.storage[1] ≈ 3.55111879238499e9
+    @test lake.waterlevel[1] ≈ 19.672653848925634
     @test lake.precipitation[1] ≈ 20.0
     @test lake.evaporation[1] ≈ 3.2
 end