GR4J leads to odd threshold behaviour for certain parameter sets

[wknoben]

Diagnosis:

• x2 (water exchange parameter) is determined by relative fullness of store S2 (R in original GR4J paper), which is controlled by x3(maximum routing store depth)
• Empty S2, no flow from x2; full S2, flow from x2 as x2's value
• Perrin (2001) says: ". In absolute value, F cannot be greater than x2: x2 represents the maximum quantity of water that can be added (or released) to (from) each model flow component when the routing store level equals x3."
• Theoretically, this works; if S2 never goes above x3, import based on x2 never goes above x2
• In practice, if S2 goes over x3, we can end up in situation where water import via x2 goes up (because S2 > x3), which makes S2 go up further, etc.
• At some point, an equilibrium will be reached where outflow from S2 through flux Qr is equal to import via x2

Why would S2 go over x3?

• Numerical inaccuracies, rounding, etc
• if x2 > x3

Possible solutions:

• Extra constraint in recharge_2 to ensure that returned flow is at most equal to "flux"
• Enforce a check that x2 cannot be greater than x3