Reservoir model
Un modelo bien conocido es el modelo del reservorio lineal, pero en la práctica este modelo tiene utilidad limitada.
El modelo de escorrentía a base del reservorio no lineal tiene más aplicabilidad universal, pero solamente vale para cuencas en las cuales se puede considerar que la lluvia tiene una distribución más o menos igual sobre el área. El tamaño máximo de la cuenca depende entonces de las características de la precipitación "Precipitación (meteorología)") en la región. Cuando el área de estudio es demasiado grande, se puede dividirlo en subcuencas y las hidrogramas respectivas pueden ser combinadas empleando modelos de simulación o modelos hidráulicos de transporte.
Linear reservoir
The hydrology of a linear reservoir (figure 1) is based on two equations:[18].
being:.
Runoff equation.
The combination of the two previous equations results in a differential equation, the solution of which is presented as:.
This is the equation of runoff, runoff, or hydraulic surface discharge, where Q and Q mean the values of Q at time T and T respectively while T–T is the step or interval in time during which the net recharge R can be assumed constant.
Computation of the total hydrograph.
Provided that the value of A is known, the total hydrograph (HT) can be obtained using a successive number of steps in time and calculating the runoff with the runoff equation at the end of each step based on the runoff at the end of the previous interval. The initial runoff must be known as well.
Unit hydrograph.
When R = 0, the discharge can be written as:.
Substituting the expression for Q into equation (1) we obtain the differential equation.
and its solution is:
Replacing S with Q/A according to equation (1) and taking a unit of time (T=1), we see that:.
This is called instantaneous unit hydrograph (HUI).[19] The availability of the HUI eliminates the need to calculate the HT by adding the partial hydroranges with the more complicated method of convolution.[20].
Reaction factor.
When the reaction factor (A) can be determined from the characteristics of the hydrological basin, the reservoir model can be used as a deterministic model or analytical model.
Otherwise, the A factor can be determined from a rainfall and runoff data file using the calibration method explained below for the nonlinear reservoir. With this method the reservoir is used as a black box "Black box (systems)").
Conversions.
Nonlinear reservoir
Contrary to the linear reservoir, the nonlinear reservoir has a reaction factor (A) that is not constant,[21] but a function that depends on S or Q (figure 2, 3).
Normally the A factor increases with Q or S because the higher the water level, the greater the discharge capacity. Therefore, the factor is called Aq instead of A.
The nonlinear reservoir does not have a usable HUI.
During periods without rain and recharge, that is R = 0, the runoff equation reduces to:.
or using a unit interval of time T – T = 1 and solving for Aq:.
Then, the reaction factor Aq can be derived from the runoff or discharge with unit intervals during dry seasons using a numerical method[22].
Figure 3 shows the relationship between Aq and Q for a small valley (Rogbom) in Sierra Leone.
Figure 4 shows the observed and simulated (calculated, reconstructed) hydrograph of the stream on the downstream side of the same valley.[23].
Net recharge
Net recharge (effective rainfall, excess rainfall) can be modeled with a fore-reservoir (figure 6) that gives recharge as overflow. The prereservoir contains the following elements:
The recharge during a unit interval of time (T–T=1) is found as: R = Rain – Sd, provided that R > 0, otherwise R = 0.
The current storage at the end of the unit interval is calculated as Sa = Sa + Rain – R – Ea, where Sa is the current storage at the beginning of the time interval.
The Curve Number (NC) method[2] presents an alternative to estimate net recharge. Here, the initial abstraction is comparable to Sm–Si where Si is the initial value of Sa in the reservoir method.
Software
Figures 3, 4 and 5 have been prepared with the RainOff[24] computer program designed to analyze the rainfall-runoff relationship through a non-linear reservoir with a pre-reservoir. The program determines the function of Aq as linear, logarithmic, or exponential. The program also contains an example of the hydrograph of an agricultural underground drainage system with a value of the reaction factor Aq that can be calculated directly from the characteristics of the system itself.[18].