Inflow

Inflow (and forecast) series are stored in historical.h5. They are standard EMPS-type timeseries. Due to normalization, the unit of the inflow series is not important. The shape is the important part. This makes it possible to use any unit for inflow series. Normalization allows for sharing the inflow series between different DETD modules without requiring any extra storage on disk for the input model.

As a convention, LTM-API expects the inflow series to be in m3/s. However, for the CLI version, it can be anything.

Inflow graph

Fig. 1: Visualization of an arbitrary inflow series

Normalization

A practical example. Given an inflow series with the following shape:

  • 10 m3/s for 2 weeks

  • 1 m3/s for 8 years, minus the 2 weeks

Over 8 EFI-years, the total number of days is 8 * 52 * 7 = 2912 days.

Total volume is (14 d * 10 m3/s) + (2898 d * 1 m3/s) = 3038 d * m3/s.

The inflow graph will be scaled to:

  • (2912/3038) * 10 m3/s = 9.5853 m3/s

  • (2912/3038) * 1 m3/s = 0.9585 m3/s

Note

The same calculation can be done with any other unit. Here is the same example using m3 as the unit. The important bit is to have a consistent time unit.

8-EFI years is (2912 days * 86400 seconds per day) = 251 596 800 seconds

Volume is (14 d * 86400 s * 10 m3/s) + (2898 d * 86400 s * 1 m3/s) = 262 483 200 m3

  • (251 596 800 s / 262 483 200 m3) * 10 m3/s = 9.5853 m3/s

  • (251 596 800 s / 262 483 200 m3) * 1 m3/s = 0.9585 m3/s

Inflow graph

Fig. 2: Visualization of an inflow series with 2 weeks with 10 m3/s inflow, while the remaining period has 1 m3/s of inflow.

Scaling

Scaling is done by multiplying the normalized inflow series with a scaling factor. A DETD module have 2 scaling factors, one for regulated inflow and one for unregulated inflow. For the API, reservoirs have the scalar regulated_inflow_scalar and plants have unregulated_inflow.

Recalculate yearly average inflow

The easiest way to recalculate the yearly average inflow is to use the pyltm.util.recalculate_yearly_average_inflow method. The complete code example is given at recalculate_average_yearly_inflow.

Four pieces of information are needed to recalculate the yearly average inflow:

  • The inflow series

  • The old period the average is calculated from

  • The old yearly average inflow

  • The new period

Below is a step-by-step walkthrough using a synthetic inflow series.

Synthetic inflow series

Fig. 3: A toy inflow series used for illustration

Scenario

  • Old period: 1960 - 1970

  • New period: 1960 - 1980

  • Old yearly average inflow: 10 m³/s

Goal

Find the new yearly average inflow.

By definition, this equation has to be satisfied.

(1)\[\frac{ \text{new period total inflow volume (A)} }{ \text{area of the inflow series for the new period (B)} } = \frac{ \text{old period total inflow volume (C)} }{ \text{area of the inflow series for the old period (D)} }\]

By drawing what we know from Figure 3:

Inflow series with total inflow volume for new and old periods

Fig. 4: Inflow series with total inflow volume for new and old periods, where the Y-axis for new total inflow volume is the unknown.

  • A: \(20y \cdot x \frac{m^3}{s}\)

  • B: \(30y \cdot unit\)

  • C: \(10y \cdot 10 \frac{m^3}{s}\)

  • D: \(10y \cdot unit\)

(2)\[\frac{ (A) }{ (B) } = \frac{ (C) }{ (D) }\]

Insert the values from the equation above:

(3)\[\frac{ 20y \cdot x \frac{m^3}{s}}{ 30y \cdot unit } = \frac{ 10y \cdot 10 \frac{m^3}{s} }{ 10y \cdot unit }\]

Isolate the unknown

(4)\[x \frac{m^3}{s} = \frac{ 10y \cdot 10 \frac{m^3}{s} \cdot 30y \cdot unit }{ 10y \cdot unit \cdot 20y \cdot }\]

Eliminate units:

(5)\[x \frac{m^3}{s} = \frac{ 10 \cdot 10 \frac{m^3}{s} \cdot 30 }{ 10 \cdot 20 }\]

Multiply and divide scalars:

(6)\[x \frac{m^3}{s} = \frac{ 10 \cdot 10 \frac{m^3}{s} \cdot 30 }{ 10 \cdot 20 } = \frac{ 300 \frac{m^3}{s} }{ 200 } = \underline{\underline{15 \frac{m^3}{s}}}\]

Utility-methods

The pyltm.util submodule contains a handful of helper functions that make working with inflow series easier:

  • normalize_inflow_series(...) - normalises a raw time-series

  • scale_inflow_series(...) - applies a user-supplied scalar

  • recalculate_yearly_average_inflow(...) - recomputes an average when the time window changes

These helpers are intentionally lightweight and are designed to be used both in the API and in your own scripts.