![](media/image1.jpeg){width="2.21875in" height="1.65625in"}**Simulating
the Value of El Niño Forecasts**

**for the Panama Canal**

Nicholas Graham and Konstantine Georgakakos

*Hydrologic Research Center, San Diego, CA*

Carlos Vargas and Modesto Echevers

*Meteorology and Hydrology Section*

*Panama Canal Authority, Panama Canal Zone, Panama*

[FACTS]{.underline}

-   The Panama Canal requires a supply of fresh water for operations.

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-   Canal fresh water storage has an operational time constant of
    months.

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-   El Niño variability strongly modulates rainfall and water supply for
    the Canal.

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-   El Niño variability is somewhat predictable at lead times of 9-12
    months.

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-   Canal inflow is modestly predictable at lead times of months.

*QUESTION*

-   Can routine El Niño predictions be used assist in Canal operational
    planning?

[DATA]{.underline}

1\) CLIMATE

-   NATURAL INFLOW INTO GATUN LAKE (1906-2000)

-   NIÑO3 SST (1906-2000; Smith and Reynolds, 2004)

-   PREDICTED NIÑO3 (NCEP; 1981-97; MONTHLY)

2\) CANAL CHARACTERISTICS (PCA)

[PROJECT DESIGN AND GOALS]{.underline}

1)  Build a basic, monthly time step, model of the Canal system,
    embodying:

    a.  Management objectives --

        i.  Reliable lockage

        ii. Additional income through hydro-power generation

        iii. Low risk

b\) Physical constraints

> i\) Gatun Lake capacity, vol. / stage, level requirements
>
> ii\) Lockage, hydropower, spillage discharge capacities

iii\) Lockage and hydropower income

> c\) Inflow predictability (3 models, each with variable uncertainty )

i\) CLIMATE - Assume every year inflow follows climatology

ii\) PERFECT - Assume future inflows are perfectly known

> iii\) FORECAST - Inflow outlooks derived from El Nino forecasts

2)  Operate the model using probabilistic inflow outlooks (i, ii, iii)
    using an optimizer to simulate management with objective forecast
    information.

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3)  Evaluate performance of simulated system in terms of added value and
    operational reliability afforded by El Nino forecast information and
    formal inclusion of uncertainty.

[CLIMATOLOGY AND PREDICTABILITY]{.underline}

-   CANAL INFLOWS HAVE A STRONG ANNUAL CYCLE

![](media/image2.jpeg){width="2.9368055555555554in"
height="2.2819444444444446in"}

-   EL NIÑO VARIABILITY MODULATES CANAL REGION RAINFALL AND INFLOWS.

> CORRELATIONS: WATER YEAR GATUN INFLOW vs NINO3 SST 1915-1999

![](media/image3.png){width="2.9715277777777778in"
height="2.015277777777778in"}

![](media/image4.jpeg){width="3.1597222222222223in"
height="2.696527777777778in"}

-   THE STRENGTH OF THE RELATIONSHIP BETWEEN EL NIÑO AND FLOW VARIES
    FROM STRONG TO VERY WEAK DURING THE YEAR.

![](media/image5.jpeg){width="3.0520833333333335in"
height="2.5305555555555554in"}

EL NIÑO VARIABILITY IS PREDICTABLE

OPERATIONAL NINO3 SST PREDICTION CORRELATIONS

1981-1998

![](media/image6.png){width="3.1013888888888888in"
height="2.0756944444444443in"}

**EL NINO PREDICTIONS REDUCE UNCERTIAINTY IN INFLOW OUTLOOKS**

FRACTIONAL REDUCTIONS IN INFLOW UNCERTAINTY (RMS)

COMPARED WITH CLIMATOLOGY

USING OPERATIONAL NINO3 SST PREDICTIONS

1981-1998

![](media/image7.png){width="2.801388888888889in"
height="2.352777777777778in"}

[CANAL SIMULATION SYSTE**M**]{.underline}

-   INITIAL STATE (GATUN LAKE VOLUME)

-   GATUN LAKE CAPACITY -- LEVEL / VOLUME RELATIONSHIP

-   LOCKAGE REQUIREMENTS, WATER USE

-   HYDROPOWER REQUREMENTS, WATER USE

-   SPILL LEVEL, POSSIBLE RANGES

-   EVAPORATION, MUNICIPAL WATER REQUIREMENTS

-   EXISTING RULE CURVE

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-   LOCKAGE INCOME

-   HYDROPOWER INCOME

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-   PROBABILISTIC INFLOW PROJECTIONS (6 MONTH HORIZON)

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-   OPTIMIZER and VIRTUAL MANAGER

PANAMA CANAL SIMULATION SYSTEM

![](media/image8.png){width="2.9in" height="2.175in"}

PARAMETERS FOR SIMULATED PANAMA CANAL SYSTEM

*GATUN LAKE PARAMETERS*

Useful volume (VU) -- 766 Mm3

Lowest useful level (HL) -- 24.84 m

Maximum (spill) level (HU) -- 26.67 m

Evaporation and Municipal withdrawal (E) 6.16 Mm3 month-1

Maximum spill rate (RUS) -- 13358.30 Mm3 month-1

Actual spill rate per month (RS) Mm3

Rule curve level for a particular month (H\*m) m

Actual level for a particular month (H\*m) m

*CANAL PARAMETERS*

Volume required per unit ship passage (VL) -- 196,820 m3 ship-1

Maximum number of ships per month (SU) -- 1200 ships month-1

Maximum lockage volume per month (RUL) -- 236.18 Mm3 month-1

Actual lockage volume per month (RL)

Volume required per unit MWH hydropower production (VH) -- 19,114 m3
MWH-1

Maximum hydropower production per month -- 17,280 MWH month-1

Maximum hydropower volume per month (RUH)-- 330.29 Mm3 month-1

Actual hydropower volume per month (RH)

*INCOME PARAMETERS*

Income per ship passage (iL) -- \$US 50,000

Maximum lockage income per month (IUL) - \$US 60M

Actual lockage income per month (IL)

Income per MWH (iH) - \$US 50

Maximum hydropower income per month (IUH)- \$US 864,000

Actual hydropower production per month (IH)

Maximum possible total income per month (IMAX) - \$US 60.864M

*ASSESSING PERFORMANCE OF CANAL SIMULATIONS*

-   Start with initial state at time t (Gatun Lake volume)

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-   Use inflow outlook (probabilistic) for next 6 months

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-   Derive optimal feasible policy (lockage, hydropower, spill) for next
    6 months.

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-   Execute optimal feasible policy for ONE month (to t+1)

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-   Tabulate results with respect to objectives

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-   Update state (Gatun Lake volume) with OBSERVED inflow

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-   Repeat

![](media/image9.png){width="2.9in" height="2.3402777777777777in"}

DOES EL NIÑO FORECAST INFORMATION HELP?

**NOTICE THE EFFECT ON INCORRECTLY SPECIFIED UNCERTAINTY**

UNCERTAINTY vs TOTAL CANAL INCOME (1981-1997)

![](media/image10.png){width="3.357638888888889in"
height="2.2131944444444445in"}

[RESULTS]{.underline}

3 SETS OF SIMULATIONS

1)  PERFECT -- PERFECT FORESIGHT.

NOMINAL UNCERTAINTY: \~ZERO

2)  FORECAST -- USE INFLOWS DERIVED FROM EL NIÑO FORECASTS.

NOMINAL UNCERTAINTY: MEAN-SQUARE FORECAST ERROR.

3)  CLIMATE -- INFLOWS ARE FROM LONG-TERM CLIMATOLOGY.

> NOMINAL UNCERTAINTY: MEAN-SQUARE CLIMATOLOGY ERROR

EACH SET OF SIMULATIONS IS ASSIGNED THE NOMINAL UNCERTAINTY, AND ALSO
VALUES RANGING FROM SMALL TO LARGE.

THIS ALLOW US TO SEE THE SENSIVITY TO CHANGES IN:

A\) THE SKILL OF THE MEAN PREDICTION

B\) THE ASSOCIATED UNCERTAINTY

**COMPARISON OF TOTAL INCOME (1981-1997)**

CLIMATOLOGY - DETERMINISTIC

FORECAST -- UNCERTAINTY 0.4

PERFECT - DETERMINISTIC

![](media/image11.png){width="3.1354166666666665in"
height="2.345138888888889in"}

EXAMPLE OF MONTHLY INCOMES:

PERFECT AND FORECAST MODELS

IN GENERAL, THE CANAL PERFORMS ROBUSTLY

![](media/image12.png){width="3.053472222222222in"
height="2.3208333333333333in"}

NORMALIZED HYDRO-POWER INCOME

![](media/image13.png){width="2.975in" height="2.3354166666666667in"}

AVERAGE SPILL

![](media/image14.png){width="2.897222222222222in"
height="2.1798611111111112in"}

COMPARISON OF BEHAVIOR: EXISTING RULE CURVE vs FORECAST SIMULATION,

EFFECT IS TO TAKE BETTER ADVANTAGE OF EXISTING SUPPLY

CIRCLES INDICATE MONTH 1 (VERIFICATION) LEVELS

FOR EACH CALENDER MONTH

![](media/image15.png){width="2.826388888888889in"
height="2.0236111111111112in"}

**TEST BEHAVIOR OF CANAL TO INCREASED LOCKAGE DEMAND**

(EFFECT IS TO *INCREASE THE SENSITIVITY TO UNCERTAINTY* SPECIFICATION)

N = 40, 48, 56 SHIPS PER DAY

AS FRACTION OF MAXIMUM POSSIBLE INCOME FOR N SHIPS DAY-1

![](media/image16.png){width="2.8194444444444446in"
height="2.147222222222222in"}

AS FRACTION OF MAXIMUM POSSIBLE INCOME FOR **40** SHIPS DAY-1

![](media/image17.jpeg){width="6.645833333333333in"
height="0.6125in"}NOTE STEEPER DEPENDENCE ON UNCERTAINTY

![](media/image18.png){width="2.826388888888889in"
height="2.252083333333333in"}

[SUMMARY]{.underline}

1)  ROUTINE EL NIÑO FORECASTS CAN BE USED TO REDUCE THE UNCERTAINTY IN
    GATUN INFLOW PROJECTIONS AT LEAD TIMES OF MONTH.

2)  THE USE OF THIS INFORMATION INCREASES SIMULATED CANAL INCOME IN
    COMPARISON TO CLIMATOLOGICAL EXPECTATIONS. VALUE = \$322M.

3)  THE VALUE OF FORECAST INFORMATION INCREASES AS THE DEMANDS ON CANAL
    RESOURCES ARE INCREASED.

4)  OPTIMAL CANAL OPERATION IS VERY SENSITIVE TO CORRECT SPECIFICATION
    OF UNCERTAINTY.

**INACCURATE FORECASTS WITH CORRECT UNCERTAINTY BETTER THAN ACCURATE
FORECASTS WITH INCORRECT UNCERTAINTY**

![](media/image19.jpeg){width="0.8645833333333334in"
height="0.4791666666666667in"}