Short-term forecasting 1 Purpose

Short-term forecasts (one to seven days ahead) are seemingly more important for flood warning and the optimization of reservoir storages for flood control than the release of water for irrigation and the environment. A common requirement for short-term forecasting is

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sewage treatment plant where treated effluent can be disposed only when flows exceed some specific threshold or a power station where the temperature of cooling water is of interest. Short-term forecasting is also commonly required for water-supply systems that abstract water directly from rivers, or for the optimi- zation of pumping schedules for conjunctive use schemes that have multiple supply sources. The typical requirement for such short-term forecasts is from one to seven days.

Three commonly used approaches for developing short-term forecast models are based on the use of recession analysis, low-flow frequency analysis and autoregressive regression models. Each of these three approaches are described in turn below.

11.2.2 Recession analysis

Recession analysis, which is described in section 5.3, provides estimates of streamflows in the absence of rainfall. Although the length of the achievable forecast period depends on the size of the drainage basin and its degree of storage, in general it is possible to derive forecasts between 1 and 20 days. The maximum length of the forecast period is evident from the slope of the derived recession curve and the degree of pes- simism concerning the likely length of time before rain is expected.

The simple nature of a recession-based forecast is illus- trated in Figure 11.2. This figure shows a master re- cession curve for a drainage basin with a sustained reduction in flow over a 20-day period starting from around 90 ML/d. Let us assume that the current flow in the river is 74 ML/d and that an estimate is needed of how long it might take before streamflows are re- duced to a threshold of 30 ML/d. The forecast might be undertaken graphically as shown in Figure 11.2, where the number of days before streamflows are re-

duced to the threshold of interest can be estimated directly as the difference between t and t0, which in this case is 11 – 2 = 9 days. Of course, if the master recession curve was fitted to a mathematical function, then the forecast could be carried out analytically. The forecast is conservatively low, in that it is based on the assumption that no rain occurs over the inter- vening period.

11.2.3 Regression analysis

Regression analysis is a more flexible tool that can be used for forecasting. The development of models for short-term forecasts will generally include streamflow and/or rainfall terms from prior time periods, for example:

Q_t+2 = a + b.Q_t + c.R + d.S_t + … (11.1) where Qt+2 represents streamflows to be forecast over the next two-day period; Qt denotes current stream- flows; R represents rainfall that has occurred over the previous day; S_t is a seasonal term; and a, b, c and d are fitted coefficients. For most short-term forecasts, the inclusion of a term representing current stream- flows (Qt) is important because of the high serial de- pendence in flow conditions, and the inclusion of the previous period’s rainfall (R) is a useful means of al- lowing for a subsequent increase in flows. It is some- times useful to include the seasonal term, S_t, which may be defined by a function such as sin(1+2πn/N)/2, where n represents the sequential day number of the year and N represents the total number of days in the year. Alternatively, to achieve a slight phase shift in seasonal response, the cosine function can be used instead of the sine function. In most cases, fitting a regression model to successive observations will in- fringe the independence requirement (an assumption required for fitting by least squares) because of the high serial dependence in the data. The simplest way of avoiding this problem is to fit the regression model to a censored dataset where intervening days of de- pendent data are excluded. Alternatively, a more sophis- ticated approach can be taken where an autoregressive model can be fitted to the residuals.

The main advantage of a regression approach is that additional terms can be included to improve the fit of the model. Ideally, some form of climate forecast could be included, yet, in practice, archives of short- term (less than seven days) climate forecasts have not been traditionally collected, or are non-stationary as a result of the improvements in forecasting methods.

0 10 20 30 40 50 60 70 80 90 100 0 2 4 6 8 10 12 14 16 18 20 Time (days) S tre amf lo w ( M L/ d) t0 t 74 ML/d 30 ML/d

Figure 11.2 Forecast based on a master recession curve

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Synoptic and global climate indices are useful for the prediction of medium-term (one to six months) fore- casts, and a variety of information on sea surface tem- peratures and measurements related to global circulation patterns are commonly used (for example, the Southern Oscillation Index (SOI), the North Atlantic Oscillation Index, the Indian Ocean Dipole and the Troup Index). The use of regression models also allows confidence intervals to be provided. Thus, rather than providing merely a single “best estimate”, confidence intervals can be provided.

The development of regression equations for stream- flow forecasts presents particular challenges, particu- larly for shorter-term periods where streamflows may be zero. The presence of zero flows creates an asym- metrical boundary in the datasets which, without care, can undermine the validity of a least-squares regression model. The simplest practical approach to mitigating this problem is to trial a range of transformations applied to both the independent (that is the predictor) and the dependent (streamflow) variates. Logarithmic and simple power transformations of the data are often useful, whereby the flow and rainfall variates are first transformed into the logarithmic domain, or raised to a power (in a range of 0.2 to 1.0). An alternative approach is to develop regression models that are conditional upon the time of year, or on a range of flow conditions of interest. Thus, it may be effective to develop separate regression models for summer and winter seasons, or for certain sets of flow condit- ions, where periods of antecedent rainfall is above or below average conditions.

11.2.4 Other models

Radar rainfall can be used to improve very short term rainfall forecasts. The most accurate method to forecast rainfall for very short lead times (1 to 2 h) is to use weather radar to estimate the spatial distribution of rainfall and then to advect the rainfall field forwards in time.

At some point in the forecast period, the errors associated with this approach exceed those from numerical weather prediction (NWP) models, and the regional rainfall forecast using this approach is projected to match the NWP model forecast.

Generally, if a large rainfall event is projected over a drainage basin, the low-flow situation is ameliorated, but the reservoir storage problem might not be resolved (Seed, 2003).

11.3 Medium-term forecasting