Integration of Meteorological Forecasts/Climate Outlooks Into Extended Streamflow Prediction (ESP) System

1.  INTRODUCTION
 
The value of utilizing long-range weather predictions for making extended hydrologic forecasts has been the subject
of debate among hydrologists for a long time, since these predictions are of marginal skill for significant portions of the
continental United States, especially at hydrologic-relevant spatial and temporal scales.  However, the interest in using
monthly and seasonal temperature and precipitation outlooks for making extended hydrologic predictions has increased
considerably in the past few years for two main reasons: (1) the prospect exists for  improved weather forecast accuracy
through enhanced ocean-atmosphere and land-surface coupled models, and (2) for a number of hydrologic applications
even a small gain in forecast skill potentially leads to larger increases in their social and  economic value.  

The portion of the National Weather Service River Forecast System that produces  probabilistic forecasts of
streamflow and streamflow-related variables for periods up to 12 months was originally called Extended 
Streamflow Prediction (ESP) system.  The original version of ESP created an ensemble of streamflow traces using 
multiple years of historical time series of precipitation and temperature as possible future meteorological realizations. 
These traces were then analyzed statistically to make a probabilistic forecast of any streamflow-related variable.  ESP
was not originally configured to handle weather forecasts as input (with the exception of a deterministic short-term 
precipitation forecast).  During the statistical analysis ESP allowed a forecaster to assign weights to simulated
streamflow traces based on his or her judgement about the similarity between the weather conditions of each historical
year and the forecast for the current year.  Since such weighting was subjective, it was generally not performed at all. 

In order to enhance long-range hydrologic predictions through climate forecasts, a methodology was developed in
the National Weather Service (NWS) to facilitate incorporation of climate outlooks into the ESP.  The schematic of 
the new Ensemble Streamflow Prediction (ESP) system with integrated weather forecasts is given in Figure 1.


Figure 1. The Schematic of the Current Extended Streamflow Prediction System


2.  METEOROLOGICAL FORECASTS/CLIMATE OUTLOOKS USED
 
The primary weather products of interest for the ESP are long-range probabilistic climate predictions that are
available from the Climate Prediction Center (CPC) of the NWS/ National Center for Environmental Predictions
(NCEP).  These products, released approximately in the middle of each month, are: monthly surface precipitation totals
and temperature outlooks for the next month, and 13 3-month outlooks (starting with a 2-week lead time, successively
lagged by one month and covering a period up to 13 months in the future). Each forecast includes maps of probability
anomalies of monthly/seasonal average surface temperature and total precipitation.  These indicate the probability of 
temperature and precipitation falling within the lower, middle, and upper third of their  climatological distributions (below-
normal, near-normal, or above-normal category).  For more information on these products visit the CPC web-page at
the  htpp://www.nnic.fb4.noaa.gov:80/products/predictions/multi_season/13_seasonal_outlooks/, or see, for example, O'Lenic
(1994). 

Since these outlooks are issued with an approximately 15-day lead time, depending on the ESP run date, they may
not be applicable for up to first two weeks of forecast period.  In the absence of probabilistic operational forecast, and
In an effort to provide some type of weather information for that period as well, two additional NCEP products were
added.  

The first one is  a 1 to 5-day  forecast, made daily at the Hydrometeorological Prediction Center (HPC).  Since March
1997, the form of a 1 to 5-day precipitation forecast is quantitative (i.e., amount of precipitation expected in inches). 
Previously this forecast was issued in categories.  A temperature forecast is expressed as a maximum and  minimum
anomaly from a 5-day climatological mean value in degrees Fahrenheit.  The products may be found at the following
web page: htpp://weather.noaa.gov/fax/nwsfax.shtml. 

The second product is 6 to 10-day outlooks of average temperature and total precipitation, issued every Monday,
Wednesday and Friday by the CPC.  The current 6 to 10-day average surface temperature forecast is given in one of
the following five categories: much-below-normal, below-normal, near-normal, above-normal, and much-above-normal; 
precipitation forecast is given in one of the following four categories: no precipitation, below-normal, near-normal, and 
above-normal (e.g., CPC www page at htpp://www.nnic.noaa.gov:80/products/predictions/6-10_day/; Van den Dool and
Rukhovets, 1994).  Because of their non-probabilistic format, both products are only transient addition to the ESP, until
new techniques for integrating NCEP global ensemble forecasts in the ESP are not more developed in the Office of
Hydrology of the NWS.


3.  METHODOLOGY

3.1 General  

The primary basis for this ESP enhancement was integration of current CPC probabilistic monthly and seasonal
climate outlooks into ESP.  The developed methodology relies upon inputs describing shifts in climatological
distributions.  It is based on adjusting historical mean-areal precipitation (MAP) and temperature (MAT) time series
relative to current meteorological forecasts/climate outlooks before being used as input into the ESP.  The  marginal
exceedence probabilities of the adjusted time series are consistent with the issued CPC forecasts.  Most of the time,
only two sets of coefficients (one for precipitation and one for temperature) are needed for an entire ESP forecast area. 
However, if the forecast area is significantly larger than a few tens of thousands of square kilometers, it may be
necessary to perform separate adjustments for two or more subareas.

The assumption was made that the observed and forecast values come from similar types of distributions. 
Temperature was modeled as a Gaussian process.  The conditional part of the precipitation distribution (i.e., non-zero
part) was assumed to be well represented by Gamma distribution.  That assumption was tested on 1948-1993 data
set from the Des Moines forecast group of the North Central River Forecast Center area.  It was showed that, in
general, Gamma (two or three parameter Gamma) provided a better fit for 5-day, monthly and seasonal totals than
Weibull or log-normal distributions could.

Differences between forecast-based expected values and climatological averages were used to define adjustment
coefficients j:
                       j  = Tfcst - Thist
where Tfcst is a distribution average temperature defined for a forecast relevant for a time interval i; and Thist is an
average temperature defined from the climatology for the same period.  Units of j have to match units in which MAT
values are given.  These coefficients are to be applied to each climatological MAT value observed during the time period
i (where that period may be a 5-day period, a month, or a 3-month period, depending on weather forecast used.)

Precipitation adjustment was performed in a slightly different manner.  Since existing CPC probabilistic forecasts
integrate zero and non-zero rainfall, unconditional probabilities were first transformed into conditional using
climatological probability of precipitation.  Although this transformation is rarely needed for monthly and seasonal data,
it is important when dealing with 5-day precipitation totals.  Once Gamma distributions were fitted to forecast-based
and climatological information, ratios of distribution averages were used as nondimensional adjustment coefficients,
 i, that were applied to each historical MAP value observed during the time i:
                          i = Pfcst/Phist
where Pfcst is a distribution average precipitation accumulation that is calculated based on a forecast applicable for a
time interval i;  Phist is an average precipitation accumulation defined from the climatology for the area of interest and
the same period of time. 

The difference in the type of adjustment used for MAP and MAT time series is derived from a different nature of the
processes.  Precipitation adjustment has to preserve a non-negativity requirement for precipitation amounts, while
temperature adjustment has to allow for both negative as well as positive temperatures.

In order to incorporate nonprobabilistic 1 to 5-day and 6 to 10-day forecasts into the ESP using the methodology
developed for probabilistic monthly/seasonal forecasts, these forecasts had to be transformed into probabilistic
statements.  This was accomplished by assigning, in advance, a distribution-anomaly number for each forecast
category.  The assigned numbers equaled the smallest difference among all non-exceedence probabilities in a specific
category and a 50 percent nonexceedence probability.  For example, for the 6 to 10-day temperature forecast an
"above normal" category defines the range of temperatures with climatological probability of nonexceedence between
70-88 percent, therefore the selected distribution shift was 20 percent (i.e., 70-50).  To account for a "no precipitation"
forecast, an assumption was made that it is a "sure event" if a climatological probability of precipitation for a given 5-day
period was less than 10 percent, otherwise, a negative 30 percent distribution shift was used.   For a 1 to 5-day
deterministic precipitation forecast, a given number was treated as expected value of  conditional Gamma distribution. 

For periods in which different forecasts overlap only the "most accurate" forecast was used to define adjustment
coefficients.  For hydrologic purposes, the meteorological forecast accuracy was assumed to be a function of lead time
and duration of the forecast period, such that forecasts of shorter duration and with a shorter lead time were considered
to be more accurate than forecasts with longer lead-times and valid periods.  In this framework a 1 to 5-day forecast
is the most accurate forecast, a 6 to 10-day forecast is more accurate than monthly/seasonal forecasts, a monthly
forecast is more accurate than a seasonal forecast covering the same period, and seasonal forecasts are only relevant
for a period of time starting at the end of a first-month forecast, but seasonal forecast accuracy does not depend on
lead time.  Finally, if there is a period that is not covered with current weather information, the relevant weather forecast
that was used at the previous ESP run is used provided that it exists and that it is not older than 30 days; otherwise,
climatology was maintained. Depending on forecast availability, periods with no forecast may arise at any time, but such
periods will occur regularly for ESP runs between the 15th of a month (when new CPC climate outlooks are issued) and
the end of a month.  


3.2  Algorithm

The first step is to query a file created at the previous ESP run in which forecasts have been updated since the last
run.  Information available from the file includes meteorological forecasts that were used to calculate adjustment
coefficients, forecast start dates and valid periods, and time series of daily coefficients that were  used to modify MAP
and MAT historical time series at the previous ESP run.  If such file does not exist, or if there has been more than one
month since the last run, the adjustment coefficients are set to their initial values; otherwise, coefficients that were
relevant to a period of time between two runs are moved to the end of time series and replaced with their initial values. 
For periods for which forecasts are updated, new adjustment coefficients are calculated.  Firstly, coefficients are defined
from 1 to 5-day and 6 to 10-day forecasts.  For a 1 to 5-day temperature forecast, an average of a maximum and
minimum 5-day mean temperature anomaly is directly applied to adjust all coinciding MAT data.  For a 6 to 10-day
period, the temperature forecast is converted into a distribution-anomaly number assigned in advance for each category
(as described in section 3.1).  Differences between forecast-based expected values and climatological averages are
used to define adjustment coefficients applied to modify MAT values.  Categorical precipitation forecasts are first turned
into probability-anomaly shifts based on anomaly numbers assigned in advance for each category, then averages of
conditional forecast-based and climatological Gamma distributions are calculated, and finally their ratios are used as
adjustment coefficients that are applied to matching MAP values.

The adjustment coefficients are then defined based on monthly/seasonal climate outlooks.  The anomaly forecasts
of precipitation are first converted to conditional-distribution probability shifts.  Ratios between forecast-based and
climatological averages (or differences for temperature) are used to define one monthly and 13 seasonal average
anomalies.  Starting at the end of the first month, calculated seasonal anomalies are used to define monthly adjustment
coefficients.  As each month is forecast in three overlapping seasonal forecasts (e.g., February is forecast in December-
January-February, January-February-March, and February-March-April), and because it is assumed that seasonal
forecast accuracy does not depend on a lead time, the final monthly coefficient is taken as a simple average of three
numbers (or two for a 45-day lead-time month).  The simple average is selected after testing several alternative
algorithms  that used all thirteen forecasts in parallel, which produced extremely unstable monthly numbers due to
inconsistencies in overlapped seasonal forecasts.  These monthly adjustment coefficients are applied to coinciding MAP
and MAT values.  Finally, climatological MAP and MAT time series are modified and written in a file to be used by the
ESP.


4.  CONCLUSIONS

The methodology was developed for integrating primarily probabilistic monthly, and seasonal climatological outlooks
into the current NWS ESP system.  A reason why non-probabilistic 1 to 5-day forecasts and 6 to 10-day outlooks were
added as well is that monthly and seasonal outlooks are not always applicable for first two forecast weeks. In addition,
5-day forecasts are believed to be more accurate at spatial and temporal scales relevant to hydrologic applications. A
methodology was introduced to account for the uncertainty in the 1 to 5-day and 6 to 10-day forecasts.  This 
methodology, as well as the forecasts themselves, should be considered only as temporary for a 1 to 14-day forecast
period for two main reasons: (1) the form of available meteorological forecasts will significantly change in the near
future, and (2) there is a joint research underway between the Office of Hydrology/ Hydrologic Research Laboratory and
NCEP to develop more skillful techniques to use NCEP ensemble-based products to prepare hydrology-relevant
probabilistic quantitative precipitation forecasts.  A verification program that will permit the NWS to evaluate the
value of using CPC long-term forecasts for hydrologic purposes has been in a test mode since March 1997.  The Des
Moines forecast group of the North Central River Forecast Center has been the test site for the program, but no
evaluation results are available at this time. 


5.  REFERENCES

Day, G. N., 1985: "Extended Streamflow Forecasting using NWSRFS," Journal of Water Resources Planning and
Management, 111(2), 157-170.
O'Lenic, E. A., 1994: Operational long-lead forecasts for the climate outlook, Tech. Proc. Bull. 418,
NOAA/NWS/CPC, 30 pp.
Van den Dool, H. M., and L. Rukhovets, 1994:  "NMC Notes, On the Weights for an Ensemble-Averaged 6-10-Day
Forecast", Weather and Forecasting, Vol. 9, No. 3, 457-465.

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