NOWCASTING OF PRECIPITATION

Isztar Zawadzki*

McGill University, Montreal, Canada

1. INTRODUCTION

Short-term methods of precipitation

nowcasting range from the simple use of

regional numerical forecasts to complex radar

data assimilation schemes. Presently, the

skill of numerical models is rather poor for

precipitation. Figure 1 shows some typical

scores for precipitation detection for two

limited area models. The skill is low, thus,

nowcasting presently requires other, mostly

heuristic, techniques

Figure 1.- Probability of detection (POD), false alarm rate (FAR), critical success index (CSI) and conditional mean absolute error (CMAE) for GEM at 15km resolution and WRF at 28km resolution for the first 24 and 60 hours, respectively for rain rates above 0.1 mm/h. Radar composites are used as truth. ________________________________

*Isztar Zawadzki, McGill University, 805 Sherbrooke St. W, Montreal, Canada H3A 2K6. Telephone (514) 398-1034, email: isztar.zawadzki@mcgill.ca

We will give here a brief description of the

method most commonly used operationally,

that is, the method based on persistence of

the precipitation pattern in the moving

coordinates (Lagrangian Persistence, or LP for

short).

All the skill values and diagrams

presented here were obtained for the Central-

Eastern United States (that is excluding the

mountainous regions) and are certainly not

universal results

2. NOWCASTING BY LP

In this method the immediate past of the

precipitation patterns is used to determine the

field of motion of the pattern. Then this field of

motion is used to forward advect the present

pattern. Longer lead times of the nowcast are

given by further advection. The quality of this

method depends on many factors but an

important one is the availability of radar

composites. Single radar LP nowcast have

useful skill for up to one hour only. The

limiting factor is the impossibility of seeing far

enough to predict what will be arriving. In

addition, the field of motion is poorly evaluated

due to range effects of scanning radar. With

continental scale composites the useful lead

times extend up to six hours.

Obviously, the physical limit to the

predictability by LP is growth and decay

(including generation of new regions of

precipitation). Let us point out that LP

includes some growth and decay. For

example, if there is some persistent

dissipation at the rear of a system this will

result in a motion pattern that is confluent. If

the dissipation at the rear continues into the

future the advection will capture the

narrowing of the pattern.

Figure 2.- Precipitation patterns 2:30 hours apart. The differential motion along the trajectories at the initial time leads to a prediction of the observed narrowing of the pattern.

An example is given in Fig. 2, where at

the initial time it can be seen within the

circled area that the motion vectors at the

rear are longer that at the front. At the later

time the pattern has narrowed. This was

predictable, and it was predicted. The decrease

in intensity within this area, however, was not

predictable by LP.

The example above illustrates that the

method of determining the velocity field and

pattern advection are critical to the method’s

skill.

Another physical limitation of LP is the

evolution of the motion field. Figure 3 shows

that around 20% of loss of skill (defined here as

the time to decorrelation to 1/e) is due to time

evolution of motion field.

Figure 3: Decorrelation between nowcasted and observed reflectivity patterns using stationary motion filed and a posteriori observed motion field during the 60 h of nowcast.

Predictability of meteorological fields is

scale dependent and the fundamental limit to

predictability due to non-linearity of the

processes governing precipitation is a difficult

issue beyond the scope of this discussion.

Here, the term predictability is used denote the

limit of skill of the method of forecast used. In

relation to LP we note that small cells evolve

rapidly and therefore are less predictable that

large scale systems. Haar wavelet scale

decomposition was used to compare nowcasts

of radar precipitation patterns and radar

observed patterns at the nowcast time for

different scales. An analysis of four days of

data is summarized in Figure 4.

Figure 4.- Life-time (as defined by the time to decorrelation to 1/e) for four days of data as a function of filtered out scales.

Since the loss of predictability is faster

the smaller the scale of the precipitation

pattern, a scale filtering, increasing with lead-

time, is needed to avoid attempts at

predicting the unpredictable.

An evaluation of the skill in precipitation

detection of a particular algorithm of LP

nowcast (MAPLE, McGill Algorithm for

Precipitation nowcasting by Lagrangian

Extrapolation), the filtered nowcast (O-

MAPLE, Optimized MAPLE*) as well as

numerical model outputs is shown in Fig. 5.

The small scales can be only predicted

by a probabilistic method. One approach is

nowcasting of fields of probability by LP. The

fields of probability are determined in the

immediate past and advected by the motion

field.

Another, more complete, possibility is

the generation of ensembles of nowcasts so

* The algorithm is described in three papers: Germann and Zawadzki (2002), Germann and Zawadzki (2004), Turner et al (2004).

that the ensemble represents the probabilities as

determined above. In addition, each member of

the ensemble is a possible realization of the

precipitation field that respects the statistical

properties (such as mean, variance,

decorrelation time and distance) of the

observations made in the immediate past.

Figure 5.- skill scores of nowcasting by LP (unfiltered and filtered) compared to numerical model outputs.

In relation to this there is another issue that

requires a statistical approach. Nowcasting of

precipitation intensity based on radar data relies

on the transformation from reflectivity Z to rain

rate R. The Z-R relationship has a strong

stochastic component that is related to the

physical processes responsible for the formation

of different raindrop size distributions. These

processes are not totally random (in the

Gaussian sense). On the contrary, they are

quite structured and correlated in space and

time. Thus the differences in the fields of Z and

R are also structured with spatial and

temporal scales of correlation.

Figure 6.- A rain rate field obtained from Z to R transformation by a climatological Z-R relationship and four stochastic realizations of the R-filed that have the same mean, variance and correlation structure of the variability in the Z-R relationship around the climatological one.

Figure 6 shows four plausible fields of

rain rate that correspond to a single reflectivity

filed. These four fields are members of an

ensemble that incorporates the uncertainty in

the Z-R relationship. To produce these

realizations we analyze the fluctuations

around a mean Z-R relationship as given by

disdrometric observations. In particular we

determine the correlation between Z and R,

the variance of the fluctuations around a

mean regression and the time structure

function of these fluctuations. A self-afine

cascade is then generated that respects the

observed stochastic properties and the result

is added to the deterministic R-field obtained

by the transformation from Z to R using the

mean Z-R regression. Each realization of the

self-affine cascade produces a member of the

ensemble. The average of the ensemble is

the deterministic R-field. The procedure is

similar to the one used by Bowler et al. (2004)

to downscale model outputs in order to

generate ensemble nowcasts.

In the same manner one can generate

an ensemble that contains as well other errors

in radar measurements (notably extrapolation

to ground) and the uncertainty due to the non-

predictability of the small scales.

3. COMBINING MODEL AND NOWCASTS

Figure 7 shows the critical success index

of the weighted (by the skill of each member

in the immediate past) average of

precipitation patterns of ensembles made of

LP nowcasts and numerical model outputs.

Figure 7.- Skill scores of precipitation forecasted by a numerical model, of filtered and non-filtered LP nowcasting and their weighted combinations.

Although the WRF model performance is

rather poor when combined with LP nowcasts

it leads to significant improvement in skill. For

short lead times, up to three hours, MAPLE is

superior. The addition of the filtered nowcast,

O-MAPLE, helps to improve the score. All

this is case dependent. Fig. 8 shows the

detection CSI for cases where model

performance was particularly good (WRF

model CSI at least 1.4 times the one in Fig.

7). These cases represent 8.8% of the

analyzed period.

Figure 8.- Same as Fig. 7 but for cases where WRF skill was significantly above the average

Again MAPLE outperforms model for

lead times of up to 3 hours. However, in this

limited sample scale filtering was particularly

effective at increasing the score. On the other

hand, the score of the ensemble including the

filtered LP nowcast is not as good as without

it. All this points out to the need of carefully

adapting the algorithm to each situation.

4. FINAL COMMENTS

Nowcasting by LP, introduced over three

decades ago, remains still the choice method

for operational nowcasting. It has better skill

than present days numerical models for up to

six hours. However, this statement must be

made with caution since radar maps are used

for verification and consequently priviledge

radar based nowcasts. It should be also

pointed out that LP nowcasts are only good in

regions where advection of precipitation

dominates over generation. In mountainous

regions LP has little skill (this also holds for

NWP).

Further improvements in the skill of LP

nowcasts will be difficult to achieve. Attempts

at incorporating tendencies have been

unsuccessful. The motion field already

captures growth and decay that leads to

persistent changes in the pattern.

It is likely that incorporating uncertainties

as well as physical information from other

sources (including information from NWP) into

a stochastic generation of ensembles is the

road to follow.

Combination of LP nowcasts with NWP

leads to improvement in skill. It is likely that

progress in technology, particularly computing

capability, will lead to improvements in

resolution of numerical models and beter data

assimilation. We should expect some

improvement in NWP. This will be

automatically incorporated into the nowcasts

obtained by combination of LP nowcasting

and NWP.

Acknowledgments Many people contributed to obtain the

results shown in this extended abstract,

notably: Gyuwon Lee, Urs Germann, Alamelu

Kilambi, Alan Seed and Barry Turner. WRF

model outputs were provided by Weather

Decision Technologies, Inc. Financial support

for this work was provided by a grant from the

Canadian Foundation for Climate and

Atmospheric Sciences (CFAS)

REFERENCES Bowler, N., C. Pierce and A. Seed, 2004: STEPS:

A probabilistic precipitation forecasting scheme which merges extrapolation nowcast with downscaled NWP. Q. J. R. Meteolol. Soc., 999, 1-34.

Germann, U. and I. Zawadzki, 2002: Scale dependence of predictability of precipitation from continental radar images. Part I: Description of methodology. Weather and Forecasting, 130, 2859-2873.

Germann, U. and I. Zawadzki, 2004: Scale dependence of predictability of precipitation from continental radar images. Part 2: Probability Forcasts. J. of Appl. Meteorology, 43, 74-89.

Turner, B., I. Zawadzki and U. Germann, 2004: Scale dependence of predictability of precipitation from continental radar images. Part 3: Operational implementation. J. of Appl. Meteorology, 43, 231–248.