Quantitative precipitation nowcasting (QPN) has become an
essential technique in various application contexts, such as early warning or
urban sewage control. A common heuristic prediction approach is to track the
motion of precipitation features from a sequence of weather radar images and
then to displace the precipitation field to the imminent future (minutes to
hours) based on that motion, assuming that the intensity of the features
remains constant (“Lagrangian persistence”). In that context, “optical
flow” has become one of the most popular tracking techniques. Yet the
present landscape of computational QPN models still struggles with producing
open software implementations. Focusing on this gap, we have developed and
extensively benchmarked a stack of models based on different optical flow
algorithms for the tracking step and a set of parsimonious extrapolation
procedures based on image warping and advection. We demonstrate that these
models provide skillful predictions comparable with or even superior to
state-of-the-art operational software. Our software library (“rainymotion”)
for precipitation nowcasting is written in the Python programming language
and openly available at GitHub (https://github.com/hydrogo/rainymotion,
). That way,
the library may serve as a tool for providing fast, free, and transparent
solutions that could serve as a benchmark for further model development and
hypothesis testing – a benchmark that is far more advanced than the
conventional benchmark of Eulerian persistence commonly used in QPN
verification experiments.
Introduction
How much will it rain within the next hour? The term
“quantitative precipitation nowcasting” refers to forecasts at high
spatiotemporal resolution (60–600 s, 100–1000 m) and short lead times of
only a few hours. Nowcasts have become important for broad levels of the
population for planning various kinds of activities. Yet they are
particularly relevant in the context of early warning of heavy convective
rainfall events and their corresponding impacts such as flash floods,
landslides, or sewage overflow in urban areas.
While recent advances in numerical weather prediction (NWP) allow us to
forecast atmospheric dynamics at a very high resolution ,
computational costs are typically prohibitive for the requirements of
operational nowcasting applications with frequent update cycles. Furthermore,
the heuristic extrapolation of rain field motion and development, as observed
by weather radar, still appears to outperform NWP forecasts at very short
lead times . Today, many
precipitation nowcasting systems are operational at regional or national
scales, utilizing various radar products, algorithms, and blending techniques
in order to provide forecasts up to 1–3 h, for example: ANC
, MAPLE , RADVOR
, STEPS , STEPS-BE
, and SWIRLS . For an extensive
review of existing operational systems, please refer to .
A variety of radar-based precipitation nowcasting techniques can be
classified into three major groups based on assumptions we make regarding
precipitation field characteristics . The first
group – climatological persistence – provides nowcasts by using
climatological values (mean or median). The second group – Eulerian
persistence – is based on using the latest available observation as a
prediction, and is thus independent of the forecast lead time. The third
group – Lagrangian persistence – allows the extrapolation of the most
recent observed precipitation field under the assumption that the intensity of
precipitation features and the motion field are persistent
. In addition, we can classify nowcasting
methods based on how predictive uncertainty is accounted for: in contrast to
deterministic approaches, ensemble nowcasts attempt to account for predictive
uncertainty by including different realizations of the motion field and the
evolution of rainfall intensity itself . In this study,
we focus our model development around the group of Lagrangian persistence
models which provide deterministic precipitation nowcasts.
Lagrangian methods consist of two computational steps: tracking and
forecasting (extrapolation) . In the tracking step, we
compute a velocity field from a series of consecutive radar images, either on
a per pixel basis
or for contiguous objects . In the second step, we use
that velocity field to advect the most recent rain field, i.e., to displace it
to the imminent future based on its observed motion. That step has been
implemented based on semi-Lagrangian schemes ,
interpolation procedures , or mesh-based models
. Different algorithms can be used for each
step – tracking and forecasting – in order to compute an ensemble forecast
.
One of the most prominent techniques for the tracking step is referred to as
“optical flow”. The original term was inspired by the idea of an
apparent motion of brightness patterns observed when a camera or the
eyeball is moving relative to the objects . Today, optical
flow is often understood as a group of techniques to infer motion patterns or
velocity fields from consecutive image frames, e.g., in the field of
precipitation nowcasting . For the
velocity field estimation, we need to accept both the brightness constancy
assumption and one of a set of additional optical flow constraints (OFCs). The
spatial attribution of OFC marks the two main categories of optical flow
models: local (differential) and global (variational)
. Local models try to set an OFC only in some
neighborhood, while global models apply an OFC for a whole image. There is
also a distinct group of spectral methods where the Fourier transform is
applied to the inputs and an OFC is resolved in the spectral (Fourier)
domain . introduced the first local
optical flow algorithm for precipitation nowcasting, and this gave rise to a new
direction of models. Bowler's algorithm is the basis of the STEPS
and STEPS-BE operational nowcasting
systems. proposed using a local Lucas–Kanade optical flow
method independently for each pixel of satellite imagery
because they found it outperformed a global Horn–Schunck
optical flow algorithm in the context of precipitation nowcasting from
infrared satellite images. , , and
used different global optical flow algorithms
for establishing the SWIRLS product for
operational nowcasting in Hong Kong.
Hence, for around two decades, optical flow algorithms have been doing their
best for state-of-the-art operational nowcasting systems around the globe.
Should research still care about them? It should, and the reason is
that – despite the abundance of publications about different types of
optical flow techniques for nowcasting applications – an open and
transparent benchmark model is yet not available, except for the most trivial
one: Eulerian persistence.
That is all the more surprising since open-source implementations of
fundamental optical flow algorithms
have been around for up to 20 years – with the OpenCV library
(https://opencv.org, last access: 28 March 2019) just being the most
widely known. Such libraries provide efficient implementations of various
optical flow algorithms for a vast number of research and application
contexts. Yet none can be applied in the QPN context out of the box –
without the need to address additional and specific challenges such as
underlying assumptions and constraints of velocity fields, pre- and
post-processing steps, or model parameterization and verification.
The aim of this paper is thus to establish a set of benchmark procedures for
quantitative precipitation nowcasting as an alternative to the trivial case
of Eulerian persistence. This study does not aim to improve the standard of
precipitation nowcasting beyond the state of the art, but to provide an open,
transparent, reproducible, and easy-to-use approach that can compete with the
state of the art, and against which future advances can be measured. To that
end, we developed a group of models that are based on two optical flow
formulations of algorithms for the tracking step – Sparse
and Dense – together with two parsimonious extrapolation
techniques based on image warping and spatial interpolation. These models are
verified against Eulerian persistence, as a trivial benchmark, and against
the operational nowcasting system of the Deutscher Wetterdienst (the German
Weather Service, DWD), as a representative of state-of-the-art models. The
different optical flow implementations are published as an open-source Python
library (rainymotion, ) that entirely relies on free
and open-source dependencies, including detailed documentation and example
workflows (https://rainymotion.readthedocs.io, last access: 28 March
2019).
The paper is organized as follows. In Sect. 2, we describe the algorithmic
and technical aspects of the suggested optical flow models. Section 3
describes the data we used and provides a short synopsis of events we used
for the benchmark experiment. We report the results in Section 4 and discuss
them in various contexts in Sect. 5. Section 6 provides a summary and
conclusions.
Description of the models and the library
The benchmark models developed in this study consist of different
combinations of algorithms for the two major steps of Lagrangian nowcasting
frameworks, namely tracking and extrapolation .
Table provides an overview of the models. The values of model
parameters adopted in the benchmark experiment have been heuristically
determined and not yet been subject to systematic optimization. However, the
rainymotion library provides an opportunity to investigate how different
optical flow model parameters can affect nowcasting results or how they can
be tuned to represent, e.g., the typical range of advection speeds of real
precipitation fields. For a description of parameters, please refer to
Sect. S1 in the Supplement or the rainymotion library documentation
(https://rainymotion.readthedocs.io/, last access: 28 March 2019).
Overview of the nowcasting models developed and their computational
performance. Nowcasting experiments were carried out for 1 h lead time at a
5 min temporal resolution (12 resulting nowcast frames in total) using the
RY radar data (spatial resolution of 1 km, grid size 900×900) and a
standard office PC with an Intel®
Core™ i7-2600 CPU (eight cores,
3.4 GHz).
The central idea around this group of methods is to identify distinct
features in a radar image that are suitable for tracking. In this context, a
“feature” is defined as a distinct point (“corner”) with a sharp gradient
of rainfall intensity. That approach is less arbitrary and scale dependent
and thus more universal than classical approaches that track storm cells as
contiguous objects e.g., because it eliminates the need
to specify arbitrary and scale-dependent characteristics of “precipitation
features” while the identification of corners depends only on the
gradient sharpness in a cell's neighborhood. Inside this group, we developed
two models that slightly differ with regard to both tracking and
extrapolation.
The first model (SparseSD, for Sparse Single Delta) uses only the two most
recent radar images for identifying, tracking, and extrapolating features.
Assuming that t denotes both the nowcast issue time and the time of the
most recent radar image, the implementation can be summarized as follows.
Identify features in a radar image at time t-1 using the Shi–Tomasi
corner detector . This detector determines the most prominent
corners in the image based on the calculation of the corner quality measure
(min(λ1,λ2), where λ1 and λ2 are
corresponding eigenvalues of the covariance matrix of derivatives over the
neighborhood of 3×3 pixels) at each image pixel (see Sect. S1 for a
detailed description of algorithm parameters).
Track these features at time t using the local Lucas–Kanade optical
flow algorithm . This algorithm tries to identify the
location of a feature we previously identified at time t-1 in the radar
image at time t, based on solving a set of optical flow equations in the
local feature neighborhood using the least-squares approach (see Sect. S1 for
a detailed description of algorithm parameters).
Linearly extrapolate the features' motion in order to predict the features'
locations at each lead time n.
Calculate the affine transformation matrix for each lead time n based
on the locations of all identified features at time t and t+n using the
least-squares approach . This matrix uniquely identifies
the required transformation of the last observed radar image at time t so
that the nowcast images at times t+1…t+n provide the smallest
possible difference between the locations of detected features at time t
and the extrapolated features at times t+1…t+n.
Extrapolate the radar image at time t by warping: for each lead time,
the warping procedure uniquely transforms each pixel location of the radar
image at time t to its future location in the nowcast radar images at times
t+1…t+n, using the affine transformation matrix. Remaining
discontinuities in the predicted image are linearly interpolated in order to
obtain nowcast intensities on a grid that corresponds to the radar image at
time t.
To our knowledge, this study is the first to apply image warping directly as
a simple and fast algorithm to represent advective motion of a precipitation
field. In Sect. S2, you can find a simple synthetic example which shows the
potential of the warping technique to replace an explicit advection
formulation for temporal extrapolation.
For a visual representation of the SparseSD model, please refer to
Fig. .
Scheme of the SparseSD model.
The second model (Sparse) uses the 24 most recent radar images, and we
consider only features that are persistent over the whole period (of 24 time
steps). The implementation can be summarized as follows.
Identify features on a radar image at time t-23 using the Shi–Tomasi
corner detector .
Track these features in the radar images from t-22 to t
using the local Lucas–Kanade optical flow algorithm .
Build linear regression models which independently parameterize changes
in coordinates through time (from t-23 to t) for every successfully
tracked feature.
Continue with steps 3–5 of SparseSD.
For a visual representation of the Sparse model, please refer to
Fig. .
Scheme of the Sparse model.
The Dense group
The Dense group of models uses, by default, the Dense Inverse Search
algorithm (DIS) – a global optical flow algorithm proposed by
– which allows us to explicitly estimate the velocity of
each image pixel based on an analysis of two consecutive radar images. The
DIS algorithm was selected as the default optical flow method for motion
field retrieval because it showed, in our benchmark experiments, a higher
accuracy and also a higher computational efficiency in comparison with other
global optical flow algorithms such as DeepFlow , and
PCAFlow . We also tested the local Farnebäck algorithm
, which we modified by replacing zero velocities by
interpolation and by smoothing the obtained velocity field based on a
variational refinement procedure (please refer to Sect. S5
for verification results of the corresponding benchmark experiment with
various dense optical flow models). However, the rainymotion library
provides the option to choose any of the optical flow methods specified above for precipitation nowcasting.
The two models in this group differ only with regard to the extrapolation (or
advection) step. The first model (Dense) uses a constant-vector advection
scheme , while the second model (DenseRotation) uses a
semi-Lagrangian advection scheme . The main
difference between both approaches is that a constant-vector scheme does not
allow for the representation of rotational motion ; a
semi-Lagrangian scheme allows for the representation of large-scale
rotational movement while assuming the motion field itself to be persistent
(Fig. ).
Displacement vectors of four proposed advection schemes:
forward or backward constant vector and forward or backward semi-Lagrangian.
There are two possible options of how both advection schemes may be
implemented: forward in time (and downstream in space) or backward in time
(and upstream in space) (Fig. ). It is yet unclear which scheme
can be considered as the most appropriate and universal solution for
radar-based precipitation nowcasting, regarding the conservation of mass on
the one hand and the attributed loss of power at small scales on the other
hand e.g., see discussion in.
Thus, we conducted a benchmark experiment with any possible combination of
forward vs. backward and constant-vector vs. semi-Lagrangian advection. Based
on the results (see Sect. S6), we use the backward scheme as the default
option for both the Dense and DenseRotation models. However, the
rainymotion library still provides the option to use the forward
scheme, too.
Both the Dense and DenseRotation models utilize a linear interpolation
procedure in order to interpolate advected rainfall intensities at their
predicted locations to the native radar grid. The interpolation procedure
“distributes” the value of a rain pixel to its neighborhood, as proposed in
different modifications by , , and
. The Dense group models' implementation can be summarized
as follows.
Calculate a velocity field using the global DIS optical flow algorithm
, based on the radar images at time t-1 and t.
Use a backward constant-vector or a backward semi-Lagrangian
scheme to extrapolate (advect) each pixel
according to the displacement (velocity) field, in one single step for each
lead time t+n. For the semi-Lagrangian scheme, we update the velocity of
the displaced pixels at each prediction time step n by linear interpolation
of the velocity field to a pixel's location at that time step.
As a result of the advection step, we basically obtain an irregular
point cloud that consists of the original radar pixels displaced from their
original location. We use the intensity of each displaced pixel at its
predicted location at time t+n in order to interpolate the intensity at
each grid point of the original (native) radar grid
, using the inverse distance weighting
interpolation technique. It is important to note that we minimize numerical
diffusion by first advecting each pixel over the target lead time before
applying the interpolation procedure (as in the “interpolate once” approach
proposed by ). That way, we avoid rainfall
features being smoothed in space by the effects of interpolation.
Persistence
The (trivial) benchmark model of Eulerian persistence assumes that for any
lead time n, the precipitation field is the same as for time t. Despite
its simplicity, it is quite a powerful model for very short lead times, and,
at the same time, its verification performance is a good measure of temporal
decorrelation for different events.
The rainymotion Python library
We have developed the rainymotion Python library to implement the above
models. Since the rainymotion uses the standard format of numpy arrays
for data manipulation, there is no restriction in using different data
formats which can be read, transformed, and converted to numpy arrays using
any tool from the set of available open software libraries for radar data
manipulation (the list is available on https://openradarscience.org,
last access: 28 March 2019). The source code is available in a Github
repository and has a documentation page
(https://rainymotion.readthedocs.io, last access: 28 March 2019) which
includes installation instructions, model description, and usage examples.
The library code and accompanying documentation are freely distributed under
the MIT software license which allows unrestricted use. The library is
written in the Python 3 programming language (https://python.org, last
access: 28 March 2019), and its core is entirely based on open-source
software libraries (Fig. ): ωradlib
, OpenCV , SciPy
, NumPy , Scikit-learn
, and Scikit-image . For generating
figures we use the Matplotlib library , and we use the
Jupyter notebook (https://jupyter.org, last access: 28 March 2019)
interactive development environment for code and documentation development
and distribution. For managing the dependencies without any conflicts, we
recommend to use the Anaconda Python distribution
(https://anaconda.com, last access: 28 March 2019) and follow
rainymotion installation instructions
(https://rainymotion.readthedocs.io, last access: 28 March 2019).
Key Python libraries for rainymotion library development.
Operational baseline (RADVOR)
The DWD operationally runs a stack of models for radar-based nowcasting and
provides precipitation forecasts for a lead time up to 2 h. The operational
QPN is based on the RADVOR module (Bartels et al., 2005; Rudolf et
al., 2012). The tracking algorithm estimates the motion field from the latest
sequential clutter-filtered radar images using a pattern recognition
technique at different spatial resolutions (Winterrath and Rosenow, 2007;
Winterrath et al., 2012). The focus of the tracking algorithm is on the
meso-β scale (spatial extent: 25–250 km) to cover mainly large-scale
precipitation patterns, but the meso-γ scale (spatial extension:
2.5–25 km) is also incorporated to allow the detection of smaller-scale
convective structures. The resulting displacement field is interpolated to a
regular grid, and a weighted averaging with previously derived displacement
fields is implemented to guarantee a smooth displacement over time. The
extrapolation of the most recent radar image according to the obtained
velocity field is performed using a semi-Lagrangian approach. The described
operational model is updated every 5 min and produces precipitation nowcasts
at a temporal resolution of 5 min and a lead time of 2 h (RV product). In
this study we used the RV product data as an operational baseline and did not
re-implement the underlying algorithm itself.
Verification experimentsRadar data and verification events
We use the so-called RY product of the DWD as input to our nowcasting models.
The RY product represents a quality-controlled rainfall depth product that is
a composite of the 17 operational Doppler radars maintained by the DWD. It
has a spatial extent of 900km×900 km and covers the whole area of
Germany. Spatial and temporal resolution of the RY product is 1km×1 km
and 5 min, respectively. This composite product includes various procedures
for correction and quality control (e.g., clutter removal). We used the
ωradlib software library for reading
the DWD radar data.
For the analysis, we selected 11 events during the summer periods of
2016 and 2017. These events are selected for covering a range of event
characteristics with different rainfall intensity, spatial coverage, and
duration. Table shows the studied events. You can also find
links to animations of event intensity dynamics in Sect. S3.
Characteristics of the selected events.
Event no.StartEndDurationMaximum extentExtent >1 mm h-1(h)(km2)(%)Event 123 May 2016 02:0023 May 2016 08:006159 31842Event 223 May 2016 13:0024 May 2016 02:3013.5135 27256Event 329 May 2016 12:0529 May 2016 23:5512160 09572Event 412 Jun 2016 07:0012 Jun 2016 19:0012150 41653Event 513 Jul 2016 17:3014 Jul 2016 01:007.5145 50162Event 64 Aug 2016 18:005 Aug 2016 07:0013168 40774Event 729 Jun 2017 03:0029 Jun 2017 05:052140 02170Event 829 Jun 2017 17:0029 Jun 2017 21:004182 56160Event 929 Jun 2017 22:0030 Jun 2017 21:0023160 82275Event 1021 Jul 2017 19:0021 Jul 2017 23:00463 69877Event 1124 Jul 2017 08:0025 Jul 2017 23:5516253 66663Verification metrics
For the verification we use two general categories of scores: continuous
(based on the differences between nowcast and observed rainfall intensities)
and categorical (based on standard contingency tables for calculating matches
between Boolean values which reflect the exceedance of specific rainfall
intensity thresholds). We use the mean absolute error (MAE) as a continuous
score:
MAE=∑i=1nnowi-obsin,
where nowi and obsi are nowcast and observed rainfall rate in the
ith pixel of the corresponding radar image and n is the number of pixels.
To compute the MAE, no pixels were excluded based on thresholds of nowcast or
observed rainfall rate.
And we use the critical success index (CSI) as a categorical score:
CSI=hitshits+falsealarms+misses,
where hits, false alarms, and misses are defined by the contingency table and
the corresponding threshold value (for details see Sect. S4).
Following studies of and , we have
applied threshold rain rates of 0.125, 0.25, 0.5, 1, and 5 mm h-1 for
calculating the CSI.
These two metrics inform us about the models' performance from the two
perspectives: MAE captures errors in rainfall rate prediction (the less the
better), and CSI captures model accuracy (the fraction of the forecast event
that was correctly predicted; it does not distinguish between the sources of errors; the
higher the better). You can find results represented in terms of additional
categorical scores (false alarm rate, probability of detection, equitable
threat score) in Sect. S4.
Results
For each event, all models (Sparse, SparseSD, Dense, DenseRotation,
Persistence) were used to compute nowcasts with lead times from 5 to 60 min
(in 5 min steps). Operational nowcasts generated by the RADVOR system were
provided by the DWD with the same temporal settings. An example of nowcasts
for lead times 0, 5, 30, and 60 min is shown in Fig. .
Example of the nowcasting models output (SparseSD and Dense
models) for the timestep, 29 May 2016, 19:15, and corresponding level of
numerical diffusion (last row).
To investigate the effects of numerical diffusion, we calculated, for the
same example, the power spectral density (PSD) of the nowcasts and the
corresponding observations (bottom panels in Fig. ) using
Welch's method . showed that the
most significant loss of power (lower PSD values) occurs at scales between 8
and 64 km. They did not analyze scales below 8 (23) km because their
original grid resolution was 4 km. We extended the spectral analysis to
consider scales as small as 21 km. Other than
, we could not observe any substantial loss of
power between 8 and 64 km, yet Fig. shows that both Dense and
Sparse models consistently start to lose power at scales below 4 km. That
loss does not depend much on the nowcast lead time, yet the Sparse group of
models loses more power at a lead time of 5 min as compared to the Dense
group. Still, these results rather confirm : they
show, as would be expected, that any loss of spectral power is most
pronounced at the smallest scales and disappears at scales about 2–3 orders
above the native grid resolution. For the investigated combination of data
and models, this implies that our nowcasts will not be able to adequately
represent rainfall features smaller than 4 km at lead times of up to 1 h.
Figure shows the model performance (in terms of MAE) as a
function of lead time. For each event, the Dense group of models is superior
to the other ones. The RV product achieves an efficiency that is comparable
to the Dense group. The SparseSD model outperforms the Sparse model for short
lead times (up to 10–15 min) and vice versa for longer lead times. For
some events (1–4, 6, 10, 11), the performance of the RV product appears to
be particularly low in the first 10 min, compared to the other models. These
events are characterized by particularly fast rainfall field movement.
Verification of the different optical flow based nowcasts in terms
of MAE for 11 precipitation events over Germany.
Figure has the same structure as Fig. but
shows the CSI with a threshold value of 1 mm h-1. For two events (7
and 10) the RV product achieves a comparable efficiency with the Dense group
for lead times beyond 30 min. For the remaining events, the Dense group
tends to outperform all other methods and the RV product achieves an average
rank between models of the Sparse and Dense groups. For the Dense group of
models, it appears that accounting for field rotation does not affect the
results of the benchmark experiment much – the Dense and DenseRotation
models perform very similarly, at least for the selected events and the
analyzed lead times. The behavior of the Sparse group models is mostly
consistent with the MAE.
Verification of the different optical flow based nowcasts in terms
of CSI for the threshold of 1 mm h-1 for 11 precipitation events over
Germany.
Figure shows the model performance using the CSI with a
threshold value of 5 mm h-1. For the majority of events, the resulting
ranking of models is the same as for the CSI with a threshold of
1 mm h-1. For events no. 2 and no. 3, the performance of the RV product
relative to the Dense models is a little bit better, while for other events
(e.g., no. 7), the Dense models outperform the RV product more clearly than for
the CSI of 1 mm kh-1.
Verification of the different optical flow based nowcasts in terms
of CSI for the threshold of 5 mm h-1 for 11 precipitation events over
Germany.
Table summarizes the results of the Dense group models in
comparison to the RV product for different verification metrics averaged over
all the selected events and two lead time periods: 5–30 and 35–60 min.
Results show that the Dense group always slightly outperforms the RV model in
terms of CSI metric for both lead time periods and all analyzed rainfall
intensity threshold used for CSI calculation. In terms of MAE, differences
between model performances are less pronounced. For the CSI metric, the
absolute differences between all models tend to be consistent with increasing
rainfall thresholds.
Mean model metrics for different lead time periods
ModelLead time (from–to), min 5–3035–60MAE, mm h-1Dense0.300.45DenseRotation0.300.45RV0.310.45CSI, threshold: 0.125 mm h-1Dense0.780.64DenseRotation0.780.64RV0.760.61CSI, threshold: 0.25 mm h-1Dense0.760.61DenseRotation0.760.61RV0.740.59CSI, threshold: 0.5 mm h-1Dense0.730.57DenseRotation0.730.57RV0.700.55CSI, threshold: 1 mm h-1Dense0.680.52DenseRotation0.680.51RV0.650.49CSI, threshold =5 mm h-1Dense0.420.24DenseRotation0.420.23RV0.390.22
You can find more figures illustrating the models' efficiency for different
thresholds and lead times in Sect. S4.
DiscussionModel comparison
All tested models show significant skill over the trivial Eulerian
persistence over a lead time of at least 1 h. Yet a substantial loss of
skill over lead time is present for all analyzed events, as expected. We have
not disentangled the causes of that loss, but predictive uncertainty will
always result from errors in both the representation of field motion and the
total lack of representing precipitation formation, dynamics, and dissipation
in a framework of Lagrangian persistence. Many studies specify a lead time of
30 min as a predictability limit for convective structures with fast
dynamics of rainfall evolution
. Our study
confirms these findings.
For the majority of analyzed events, there is a clear pattern that the Dense
group of optical flow models outperforms the operational RV nowcast product.
For the analyzed events and lead times, the differences between the Dense and
the DenseRotation models (or, in other words, between constant-vector and
semi-Lagrangian schemes) are negligible. The absolute difference in
performance between the Dense group models and the RV product appears to be
independent of rainfall intensity threshold and lead time
(Table ), which implies that the relative advance of the Dense
group models over the RV product increases both with lead time and rainfall
intensity threshold. A gain in performance for longer lead times by taking
into account more time steps from the past can be observed when comparing the
SparseSD model (looks back 5 min in time) against the Sparse model (looks
back 2 h in time).
Despite their skill over Eulerian persistence, the Sparse group models are
significantly outperformed by the Dense group models for all the analyzed
events and lead times. The reason for this behavior still remains unclear. It
could, in general, be a combination of errors introduced in corner tracking
and extrapolation as well as image warping as a surrogate for formal
advection. While the systematic identification of error sources will be
subject to future studies, we suspect that the local features
(corners) identified by the Shi–Tomasi corner detector might not be
representative of the overall motion of the precipitation field: the
detection focuses on features with high intensities and gradients, the motion
of which might not represent the dominant meso-γ-scale motion
patterns.
There are a couple of possible directions for enhancing the performance for
longer lead times using the Dense group of models. A first is to use a
weighted average of velocity fields derived from radar images three (or more)
steps back in time (as done in RADVOR to compute the RV product). A second
option is to calculate separate velocity fields for low-and high-intensity
subregions of the rain field and advect these subregions separately (as proposed in ) or find an optimal weighting procedure. A
third approach could be to optimize the use of various optical flow
constraints in order to improve the performance for longer lead times, as
proposed in , , or
. The flexibility of the rainymotion software
library allows users to incorporate such algorithms for benchmarking any
hypothesis, and, for example, implement different models or parameterizations for
different lead times. also showed a significant
performance increase for longer lead times by using NWP model winds for the
advection step. However, did not obtain any
improvement compared to RADVOR for longer lead times by incorporating NWP
model winds into the nowcasting procedure.
Advection schemes properties and effectiveness
Within the Dense group of models, we could not find any significant
difference between the performance and PSD of the constant-vector (Dense
model) and the semi-Lagrangian scheme (DenseRotation). That confirms findings
presented by , who found that the constant vector
and the modified semi-Lagrangian schemes have very similar power spectra,
presumably since they share the same interpolation procedure. The theoretical
superiority of the semi-Lagrangian scheme might, however, materialize for
other events with substantial, though persistent rotational motion. A more
comprehensive analysis should thus be undertaken in future studies.
Interpolation is included in both the post-processing of image warping
(Sparse models) and in the computation of gridded nowcasts as part of the
Dense models. In general, such interpolation steps can lead to numerical
diffusion and thus to the degradation or loss of small-scale features
. Yet we were mostly able to contain such adverse
effects for both the Sparse and the Dense group of models by carrying out
only one interpolation step for any forecast at a specific lead time. We
showed that numerical diffusion was negligible for lead times of up to 1 h
for any model; however, as has been shown in , for
longer lead times these effects can be significant, depending on the
implemented extrapolation technique.
Computational performance
Computational performance might be an important criterion for end users
aiming at frequent update cycles. We ran our nowcasting models on a standard
office PC with an Intel®
Core™ i7-2600 CPU (eight cores, 3.4 GHz), and on
a standard laptop with an Intel®
Core™ i5-7300HQ CPU (four cores, 2.5 GHz). The
average time for generating one nowcast for 1 h lead time (at 5 min
resolution) is 1.5–3 s for the Sparse group and 6–12 s for the Dense group. The Dense group is computationally more expensive due to
interpolation operations implemented for large grids (900×900 pixels). There is also potential for increasing the computational
performance of the interpolation.
Summary and conclusions
Optical flow is a technique for
deriving a velocity field from consecutive images. It is widely used in image
analysis and has become increasingly popular in meteorological applications over
the past 20 years. In our study, we examined the performance of optical-flow-based models for radar-based precipitation nowcasting, as implemented in the
open-source rainymotion library, for a wide range of rainfall events
using radar data provided by the DWD.
Our benchmark experiments, including an operational baseline model (the RV
product provided by the DWD), show a firm basis for using optical flow in
radar-based precipitation nowcasting studies. For the majority of the
analyzed events, models from the Dense group outperform the operational
baseline. The Sparse group of models showed significant skill, yet they
generally performed more poorly than both the Dense group and the RV product. We
should, however, not prematurely discard the group of Sparse models before we
have not gained a better understanding of error sources with regard to the
tracking, extrapolation, and warping steps. Combining the warping procedure for the extrapolation step with the Dense
optical flow procedure for the tracking step (i.e., to advect corners
based on a “Dense” velocity field obtained by implementing one of the dense
optical flow techniques) might also be considered. This opens the way for merging two different model
development branches in the future releases of the rainymotion
library.
There is a clear and rapid model performance loss over lead time for events
with high rainfall intensities. This issue continues to be unresolved by
standard nowcasting approaches, but some improvement in this field may be
achieved by using strategies such as merging with NWP results and
stochastic modeling of rainfall field evolution. Admittedly, deterministic
nowcasts in a Lagrangian framework account neither for precipitation
intensity dynamics nor for the uncertainties in representing precipitation
field motion. At least for the latter, the rainymotion library
provides ample opportunities to experiment with forecast ensembles, based on
various tracking and extrapolation techniques. Furthermore, we suppose that
using new data-driven models based on machine and deep learning may increase
the performance by utilizing and structuring common patterns in the massive
archives of radar data.
We do not claim that the developed models will compete with well-established
and excessively tuned operational models for radar-based precipitation
nowcasting. Yet we hope our models may serve as an essential tool for
providing a fast, free, and open-source solution that can serve as a benchmark
for further model development and hypothesis testing – a benchmark that is
far more advanced than the conventional benchmark of Eulerian persistence.
Recent studies show that open-source community-driven software advances the
field of weather radar science .
Just a few months ago, the pySTEPS (https://pysteps.github.io, last
access: 28 March 2019) initiative was introduced “to develop and maintain an
easy to use, modular, free and open-source python framework for short-term
ensemble prediction systems”. As another piece of evidence of the dynamic
evolution of QPN research over the recent years, these developments could
pave the way for future synergies between the pySTEPS and rainymotion
projects – towards the availability of open, reproducible, and skillful
methods in quantitative precipitation nowcasting.
Code and data availability
The rainymotion library is free and open-source. It
is distributed under the MIT software license, which allows unrestricted use.
The source code is provided through a GitHub repository
, the snapshot of the rainymotion v0.1 is also
available on Zenodo: 10.5281/zenodo.2561583, and the
documentation is available on a website
(https://rainymotion.readthedocs.io, last access: 28 March 2019). The
DWD provided the sample data of the RY product, and they are distributed with
the rainymotion repository to provide a real-case and reproducible example
of precipitation nowcasting.
The supplement related to this article is available online at: https://doi.org/10.5194/gmd-12-1387-2019-supplement.
Author contributions
GA performed the benchmark experiments, analyzed the data,
and wrote the paper. MH coordinated and supervised the work, analyzed
the data, and wrote the paper. TW assisted in the data retrieval and
analysis and shared her expertise in DWD radar products.
Competing interests
The authors declare that they have no conflict of
interest.
Acknowledgements
Georgy Ayzel was financially supported by Geo.X, the Research Network for
Geosciences in Berlin and Potsdam. The authors thank Loris Foresti, Seppo
Pulkkinen, and Remko Uijlenhoet for their constructive comments and
suggestions that helped to improve the paper. We acknowledge the support of
Deutsche Forschungsgemeinschaft (German Research Foundation) and the Open Access
Publication Fund of Potsdam University.
Review statement
This paper was edited by Axel Lauer and reviewed by Seppo
Pulkkinen, Remko Uijlenhoet, and Loris Foresti.
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