concepts and principles of rainfall estimation from radar:...

Indian Journal of Radio & Space Physics Vol 41, August 2012, pp 389-402

Concepts and principles of rainfall estimation from radar: Multi sensor environment and data fusion

V Chandrasekar1,$,* & Robert Cifelli2

1Colorado State University, Fort Collins 80523, USA

2National Oceanic and Atmospheric Administration (NOAA), Earth System Research Laboratory, Boulder 80305, USA

$E-mail: [email protected]

Received 23 July 2012; accepted 25 August 2012

Rainfall estimation has been pursued nearly since the dawn of civilization. It is also one of the most commonly used applications of modern, meteorological radars in most operational systems. Multi sensor approaches have made great strides in addressing the rainfall estimation problem through better sensor calibration and improved integration of observations at scales spanning many orders of magnitude such as radar, satellite and rain gauges. Data fusion techniques have demonstrated advantages in precipitation retrievals, especially for radar observations at attenuated frequencies. Data fusion has also shown benefits in merging data from multiple radars, as well as radars and satellites. This paper describes essential concepts of multi sensor rainfall estimation with a radar focus. Validation concepts for remote estimation of rainfall are also presented. Examples of data fusion and validation are illustrated through rainfall estimate comparisons between gauge and radar networks.

Keywords: Radar rain estimation, Precipitation estimation, Data fusion, Quantitative precipitation estimation (QPE)

PACS Nos: 92.60.jf; 84.40.Xb

1 Introduction

The measurement of rainfall is an important problem that has been pursued since the earliest time in civilization. Almost every segment of domestic and international economies is impacted by the amount and distribution of precipitation. Therefore, large infrastructure around the world has been acquired and installed over a period of time to directly measure rainfall using rain gauges or estimate the quantity with remote sensing instrumentation such as radar. Radar rainfall estimation has been a very active field that has simultaneously seen great progress and challenges. There are a number of advantages of using radar, including the fact that the radar can observe precipitation over a wide area in a relatively short period of time and can provide advanced warning of precipitation systems that will impact a region. Traditionally rainfall estimation from radars started with reflectivity rainfall relations, commonly referred as Z-R relations. These relations have usually been applied to single polarization radar systems and are still in practice today. However, advance techniques using dual-polarization technologies are now moving into operational applications e.g. upgrade of the US

Next-Generation Radar (NEXRAD) operational network in the US is now taking place. Dual polarization offers a number of advantages over single polarization radar rainfall estimation because more information about the rainfall microphysics can be gleaned. However, fundamental challenges in radar rainfall estimation remain.

Numerous experiments are being conducted to quantify the error structure of rainfall. The net result of these experiments has shown two fundamental aspects of rainfall estimation namely:

a) the physical science aspects and

b) the engineering problem1

The physical science process essentially represents the tracking of the microphysical properties of rainfall from radar observations and is fundamentally related to the raindrop size distribution. Numerous efforts have been introduced in the dual polarization radar literature for tracking the raindrop size distribution and subsequently estimating rainfall rate. Although improvements in rainfall estimation can be realized from dual polarization, various experiments done to compare rainfall rate from radar to ground

INDIAN J RADIO & SPACE PHYS, AUGUST 2012

390

observations exposed the extensive challenges that were not purely rainfall physics, but were related to engineering issues, such as beam averaging, calibration bias, clutter contamination, height of the radar measurement, and bright band contamination. Often, efforts to obtain good rainfall estimation attempted to simultaneously address the physical science and engineering issues without separation. Many authors have called attention to this separation2. Cifelli & Chandrasekar1 explicitly tried to address this in their article.

Until recently, the question remained unanswered as to whether a radar that measured rainfall very close to the ground, without calibration biases, and by using measurements without significant beam averaging or bias contamination, could measure as accurately as postulated by the physics of the rainfall process. The work by Wang & Chandrasekar3 using data collected from the X-band Collaborative Adaptive Sensing of the Atmosphere (CASA) network essentially showed that such a radar sampling strategy could result in highly accurate rainfall estimation. This study demonstrated a factor of three improvements in the accuracy of rainfall estimates compared to the NEXRAD dual polarization estimates. Similar results have also been demonstrated by initiatives led by National Research Institute for Earth Science and Disaster Prevention (NIED) in Japan4-7.

Flooding is one of the most common natural hazards that produce substantial loss of life and property and is a very important application of radar rainfall estimation. According to the US National Academy report, floods are responsible for more deaths nationwide than any other weather phenomenon8. Rapid development in urban regions decreases the response time of urban watersheds to rainfall and increases the chance of localized flooding events over a small spatial domain5. The scales of urban floods are fairly small with large temporal variability. Moreover, runoff can be intense with fast response time (i.e. coefficient of runoff essentially equal to 1.0). Successful monitoring of urban floods requires high spatiotemporal resolution and accurate precipitation estimation because of the rapid flood response as well as the complex hydrologic and hydraulic characteristics in an urban environment.

An innovative densely networked sensing paradigm, called Distributed Collaborative Adaptive Sensing (DCAS), has been introduced to overcome the resolution and coverage limitations of traditional

weather radars using lower cost, densely networked radar systems9,10. While DCAS was originally introduced for severe weather applications, this strategy also turns out to be very advantageous for addressing the flooding problem, as shown by Wang & Chandrasekar3. The DCAS radar network is capable of high-resolution observation over a large coverage area11. The network centric sensing paradigm greatly improves the system capability and measurement accuracy9. By reducing the maximum range and by operating at X-band, one can ensure good cross range resolution with a small-size antenna and keep the radar beam closer to the ground. The individual sensing node can be constructed from small-size radar units that are easily amenable to ubiquitous urban deployment. A recent National Academy study has explained the salient features of the DCAS system for complex terrain12.

Now that the importance of a radar network-centric paradigm has been shown to improve rainfall estimation, this type of approach can be extended to multiple sensors. The concept of a ‘multi sensor approach’ to rainfall has been widely proposed within the precipitation community for some time. The multi sensor concept is used all the way from satellite rainfall applications focussed at the global scale13,14 to hydrologic applications aimed at estimating rainfall at a local basin scale15,16. Unfortunately multi-sensor has also become a ‘catch-all phrase’, reflecting different philosophies about combining information from different sensors. The distinction between approaches to combining different sensor information is important: the fact that multiple sensors are used does not mean that the integrated rainfall observations are better, unless they are put together with proper scale representation prior to multi-scale merging. This issue was shown explicitly in a study combining the Tropical Rainfall Measuring Mission (TRMM) radar rainfall and ground rainfall estimates17,18. It is essential that a proper architectural framework is developed for deriving rainfall estimates from multiple sources. The classification of different multi-sensor approaches based on technique and application is presented in this paper. The paper describes the essential concepts of multi sensor rainfall estimates with a radar focus. 2 Basic principles of radar rainfall estimation

Radars have been used to detect precipitation echoes since the beginning of World War II.

CHANDRASEKAR & CIFELLI: RAINFALL ESTIMATION FROM RADAR

391

Quantitative estimates of rain rate from radar can be traced back to Wexler & Swingle19 and Marshall et al.

20, using relations between radar reflectivity factor (Z) and rain rate (R). Rainfall relations between Z and R are referred to as Z-R relations and are the most common technique to estimate rainfall with radar.

The most important reason for using radar to estimate precipitation is the fact that, compared to a network of rain gauges, the radar (or combinations of radars) can sample a large area (> 30,000 km2 for a weather radar sampling out to 100 km) over a short period of time (< 60 sec) as well as provide information on the movement and evolution of precipitating systems. However, radar is a remote measurement tool, using microwave backscatter to detect echo targets (e.g. precipitation particles). Therefore, assumptions are necessary to convert the radar measurements into an estimate of rainfall intensity or accumulation.

Factors that influence radar rainfall estimation can be routed into two broad categories: basic science and applied science, or engineering problems. It is useful to distinguish these categories in order to understand how practical considerations imposed by applied science issues limit the improvement in rainfall estimation anticipated from theoretical expectations of dual polarization radar retrievals (basic science). To be successful at radar rainfall estimation, both the basic and applied science issues must be addressed. Applied science issues include topics such as geometric and sampling considerations of the radar compared to ground-based measurements (rain gauges). Cifelli & Chandrasekar1 provide a detailed accounting of the various factors classified as basic and physical science issues impacting rainfall estimation.

Applied science issues include calibration and measurement bias as well as geometric and sampling differences of the radar and ground-based measurements. For example, the radar beam samples precipitation in the cloud and the sample volume is many orders of magnitude greater than the single point measurement of a rain gauge, which measures precipitation at the ground. Also, microphysical processes such as evaporation, drop coalescence and break-up can modify the precipitation between the cloud and the ground and further complicate the comparison.

Basic science issues refer to the physical models that are used to represent the microphysical properties

such as drop size distribution (DSD) and their relationship to the observed radar variables. For single polarization radar, rainfall (R) estimation is closely tied to the radar reflectivity (Z) via one or more Z-R relations. Radar reflectivity is sensitive to the 6th power of the DSD, which can vary widely within a precipitation region so that Z-R relations often result in rainfall estimation with large uncertainty21. In contrast, dual polarization radar can take advantage of differential propagation phase information, which is somewhat less sensitive to variations in the DSD and is immune to partial beam blocking and calibration bias. Therefore, dual polarization radar is less sensitive to basic science issues compared to single polarization radar and usually provides a more robust radar rainfall estimate compared to single polarization. For the remainder of the discussion, emphasis is placed on dual polarization systems for radar rainfall estimation.

Dual polarization techniques can be applied at multiple stages of radar rainfall estimation. These stages are referred to as pre-processing, classification, and quantification. Each of these stages has been discussed extensively in the literature, so only a brief overview is provided here. Pre-processing includes quality control (QC) procedures such as clutter removal and attenuation correction. In the analysis of radar data, QC (removal of non-precipitation echoes) can be critically important. This is especially true with traditional single polarization Doppler radars, where only radar reflectivity, radial velocity, and spectral width parameters may be available. One of the beneficial aspects of dual polarization radar is identification of contaminated reflectivity measurements. Detection of contaminations such as anomalous propagation, ground clutter, and suppression of range folded echoes can be accomplished with significantly better skill than single polarization radar systems. After the completion of pre-processing procedures, classification of hydrometeor types can be accomplished. Classification is also referred to as hydrometeor identification (HID). The most important classification for the purposes of rainfall estimation is the identification of non meteorological echoes and of ice in the radar volume. Ice can be especially problematic for rainfall estimation using R(Z) methods.

Quantification of rainfall occurs after the pre-processing and classification stages and can be broadly classified into physically and statistically based approaches. Physical methodologies utilize


392

parametric relations between radar measurements and assumed characteristics of the DSD and do not rely on ground measurements to calibrate the radar observations. Physical based techniques are based on the relationship between forward and backscatter characteristics and rainfall are the most commonly used application of dual polarization radar rainfall estimation. Rainfall estimation is usually accomplished using reflectivity (at a specific polarization, mostly horizontal Zh,), differential reflectivity (Zdr), and specific differential phase (Kdp), either alone or in combination. There are five general forms (Ref. 1 and references therein for a detailed description):

R(Zh) = a Z b … (1a)

R(Kdp) = a kdpb … (1b)

R(Zh,Zdr)= aZhb Zdr

c … (1c)

R(Zdr,Kdp) = a Zdrb Kdp

c … (1d)

R(Zh,Kdp,Zdr) = a Zhb Kdp

c Zdrg … (1e)

It should be noted that in the above equations a, b, c, d and g are generic constants.

Each of the rainfall relations has certain advantages and disadvantages in terms of overall error that are related to both physical and engineering issues described above. As discussed in Cifelli & Chandrasekar1, rainfall algorithms that use Zh or Zdr are subject to bias and differential bias errors, respectively. At frequencies such as S-band, calibration error is the dominant source of the bias, which is considered an engineering issue. However, at C and X-bands, bias can be caused by calibration or performance of attenuation correction procedures, a basic science issue. Therefore, it is anticipated that these higher frequencies will be subject to both basic and applied science issues. Specific differential phase

(Kdp) is a unique radar rainfall estimator and there are advantages and disadvantages for rainfall estimation compared to Zh and Zdr, with more advantages than disadvantages. Unlike the estimators that use reflectivity, Kdp is immune to all bias errors but needs to be estimated over a specified path (applied science) and the sensitivity is frequency dependent (basic science). While R(Kdp) is less sensitive at S-band and therefore, less useful in light rainfall22, it is widely used at X-band (due to the basic science property), whereas R(Zh) and R(Zh,Zdr) have larger errors at X-band due to applied science issues described above. For C-band, the error structure is in between S and X-band. Although, the above discussion is simplified to bias and parameterization errors, additional applied science issues such as ice/bright band contamination and clutter rejection should also be considered, that exist at all frequency bands.

The fact that the performance of rainfall estimators varies with intensity and precipitation type has led to a synthesis approach that combines the strengths of all the measurement estimators with reference to both basic and engineering considerations. An example of a hybrid/optimization algorithm is the CSU-HIDRO algorithm presented in Cifelli et al.23 (Figs 1 and 2). This algorithm is tailored to S-band radar applications, as shown in Fig. 1, is repeated below:

R(Kdp,Zdr)=90.8(Kdp)0.9310(-0.169Zdr) … (2a)

R(Kdp)=40.5(Kdp)0.85 … (2b)

R(Zh,Zdr)=6.7X10-3(Zh)0.92710(-0.343Zdr) … (2c)

R(Zh)=0.0170(Zh)0.7143 … (2d)

R(Zh)=0.0170(Zhrain)0.7143 … (2e)

This concept has been further advanced to calculate HID directly for rainfall estimation as opposed

Fig. 1 — Flow chart of HID procedure utilized by the CSU-HIDRO algorithm; output HID is used as input to drive an optimized rainfall estimation procedure at S-band


393

for particle discrimination first and then rainfall24 (Fig. 3). The HID methodology in Lim et al.

24 is generalized for application to frequencies ranging from S to X-band. 3 Multi sensor approaches to Quantitative

Precipitation Estimation (QPE)

As noted above, there are different approaches to multi sensor rainfall estimation. Techniques to combine sensor information can range from bias correcting observations from one sensor with

information from another25-27 to optimal estimation of the different data sources based on error characteristics14,28. The appropriate technique of multi sensor estimation depends on the time and space scale application. For example, although a climatological Z-R may be appropriate for long term (e.g. monthly) rainfall estimates, it would not be appropriate for storm specific applications such as flash flood events.

With respect to radar and rain gauge data, the multi sensor approach generally is to use the rain gauge as the ‘truth’ so that estimates from radar are adjusted to

Fig. 2 — Schematic representation of how HID is coupled to radar-rainfall estimation in the CSU-HIDRO technique23

Fig. 3 — Flow chart of HID methodology in Lim et al.24


394

match the characteristics of the rain gauge(s). For operational applications, this procedure is relatively easy to implement, because it adjusts different estimates from each sensor to agree with each other; however, the assumption of gauges as the source of validation is not strictly valid since gauges suffer from a number of error sources, all the way from sampling errors to representativeness29-33. A description of several operational systems is described in order to illustrate similarities and differences in the approach to multi sensor QPE. This is important since the uncertainty in QPE is dependent on the input data and the methodology to combine the sensor information. Based on this information, system architecture is presented that takes advantage of these QPE approaches.

The National Oceanic and Atmospheric Administration (NOAA), which includes the National Weather Service (NWS), have developed several multi sensor QPE systems that utilize gauge, radar, and satellite information. These systems include: Multi-sensor Precipitation Estimator (MPE)34,35 system developed by the Office of Hydrologic Development (OHD) and used at the River Forecast Centers (RFCs) and Weather Forecast Offices (WFOs); Climate Prediction Center (CPC) Morphing Technique (CMORPH)36 developed and used by the CPC; and the Multi-radar Multi-sensor (MRMS)37 system developed and operated by the National Severe Storms Lab (NSSL). Each of these systems incorporates precipitation measurements and remotely sensed estimates into a mosaicked precipitation analysis or dataset. Applications of these precipitation datasets range from hydrologic models to global climate analysis. 3.1 Multi sensor Precipitation Estimation

Multi sensor Precipitation Estimation System (MPE) produces aerial estimation of rainfall amounts based on both remotely sensed data (the digital precipitation array, or DPA product, from the WSR-88D radars, and Satellite Precipitation Estimate or SPE product) and ‘ground truth’ observations (rain gauges). The multi sensor estimate data are developed on a 4 km Hydrologic Rainfall Analysis Project (HRAP) grid, and are produced with an hourly temporal scale. MPE produces a number of precipitation estimate fields from combinations of various estimates and observations. Critical to this development is the calculation of bias values between each radar estimate and precipitation gauge

observations. Bias correction may be applied to the estimate field prior to the creating a multi-radar mosaic, and merging the mosaic with precipitation gauge observations. The merging process utilizes a single optimization estimation procedure outlined by Seo28. One of the important features of MPE is the ability to edit or quality control the gridded data fields as well as the point gauge observations. The high degree of flexibility in the MPE software allows each NWS office to produce the hourly best estimate QPE data from whichever estimate and observations are deemed applicable. In practice, this is a combination of radar and gauge data but may also include satellite estimates and even input from other systems such as MRMS. 3.2 Climate Prediction Center (CPC) Morphing Technique

(CMORPH)

CMORPH produces global precipitation analyses with a base spatial resolution of 8 km grid length at the equator and a temporal resolution of one-half hour. CMPORH is a technique for combining precipitation estimates rather than a separate satellite precipitation algorithm. The technique utilizes a Kalman filter based integration framework to synthesize precipitation estimates from all available geostationary and low earth orbit satellites38. CMORPH also leverages gauge observation data, where available, from the CPC Unified Precipitation Analysis. On-going efforts include incorporating gauge data directly into the CMORPH analysis14 and radar data (where available). 3.3 Multi Radar Multi Sensor System (MRMS)

MRMS is the updated name for the National Mosaic and Next Generation Multi sensor QPE (Q2) commonly referred to as NMQ system. MRMS ingests data from WSR-88D radars, rain gauges, satellite imagery and the rapid update cycle numerical model (RUC). MRMS QPE (or Q2 as it is commonly known) is developed from real-time observations and estimates, primarily gauge and radar. At the highest resolution, Q2 data has a spatial resolution of 1 km grid length and 5 minute temporal resolution. MRMS also develops precipitation estimate information at coarse temporal and spatial resolution (e.g. 1 h, 4 km HRAP similar to MPE). Although MRMS produces a similar QPE product suite as MPE (e.g. radar only, gauge only, gauge adjusted radar, etc.), different techniques are utilized to create the various QPE products. However, unlike MPE, MRMS does not


395

have a combined radar-gauge QPE product. One of the unique features of MRMS is the real-time verification of QPE against gauge observations.

3.4 Attributes of a Multi sensor Precipitation System

The above systems each have advantages and disadvantages in terms of their ability to produce multi sensor estimates of precipitation. For example, MRMS utilizes adaptive Z-R relationships and a vertical profile of reflectivity correction as well as producing products at high resolution (1 km, 5 min) but does not produce a blended QPE product37,39 as is done in MPE. CMORPH incorporates GOES IR, passive microwave, and rain gauge information but suffers from large latency of the product delivery and does not currently utilize radar data.

Ideally, a system architecture could be developed that combines the best features of the different multi sensor QPE systems described above. Such a system is represented by the flow chart in Fig. 4. The desirable functional requirements of such a system could include:

• Data ingest capability including grid decoding, projection and coordinate manipulations. Some systems have adopted Geographic Information Systems (GIS) to enable this capability;

• QC, and Quality assurance capability;

• Data integration system that objectively combines observations and or estimates with some preferential weighting function;

• Metadata function that supports the development of robust information that includes the source of the estimate or observation used in the analysis as well as any manipulations performed by the quality control quality assurance functions;

• Hierarchical processing, at different levels of data, including data assimilation and bias correction;

• Capability to perform, real-time verification and validation for assessing the system performance across multiple scales and that also defines the uncertainty bounds in the data;

• Data publication and archive function that communicates the dataset in community adopted standards; and

• A framework to gather developer, user, and stakeholder feedback.

The design requirements of such a system include:

• Common platform or framework for development;

• Modular system that separates the engineering functions (e.g. data flow) from the physical functions (e.g. change in algorithm coefficients or parameters and morphing techniques); and

Fig. 4 — Draft QPE system architecture with key functions/components identified in the NOAA multi sensor precipitation workshop


396

• End-to-end evaluation and monitoring capabilities.

An example of architecture of how the above functional requirements could be built into the QPE system architecture is shown in Fig. 4. This architecture diagram is one possible rendering of the discussions that were recently held in a NOAA QPE workshop40.

4 Data fusion concepts applied to rainfall estimation Data fusion is a multifaceted process dealing with

the association, estimation and combination of data and information from single or multiple sources to achieve refined estimates and complete and timely assessments of situations and their significance41. However, this generic description can be refined to rainfall estimation in a more specific way as it is developed here with some examples. Before such a definition is made, the concept of image fusion should also be mentioned, because often analysts display rainfall observations as images. Image fusion is the process of combining information from two or more images of a rainfall scene into a single composite image that is more informative and is more suitable for visual perception or processing. Image fusion is a process of combining images, obtained by sensors of different types, or wavelengths simultaneously viewing of the same rain scene, to form a composite image. Thus, it can be seen that these concepts need to be defined with a specific application at hand.

Multi sensor data fusion for rainfall that is the topic of consideration here can take place at different levels and different scales. Any data fusion can happen at four distinct levels namely signal level, pixel level, feature level and decision level.

In signal-based fusion, signals from different sensors are combined to create a new signal with a better signal-to noise ratio than the original signals. Pixel-based fusion is performed on a pixel-by-pixel basis. It generates a fused image in which information associated with each pixel is determined from a set of pixels in source images to improve the performance of image processing tasks such as segmentation.

Feature-based fusion at feature level requires an extraction of objects recognized in the various data sources. It requires the extraction of salient features, which are dependent on their environment such as pixel intensities, edges or textures. These similar features from input images are fused. The highest level fusion is decision-level fusion that consists of merging information at a higher level of abstraction,

combines the results from multiple algorithms to yield a final fused decision. Input images are processed individually for information extraction. The obtained information is then combined applying decision rules to reinforce common interpretation. For the rainfall problem, there are some examples that can be cited at signal level fusion and pixel level fusion. The following presents two distinct examples from the rainfall literature that have performed signal level and pixel level fusion, without explicitly using this terminology.

4.1 Signal level fusion of multi radar observations

The signal level fusion gets into the fundamental description of the radar signal in terms of the precipitation microphysics and electromagnetic description, that the underlying rainfall field is observed in terms of its basic descriptors such as raindrop size distribution or the reflectivity fields. Consider for example, the network of radars at attenuating frequency such as X-band. Figure 5 shows the concept diagram of a network of X-band radar beam observations. When the same precipitation volume is simultaneously observed by radars from multiple directions, the observations from each radar is a combination of forward scatter (propagation) and backscatter (reflectivity) properties of precipitation. Figure 6 shows the general concept of signal fusion in a multiple radar environment for rainfall. Chandrasekar & Lim42 developed retrievals for this problem at X-band, while Yoshikawa et al.

43 addressed DSD retrievals from multiple signal level fusion. This approach was even taken to a more advanced level by Bolen & Chandrasekar18,

Fig. 5 — Concept diagram to show a network of X band radar observations


397

who performed signal fusion of observations of ground based and space borne radars and addressed the challenges associated with it. Lim et al.

44 described the challenges associated with performed fusion from two scanning radar signals. In summary, due to advancement of technology with precision positioning of antennas and advanced signal processors, signal level fusion from multiple radars is becoming a reality. 4.2 Pixel level data fusion

The measured reflectivity is smoothed in azimuth and elevation due the effective antenna pattern. In this paper,

only the smoothing in azimuth or elevation is considered. The intrinsic reflectivity Z (mm6m−3) can be discretized according to the desired cross range resolution. The along range resolution is determined by the pulse width. Thus, the two-dimensional combination, of along range and cross range resolutions, make up a precipitation resolution pixel. However, precipitation observation is a three dimensional volume and its observation volume element is a Voxel (or a volume pixel). In order to make the discussion simple, the two dimensional maps of rainfall are considered and the discussion is limited to pixels. The measured reflectivity is in discrete form that can be written as:

Fig. 6(a) — Comparison of multi-day precipitation accumulation in northern California using (left) Mmosaic and (right) Gmosaic techniques [color contours indicate amounts (mm); circles represent independent rain gauges from HMT]

Fig. 6(b) — Scatter plot of hourly MPE rainfall accumulation (mm) with independent HMT gauges over an approximate 4 day period [(left) Mmosaic and (right) Gmosaic; correlation, normalized bias, and RMS error are indicated in each plot]


398

zm = Fz + ε … (3)

where, zm, is the vector of measured reflectivity in azimuth at a given range; matrix F, is the smoothing kernel from the antenna pattern; z, the vector of intrinsic reflectivity; and ε, the noise in the reflectivity measurements. The equation is an ill-posed problem since F is not full-rank and is under determined because dim(z) > dim(zm). Equation (3) is formulated for measurements made at a given range along azimuth but can be extended to two dimensional distribution of reflectivity. It is important to note that unlike traditional image processing applications, the spreading function is position variant. In a networked overlapping observation system such as N radars, the governing equations relating the measured reflectivity and the intrinsic reflectivity distribution at the any given node

radar node is given as a solution to N equations of the form of Eq. (3), which creates an opportunity for pixel level fusion. If the observation pixels are solved taking into account the antenna (or sensor) smooth function, then it becomes a pixel level fusion. If the antenna pattern is a narrow pencil beam, then it becomes a simple average system. Thus, comparing the observation concept (primarily modeling sensor smoothing) and signal model, the distinction between pixel level fusion and signal level fusion can be noted.

5 Validations

An important aspect of QPE is verification. Because QPE is dependent on imperfect input information, the resulting output will have uncertainty that varies in time and space. QPE, therefore, has to be evaluated in order to quantify the uncertainty of the estimates. The accuracy of multi-sensor QPE varies by a number of factors, including geographic location (e.g. flat versus complex terrain), precipitation type (e.g. cool season stratiform versus warm season convective), sensor density (e.g. a rain gauge network), and sensor type. As noted above, the QPE product needs to be optimized for all these considerations so that the most appropriate information is used for a given time and place. Several studies have been conducted to evaluate the relative performance of the different operational QPE products45-47. These studies have proven useful for comparative purposes, however, there has been no systematic attempt to analyze the fundamental causes of regional and temporal performance variability so that improvements can be made to multi sensor QPE.

Although radar geometry and gauge network density are often sufficient to estimate QPE in areas

of relatively flat terrain48, QPE is extremely challenging in steep topographic regions due to a combination of applied science issues related to sampling. In particular, radar beams are often blocked or scanned above the liquid precipitation zone while rain gauge density is often too low to properly characterize the spatial distribution of precipitation. Due to poor radar coverage, rain gauge networks are used by the NWS River Forecast Centers as the principal source for QPE across the western US. However, there has been little evaluation to determine the relative performance of gauge-only radar and blended radar-gauge QPE products in the western U.S.

Validation can be done many ways, but in essence, consists of an evaluation of the QPE product using independent data. However, because the QPE and the independent data may be at different scales (e.g. a gridded QPE compared to a point rain gauge measurement), the evaluation is complicated. Differences between the point rainfall rate of the rain gauge and mean areal rainfall of a radar is due to a combination of basic and applied science issues: small scale rainfall variability and the difference in sensor measurement area29,31,49. Figure 6 shows a comparison of gridded QPE using the MPE system. MPE-Best refers to the combined radar-gauge product (Mmosaic) that uses bias adjusted radar, gauge, and PRISM (Parameter-elevation Regressions on Independent Slopes Model)50 monthly precipitation climatology information as well as the single optimization estimation procedure to construct a gridded QPE product. MPE-Gauge only (Gmosaic) is a gauge product that uses a combination of distance weighting and PRISM to interpolate the gauge point data to a grid. Figure 6(b) shows a scatter plot of the hourly Mmosaic and Gmosaic QPE grids compared to independent gauge data collected by the Hydrometeorology Testbed (HMT) program in California. For this particular event, the Mmosaic is better correlated to the independent gauges but more biased compared to the Gmosaic. More analyses are needed to determine whether the differences are terrain dependent and whether the differences are robust over different time intervals (e.g. 24 h vs 6 h).

Evaluation of QPE can also be performed based on the impact of the precipitation on the resulting hydrologic runoff through simulation experiments16,46,51-54. The advantage of this approach is that the cumulative impact of different QPE forcing on hydrologic runoff can be assessed, however, the


399

difficulty arises from separating errors due to the hydrologic model from errors in the QPE.

The CASA project has conducted extensive validation studies on radar rainfall estimation using X-band dual-polarization radars. Since 2007, the network of four radars in Southwest Oklahoma were operated, mostly during the spring storm season, to demonstrate the value added impact of this networked weather radar system compared to conventional weather radar systems11. For use in the radar rainfall algorithm, a wide range of coefficients has been reported for the R-Kdp power law relation32 at both S-band and X-band. For fair comparison, the KOUN’s R-Kdp relations was selected, that has been evaluated at S-band for the prototype WSR-88D system55. The relation was scaled to X-band with respect to wavelength for rainfall conversion in the IP1 test bed, resulted as:

791.015.18 dpKR = … (4)

The performance of the IP1 QPE product was evaluated for all major rain events against the USDA Agriculture Research Service’s gauge network (MicroNet) in the Little Washita watershed, which comprises 20 weather stations in the center of the test bed as shown in Fig. 7. Five years of data were analyzed including events of different storm types such as severe thunderstorm, convective line, wide spread stratiform rain, and cold front system. Overall, the hourly rainfall estimates compared to the gauge

measurements have a very small bias of 3.74% and a normalized standard error of 25%. These aggregate numbers show the excellent performance of the CASA QPE system over a 5-years time period. The performance is also improved about a factor of three over the current long range weather radar estimates of rainfall reported in the literature for corresponding S-band radar systems operating as a standalone systems, instead of a network. Figure 8 shows a sample map of

Fig. 8 — (a) A sample instantaneous rainfall map from the CASA X-band radar network and (b) Sample hourly rainfall map from the CASA X-band radar network

Fig. 7 — Locations of the USDA ground gauges (denoted by x) in the CASA’s IP1 network


400

instantaneous and hourly rainfall map, which are typical products of the CASA radar network.

6 Summary and Conclusions

Rainfall estimation has been pursued since the earliest of civilizations because of water’s importance as a primordial element of life. Moreover, rainfall estimation is one of the most commonly used applications of weather radars in most operational systems. Historically, rain gauges have been the sources of rainfall information and those are point measurements. The introduction of radar for rainfall observations, opened up the rainfall measurement field extensively. The very fact that rainfall can be observed in three dimensions, with fairly high temporal and spatial resolution (on the order of minutes and few hundred meters to a kilometer), created opportunities for radar application such as now casting and warning, but also posed several challenges. The fact that rainfall estimation remains the most common application of operational radars demonstrates that advantages overweigh the challenges.

The key challenges of rainfall estimation from radars can be classified into basic science issues and engineering problems. Dual-polarization radar techniques have shown great promise in addressing both issues, but more importantly the physical science issues, such as DSD estimation and detecting ice contamination. Multi sensor estimates have made great strides in addressing the rainfall estimation problem through better calibration, improving observations at multiple scales such as radar, satellite and gauge scales, while at the same time removing bias across platforms. Data fusion techniques, have demonstrated advantages in retrievals, especially in radar observation at attenuated frequencies such as X-band. Data fusion has also shown benefits in merging data from radars and satellites. Validation of radar rainfall estimates have been a challenge mainly because of the representativeness issues and scale issues of validating systems such as rain gauges. Nevertheless, network of gauges and disdrometers are becoming increasingly common for radar rainfall validation. Networks of short range dual polarization X-band radars scanning at low elevations angles have shown great promise for estimating hourly rainfall observations accurately with negligible bias and a standard error of 25%. These systems are now being applied to deal with urban scale flooding issues

that cannot be adequately addressed by current operational radar and gauge networks alone.

Acknowledgements

The authors acknowledge discussions with large number of scientists, engineers and students in both organizations who work on the MPE rainfall problem. The research work presented in this paper is supported by the National Science Foundation, NASA PMM program and the NOAA research programs. The authors acknowledge assistance from Haonan Chen in preparing this paper.

References 1 Cifelli R & Chandrasekar V, Dual polarization radar rainfall

estimation, in Rainfall: State of the Science, F Y Testik & M Gebremichael, Eds (Am Geophys Union, Washington), 2010, pp 105-125, doi: 10.1029/2010GM001026.

2 Zawadzki I, Factors affecting the precision of radar measurements of rain, Preprints, 22nd Int Conf on Radar

Meteorology (Am Meteorol Soc, Zurich, Switzerland), 1984 pp 251-256.

3 Wang Yanting & Chandrasekar V, Quantitative precipitation estimation in the CASA X-band dual-polarization radar network, J Atmos Ocean Technol (USA), 27 (2010) pp 1665–1676.

4 Maki M, Iwanami K, Misumi R, Park S -G, Moriwaki H, Maruyama K -I, Watabe I, Lee D -I, Jang M, Kim H -K, Bringi V N & Uyeda H, Semi-operational rainfall observations with X-band multi-parameter radar, Atmos Sci

Lett (USA), 6 (2005) pp 12–18.

5 Maki M, Maesaka T, Misumi R, Iwanami K, Suzuki S, Kato A, Shimizu S, Kieda K, Yamada T, Hirano H, Kobayashi F, Masuda A, Moriya T, Suzuki Y, Takahori A, Lee D -I, Kim D -S, Chandrasekar V & Wang Y, X-band polarimetric radar network in the Tokyo metropolitan area - X-NET, Proc of

Fifth European Conf on Radar in Meteorology and

Hydrology (Helsinki, Finland), 2008.

6 Park S -G, Bringi V N, Chandrasekar V, Maki M & Iwanami K, Correction of radar reflectivity and differential reflectivity for rain attenuation at X Band. Part I: Theoretical and empirical basis, J Atmos Ocean Technol (USA), 22 (2005a) pp 1621–1632.

7 Park S -G, Maki M, Iwanami K, Bringi V N & Chandrasekar V, Correction of Radar Reflectivity and Differential Reflectivity for Rain Attenuation at X Band. Part II: Evaluation and Application, J Atmos Oceanic Technol

(USA), 22 (2005), 1633–1655.

8 National Research Council, Flash flood forecasting over

complex terrain: With an assessment of the sulphur mountain

NEXRAD in Southern California (National Academy Press, USA), 2005.

9 Junyent Francesc & Chandrasekar V, Theory and characterization of Weather Radar Networks, J Atmos Ocean

Technol (USA), 26 (2009) pp 474–491.

10 Junyent F, Chandrasekar V, McLaughlin D, Insanic E & Bharadwaj N, The CASA Integrated Project 1: Networked Radar System, J Atmos Ocean Technol (USA), 27 (2010) pp 61–78.


401

11 Chandrasekar V, McLaughlin D, Brotzge J, Zink M, Philips B & Wang Y, Distributed collaborative adaptive radar network: Preliminary results from the CASA IP1 testbed, in 2008 IEEE Radar Conf, Rome, Italy, 2008.

12 National Research Council, Observing eeather and climate

from the ground up: A nationwide network of networks (National Academy Press, USA), 2008.

13 Huffman George J, Adler Robert F, Rudolf Bruno, Schneider Udo & Keehn Peter R, Global precipitation estimates based on a technique for combining satellite-based estimates, rain gauge analysis, and NWP model precipitation information, J Clim (USA), 8 (1995) pp 1284–1295.

14 Xie P & Xiong A -Y, A conceptual model for constructing high-resolution gauge-satellite merged precipitation analyses, J Geophys Res (USA), 116 (2011) D21106, doi: 10.1029/2011JD016118.

15 Fulton Richard A, Sensitivity of WSR-88D rainfall estimates to the rain-rate threshold and rain gauge adjustment: A flash flood case study, Weather Forecast (USA), 14 (1999) pp 604–624.

16 Gourley Jonathan J, Hong Yang, Flamig Zachary L, Wang Jiahu, Vergara Humberto & Anagnostou Emmanouil N, Hydrologic evaluation of rainfall estimates from radar, satellite, gauge, and combinations on Ft. Cobb basin, Oklahoma, J Hydrometeorol (USA), 12 (2011) pp 973–988.

17 Bolen Steven M & Chandrasekar V, Quantitative cross validation of space-based and ground-based radar observations, J Appl Meteorol (USA), 39 (2000) pp 2071–2079.

18 Bolen Steven M & Chandrasekar V, Methodology for aligning and comparing spaceborne radar and ground-based radar observations, J Atmos Oceanic Technol (USA), 20 (2003) pp 647–659.

19 Wexler R & Swingle D, Radar storm detection, Bull Am

Meteorol Soc (USA), 28 (1947) pp 159–167.

20 Marshall J S, Langille R C & Palmer W M, Measurement of rainfall by radar, J Atmos Sci (USA), 4 (1947) pp 186–192.

21 Chandrasekar V, Meneghini R & Zawadzki I, Global and local precipitation measurements by radar, Meteorol Monogr

(USA), 30 (2003) pp 215–215.

22 Matrosov S Y, Cifelli R, Kennedy P C, Nesbitt S W, Rutledge S A, Bringi V N & Martner B E, A comparative study of rainfall retrievals based on specific differential phase shifts at X- and S-band radar frequencies, J Atmos

Ocean Technol (USA), 23 (2006) pp 952–963.

23 Cifelli R, Chandrasekar V, Lim S, Kennedy P C, Wang Y & Rutledge S A, A new dual-polarization radar rainfall algorithm: Application in Colorado precipitation events, J Atmos Ocean Technol (USA), 28 (2011) pp 352-364.

24 Lim S, Cifelli R, Chandrasekar V & Matrosov S Y, Precipitation classification and quantification using X-band dual-polarization weather radar: Application in the hydrometeorology testbed, J Atmos Ocean Technol (USA) (communicated).

25 Collier C G, Larke P R & May B R, A weather radar correction procedure for real-time estimation of surface rainfall, Q J R Meteorol Soc (UK), 109 (1983) pp 589–608.

26 Smith J A & Krajewski W F, Estimation of the mean field bias of radar rainfall estimates, J Appl Meteorol (USA), 30 (1991) pp 397–412.

27 Seo D -J & Breidenbach J P, Real-time correction of spatially non uniform bias in radar rainfall data using rain gauge measurements, J Hydrometeorol (USA), 3 (2002) pp 93-111.

28 Seo D -J, Real-time estimation of rainfall fields using radar rainfall and rain gauge data, J Hydrol (USA), 208 (1998) pp 37-52.

29 Seed A & Austin G L, Variability of summer Florida rainfall and its significance for the estimation of rainfall by gauges, radar and satellites, J Geophys Res (USA), 95 (1990) pp 2207–2215.

30 Kitchen M & Blackall R M, Representativeness errors in comparisons between radar and gauge measurements of rainfall, J Hydrol (USA), 134 (1992) pp 13–33.

31 Ciach G J & Krajewski W F, On the estimation of radar rainfall error variance, Adv Water Resour (USA), 22 (1999) pp 585-595.

32 Bringi V N, Keenan T D & Chandrasekar V, Correcting C-band radar reflectivity and differential reflectivity data for rain attenuation: A self-consistent method with constraints, IEEE Trans Geosci Remote Sens (USA), 39 (2001) pp 1906–1915.

33 Germann U & Joss J, Variograms of radar reflectivity to describe the spatial continuity of alpine precipitation, J Appl

Meteorol (USA), 40 (2001) pp 1042-1059.

34 Lawrence B A, Shebsovich M I, Glaudemans M J & Tilles P S, Enhancing precipitation estimation capabilities

at National Weather Service field offices using multi-sensor

precipitation data mosaics, Preprints 19th International Conference on Interactive Information Processing Systems for Meteorology, Oceanography and Hydrology, Am Meteorol Soc, Long Beach, California, 2003.

35 Glaudemans M, Tilles P & Lawrence B, Interactive quality

control and operational product generation of hourly

multi-sensor precipitation estimates in the NWS, Preprints 25th Conf on International Information and Processing Systems (IIPS) (Am Meteorol Soc, Phoenix, Arizona), 2009, 5B.3.

36 Joyce R J, Janowiak J E, Arkin P A & Xie P, CMORPH: A method that produces global precipitation estimates from passive microwave and infrared data at high spatial and temporal resolution, J Hydrometeorol (USA), 5 (2004) pp 487-503.

37 Zhang J, Howard K, Langston C, Vasiloff S, Kaney B, Arthur A, Van Cooten S, Kelleher K, Kitzmiller D, Ding F, Seo D J, Wells E & Dempsey C, National Mosaic and Multi-Sensor QPE (NMQ) System: Description, results, and future plans, Bull Am Meteorol Soc (USA), 92 (2011) pp 1321–1338.

38 Joyce R J & Xie P, Kalman filter based CMORPH, J Hydrometeorol (USA), 12 (2011) pp 1547-1563.

39 Zhang J, Langston C & Howard K, Bright band identification based on vertical profiles of reflectivity from the WSR-88D, J Atmos Ocean Technol (USA), 25 (2008) pp 1859–1872.

40 Cifelli R et al., NOAA Data Fusion Mini Workshop Report (Silver Springt, MD, USA), 2012.

41 Klein L A, Sensor and data fusion: A tool for information

assessment and decision making (SPIE Press, Bellingham, WA, USA), 2004.

42 Chandrasekar V & Lim S, Retrieval of reflectivity in a networked radar environment, J Atmos Ocean Technol

(USA), 25 (2008) pp 1755–1767


402

43 Yoshikawa E, Chandrasekar V, Ushio Tomoo & Kawasaki Zen, Bayesian Formulation of DSD retrieval algorithm for

dual-polarized X-Band Weather Radar Network, IEEE International Geoscience and Remote Sensing Symposium (IGARSS2012), Munich, Germany, 22-27 July 2012.

44 Lim S, Chandrasekar V, Lee P & Jayasumana A P, Real-time implementation of a network-based attenuation correction in the CASA IP1 testbed, J Atmos Ocean Technol (USA), 28 (2011) pp 197–209.

45 Kitzmiller D et al., A comparison of evolving multi sensor

precipitation estimation methods based on impacts on flow

prediction using a distributed hydrologic model, Preprints, 22nd Conf on Hydrology, New Orleans, LA, Am Meteorol Soc, 2008, P3.4 (http://ams.confex.com/ams/pdfpapers/ 134451.pdf).

46 Kitzmiller D, Van Cooten S, Ding F, Howard K, Langston C, Zhang J, Moser H, Zhang Y, Gourley J J, Kim D & Riley D, Evolving multi sensor precipitation estimation methods: Their impacts on flow prediction using a distributed hydrologic model, J Hydrometeorol (USA), 12 (2011) pp 1414–1431.

47 Wu W, Kitzmiller D & Wu S, Evaluation of radar precipitation estimates from the National Mosaic and Multi sensor Quantitative Precipitation Estimation System and the WSR-88D Precipitation Processing System over the Conterminous United States, J Hydrometeorol (USA), 13 (2012) pp 1080–1093.

48 Gourley J J, Hong Y, Flamig Z L, Li L & Wang J, Intercomparison of rainfall estimates from radar, satellite, gauge, and combinations for a season of record rainfall, J Appl Meteorol Climatol (USA), 49 (2010a) pp 437–452.

49 Anagnostou E N, Krajewski W F & Smith J A, Quantification of radar rainfall uncertainty, J Atmos Ocean

Technol (USA), 16(2) (1999) pp 206-215.

50 Daly C, Neilson R P & Phillips D L, A statistical-topographic model for mapping climatological precipitation over mountainous terrain, J Appl Meteorol (USA), 33 (1994) pp 140-158.

51 Yilmaz K K, Hogue T S, Hsu K -L, Sorooshian S, Gupta H V & Wagener, Intercomparison of rain gauge, radar, and satellite-based precipitation estimates with emphasis on hydrologic forecasting. J. Hydrometeorol (USA), 6 (2005) pp 497–517.

52 Su F, Hong Y & Lettenmeaier D P, Evaluation of TRMM Multi satellite Precipitation Analysis (TMPA) and its utility in hydrologic prediction in the La Plata Basin, J

Hydrometeorol (USA), 9 (2007) pp 622–640.

53 Behrangi A, Khakbaz B, Jaw T C, AghaKouchak A, Hsu K & Sorooshian S, Hydrologic evaluation of satellite precipitation products over a mid-size basin, J Hydrol (USA), 397(3-10) (2011) pp 225-237.

54 Gourley J J, Giangrande S E, Hong Y, Flamig Z L, Schuur T & Vrugt J A, Impacts of polarimetric radar observations on hydrologic simulation, J Hydrometeorol (USA), 11 (2010b) pp 781–796.

55 Ryzhkov A V, Giangrande S E & Schuur T J, Rainfall estimation with a polarimetric prototype of WSR-88D,

J Appl Meteorol (USA), 44 (2005) pp 502-515.

56 Huffman George J, Adler Robert F, Morrissey Mark M, Bolvin David T, Curtis Scott, Joyce Robert, McGavock Brad & Susskind Joel, Global precipitation at one-degree daily resolution from multi satellite observations, J Hydrometeorol (USA), 2 (2001) pp 36–50.

concepts and principles of rainfall estimation from radar:...

Documents