38 Applications of Remote Sensing in Numerical Weather Prediction

Soma Sen Roy

1. Learning outcomes
2. Introduction
3. Satellite data assimilation
3.1. Different ways of sensing the earth/atmosphere
3.1.1. Atmospheric sounding channels from passive instruments
3.1.2. Surface sensing channels from passive instruments
3.1.3. Surface sensing channels from active instruments
3.1.4. Other technologies
3.2. Weighting functions
3.3. The inverse problem
3.3.1. Locally produced or “1D-Var” retrieval
3.3.2. Direct assimilation of radiances
4. Radar data assimilation
4.1. Radar wind assimilation
4.2. Radar reflectivity assimilation
4.2.1. Nudging
4.2.2. Variational assimilation
4.2.3. Ensemble kalman filtering
4.3. Radar data assimilation in NWP models in India
5. Summary

1. Learning outcomes

After studying this module, you shall be able to:

• Understand the requirement of remote sensing data for initialization of numerical weather prediction (NWP) model to improve forecast skill
• Understand different types of available satellite sensors and their challenges towards data assimilation
• Understand modification of the radiative transfer equation for each type of satellite sensors Know the purpose of weighting functions and the challenges
• Understand the basics of extraction of the atmospheric temperature profile from a set of measured radiances
• Understand the basics of data assimilation procedures through assimilating the satellite and radar data into NWP models

2. Introduction

Numerical Weather Prediction is mainly an initial-boundary-values problem; i.e., given an estimate of the initial state of the atmosphere, ocean and land surface, the model forecasts their evolution. A greater number of high quality observations that more fully represent the complete nature of the initial atmosphere and land surface would greatly improve the forecasting capabilities of NWP models. Operational data used at NWP centres consist of various data types obtained from the global observing system. The backbone of this system is provided by surface observations from land and ship stations, and vertical soundings from radiosonde and pilot balloons. These observations have provided a stable source of information over the years. But their horizontal distribution is far from homogeneous. The lack of reliable in situ data from underdeveloped and sparsely populated regions, with which to initialize the NWP model is the most challenging problem regarding accurate forecasting. However despite no large increase in the amount of land based observations, over the last few years, model performance has reached unprecedented levels of accuracy. Figure 1 shows the anomaly correlation of the geopotential errors at 500 hPa for 3-day, 5-day,7-day and 10-day forecasts of 500 hPa geopotential height, averaged for the northern and southern hemispheres for the ECMWF (European Centre for Medium Range Weather Forecasting) model for various forecast ranges during  1980 to 2010. Although this gain in predictability has been brought by the various components of the NWP system (model dynamics, physics, data assimilation), it is believed that a large part of this gain can be attributed to the data amount and their assimilation improvements (Rabier, 2005). Since the 1970s, these other data types that have emerged include drifting buoys, aircraft measurements, wind profilers, satellite radiances, satellite cloud-drift winds and scatterometers. Major scientific advances such as 4D-Var, and Ensemble Kalman Fillter methods of data assimilation and improvements in error specifications; combined with a large increase in available observations, has indeed led to significant improvements in forecast performance. In particular, over large parts of the primarily oceanic southern hemisphere, assimilation of satellite data provides the best possible estimates of the prevailing atmosphere. Remote sensing observations from satellite and radars are expanding rapidly and becoming a major, horizontally homogeneous, source of information in current systems but are more complex to use in data assimilation. One of the major advances has been the direct use of raw radiance observations in data assimilation in variational systems in the last decade or so in most NWP centres. To explain this approach, let us discuss the basics of data assimilation in general and assimilation of satellite and radar data in particular, into NWP models.

Procedures of atmospheric data assimilation combines multiple information coming from different sources namely the outputs from forecast models, and available observations etc. Using these information, the model is run on daily basis, for up to a few days, to produce the forecast products which will guide the forecasters in their weather prediction. The analyses can also be used to help understand atmospheric properties, for instance in the context of field experiments or re-analyses over long periods of time. Data assimilation is usually performed in a sequential manner, with a time series of ‘assimilation cycles’, including model integration, and a correction due to observations. As a new set of observations becomes available every six or twelve hours, a short-range forecast (so-called ‘background’) is updated with the new set of data into a new analysis of the atmosphere. This analysis is then propagated in time with the forecast model to provide a new background field for the next assimilation cycle. This series of steps in the data assimilation process shows that the atmospheric model is the basic ingredient, which allows time continuity in our evaluation of the atmospheric flow. However, observations are the crucial elements allowing constant re-adjustment of the model trajectory to produce a reasonable estimate of the true atmospheric state. Developments in the global observing system and in the processing of these observations lead to a significant impact on the quality of the analysis. Each source of information about the atmospheric state is characterized by various errors (mainly instrument or representativeness errors for the observations, forecast error for the background information). There is a need for a statistical approach to mix these various pieces of information together to get an analysis, taking these error characteristics into account. In other words, one needs to find the best compromise between the various sources of information, trusting each of them according to their error statistics.

3. Satellite data assimilation

It is important to realize that the measured quantities by satellite instruments do not relate directly to geophysical quantities. The conversion of measured quantities into geophysical quantities is an inverse problem that data assimilation schemes try to solve in an optimal way. As such, satellite instruments, whether active or passive, do not measure atmospheric properties such as temperature, humidity or wind; instead these sensors measure the radiance L that reaches the top of the atmosphere at a given frequency ν. The radiance is related to geophysical parameters through the radiative transfer equation. In short, the radiative transfer equation can be summarized as follows:

Where, B(ν, T(Z)) is the Planck radiance for a scene temperature T at altitude Z, and τ(ν) the transmittance from altitude Z to space (Thepaut, 2003). Note that Eq. 1 is a particular case of the generalized direct problem mapping the atmospheric model Xb to a given observation Y, Y = H (Xb), the observation operator H being in this specific case the radiative transfer equation.

3.1. Different ways of sensing the earth/atmosphere

By selecting radiation at different frequencies (or channels), a satellite instrument can provide information on a range of geophysical variables (e.g. upper air temperature, surface parameters, clouds). There are two types of satellite sensors based on their principle of works, viz., active and passive sensors. Passive instruments sense radiation emitted by the surface and/or atmosphere (or the solar radiation reflected by it). Active instruments emit radiation and measure how much of it is reflected or backscattered by the surface and/or atmosphere.In general, the channels currently used for NWP applications may be considered as one of 3 different types.

3.1.1. Atmospheric sounding channels from passive instruments

These channels are located in parts of the infrared and microwave spectrum for which the main contribution to the measured radiance L at a given frequency ν that reaches the top of the atmosphere is described by the first term of the right hand side of Eq

These channels avoid frequencies for which surface radiation or cloud contributions are important. These  channels  are  primarily     used  to  obtain  information  about  atmospheric  temperature  and  humidity. Atmospheric sounding channels from the HIRS (High resolution Infrared Sounder) and AMSU (Advanced Microwave Sounding Unit) on board NOAA satellites fall into this category.

3.1.2. Surface sensing channels from passive instruments

These channels, called “imaging” channels, are located in atmospheric “window” regions of the infra-red and microwave spectrum at following frequencies where there is very little interaction with the atmosphere and the main contribution to the measured radiance is taken place:

Where, Tsurf is the surface temperature and ε the surface emissivity. These channels are primarily used to obtain information on surface temperature and quantities that influence the surface emissivity such as wind (through the roughness over sea) and vegetation (land). They can also be used to obtain information on cloud top (in the Infrared) and rain (in the microwave). In addition, sequences of Infrared images from geostationary satellites can be used to track the cloud movement and indirectly derive wind information.

3.1.3. Surface sensing channels from active instruments

These instruments (e.g. scatterometer) emit microwave radiation towards the surface in the atmospheric window parts of the spectrum such that radiance scattered back from the surface is:

These instruments provide information on ocean winds. Some similar active instruments such as altimeters and SARS (Synthetic Aperture Radars) provide information on wave height and spectra.

3.1.4. Other technologies

Active instruments operating in the visible (Lidars) or the microwave (radars) can also analyse the signal backscattered from atmospheric targets such as molecules, aerosols, water droplets or ice particles. Penetration capability of these active instruments allow the derivation of information on cloud base, cloud top, wind profiles (Lidars) or cloud and rain profiles (radars).

Radio-occulation of the earth’s atmosphere using GPS (Global Positioning System) is another novel way of extracting atmospheric information. This method exploits an already existing technology due to the GPS constellation (originally designed for other applications). GPS receivers such as the GRAS instrument (Global navigation satellite system Receiver for Atmospheric Sounding) instrument on board METOP satellite), measure the Doppler shift of a GPS signal refracted along the atmospheric limb path. This refraction is proportional to (among other parameters) the density of the atmosphere, and therefore indirectly to temperature and humidity profiles. Provided a sufficient number of receivers are installed on Low Earth Orbits, this technique could offer high vertical resolution (balanced by a somewhat coarse horizontal resolution of ~200- 300 km), self-calibrated and “all weather” observations of atmospheric temperature (and possibly humidity).

3.2. Weighting functions

Let us consider the simple case of a channel for which the primary absorber is a well-mixed gas (in this case oxygen or carbon dioxide). It can be shown that the measured radiance is a weighted average of the atmospheric temperature profile, which can be obtained by reducing the Eq. 1 as:

the radiance to a single atmospheric level (a). The vertically constant weighting function corresponds to a sensitivity of the radiance to the mean temperature between the surface and the top of the atmosphere (b).

In reality, the shape of the real atmospheric weighting functions are somewhere in between these two idealized cases (see Figure 3 illustrating the AMSU-A temperature weighting functions). As we can see, they are fairly broad, i. e. the associated radiances sense the temperature of very broad atmospheric layers. A reasonable vertical sampling of the atmosphere by satellite radiances therefore comes from an appropriate selection of channels, with varying absorption strengths.

3.3. The inverse problem

The problem of extracting the atmospheric temperature profile from a set of measured radiances is called the retrieval or inverse problem. Unfortunately, with a finite number of channels and with weighting functions that are generally quite broad, the inverse problem is generally ill-posed (i. e. an infinite number of different temperature profiles could give the same measured radiance). If one wants to utilize satellite radiances to determine the initial conditions of a NWP model, the role of data assimilation is to solve this ill-posed problem. Any technique requires the use of prior information, the quality of which will drive the accuracy of the final retrieved product. Let us write the (1D) inversion equation simply as:

where,

Xb represents the atmospheric background, or prior information, Y represents the radiance observation,

B and R represent the associated error covariance matrices Xa represents the final analysis

It is clear from Eq. 6 that it is through the convolution of B and H (jacobian of H, proportional to its weighting function) that a given measurement information will be distributed in space and among different geophysical quantities defining the atmospheric state. In particular, since satellite radiances sense very broad layers, the vertical propagation of an observed increment is left to B. The design of B is therefore crucial for a proper assimilation of satellite radiances. On can easily see that the complexity of the problem increases when radiance information has to be further distributed through temperature, moisture and other atmospheric quantities (ozone, CO2, clouds, rain) for which the direct modeling is difficult and the error statistics (e.g. the associated B) poorly known. Additional complexity occurs when H incorporates the horizontal/vertical (3D-Var) and time (4D-Var) dimension. Different options have been commonly used to use satellite data in NWP data assimilation and solve Eq. 6.

3.3.1. Locally produced or “1D-Var” retrieval

The retrievals are produced by the NWP centre using background information ofa short-range forecast (typically 6 hour). The retrieval is the outcome of an optimal estimation, which involves the minimizing of: for example, a cost function or solving the standard optimum interpolation equation. It also involves adjusting atmospheric profiles to background atmospheric profiles and measured radiances. In that case, prior information is generally very accurate and contains information about important atmospheric phenomena (such as fronts, tropopause folding, etc). In principle, the error characteristics (covariances) of the prior information and resulting retrieval should be better known. This ingredient is vital for the subsequent assimilation process. However, the error characteristic of the retrieval may remain complicated due to its correlation with the forecast background that is in fact used twice in the subsequent assimilation.

3.3.2. Direct assimilation of radiances

Variational techniques such as 3D-Var or 4D-Var (Rabier et al. 1998) allow the direct assimilation of radiance observations and therefore avoid the need for an explicit retrieval step. The retrieval step is essentially incorporated within the main analysis by finding the model variables that minimize a cost function measuring,the departure between the analysed state and both the background and available observations. In this case, the forecast background still provides the prior information to supplement the radiances. However, it is not used twice (as it is in a 1D-Var preprocessor context) and this avoids the problem of assimilating retrievals with complicated error structures. Furthermore, the inversion is further constrained by the simultaneous assimilation of other observations. Note in particular that in 4D-Var, the adjustments forced by radiances at different times of the assimilation window will be consistent with the forecast model physics and dynamics. Also, the characterization of observational errors in radiance space is much easier. In practice, the approach adopted by NWP centres is pragmatic and observations are used in the space where errors are easier to characterize. As it happens, the “model-to-satellite” approach tends to become the rule, but exceptions exist. For example, atmospheric motion winds derived from cloud tracking are assimilated in all NWP systems because the direct assimilation of cloud information is not mature enough. Figure 4 (a,b,c,d) illustrate the daily data statistics of some of the satellite data assimilated into the Global Forecast System (GFS) model installed at India Meteorological Department.

4. Radar data assimilation

       Thunderstorms  and  convective  storm  systems  are  perhaps  the  most  important  small-scale meteorological elements in India and other tropical countries. Skill in forecasting initiation, growth and movement of thunderstorms and their associated quantitative precipitation has historically been low. One of the crucial aspects for increasing the skill of the Quantitative Precipitation Forecast (QPF) of convective systems is to run numerical models at resolutions that can resolve the convective processes. Another important aspect is to initialize the models with observations that can describe the mesoscale and convective-scale state of the atmosphere. Since Doppler radar is one of the important instruments that are able to sample the convective-scale details, and operational radar networks rarely have dual-Doppler coverage (two radars observing the same spot), researchers have focused their studies on the extraction of information from single Doppler observations. Various techniques were developed to assimilate single-Doppler observations (radial velocity and reflectivity) or the derived quantities   (e.g.   precipitation)   into   high-resolution    numerical   models.   Some   of   the   quantities assimilated into NWP models may be:

Wind:

• – VAD (Velocity Azimuth Display), which is an estimated wind profile from radial wind measurements on all vertical elevation
• – Radial wind super-observations, which means a spatial averaging (smoothing) of the raw data over some pixels in order to get rid of horizontal correlations of observation errors
• – Raw radial winds are also used to be filtered for spatial smoothing

Reflectivity:

• – Cmax, which is the maximum reflectivity value of all elevations above the given pixel
• – Column of elevation’s reflectivity values above the given pixel – volume data
• – Estimated instantaneous precipitation, accumulated precipitation etc.
• – Interpolation of any above to a regular grid

One has to mention that the radiation emittedby radar, is scattered back not only from the targets in our interest i.e. raindrops, but also from orography, birds, insects, which makes necessary to apply an important amount of extra processing of the raw data (filters, corrections, etc.). The figure 5 below, (from Boloni, 2008) gives a very general overview of the existing radar assimilation schemes applied in NWP models.

4.1. Radar wind assimilation

Radar wind is assimilated with the Variational method (3/4DVAR) in many NWP models (HIRLAM, UM, AROME, MM5, WRF, ARPS). Most of the applications use radar radial wind information (Lindskog et al., 2003, Roy Bhowmik et al, 2011 for example) but there are examples of VAD assimilation as well (Lindskog et al., 2003). In case of VAD, the wind profile is assimilated similarly to radiosonde and wind profiler data (the observation operator consist of horizontal and vertical interpolations of the model wind to the location of the radar wind profile values). Radial wind data are often used as super-observations or they are processed with filters in order to smooth the very high-resolution raw information. The observation operator for radial wind data consist of a projection of the model wind u (zonal) and v (meridional) components at the observation location towards the radar (still in azimuthal direction):

Where, Φ is the elevation angle of the radar beam, d is the distance from the radar, r is the radius of the Earth and h is the height of the radar instrument (above the mean sea level). As in all variational assimilations, both VAD and radial wind observations are meant to produce analysis increments in the function of the background and observation errors. Most of the variational analysis applications are multivariate, that is radar wind observations produce not only wind but also pressure, temperature and humidity analysis increments.

4.2. Radar reflectivity assimilation

Reflectivity or post-processed information from reflectivity is assimilated with different approaches in different NWP models. The main approaches in use are Nudging, Variational analysis and Ensemble Kalman Filtering. Contrary to the case of radar wind, the assimilation of reflectivity information requires complicated observation operators including moist physics.

4.2.1. Nudging

Nudging in general aims to force the model state towards available observations during the model integration. This is done through introducing a relaxation term, which measures the ‘observation minus model’ distance. With the Nudging scheme, one does not assimilate the reflectivity itself but the precipitation estimated from it. A popular way of nudging precipitation information is the Latent Heat Nudging (LHN) (Jones and Macpherson, 1997). In LHN, an extra temperature tendency is added to the thermodynamic equation, accounting for the latent heating that would generate similar rain in the model as the observation, according to the model physics:

tendency, and ΔTLH is the needed latent heat for adjusting the model precipitation (RRm) to the observed precipitation (RRo) according to the model physics. The scheme implies that first model and observation rain are compared in the observation points i.e. the observation operator consist of the model moist physics and an interpolation to the observation points. It is to be noted, that the full physics can be used and there is no need for its adjoint. Other nudging schemes adjust the model humidity profile instead of the temperature (i.e. Davolio and Buzzi, 2004). The adjustment is proportional to the difference between the model and observed rain and it differs according to the model precipitation type (stratiform or convective).

4.2.2. Variational assimilation

In variational assimilation (3/4DVAR), the information from radar reflectivity is taken into account through a new Jo term, which measures the distance of the background and the radar information (reflectivity, rain, or derived temperature and humidity profiles). There are differences in the observation operators, which is arising due to the ‘model to reflectivity’ transformation depending on the implementation.

• Direct assimilation: Some implementations assimilate directly the reflectivity itself in the 3/4DVAR. Such examples are the MM5 and WRF implementations (Xiao et al., 2006). Here the control variable is the total water content (qt), which is first repartitioned to model rain water (qr), cloud water (qc) and water vapor (qv) through warm rain physics. The model rain water (qr) is then used to compute simulated ‘model’ reflectivity. Jo is then computed in the ‘reflectivity space’ and its gradient is computed with respect to reflectivity. Finally, the adjoint of the reflectivity operator and the repartitioning warm rain physics are used to compute the gradient with respect to the control variable (qt), i.egradJo and gradJb can be added and a new search of the minimization can start.

• At Meteo-France (AROME), a two-step approach is applied, first providing 1D humidity pseudo observation profiles derived from reflectivity and second, assimilating these 1D profiles in the 3DVAR just like radiosonde observations. The humidity pseudo observations in AROME are generated via a Bayesian method. One has to know that at Meteo France, reflectivity observations are available as vertical profiles on several elevations in the location of the radar pixels. The 1D Bayesian method provides the humidity profile pseudo observation ypo as the linear combination of background humidity profiles (xi) in the neighborhood of the given radar reflectivity profile (yz).

In the above equation, HZ(x) is the simulated reflectivity by the radar simulator, and RZ is the observation error covariance matrix.

One can see that the weight of a given background humidity profile depends on the departure of its reflectivity equivalent from the observed radar reflectivity profile. The radar simulator provides the reflectivity equivalent of the background humidity,which is the backscattered signal from the model hydrometeor particles provided by the full moist physics. A limitation of the 1D Bayesian method is that if there is no any precipitation in the model near the observed reflectivity, there is no chance to  find a good linear combination of neighboring humidity profiles, i.e. a “too dry” humidity pseudo observation will be proposed. There is an attempt to get rid of this limitation by forcing saturation in those model grid points, which are in the neighborhood of observed reflectivity profiles (Montmerle et al., 2007, Watterlot et al., 2008).

• At ECMWF (European Centre of Medium Range Weather Forecasting). a two-step approach is implemented as well (Lopez and Bauer, 2006, Marécal and Mahfouf, 2003). Here, hourly-cumulated rain observations from radars and gauges are used to produce 1D Total Column Water Vapor (TCWV) observations via 1DVAR minimization. The 1DVAR control variables are specific humidity and temperature and the applied observation operator consist of interpolations and of linearized moist physics, which transforms the model humidity and temperature into precipitation in order to provide the observation minus background differences in the 1DVAR Jo. The 1DVAR minimization will find first a humidity profile, which fits both the background and the observations in the variational sense, then the vertical profile of humidity increments is integrated to TCWV. The TCWV observations are used in the 4DVAR assimilation. Note, that the 1DVAR method has limitations as well to produce TCWV pseudo observations if the model background is not rainy. In this case the cost function used in the 1DVAR:

which is not depending any more on the model humidity and temperature x as x=xBand H(x)=0. Another drawback of this method is that the background is used twice during the analysis (first in the 1D- and second in the 4DVAR), which leads to relatively weak analysis increments.

• The operational JMA 4DVAR assimilates hourly-cumulated precipitation with a one step approach (Koizumi et al., 2005). There a Jrain is added to the cost function, which measures the distance of the model and observed precipitation (note that the observed precipitation is interpolated onto a regular grid before running the analysis). The model precipitation is generated with the moist physics of the model. The gradient of Jrain is projected back to the control variable space with the adjoint of the moist physics.

4.2.3. Ensemble kalmanfiltering

The EnKF (Ensemble Kalman Filter) and ETKF (Ensemble Transform Kalman Filter) methods were tested at the University of Oklahoma and at NCAR (National Centre for Atmospheric Research) (Synder and Zhang, 2003, Tong and Xue, 2004). In these tests simulated radar observations were used in storm cases and were focusing on the impact of flow dependent background errors mostly.

The temperature adjustment scheme based on the moist adiabatic temperature profile is used in the cloud analysis scheme. Half an hour intermittent assimilation cycles are performed within 3-h assimilation window from 0000 to 0300 UTC. The life cycle used for Incremental Analysis Update (IAU) is 30 min and forecast is issued at the end of 0300 UTC for 21 hours ahead. As may be noted from the figures 6b and 6c, the forecast for tropical cyclone OGNI improves over the control run, once radar data is assimilated into the model.

field Similarily, the WRF VAR assimilation procedure (Sun and Crook 1997), adopted in IMD to ingest radar data into WRF model is displayed in figure 7a. The multi-radar data ingest statistics are displayed in figure 7b and 7c.

5. Summary

• Improvement in Numerical Weather Prediction models in recent years is mainly due to the assimilation of increasing amount of remote sensing data as well as observations, which providebetter and homogenous data sources for accurate estimation of model analysis field.
• There are two types of satellite sensors based on their principle of works, viz., active and passive sensors. However, satellite instruments mainly measure the radiation emitted by objects on the surface or different layers of the atmosphere. The conversion of measured quantities into geophysical quantities is an inverse problem that data assimilation schemes try to solve in an optimal way by solving the radiative transfer equation.
• The purpose of the weighting function is to provide the information of the vertical absorption profile of a satellite channel into the radiative transfer equation.
• While older techniques of assimilation focus on model assimilation of retrieved geophysical information from the radiance data of satellites, more recent variational techniques such as 3D-Var or 4D-Var allow the direct assimilation of radiance observations and therefore avoid the need for an explicit retrieval step.
• Radar data assimilation is most useful for mesoscale short-range forecasting over tropical countries, which have less skill of forecast. Traditionally, single-Doppler observations (radial velocity and reflectivity) and derived quantities (e.g.VAD, precipitation) are assimilated into high-resolution numerical models.
• In variational assimilation, both VAD and radial wind observations are meant to produce analysis increments in the function of the background and observation errors.
• Assimilation of reflectivity or post-processed information from reflectivity is more complicated. The main approaches in use are Nudging, Variational analysis and Ensemble Kalman Filtering.