An important source of error in weather forecasting is the uncertainty of the initial conditions used in creating the forecast. One of the contributing factors in these types of errors is the inhomogeneity in the spatial and time coverage of the operational observation network. An example is the lack of reliable observations over large areas over the oceans and the poles. The advent of satellite technology has greatly increased the observational network but the use of satellites may be limited by availability, position and atmospheric conditions. Aircraft equipped with dropwindsondes or remote controlled craft could also be deployed to increase the number of observations in these under-observed areas. Additional accurate measurements of the initial conditions would reduce the analysis error in forecast models thus reducing the forecast error that is produced by uncertainty in the initial analysis and therefore improve the forecast. Due to time constraints and the expense of making additional observations to supplement the current observational network ,it would be beneficial to first identify those regions where additional observations would most reduce the forecast error and use mobile observation platforms such as aircraft or satellite to obtain the supplemental observations. In this way the observational network could adapt to the changing dynamic conditions that effect the forecast. The effectiveness of this adaptive observational network would depend on the ability to estimate the reduction in forecast error due to different possible deployments of observations. The methods used to make these estimates must not only be effective but also need to be computed rapidly enough so that there is time to make the necessary preparations for deployment. Such adaptive observations would be most useful for improving the forecasts for high impact weather events such as heavy snow, high winds or flooding. The region that is expected to be impacted by these weather events that we want to improve the forecast of is referred to as the “verification region” .The use of strategically deployed observations is known as “targeting” and the region that is chosen for supplemental observations is referred to as the “target region” . The strategically deployed supplemental observations are called the “targeted observations”. One targeting method that has been used with success is the ETKF or ensemble transform Kahlman filter.

The idea that ensemble perturbations can be used to to estimate the prediction and analysis error covariance matrices was first discussed in Bishop and Toth, 1999. The ensemble transform technique uses ensemble forecasts to construct approximations to the prediction error covariance matrix. Different, distinct approximations can be made for each possible deployment of additional observations. Thus the optimal deployment would be the one that minimizes the the expected forecast error. For an ideal ensemble forecast (one where the ensemble mean is indistinguishable from the actual state of the atmosphere with a number of ensemble perturbations that approaches infinity) the ensemble's perturbation covariance matrix would be equivalent to the prediction error covariance matrix and the future analysis error covariance matrix could be obtained by evaluating the ensemble's perturbations at their initialization time. This connection between the ensemble perturbation covariance matrix and the prediction and analysis covariance matrices indicates how observations should effect the ensemble spread. The spread should be less in a region that contains supplemental observations than for the same region with an ensemble that does not include the supplemental observations. The difference between the spreads would propagate downstream and if this effect extended to the verification region at the verification time it would be expected that the additional observations reduced the expected prediction error. Bishop and Toth summarized the ensemble transform technique using the following five steps.

1) creation of an ensemble forecast initialized at the analysis time and calculation of the perturbations of the ensemble members about the mean forecast.

2. estimation at the future analysis time of the analysis error covariance matrices corresponding to each of the distinct possible deployments of observations.

3. calculation of the corresponding transformation matrices that map the analysis error covariance matrix into the prediction error covariance matrix.

4. evaluation of the measure of prediction error for each possible deployment of observations.

5. implementation of the the deployment of observational resources which minimizes the measure of prediction error.

The ability of the ensemble transformation technique to identify upstream regions that are dynamically connected to the verification region was confirmed during the FASTEX and NORPEX experiments. The effectiveness of the technique was found to improve significantly as the number of ensemble perturbations was increased.

The Fronts and Atlantic Storm-Track Experiment, FASTEX was conducted in January and February of 1977 to study the development of frontal cyclones off the coast of Ireland and to provide upstream observations in order to improve forecasts. Szunyogh et al,1999 focused on the February FASTEX cases which used the ET technique as the main tool for locating observation sites. Because the ET technique estimates the analysis-error variance by the ensemble-forecast spread, it is necessary to show that this relationship holds in order to verify that the ET technique is a valid approach for choosing observations sites. They authors found a good correlation between the ensemble spread and the short-range forecast error during FASTEX suggesting that the technique is valid. Another necessary condition is that the signal or difference between the forecast/analysis with and without additional observations propagates into the verification region at the specified verification time. For the FASTEX cases investigated ,a substantial portion of the dominant signal did propagate into the verification region. Furthermore the amplification rate of the signals was significantly greater than the rate for mock signals from adjacent areas demonstrating that the ET method is capable of identifying areas of amplifying analysis errors. Generally the supplemental observations had a positive effect on the forecast but there were instances in which the additional observations actually degraded the forecast. The forecast improvement from the targeted observations was found to be correlated with the error in the control forecast. In other words it is more difficult to improve a very good forecast than a bad one. The improved forecasts were also correlated with signals that amplified in the verification region suggesting that targeted observations should only be taken when the signal is expected to amplify. The maximum forecast error reduction was on the order of 10%. It is possible that forecast-error reduction from targeted observations may have had less of an impact in FASTEX because the downstream region is so well observed. Problems with the ET technique include spurious correlation due to the small number of ensembles and errors due to model deficiencies. The results of FASTEX demonstrated that the ET technique is a useful tool in identifying regions for targeted observations.

The results of the FASTEX study were confirmed in the NORPEX field program. The North Pacific Experiment, NORPEX was an operational test of targeted observing techniques conducted in January and February of 1998. The primary goal of this experiment was to improve short range forecasting of high impact weather events through the judicial use of targeted observations. The objective targeting in NORPEX builds on the experience gained in FASTEX. The supplementary observations were obtained by dropsonde equipped reconnaissance aircraft stationed in Alaska and Hawaii, and advanced and experimental satellite data from GOES-8 and GMS-5. Unlike FASTEX the NORPEX aircraft missions were almost totally tasked according to objective targeting guidance. The objective targeting methods applied in NORPEX were the Ensemble Transformation method(ET) and the method of Singular Vectors (a comparison of the two methods is found in Majumdar, 2002). The methods often identified similar regions as optimal for targeting. The dropsonde observations were targeted to improve the forecasts for major wind or precipitation events . Forecast uncertainty was also a consideration when choosing a target region. A MRF model which excluded the dropsonde data was run in parallel to allow evaluation of the impact of the targeted data. For the 27 targeting cases the forecasts were improved by about 10% on average. The forecasts were generally more greatly improved when the control forecast (forecast with no supplemental observations)error was greater. The satellite wind data had a greater positive influence on the forecasts than the dropsonde data, most likely due to the greater frequency of these observations. Two factors that may later prove to be of significance during the NORPEX experiment were 1) there was a particularly high level of forecast skill during the time period of this experiment, probably due to a strong El Nino signal. 2) The flow regime was predominantly zonal with a strong upper level jet during the experiment period.

Bishop, Etherton and Majumdar, 2000 introduce a the ensemble transform Kahlman filter in order to estimate the effect of observations on forecast error. The main advantages of the ETKF compared to the ET technique is that it is much faster and more importantly it explicitly estimates the the effect of observations on forecast error variance. The Kahlman filter is the procedure used to obtain the covariance matrix of the error in the initial state variables at some time after all observations have been incorporated. In this manner the Kahlman filter could predict the reduction in forecast error that would be imparted by each distinct combination of possible deployments of observations. The ETKF also includes the observation error in order to more accurately predict the actual forecast improvement due to adaptive observations. This paper outlines the methods used to determine the error covariance matrices and propagate them forward in time in order to predict the reduction in forecast error that would be expected for each of the feasible additional deployments of observations. The ETKF is able to specify the effect of observations in a theoretically more consistent way than the ET technique. The ETKF is also capable of using the error covariance information to assess the impact of a second set of observations. Serial assimilation theory to determine the optimal deployment of observations given that the best site for a single observation was also observed is described in the appendix to this paper.

The ETKF has been used in the Winter Storm Reconnaissance Program in 1999 along with the Ensemble Transform technique and exclusively since 2000. Majumdar etal, 2002(part 2) describes the practical application of the ETKF as implemented in the WSR. This paper uses the term “signal realization” to refer to the difference between an initial state estimate that uses supplemental observations and one that does not. The time evolution of this signal indicates the success of the targeted observations. The signal variations can be described by a signal covariance matrix where the diagonal terms give the variance that would be obtained by assimilating a specific set of targeted observations with the ETKF. If the background and observational errors are accurately specified and the errors evolve linearly then the signal variance is equal to the reduction in error variance due to the targeted observations. Certain adjustments to the theory presented in Bishop, Etherton and Majumdar, 2001 (Part 1) that were required for implementation of the ETKF are also described in Part 2. The logistics of flight planning and the availability of ensembles make it necessary to use ensembles that are valid at least 36 hours after the initialization time for the operational ETKF. Also since many aspects of the observation error cannot be known in advance, the routine observations during the intervening time period are ignored when estimating the analysis error covariance matrix. Part 2 also evaluates the performance of the ETKF in the 2001 WSR program. The authors were able to deduce a linear, increasing relationship is between ETKF and NCEP signal variance for both the target and verification times. A monotonic, increasing relationship was also found to exist between the variance of operational NCEP signal realizations and the reduction in forecast error resulting from the targeted observations

Majumdar elat 2001 uses data from the 2000 WSR to determine whether a linear, increasing relationship exists between the ETKF signal variance and the variance of the operational NCEP signal and also whether a similar relationship exists between the signal variance of NCEP forecasts and the reduction in NCEP forecast error variance. The NCEP signal variance can be estimated from the ETKF using a scaling factor if the first relationship holds and then using both relationships the ETKF could be used to estimate the reduction in forecast error due to targeted observations. The first result showed that rescaling by a factor of 1/8 enables the ETKF to approximately predict the NCEP signal variance at the analysis time. This factor indicates that the ETKF overestimates the NCEP signal variance by nearly one order of magnitude suggesting that the estimate of the routine analysis error covariance matrix leads to large local error estimates. Similar results occur when comparing the variances at the verification time however in this case the scaling factor is 1/14. The increased scaling factor indicates that the ETKF predicted signal variance has a growth rate larger than the that of the operational NCEP signal. This results suggests that the correspondence between the two signals may be less clear at the verification time than at the analysis time. A non-linear, monotonically increasing relationship was found between th NCEP forecast signal variance and the reduction in the NCEP forecast error variance. These results give us increased confidence that the ETKF can be used to predict the benefit of various deployments of observations. The relationship between the ETKF signal variance and the operational NCEP signal can also be used to improve data quality control schemes.

Szunyogh etal 2000 evaluates the effects of targeted dropsonde data on the operational NCEP MRF analysis-forecast system during the 1999 Winter Storm Reconnaissance program. This was the first time that all the components of the targeting procedure were used in a quasi-operational manner. This field experiment used the strategic deployment of dropsonde missions in the Pacific storm track region to improve initial conditions for short and medium range numerical weather forecasts for specific weather events over the United States. The second half of this program used the ETKF method to compute the optimal flight track from a set of 22 possible pre-designed tracks. This was also the first quasi-operational use of the ETKF. Another difference between WSR and previous field experiments using targeted observations involves changes to the MRF which include the time interpolation of the background forecast as well as changes in the background error. The forecasts using targeted data were improved by these changes, in particular, the phenomenon of an initial adjustment process observed in previous field programs did not occur in WSR. The authors attribute this to the changes in the MRF. The effects of the dropsonde data were evaluated by setting up a parallel control forecast/analysis cycle that excluded the dropsonde data but which was identical in all other respects. This is the same procedure used in the earlier NORPEX and CALJET field experiments. The areas of high baroclinic instability over the North Pacific were found to be associated with large analysis errors and as a result large first guess errors. The dropsonde data was found to have a positive effect on the analyses since they improved the first guess forecasts at later analysis times. In 12 out of 14 cases the operational(dropsonde inclusive) forecast was superior to the control forecast due to the influence of past dropsonde data. There was also a strong correlation between the the analysis and the 6-hr forecast errors indicating that a primary source of analysis errors in the Pacific storm track region are due to errors in the basic background forecasts. The The dropsonde data improved/degraded the surface pressure forecast in 9/3 cases and the wind forecast in 8/4 cases out of 14 cases where the verification region was on the west coast. For the 9 cases where the verification region was on the east coast the surface pressure forecast improved/degraded in 5/2 cases and the wind forecasts improved/degraded in 6/3 cases. The targeted dropsonde data was deemed to have a positive influence on the individual forecasts when either both wind and pressure forecasts were improved or if the forecast was improved for one variable but unchanged for the other variable. Out of the total 25 cases there was an improved forecast in 18 cases. The forecast was degraded for 5 of the cases and neither improved nor degrades the forecast in 2 cases. On average the forecast error were reduced by 10 to 20% along the storm track. The forecast improvements were found to have a strong correlation with zonal flow regimes. So far it is not clear that any further research has confirmed this relationship. This paper also examines the propagation of the signal from the dropsonde data. Where the signal is defined as the difference between the analysis/forecast with the dropsonde data and one that does not include this data. The signal was observed to propagate at an average speed of 30º per day in an eastward direction along the storm track. The speed and general behavior of the signal was found to be in good agreement with the storm track model based on the concept of downstream development described in Chang and Orlanski 1993. The signal was weaker in areas of weak low-level baroclinicity but rapidly deepened in areas of stronger baroclinicity and more intense baroclinic energy conversion. The maximum signal propagated into the verification region at the verification time in all 14 of the West coast cases. For the west coast cases the average verification region was at 124.1W and 43.2N with a 36 hour lead time but for the east coast cases there was a larger diversity in verification times and regions