DAOS report for WGNE Tom Hamill (NOAA) for Carla Cardinali (ECMWF) and the

Transcription

1 DAOS report for WGNE 2016 Tom Hamill (NOAA) for Carla Cardinali (ECMWF) and the rest of the DAOS working group 1

2 WWRP/DAOS terms of reference The Data Assimilation and Observing Systems (DAOS) working group (WG) will provide guidance to the WWRP on international efforts to optimise the use of the current WMO Global Observing System (GOS). It will also provide guidance on which data assimilation methods may provide the highest quality analysis products possible from the GOS. Through these activities, the DAOS WG will facilitate the development of advanced numerical weather prediction (NWP) capabilities, especially to improve high impact weather forecasts. DAOS will be primarily concerned with data assimilation and observing system issues from the convective scale to planetary scales and for forecasts with time ranges of hours to weeks. To achieve its mission, the DAOS WG will: Provide community consensus guidance on data assimilation issues, including the development of advanced methods for data assimilation. Promote research activities that will lead to a better use of existing observations and that will objectively quantify the impact of current and future observation for NWP. Assist WWRP projects and other WMO working groups in achieving their scientific objectives by providing expert advice on the use of observations and data assimilation techniques (e.g. WGNE, IPET OSDE, MWFR). To organize and provide the scientific steering committee for the WMO Data Assimilation Symposium, which is to be held approximately every 4 years. 2

3 DAOS membership Tom Hamill (leaving 2016) and Carla Cardinali, cochairs. Seeking new co chair from existing members. Members: Mark Buehner (Env. Canada, assim methods) Saroja Polavarapu (Env. Canada, carbon DA) Daryl Kleist (U. MD, assim methods.) Chris Velden (U. Wisconsin, leaving 2016; satellite obs) Mikhail Tsyrulnikov (Roshydromet, leaving 2016; assim methods) Nadia Fourrie (Meteo France, satellite, mesoscale DA) Sharan Majumdar (U. Miami; OSSEs, observations) Stefan Klink (DWD; conventional observations) 3

4 Priorities in filling vacant DAOS positions Coupled DA expertise (esp. ocean/land/atm). Non Gaussian DA expertise (e.g., particle filters), with application to mesoscale DA. Replacing satellite observation expertise with departure of Roger Saunders (previous co chair) and Chris Velden. Aerosol DA. Crowd sourced observations. Geographic balance (esp. S. America, Japan). Gender balance. We welcome nominations for replacement members in concordance with these priorities. 4

5 2017 WMO international symposium on data assimilation Currently evaluating two strong bids from Brazil and Meteo France. We wish we could choose both. If WGNE has workshops/meetings planned, we can pass along information about each as a potential host. 5

6 DAOS statement / white paper on OSSEs OSSEs, despite challenges, useful for estimating future observing system impact and for other studies, i.e., changes in assimilation methodology on observation impact. International coordination on OSSEs desirable. Sharan Majumdar will be leading DAOS in the preparation of a short paper representing international consensus on recommendations for OSSE use and development. Prepared in ~ ½ year time frame. 6

7 Satellite status report (Beijing, Oct 2015) The constellation of operational geostationary and polar orbiting satellites remains stable, though a few polar orbiting satellites are no longer providing data (MADRAS, OSCAT, TRMM). Japan s Himawari 8 geostationary satellite is becoming operational, with 9 to be launched in The next generation of geostationary satellites in Europe (Meteosat) and United States (GOES R) are set to be launched during the remainder of the decade. Atmospheric Motion Vectors (AMVs) are now available from a large number of geostationary and polar orbiting satellites, and rapid scan mode will be activated aboard Himawari 8 focused on Japan and selected typhoons in CIMSS / University of Wisconsin will be providing reprocessed GOES AMVs back to 1995, for delivery in 2016 for use in global reanalyses. A variety of polar and other Low Earth Orbit satellites are planned for launch in the near future. NASA and JAXA have launched the Global Precipitation Mission (GPM) Core Observatory that is designed to work with, and anchor, the constellation of satellites and ground systems from the partner agencies of Japan, Europe, India, as well as U.S. agencies. It will seamlessly combine all the measurements into a single global precipitation data set every 3 hours. 7

8 Conventional systems report (Beijing, Oct 2015) Global aircraft observations increasing with approx. 750,000 obs generated per day in ASAP fleets providing raob data from traveling cargo ships. The European fleet comprises of 18 ships (thereof 15 merchant ships in regular line service) operating in the North Atlantic and the Japanese fleet comprises of 2 governmental research ships performing soundings mainly in the North Pacific. Ground based GNSS Zenith total delay (ZTD) data provide humidity information to NWP. Time resolution is high, spatial resolution varies with region. During the last year the density of sites has increased, particularly in parts of Europe. Growing wind profiler networks respond to the need for more wind observations as documented e.g. in the WMO Statements of Guidance concerning global NWP. In terms of number of observing sites the North American and European networks are stable whilst the Australian network is growing and the Asian network is even growing strongly. Number of operating barometer buoys has again increased over the last year with 850 in operation in Sep versus 700 in June 2014 and 400 in June A good coverage is achieved in the North Atlantic and Indian Ocean, lesser in tropical areas. The coverage in the Arctic has improved significantly. It is still insufficient in large areas of the Pacific Ocean The number of visual observations (waves, visibility, clouds, past and present weather) taken on Voluntary Observing Ships (VOS) has continued to decrease. S band reservation for weather radars is under threat at the World Radiocommunication Conference in November On global scale the illegal use of the C band for telecommunication is a major problem. Concerning this issue there s an accepted article in BAMS: The Threat to Weather Radars by Wireless Technology 8

9 Assimilation methodology advances (slides mostly c/o Mark Buehner, Env. Canada) 9

10 Perceived strengths and weaknesses in assimilation methodologies Characteristic Ensemble DA Variational DA Covariance estimation issues Flow dependence of forecast error covariances Model uncertainty treatment Full use of obs Scalability Large sampling error w/o large ensemble; addressed through ad hoc localization Good Adequacy depends upon fidelity of stochastic physics Poor; cost scales with number of obs, EnKF can actually do worse with too many obs. Good; ensemble forecasts parallelize, methods like LETKF readily parallelize. Sampling error irrelevant, but use of tangent linear and adjoint problematic if phenomena are inherently non linear OK (ECMWF uses ensemble of DA to estimate variances but not covariances) Challenging; weak constraint 4D Var has proven difficult to develop, and form of model error Q is an issue Good; costs increase only moderately with more observations. Challenging. we seek hybridization methods that leverage the advantages of each methodology 10

11 4D En Var 4D Var variational solution for mean state, but with evolution of forecast error covariances through assimilation window estimated with ensemble. Tradeoff: accepting more sampling error from using precalculated ensembles, with less linearization error (not using adjoint/tlm). Scalability improved via use of ensembles. Model uncertainty improved via use of ensembles. 4D En Var updates mean state alone; what to do about updating perturbations for ensemble initialization? 11

12 Results: 4D En Var for mean, EnKF for perturbations Control member forecasts (deterministic forecast from mean analysis) 24h global forecasts 72h global forecasts U RH U RH Z T Z T Verification against ERA interim Using EnVar with all GDPS obs to only update the ensemble mean gives significant improvements for control member vs. current EnKF 12

13 Options for updating ensemble of members EnKF for perturbations, as in previous slide. Typically use less than full set of observations. Must maintain separate EnKF analysis code as well as variational code. En 4D En Var (next slide): Run an ensemble of 4D En Vars, typically with perturbed observations, to provide an ensemble of analyses. Running multiple 4D Vars is expensive. Permits getting rid of EnKF code base. EVIL (Ensemble Variational with Integrated Lanczos; Tom Auligne, MWR in review). 4D En Var for mean Solve inverse of En Var cost function Hessian, explicitly solve for leading eigenvectors of analysis error covariance, re form ensemble from those. Follows old articles by Barkmeijer et al (1998, 1999 QJ) but now using flowdependent B. Mean Pert (following A. Lorenc, UK Met Office): 4D En Var for mean state. Simplifications for update of perturbations (fewer iterations, fewer observations, using static B), etc. 13

14 Ensemble of Variational Analyses (EDA) Some centers now using this approach (ECMWF, Meteo France) Use an ensemble of EnVar data assimilation cycles, each assimilating independently perturbed observation values: similar to EnKF, but very costly! Forecast Ensemble of Forecasts Analysis, x a Background, b x b x Analyses a( i) x, i 1: N ens Backgrounds b( i) x, i 1: N ens EnVar Analysis Ensemble B from EnKF Random System-error Perturbations + Ensemble of EnVar Analyses Ensemble B from EnKF or ens-envar Observations, o y R Deterministic EnVar Perturbed observations o( i) y, i 1: N ens Obs, o y Ensemble of EnVars R 14

15 EVIL for updating perturbations Tests with EVIL not promising: After initial tests with Lanczos minimizer, used a stand alone iterative Eigen solver (ARPACK) to avoid limitations of obtaining eigenvectors from variational minimization For full global system, requires prohibitively large number of Eigenvectors for reasonable update to ensemble perturbations (1600 still not enough! Equivalent to 3200 variational iterations) To be able to compute 1600 vectors requires significant simplifications to cost function (only climatological B) Calculation of eigenvectors is inherently sequential, therefore difficult to parallelize over large number of processors. In principle might be able to solve inverse Hessian locally to parallelize, speed computations. But how to stitch together locally calculated perturbations an unsolved problem. 15

16 Analysis increment for 300 hpa temperature for one ensemble member Ensemble of full EnVars, 70 iterations Direct update with 400 Hessian eigenvectors Stochastic EVIL Perturbation minimization, 20 iterations Direct update with 1600 Hessian eigenvectors For similar computational cost, minimization much more effective than EVIL 16

17 Separate minimization for each perturbation 4D En Var for mean, simplified var for perturbations Initial test uses the following (extreme) simplifications: Keep same number of iterations as deterministic system (70) Only climatological B matrix with reduced resolution (3D Var) Reduced quantity of observations: no AIRS, IASI, CRIS, SSMIS, GeoRad (not used in current EnKF) The simplified B matrix and reduced volume of observations reduce the memory requirements while also decreasing the execution time Reduction in size of problem allows many jobs to be run in parallel: 1 Perturbation update has 2.5% the cost of full 4DEnVar! 256 members takes ~24 min wall clock on 2048 processors Trivial to parallelize further (up to 256 jobs, each taking < 1min) Experiments cover 3 January 15 January 2015 (26 forecasts) 17

18 Results: 3D Var vs. current EnKF for perturbations Background ensemble Analysis ensemble (after adding system error perturbations) Perturbation increments computed with: Current EnKF 3DVar , 7 days after spin up Ensemble spread for Psfc (hpa) both experiments use EnVar for mean 18

19 Results: 3D Var vs. current EnKF for perturbations Control member forecasts (deterministic forecast from mean analysis) 24h global forecasts 72h global forecasts U RH U RH Z T Z T Verification against ERA interim Using 3DVar with reduced set of obs for perturbations is nearly equivalent to using Current EnKF for perturbations (both use EnVar for ens. mean) 19

20 Further tests: impact of VarEnKF* vs. current EnKF Ensemble mean: EnVar with full set of GDPS obs* vs. Current EnKF Ensemble perturbations: 3DVar vs. Current EnKF Experiments cover 3 January 15 January 2015 (26 forecasts) * Also includes non zero inter channel obs error correlations and hybrid background error covariances (10% B nmc + 90% B ens ) 20

21 Results: VarEnKF vs. current EnKF Control member forecasts (deterministic forecast from mean analysis) 24h global forecasts 72h global forecasts U RH U RH Z T Z T Verification against ERA interim Using full 4D En Var for mean and 3D Var for perturbations (VarEnKF) gives significant improvement vs. using current EnKF 21

22 Results: CRPS for VarEnKF vs. current EnKF Continuous ranked probability score measures accuracy of ensemble pdf relative to observations U 250hPa (m/s) T 250hPa (K) U 500hPa (m/s) T 500hPa (K) VarEnKF gives similar or improved CRPS vs. Current EnKF 22

23 Other interesting methodology results and discussions in DAOS Buehner: results of scale dependent localization (see supplementary slides here). Tsyrulnikov: stochastic B. current approaches assume background error covariances are known, but one can formulate the problem treating B as a random variable that is updated alongside the mean state. 23

24 DAOS sponsored workshops and symposia W2016/ abstract submission now open 24

25 Conclusions DAOS seeking nominations for new members. DAOS continues to try to promote international collaboration in rational evolution of OS, act as conduit of information for developments in DA methodologies. Working to be more supportive of other parts of WMO, including PPP, S2S, HiWeather. Maintain and strengthen ties to WGNE, WCRP, others. 25

26 Scale dependent ensemble covariance localization DAOS working group meeting April 2016 Mark Buehner Data Assimilation and Satellite Meteorology Research Section With contributions from Anna Shlyaeva and Jean-François Caron

27 Scale dependent covariance localization Motivation Currently, EnVar uses single horizontal and vertical localization length scales, very similar to our EnKF Comparing various studies, seems it is best to use different amount of localization depending on application: convective scale assimilation: ~10km mesoscale assimilation: ~100km global scale assimilation: ~1000km 3000km In the future, global systems will resolve convective scales Therefore, need a general approach for applying appropriate localization to wide range of scales in a single analysis procedure: Scale dependent localization Possible in EnVar, since localization acts directly on model space covariances (not BH T and HBH T or R)

28 Scale dependent covariance localization General Approach Ensemble perturbations decomposed with respect to a series of overlapping spectral wavebands (filter coefficients sum to 1 for each wavenumber) Apply scale dependent spatial localization to the scaledecomposed ensemble covariances, both within scale and between scale covariances Keeping the between scale covariances is necessary to maintain heterogeneity of ensemble covariances (Buehner and Charron, 2007; Buehner, 2012) Motivation different than spectral localization where the between scale covariances are set to zero

29 Scale dependent covariance localization 1D Idealized System Idealized system on 1D periodic domain Assume a simple true heterogeneous covariance function that is a spatially varying weighted average of 2 Gaussian functions with different length scales: total = small scale + large scale Length scales of Gaussian functions: large scale: 7 grid points small scale: 0.7 grid points Middle of domain dominated by small scale errors, both ends dominated by large scales

30 Scale dependent covariance localization 1D Idealized System Ensemble perturbations decomposed with respect to 3 overlapping spectral wavebands:

31 Scale dependent covariance localization 1D Idealized System Scale dependent homogeneous spatial localization functions (Gaussian) are specified with length scales: 10, 3, and 1.5 grid points Localization of between scale covariances constructed to ensure full matrix is positive semidefinite: L i,j = (L i,i ) 1/2 (L j,j ) T/2 btwn scales i& j Within scale Between scale

32 Scale dependent covariance localization 1D Idealized System Mostly large scale at both ends of the domain (top panel) and mostly small scale at the middle (bottom panel) Generate a random sample of 50 ensemble members and compute raw sample ensemble covariance

33 Scale dependent covariance localization 1D Idealized System From 5000 random realizations, compute mean and stddev of the error of 50 member ensemble covariances with several types of localization: raw ens B localization 10 localization 1.5 scale dependent loc. Stddev Error Mean Error

34 Scale dependent covariance localization 1D Idealized system: Conclusions Variation in the amount of localization as a function of scale: reduces the between scale covariances spectral localization not possible to keep all heterogeneity and severely increase localization of small scales (trade off) Using scale dependent spatial localization results in: similar mean error of covariance vs. only large scale localization (both are much better than only small scale localization) better stddev error of covariance vs. only large scale localization, especially in areas where true covariances dominated by small scales

35 Scale dependent covariance localization Implementation in EnVar Current (standard) Approach Analysis increment computed from control vector (B 1/2 preconditioning: Δx=B 1/2 v) using: x x e k k j e L 1/ 2 k v k where e k is normalized member k perturbation Scale dependent Approach (Buehner and Shlyaeva, 2015, Tellus) Varying amounts of smoothing applied to same set of amplitudes for a given member k, j L 1/ 2 j where e k,j is scale j of normalized member k perturbation v k k: member index k: member index j: scale index

36 Scale dependent covariance localization 2D Sea Ice Ensemble Ensemble of sea ice concentration background fields (60 members, timelagged ensemble) from the Canadian Regional Ice Prediction System ensemble of 3DVar analyses experiment Ensemble mean ice concentration Ensemble spread Work of Anna Shlyaeva

37 Scale separation of ensemble perturbations with diffusion operator Apply diffusion with increasing length scales to the original ensemble perturbations Decompose into different scales by taking differences between perturbations before and after each level of diffusion Example: e original ensemble perturbation; D n diffusion with lengthscale n e 1 = D 10km (e) e 2 = D 30km (e 1 )e 3 = D 100km (e 2 ) Scale 4 (smallest): e e 1 Scale 3: e 1 e 2 Scale 2: e 2 e 3 Scale 1 (largest): e 3 Scale decomposed perturbations sum up to the original e Work of Anna Shlyaeva

38 Scale separation with diffusion operator: Example of one ensemble perturbation Scale 4 (smallest) Scale 3 Original perturbation Scale 2 Scale 1 (largest) Work of Anna Shlyaeva

39 Scale separation with diffusion operator: Ensemble spread for each scale Scale 4 (smallest) Scale 3 Full ensemble spread Scale 2 Scale 1 (largest) Work of Anna Shlyaeva

40 Homogeneous correlation functions and chosen localization functions for each scales Localization length scales: 500km, 150km, 50km, 30km (Gaussian like functions) Work of Anna Shlyaeva

41 Assimilation of 2 observations One obs in area dominated by large scale error, other in area of small scale error Background field and obs 30km localization 500km localization No localization 150km localization Scale dep. localization

42 Idealized data assimilation experiment setup True state: x t = x i (ith member) mean(x) = x t e i, e i ~ N(0,B) Background: x b = x t + e j e j = x j mean(x), e j ~ N(0,B) Observations: observe every 4th grid point, with random gaps e j (real background error) not used in ensemble B for assimilation Error Error (Ice Pack) Error (MIZ) Background Analysis 500km loc Analysis 30km loc Analysis S D loc Largest scale Smallest scale Largest scale Smallest scale Largest scale Smallest scale Work of Anna Shlyaeva

43 Scale dependent covariance localization 2D Sea Ice Ensemble: Conclusions Scale separation can be performed using a diffusion operator (convenient for systems that use diffusion operator or recursive filter for modelling B) Strong spatial variation in partition of error wrt scale leads to strong spatial variation in overall strength of localization (similarity with adaptive localization) Scale dependent localization results in lowest analysis error for all scales in regions dominated by either small scale or large scale error in idealized DA experiments

44 First application to realistic NWP Horizontal Scale Decomposition Spectral filter response functions for decomposition with respect to 3 horizontal scale ranges km 2000 km 500 km Large scale Medium scale Small scale Work of Jean Francois Caron

45 Global NWP application: Horizontal Scale Decomposition Perturbations for ensemble member #001 Temperatureat ~700hPa Full Large scale Small scale Medium scale +2 0 Work of Jean Francois Caron 2

46 Scale dependent covariance localization Impact in single observation DA experiments B ens Std hloc B ens No hloc 700 hpa T observation at the center of Hurricane Gonzalo (October 2014) hloc: 2800km B ens SD hloc B nmc Normalized temperature increments (correlation like) at 700 hpa resulting from various B matrices hloc: 1500km / 4000km / 10000km Work of Jean Francois Caron

47 Scale dependent covariance localization Impact in single observation DA experiments B ens Std hloc B ens No hloc 700 hpa T observation at the center of a High Pressure hloc: 2800km B ens SD hloc B nmc Normalized temperature increments (correlation like) at 700 hpa resulting from various B matrices hloc: 1500km / 4000km / 10000km Work of Jean Francois Caron

48 Scale dependent covariance localization Forecast impact 1.5 month trialling (June July 2014) in our global NWP system. 3DEnVar with 100% B ens used in both experiments 1) Control experiment with hloc = 2800 km, vloc = 2 units of ln(p) 2) Scale Dependent experiment with a 3 horizontal scale decomposition I. Small scale uses hloc = 1500 km II. Medium scale uses hloc = 2400 km III. Large scale with uses = 3300 km Ad hoc values, smaller that those used for 1 obs Same vloc [2 units of ln(p)] for every horizontal scale Work of Jean Francois Caron

49 Scale dependent covariance localization Forecast impact Comparison against ERA Interim Control Scale Dependent U RH T+24h World Z T Work of Jean Francois Caron

50 Scale dependent covariance localization Forecast impact Comparison against ERA Interim Std Dev difference for U Control is better Scale Dependent is better T+24h Zonal mean South Pole North Pole Work of Jean Francois Caron

51 Summary and Future Work Preliminary results using a horizontal scale dependent horizontal localization indicates small forecast improvements in our global NWP system (using 3DEnVar and 100% ensemble B). Expect larger improvements in a system with larger range of scales assimilating dense high resolution observations and/or with fewer ensemble members Up next Optimize the horizontal localization length scales used for each horizontal scale band. An objective approach is needed. Tried several, so far without success! Examine the impact of horizontal scale dependent vertical localization Examine the impact of vertical scale dependent vertical localization. Work of Jean Francois Caron

52 Scale dependent covariance localization General Conclusions Scale dependent localization is feasible, but more expensive than singlescale localization (like having a larger ensemble) To reduce computational cost, take advantage of lower resolution for large scales by degrading grid resolution (like with wavelets) Approach may provide net benefit by appropriately resolving background error over a wide range of scales with relatively small ensemble when assimilating all obs simultaneously Alternatives for future large domain, high resolution DA: Use broad localization (to avoid messing up large scales) with huge ensembles (to reduce sampling error for small scales) Other approaches seem more ad hoc: e.g. varying localization for different subsets of members, varying localization for different subsets of observations