Model Error and Parameter Estimation in a Simplied Mesoscale Prediction Framework, Part I:

Transcription

1 Model Error and Parameter Estimation in a Simplied Mesoscale Prediction Framework, Part I: Model Description and Sources of Uncertainty Guillaume Vernieres, Josh Hacker, Montse Fuentes

2 Topics Mesoscale forecasting - some background. Data assimilation at mesoscales. Types of error in mesoscale models. A column model to emulate a full 3D mesoscale model, and experience with it. Some naive parameter estimation experiments.

3 Mesoscales Horizontal wind spectra in the frequency domain. Vinnichenko 197 Vander Hoven 1957

4 Mesoscale Prediction Times Mesoscale prediction is fundamentally an initial condition problem. Prediction time (hours) Forecast Nowcast Nowcasting is typically done by extrapolating current conditions because dynamical models have less skill at these time scales. A place for better data assimilation and accounting for model error?

5 that significant wind speed errors exist in the initial conditions of both models, as a result of interpolation from the ETA analyses. These errors appear to spin down quickly in the first few hours of the forecasts, in both models. Finally, the two models perform pretty evenly in the surface moisture forecasts (not shown). Forecast Error at the Surface T_BIAS (C) SPD_BIAS (m/s) WRF MM5 GMT hours Fig. IMAGE 3. Domain TOY Workshop, average of BIAS May 27 errors of surface temperature (a) and wind speed (b) of -12 (solid a b time surface wind, with a maximum bias of ~1.5 m/s occurred at noon time. In contrast, the biases are much smaller in MM5, thanks again to the improved MRF PBL scheme in the MM5 model. It is interesting to see that the short-range (12 24 h) forecasts have somewhat smaller bias than the shorter (-12h) nowcasts for both temperature and wind speed. This may be related to the model dynamic and diabatic spin-up from the cold-start initialization. Nevertheless, short-range forecasts generally show larger RMSE errors than the nowcasts (not shown). Finally, during the night-time, the surface forecast errors of the two models are rather similar and both present a little bit of warm bias and an overestimate of wind speeds. Upper-air verification statistics for the same period are calculated, and the RMSE errors of temperature, Errors humidity near the and wind surface from the MM5 and WRF forecasts are compared Fig. 4. First, some discrepancies are oftencan dominated be seen between by the initial conditions bias, and (-h forecasts) showof athe diurnal two models, although both are interpolated from the same ETA analyses. These evolution. differences exist in most layers, and the magnitudes are comparable to the differences between the 12-h forecasts of the two models. Unlike those in the surface forecasts, the forecast errors in the upperair grow with time in the two models are very similar, in terms of both the error sizes and the height distribution. Both models have the largest error growth of moisture and temperature in the lower troposphere and a relatively uniform wind error growth at different heights. However, the two models do differ in many details. The MM5 forecasts in the lower troposphere are more accurate than WRF, especially for the temperature and moisture fields, whereas WRF shows

6 Lack of Variability the Surface and found that forecasts (not s dicating that the NSSL ensemble Figure 2 also mass variables levels. NSSL an gesting that the balanced as in t levels (MSLP spread and som ative growth, i. upper levels (H h, NSSL show NCP1, NCP2, spread at the growth of the of the NSSL en to the fact that domain are the cause of the us lower levels ma the precipitatio ics. The most not that the full ens of the individua Ensembles are extremely underdispersive and show little intrinsic error growth near the surface in the short range, leading to experimentation with \multi-model" ensembles (FULL). From Hou et al. 21 MWR.

7 Information in Surface Observations Surface observations are relatively dense and inexpensive to gather. Typically under-utilized in operational data assimilation. Model error? Constraints in the assimilation systems? Potential to to tell us something about the state of the overlying PBL. Potential to to tell us something about the model, including values of parameters.

8 Column Model Environment A 1-D PBL modeling framework: various land-surface and PBL parameterizations, forced. Original model development by Mariusz Pagowski, NOAA/ESRL. Internal dynamics for ageostrophic wind, diusion equation, etc. Geostrophic and radiative forcing from a mesoscale model (e.g. RUC or WRF) or observations. Cheap! Thousands of realizations possible with a quick turn-around

9 = f c (V V g ) = f c (U U g ) v Prognostic in U, V,, and Q with parameterization providing closure. Parameterization is the same as in the Weather Research and Forecast (WRF) model.

10 = f c (V V g ) U (U; V; ; Q; P) = f c (U U g ) V (U; V; ; Q; P) = T (U; V; ; Q; P) = Q (U; V; ; Q; P) Closure terms are functions of the resolved state (forcing and diusion), and myriad parameters P.

11 Model Formulation = f c (V V g ) + V ru = f c (U U g ) + V rv = w = V v Advection acts to relax the column state toward an imposed 3D state.

12 Skill in PBL State Estimates: T Height AGL (m) 25 (a) MAE ( C) 25 (c) 2 Height AGL (m) 25 (b) MAE ( C) 25 (d) 2 Using only screen-height (surface) observations, skillful proles are estimated at all times of day: (a) 1PM LT, (b) 7PM LT, (c) 1AM LT, and (d) 7AM LT. Height AGL (m) 15 1 Height AGL (m) MAE ( C) MAE ( C) Figure 2: MAE profiles of for the assimilation experiments (solid) and climatological simulations (dashed), presented in order of increasing time from initialization (7 LT). Verification times are (a) 13 LT, (b) 19 LT, (c) 1 LT, and (d) 7 LT.

13 Skill in PBL State Estimates: U Height AGL (m) Height AGL (m) 25 (a) MAE (m/s) 25 (c) Height AGL (m) Height AGL (m) 25 (b) MAE (m/s) 25 (d) Using only screen-height (surface) observations, skillful proles are estimated at all times of day: (a) 1PM LT, (b) 7PM LT, (c) 1AM LT, and (d) 7AM LT MAE (m/s) MAE (m/s) Figure 4: Same as Fig. 2 but for the -wind component.

14 Skill in PBL State Estimates: Q v Height AGL (m) Height AGL (m) 25 (a) MAE (g/kg) 25 (c) Height AGL (m) Height AGL (m) 25 (b) MAE (g/kg) 25 (d) Using only screen-height (surface) observations, skillful proles are estimated at all times of day: (a) 1PM LT, (b) 7PM LT, (c) 1AM LT, and (d) 7AM LT MAE (g/kg) MAE (g/kg) Figure 3: Same as Fig. 2 but for.

15 State Augmentation Data assimilation to estimate a discrete system state Z at time t. Z is a joint state, with both state variables and parameters. X represents state variables. x is a set of parameters, which may or may not be physical. Then Z = (X; x). Given all observations up to the current time, Y t, we want to estimate p(z t jy t ). These experiments are to estimate parameters in a land-surface scheme, given screen-height observations and an evolving model.

16 A Parameter to Modify Soil Moisture An exchange coecient for moisture, Q c, is computed: Q c = M 1w q q q 1 M is a moisture availability parameter f,1g. 1 is density at the rst atmospheric model level. q and q 1 are moisture contents at the surface and the rst atmospheric level, repsectively. w q is the parameterized kinematic moisture ux. Provides a lower boundary condition (forcing) for the atmospheric model.

17 Estimate a Single Parameter Spread and error Individual estimates Correlations Forecast Hour Forecast Hour Forecast Hour Single parameters (moisture availability) can be estimated when the true value is known.

18 Correlations Without Assimilation r( M,T 2 ) r( THC,T 2 ) /3 5/4 5/5 5/6 5/7 5/8 5/9 5/1 5/11 5/12 5/13 5/14 Analysis Day.5.5 Correlation coecients of T 2 with parameters M and T HC, for 1 ensemble members integrated for 1 days. Parameter distributions are xed. Distributions chosen as with = :1M and :1T HC. 5/3 5/4 5/5 5/6 5/7 5/8 5/9 5/1 5/11 5/12 5/13 5/14 Analysis Day

19 Correlations With Assimilation r( M,T 2 ) r( THC,T 2 ) Estimated Not Estimated 5/3 5/4 5/5 5/6 5/7 5/8 5/9 5/1 5/11 5/12 5/13 5/14 Analysis Day.5.5 Estimated Not Estimated 5/3 5/4 5/5 5/6 5/7 5/8 5/9 5/1 5/11 5/12 5/13 5/14 Analysis Day Correlation coecients of T 2 with parameters M and T HC, for 1 ensemble members integrated for 1 days. Parameter distributions are estimated while assimilating. Correlations change, transitions more pronounced.

20 Dependent Parameters M THC M and T HC are linearly dependent when estimated. Here is at UTC for over 1 days, but this is true at any time. Cannot be distinguished, thus could be replaced by a single parameter.

21 Distribution Improves Assimilation MAE T 2 (K) Fixed, avg =.7346 Distributed, avg = Compared to single xed parameter values, distributed parameters result in a better t to observations. The eect is particularly true during transitions..5 5/4 5/5 5/6 5/7 Analysis Time (UTC)

22 Estimation Improves Assimilation MAE T 2 (K) Estimated, avg = Not Estimated, avg = Compared to xed distributed parameter values, estimated parameters result in a better t to observations /4 5/5 5/6 5/7 Analysis Time (UTC)

23 Error in the Prole Dierences in error (estimated { xed distribution) show the prole is generally improved, especially during the growth phase of the PBL.

24 Summary and Open Questions: Parameter Estimation State augmentation is a useful parameter estimation approach in observation system simulation experiments (OSSEs), but is much more dicult in real-data applications. Much more work to do: How will a free bias parameter behave? Can we nd distributions that make a better forecast in the face of other, unknown, model errors? Can we nd appropriate stochastic processes to propagate the parameter distributions in time?