On the Predictability of Coastal Winds Using an Adjoint Modeling System James D. Doyle and Clark Amerault, Naval Research Laboratory, Monterey, CA High-resolution models have been routinely applied to coastal regions. Surface forecasts are often used to force ocean models Predictability of coastal flows has yet to be addressed. What controls the predictability of winds in the coastal boundary layer?

COAMPS (0-12h) & Monterey Bay Buoy Motivation COAMPS Winds at 90 m (2005) Jiang et al. 2008 Wind maxima along near coastal promontories due to hydraulic-like boundary layer transitions Winant et al. 1988 Hydraulic Jump Expansion Fan Mountains 22 m s-1 18 m s-1 10 m s-1 Thicker Thin ● COAMPS (0-12h) & Monterey Bay Buoy Category 1 storm – 70 kt maximum winds, 965 hPa. Errors > 5 m s-1 Wind forecasts are quite skillful (RMS ~1.8 m s-1, bias < 0.5 m s-1) Episodes of poor wind forecasts (independent of resolution) Upwelling Relaxation

COAMPS Adjoint Sensitivity Adjoint Allows for the Mathematically Rigorous Calculation of Forecast Sensitivity J: response function xi: state vector at initial time ti xt: state vector at final time tf MT: adjoint of non-linear model, M Sensitivity of the response function at final time tf to the initial state at time ti Adjoint-Based “Optimal” Perturbations wj: weighting parameter s: scaling parameter (umax~1 m s-1) COAMPS® Nonlinear, Adjoint, Tangent Linear Model Setup Dx=9 km, 12 h forecasts carried out PBL, Surface Flux, No moisture (moist tests w/ microphysics not shown) J: Kinetic Energy in a Box (lowest 1 km or 7 model levels) Adjoint Sensitivities for a Prototypical Case (2007) and entire August 2003 1) Data Assimilation Currently, COAMPS uses MVOI operationally with 3D-VAR in the test phase. MM5 is typically applied without any data assimilation or with nudging. MM5 developers claim to have a 4D-VAR system, but data assimilation experts agree that it is less sophisticated (and presumably accurate) than 3D-VAR systems because it makes use of no information regarding the statistics of the background fields (background error coveriances). This MM5 4D-VAR Lite scheme can be thought of as “advanced nudging”. Currently, AFWA and most quasi-operational MM5 runs do not assimilate any observations. (See Attached Data Assimilation Slides). 2) Data Assimilation Cycle COAMPS is always run with a cycle, which is desirable for an operational model because of the retention of mesoscale structures through the background fields. MM5 is never run with a data assimilation cycle. Systematic errors of MM5 are generally unknown because the model is initiated as a cold start. 3) Initialization A digital filter has been developed that integrates the model forward and backwards to filter out spurious noise excited during the initialization process. 4) Advection COAMPS has capability of an advection scheme that has 2nd or 4th order truncation error numerics. 5) Grid Scheme COAMPS uses a scheme C staggering while MM5 uses a scheme B. Geostrophic adjustment process is somewhat more accurate with a scheme C grid (see Haltiner and Williams text book). Conceptually, this may be because the divergence can be more accurately calculated in a scheme C system than B. 6) Boundary Layer COAMPS makes use of a predictive equation for TKE using Mellor-Yamada Level 2.5 scheme. MM5 has several versions of a M-Y 2.0 scheme including Blackadar and Troen and Mahrt schemes. MM5 also has the Burk-Thompson scheme (level ~3.0), which is used typically in a research mode because of expense. 7) Convection Both models have options for Kuo and Kain-Fritsch convective parameterizations. MM5 uses a simplified Arakawa-Schubert scheme (Grell) and a similar scheme is being incorporated into COAMPS in FY99. 8) Microphysics COAMPS has microphysical “bulk-type” predictive equations for cloud water, rain water, ice crystals, and snow crystals. MM5 typically makes use of simpler “bulk-type mixed phase” microphysics. In this scheme, when the temperature is cold enough the cloud/rain water equations become ice/snow equations. Other more sophisticated options may be available but typically are not used in operations. AFWA does use a more complex scheme for operations that uses mixed phase microphysics. 9) Radiation Both models use 2 stream radiation models. COAMPS’s Harschvardhan scheme is somewhat more sophisticated because it was design for a global model (radiation parameterizations are more important on longer time scales). 10) Idealized Capability Idealized tests are important to validate the model dry dynamics through the simulation of simple test problems. COAMPS can easily be tested with idealized initial conditions and radiation lateral boundary conditions. MM5 cannot easily be applied with idealized initial states. MM5 has not been evaluated on many of the simple fundamental test problems as other models have such as RAMS, COAMPS, ARPS etc. 11) Nest Grids Both models have very flexible options for grid nesting and have similar grid telescoping characteristics (3 to 1 nesting grid increment ratio) 12) Predictive Equations COAMPS has 11 predictive equations (u,v,w, potential temperature, water vapor, pert. Exner function, cloud water, rain water, ice crystals, snow crystals, and turbulent kinetic energy). This does not include the aerosol tracer equation(s). The typical version of MM5 has 7 predictive equations (u,v,w, temperature, mixing ratio, pressure, cloud water, rain water) Despite having 4 more predictive equations, COAMPS is 2 times faster on a C90 than MM5 (for the same domain size according to documented MM5 statistics). 13) Adjoint/TLM Both models have developed adjoint/tangent linear modeling systems for future data assimilation functionality. 14) Ocean Coupling COAMPS has been coupled to wave (WAM) and ocean circulation models (POM, MOM, NCOM). MM5 has been used in a research and development model with POM, however, there is no commitment to incorporate an ocean system into the permanent version of the model. 15) Projected Lifespan It is expected that the Weather Research and Forecasting (WRF) model will replace MM5 in the next 2-3 years. MM5 has inherited a long history of poor and unusual coding practices that limit somewhat the flexibility of the model. This WRF modeling system makes use of many of the dry dynamics features that are currently contained in COAMPS. However, the WRF researchers are likely to use density as a predictive equation, which differs from the COAMPS Exner function approach. The WRF will be a completely new modeling system that will require significant effort to transition to any operational site.

Non-Linear Model Forecast (July 25, 2007) COAMPS 10-m Wind Analysis 10-m Winds at 12 h 12Z 25 July 2007 00Z 26 July 2007 Monterey Bay Response Function Response Function Category 1 storm – 70 kt maximum winds, 965 hPa. Typical summer-time case selected (25 July 2007). Horizontal resolution is 9 km (30 L). Response function box centered on Monterey Bay.

Adjoint Model Sensitivity Fields U-Wind Sensitivity (KE/u) q Sensitivity (KE/q) Category 1 storm – 70 kt maximum winds, 965 hPa. 500-m 500-m The u and q sensitivity maxima are located within the BL near coastal promontories and regions of significant terrain. Key sensitivity regions can propagate > 500 km/12 h Small sensitivity to the 10-m u and q.

Sensitivity During Upwelling Conditions Mean q (K) & Normal Wind (m s-1) q Sensitivity (KE/q) 19 m s-1 ● U-Wind Sensitivity (KE/u) v-Wind Sensitivity (KE/u) Category 1 storm – 70 kt maximum winds, 965 hPa. Sloped sensitivity regions along the inversion. Increase in the inversion strength results in stronger MBay winds. Increase in winds near the topography, stronger low-level winds.

Adjoint Model SST Sensitivity SST Sensitivity (KE/SST) Non-Local Sensitivity Local Category 1 storm – 70 kt maximum winds, 965 hPa. SST sensitivity shows both local and non-local (>250 km / 12h) characteristics. Weaker ground temperature sensitivity over land.

Evolved Optimal Adjoint Perturbations Evolved (12 h) Optimal Adjoint Wind Speed Perturbations (500 m) 3 m s-1 (6x growth in 12 h) Category 1 storm – 70 kt maximum winds, 965 hPa. Initial adjoint perturbations are ~ 1 K or 1 m s-1. Evolved optimal adjoint perturbations show 6x growth in 12 h at 500 m.

Mean Conditions for August 2003 Upwelling Conditions (23 Days) 500-m Winds at 12 h Relaxation Conditions (8 Days) 500-m Winds at 12 h Category 1 storm – 70 kt maximum winds, 965 hPa. Strong coastal jet during upwelling state. Relaxation conditions features weak trough and mean SW flow along central coast.

Sensitivity During August 2003 U-Wind Sensitivity (KE/u) q Sensitivity (KE/q) Larger sensitivity during upwelling state. q more sensitive than u (upwelling) u and q similar (relaxation) Upwelling 500-m 500-m Relaxation 500-m Category 1 storm – 70 kt maximum winds, 965 hPa.

Sensitivity During Upwelling Conditions Mean q (K) & Normal Wind (m s-1) q Sensitivity (KE/q) 13 m s-1 ● U-Wind Sensitivity (KE/u) v-Wind Sensitivity (KE/u) Category 1 storm – 70 kt maximum winds, 965 hPa. Sloped sensitivity regions along the inversion. Sensitivity to shear within and above the BL.

Conclusions Adjoint sensitivity for boundary layer winds along the California coast has been examined for all of August 2003 and a July 2007 case. Sensitivity maxima located upstream along the sloped BL inversion in expansion fan regions during NW flow conditions. Sensitivity maxima near coastal terrain. Sensitivity maxima within upstream (local) BL in relaxation conditions. Short-range predictability of coastal winds. Key sensitivity regions can propagate > 500 km/12 h – in some cases faster than advective speed (gravity waves?) BL winds often quite predictable (growth < 2x or 2 m s-1/12 h) occasionally less predictable (growth > 4x or 4 m s-1/12 h) characterized by strong interactions with (far) upstream terrain

Evolved Optimal Adjoint Perturbations Upwelling State 500-m Winds at 12 h Relaxation State 500-m Winds at 12 h 3 m s-1 1.5 m s-1 Category 1 storm – 70 kt maximum winds, 965 hPa. Evolved wind perturbations grow 2 times more rapidly in the upwelling periods. Perturbations propagate at advective speed 10 m s-1 (upwelling) and 5 m s-1 (relaxation)