1. Reporter : Prudence Chien
The Impact of Positive-Definite Moisture Transport on NWP Precipitation Forecasts
Reporter : Prudence Chien
Reference:
Skamarock, W.C., and M.L. Weisman, 2009: The Impact of Positive-Definite Moisture Transport on NWP Precipitation Forecasts. Mon. Wea. Rev., 137, 488–494.

2. Outline Introduction ARW positive-definite transport formulation
Forecast examples
Discussion

3. Introduction
Numerical transport scheme handle strong gradients and discontinuities present in the simulated cloud and precipitation fields.
Model results exhibit a systematic positive bias in precipitation amounts, especially for the higher precipitation thresholds often associated with deep convection (e.g., Done et al. 2004;Weisman et al. 2008; Kain et al. 2008).
The effect of moisture transport schemes on precipitation is the explicit emphasis of the present work.

4. There is a significant spurious source of water when non-PD schemes are used for moisture transport in the ARW test simulations.
These spurious sources arise from the clipping of negative water species mixing ratios produced by the standard (non PD) ARW advection scheme, and setting any negative mixing ratios to zero after the transport step is complete.
In this study, the authors present the formulation of non-PD and PD used in the ARW model, together with results demonstrating the beneficial impact of the PD scheme on the moisture budget and precipitation forecasts.

5. From: Monotonic and Postive Definite Transport Options in the ARW V3
From: Monotonic and Postive Definite Transport Options in the ARW V3.1 Release

6. Formulation (non-PD) φ : scalar mixing ratio μ : column mass
η : vertical coordinate
Via Runge-Kutta 3rd-order

7. Formulation (PD) IF R(F) : a renormalized flux
F1 : 1st-order upwind flux IF
Negative mixing ratio
Positive mixing ratio

8. From: Monotonic and Postive Definite Transport Options in the ARW V3
From: Monotonic and Postive Definite Transport Options in the ARW V3.1 Release

10. Forecast examples
Case A1 : 5 June 2005 A severe squall line with embedded supercells Δx = 4km initialized at 0000UTC, forecast 36h
Case A2 : 14 April 2007 A strong synoptic-scale cyclone with widespread, heavy stratiform precipitation and embedded convection occurring over most of this region Δx = 3km initialized at 0000UTC, forecast 36h
Case B : 2005 and 2007 summer seasons

11. Case A1
5 June 2005
12~36h
24-h accumulated precipitation
Case A2
14 April 2007
12~36h
24-h accumulated precipitation

13. Case B : 2005 and 2007 summer seasons

14. Discussion
It is difficult to forecast high-precipitation events accurately, which are most often small scale in both space and time.
Using PD limiter in the ARW model has remedied an obvious physical error of the nonconservation of water.
But PD scheme has not completely removed the positive bias in the high-resolution forecasts.
The results of this study are primarily relevant for convective permitting resolutions where clouds and convective elements are poorly resolved.