# Presentation: 515474

## MJO simulation diagnostics

- Part 2 - Application to several climate models
- Figure list - last update 21/SEP/2008

## Table 1. Brief descriptions of models used in this study

| Model
(group) | Horizontal
Resolution
-AGCM | Vertical
Resolution (top level)
-AGCM | Cumulus parameterization | Integration | Reference |
| --- | --- | --- | --- | --- | --- |
| CAM3.5
(NCAR) | 1.9o lat x 2.5o lon | 26
(2.2hPa) | Mass flux 
(Zhang and McFarlane 1995) | 20 years
01JAN1986-31DEC2005 | Neale et al. (2007) |
| CAM3z
(SIO) | T42(2.8o) | 26
(2.2hPa) | Mass flux 
(Zhang and McFarlane 1995) | 15 years
29JAN1980-23JUL1995 | Zhang et al. (2005) |
| CFS
(NCEP) | T62(1.8o) | 64
(0.2hPa) | Mass flux
(Hong and Pan 1998) | 20 years | Wang et al. (2005) |
| CM2.1
(GFDL) | 2o lat x
 2.5o lon | 24
(4.5hPa) | Mass flux
(RAS; 
Moorthi and Suarez 1992) | 20 years | Delworth et al. (2006) |
| ECHAM4
/OPYC*
(PCMDI) | T42(2.8o) | 19
(10hPa) | Mass flux
(Tiedtke 1989, adjustment closure Nordeng 1994) | 20 years | Roeckner et al. (1996),
Sperber et al. (2005) |
| GEOS5
(NASA) | 1o lat x 1.25o lon | 72
(0.01hPa) | Mass flux
(RAS; 
Moorthi and Suarez 1992) | 12 years
01DEC1993-30NOV2005 | To be documented |
| SNUAGCM
(SNU) | T42(2.8o) | 20
(10hPa) | Mass flux 
(Numaguti et al. 1995) | 20 years
01JAN1986-31DEC2005 | Lee et al. (2003) |
| SPCAM
(CSU) | T42(2.8o) | 26
(3.5hPa) | Superparameterization (Khairoutdinov and
 Randall 2003) | 19 years
01OCT1985-25SEP2005 | Khairoutdinov et al. (2005) |

## Table 2. Summary of results from different EOF analyses. 

- *: 1st and 2nd modes are separated from 3rd mode by
- North’s criterion (dof = number of day/50)

| Data source | Analyzed field | Explained variance of EOF1 and EOF2 | Fraction of leading PC’s variance in 30-80 day band | Mean Coh2 of PC1 and PC2 in 30-80 day band |
| --- | --- | --- | --- | --- |
| Observation
(AVHRR/NCEP1) | U200 map | 15.92%* | 54.77%, 52.58% | 0.54 |
|  | CEOF | 43.12%* | 57.97%, 59.91% | 0.77 |
| CAM3.5 | U200 map | 12.35% | 34.98%, 35.18% | 0.50 |
|  | CEOF | 30.91%* | 31.01%, 31.59% | 0.63 |
| CAM3z | U200 map | 15.09% | 34.38%, 33.90% | 0.45 |
|  | CEOF | 29.44%* | 32.95%, 31.33% | 0.60 |
| CFS | U200 map | 14.4%* | 42.85%, 42.91% | 0.38 |
|  | CEOF | 30.29%* | 47.02%, 42.83% | 0.68 |
| CM2.1 | U200 map | 9.58% | 34.27%, 32.13% | 0.05 |
|  | CEOF | 21.17% | 31.92%, 33.67% | 0.39 |
| GEOS5 | U200 map | 10.86% | 43.64%, 38.21% | 0.08 |
|  | CEOF | 26.65%* | 39.45%, 38.13%  | 0.49 |
| ECHAM4/OPYC | U200 map | 17.41%* | 47.39%, 46.97% | 0.54 |
|  | CEOF | 35.54%* | 49.97%, 47.86% | 0.73 |
| SNU (need to be updated) | U200 map | 13.25% | 43.06%, 34.93% | 0.24 |
|  | CEOF | 26.24%* | 40.00%, 39.96% | 0.62 |
| SPCAM | U200 map | 16.2%* | 45.02%, 40.73% | 0.49 |
|  | CEOF | 34.71%* | 45.17%, 44.44% | 0.70 |

## Table 3. Average of e-folding time scale over all initial phases

| OBS  | CAM3.5  | CAM3z  | CFS  | CM2.1  | ECHAM4/OPYC  | GEOS5  | SNU  | SPCAM  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| 31.2 | 20.5 | 21.5 | 24.9 | 20.7 | 28.9 | 20.7 | 22.8 | 24.5 |

## Figure 1: November-April mean precipitation (shaded) and 850hPa zonal wind (contoured) of a) CMAP/NCEP1, b) CAM3.5, c) CAM3z, d) CFS, e) CM2.1, f) ECHAM4/OPYC, g) GEOS5 h) SNU and i) SPCAM. Contours of mean 850hPa zonal wind are plotted every 3 ms-1, zero line is represented by thick solid line. Unit is mmday-1 for precipitation and ms-1 for 850hPa zonal wind.

**Notes:**
 - Double ITCZ problem is appeared in two couple models (CM2.1 and CFS) but not much serious in other models.
 - Simulated SPCZs are stronger than that of observation in 5 models (SNU, SPCAM, CAM3z, ECHAM4/OPYC and CM2.1) and they have stronger subseasonal variability (Fig. 3). This result is consistent with Slingo et al. (1996)’s one.
 - The westerlies in equatorial Indian Ocean is well reproduced by ECHAM4/OPYC and is partly simulated in GEOS5, CAM3.5, CM2.1 and CFS
 - Zonally elongated westerlies in west Pacific is suggested as the proxy of eastward propagation in one modeling study (Inness et al. 2003). This feature is at least partly simulated in the 5 models which have intense SPCZs.

## Figure 2 : Scatter plot of pattern correlation and normalized RMSE for a) precipitation b) 850hPa zonal wind, c) zonal wind shear (200hPa-850hPa), d) outgoing longwave radiation, e) 200hPa zonal wind and f) sea surface temperature. The region for pattern correlation and normalized RMSE is 40E-220E, 25S-15N. RMSE is normalized by standard deviation of observed value.

**Notes:**
 - Figure 2 is scatter plots for skill of mean state of important variables in MJO simulation.
 - This plot can be used for quantitative comparison if future intercomparison study use same diagnostics.

## Figure 3 : As in Figure 1, except for variance of 20-100 day band pass filtered precipitation and 850hPa zonal wind. Contours of 850hPa zonal wind variance are plotted every 3 m2 s-2, 9 m2 s-2 line is represented by thick solid line. The unit is mm2 day-2 for precipitation and m2 s-2 for zonal wind.

## Figure 4 : November-April wavenumber-frequency spectra of 10oN-10oS averaged precipitation (shaded) and 850hPa zonal wind (contoured). a) CMAP/NCEP1, b) CAM3.5, c) CAM3z, d) CFS, e) CM2.1, f) ECHAM4/OPYC, g) GEOS5 h) SNU and i) SPCAM. Individual November-April spectra were calculated for each year, and then averaged over all years of data. Only the climatological seasonal cycle and time mean for each November-April segment were removed before calculation of the spectra. Units for the precipitation (zonal wind) spectrum are mm2 day-2 (m2 s-2) per frequency interval per wavenumber interval. The bandwidth is (180 d)-1.

**Notes:**
- Variance map includes all of the zonal wavenumber components and it is not able to examine what is the prefer time scale for model’s subseasonal variability. (need for wavenumber-frequency diagram)
- In the case of models here, U850 is better than precipitation, consistent to Zhang et al. (2006).
- For precipitation, models (SNU, GEOS5, CAM3.5, ECHAM4/OPYC, CM2.1 and CFS) have spectral peak within the sub-seasonal time scale smaller than that in the low frequency (period longer than 80 day) part.
- General statement which has been used in many literature “model has faster and weaker MJO signal” seems not to be appropriate at least for U850.

## Figure 5 : Scatter plot of east/west ratio. East/west ratio is calculated by dividing the sum of eastward propagating power by westward propagating counterpart within wavenumber 1-6 (1-3 for zonal wind), period 30-80 days.

**Notes:**
 - There is proportionality between the east/west ratio of precipitation and U850.
 - Most of the models have comparable (SNU, GEOS5, CAM3z and CM2.1) or larger (SPCAM, ECHAM4/OPYC and CFS) value than observation for U850. 
 - For rainfall, however, none of the model can reach to observed ratio.

## Figure 6 : First two CEOF modes of 20-100 day 15oS-15oN averaged NCEP1 850 hPa and 200 hPa zonal wind and OLR. a) AVHRR/NCEP1, b) CAM3.5, c) CAM3z, d) CFS, e) CM2.1, f) ECHAM4/OPYC, g) GEOS5 h) SNU and i) SPCAM. The total variance explained by each mode is shown. The coherence squared between principle components of two modes within 30-80 day period is given above the upper panel. Sign and location (upper or lower) of each mode are arbitrarily adjusted to be similar to observation. The mode which has large percentage variance is the first mode.

**Notes:**
- Model’s own MJO mode is extracted by combined EOF method and the similarity of the mode with observed one can be confirmed by the pattern of first and second eigen vectors, spectra of PCs and coherence squared between PCs (values above the upper panal).

## Figure 7 : The time series spectrum of the unfiltered PC derived by projecting PC onto the unfiltered data matrix (Blue: 1st , Green: 2nd mode). Dashed lines show the red noise spectrum and upper and 95% confidence limits on this red noise spectrum.

## Figure 8 Composited curves of the MJO index from combined EOF in PC1 and PC2 phase space. X and y axes are normalized PC1 and PC2, respectively. For each initial phase, strong cases are selected based on the distance between origin and point (distance>1.5). Then 40 days from initial day are averaged over all strong cases. (Blue: from odd number initial phase, Green: from even number initial phase)

**Notes:**
 - In observation, MJO amplitude (defined as sqrt(RMM1^2+RMM^2)) is maintained as “not weak (amplitude > 1)” for all phases after 20 days from initial day when the MJO is strong (amplitude > 1.5). All the models, however, fail to retain strong MJO and it is represented here as the lines fall into the inner circle. Both in the model and observation, the shape of the curves are not symmetric with respect to the origin of coordinates. It means that there is a phase in where the MJO is maintained more in terms of amplitude compared to other phase. Therefore, such features can be a characteristics of observation and models.

## Figure 9 : Averaged MJO index composite over all initial phases drawn on relative degree-amplitude space. Each panel shows different lead time from initial day. x-axis is relative degree to initial value and y-axis is amplitude. Dots over curves denote every 5 days after initial day.

## Figure 10: Phase-longitude diagram of OLR (contour, interval-5, green-positive/purple-negative) and evaporation (shaded). Phases are from MJO life-cycle composite and values are 5S-5N averaged. The unit of OLR and evaporation is W m-2.

**Notes:**
 - If the wind induced surface heat exchange (WISHE) mechanism is working, positive evaporation anomalies should be located in the east of the convective activity. However, this is not the case in the model group here. Most of the models produce positive evaporation anomaly in the west of the convective anomaly while they are coincidental (or evaporation slightly lead convection) in CFS.

## Figure 11 : Same as figure 10, except for 925hPa moisture convergence. The unit of convergence is kg kg-1 s-1.

## Figure 12a : Height-phase diagram of specific humidity anomalies specific humidity anomalies (shaded) at three different longitudes 80E (left), 130E (middle) 140W (right) averaged 5S-5N. Phases are defined as in figure 10. The units for specific humidity are g kg-1. OLR anomalies (averaged 5S-5N) are plotted in lower panel. The units for OLR are W m-2. 

## Figure 12b : (Continued) 

- Figure 12b : (Continued)

## Figure 13 : Relative humidity composite based on precipitation a) ERA40/GPCP, b) CAM3.5, c) CAM3z, d) CM2.1, e) ECHAM4/OPYC, f) SNU and g) SNU without convective inhibition function. Based on precipitation intensity (in log scale), relative humidity is averaged for each bin. Target area is the warm pool region (50E-180E, 10S-10N).

## Figure 13 : Annual mean stratiform rain fraction of a) TRMM 3A25 product, b) CAM3.5, c) CAM3z, d) ECHAM4/OPYC, e) SNU and f) SNU (no trigger). Areas with annual mean rain of less than 2mm day-1 are not included.

## Supplement

## Figure 5a : East/West ratio defined as the ratio between eastward propagating (positive frequency in wavenumber-frequency diagram) and westward propagating (negative frequency) power within 30-80 day period. In each component, power includes wavenumber 1 (1-3) components for PRCP (U850).