4. Results

y bo

276 Advanced Applications for Artificial Neural Networks

α<sup>l</sup> ¼

observations around that grid point <sup>ð</sup>yo

observation,

ijk <sup>¼</sup> xp � yo

i � �<sup>2</sup> þ ðyp � yo

r2

the <sup>ð</sup>yo <sup>i</sup> , yo <sup>j</sup> , yo

MLP-DA.

3.2. Generalization process

the LETKF analyses.

NN activation.

<sup>i</sup>�m,j�m, <sup>k</sup>�<sup>m</sup> <sup>¼</sup> yo

ðm ¼ 1, 2, …, MÞ

8 < :

jÞ

<sup>2</sup> <sup>þ</sup> zp � yo

process and also adds positive flags in the observation mask.

k � �<sup>2</sup>

> <sup>i</sup> , yo <sup>j</sup> , yo

ijk ð Þ <sup>6</sup> � <sup>γ</sup> <sup>r</sup><sup>2</sup> ijk þ<sup>X</sup> 6

0 ð Þ if there is no observation

where <sup>b</sup>y<sup>o</sup> is the weighted observation, <sup>M</sup> is the number of discrete layers considered around

Each observation's influence computed on a certain grid point is a new location, hereafter referred to as pseudo-observation, which adds values to the three input vectors to NN training

Then, the grid points to be considered in MLP-DA analysis are greater than grid points considered to LETKF analysis, although these calculations are made without interference on LETKF system. The back-propagation algorithm stops the training process using the criteria cited at item 6 above (Section 3), after obtaining the best set of weights; it is a function of smallest error between the MPL-NN analysis and the target analysis (e.g., when the root mean square error between the calculated output and the input target vector is less than 10�<sup>5</sup>

learning process is the same for each MLP of the set of 30 NN and takes about 15 min to get the fixed weights before the MLP-DA data assimilation cycle or generalization process of

The training is performed with combined data from January, February, and March of 1982, 1983, and 1984, and in generalization process, MLP-DA is able to perform analyses similar to

The generalization process is indeed the data assimilation process. The MLP-DA results a global analysis field. The MLP-DA activation is entering by input values (only 6 hours forecast and observations) at each grid point once, with no data used in the training process. The input vectors are done at grid model point, where it is marked (by positive flag mask) with observation or pseudo-observation (Eq. 10). The procedure is the same for all NN but one NN for each region, and each prognostic variable has own connection weights. All NNs have one hidden layer, with the same number of neurons for all regions. The regional grid points are put in the global domain to make the analysis field after generalization process of the MLP-DA, e.g., the activation of 30 NN results a global analysis. The regional division is only for inputting each

<sup>1</sup> if there is observation; and : <sup>γ</sup>new <sup>¼</sup> <sup>γ</sup>old <sup>þ</sup> <sup>1</sup> � �

<sup>k</sup>Þ is the coordinate of the observation, and γ is a counter of grid points with

l¼1 αl yo

i�m,j�m, k�m r2 ijk

, where (xp, yp, zp) is coordinate of the grid point, and

<sup>k</sup>Þ. If γ = 6, there is no influence to be considered.

(10)

). The

The input and output values of prognostic variables (ps, u, v, T, and q) are processed on grid model points for time integrations to an intermittent forecasting and analysis cycle. Taking into account the pseudo-observation (Eq. 10), two grid layers (M = 2) around a given observation are considered.

The results show the comparison of analysis fields, generated by the MLP-DA, the LETKF, and the true model fields. The global surface pressure fields (at 11 January 1985 1800 UTC) and differences between the analyses are shown in Figure 4. The analysis fields and the differences between both assimilation, for 11 January 1985 at 1800 UTC at 950 and 500 hPa are also shown, for at 18 UTC at levels 950 hPa (near surface) and 500 hPa are also shown, for T, u, v, and q meteorological global fields, in Figures 5–10. These results show that the application of MLP-DA, as an assimilation system, generates analyses similar to those calculated by the LETKF system. Sub-figure (d) from Figures 5–10 shows very small differences between the MLP-DA and LETKF analyses. The difference field of absolute temperature (K) at 500 hPa is about 3 degrees; and the difference field of humidity at 950 hPa is about 0.002 kg/kg.

Figure 4. Surface pressure (PS) [Pa]—Jan/11/1985 at 18 UTC (a) LETKF analysis, (b) ANN analysis, (c) true model, and (d) differences analysis.

Figure 5. Absolute temperature (T) [K] Fi-950 hPa, Jan/11/1985 at 18 UTC. (a) LETKF analysis, (b) ANN analysis, (c) true model, and (d) differences analysis.

Figure 6. Absolute temperature (T) [K] at 500 hPa—Jan/11/1985 at 18 UTC (a) LETKF analysis, (b) ANN analysis, (c) true model, and (d) differences analysis.

Figure 7. Zonal wind component (u) [m/s] at 500 hPa—Jan/11/1985 at 18 UTC. (a) LETKF analysis, (b) ANN analysis, (c) true model, and (d) differences analysis.

Data Assimilation by Artificial Neural Networks for an Atmospheric General Circulation Model http://dx.doi.org/10.5772/intechopen.70791 279

Figure 8. Meridional wind component (v) [m/s] fields at 500 hPa—Jan/11/1985 at 18 UTC (a) LETKF analysis, (b) ANN analysis, (c) true model, and (d) differences analysis.

Figure 5. Absolute temperature (T) [K] Fi-950 hPa, Jan/11/1985 at 18 UTC. (a) LETKF analysis, (b) ANN analysis, (c) true

Figure 6. Absolute temperature (T) [K] at 500 hPa—Jan/11/1985 at 18 UTC (a) LETKF analysis, (b) ANN analysis, (c) true

Figure 7. Zonal wind component (u) [m/s] at 500 hPa—Jan/11/1985 at 18 UTC. (a) LETKF analysis, (b) ANN analysis,

model, and (d) differences analysis.

278 Advanced Applications for Artificial Neural Networks

model, and (d) differences analysis.

(c) true model, and (d) differences analysis.

Monthly average of absolute temperature analyses fields was obtained. The field of differences between the analyses (LETKF and MLP-DA) for data assimilation cycles is shown in Figure 11. The differences are slightly larger in some regions, such as the northeast regions of North America and South America.

The root mean square error (RMSE) of the absolute temperature analyses related to true model is calculated by fixing a point at longitude (87 W) for all latitude points. Figure 12 shows the temperature RMSEs for the entire period of the assimilation cycle (January 1985). Subfigure (a) for Figure 12 shows the RMSE of the LETKF analysis by line and the RMSE of the MLP-DA analysis by circles; and subfigure (b) for Figure 12 shows the differences between LETKF and MLP-DA analyses RMSE. The differences are less than 10<sup>3</sup> .

Figure 9. Specific humidity (q) at 950 hPa—Jan/11/1985 at 18 UTC (a) LETKF analysis, (b) ANN analysis, (c) true model, and (d) differences analysis.

Figure 10. Specific humidity (q) at 950 hPa—Jan/11/1985 at 18 UTC (a) LETKF analysis, (b) ANN analysis, (c) true model, and (d) differences analysis.

Figure 11. Differences field of the average of absolute temperature MLP-DA analysis and LETKF analysis for the assimilation cycle.

Figure 12. Meridional root mean square error for entire period of the assimilation cycles. RMSE analyses to the "true" state to (a) the errors of the LETKF analysis (line) and the errors of MLP-DA analysis (circles) to the absolute temperature at 500 hPa. (b) Differences of RMSE analyses.

#### 4.1. Computer performance

Several aspects of modeling stress computational systems and push the capability requirements. These aspects include increased grid resolution, the inclusion of improved physics processes and concurrent execution of earth-system components, and coupled models (ocean circulation and environmental prediction, for example).

Often, real-time necessities define capability requirements. In data assimilation, the computational requirements become much more challenging. Observations from Earth-orbiting satellites in operational numerical prediction models are used to improve weather forecasts. However, using the amount of satellite data increases the computational effort. As a result, there is a need for an assimilation method able to compute the initial field for the numerical model in the operational window time to make a prediction. At present, most of the NWP centers find it difficult to assimilate all the available data because of computational costs and the cost of transferring huge amounts of data from the storage system to the main computer memory.

The data assimilation cycle has a recent forecast and the observations as the inputs for assimilation system. The described MLP-DA system produced an analysis to initiate the actual cycle. This time simulation experiment is for January 1985 (28 days). There were 2075 observations inserted at runs of 0600 and 1800 UTC for surface variables, and 12,035 observations inserted at runs of 0000 and 1200 UTC for all upper layer variables.

The LETKF data assimilation cycle initiates running the ensemble forecasts with the SPEEDY model, and each analysis produced to each member at the latter LETKF cycle to result 30 (members) 6-hour forecasts; the second step is to compute the average of those forecasts. After, with a set of observations and the mean forecast, the LETKF system is performed. The LETKF cycle results one analysis to each member for the ensemble and one average field of the ensemble analyses. The MLP-DA data assimilation cycle is composed by the reading of 6-hour forecast of SPEEDY model from latter cycle and reading the set of observations to the cycle time, the division of input vectors, the activation of MLP-DA, and the assembly of output vectors to a global analysis field.

The MLP-DA runtime measurement initiates after reading the 6-hour forecast of SPEEDY model from latter cycle and the set of observations. The time of generalization includes the division of observation and prediction fields into regions, and the execution of the various trained networks by gathering all regions in a global analysis. It initiates after reading the mean 6-hours forecast of SPEEDY model and the set of observations. The LETKF time includes the results of 30 analyses and one mean ensemble analysis. The comparison in Table 1 is the data assimilation cycles for the same observations points and the same model resolution to the same time simulations. LETKF and MLP-DA executions are performed independently. Considering the total execution time of those 112 cycles simulated, the computational performance of the MLP-DA data assimilation is better than that obtained with the LETKF approach. These results show that the computational efficiency of the NN for data assimilation to the SPEEDY model, for the adopted resolution, is 90 times faster and produces analyses of the same quality (Table 1). Considering only the analyses execution time of those 112 data assimilation processes simulated, the computational efficiency of MLP-DA is 421 times faster than LETKF process. Table 2 shows the mean execution time of each element to one cycle of the LETKF data assimilation method (ensemble forecast and analysis) and the MLP-DA method (model forecast and analysis). The computational efficiency of one MLP-DA execution keeps the relationship about speed-up, comparing with one LETKF execution (421 times faster). Details for this experiment can be found in Ref. [6].

4.1. Computer performance

at 500 hPa. (b) Differences of RMSE analyses.

and (d) differences analysis.

280 Advanced Applications for Artificial Neural Networks

assimilation cycle.

Several aspects of modeling stress computational systems and push the capability requirements. These aspects include increased grid resolution, the inclusion of improved physics

Figure 12. Meridional root mean square error for entire period of the assimilation cycles. RMSE analyses to the "true" state to (a) the errors of the LETKF analysis (line) and the errors of MLP-DA analysis (circles) to the absolute temperature

Figure 10. Specific humidity (q) at 950 hPa—Jan/11/1985 at 18 UTC (a) LETKF analysis, (b) ANN analysis, (c) true model,

Figure 11. Differences field of the average of absolute temperature MLP-DA analysis and LETKF analysis for the


Table 1. Total running time of 112 cycles of complete data assimilation (analysis and forecasting).


Table 2. Mean time of one execution (hour:min:sec:lll).
