Task: Data-Imputation (source dataset: tablib)

Please fill in the missing value in the input table. The missing value is denoted by '[MISSING]'. Please only return the value filled in. Do not return the whole table.

No explanation, return the value filled in JSON format: {"value": "filled_value"}. 

Input Table:
| Parameter                                 |      AR5-IR | AR5-PI        |   MESMO (lowest decay) |   ACC2 (highest decay) |   Expectation | Notes                                                                                                                                           |
|:------------------------------------------|------------:|:--------------|-----------------------:|-----------------------:|--------------:|:------------------------------------------------------------------------------------------------------------------------------------------------|
| a_0                                       |   0.2173    | [MISSING]     |                 0.285  |                 0.178  |        0.217  | None                                                                                                                                            |
| a_1                                       |   0.224     | 0.1924        |                 0.294  |                 0.165  |        0.224  | None                                                                                                                                            |
| a_2                                       |   0.2824    | 0.2423        |                 0.238  |                 0.38   |        0.283  | None                                                                                                                                            |
| a_3                                       |   0.2763    | 0.4108        |                 0.183  |                 0.277  |        0.276  | None                                                                                                                                            |
| rho_0                                     |   1e-06     | 1e-06         |                 1e-06  |                 1e-06  |        1e-06  | None                                                                                                                                            |
| rho_1                                     |   0.0025355 | 0.003614022   |                 0.0022 |                 0.0026 |        0.003  | None                                                                                                                                            |
| rho_2                                     |   0.0273673 | 0.032520325   |                 0.04   |                 0.0271 |        0.027  | None                                                                                                                                            |
| rho_3                                     |   0.2323    | 0.22426553    |                 0.4965 |                 0.2686 |        0.232  | None                                                                                                                                            |
| Emissions in 2009 (GtCO2)                 |  35.7004    | 35.700377533  |                35.7004 |                35.7004 |       35.7004 | None                                                                                                                                            |
| S_0 in 2010 (ppm)                         |  52.857     | 52.856985915  |                52.857  |                52.857  |       52.857  | None                                                                                                                                            |
| S_1 in 2010 (ppm)                         |  37.4585    | 37.458497187  |                37.4585 |                37.4585 |       37.4585 | None                                                                                                                                            |
| S_2 in 2010 (ppm)                         |  16.0382    | 16.038169761  |                16.0382 |                16.0382 |       16.0382 | None                                                                                                                                            |
| S_3 in 2010 (ppm)                         |   3.4034    | 3.403396124   |                 3.4034 |                 3.4034 |        3.4034 | None                                                                                                                                            |
| Pre-industrial CO2 (ppm)                  | 278         | 278.0         |               278      |               278      |      278      | None                                                                                                                                            |
| Conversion factor ppm to GtCO2            |   7.81      | 7.81          |                 7.81   |                 7.81   |        7.81   | Conversion factor from CDIAC (https://cdiac.ess-dive.lbl.gov/pns/convert.html#3.)                                                               |
| Cumulative CO2 emissions, 1750-2010 (GtC) | 521.489     | 521.488603761 |               521.489  |               521.489  |      521.489  | None                                                                                                                                            |
| Temperature in 2010                       |   0.854     | 0.854         |                 0.854  |                 0.854  |        0.854  | None                                                                                                                                            |
| r_{0}                                     |  32.4       | 32.4          |                32.4    |                32.4    |       32.4    | Source of uncertainty estimate: Millar et al. (2017, p7219), who report specifying a Gaussian distribution with 5-95% C.I. of +/-13% of default |
| r_{C}                                     |   0.019     | 0.019         |                 0.019  |                 0.019  |        0.019  | As above                                                                                                                                        |
| r_{T}                                     |   4.165     | 4.165         |                 4.165  |                 4.165  |        4.165  | As above                                                                                                                                        |
| Max iIRF_100                              |  96.6       | 96.6          |                96.6    |                96.6    |       96.6    | Source: Frank Venmans' fit of FAIR carbon cycle feedback as described in Dietz et al. (2021, JAERE)                                             |
| alpha fit 1                               |   0.0107    | 0.0107        |                 0.0107 |                 0.0107 |        0.0107 | Source: Frank Venmans' fit of FAIR carbon cycle feedback as described in Dietz et al. (2021, JAERE)                                             |
| alpha fit 2                               |   0.0866    | 0.0866        |                 0.0866 |                 0.0866 |        0.0866 | Source: Frank Venmans' fit of FAIR carbon cycle feedback as described in Dietz et al. (2021, JAERE)                                             |



row_idx: 0
col_idx: 2
col_name: AR5-PI
label: 0.1545
output: value: 0.1545
tablib_key: tables/job=github_000005/batch=009026/fGdxi691VBupYgOV640jYFhr0uhUtfcfy-lA2WzmTH0=