## Introduction

Accumulated variables are those which are aggregated over a particular time periods.

The tables below show how accumulated variables from a number of C3S and ECMWF datasets should be processed to derive values for an hour, a day, a month and a year.

As these can be stored in different ways in different datasets, it is important that they are interpreted correctly.

For illustration, 'total precipitation' and 'solar radiation' are used, but the same processing should be applied to all precipitation and radiative flux variables.

### Hydrological parameter table

Dataset | Variables | What it is | Grib units | Netcdf Units | To get the total precipitation for an hour (mm) | To get the total precipitation for a day (mm) | To get the total precipitation for a month (mm) | To get the total precipitation for a year (mm) |
---|---|---|---|---|---|---|---|---|

ERA5 reanalysis (hourly data) | Total precipitation | Accumulations are over the hour (the processing period) ending at the validity date/time | m (of water equivalent per hour) | m (of water equivalent per hour) |
\[ \text{tp}\ [\text{mm}] = \text{tp}\ [\text{m}] \cdot 1000 \]
Total precipitation over the one hour ending at forecast step. | \( \text{tp}\ [\text{mm}] = \left( \sum_{h = 1}^{23}\text{tp}_{h}\ [\text{m}] + \text{tp}_{d+1\ 00\text{UTC}}\ [\text{m}] \right) \cdot 1000 \) where h is the hour and d the day of interest (d+1 is the following day). The total precipitation over 24 hours is the sum of the individual total precipitation values for each hour. | \( \text{tp}\ [\text{mm}] = \sum_{n = 1}^{N} \left( \sum_{h = 1}^{23}\text{tp}_{h}\ [\text{m}] + \text{tp}_{d+1\ 00\text{UTC}}\ [\text{m}] \right)_{n} \cdot 1000 \) where | \( \text{tp}\ [\text{mm}] = \sum_{n = 1}^{N} \left( \sum_{h = 1}^{23}\text{tp}_{h}\ [\text{m}] + \text{tp}_{d+1\ 00\text{UTC}}\ [\text{m}] \right)_{n} \cdot 1000 \) whereN is the number of days in the year. |

ERA5 ensemble members (3 hourly data) | Total precipitation | Accumulations are over the 3 hours (the processing period) ending at the validity date/time | m (of water equivalent per 3 hours) | m (of water equivalent per 3 hours) | \( \text{tp}\ [\text{mm}] = \text{tp}\ [\text{m}] \cdot 1000 \) | \( \text{tp}\ [\text{mm}] = \left( \sum_{h} \text{tp}_{h} [\text{m}] \right) \cdot 1000 \) where h are the day timesteps available: 03 UTC, 06 UTC, 09 UTC, 12 UTC, 15 UTC, 18 UTC, 21 UTC and 00 UTC of the day after. The total precipitation over 24 hours is the sum of 8 | \( \text{tp}\ [\text{mm}] = \sum_{n = 1}^{N} \left(\sum_{h} \text{tp}_{h}[\text{m}] \right)_{n} \cdot 1000 \) where h are the day timesteps available: 03 UTC, 06 UTC, 09 UTC, 12 UTC, 15 UTC, 18 UTC, 21 UTC and 00 UTC of the day after and | \( \text{tp}\ [\text{mm}] = \sum_{n = 1}^{N} \left(\sum_{h} \text{tp}_{h}[\text{m}] \right)_{n} \cdot 1000 \) where h are the day timesteps available: 03 UTC, 06 UTC, 09 UTC, 12 UTC, 15 UTC, 18 UTC, 21 UTC and 00 UTC of the day after, and |

ERA5 monthly averaged reanalysis | Total precipitation | The accumulations in monthly means of daily means have been scaled to have units that include "per day" | m (of water equivalent per day) | m (of water equivalent per day) | N/A | N/A |
\( \text{tp}\ [\text{mm}] = \text{tp}\ [\text{m/day}] \cdot 1000 \cdot N \)
where |
\( \text{tp}\ [\text{mm}] = \sum_{n = 1}^{12}(\text{tp}\ [\text{m/day}] \cdot 1000 \cdot N)_{\text{n}} \)
where N is the number of days in the month and n is the number of the month. |

ERA5 monthly averaged ensemble members | Total precipitation | The accumulations in monthly means of daily means have been scaled to have units that include "per day" | m (of water equivalent per day) | m (of water equivalent per day) | N/A | N/A |
\( \text{tp}\ [\text{mm}] = \text{tp}\ [\text{m/day}] \cdot 1000 \cdot N \)
where |
\( \text{tp}\ [\text{mm}] = \sum_{n = 1}^{12}(\text{tp}\ [\text{m/day}] \cdot 1000 \cdot N)_{\text{n}} \)
where |

ERA5-Land hourly data | Total precipitation | Accumulations are from 00 UTC to the hour ending at the forecast step | m (of water equivalent) | m (of water equivalent) | \( \text{tp}\ [\text{mm}] = \left\{ \begin{array}{ll} \text{tp}_{h}\ [\text{m}] \cdot 1000 & h = 01 \text {UTC} \\ (\text{tp}_{h}\ [\text{m}]\ -\ \text{tp}_{h-1}\ [\text{m}])\ \cdot 1000 & \text{otherwise} \\ \end{array} \right. \) | \( \text{tp}\ [\text{mm}] = \text{tp}_{d+1\ 00\text{UTC}}\ [\text{m}]\ \cdot 1000 \) where The time step labelled | \( \text{tp}\ [\text{mm}] = \left( \sum_{n = 1}^{N}\text{tp}_{d+1\ 00\text{UTC},n}\ [\text{m}] \right)\cdot 1000 \) where The time step labelled | \( \text{tp}\ [\text{mm}] = \left( \sum_{n = 1}^{N}\text{tp}_{d+1\ 00\text{UTC},n}\ [\text{m}] \right) \cdot 1000 \) where The time step labelled |

ERA5-Land monthly averaged data | Total precipitation | The accumulations in monthly means of daily means have units that include "per day". | m (of water equivalent per day) | m (of water equivalent per day)
| N/A | N/A |
\( \text{tp}\ [\text{mm}] = \text{tp}\ [\text{m/day}] \cdot 1000 \cdot N \)
where | \( \text{tp}\ [\text{mm}] = \sum_{n = 1}^{12}(\text{tp}\ [\text{m/day}] \cdot 1000 \cdot N)_{\text{n}} \) where |

Seasonal daily data | Total precipitation | 24 hour aggregation since the beginning of the forecast | m | m |
\( \text{tp}\ [\text{mm/hr}] = \frac{(\text{tp}_{t2}\ [\text{m}] - \text{tp}_{t1}\ [\text{m}])\cdot 1000}{24} \)
where t |
\( \text{tp}\ [\text{mm}] = (\text{tp}_{t2}\ [\text{m}] - \text{tp}_{t1}\ [\text{m}])\cdot 1000 \)
where t |
\( \text{tp}\ [\text{mm}] = (\text{tp}_{t_2}\ [\text{m}] - \text{tp}_{t_1}\ [\text{m}])\cdot 1000 \)
where t | N/A For seasonal forecasts, as data only cover 7 months |

Seasonal Monthly data | Total precipitation | The accumulations in monthly means have units that include " | m/s | m/s | N/A | N/A |
\( \text{tp}\ [\text{mm}] = \text{tp}_{t1}\ [\text{m}]\cdot 1000 \)
where t | N/A For seasonal forecasts, as data only cover 7 months |

ERA-Interim sub-daily data | Total precipitation | Accumulations are from the beginning of the forecast | m (of water equivalent) | m (of water equivalent) | N/A NOT AVAILABLE HOURLY | \( \text{tp}\ [\text{mm}] = (\text{tp}_{12\ 00\text{UTC}}\ + \text{tp}_{12\ 12\text{UTC}}\ [\text{m}])\ \cdot 1000 \) where the time step labelled | \( \text{tp}\ [\text{mm}] = \sum_{d = 1}^{N}(\text{tp}_{12\ 00\text{UTC}}\ + \text{tp}_{12\ 12\text{UTC}}\ [\text{m}])_{d} \cdot 1000 \) where | \( \text{tp}\ [\text{mm}] = \sum_{d = 1}^{N}(\text{tp}_{12\ 00\text{UTC}}\ + \text{tp}_{12\ 12\text{UTC}}\ [\text{m}])_{d} \cdot 1000 \) where |

### Energy and momentum fluxes table

Dataset | Variables | What it is | Grib units | Netcdf Units | To get the average energy flux (Wm | To get the average energy flux for a day (Wm^{-2}) | To get the average energy flux for a month (Wm^{-2}) | To get the average energy flux for a year (Wm^{-2}) | |
---|---|---|---|---|---|---|---|---|---|

ERA5 daily data | Surface Solar Radiation (SSR) | Accumulations are over the hour (the processing period) ending at the forecast step | Jm | Jm^{-2} |
\( \text{SSR}\ [\text{Wm}^{-2}] = \text{SSR}\ [\text{Jm}^{-2}]\ /\ 3600\ [\text{s}] \)
Average flux over the one hour ending at forecast step. | \( \text{SSR}\ [\text{Wm}^{-2}] = \frac{ \sum_{h = 1}^{23} \text{SSR}_{h}\ [\text{Jm}^{-2}] + \text{SSR}_{d+1 00\text{UTC}}\ [\text{Jm}^{-2}]}{86400\ [\text{s}]} \) The average flux over 24 hours is the sum of the individual fluxes for each hour divided by the number of seconds in a day. | \( \text{SSR}\ [\text{Wm}^{-2}] = \frac{\sum_{n = 1}^{N} \left( \sum_{h = 1}^{23} \text{SSR}_{h}\ [\text{Jm}^{-2}] + \text{SSR}_{d+1 00\text{UTC}}\ [\text{Jm}^{-2}] \right)_{n}}{N \cdot 86400\ [\text{s}]} \) where The average flux over a month is the sum of the individual fluxes for each day divided by the number of seconds in the month. | \( \text{SSR}\ [\text{Wm}^{-2}] = \frac{\sum_{n = 1}^{N} \left( \sum_{h = 1}^{23} \text{SSR}_{h}\ [\text{Jm}^{-2}] + \text{SSR}_{d+1 00\text{UTC}}\ [\text{Jm}^{-2}] \right)_{n}}{N \cdot 86400\ [\text{s}]} \) where The average flux over a year is the sum of the individual fluxes for each day divided by the number of seconds in the year. | |

ERA5 daily ensemble data | SSR | Accumulations are over the 3 hours (the processing period) ending at the forecast step | Jm^{-2} | Jm^{-2} |
\( \text{SSR}\ [\text{Wm}^{-2}] = \text{SSR}\ [\text{Jm}^{-2}]\ /\ (3 \cdot 3600)\ [\text{s}] \)
Average flux over the three hours ending at forecast step. | \( \text{SSR}\ [\text{Wm}^{-2}] = \left( \sum_{h} \text{SSR}_{h}[\text{Jm}^{-2}] + \text{SSR}_{d+1 00\text{UTC}}\ [\text{Jm}^{-2}] \right) / 86400 \) where h are the day timesteps available: 03 UTC, 06 UTC, 09 UTC, 12 UTC, 15 UTC, 18 UTC, 21 UTC and 00 UTC of the day after. The average flux over 24 hours is the sum of 8 | \( \text{SSR}\ [\text{Wm}^{-2}] = \sum_{n = 1}^{N} \left( \sum_{h} \text{SSR}_{h} [\text{Jm}^{-2}] + \text{SSR}_{d+1 00\text{UTC}}\ [\text{Jm}^{-2}] \right)_{n} / N \cdot 86400 \) where h are the day timesteps available: 03 UTC, 06 UTC, 09 UTC, 12 UTC, 15 UTC, 18 UTC, 21 UTC and 00 UTC of the day after and The average flux over a month is the sum of the individual fluxes for each day (computed as the sum of 8 | \( \text{SSR}\ [\text{Wm}^{-2}] = \sum_{n = 1}^{N}\left( \sum_{h} \text{SSR}_{h} \right)_{n} / N \cdot 86400 \) where h are the day timesteps available: 03 UTC, 06 UTC, 09 UTC, 12 UTC, 15 UTC, 18 UTC, 21 UTC and 00 UTC of the day after and The average flux over a year is the sum of the individual fluxes for each day (computed as the sum of 8 | |

ERA5 monthly averaged data | SSR | Monthly means of mean daily fluxes The accumulations in monthly means of daily means have been scaled to have units that include "per day" | Jm^{-2} | Jm^{-2} | N/A | N/A | \( \text{SSR}\ [\text{Wm}^{-2}] = \text{SSR}\ [\text{Jm}^{-2}]\ \cdot \frac{N}{N\cdot 86400}\ [\text{s}] = \frac{\text{SSR}\ [\text{Jm}^{-2}]}{86400\ [\text{s}]} \) where - Multiply by N to obtain total monthly flux from mean daily flux
- Divide by number of seconds in the month
| \( \text{SSR}\ [\text{Wm}^{-2}] = \frac{ \sum_{m = 1}^{12} \text{SSR}_{m}\ [\text{Jm}^{-2}]\ \cdot N_{m}}{D\cdot 86400\ [\text{s}]} \) where N m, and D is the number of days in the year.- Multiply each value by the number of days in the month
- Sum them together
- Divide by number of seconds in the year
| |

ERA5 monthly averaged ensemble data | SSR | Monthly means of mean daily fluxes | Jm^{-2} | Jm^{-2} | N/A | N/A | \( \text{SSR}\ [\text{Wm}^{-2}] = \text{SSR}\ [\text{Jm}^{-2}]\ \cdot \frac{N}{N\cdot 86400}\ [\text{s}] = \frac{\text{SSR}\ [\text{Jm}^{-2}]}{86400\ [\text{s}]} \) where N is the number of days in the month. - Multiply by N to obtain total monthly flux from mean daily flux
- Divide by number of seconds in the month
| \( \text{SSR}\ [\text{Wm}^{-2}] = \frac{\sum_{m = 1}^{12} \text{SSR}_{m}\ [\text{Jm}^{-2}]\ \cdot N_{m}}{D\cdot 86400\ [\text{s}]} \) where N m, and D is the number of days in the year.- Multiply each value by the number of days in the month
- Sum them together
- Divide by number of seconds in the year
| |

ERA5-Land hourly data | SSR | Accumulations are from 00 UTC to the hour ending at the forecast step | Jm^{-2} | Jm^{-2} | \( \text{SSR}\ [\text{Wm}^{-2}] = \left\{ \begin{array}{ll} \frac{\text{SSR}_{h}\ [\text{Jm}^{-2}]}{3600\ [\text{s}]} & h = 01 \text {UTC} \\ \frac{\text{SSR}_{h}\ [\text{Jm}^{-2}]\ -\ \text{SSR}_{h-1}\ [\text{Jm}^{-2}]}{3600\ [\text{s}]} & \text{otherwise} \\ \end{array} \right. \) | \( \text{SSR}\ [\text{Wm}^{-2}] = \frac{\text{SSR}_{d+1\ 00\text{UTC}}\ [\text{Jm}^{-2}]}{86400\ [\text{s}]} \) where The time step labelled | \( \text{SSR}\ [\text{Wm}^{-2}] = \frac{\sum_{d = 1}^{N}\text{SSR}_{d+1\ 00\text{UTC}}\ [\text{Jm}^{-2}]}{N\cdot 86400\ [\text{s}]} \) where The time step labelled | \( \text{SSR}\ [\text{Wm}^{-2}] = \frac{\sum_{d = 1}^{N}\text{SSR}_{d+1\ 00\text{UTC}}\ [\text{Jm}^{-2}]}{N\cdot 86400\ [\text{s}]} \) where The time step labelled | |

ERA5-Land monthly averaged data | SSR | Accumulations are created from data with a forecast period falling within the month. Monthly means of daily means for accumulations are created from the last forecast step (24) of the forecasts for each day of the month. | Jm^{-2} | Jm^{-2} | N/A | N/A | \( \text{SSR}\ [\text{Wm}^{-2}] = \text{SSR}\ [\text{Jm}^{-2}]\ \cdot \frac{N}{N\cdot 86400}\ [\text{s}] = \frac{\text{SSR}\ [\text{Jm}^{-2}]}{86400\ [\text{s}]} \) where - Multiply by
*N*to obtain total monthly flux from mean daily flux - Divide by number of seconds in the month
| \( \text{SSR}\ [\text{Wm}^{-2}] = \frac{ \sum_{m = 1}^{12} \text{SSR}_{m}\ [\text{Jm}^{-2}]\ \cdot N_{m}}{D\cdot 86400\ [\text{s}]} \) where m, and D is the number of days in the year.- Multiply each value by the number of days in the month
- Sum them up
- Divide by number of seconds in the year
| |

Seasonal daily data | SSR | 24 hour aggregation since the beginning of the forecast | Jm^{-2} | Jm^{-2} | N/A |
\( \text{SSR}\ [\text{Wm}^{-2}] = \frac{(\text{SSR}_{t2}\ [\text{Jm}^{-2}] - \text{SSR}_{t1}\ [\text{Jm}^{-2}])}{24*60*60} \)
where t |
\( \text{SSR}\ [\text{Wm}^{-2}] = \frac{(\text{SSR}_{t_2}\ [\text{Jm}^{-2}] - \text{SSR}_{t_1}\ [\text{Jm}^{-2}])}{N*24*60*60} \)
where t | N/A For seasonal forecasts, as data only cover 7 months | |

Seasonal monthly data | SSR | The accumulations in monthly means have units that include " | Wm^{-2} | Wm^{-2} | N/A | N/A | N/A | N/A For seasonal forecasts, as data only cover 7 months |

**Notes**

^{1 }Please,** note that the convention for accumulations used in ERA5-Land differs with that for ERA5**. The accumulations in the short forecasts of ERA5-Land (with hourly steps from 01 to 24) are treated the same as those in ERA-Interim or ERA-Interim/Land, i.e., they are accumulated from the beginning of the forecast to the end of the forecast step. For example, runoff at day=D, step=12 will provide runoff accumulated from day=D, time=0 to day=D, time=12. The maximum accumulation is over 24 hours, i.e., from day=D, time=0 to day=D+1,time=0 (step=24).