# Conversion table for accumulated variables (total precipitation/fluxes)

## 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

DatasetVariablesWhat it isGrib unitsNetcdf UnitsTo 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 precipitationAccumulations are over the hour (the processing period) ending at the validity date/timem (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 N is the number of days in the month.

$$\text{tp}\ [\text{mm}] = \sum_{n = 1}^{N} \left( \sum_{h = 1}^{23}\text{tp}_{h}\ [\text{m}] + \text{tp}_{d+1\ 00\text{UTC}}\ [\text{m}] \right)_{n} \cdot 1000$$

where N is the number of days in the year.
ERA5 ensemble members (3 hourly data)Total precipitationAccumulations are over the 3 hours (the processing period) ending at the validity date/timem (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 3-hour total precipitation values.

$$\text{tp}\ [\text{mm}] = \sum_{n = 1}^{N} \left(\sum_{h} \text{tp}_{h}[\text{m}] \right)_{n} \cdot 1000$$

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 N is the number of days in the month.

$$\text{tp}\ [\text{mm}] = \sum_{n = 1}^{N} \left(\sum_{h} \text{tp}_{h}[\text{m}] \right)_{n} \cdot 1000$$

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 N is the number of days in the year.

ERA5 monthly averaged reanalysis
Total precipitationThe 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/AN/A

$$\text{tp}\ [\text{mm}] = \text{tp}\ [\text{m/day}] \cdot 1000 \cdot N$$

where N is the number of days in the month.

$$\text{tp}\ [\text{mm}] = \sum_{n = 1}^{12}(\text{tp}\ [\text{m/day}] \cdot 1000 \cdot N)_{\text{n}}$$

where N is the number of days in the month and n is the number of the month.

ERA5 monthly averaged ensemble members
Total precipitationThe 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/AN/A

$$\text{tp}\ [\text{mm}] = \text{tp}\ [\text{m/day}] \cdot 1000 \cdot N$$

where N is the number of days in the month.

$$\text{tp}\ [\text{mm}] = \sum_{n = 1}^{12}(\text{tp}\ [\text{m/day}] \cdot 1000 \cdot N)_{\text{n}}$$

where N is the number of days in the month and n is the number of the month.

ERA5-Land hourly dataTotal precipitation

Accumulations are from 00 UTC to the hour ending at the forecast step 1

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 d is the day for which the total precipitation is being computed.

The time step labelled d+1 00UTC should also be taken because it contains the accumulated total precipitation over the previous 24 hours.

$$\text{tp}\ [\text{mm}] = \left( \sum_{n = 1}^{N}\text{tp}_{d+1\ 00\text{UTC},n}\ [\text{m}] \right)\cdot 1000$$

where d is the day for which the total precipitation is being computed and N is the number of days in the month.

The time step labelled d+1 00UTC should also be taken because it contains the accumulated total precipitation over the previous 24 hours. This implies that the sum goes from the 2nd of the month to the 1st of the next month (inclusive).

$$\text{tp}\ [\text{mm}] = \left( \sum_{n = 1}^{N}\text{tp}_{d+1\ 00\text{UTC},n}\ [\text{m}] \right) \cdot 1000$$

where d is the day for which the total precipitation is being computed and N is the number of days in the year.

The time step labelled d+1 00UTC because it contains the accumulated total precipitation over the previous 24 hours. This implies that the sum goes from 2nd January of the year to 1st January of the next year (inclusive).

ERA5-Land monthly averaged dataTotal 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/AN/A

$$\text{tp}\ [\text{mm}] = \text{tp}\ [\text{m/day}] \cdot 1000 \cdot N$$

where N is the number of days in the month.

$$\text{tp}\ [\text{mm}] = \sum_{n = 1}^{12}(\text{tp}\ [\text{m/day}] \cdot 1000 \cdot N)_{\text{n}}$$

where N is the number of days in the month and n is the number of the month.

Seasonal daily dataTotal precipitation24 hour aggregation since the beginning of the forecastmm

$$\text{tp}\ [\text{mm/hr}] = \frac{(\text{tp}_{t2}\ [\text{m}] - \text{tp}_{t1}\ [\text{m}])\cdot 1000}{24}$$

where t2 is the day of interest, t1 is the day before t2, tpt2 is the total precipitation at t2, and tpt1 is the total precipitation at t1.

$$\text{tp}\ [\text{mm}] = (\text{tp}_{t2}\ [\text{m}] - \text{tp}_{t1}\ [\text{m}])\cdot 1000$$

where t2 is the day of interest, t1 is the day before t2, tpt2 is the total precipitation at t2, and tpt1 is the total precipitation at t1.

$$\text{tp}\ [\text{mm}] = (\text{tp}_{t_2}\ [\text{m}] - \text{tp}_{t_1}\ [\text{m}])\cdot 1000$$

where t2 is the 1st day of the month after the month of interest, t1= is the 1st day of month before t2,  tpt2= is the total precipitation at t2, and tpt1 is the  total precipitation at t1.

N/A For seasonal forecasts, as data only cover 7 months
Seasonal Monthly dataTotal precipitation

The accumulations in monthly means have units that include "per second".

m/sm/sN/AN/A

$$\text{tp}\ [\text{mm}] = \text{tp}_{t1}\ [\text{m}]\cdot 1000$$

where t1 is the month of interest, N1 is the number of days in t1, and tpt1 is the result of (total precipitation at t1 * N1 * 24 * 60 * 60).

N/A For seasonal forecasts, as data only cover 7 months

ERA-Interim sub-daily data

Total precipitationAccumulations are from the beginning of the forecastm (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 12 has to be selected from time reference 00UTC  plus the time step labelled 12 selected from time reference 12UTC because they contain the accumulated total precipitation over the 24 hours for each day.

$$\text{tp}\ [\text{mm}] = \sum_{d = 1}^{N}(\text{tp}_{12\ 00\text{UTC}}\ + \text{tp}_{12\ 12\text{UTC}}\ [\text{m}])_{d} \cdot 1000$$

where d is the day for which the total precipitation is being computed and N is the number of days in the month.

$$\text{tp}\ [\text{mm}] = \sum_{d = 1}^{N}(\text{tp}_{12\ 00\text{UTC}}\ + \text{tp}_{12\ 12\text{UTC}}\ [\text{m}])_{d} \cdot 1000$$

where d is the day for which the total precipitation is being computed and N is the number of days in the year.

### Energy and momentum fluxes table

DatasetVariablesWhat it isGrib unitsNetcdf Units

To get the average energy flux (Wm-2)

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

Accumulations are over the hour (the processing period) ending at the forecast step

Jm-2

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 N is the number of days in the month.

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 N is the number of days in the year.

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 stepJm-2Jm-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 3-hour fluxes divided by the number of seconds in a day.

$$\text{SSR}\ [\text{Wm}^{-2}] = \sum_{n = 1}^{N} \left( \sum_{h} \text{SSR}_{h} [\text{Jm}^{-2}] + \text{SSR}_{d+1 00\text{UTC}}\ [\text{Jm}^{-2}] \right)_{n} / N \cdot 86400$$

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 n is the number of days in the month.

The average flux over a month is the sum of the individual fluxes for each day (computed as the sum of 8 3-hour fluxes) divided by the number of seconds in the month.

$$\text{SSR}\ [\text{Wm}^{-2}] = \sum_{n = 1}^{N}\left( \sum_{h} \text{SSR}_{h} \right)_{n} / N \cdot 86400$$

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 N is the number of days in the year.

The average flux over a year is the sum of the individual fluxes for each day (computed as the sum of 8 3-hour fluxes) divided by the number of seconds in the year.

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-2Jm-2N/AN/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.

1. Multiply by N to obtain total monthly flux from mean daily flux
2. 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 is the number of days in the month m, and D is the number of days in the year.

1. Multiply each value by the number of days in the month
2. Sum them together
3. Divide by number of seconds in the year

ERA5 monthly averaged ensemble dataSSR

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-2Jm-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.

1. Multiply by N to obtain total monthly flux from mean daily flux
2. 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 is the number of days in the month m, and D is the number of days in the year.

1. Multiply each value by the number of days in the month
2. Sum them together
3. Divide by number of seconds in the year

SSR

Accumulations are from 00 UTC to the hour ending at the forecast step1

Jm-2Jm-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 d is the day for which the average flux is being computed.

The time step labelled d+1 00UTC is selected because it contains the accumulated flux over the previous 24 hours.

$$\text{SSR}\ [\text{Wm}^{-2}] = \frac{\sum_{d = 1}^{N}\text{SSR}_{d+1\ 00\text{UTC}}\ [\text{Jm}^{-2}]}{N\cdot 86400\ [\text{s}]}$$

where d is the day for which the average flux is being computed and N is the number of days in the month.

The time step labelled d+1 00UTC because it contains the accumulated flux over the previous 24 hours. This implies that the sum goes from the 2nd of the month to the 1st of the next month, inclusive.

$$\text{SSR}\ [\text{Wm}^{-2}] = \frac{\sum_{d = 1}^{N}\text{SSR}_{d+1\ 00\text{UTC}}\ [\text{Jm}^{-2}]}{N\cdot 86400\ [\text{s}]}$$

where d is the day for which the average flux is being computed and N is the number of days in the year.

The time step labelled d+1 00UTC because it contains the accumulated flux over the previous 24 hours. This implies that the sum goes from 2nd January of the year to 1st January of the next year, inclusive.

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.

The accumulations in monthly means of daily means have been scaled to have units that include "per day"

Jm-2Jm-2N/AN/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.

1. Multiply by N to obtain total monthly flux from mean daily flux
2. 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 Nm is the number of days in the month m, and D is the number of days in the year.

1. Multiply each value by the number of days in the month
2. Sum them up
3. Divide by number of seconds in the year

Seasonal daily dataSSR24 hour aggregation since the beginning of the forecastJm-2Jm-2N/A

$$\text{SSR}\ [\text{Wm}^{-2}] = \frac{(\text{SSR}_{t2}\ [\text{Jm}^{-2}] - \text{SSR}_{t1}\ [\text{Jm}^{-2}])}{24*60*60}$$

where t2 is the day of interest, t1 is the day before t2, SSRt2 is the SSR at t2, and SSRt1 is the SSR at t1

$$\text{SSR}\ [\text{Wm}^{-2}] = \frac{(\text{SSR}_{t_2}\ [\text{Jm}^{-2}] - \text{SSR}_{t_1}\ [\text{Jm}^{-2}])}{N*24*60*60}$$

where t2 is the 1st day of month after the month of interest, t1 is 1st day of month before t2, N is number of days in month of interest, SSRt2 is the SSR at t2, and SSRt1= is the SSR at t1.

N/A For seasonal forecasts, as data only cover 7 months
Seasonal monthly dataSSR

The accumulations in monthly means have units that include "per second".

Wm-2Wm-2N/AN/AN/AN/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).

This document has been produced in the context of the Copernicus Climate Change Service (C3S).

The activities leading to these results have been contracted by the European Centre for Medium-Range Weather Forecasts, operator of C3S on behalf of the European Union (Delegation Agreement signed on 11/11/2014 and Contribution Agreement signed on 22/07/2021). All information in this document is provided "as is" and no guarantee or warranty is given that the information is fit for any particular purpose.

The users thereof use the information at their sole risk and liability. For the avoidance of all doubt , the European Commission and the European Centre for Medium - Range Weather Forecasts have no liability in respect of this document, which is merely representing the author's view.

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