Forecasting atmospheric

Human activities have significantly influenced the carbon cycle of the earth
system since industrialization, with the accumulation of greenhouse gases (GHG) in
the atmosphere leading to radiative forcing and climate change
(IPCC, 2014). The carbon exchange between the surface and the
atmosphere still remains largely uncertain due to the complexity of
processes and a lack of observations (Le Quéré et al., 2009).
Therefore, more measurements are needed, especially over emission hotspots
and regions lacking observations. Field campaigns to measure greenhouse
gases, such as research flights and measurements in remote areas, can fill
the observation gap in the troposphere and over regions not covered by
existing networks, but they are often time limited. To make the best use of
these limited measurements, field campaigns require careful planning. An
atmospheric

The research campaign CoMet (Carbon Dioxide and Methane Mission), organized
by the Deutsches Zentrum für Luft- und Raumfahrt (DLR),
made a series of airborne and ground-based measurements of greenhouse gases
in Europe. The campaign took place from 15 May to 12 June 2018, during
which four aircraft participated, including the High Altitude and LOng Range
Research Aircraft (HALO) and three light aircraft. During the campaign, HALO
was equipped with an integrated path differential absorption (IPDA) lidar
(CHARM-F) (Amediek et al., 2017) and carried out nine flights with a
total of 65 flight hours. Continuous online in situ

During the planning of the campaign, a

There are several existing models that can simulate atmospheric

There are many models that can simulate biospheric

The

In our case, we predict

The model VPRM is one of the commonly used surface flux models in
atmospheric

Back to this study, our aim is to investigate the feasibility of using such a data-driven model to predict near-future carbon fluxes. Given the uncertainties in meteorological forecasts, the near-real-time MODIS product and all the necessary extrapolations, it is not clear if such a model can still predict realistic carbon fluxes.

This study describes the development and assessment of a biospheric

Diagram of the VPRM forecasting system. The top two levels show the drivers which are predicted into the future, while the bottom three boxes are based on the standard VPRM model (Mahadevan et al., 2008).

The

This section describes the framework of the VPRM forecasting model for
biospheric

For the meteorological input data, we use hourly ECMWF 5 d forecasts of temperature and shortwave radiation. The EVI and LSWI indices are derived from MODIS surface reflectance data. These provide the indices for an average of the past 8 d, and we forecast these indices for the next 5 d based on linear extrapolation or persistence. We then use these predicted input data to generate NEE using VPRM.

The flux estimation is based on VPRM, a light use efficiency (LUE) model
that calculates GPP with remote sensing data and meteorological data as
inputs. The equation of GPP estimation is as follows:

The

The input of VPRM can be categorized into two groups: remote sensing data
and meteorological data. The remote sensing data consist of EVI and LSWI at
10 km spatial resolution (the same resolution as the atmospheric transport
model), where the EVI and LSWI are aggregated from MODIS surface reflectance
8 d L3 Global 500 m (MOD09A1) version 6 data. It should be noted that in
the forecasting model, the MODIS NRT surface reflectance data (MOD09A1N)
would be used. A locally weighted least-squares (LOESS) filter
(alpha

To use this diagnostic model in a predictive mode, we need to forecast all VPRM input variables 5 d into the future. Remote sensing data and meteorological data are predicted in different ways.

For the meteorological data, forecasts from a numerical weather prediction (NWP) model are needed. In this study, in order to assess the errors brought in by the meteorological forecasting, 5 d forecasts of 2 m temperature and downward shortwave radiation at the surface for each day of the year were used. The meteorological forecast is from the ECMWF operational forecast archive, with class “od” and type “fc”.

As for the remote sensing data, three sources of error had to be considered: the error induced by using the NRT version of the MODIS reflectances rather than the final product, the error of estimating the value of the indices into the future and the effect of the LOESS filter on the end value of the dataset.

We begin by describing the LOESS filter. This filter is usually applied to a full year of data, and when smoothing a truncated dataset there is an edge effect, meaning that when new data are added to the time series and the smoothing is repeated, the output at the former edge point will change slightly. In the following section we define the error caused by such an edge effect as “error due to data truncation”.

Following the filtering, the smoothed data are extrapolated 5 d into the future, either by linear extrapolation or by assuming persistence. The optimal extrapolation method was selected after testing the error contribution of each method.

The last error source comes from the difference between MODIS NRT and the
standard product. The standard product is processed with the best available
ancillary, calibration and geolocation information, while changes have been
made in the NRT processing to expedite the data availability (see

There are uncertainties in the model, in the forecast data as well as in the eddy covariance measurement, and each of these uncertainties has different impact on the final product of the flux forecast. Therefore, before getting into the error quantification and model evaluation, we will briefly discuss their roles in this study.

The uncertainty in the flux measurement has to be considered before being used as the “truth” in the model–data comparison. The uncertainty in flux measurement from eddy covariance tower and its impact on modeling have been well investigated by previous studies. Hollinger and Richardson (2005) attribute the random error in flux measurement to three reasons: the error associated with measurement system, the error associated with turbulence transport and the statistical error relating to footprint heterogeneity. They establish the method for flux measurement error estimation and analyze it on half-hourly timescale. Chevallier et al. (2012) calculate the flux measurement uncertainty on daily timescale based on hourly uncertainty estimation from Lasslop et al. (2008) and conclude that the daily uncertainty is small comparing to the daily NEE magnitude. A similar approach is used in Broquet et al. (2013), where the uncertainty in daily flux measurement is ignored in observation–model comparison. Therefore, in this study, where all comparisons are concerned with daily timescales, uncertainty from flux measurements can be neglected.

Estimating carbon fluxes with the data-driven model VPRM will result in additional uncertainties. These uncertainties are associated with uncertainties in the driving data, the misrepresentation of the LUE approach for vegetation processes and the spatial representation. We treat these uncertainties as an inherent part of the model, since they will exist despite whatever “good” data we are using to drive the model. We define these uncertainties as the VPRM “model error”, which can be quantified by comparing the flux estimation with best driving data available for VPRM to the flux measurement. This model error, as an inherent error in VPRM, is then chosen as a criterion for the evaluation of the forecasting result.

The selected FLUXNET2015 sites used for data–model comparison in this research.

Lastly the error added by the flux forecasting needs to be considered. As described in Sect. 2.1.2, the flux forecast is made by predicting the driving data. Such a prediction has different impact on different variables, thus introducing different uncertainties. For meteorological data, they are from the Integrated Forecasting System (IFS) model of ECMWF, which will contain model error and representation error as any NWP model (Simmons et al., 1995; Simmons and Hollingsworth, 2002). Furthermore, the model error accumulates in weather forecasting, which means the further we predict into the future, the larger the error will be. As for the MODIS data, the use of NRT data and the extrapolation we apply will surely introduce uncertainties. In addition, VPRM applies LOESS filter in the MODIS data processing to reduce noise, which means the data are constrained by the neighboring information. However, when forecasting, the data can only be constrained by the past, leading to another potential error source.

Altogether, the potential error sources of this flux forecasting system are as follows: (1) the VPRM model error (2) using meteorological model data rather than site-level meteorological data; (3) using ECMWF 5 d forecast meteorology, which accumulates extra error to its initial field; (4) using NRT MODIS data; (5) using LOESS filtering to smooth the MODIS data; and (6) the prediction of MODIS data. Error (6) contains two parts: (6a) EVI prediction and (6b) LSWI prediction. In the following discussion we use the numbering (1) to (6) to denote these error sources. The model error (1) defined above is regarded as a criterion for the forecast evaluation. We define (2) to (6) as the “forecast errors”, since they are introduced by the flux forecasting. In this study, we aim to quantify the forecast error and the error contribution from each of the error sources, then evaluate the sum of forecast errors against the model error.

In order to quantify both the model error and the forecast error, a hindcast
using the

The experiment setup and the error sources addressed in each simulation. The numbering in the last column corresponds to the error from (1) the VPRM model, (2) the meteorological analysis, (3) the meteorological forecast, (4) the MODIS NRT data, (5) data truncation and (6) the prediction of MODIS indices.

The surface

To test the error contribution of the model and the 5 d flux forecast,
experiments using the VPRM forecast model were carried out to evaluate the
error contribution from different sources separately, as shown in Table 2. A
control simulation and six experimental simulations (simulations a to f)
were conducted. Although the

The control simulation uses standard VPRM as a reference model with “perfect” input, meaning the MODIS EVI and LSWI standard products as well as shortwave radiation and temperature observed at the flux site. By comparing the modeled NEE to flux measurements, we can estimate the VPRM model error (1).

The experimental simulations (a) to (f) then included the error sources (2) to
(6) in the VPRM model input data separately, and these are compared to the
reference simulation in order to isolate the individual error contributions.
The experiments aim to estimate the upper limit of forecast error, and therefore
in simulations (b) and (f), 96 to 120 h meteorological forecasts, i.e., the
last day (fifth) of a 5 d forecast, were used for each day of the year. For
simulations (d) and (f), since the MODIS EVI and LSWI products have an 8 d
period, MODIS data were first linearly interpolated to a daily scale. Then
for each day of the year, MODIS data on the

There is a challenge in simulation (e) in that there are no archived NRT data for 2014, and thus it is impossible to have a comparison on the same basis as the other simulations. Instead we look at the model's sensitivity of NEE to EVI and LSWI bias, and we also compare the NRT EVI and LSWI, which we archived from February to June in 2018 for 120 d, to the standard MODIS product over the same period. In this way we were able to estimate the magnitude of the NRT indices' error and its impact on the model's output NEE.

In order to make the 33 different site results comparable, the simulation
output NEE was first aggregated to daily averages and then normalized by
the range (i.e., the difference between maximum and minimum) of annual NEE at
each site. The Bias

Example of the data normalization at station BE-Bra:

Normalized mean absolute error (MAE) of NEE for each error source. The compared objects are simulations (a) to (f), the reference simulation (ref.) and FLUXNET observation (obs.). Error sources (1) to (6) described in Sect. 2.2 can be isolated by calculating the MAE between different simulations.

By comparing the NEE output from each experimental simulation, the impact of each error source on flux forecasting can be isolated and evaluated. The normalized mean absolute error (MAE) of NEE at all 33 sites is presented in Table 3. The MAE of the total forecast error is 0.071, which is smaller than the VPRM model error of 0.159. This indicates that the forecast model is reasonably capable of predicting fluxes on diurnal timescales.

Among all forecast errors, the meteorological error accounts for the largest contribution. The meteorological error can be decomposed into (2) analysis error and (3) meteorological forecast error. The former corresponds to using meteorological analysis rather than observational data, while the latter comes from the numerical meteorological forecasting and can be estimated by comparing simulations (b) and (a). The analysis error and meteorological forecast error are of the same order of magnitude, namely 0.046 and 0.065, respectively.

The meteorological error is then analyzed further by dividing it into the
photosynthetic part (Bias

Figure 3a–c share the same

The Bias

This seems to suggest that Bias

The MODIS error consists of three parts: using NRT products, using extrapolated indices and using truncated time series. These are tested in simulations (c), (d) and (e), respectively. In general, the MODIS error is less important than the meteorological error, and the errors due to data truncation, EVI extrapolation and LSWI extrapolation result in errors of similar magnitude: 0.015, 0.013 and 0.010, respectively.

Bias

As described in Sect. 2.1.1, the MODIS input data first need to be smoothed by a LOESS filter to reduce the noise. LOESS performs a local regression on the time series. Because the point at the end of the time series lacks a constraint from future data, it results in an error when the data are truncated. This error source is evaluated in simulation (c), where for each 8 d value, only data before this time are filtered. Thus the only difference between simulation (c) and the reference simulation is whether each MODIS-derived index is constrained by all local data or only constrained by preceding data. Comparing simulation (c) and the reference simulation finds that the error due to lack of constraint from future MODIS data introduces a MAE of 0.015.

For MODIS data extrapolation, different methods were tested in an attempt to minimize forecast error. Climatological values of EVI and LSWI were considered, but they lack the advantage of a data-driven approach for realistic estimation. After testing various alternatives, two simple methods were considered: linear extrapolation based on the last three data points and persistence (assuming the indices stay the same for the next 5 d). Figure 5 shows the NEE bias distribution by using linear extrapolation or persistence to predict EVI and LSWI. For both indices, using the assumption of persistence results in a smaller error. The biases for the two extrapolation methods have similar distributions, but there are more outliers for linear extrapolation. This is due to the fact that linear extrapolation results in larger errors when the data are fluctuating.

Finally, the difference between using MODIS NRT data and standard data has
to be considered. This includes the effect of using different attitude and
ephemeris data in processing, as well as using different ancillary data
products for the Level 2 processing. For L2 Land Surface Reflectance data,
National Oceanic and Atmospheric Administration Global Forecast System (GFS)
ancillary product are used instead of the Global Data Assimilation System
(GDAS) products used in the standard processing – this is described at NASA's
Land, Atmosphere Near real-time Capability for EOS (LANCE) website

The normalized error of NEE as a result of MODIS NRT error
at 33 sites. Overall, 120 d from February to June in the year 2018 of MODIS NRT
data are used to first calculate the EVI/LSWI differences, then multiplied by the
sensitivities in Table 4 and normalized by the same scalar in the previous
research. The flux sites in

This presented a challenge, as no MODIS NRT data were archived for the test year 2014. Thus it was impossible to carry out a similar error evaluation as was done for other error sources. Therefore, we first use NRT EVI and LSWI that we archived for 120 d from February to June 2018 to calculate the MAE of the two indices to standard products at all flux sites. The MAE of NRT EVI and LSWI for all sites are 0.018 and 0.026, respectively. Considering the mean EVI and LSWI, which are 0.21 and 0.11 during this period, the magnitude of NRT EVI error is less than 10 % of EVI's magnitude, while the number is 24 % for the magnitude of NRT LSWI error.

The impact of the errors in these NRT indices on the model is determined by the model's sensitivity to EVI and LSWI. To investigate this sensitivity, we use the result from simulation (d) and the reference simulation, and we look at the difference in input EVI and LSWI and the corresponding difference in output NEE. The model's sensitivity is different during the growing and the non-growing seasons, as in the non-growing season there would be no vegetation production anyway from a slight change of EVI and LSWI.

The model's sensitivity of NEE to EVI/LSWI for four
seasons. The result of simulation (d) is used in the sensitivity calculation.
Linear regression is applied to the change in EVI and the change in
corresponding NEE, the maximum sensitivity appears in summer, with a slope
of

Therefore, the model sensitivity is analyzed for each season separately, as
shown in Table 4. Difference in indices and the corresponding difference in
daily NEE are applied with linear regression, and the rate of the linear
function is regarded as model sensitivity. The maximum sensitivity for both
EVI and LSWI is in summer, with

The Bias

Mean absolute error of the forecast error compared to the VPRM model error at each flux observation site. The model error (1) is generally larger than the total forecast error (2) to (6), and the forecast error does not differ significantly across vegetation types. The order of the flux site is the same as in Fig. 6.

Unlike the forecast error discussed above, the Bias

Mean absolute error for different error sources at each
flux observation site. The meteorological error (2, meteorological model,

The MAE is also calculated at each flux measurement site and clustered according to vegetation types, as shown in Fig. 8. Generally the VPRM model error (grey) is larger or similar to the forecast error (blue), consistent with Table 3. Moreover the forecast error does not differ significantly over different vegetation types. Figure 9 shows the error contribution from each source; the meteorological error (error 2 in dark blue and error 3 in light blue) is the dominant contributor at each site and has a similar contribution for different vegetation types. The data truncation error (4) has a stronger influence on some grass sites, because EVI at these sites is highly variable, possibly due to mowing and regrowing during the growing season. Overall, except for the data truncation error, all forecast error sources have a similar impact on each flux observation site. This shows that the forecast ability does not vary over different vegetation types.

The forecast errors are also tested on the European domain from March to June (the season over which the CoMet campaign took place) in 2014, to analyze its spatial patterns. Three experiments have been done to represent the meteorological error (including analysis error and meteorological forecast error), the MODIS error (including extrapolation error and data truncation error) and the total forecast error (a combination of meteorological error and MODIS error). Figure 10 shows the mean VPRM NEE during the period and the corresponding spatial distribution of each error (in MAE).

By comparing Fig. 10a and b, it can be seen that the MAE of the total forecast error has a strong spatial relationship with the mean NEE, which indicates that the forecast error has a similar impact in all places. On a spatial level, the meteorological component still dominates compared to the MODIS error.

In the context of atmospheric

Monthly carbon budget from March to June for original and forecast model for the European domain. The overall forecast flux budget is close to the original model, indicating the forecast flux model is appropriate for use in the GHG concentration forecasting system.

The flux budget over the European domain was also calculated and is shown in Fig. 11. The carbon budget of the flux forecast model (in dark blue) is
close to the original VPRM model (in grey); thus we are able to confidently
use this flux forecast model in the atmospheric GHG concentration
forecasting system and predict reasonable

As mentioned in the introduction, we are aiming for not only a flux forecast but finally an atmospheric GHG concentration forecasting system. While this study has quantified how each error source affects the predicted biospheric fluxes, the next step is to use such predicted fluxes in an atmospheric transport model run in forecast mode and to assess the prediction error from each source in concentration space.

Based on the VPRM model, we developed a forecasting model that can predict
biospheric NEE for the next 5 d and assess the error contribution
from each aspect of forecasting. This

The code for forecast VPRM model and the model outputs are available from

The experiments were planned by CG, JM, KUT and JC. CG prepared the standard VPRM model. JC made the forecast model and performed the model simulation and assessment. JM extensively commented and revised the paper. JC prepared the paper with contribution from all coauthors.

The authors declare that they have no conflict of interest.

We acknowledge the use of data products from the Land, Atmosphere Near real-time Capability for EOS (LANCE) system operated by NASA's Earth Science Data and Information System (ESDIS) with funding provided by NASA Headquarters. We acknowledge ECMWF for providing access to the ECMWF's archived data. This work used eddy covariance data acquired and shared by the FLUXNET community, including these networks: AmeriFlux, AfriFlux, AsiaFlux, CarboAfrica, CarboEuropeIP, CarboItaly, CarboMont, ChinaFlux, Fluxnet-Canada, GreenGrass, ICOS, KoFlux, LBA, NECC, OzFlux-TERN, TCOS-Siberia and USCCC. The ERA-Interim reanalysis data are provided by ECMWF and processed by LSCE. The FLUXNET eddy covariance data processing and harmonization was carried out by the European Fluxes Database Cluster, AmeriFlux Management Project and Fluxdata project of FLUXNET, with the support of CDIAC and ICOS Ecosystem Thematic Center as well as the OzFlux, ChinaFlux and AsiaFlux offices.

The research is funded by the MPG (Max Planck Society) through the CoMet campaign and by the BMBF (German Federal Ministry of Education and Research) through AIRSPACE (FK 01LK1701C). Jinxuan Chen is funded by a PhD project from IMPRS-gBGC (the International Max Planck Research School for Global Biogeochemical Cycles). The article processing charges for this open-access publication were covered by the Max Planck Society.

This paper was edited by Tomomichi Kato and reviewed by two anonymous referees.