# Modeling Gross Primary Production of Agro-Forestry Ecosystems by Assimilation of Satellite-Derived Information in a Process-Based Model

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## Abstract

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## 1. Introduction

- determine the ecophysiological parameters exploiting site level EC measurements;
- determine the spatially variable parameters necessary for modeling poplar productivity over large areas through assimilation of RS data into the optimized BIOME-BGC.

- a modified version of BIOME-BGC (named PROSAILH-BGC) which was developed by coupling BIOME-BGC with the vegetation radiative transfer models PROSPECT and SAILH. The aims of this coupling were twofold: i) to improve the description of the radiative transfer regime within the canopy and ii) to allow assimilation of remotely-sensed vegetation indexes time series, such as MODIS NDVI, into the process-based model.
- an inverse modeling approach developed for the optimization of the key [25] ecophysiological parameters of the PROSAILH-BGC. In this first-step optimization, model parameters were optimized for poplar plantations by inverting the model against EC data measured at the experimental field site.
- a technique developed for assimilation of MODIS NDVI data into the process model. For this purpose we inverted the PROSAILH-BGC against the MODIS NDVI (second-step optimization) in order to retrieve key drivers [25] of modeled GPP (e.g. start and end of growing season, maximum leaf carbon during the year).
- the evaluation of model accuracy: daily and yearly GPP modeled after two-step optimization were compared to site observations.

## 2. Data

#### 2.1. Experimental Field Site Information

^{-1}per year [27]. The soil texture is sandy-loam (60.4% sand, 30% silt and 9.6% clay). The nitrogen and carbon content of the soil, measured to a depth of 100 cm, are 1.36 kgN m

^{-2}and 5.23 kgC m

^{-2}, respectively.

^{-1}. Mean tree height, mean diameter at breast height (DBH) and the stem basal area, measured in 2005, were 26.3 (± 4.5) m (n = 8), 32.9 (± 5.7) cm (n = 266) and 20.45 m

^{2}ha

^{-1}, respectively. The leaf area index (LAI) was measured during the growing season every two weeks with LAI-2000 PCA plant canopy analyzer (LI-COR Inc., Lincoln NE, USA) as described in [28]. The LAI showed a seasonal variability with a maximum value of about 2.0 m

^{2}m

^{-2}reached generally in July. The mean specific leaf area (SLA) of poplar leaves was 12.3 (± 1.8) m

^{2}kgC

^{-1}. SLA was estimated by extracting a known sub-area from the leaves collected during the growing season. Three leaves, at two different canopy levels (bottom and top), from three plants around the flux tower and from three plants located in the nearby stand were sampled. The leaves were collected every month from May to August for a total of five sampling dates.

#### 2.2. Micrometeorological Data

_{2}fluxes were corrected and filtered following [30] in order to assess the quality of measured data and to discard the half-hourly data not fulfilling the hypothesis necessary for the application of the EC technique (i.e. steady state and integral turbulence characteristics of the vertical wind [31]). Data were corrected for storage of CO

_{2}in the air layer below the measuring height [32]. Missing half-hourly data caused by malfunctioning of system, periodical calibration of instruments, u* filtering or data quality check not fulfilled, were filled with the marginal distribution sampling method [33].

_{2}(NEE). Half-hourly GPP can be estimated from NEE via the general equation:

_{eco}), was estimated using the partitioning method described in [33]. Both the MDS and the partitioning algorithm were implemented in an online tool [33], widely employed by the Carboeurope-IP project and FLUXNET network for both gap-filling and partitioning [34,35] of fluxes.

_{t}) was measured by means of a transect of 3 quantum sensors (LI-190S, LI-COR Inc., Lincoln NE, USA) and used to investigate the radiative regime within the canopy. All meteorological data were stored as half-hourly means on a data logger (DL2 DELTA-T Devices, Burwell, Cambridge, UK).

#### 2.3. Remotely Sensed Data

_{MODIS}) were affected by errors related to the presence of cloudy sky conditions over the compositing period. In order to reduce this influence and to reconstruct high-quality vegetation index time series, the original MODIS NDVI time series were processed following the method proposed by [36], which is based on the recursive application of a Savitzky-Golay filter [37]. The smoothed MODIS NDVI time series of the studied poplar plantation were then extracted as the average of the three pixels within the experimental field.

## 3. Methods

#### 3.1. BIOME-BGC Description

^{-2}day

^{-1}) was modeled as the net accumulation or loss of carbon by the entire soil-stand system and was determined by the differences between GPP (kgC m

^{-2}day

^{-1}), resulting from the processes of photosynthesis, and R

_{eco}(kgC m

^{-2}day

^{-1}), resulting from the respiration processes. The LAI (m

^{2}m

^{-2}) is a key variable of BIOME-BGC controlling canopy radiation absorption, water interception, photosynthesis and litter input to detrital pools [40].

_{leaf}), carbon allocation parameter (e.g. new fine root to new leaf carbon, FR:LC), maximum stomatal conductance (g

_{c,MAX}), canopy water interception, light extinction coefficients and SLA.

_{MAX}and maximum stem carbon) and initial soil carbon in the different soil pools. The model also requires the bud-burst date (ONDAY), in which the growing season starts, and the day of the end of growing season (OFFDAY). These phenological parameters strongly influence the seasonal pattern and magnitude of simulated carbon fluxes [25].

#### 3.2. PROSAILH-BGC Description

_{t}, PAR absorbed by the canopy and site albedo. These variables are then forced into the BIOME-BGC and used for daily simulations.

_{PROSAILH-BGC}), which is computed using simulated canopy spectral reflectance taking into account MODIS spectral characteristics and sun-sensor geometry.

## 3.3. Basic Model Parameterization

_{MAX}and first-year maximum stem carbon) were obtained from a specific stand characterization conducted during the years 2002 and 2003. We avoided the “spin up and go” mode, which initializes site characteristics and finds an internal equilibrium (i.e. steady-state) of the model state variables [25], because poplar plantations are typical managed and disturbed ecosystems far from the steady-state. With the exception of SLA, which was measured on site, all the ecophysiological parameters required by BIOME-BGC were derived from literature [10,25,45,46] and are reported in Appendix I.

#### 3.4. PROSAILH-BGC Optimization

_{i}and mod

_{i}indicate the i

^{th}observed and i

^{th}modeled daily data, respectively. mod is a function of the parameter vector θ.

- In the first step the model was optimized against GPP observations to estimate the ecophysiological parameters (Figure 2) for poplars for a further large-scale application. The target variables selected for optimization were C:N
_{Leaf}, the percentage of leaf nitrogen in RUBISCO (PLNR), FRC:LC and g_{s,MAX}. We selected these parameters because they exert a significant influence on the modeled carbon fluxes, as pointed out by the sensitivity analysis described in [25]. In this step phenological observations (ONDAY, OFFDAY) and LC_{MAX}were fixed to the observed values.Model ecophysiological parameters and their relative standard errors were estimated by using a bootstrapping algorithm with N = 500 resampling as described in [49]. The median of the distribution generated by bootstrapping for each parameter represents the estimated parameter value, while the standard deviation is a good measure of the error associated with the parameters. - In the second step we estimated phenological and standing biomass related parameters by inverting the model against remotely sensed NDVI time series. The algorithm determines ONDAY, OFFDAY and LC
_{MAX}which minimize the cost function calculated using NDVI_{MODIS}as observation and the NDVI_{PROSAILH-BGC}as modeled data (Figure 3). These parameters were chosen because of their importance for the model application at spatial scale. In fact, process-based models, and in particular BIOME-BGC, are sensitive to parameters describing the development of the canopy such as phenological data and parameters related to maximum LAI [25]. Thus, in this step we evaluate the accuracy of the proposed method in retrieving these important data, usually lacking over large areas.

#### 3.5. Evaluation of Model Accuracy

^{2}of the linear regression observed vs modeled were also used for the evaluation of model accuracy.

_{MAX}with the observed ones. Finally, we evaluated the error in the annual GPP budget introduced using the proposed method and the BIOME-BGC internal phenological routine. As an overall evaluation of the proposed method, the observed GPP and the GPP modeled with PROSAILH-BGC optimized in the first step and using the phenological dates and the LC

_{MAX}derived from the second step were compared.

## 4. Results and Discussion

#### 4.1. Radiative Regime Description of PROSAILH-BGC

_{t}with the two models. Results showed a reduction in the bias of PAR

_{t}using the PROSAILH-BGC (Figure 4). In fact, although the r

^{2}did not improve using PROSAILH-BGC, PAR

_{t}simulated with the coupled model was closer to the 1:1 line than the PAR

_{t}modeled by BIOME-BGC, thus leading to a reduction in RMSE between modeled and observed data (from 144.9 μmol m

^{-2}s

^{-1}to 111.2 μmol m

^{-2}s

^{-1}).

#### 4.2. First-step Optimization - PROSAILH-BGC Eecophysiological Parameter Estimates

_{opt}) showed considerable differences with respect to the original literature-based parameterization (used for Reference Models 1 and 2). In particular, FRC:LC showed a sensible increase (from 0.333 to 1.969). This optimized value is consistent with values published for broadleaved species ([25] (with values from 0.54 to 1.59 found) and for other poplar species ([10] (for which a value of 1.2 was reported). This may therefore indicate that the original ecophysiological parameterization based on the works of [10,25,45,46] was unsuited for the investigated poplar species.

^{-2}day

^{-1}), between the optimized values and the Reference Model 2. Cumulated yearly GPP for 2002 simulated with the optimized model was 1546 gC m

^{-2}year

^{-1}, with good agreement with the measured data of 1578 gC m

^{-2}year

^{-1}. Conversely, GPP simulated by PROSAILH-BGC with the original parameterization was 1362 gC m

^{-2}year

^{-1}, while yearly GPP simulated with the Reference Model 2 (i.e. literature ecophysiological parameterization and phenology derived from site observations) was 1330 gC m

^{-2}year

^{-1}, with an underestimation of about 248 gC m

^{-2}year

^{-1}.

^{2}= 0.78 for both the models), the RMSE decreased from 1.81 gC m

^{-2}day

^{-1}to 1.41 gC m

^{-2}day

^{-1}and EF increased from 0.67 to 0.76 as a consequence of the optimization. This improvement in model accuracy underscores that the main effect introduced by the optimized parameters was the reduction of the bias with a reduction of the systematic underestimation of the model. Conversely, the correlation between observations and modeled data did not improve when using the optimized parameterization because the daily variability of simulated fluxes is mainly driven by meteorological data.

#### 4.3. Second-Step Optimization - Phenological and Standing Biomass Parameter Estimates

_{PROSAILH}explained about 75% of NDVI

_{MODIS}variance and showed good agreement between observed and modeled data (Figure 5b). For low NDVI values an underestimation of modeled NDVI was observed.

_{MAX}estimated with second-step optimization for 2002 and 2003 showed good agreement with the values observed at the experimental site (Table 3).

_{MAX}values were estimated with good accuracy (mean error = 4.1%) as shown in Table 3.

_{MODIS}signal, particularly noteworthy in the period immediately before the beginning and after the end of the growing season as shown in Figure 5a. However, these discrepancies between observed and modeled phenological dates are similar to those reported in others studies [52].

_{PROSAILH-BGC 1-step}); in fact, underestimation of the cumulated annual GPP was -10.4% for 2002 and -11.8% for 2003. The yearly GPP estimated after two-step optimization (GPP

_{PROSAILH-BGC 2-step}) showed good accuracy with an underestimation of 1.8% and 5.6% for 2002 and 2003, respectively. These results underline the importance of the phenological parameters in determining the annual GPP budget. Obviously, for application at regional scale, the parameterization of the model with the observed phenology is not operatively feasible. Hence, the proposed method may be considered an important option for determining these parameters.

## 5. Summary and Conclusions

^{2}= 0.75) and key phenological dates were retrieved with far better accuracy than the ones modeled by the internal phenological model: ONDAY and OFFDAY were determined with a mean error of 6 and 7 days, respectively, while with the internal phenological model the mean error was 17 days for ONDAY and 20 days for OFFDAY. The error in the dates estimated with second-step optimization may be due to the development of a green understory which affected the NDVI signal immediately before tree bud-burst and persisted after overstory leaf senescence. In the same computational step, maximum leaf carbon was also retrieved with an average error of 4.1%.

^{2}= 0.72, EF = 0.70, RMSE = 1. 80 gCm

^{-2}day

^{-1}) and yearly time steps. In particular, for the annual cumulated GPP we found a sensible reduction in the underestimation of modeled GPP after the two-step optimization compared to the results obtained using Reference Model 1, Reference Model 2 and also using the first-step optimized PROSAILH-BGC with phenology determined by the internal routine.

## Acknowledgments

## Appendix I

ECOPHYSIOLOGICAL PARAMETERS - Clone I-214 (Populus x canadensis Moench) | ||
---|---|---|

78 | (yday) | yearday to start new growth (when phenology flag = 0) |

315 | (yday) | yearday to end litterfall (when phenology flag = 0) |

0.12 | (prop.) | transfer growth period as fraction of growing season |

0.38 | (prop.) | litterfall as fraction of growing season |

1.0 | (1/yr) | annual leaf and fine root turnover fraction |

0.70 | (1/yr) | annual live wood turnover fraction |

0.008 | (1/yr) | annual whole-plant mortality fraction |

0.0 | (1/yr) | annual fire mortality fraction |

1.2 | (ratio) | (ALLOCATION) new fine root C: new leaf C |

2.2 | (ratio) | (ALLOCATION) new stem C: new leaf C |

0.16 | (ratio) | (ALLOCATION) new live wood C: new total wood C |

0.22 | (ratio) | (ALLOCATION) new croot C: new stem C |

0.5 | (prop.) | (ALLOCATION) current growth proportio |

25.06 | (kgC/kgN) | C:N of leaves |

55.0 | (kgC/kgN) | C:N of leaf litter, after retranslocation |

42.0 | (kgC/kgN) | C:N of fine roots |

50.0 | (kgC/kgN) | C:N of live wood |

550.0 | (kgC/kgN) | C:N of dead wood |

0.38 | (DIM) | leaf litter labile proportion |

0.44 | (DIM) | leaf litter cellulose proportion |

0.18 | (DIM) | leaf litter lignin proportion |

0.34 | (DIM) | fine root labile proportion |

0.44 | (DIM) | fine root cellulose proportion |

0.22 | (DIM) | fine root lignin proportion |

0.77 | (DIM) | dead wood cellulose proportion |

0.23 | (DIM) | dead wood lignin proportion |

0.041 | (1/LAI/d) | canopy water interception coefficient |

0.54 | (DIM) | canopy light extinction coefficient |

2.0 | (DIM) | all-sided to projected leaf area ratio |

12.30 | (m2/kgC) | canopy average specific leaf area (projected area basis) |

2.0 | (DIM) | ratio of shaded SLA:sunlit SLA |

0.038 | (DIM) | fraction of leaf N in Rubisco |

0.006 | (m/s) | maximum stomatal conductance (projected area basis) |

6E-5 | (m/s) | cuticular conductance (projected area basis) |

0.01 | (m/s) | boundary layer conductance (projected area basis) |

-0.34 | (MPa) | leaf water potential: start of conductance reduction |

-2.2 | (MPa) | leaf water potential: complete conductance reduction |

1100.0 | (Pa) | vapor pressure deficit: start of conductance reduction |

3600.0 | (Pa) | vapor pressure deficit: complete conductance reduction |

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**Figure 1.**Flow chart of the PROSAILH-BGC model. Yellow blocks represent the models, parallelepipeds represent the input parameters, grey boxes represent the state variables passed between the coupled models, while the red boxes are the model outputs (NDVI and GPP).

**Figure 2.**Flow chart of first-step optimization. Yellow blocks represent the models, parallelepipeds represent the model input parameters and the data for model optimization, grey boxes represent the state variables passed between coupled models while the red box is the model output.

**Figure 3.**Flow chart of second-step optimization. Yellow blocks represent the models, parallelepipeds represent the model input parameters and the data for model optimization, grey boxes represent the state variables passed between coupled models while the red box is the model output.

**Figure 4.**Relationship between modeled and observed PAR

_{t}. Red circles represent data modeled with BIOME-BGC while white circles represent data modeled with PROSAIL-BGC. Dashed lines represent the 95% confidence intervals of the linear regression between PAR

_{t}modeled (with BIOME-BGC in red and PROSAIL-BGC in black) and observed data. Grey line is the 1:1 line. b[0] is the intercept, blsqb;1] is the slope and p is the significance of the linear regression analysis.

**Figure 5.**a) Time series of NDVI

_{MODIS}(full circles) and NDVI

_{PROSAILH-BGC}(open circles) for the time period 2002-2003. b) Scatterplot of NDVI

_{MODIS}and NDVI

_{PROSAILH-BGC}. Black triangles are the NDVI data for the growing season (for the days between ONDAY and OFFDAY) while open triangles are data for the dormant period. The black straight line is the regression line calculated on the whole dataset, the dashed lines represent the 95 confidence intervals, the grey line is the 1:1 line. b[0rsqb; is the intercept, blsqb;1rsqb; is the slope and p is the significance of the linear regression analysis observed vs modeled.

**Figure 6.**a) Time courses of modeled (red straight line) and observed (blue dotted line) GPP for 2002 and 2003. b) Scatterplot of observed and modeled GPP, data from both the growing seasons were plotted with exclusion of data of the dormant period. The black straight line is the regression line, the dashed lines represent the 95 confidence intervals, the grey line is the 1:1 line. blsqb;0rsqb; is the intercept, blsqb;1rsqb; is the slope and p is the significance of the linear regression analysis observed vs modeled.

**Table 1.**Parameterization of PROSAILH: leaf structure parameter (N), chlorophyll a+b concentration (C

_{AB}), leaf water content (C

_{w}), dry matter content (C

_{M}), Leaf Area Index (LAI) mean leaf inclination angle (θ

_{L}), hot spot size parameters (S

_{L}), the background brightness factor (α

_{S}). LAI is variable because it is estimated daily by BIOME-BGC.

PROSAIL Parameters | Values | |
---|---|---|

N | - | 1.37 |

C_{AB} | μg cm^{-2} | 45 |

C_{w} | g cm^{-2} | 0.0092 |

C_{M} | g cm^{-2} | 0.0065 |

LAI | m^{2} m^{-2} | variable |

θ_{L} | deg | 56.5 |

S_{L} | - | 0.005 |

α_{s} | - | 1 |

**Table 2.**Original (θ

_{or}) and optimized (θ

_{opt}) parameters of the PROSAILH-BGC model. Standard errors of parameter estimates, calculated with the bootstrap algorithm, are shown in parentheses.

Parameter | Unit | θ_{or} | θ_{opt} |
---|---|---|---|

FRC:LC | - | 0.333 | 1.969 (±0.420) |

Leaf C:N | kgC kgN^{-1} | 15.59 | 20.93 (±2.50) |

PLNR | - | 0.088 | 0.1050 (±0.011) |

g_{s,MAX} | m s^{-1} | 0.006 | 0.0041 (±0.001) |

**Table 3.**Start (ONDAY) and end (OFFDAY) of growing season, maximum leaf carbon (LC

_{MAX}) observed and estimated with second-step model optimization. The ONDAY and OFFDAY estimated with the internal phenological model (Internal phenology) were also reported. DOY is Day Of Year.

Year | ONDAY. | OFFDAY | LC_{MAX} | |
---|---|---|---|---|

DOY | DOY | kgCm^{-2} | ||

2002 | Obs. | 91 | 267 | 0.164 |

Second-step | 88 | 260 | 0.159 | |

Internal phenology | 100 | 289 | - | |

2003 | Obs. | 78 | 315 | 0.155 |

Second-step | 70 | 309 | 0.147 | |

Internal phenology | 107 | 297 | - |

**Table 4.**Annual GPP measured and simulated by BIOME-BGC with parameterization from literature and internal phenology (Reference Model 1), BIOME-BGC with parameterization from literature and observed phenology (Reference Model 2), by PROSAILH-BGC after first-step optimization with the internal phenology (GPP

_{PROSAILH-BGC 1-step}) and the final results obtained with PROSAILH-BGC after two step optimization.

Year | GPP_{measured}gC m ^{-2}yr^{-1} | GPP_{Reference Model 1}gC m ^{-2}yr^{-1} | GPP_{Reference Model 2}gC m ^{-2}yr^{-1} | GPP_{PROSAILH-BGC 1-step}gC m ^{-2}yr^{-1} | GPP_{PROSAILH-BGC 2-step}gC m ^{-2}yr^{-1} |
---|---|---|---|---|---|

2002 | 1,578 | 1,253 | 1,330 | 1,414 | 1,550 |

2003 | 1,473 | 1,084 | 1,265 | 1,299 | 1,391 |

© 2009 by the authors; licensee Molecular Diversity Preservation International, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

## Share and Cite

**MDPI and ACS Style**

Migliavacca, M.; Meroni, M.; Busetto, L.; Colombo, R.; Zenone, T.; Matteucci, G.; Manca, G.; Seufert, G.
Modeling Gross Primary Production of Agro-Forestry Ecosystems by Assimilation of Satellite-Derived Information in a Process-Based Model. *Sensors* **2009**, *9*, 922-942.
https://doi.org/10.3390/s90200922

**AMA Style**

Migliavacca M, Meroni M, Busetto L, Colombo R, Zenone T, Matteucci G, Manca G, Seufert G.
Modeling Gross Primary Production of Agro-Forestry Ecosystems by Assimilation of Satellite-Derived Information in a Process-Based Model. *Sensors*. 2009; 9(2):922-942.
https://doi.org/10.3390/s90200922

**Chicago/Turabian Style**

Migliavacca, Mirco, Michele Meroni, Lorenzo Busetto, Roberto Colombo, Terenzio Zenone, Giorgio Matteucci, Giovanni Manca, and Guenther Seufert.
2009. "Modeling Gross Primary Production of Agro-Forestry Ecosystems by Assimilation of Satellite-Derived Information in a Process-Based Model" *Sensors* 9, no. 2: 922-942.
https://doi.org/10.3390/s90200922