Estimation of Net Primary Productivity: An Introduction to Different Approaches

Abstract

The net primary productivity (NPP) is defined as the net carbon gain by plants in natural and agricultural ecosystems, which is computed by subtracting the autotrophic respiration from the gross photosynthetic carbon uptake by the ecosystems. It acts as the indicators of carbon sequestration, ecosystem health, and agricultural yield which are important in the context of climate change, its impact and mitigation, and food security. The NPP can be estimated in multiple ways including the direct and indirect measurements and modelling. The various direct NPP measurements are ground-based in situ observations of ecosystem-atmosphere carbon flux such as the micrometeorological flux-gradient method, eddy covariance, flux chamber measurements etc. The indirect measurements of NPP include the satellite-derived NPP estimates which are computed from the directly measured spectral reflectances, using different biophysical relations such as the light use efficiency model etc. However the accuracy of these products varies geospatially and largely depends on the retrieval of input parameters and representativeness of underlying model parameterization. There are two major modelling approaches to estimate the NPP namely bottom-up and top-down estimates. The bottom-up models compute the NPP from the directly recorded variables such as temperature, precipitation, radiation, wind, atmospheric CO₂ concentration etc. using the biome-specific functional relations due to which these are also known as the process-based models. The top-down or inverse models use the matrix inversion method to predict the sources and sinks of CO₂ emission in a region from the directly measured concentrations by the surface stations and/or satellites and thus the NPP of that region. The NPP estimates from measurements and models are used to calculate the carbon budgets at different scales from ecosystem-level to global scale. However significant uncertainties exist in such estimates due to insufficient surface measurements, under-representation of several regions and ecosystems, imperfect boundary conditions and parameterizations in models. While the direct measurements provide more accurate estimates of NPP, these require to be carried over for long duration using multiple different instruments which are prone to errors and data-loss whereas the models can provide large-scale estimates of NPP but need to be validated against realistic in situ measurements across an wide array of ecosystems. The aforementioned aspects of NPP estimation are discussed in detail in the present chapter.

1 Introduction

Since the industrial revolution the atmospheric CO₂ concentration (c_a in ppm) has risen from ~280 to 416 ppm (till the time of writing this book chapter) in an unprecedented rate (https://www.esrl.noaa.gov/gmd/ccgg/trends/mlo.html). Due to the increased energy demand the carbon stored in fossil fuel deposits has been burnt and released into the atmosphere. To meet the food and fibre demands of an increasing population the rapid agricultural expansion has taken place at the cost of natural ecosystems such as forests. The increased amount of atmospheric greenhouse gases of which CO₂ is a major component, is changing the Earth’s radiation feedback resulting in global warming and paving the way for climate change (IPCC 2013).

Such climate change is predicted to have adverse effects on the Earth such as abrupt changes in atmospheric and oceanic circulation patterns, polar ice cap melt, sea-level rise, shifting treeline, increased frequency and intensity of extreme events etc. In order to devise the climate change mitigation strategies the sources and sinks of atmospheric CO₂ need to be identified and their strengths and patterns need to be characterised. The terrestrial ecosystems play a regulatory role in the Earth’s radiation budget due to their roles in determining the surface albedo and photosynthetic carbon uptake (Betts 2000). According to the global carbon budget 2019 (Friedlingstein et al. 2019) the terrestrial ecosystems were the largest sink of atmospheric CO₂ in the latest decade during 2009–2018 with a sink-strength of 3.2 ± 0.6 GtC y⁻¹. Several land-based mitigation strategies are designed based on these ecosystems such as afforestation and reforestation, biochar, bioenergy with carbon capture and storage etc. (Minx et al. 2018). Moreover proper quantification of the carbon cycles of these ecosystems is important to estimate the intended nationally determined contribution (INDC) of the nations in compliance with the Paris climate accord.

The changes in c_a, trends of air temperature and precipitation due to climate change will modify the capacity and pattern of the photosynthetic carbon uptake by terrestrial ecosystems (IPCC 2019). The response of the ecosystems to such changes remains uncertain which is required for the climate change impact assessment. For this purpose the long-term observations of terrestrial carbon cycle are required. It is predicted that in changed environmental conditions the indigenous plant species are at high risk to be replaced by the more sturdy invasive species, thus resulting in the extinction of species and loss of biodiversity (Bongaarts 2019). The accelerated c_a is also predicted to cause forest dieback in several regions (Cox et al. 2004).

In this contest, the present chapter is aimed at the estimation of net primary productivity (NPP), a component of the carbon cycle and its significance. The different observation and modelling techniques to achieve this are discussed in the subsequent sections. In compliance with the theme of this book, the contents of this chapter are restricted to the forest ecosystems. It is to be noted that NPP estimation of aquatic ecosystems such as marine phytoplankton is a different topic and not discussed here. Also the agricultural ecosystems are not included as those are not considered as natural ecosystems. Considering the wide span of the subject matter and a vast amount of literature existing on the different aspects of the same, I have not tried to make this chapter as a comprehensive review article but as an indicative document on the progress done in this field and its present status. The future directions from here are also discussed briefly towards the end. This topic being an interdisciplinary one, care has been taken in the formulation of the chapter to make it apprehensible to the potential readers who belong to different academic and professional backgrounds.

2 Data and Modelling

2.1 The Carbon Cycle Components

The flux of any variable is defined as the amount of that variable exchanged across a unit surface per unit time. In this regard the vertical CO₂ flux (F_c) between the ecosystem and atmosphere is the measure of carbon exchanged between the ecosystem and atmosphere, also known as the net ecosystem exchange (NEE). It is a resultant of the photosynthetic uptake and respirative loss of carbon which are defined as the gross primary productivity (GPP) and total ecosystem respiration (TER) respectively. The TER is comprised of respired carbon fluxes by the autotrophs and heterotrophs which are defined as autotrophic respiration (R_A) and heterotrophic respiration (R_H) respectively. As per the meteorological convention the negative and positive values of NEE stand for the carbon gain and loss by the canopy, which is opposite to the convention followed in ecology. The net ecosystem productivity (NEP) is defined as the negative of NEE. According to these definitions (Chapin et al. 2006),

$$GPP = NPP + R_{A}$$

(2.1)

$$NPP = NEE + R_{H}$$

(2.2)

and,

$$TER = R_{A} + R_{H}$$

(2.3)

All the variables used this book chapter are described in Table 2.1.

Table 2.1 Variables used in the present study, listed alphabetically

2.2 In Situ Measurements

The NEE can be directly estimated from the observations in contrast with GPP and TER. Hence the GPP and TER are estimated from the NEE measurements using a set of ecophysiological relations among the ecosystem and environmental variables. Following are the different methodologies for measuring NEE.

2.2.1 Eddy Covariance Measurements

The eddy covariance (EC) method is probably the most accurate technique for estimating the biosphere–atmosphere scalar and energy fluxes using the direct measurements of wind parameters and scalars. It has been widely used across the globe for continuous monitoring of long-term CO₂ exchange by the ecosystems in different geographical location, altitudes and terrains (Baldocchi 2003; Deb Burman et al. 2020a, b). Several continental, regional and national networks exist comprising the dense arrays of such towers (Baldocchi et al. 2001; Beringer et al. 2016; Deb Burman et al. 2017; Deb Burman et al. 2018; Rebmann et al. 2018). A comprehensive global map of such active and past EC flux towers can be found in Burba (2019).

Any variable in the atmosphere is exchanged and mixed among the layers by the random turbulent wind motions, also known as the eddies. In EC method these eddies of different temporal scales are sampled by the fast (5, 10 or 20 Hz) measurements of wind velocity components and gas concentrations. Finally the contributions of all such eddies are summed up to compute the net fluxes using the Reynolds averaging technique (Reynolds 1895; Deb Burman et al. 2018). The ecosystem-atmosphere CO₂ flux (F_c in µmol m⁻² s⁻¹) is computed from the vertical component of wind velocity (w in m s⁻¹) and atmospheric CO₂ molar concentration (c in µmol m⁻³) which can be expressed as follows,

$$F_{c} = \overline{{w^{\prime}c^{\prime}}}$$

(2.4)

and

$$X{'} = X - \overline{X}$$

(2.5)

where X′ stands for the instantaneous fluctuations in the measured values of variable X from its mean over the averaging period ($\overline{X}$). The overbar denotes the temporal averaging which is usually done every 30 or 60 min.

A typical EC measurement setup for CO₂ includes sonic anemometer and infrared gas analyser for wind velocity and CO₂ concentration measurements respectively, which are usually placed at a single height above the ecosystem canopy or at several recommended heights within the canopy (Deb Burman et al. 2019). These measurement heights determine the footprint or representativeness of the EC measurement (Kormann and Meixner 2001; Kljun et al. 2015). In addition the EC tower is instrumented at various levels and depths with a set of associated meteorological, radiation and soil sensors (Aubinet et al. 2012). The fast measurements by EC sensors are prone to various errors such as the random spikes, faulty measurement values due to inaccurate sensor geometry, density fluctuation of the ambient air due to the presence of moisture, obstruction of the wind by the sensors etc. The raw EC data is rigorously filtered for removing such errors following a set of recommended pre-processing techniques such as despiking (Vickers and Mahrt 1997; Mauder et al. 2013), detrending, coordinate rotations (Kaimal and Finnigan 1994), angle of attack correction (Kaimal and Finnigan 1994), Webb-Pearman-Leuning correction (Mauder et al. 2013), low (Moncrieff et al. 1997) and high-pass noise filtering (Moncrieff et al. 2004), time-lag between velocity and concentration measurements (Burba 2013) etc. Such a flux tower is shown in Fig. 2.1 which is installed at the Pichavaram mangrove ecosystem as part of the MetFlux India network in Tamil Nadu, India (Deb Burman et al., 2017; Gnanamoorthy et al. 2019; Chakraborty et al. 2020; Gnanamoorthy et al. 2020).

Fig. 2.1

A surface flux tower instrumented at multiple levels with eddy covariance and other associated measurement sensors at the Pichavaram mangroves, Tamil Nadu, India; this tower is part of the MetFlux India network

While implementing these corrections the resulting half-hourly NEE values are flagged according to a 10-point scale from 0 to 9 with increasing order suggesting reduced confidence (Foken et al. 2004). Such classification takes into account the atmospheric conditions including non-stationary and non-integral turbulences. The choice of best quality data depends on the requirement. Usually for developing the functional relationships between carbon flux and environment, the data values not exceeding flag 2 are used while in some cases such strict quality-control results in 60–65% of data loss, mostly during nighttime rendering the remaining data heavily biased towards daytime. In such cases the flags are gradually relaxed for more uniform representation of day and nighttime values in the final data record. The friction velocity (u*) is a measure of the atmospheric turbulence (Foken 2008). At very low values of turbulence the fundamental principles of EC measurement are violated. To avoid this condition u*-filtering is done in which the NEE values corresponding to u* below a certain threshold are rejected. This u*-threshold determination is crucial for the accurate estimation of NEE and several recipes exists to determine this (Gu et al. 2005; Barr et al. 2013); Wutzler et al. 2018) . Apart from these a certain amount of CO₂ is trapped in the canopy that does not mix with the atmosphere by turbulent mixing. This is termed as the storage flux (Baldocchi 2003). The storage flux between ground and measurement height h (F_s) is computed from the measured CO₂ concentration (c) time series at height h as follows,

$$F_{s} = \int\limits_{0}^{h} {\frac{\partial c}{{\partial t}}} dz$$

(2.6)

Finally the NEE is computed as (F_c + F_s). All of these measures are documented in several books such as Burba and Anderson (2007) and Aubinet et al. (2012). The various quality-control measures result gaps in the data. Gaps also occur due to the instrument malfunctioning at several times. However to account for the NEP of any ecosystem, continuous measurement record is required which is achieved by filling the gaps in data. Several recipes of gap-filling exist in literature e.g. mean diurnal variation (MDV), marginal distribution sampling (MDS), look-up table (LUT) etc. (Moffat et al. 2007; Reichstein 2005). Selection of any particular recipe for gap-filling depends on various factors such as the extent and severity of data loss, environmental conditions, local climatology, availability of supporting measurements etc. These recipes have evolved over years owing to active research by several groups and are documented elsewhere (Falge et al. 2001).

Although the EC measurement offers an unprecedented advantage of real time monitoring of NEP of any ecosystem it has its own limitations (Massman and Lee 2002). Advective fluxes remain difficult to be separated from the vertical exchange (Paw et al. 2000; Etzold et al. 2010). The fluxes measured over mountainous, undulated terrains are laced with lots of measurement uncertainty (Geissbühler and Siegwolf 2000). During low-turbulence conditions, mostly in the nocturnal periods fluxes are severely undermined (Aubinet et al. 2010). The EC method is still under active research and evolving fast. A large number of scientific publications and references exist on this technique, its development and adaptations not all of which are possible to be included in the limited span of the present chapter. Interested readers however are suggested to read several such articles appearing in the meteorology, forestry and agricultural journals.

2.2.2 Gradient Flux Measurements

In the absence of direct EC measurements F_c can be estimated from the spatial gradient of mean CO₂ molar concentration ($\overline{c}$ in µmol m⁻³) assuming a diffusive model. In this model $\overline{c}$ is assumed to vary slowly and the Reynolds averaged covariance F_c is parameterized as the function of vertical gradient of $\overline{c}$ as follows,

$$F_{c} = - K_{c} \frac{{\partial \overline{c}}}{\partial z}$$

(2.7)

where, K_c is defined as the eddy diffusivity factor for carbon dioxide. It has the unit of m² s⁻¹. Due to the turbulent diffusion CO₂ is transported from high concentration zone to low concentration zone. Hence the negative sign is introduced in Eq. (2.7) to maintain conformity with the flux convention described earlier. In a simplistic setup with two-level measurements Eq. (2.7) can be reformulated as,

$$F_{c} = - K_{c} \frac{{\overline{c(2)} - \overline{c(1)} }}{z(2) - z(1)}$$

(2.8)

where, ${\overline{c(1)} }$ and ${\overline{c(2)} }$ stand for the mean CO₂ concentrations at lower (z(1)) and upper (z(2)) measurement heights respectively (Lee 2018).

Although convenient in the absence of fast measurements, the gradient flux measurement technique is heavily criticised for several reasons. In the gradient flux formulation the spatial heterogeneity of CO₂ source strength at the horizontal surfaces of concentration measurement is not considered. Moreover the vertical variation in CO₂ source strength is overlooked (Dyer 1974). This problem is partially circumvented by introducing more concentration measurements in the intermediate levels and fitting a vertical profile to the measured values for computing the gradient. K_chas a strong functional dependency on atmospheric stability for which a set of empirically determined stability correction factors are introduced for better estimation of F_c (Dyer and Hicks 1970; Businger et al. 1971). In practical applications the gradient flux method is mostly used in conjunction with the primary EC measurement with iterative determination of K_cfrom the latter set of measurements.

2.2.3 Resistance Methods

Assuming a constant flux layer, where F_c does not vary with height, Eq. (2.7) can be reformulated as,

$$\overline{c} = - F_{c} \int\limits_{0}^{h} {\frac{1}{{K_{c} }}} dz$$

(2.9)

or,

$$F_{c} = -\overline{c}\frac{1}{{{\text{r}}_{{\text{a,c}}} }}$$

(2.10)

where,

$$r_{a,c} = \int\limits_{0}^{h} \frac{1}{K_{c}} dz$$

(2.11)

is defined as the aerodynamic resistance to CO₂ transfer, in analogy to the electrical resistance as defined in the Ohm’s law (Lee 2018). The r_a,c increases with increasing stability and depth of the diffusion layer. Increased turbulence in the atmosphere decreases r_a,c.

In addition to aerodynamic resistance, the plant-atmosphere photosynthetic CO₂ exchange pathway involves leaf boundary layer and stomatal resistances, connected in series as the CO₂ molecules transport through these sequentially. The layer of atmosphere in close vicinity of the leaves is usually thin but unperturbed. The exchange of CO₂ through this layer only takes place through molecular diffusion which gives rise to the leaf boundary layer resistance (r_b).

The stomatal resistance (r_s in s m⁻¹) is defined as the resistance faced by CO₂ molecules while escaping to the atmosphere from the stomatal cavity. The plant-atmosphere CO₂ and water vapour exchanges by photosynthesis and transpiration respectively, are coupled by the stomatal opening and closure mechanism (Farquhar and Sharkey 1982). There are two major schemes to parameterize r_s. According to the Jarvis-Stewart formulation (Jarvis 1976; Stewart 1988), r_s is empirically determined from radiation, leaf temperature, vapour pressure deficit (VPD) and soil moisture content.

In another approach, introduced by Ball et al. (1987) and Collatz et al. (1991) r_s is expressed as a function of net CO₂ uptake (A_n) and relative humidity and CO₂ concentration at the leaf surface (h_s and c_s, respectively) as follows,

$$r_{s} = \frac{1}{{m\frac{A_{n} \cdot h_{s}}{{cs}} + b}}$$

(2.12)

where, m and b are the linear regression parameters derived experimentally. These models have been widely used by several researchers and adopted according to different climate types (Leuning 1990; Tuzet et al. 2003; Whitley et al. 2008; Ye and Yu 2008). The inverse of any resistance parameter is defined as the corresponding conductance. In simplified bigleaf models where the entire ecosystem is considered to behave like a single leaf (Monteith et al. 1965), the canopy resistance (r_c) is used to compute the ecosystem-atmosphere fluxes. However, the interpretation of r_c is not trivial. In a simplistic formulation where all the leaves in the canopy can be considered as individual resistors with stomatal resistance r_s connected in parallel, r_ccan be expressed as r_c/n where n is the number of leaves in the canopy.

2.2.4 Modified Bowen Ratio Method

The Bowen ratio (B) is defined as the ratio of sensible (H in W m⁻²) and latent (LE in W m⁻²) heat fluxes. It has been widely used to estimate LE from the energy flux measurements in the absence of water vapour measurement assuming a perfect closure of the surface energy budget known as the Bowen ratio method (Stull 1988). This technique is modified to estimate F_c from the vertical flux of water vapour (F_q in mmol m⁻² s⁻¹) in the absence of fast measurement of c from the two level slow measurements of $\overline{q}$ and $\overline{c}$ as follows,

$$F_{c} = \frac{{\overline{c(2)} - \overline{c(1)} }}{q(2) - q(1)} \cdot F_{q}$$

(2.13)

where, ${\overline{c(1)} }$ and ${\overline{q(1)} }$ are the values of c and atmospheric water vapour molar concentration (q in mmol m⁻³) at lower measurement height (z1) and ${\overline{c(2)} }$ and ${\overline{q(2)} }$ are the values of c and q at upper measurement height (z2). This technique assumes the eddy diffusivities of CO₂ and water vapour transport (i.e. K_c and K_q, respectively) are equal to each other and is known as the modified Bowen ratio method (Meyers et al. 1996).

2.2.5 Associated Micro-meteorological Methods

There have been several micrometeorological methods proposed to measure F_c in the absence of fast EC measurements, using the available slow gas concentration measurements as described below.

2.2.5.1 Disjunct Eddy Covariance

The disjunct eddy covariance (DEA) is a modification of EC method first proposed by Rinne et al. (2001) for measuring the fluxes of volatile organic compounds (VOC). In this method the turbulence is assumed to be fully developed and hence the time series of w and gas concentration are sampled at a much coarser temporal scale than EC method. This method has been used by few researchers to estimate F_c as well with good confidence (Hörtnagl et al. 2010; Baghi et al. 2012).

2.2.5.2 Eddy Accumulation

The eddy accumulation (EA) method is a modified version of the EC method where air samples are stored in two separate containers based on updraft and downdraft (Hicks and McMillen 1984). The collection time is proportional to the strength of updraft or downdraft i.e. the magnitude of w. After the data is collected for 30 or 60 min the average CO₂ concentration in both the collection volumes is measured and subtracted from each other for computing F_c (the detailed mathematical formulation is similar to the EC method). Instead of sampling all the eddies separately as done in the EC method (within the practically limiting smallest and largest time scales, as decided by the sampling frequency and averaging time), in EA method all the eddies are augmented according to upward or downward motions and the mean concentration for both of these segments are computed. This method was first proposed by Desjardins (1972).

2.2.5.3 Relaxed Eddy Accumulation

The relaxed eddy accumulation (REA) is a modification of the EA technique where the air volumes are sampled separately at constant flow rate for updrafts and downdrafts, with the separate measurements of CO₂ concentrations for both the volumes. Finally the difference between updraft and downdraft averages of CO₂ molar concentrations ($\overline{c_{u}}$ and $\overline{c_{d}}$ respectively) is multiplied by the standard deviation of vertical velocity (σ_w) during the entire duration of updraft or downdraft event and an empirically determined dimensionless factor of proportionality (β) to compute F_c as follows,

$$F_{c} = \beta \cdot \sigma_{w} \cdot \left( {\overline{c_{u}} - \overline{c_{d}} } \right)$$

(2.14)

This method had been first proposed by Businger and Oncley (1990) who also proposed the value of β to be 0.6. However the choice of β is a major source of uncertainty of this method which was later shown to vary within 0.40–0.63 under different experimental conditions by several researchers (Baker et al. 1992; Milne et al. 1999). Additionally the accurate segregation of air samples in updraft and downdraft periods and precise measurement of $\overline{c_{u}}$ and $\overline{c_{d}}$ are essential which are difficult to be achieved in field conditions (Pattey et al. 1993). The REA has been mostly used in the measurements of trace gas, aerosol, VOCs and isotopic fluxes (Guenther et al. 1996; Valentini et al. 1997; Myles et al. 2007) for which fast concentration measurements are not available, as required by the EC technique. However, several inter comparison studies have shown the REA to perform well in estimating F_c under strict measurement control as compared to EC method in agricultural and forest ecosystems (Pattey et al. 1993; Gaman et al. 2004). There have been several modifications of REA since its inception such as the hyperbolic relaxed eddy accumulation (HREA) by Bowling et al. (1999) etc. which I am not going to discuss in detail in the limited span of the present chapter. The interested readers are suggested to read the relevant literature for the detailed information on these techniques.

2.2.5.4 Chamber-Based Measurements

In the chamber-based methods enclosure chambers are used to isolate a part of the atmosphere within which the CO₂ concentration is allowed to change only by the respiration or photosynthesis by the plant, part of plant or soil enclosed by these chambers. The F_c is computed from the change in c over the sampling time interval. The walls of the chambers are impermeable and do not allow the CO₂ inside to interact with the ambient atmosphere through diffusion. In static chamber methods the ambient air flow is restricted (Wang et al. 2010) whereas in dynamic chamber methods the ambient air is allowed to flow through the chamber at a constant base flow rate (Ohkubo et al. 2007). Several different geometries of the chambers exist (Kutsch et al. 2010).

The operation of flux chambers can be manual or automatic. These are portable and have less stringent requirements than the EC technique. However they significantly alter the microclimate within the chamber volume e.g. the opaque chambers increase the probability of dark respiration, static chambers hinder the turbulent mixing etc. Despite the ease of installation of the flux chambers, these methods have small footprint, are not suitable for long term canopy-scale CO₂ flux measurements in tall forest ecosystems and mostly used for grasslands with small canopy height or leaf, bole and soil respiration components (Law et al. 1999).

Once NEE is estimated by the above-mentioned methods, it is partitioned into GPP and TER using respiration (Reichstein 2005), light-use efficiency (Lasslop et al. 2010), isotopic fractionation (Bowling et al. 2001) or statistical correlation based methods (Skaggs et al. 2018).

2.3 Satellite Measurements

In situ measurements by far provide the most realistic estimates of the carbon cycle of terrestrial ecosystems. However, these have limited footprints. A dense network of ground-based towers instrumented with multiple sensors is required to be deployed for estimating the NPP of any region, as outlined in the previous section. Also the measurements need to be continued seamlessly at least for several years before a reasonable estimation can be achieved with the seasonal, intra-seasonal and inter-annual variabilities (Baldocchi 2001). Establishing such networks are challenging in remote and inaccessible locations. Moreover the ground-based measurement systems are marred by severe data loss due to power shortage, adverse weather conditions etc. Maintaining such systems required long-term dedicated effort, human involvement and have high establishment and operating costs. The data collection, processing and interpretation can be tedious for difficult terrains such as mountainous regions, dense rainforests etc. In view of these NPP can be remotely monitored using satellite and other remote sensing techniques as described below.

2.3.1 Vegetation Indices

Vegetation indices (VIs) are spectral transformations of the reflectances recorded by satellite sensors in multiple bands of the electromagnetic spectrum (Huete et al. 2002). These are dimensionless and used for monitoring the vegetation health and photosynthetic activities at different spatio-temporal scales. Different VIs are formulated such as the normalized difference vegetation index (NDVI), leaf area index (LAI), enhanced vegetation index (EVI), land-surface water index (LSWI), soil-adjusted vegetation index (SAVI) etc. which are used in combination with the meteorological measurements as input to the bottom-up models for predicting the NPP (Liu et al. 1997) or GPP (Deb Burman et al. 2017). The LAI is defined as the total one-sided leaf surface area relative to per unit ground area (Watson 1947) which can be estimated from the ground-based or satellite measurements (Bréda 2003; Deng et al. 2006). It is closely connected with NDVI which is estimated from the surface reflectances as defined below,

$$NDVI = \frac{\alpha _{nir} - \alpha _{vis}}{{\alpha _{nir} + \alpha _{vis}}}$$

(2.15)

where, α_nir and α_vis are the averaged surface reflectances in the visible and near infrared regions of the electromagnetic radiation spectrum, respectively (Carlson and Ripley 1997). The EVI is an adaptation of NDVI corrected for the atmospheric and canopy background noises which is more sensitive towards dense canopies (Jiang et al. 2008). On a similar note, the LSWI is a modification of NDVI that takes care of the effect of vegetation leaf structure, moisture contents in leaf and soil on the spectral reflectances (Fensholt and Sandholt 2003; Xiao et al. 2004). The SAVI is a modification of NDVI adjusted for the soil brightness effect as defined by Huete (1988).

Different adaptations of this methodology exists in literature where the VI had either been estimated from the satellites such as LANDSAT (Ganguly et al. 2012), Moderate Resolution Imaging Spectroradiometer (MODIS) (Demarty et al. 2007), Advanced Very High Resolution Radiometer (AVHRR) (Buermann et al. 2001) etc. or the ground-based measurements (Deb Burman et al. 2017) and the meteorological variables are either taken from the surface measurements (Bao et al. 2016; Deb Burman et al. 2017), remote sensing observations (Sims et al. 2008), model predictions (Yan et al. 2016) or a suitable assimilation of these (Demarty et al. 2007). The functioning of bottom-up models is described in Sect. 2.2.4.1 of this chapter. The development of VIs from reflectances measured by the satellites is challenging due to multiple constraints, such as atmospheric scattering, vegetation structure, leaf inclination, albedo etc. (Knyazikhin et al. 1998) and hence remains to be an active area of research.

2.3.2 Light Use Efficiency Approach

According to Monteith (1972, 1977) the photosynthetic yield of any ecosystem is directly proportional to the amount of solar radiation absorbed by the canopy in absence of any water or nutrient stress in soil. The plants absorb solar radiation in the photosynthetically active radiation (PAR) or visible range of the electromagnetic spectrum (wavelength varying within 400–700 nm) (Alados et al. 1996). The amount of PAR absorbed by the plants is known as the absorbed photosynthetically active radiation (APAR) which is related to PAR as follows,

$$APAR = fAPAR*PAR$$

(2.16)

where, fAPAR is known as the fraction of photosynthetically active radiation. This is the basis of light use efficiency (LUE) approach to estimate NPP of any ecosystem formulated as,

$$NPP = fAPAR \, * \, PAR \, * \, \varepsilon$$

(2.17)

where, ε is the effective LUE of the ecosystem in the measured environmental condition that varies widely across the ecosystems depending on their geographical location, species type, canopy structure, presence of enzymes, evaporative demand, temperature stress, availabilities of moisture and nutrients etc. It is expressed as a downscaled fraction of the theoretical maximum LUE, ε_max as,

$$\varepsilon = \varepsilon_{\max } *f$$

(2.18)

where the factor f accounts for the deviation of ε from ε_max owing to the non-optimal environmental conditions (Monteith 1972). Initially ε_max was largely thought be constant at 0.405 gC MJ⁻¹ (Potter et al. 1993), which was later found to vary between a wider range (Ahl et al. 2004; Yu et al. 2009). Multiple models use this methodology to predict NPP such as the Carnegie-Ames-Stanford Approach (CASA) (Potter et al. 1993), Vegetation Photosynthesis Model (VPM) (Xiao et al. 2004), Physiological Principles for Predicting Growth (3-PG) (Coops et al. 2005) etc.

2.3.3 Derived Biophysical Products

Using the LUE approach a daily NPP product MOD17 is developed from the Moderate Resolution Imaging Spectroradiometer (MODIS) observations. It was shown by several researchers that compared to NPP, GPP has a better correlation with APAR (Raymond Hunt 1994; Prince and Goward 1995). Hence while developing the MOD17 product, the GPP and respiration components (including growth respiration GR and maintenance respiration MR) are calculated separately and subtracted to produce NPP (Running et al. 1999). The GPP is calculated daily directly from the fAPAR measured by MODIS and PAR from an assimilated data product whereas the GR and MR are calculated from the carbon allometric equations of plants and LAI estimates by MODIS namely MOD15 (Myneni et al. 1999). The biome-specific plant-physiological parameters governing the carbon allometric equations are derived from a bottom-up model Biome-BGC (Running and Hunt 1993). The functioning of such models is discussed in 2.2.4.1 of the present chapter. The MOD17 product is validated across several in situ measurements such as FLUXNET (Running et al. 1999; Zhao et al. 2005; Turner et al. 2006).

2.3.4 Solar Induced Fluorescence

The Solar-Induced Fluorescence (SIF) stands for the part of energy released from the chlorophyll-a (expressed in the unit of W m⁻² sr⁻¹ µm⁻¹) after absorbing the PAR, in the light pathway of photosynthesis, apart from the electron transport and thermal energy dissipation. It has a typical wavelength range of 650–800 nm, which is larger than the absorbed radiation. The strongest peak in SIF spectrum occurs at around740 nm, in the far-red or near-IR regime with the second strongest peak appearing at around 685 nm, in the red zone (Meroni et al. 2009; Mohammed et al. 2019). This can be attributed to the fact that in optimum condition PSI photosystem emits preferably in near-IR whereas the PSII photosystem emits in both red and near-IR (Govindje 1995).

Globally, the SIF is seen to have linear dependencies with GPP estimates from top-down and bottom-up approaches (Zhang et al. 2014; Cui et al. 2017). In a simplistic model (Guanter et al. 2014) the SIF observed from space can be related to GPP in the following way, similar to the LUE formulation described in (2.17) as,

$$GPP = SIF\left( \lambda \right)*\frac{\varepsilon }{\varepsilon _{F}}$$

(2.19)

where, SIF(λ) corresponds to the SIF measurement at wavelength λ (usually taken as either of 685 or 740 nm) and ε_F is an efficiency factor for SIF, analogous to ε. In present times, a plethora of SIF estimates are available from different satellite-based sensors e.g. ENVironmental SATellite (ENVISAT) (Guanter et al. 2007), Greenhouse gases Observing SATellite (GOSAT) (Guanter et al. 2012), Global Ozone Monitoring Experiment-2 (GOME-2) (Joiner et al. 2013), SCanning Imaging Absorption SpectroMeter for Atmospheric CHartographY (SCIAMACHY) (Wolanin et al. 2015), Orbiting Carbon Observatory-2 (OCO-2) (Sun et al. 2017), TROPOspheric Monitoring Instrument (TROPOMI) (Köhler et al. 2018) etc. and have been used extensively in GPP estimation (Wagle et al. 2016; He et al. 2020). Different algorithms have been designed based the wavelength, atmospheric condition and canopy type. It is worthwhile to note that in a recent work Patel et al. (2018) found out the exponential relationship between cropland NPP, estimated from ground-based harvesting estimates and 740 nm SIF, measured by GOME-2 over the Indo-Gangetic Plain in India which can be further exploited for NPP estimation and harvest yield prediction.

2.3.5 Other Remote Sensing Measures

In conjunction with the ground-based and satellite measurements, aircrafts (Cihlar et al. 1992; Desjardins et al. 1992; Macpherson et al. 1992; Chou et al. 2002) and unmanned aerial vehicles (Pirk et al. 2017) have been used for CO₂ flux measurements. The instrumentation of such campaigns include vertical concentration profile, EC (Oechel et al. 1998), VI and SIF (Zarco-Tejada et al. 2013) measurements. The SIF measurements have also been deployed on the ground (Grossmann et al. 2018). The working principle of these measurements remain the same as discussed earlier but additional quality control measures are implemented to account for the complexities arising in such measurements.

2.4 Modelling

The observations provide real time diagnostic information about the NPP. However for prediction of the ecosystem health and carbon sequestration in response to the changes in climate and environmental conditions prognostic information is required, which can be achieved by the models (Prentice et al. 2001; Levy et al. 2004). The models are a set of mathematical equations, algebraic, differential, integral or a combination of these to describe the coupled meteorological and ecophysiological processes. These equations are built upon the theories as well as the phenomenological relations derived from the observations (Bonan et al. 2011) and can be solved analytically or numerically. These models are tested by comparing the predicted variables against their direct observations for a certain measurement interval. This process is known as the calibration. Further a calibrated model is run again for a different time interval and the simulated output is checked against the measurement, thus validating the model (Enting and Pearman 1986; Friend et al. 2007). In a sense the models act as a bridge between the observations and predictions. There are two major modelling approaches as described below.

2.4.1 Bottom-Up Approach

As the name suggests, in bottom-up approach the leaf or canopy scale measurements are upscaled to local, national, regional or global scales using the biogeophysical and biogeochemical processes. Hence these models are also known as the process-based models (Ito and Oikawa 2002). The vegetation growth and decay in process-based models depend on climate forcing and environmental conditions which are improvement over the traditional land-surface models where the vegetation is prescribed with no dynamical change (Foley et al. 1996; Clark et al. 2011; Lawrence et al. 2011). Due to this property the process-based models can be used for ecosystem growth prediction under changed climate such as crop production in a water-stressed condition (Gervois et al. 2004). Hence the process-based models are known as the dynamic global vegetation models, abbreviated as DGVM (Sitch et al. 2003; Prentice and Cowling 2013). These models can be simulated at a point or grid scale as a standalone model or a constituent module of a couple climate, general circulation or Earth system model (Zeng et al. 2002; Bonan and Levis 2006; Kato et al., 2009). Either of surface measurements, satellite products, reanalysis datasets or a suitable combination of these are used as input variables to the process-based models. The input data can be provided at multi-temporal time scales e.g. half-hourly, hourly, daily etc. (Williams et al. 1996; Deb Burman et al. 2017).

The process-based models have different components i.e. soil, ecosystem, atmosphere, hydrology etc. linked to each other by different complex feedback mechanisms which can be broadly classified into two categories namely, biogeochemistry and biogeophysics (El-Masri et al. 2013). Input variables of these models vary among different formulations. However, most of these models require meteorological parameters such as the shortwave and longwave radiations, air temperature, pressure, humidity, wind speed, precipitation, c_a etc. as input. In addition, VIs such as LAI are required by several models.

The photosynthesis in the models is parameterized according to the pathways i.e. C3 (Farquhar et al. 1980; Collatz et al. 1991), C4 (Collatz et al. 1992), CAM (Cortázar and Nobel 1990; Kluge and Ting 2012) etc. where the carbon assimilation is governed by the availability of PAR (Sellers et al. 1992), RuBisCO activity (Bernacchi et al. 2001), phosphophenolpyruvate (PEP)-carboxylase enzyme functionality (Vidal and Chollet 1997), electron transport capacity, leaf nitrogen content (Kattge et al. 2009) etc. In addition the air temperature, moisture demand and soil moisture also affect the carbon uptake by stomatal opening and closure resulting from heat and water stresses. The amount of PAR absorbed by the plants depends on leaf structure, orientation and area, incident PAR and albedo (Knyazikhin et al. 1998; Dai et al. 2004; Fensholt et al. 2004). The incident PAR can be directly measured or computed from the incoming solar radiation (Deb Burman et al. 2020a, b) whereas the leaf area is computed from LAI. As the carbon and water cycles are interlinked with nutrient cycles e.g. nitrogen, phosphorus etc. such models also need information regarding soil bulk density, organic matter content, texture and nutrient profiles for spin-up (Thornton and Rosenbloom 2005; Oleson et al. 2013).

A part of the total photosynthetic carbon uptake or gross primary productivity (GPP) is lost to the atmosphere by respiration. Different respiration components include growth and maintenance respirations of leaves, stems and roots (Barman et al. 2014a, b) which are computed from the direct temperature dependence of respiration (Ryan 1991) or a temperature dependent activation factor (Arora and Boer 2005). This approach is slightly different from the observational approach where the autotrophic and heterotrophic respirations are clubbed together as total ecosystem respiration (TER) and computed from the nighttime temperature dependence of F_c by statistical regression (Lloyd and Taylor 1994). Finally the GPP is computed as the sum of TER and F_c.

Next, the fixed carbon is allocated among different pools i.e. root, leaf, stem, bole, litter etc. using the experimentally determined parameter values e.g. leaf area per unit carbon, leaf nitrogen content etc. (Sitch et al. 2003). A schematic of such a process-based model showing different compartments of carbon allocation and their interrelation is shown in Fig. 2.2, reprinted with permission from El-Masri et al. (2013). The plants are not modelled individually in the process-based models, as that would require much detailed parameterization and more computational resources, rather the plants are broadly categorized into several plat functional types (PFTs). Such clubbing of plants is implemented based on their photosynthesis pathway, geographical and climatological distributions such as tropical broadleaf deciduous, boreal coniferous evergreen, shrub, tundra, pasture, grassland etc. (Poulter et al. 2011). It is worthwhile to note here that several ecosystems remain poorly or under-represented in such models due to the lack of understanding of their ecophysiological processes owing to a lack of adequate experimental evidences or complexity in modelling those such as mangrove, rice paddy etc. (Langerwisch et al. 2018; Kumar and Scheiter 2019). For regional or global scale applications the vegetation map is prescribed to the bottom-up models as land cover and use map (Ramankutty and Foley 1999; Klein Goldewijk et al. 2011). The representativeness and accuracy of these maps remain a crucial control of uncertainty of the NPP estimation by these models (Arora and Boer 2010).

Fig. 2.2

A schematic diagram of the different carbon pools and processes in a process-based ecosystem model Integrated Science Assessment Model (ISAM) (reprinted from El-Masri et al. (2013) with permission)

2.4.2 Top-Down Approach

The alternate approach to model the Earth-atmosphere trace gas fluxes is the top-down approach. As evident in its name, in this method the atmospheric trace gases concentrations are observed at multiple spatial and temporal scales and the sources and sinks responsible for these distributions are computed by a backward modelling approach (Gurney et al. 2004; Rayner et al. 2005). This methodology is also known as the inverse modelling which is opposite in approach to the bottom-up modelling where a forward scheme is implemented. The variables (ψ) and observations (χ) matrices are connected by the following relation,

$$G \cdot \psi = \chi$$

(2.20)

where G is the coefficient matrix. The basic problem in inverse modelling lies in finding the inverse of G which is mostly calculated by Bayesian inversion (Heimann and Kaminski 1999). The observed spatio-temporal distribution of trace gases are apportioned into potential sources and sinks using atmospheric transport models (Kaminski et al. 1999) which can be solved in Lagrangian (Pisso et al. 2019), Eularian (Pillai et al. 2012) or hybrid schemes (Siqueira et al. 2000). The terrestrial sources and sinks of atmospheric CO₂ include the natural and agricultural ecosystems which are our elements of interest in the present chapter. A good knowledge of the biospheric-atmospheric CO₂ exchange, its seasonal variation and controlling parameters is required for the proper evaluation of NEP using inverse methods. The limited scope of the present chapter will not allow me to go into the mathematical and technical details of these techniques but the interested readers are suggested to consult the available vast scientific literature for more insight (Bousquet et al. 1999; Gurney et al. 2002; Peylin et al. 2013).

This apparently simple problem is not very straightforward in reality as I discuss next. A plethora of different sets of available data are used in inverse modelling. These include surface observations (Pickett-Heaps et al. 2011), aircraft measurements (Pisso et al. 2019), ship measurements (Bousquet et al. 1999), satellite products (Houweling et al. 2003, 2015) etc. The measurements of atmospheric traces gases concentrations and fluxes are not spread uniformly across the globe. While some regions are well-mapped with dense observation networks with measurements carried at high temporal resolution (Bousquet et al. 1999) such as north America, some regions do not have adequate observation stations or high frequency measurements (Heimann and Kaminski 1999) such as India (Nalini et al. 2019). Aircraft measurements are costly and still limited in number like the ship observations (Patra et al. 2011). The satellite observations are often contaminated with scattering at different levels, boundary-layer dynamics and presence of clouds which are more prominent over the tropical regions (Rayner et al. 2002; Pandey et al. 2016). Together these result in the data gaps in χ.

In such cases the inverse problem becomes ill-posed with the number of observations being less than the number of control variables and an unique solution to the inverse problem ceases to exist (Heimann and Kaminski 1999). Moreover the errors in χ result in inaccurate estimation of the inverse of G. In case of Bayesian inversion the directly measured surface fluxes (Chevallier et al. 2006) or bottom-up model outputs (Dargaville et al. 2002; Patra et al. 2011) are provided to constrain the problems as a priori information of source and sink strengths. Subsequently the source and sink strength are predicted from the inverse models. These a posteriori estimates are subsequently compared with the a priori information. To reduce the uncertainty in this process a cost function is defined between the observed and simulated concentrations and a priori and a posteriori flux estimates (Kadygrov et al. 2009) which is subsequently minimized by several optimization methods used in data assimilation such as Kalman filter, 4D-var etc. (Liu et al. 2016). Apart from these the errors in transport model formulation propagate in the source and sink patterns by the inverse models (Bousquet et al. 1996; Schuh et al. 2019). The success of inverse modelling of any trace gas requires a proper understanding of the trace gas species chemistry. It has been mostly successful for long-lived trace gases such as CO₂, CH₄ etc. which take part in the long-range transport. Often to reduce the computational cost the Earth surface is divided into several regions (typically less than 100) and the average flux for each of these zones are modelled by the inverse models. A schematic of different regions used in the TRANSCOM inversion is shown in Fig. 2.3 (reprinted with permission from Houweling et al. (2015)). However such averaging reduces the spatial heterogeneity and increases the probability of misrepresentation of any region. For example it has been argued (Valsala et al. 2013) that the terrestrial biospheric CO₂ fluxes in the Carbon Tracker dataset (Peters et al. 2007) is misrepresented over the Indian subcontinent as no CO₂ measurement from this region had been used as a priori flux in the Carbon Tracker dataset due to which the flux over this region is highly biased by the emissions from neighbouring regions such as China, Korea, Kazakhstan, Indonesia etc. which belong to the same averaged spatial domains as India namely Eurasian Temperate and Asia Tropical.

Fig. 2.3

A schematic showing the different land (and ocean) zones used in the TRANSCOM inversion (reprinted with permission from Houweling et al. (2015))

3 Discussion and Conclusions

Several studies have reported the different components of carbon cycle including NPP at global, regional and ecosystem levels using different techniques discussed above or a combination of these (Beer et al. 2010; Jung et al. 2011; Barman et al. 2014b; Tramontana et al. 2016). According to the multi-model study by Cramer et al. (1999) the global NPP ranges within 44.4–66.3 Gt C y⁻¹. This is shown in Fig. 2.4 which is reprinted from Cramer et al. (1999) with permission. Based on the MODIS measurements the average global NPP is 56 Gt C y⁻¹(Zhang et al. 2009). According to the combined bottom-up and top-down CO₂ data assimilation approach by Rayner et al. (2005) the global NPP is approximately 40.5 Gt C y⁻¹. Such studies are important to know about the sources and sinks of atmospheric CO₂ and their annual patterns. These are required not only to assess their roles in global climate change but also to predict the effect of future climate change on these ecosystems e.g. increased air temperature, increased c_a etc. However, due to the sparsity of measurements such estimates have often been riddled with lots of uncertainties both at global and regional levels (Graven et al. 2013; Patra et al. 2013; Cervarich et al. 2016). Moreover, still significant differences exist among observed, bottom-up and top-down modelled estimates of ecosystem carbon uptake (Bastos et al. 2020). In order to devise the climate change mitigation strategies the relations among plant carbon uptake and environmental variables need to be accurately known and represented in the assessment models. The terrestrial carbon cycle components predicted by the different models taking part in coupled modelintercomparison project (CMIP) (Meehl et al. 2000) differ significantly from each other due to the apparent inconsistency in the underlying land carbon cycle formulations (Anav et al. 2013; Friedlingstein et al. 2014). Such uncertainties can be reduced by improved parameterizations which can derived from the long-term measurements in the diverse ecosystem types using an optimally designed denser network of surface measurements.

Fig. 2.4

A global map of the average annual NPP (gC m⁻² y⁻¹) estimated by an ensemble of models (reprinted with permission from Cramer et al. (1999)).