The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

Published eddy covariance measurements of carbon dioxide (CO2) exchange between vegetation and the atmosphere from a global network are distilled, synthesised and reviewed according to time scale, climate and plant functional types, disturbance and land use. Other topics discussed include history of the network, errors and issues associated with the eddy covariance method, and a synopsis of how these data are being used by ecosystem and climate modellers and the remote-sensing community. Spatial and temporal differences in net annual exchange, FN, result from imbalances in canopy photosynthesis (FA) and ecosystem respiration (FR), which scale closely with one another on annual time scales. Key findings reported include the following: (1) ecosystems with the greatest net carbon uptake have the longest growing season, not the greatest FA; (2) ecosystems losing carbon were recently disturbed; (3) many old-growth forests act as carbon sinks; and (4) year-to-year decreases in FN are attributed to a suite of stresses that decrease FA and FR in tandem. Short-term flux measurements revealed emergent-scale processes including (1) the enhancement of light use efficiency by diffuse light, (2) dynamic pulses in FR following rain and (3) the acclimation FA and FR to temperature. They also quantify how FA and FR respond to droughts and heat spells.

/pdf/breathing-of-the-terrestrial-biosphere-lessons-learned-from-3gb2mq3tna.pdf

‘Breathing’ of the terrestrial biosphere: lessons learned from a global network of carbon dioxide flux measurement systems

Terrestrial ecosystems sequester 2.1 Pg of atmospheric carbon annually. A large amount of the terrestrial sink is realized by forests. However, considerable uncertainties remain regarding the fate of this carbon over both short and long timescales. Relevant data to address these uncertainties are being collected at many sites around the world, but syntheses of these data are still sparse. To facilitate future synthesis activities, we have assembled a comprehensive global database for forest ecosystems, which includes carbon budget variables (fluxes and stocks), ecosystem traits (e.g. leaf area index, age), as well as ancillary site information such as management regime, climate, and soil characteristics. This publicly available database can be used to quantify global, regional or biome-specific carbon budgets; to re-examine established relationships; to test emerging hypotheses about ecosystem functioning [e.g. a constant net ecosystem production (NEP) to gross primary production (GPP) ratio]; and as benchmarks for model evaluations. In this paper, we present the first analysis of this database. We discuss the climatic influences on GPP, net primary production (NPP) and NEP and present the CO2 balances for boreal, temperate, and tropical forest biomes based on micrometeorological, ecophysiological, and biometric flux and inventory estimates. Globally, GPP of forests benefited from higher temperatures and precipitation whereas NPP saturated above either a threshold of 1500 mm precipitation or a mean annual temperature of 10 degrees C. The global pattern in NEP was insensitive to climate and is hypothesized to be mainly determined by nonclimatic conditions such as successional stage, management, site history, and site disturbance. In all biomes, closing the CO2 balance required the introduction of substantial biome-specific closure terms. Nonclosure was taken as an indication that respiratory processes, advection, and non-CO2 carbon fluxes are not presently being adequately accounted for.

/pdf/co2-balance-of-boreal-temperate-and-tropical-forests-derived-4w27l6q0ii.pdf

CO2 balance of boreal, temperate, and tropical forests derived from a global database

The Data Assimilation Research Testbed (DART) is an open-source community facility for data assimilation education, research, and development. DART's ensemble data assimilation algorithms, careful ...

/pdf/the-data-assimilation-research-testbed-a-community-facility-1zv8p7e6iy.pdf

The Data Assimilation Research Testbed: A Community Facility

https://escholarship.org/content/qt0nv498zp/qt0nv498zp.pdf?t=msuukg

Deriving a light use efficiency model from eddy covariance flux data for predicting daily gross primary production across biomes

There are two broad approaches to quantifying landscape C dynamics - by measuring changes in C stocks over time, or by measuring fluxes of C directly. However, these data may be patchy, and have gaps or biases. An alternative approach to generating C budgets has been to use process-based models, constructed to simulate the key processes involved in C exchange. However, the process of model building is arguably subjective, and parameters may be poorly defined. This paper demonstrates why data assimilation (DA) techniques - which combine stock and flux observations with a dynamic model - improve estimates of, and provide insights into, ecosystem carbon (C) exchanges. We use an ensemble Kalman filter (EnKF) to link a series of measurements with a simple box model of C transformations. Measurements were collected at a young ponderosa pine stand in central Oregon over a 3-year period, and include eddy flux and soil C02 efflux data, litterfall collections, stem surveys, root and soil cores, and leaf area index data. The simple C model is a mass balance model with nine unknown parameters, tracking changes in C storage among five pools; foliar, wood and fine root pools in vegetation, and also fresh litter and soil organic matter (SOM) plus coarse woody debris pools. We nested the EnKF within an optimization routine to generate estimates from the data of the unknown parameters and the five initial conditions for the pools. The efficacy of the DA process can be judged by comparing the probability distributions of estimates produced with the EnKF analysis vs. those produced with reduced data or model alone. Using the model alone, estimated net ecosystem exchange of C (NEE)= -251 f 197g Cm-2 over the 3 years, compared with an estimate of -419 f 29gCm-2 when all observations were assimilated into the model. The uncertainty on daily measurements of NEE via eddy fluxes was estimated at 0.5gCm-2 day-1, but the uncertainty on assimilated estimates averaged 0.47 g Cm-2 day-1, and only exceeded 0.5gC m-2 day-1 on days where neither eddy flux nor soil efflux data were available. In generating C budgets, the assimilation process reduced the uncertainties associated with using data or model alone and the forecasts of NEE were statistically unbiased estimates. The results of the analysis emphasize the importance of time series as constraints. Occasional, rare measurements of stocks have limited use in constraining the estimates of other components of the C cycle. Long time series are particularly crucial for improving the analysis of pools with long time constants, such as SOM, woody biomass, and woody debris. Long-running forest stem surveys, and tree ring data, offer a rich resource that could be assimilated to provide an important constraint on C cycling of slow pools. For extending estimates of NEE across regions, DA can play a further important role, by assimilating remote-sensing data into the analysis of C cycles. We show, via sensitivity analysis, how assimilating an estimate of photosynthesis - which might be provided indirectly by remotely sensed data - improves the analysis of NEE.

/pdf/an-improved-analysis-of-forest-carbon-dynamics-using-data-3ndl7zwqut.pdf

Meredith R. Kurpius

Papers

An improved analysis of forest carbon dynamics using data assimilation