Description: The terrestrial carbon (C) cycle has been commonly represented by a series of C balance equations to track C influxes into and effluxes out of individual pools in earth system models (ESMs). This representation matches our understanding of C cycle processes well but makes it difficult to track model behaviors. It is also computationally expensive, limiting the ability to conduct comprehensive parametric sensitivity analyses. To overcome these challenges, we have developed a matrix approach, which reorganizes the C balance equations in the original ESM into one matrix equation without changing any modeled C cycle processes and mechanisms. We applied the matrix approach to the Community Land Model (CLM4.5) with vertically resolved biogeochemistry. The matrix equation exactly reproduces litter and soil organic carbon (SOC) dynamics of the standard CLM4.5 across different spatial-temporal scales. The matrix approach enables effective diagnosis of system properties such as C residence time and attribution of global change impacts to relevant processes. We illustrated, for example, the impacts of CO2 fertilization on litter and SOC dynamics can be easily decomposed into the relative contributions from C input, allocation of external C into different C pools, nitrogen regulation, altered soil environmental conditions, and vertical mixing along the soil profile. In addition, the matrix tool can accelerate model spin-up, permit thorough parametric sensitivity tests, enable pool-based data assimilation, and facilitate tracking and benchmarking of model behaviors. Overall, the matrix approach can make a broad range of future modeling activities more efficient and effective.

Description: Ponds and lakes are abundant in Arctic permafrost lowlands. They play an important role in Arctic wetland ecosystems by regulating carbon, water, and energy fluxes and providing freshwater habitats. However, ponds, i.e., waterbodies with surface areas smaller than 1.0 × 10**4 m**2, have not been inventoried on global and regional scales. The Permafrost Region Pond and Lake (PeRL) database presents the results of a circum-Arctic effort to map ponds and lakes from modern (2002-2013) high-resolution aerial and satellite imagery with a resolution of 5 m or better. The database also includes historical imagery from 1948 to 1965 with a resolution of 6 m or better. PeRL includes 69 maps covering a wide range of environmental conditions from tundra to boreal regions and from continuous to discontinuous permafrost zones. Waterbody maps are linked to regional permafrost landscape maps which provide information on permafrost extent, ground ice volume, geology, and lithology. This paper describes waterbody classification and accuracy, and presents statistics of waterbody distribution for each site. Maps of permafrost landscapes in Alaska, Canada, and Russia are used to extrapolate waterbody statistics from the site level to regional landscape units. PeRL presents pond and lake estimates for a total area of 1.4 × 10**6 km**2 across the Arctic, about 17 % of the Arctic lowland ( 〈 300 m a.s.l.) land surface area. PeRL waterbodies with sizes of 1.0 × 10**6 m**2 down to 1.0 × 10**2 m**2 contributed up to 21 % to the total water fraction. Waterbody density ranged from 1.0 × 10 to 9.4 × 10**1/km². Ponds are the dominant waterbody type by number in all landscapes representing 45-99 % of the total waterbody number. The implementation of PeRL size distributions in land surface models will greatly improve the investigation and projection of surface inundation and carbon fluxes in permafrost lowlands.