The Permafrost Water Balance Model (PWBM) (Rawlins et al., 2003; Rawlins et al., 2013 Rawlins et al., 2019) simulates all major elements of the water cycle, including snow storage, sublimation, transpiration, and surface evaporation, and soil freezing and thawing and freezing. The model is a descendant of the Water Balance Model introduced by Vorosmarty et al. (1989). The PWBM has been used to investigate causes behind the record Eurasian discharge in 2007 (Rawlins et al., 2009); to corroborate remote sensing estimates of surface water dynamics (Schroeder et al., 2010); and to quantify present and future water cycle changes in the area of Nome, Alaska (Clilverd et al., 2011}. In a comparison against observed river discharge, PWBM-simulated SWE fields compared favorably (Rawlins et al., 2007). Soil temperatures are simulated dynamically through a 1-D nonlinear heat conduction with phase change scheme embedded within the PWBM (Rawlins et al., 2013; Nicolsky et al., 2017). The model is run at an intrinsic daily time step. Simulations can be forced with meteorological data on a distributed spatial grid or the model can be run at a single point. The PWBM includes a multi-layer snow model that accounts for wind compaction, change in density due to fresh snowfall, and depth hoar development with time. Runoff is the sum total of surface (overland) and subsurface flow each day. Subsurface runoff occurs when the amount of water in a soil layer exceeds field capacity. Additional details can be found in Rawlins et al. (2003), Rawlins et al. (2013) and associated appendices.

Model history

The Water Balance Model (WBM) and its descendants predict spatially and temporally varying components of the hydrological cycle and multi constituent water quality variables. The inaugural WBM (Vörösmarty et al. 1998) was one of the first macroscale hydrological models, and over the years the model family has been applied for a number of research projects at scales varying from local watersheds to the global system of rivers.

The earliest version of the PWBM (Rawlins et al., 2003), initially the Pan-Arctic Water Balance Model, included a submodel scheme involving the Stefan Solution for simulating daily changes in soil freezing and thawing. This embedded module was driven by air temperature, model simulated soil moisture content, and soil and other physiographic data. The PWBM v1 also included two soil layers: a root zone that gains water from infiltration and loses water via evapotranspiration and horizontal and vertical drainage, and a deep zone that gains water via root zone vertical drainage and loses water via horizontal drainage. Model simulations revealed highest runoffs are found across northeastern Canada, southern Alaska, and Norway. Lowest amounts were noted along the highest latitudes of the terrestrial Arctic in North America and Asia.

Other model applications have included attribution studies. PWBM simulations across northern Eurasia were used in Rawlins et al. (2006) to posit the hypothesis that much of the river discharge increase from Eurasia between 1936 and 1999 was driven by a divergence in seasonal snowfall (increased) and rainfall (decreased), and hat increased cold season precipitation may be a significant driver of the discharge changes. Simulations with PWBM suggest that record discharge in year 2007 was due in part to strong positive anomalies in late winter snow water equivalent across much of northern Eurasia (Rawlins et al., 2009). Positive net precipitation anomalies then continued into summer, further contributing to discharge. A study of future changes in recharge for an area near an aquifer near Nome, Alaska using the PWBM point to a significant decrease in the proportion of snowfall in annual precipitation by, on average, 9-25% (Clilverd et al., 2011). The study found that increases in effective precipitation were predicted to be great enough to sustain sufficient groundwater recharge.

Improvements to the representation of soil and snowpack dynamics were described in Rawlins et al. (2013). The updated PWBM soil model discretizes a 60 meter soil column which contains 23 layers, with layer thickness increasing with depth. The model simulates snow/ground temperature dynamics in a more physically based manner, using the 1-D heat equation with phase change (Nicolsky et al., 2007). The changes allow for much greater detail with multiple variables varying with depth, with 10 vertical node in the upper 1 m of soil. Simulations show that thermal conductivity can range by a factor of 5 or more in the upper meter of soil.

Based on two simulations for the periods 1996–1999 and 2066–2069 for a single grid cell in central Alaska the authors also suggested a potential for a drying of soils in the presence of increases in ALT, annual total precipitation, and winter snowfall.

The model is well suited for application across the North Slope region. Active-layer thickness (ALT) simulated using the PWBM was found to be more similar to in situ observations and airborne radar retrievals in continuous permafrost areas than in lower permafrost probability areas (Yi et al., 2018). The influence of snow cover and soil thermal dynamics on the seasonal and spatial variability in soil CO2 respiration has been quantified by coupling PWBM to a dynamic soil carbon model (Yi et al. 2013, Yi et al. 2015). A key model attribute is its ability to dynamically simulate the direct influence the snowpack exerts on soil temperature (Yi et al. 2019), with deeper snowpacks promoting warmer soils and associated effects, such as enhancement of soil decomposition and respiration from deeper (> 0.5 m) soil layers (Yi et al. 2015).

The latest version (PWBM v3) was used in a recent study quantify baseline conditions and investigate the changing character of hydrological elements for Arctic watersheds between Utqiagvik (formerly Barrow)) and just west of Mackenzie River over the period 1981–2010 (Rawlins et al., 2019). The region exports the region exports approximately 31.9 km3 of freshwater each year. The study documented significant increases in simulated cold season discharge (CSD) for several large North Slope rivers including the Colville and Kuparuk and for the region as a whole along with significant increase in the

proportion of subsurface runoff to total runoff. Relatively large increases in simulated active-layer thickness (ALT) suggest a physical connection between warming climate, permafrost degradation, and increasing subsurface flow to streams and rivers.

More recently the model includes parametrization for loading of riverine dissolved organic carbon (DOC). The new modules leverage the PWBMs explicit representation of soil freeze/thaw dynamics and variations in soil organic carbon content with depth to estimate dynamics including representative of processing controlling the characteristic seasonal variations in DOC loading for the Yukon and Mackenzie Rivers, and watersheds spanning the region between them, over the period 1981-2010. Model calibration and validation involve a multi-parameter sensitivity analysis using observational records of river discharge and riverine DOC concentrations and export.

References

Clilverd, H.M., White, D.M., Tidwell, A.C. and Rawlins, M.A., 2011. The Sensitivity of Northern Groundwater Recharge to Climate Change: A Case Study in Northwest Alaska 1. JAWRA Journal of the American Water Resources Association, 47(6), pp.1228-1240.

Nicolsky, D.J., Romanovsky, V.E., Alexeev, V.A. and Lawrence, D.M., 2007. Improved modeling of permafrost dynamics in a GCM land?surface scheme. Geophysical research letters, 34(8).

Nicolsky, D.J., Romanovsky, V.E., Panda, S.K., Marchenko, S.S. and Muskett, R.R., 2017. Applicability of the ecosystem type approach to model permafrost dynamics across the Alaska North Slope. Journal of Geophysical Research: Earth Surface, 122(1), pp.50-75.

Rawlins, M. A. , R.B. Lammers, S. Frolking, B. Fekete, C.J. Vörösmarty, 2003. Simulating Pan-Arctic Runoff with a Macro-Scale Terrestrial Water Balance Model. Hydrological Processes, 17, pp. 2521-2539. link to article

Rawlins, M.A., Willmott, C.J., Shiklomanov, A., Linder, E., Frolking, S., Lammers, R.B. and Vörösmarty, C.J., 2006. Evaluation of trends in derived snowfall and rainfall across Eurasia and linkages with discharge to the Arctic Ocean. Geophysical Research Letters, 33(7).

Rawlins, M.A., Serreze, M.C., Schroeder, R., Zhang, X. and McDonald, K.C., 2009. Diagnosis of the record discharge of Arctic-draining Eurasian rivers in 2007. Environmental Research Letters, 4(4), p.045011.

Rawlins, M.A., Nicolsky, D.J., McDonald, K.C. and Romanovsky, V.E., 2013. Simulating soil freeze/thaw dynamics with an improved pan?Arctic water balance model. Journal of Advances in Modeling Earth Systems, 5(4), pp.659-675.

Rawlins, M.A., Cai, L., Stuefer, S.L. and Nicolsky, D., 2019. Changing characteristics of runoff and freshwater export from watersheds draining Northern Alaska. The Cryosphere, 13(12).

Schroeder, R., Rawlins, M.A., McDonald, K.C., Podest, E., Zimmermann, R. and Kueppers, M., 2010. Satellite microwave remote sensing of North Eurasian inundation dynamics: development of coarse-resolution products and comparison with high-resolution synthetic aperture radar data. Environmental Research Letters, 5(1), p.015003.

Vörösmarty, C.J., C.A. Federer and A. Schloss (1998). Potential evaporation functions compared on U.S. watersheds: Implications for global-scale water balance and terrestrial ecosystem modeling. Journal of Hydrology 207: 147-69. link to article

Yi, Y., Kimball, J.S., Rawlins, M.A., Moghaddam, M. and Euskirchen, E.S., 2015. The role of snow cover affecting boreal-arctic soil freeze–thaw and carbon dynamics. Biogeosciences, 12, p.5811.

Yi, Y., Kimball, J.S., Chen, R., Moghaddam, M., Reichle, R.H., Mishra, U., Zona, D. and Oechel, W.C., 2018. Characterizing permafrost active layer dynamics and sensitivity to landscape spatial heterogeneity in Alaska. The Cryosphere, 12(1), p.145.

Yi, Y., Kimball, J.S., Chen, R.H., Moghaddam, M. and Miller, C.E., 2019. Sensitivity of active-layer freezing process to snow cover in Arctic Alaska. The Cryosphere, 13, p.197.