The Multi-Advective Water Mixing Approach for Transport through Heterogeneous Media

Finding a numerical method to model solute transport in porous media with high heterogeneity is crucial, especially when chemical reactions are involved. The phase space formulation termed the multi-advective water mixing approach (MAWMA) was proposed to address this issue. The water parcel method (WP) may be obtained by discretizing MAWMA in space, time, and velocity. WP needs two transition matrices of velocity to reproduce advection (Markovian in space) and mixing (Markovian in time), separately. The matrices express the transition probability of water instead of individual solute concentration. This entails a change in concept, since the entire transport phenomenon is defined by the water phase. Concentration is reduced to a chemical attribute. The water transition matrix is obtained and is demonstrated to be constant in time. Moreover, the WP method is compared with the classic random walk method (RW) in a high heterogeneous domain. Results show that the WP adequately reproduces advection and dispersion, but overestimates mixing because mixing is a sub-velocity phase process. The WP method must, therefore, be extended to take into account incomplete mixing within velocity classes.

A Novel Approach to Obtain Diurnal Variation of Bio-Optical Properties in Moving Water Parcel Using Integrated Drifting Buoy and GOCI Data: A Case Study in Yellow and East China Seas

Ocean processes that can influence rapidly changing ocean color include water-mass movement and bio-optical property changes in the water parcel. Traditionally, diurnal variability of bio-optical properties relies on daily time series at fixed locations by satellite sensors or in situ observations. There is a lack of an effective way to observe diurnal variation of bio-optical properties in a moving water parcel on a large scale. In this paper, we propose a new method to acquire diurnal variation of bio-optical properties in a moving water parcel. The novel approach integrates drifting buoy data and GOCI data. The movement of surface current was tracked by a drifting buoy, and its spatiotemporally matching bio-optical properties were obtained via the GOCI data. The results in the Yellow and East China seas during the summers of 2012 and 2013 show that the variation of time series following the movement of water parcel was obviously different from that obtained at fixed locations. The hourly differences of the former are 15.7% and 16.3% smaller than those of the latter for Chl a and total suspended sediment (TSS), respectively. The value of ag440 was more stable within the moving water parcel than in the fixed location. Our approach provides a simple and feasible way for observing diurnal variability of bio-optical properties in a moving surface water parcel.

Towards Application of StorAge Selection Functions in Large-Scale Catchments with Heterogeneous Travel Times and Subsurface Reactivity

<p>StorAge Selection (SAS) functions describe how a catchment selectively removes water and solute of different ages via discharge, thus controlling transit time distributions (TTDs) and solute composition of discharge. Previous studies have successfully applied SAS functions in a spatially lumped approach to capture catchment-scale transport phenomena of (non-)conservative solutes. The lumped approach assumes that water and solutes within a water parcel of a specific age are well-mixed. While this assumption does not cause any changes in the age of water, the spatial heterogeneity of solute concentrations within this water parcel is lost. In addition, in large catchments, headwater sub-catchments and lowland sub-catchments could behave in different ways, e.g., the transit times (TTs) and reaction rates between headwater and lowland sub-catchment could be of different magnitudes. This, in turn, might not be sufficiently represented in a lumped approach of SAS functions.</p><p>In this study, we applied the mHM-SAS model (Nguyen et al., 2020) with a semi-distributed approach of SAS functions. The nested mesoscale catchment (Selke catchment, Germany) with heterogeneous land use management practices, TTs, and subsurface reactivity was used as a case study. In addition to spatial variability, a functional relationship between the parameters of the SAS functions and storage dynamics was introduced to capture temporal dynamics of the selection preference for discharge. High frequency instream nitrate data were used to validate the proposed approach. Results show that the proposed approach can well represent nitrate export at both sub-catchment and catchment levels. The model reveals that catchment nitrate export is controlled by (1) the headwater sub-catchment with fast TTs and a high denitrification rate, and (2) the lowland sub-catchment with longer TTs and a low denitrification rate. In general, the proposed approach serves as a promising tool for understanding the interplay of transport and reaction times between different sub-catchments, which controls nitrate export in a mesoscale heterogeneous catchment.</p><p>Nguyen, T. V., Kumar, R., Lutz, S. R., Musolff, A., Yang, J., & Fleckenstein, J. H. (2020). Modeling Nitrate Export from a Mesoscale Catchment Using StorAge Selection Functions. Water Resources Research, 56, e2020WR028490</p>

A Pressure-Invariant Neutral Density Variable for the World's Oceans

We present a new method to calculate the neutral density of an arbitrary water parcel. Using this method, the value of neutral density depends only on the parcel’s salinity, temperature, latitude, and longitude and is independent of the pressure (or depth) of the parcel, and is therefore independent of heave in observations or high-resolution models. In this method we move the parcel adiabatically and isentropically like a submesoscale coherent vortex (SCV) to its level of neutral buoyancy on four nearby water columns of a climatological atlas. The parcel’s neutral density γSCV is interpolated from prelabeled neutral density values at these four reference locations in the climatological atlas. This method is similar to the neutral density variable γn of Jackett and McDougall: their discretization of the neutral relationship equated the potential density of two parcels referenced to their average pressure, whereas our discretization equates the parcels’ potential density referenced to the pressure of the climatological parcel. We calculate the numerical differences between γSCV and γn, and we find similar variations of γn and γSCV on the ω surfaces of Klocker, McDougall, and Jackett. We also find that isosurfaces of γn and γSCV deviate from the neutral tangent plane by similar amounts. We compare the material derivative of γSCV with that of γn, finding their total material derivatives are of a similar magnitude.

The Coupled Ocean–Atmosphere Hydrothermohaline Circulation

The thermohaline circulation of the ocean is compared to the hydrothermal circulation of the atmosphere. The oceanic thermohaline circulation is expressed in potential temperature–absolute salinity space and comprises a tropical cell, a conveyor belt cell, and a polar cell, whereas the atmospheric hydrothermal circulation is expressed in potential temperature–specific humidity space and unifies the tropical Hadley and Walker cells as well as the midlatitude eddies into a single, global circulation. The oceanic thermohaline streamfunction makes it possible to analyze and quantify the entire World Ocean conversion rate between cold–warm and fresh–saline waters in one single representation. Its atmospheric analog, the hydrothermal streamfunction, instead captures the conversion rate between cold–warm and dry–humid air in one single representation. It is shown that the ocean thermohaline and the atmospheric hydrothermal cells are connected by the exchange of heat and freshwater through the sea surface. The two circulations are compared on the same diagram by scaling the axes such that the latent heat energy required to move an air parcel on the moisture axis is equivalent to that needed to move a water parcel on the salinity axis. Such a comparison leads the authors to propose that the Clausius–Clapeyron relationship guides both the moist branch of the atmospheric hydrothermal circulation and the warming branches of the tropical and conveyor belt cells of the oceanic thermohaline circulation.

Perspectives of transient tracer applications and limiting cases

Currently available transient tracers have different application ranges that are defined by their temporal input (chronological transient tracers) or their decay rate (radioactive transient tracers). Transient tracers range from tracers for highly ventilated water masses such as sulfur hexafluoride (SF6) through tritium (3H) and chlorofluorocarbons (CFCs) up to tracers for less ventilated deep ocean basins such as argon-39 (39Ar) and radiocarbon (14C). In this context, highly ventilated water masses are defined as water masses that have been in contact with the atmosphere during the last decade. Transient tracers can be used to empirically constrain the transit time distribution (TTD), which can often be approximated with an inverse Gaussian (IG) distribution. The IG-TTD provides information about ventilation and the advective/diffusive characteristics of a water parcel. Here we provide an overview of commonly used transient tracer couples and the corresponding application range of the IG-TTD by using the new concept of validity areas. CFC-12, CFC-11 and SF6 data from three different cruises in the South Atlantic Ocean and Southern Ocean as well as 39Ar data from the 1980s and early 1990s in the eastern Atlantic Ocean and the Weddell Sea are used to demonstrate this method. We found that the IG-TTD can be constrained along the Greenwich Meridian south to 46° S, which corresponds to the Subantarctic Front (SAF) denoting the application limit. The Antarctic Intermediate Water (AAIW) describes the limiting water layer in the vertical. Conspicuous high or lower ratios between the advective and diffusive components describe the transition between the validity area and the application limit of the IG-TTD model rather than describing the physical properties of the water parcel. The combination of 39Ar and CFC data places constraints on the IG-TTD in the deep water north of the SAF, but not beyond this limit.

An oscillating bottom boundary layer connects the littoral and pelagic regions of Lake Opeongo, Canada

The movement of a thermocline can drive strong benthic currents, which can transport nutrients from sediments into the water column via pore water advection or sediment resuspension. We report field observations of near-shore benthic velocities and offshore thermocline movements in Lake Opeongo; a medium-sized lake typical of the Canadian Shield. We find that during large thermocline deflections there are sustained currents >6 cm s−1 in the near-shore benthic layer. The mean current was 1.75 cm s−1 and the maximum current is 10.3 cm s−1. At our site, the net transport is offshore even though the thermocline oscillates up and down so that currents are sometimes upslope and inshore. We estimate the excursion length of a water parcel over the 31-day deployment period, and determine that the mean daily excursion length is 630 m, with the maximum value being 2 km offshore. Given that the south arm of Lake Opeongo is 6 km long and 0.6 km wide, the predicted excursion length of water implies that there is strong connectivity between the sediment in the littoral zone, and the metalimnetic waters offshore. As Lake Opeongo is oligotrophic, any nutrient pulses from the sediment will be quickly taken up by the plankton.

Energy Conversion, Mixing Energy, and Neutral Surfaces with a Nonlinear Equation of State

A local neutral plane is defined so that a water parcel that is displaced adiabatically a small distance along the plane continues to have the same density as the surrounding water. Since such a displacement does not change the density field or the gravitational potential energy, it is generally assumed that it does not produce a restoring buoyancy force. However, it is here shown that because of the nonlinear character of the equation of state (in particular the thermobaric effect) such a neutral displacement is accompanied by a conversion between internal energy E and gravitational potential energy U, and an equal conversion between U and kinetic energy K. While there is thus no net change of U, K does change. This implies that a force is in fact required for the displacement. It is further shown that displacements that are orthogonal to a vector P do not induce conversion between U and K, and therefore do not require a force. Analogously to neutral surfaces, which are defined to be approximately orthogonal to the dianeutral vector N, one may define “P surfaces” to be approximately orthogonal to P. These P surfaces are intermediate between neutral surfaces and surfaces of constant σ0 (potential density reference to the surface). If the equation of state is linear, there exists a well-known expression for the mixing energy in terms of the diapycnal flow. This expression is here generalized for a general nonlinear equation of state. The generalized expression involves the velocity component along P. Since P is not orthogonal to neutral surfaces, this means that stationary flow along neutral surfaces in general requires mixing energy.

Lagrangian Analysis of the Meridional Overturning Circulation in an Idealized Ocean Basin

The Lagrangian ocean model is used as a tool to simulate the response of the basin-scale overturning circulation to spatially variable diapycnal mixing in an idealized ocean basin. The model explicitly calculates the positions, velocities, and tracer properties of water parcels. Owing to its Lagrangian formulation, numerical diffusion is completely eliminated and water parcel pathways and water mass ages can be quantified within the framework of the discrete, advective transit time distribution. To illustrate the ventilation pathways, simulated trajectories were tracked backward in time from the interior ocean to the surface mixed layer where the water parcel was last in contact with the atmosphere. This new diagnostic has been applied to examine the response of the meridional overturning circulation to highly localized diapycnal mixing through sensitivity experiments. In particular, the focus is on three simulations: the first holds vertical diffusivity uniform; in the second, the vertical diffusivity is confined within an equatorial box; and the third simulation has a diffusivity pattern based on idealized hurricane-induced mixing. Domain-integrated deep ventilation rates and heat transport are similar between the first two cases. However, locally enhanced mixing yields about 30% younger water mass age in the tropical thermocline due to intense localized upwelling. In the third simulation, a slower ventilation rate of deep waters is found to be due to the lack of abyssal mixing. These results are interpreted using the classical theories of abyssal circulation, highlighting the strong sensitivity of the ventilation pathways to the spatial distribution of diapycnal mixing.