Stream temperature prediction in ungauged basins: review of recent approaches and description of a new physics-derived statistical model

The development of stream temperature regression models at regional scales has regained some popularity over the past years. These models are used to predict stream temperature in ungauged catchments to assess the impact of human activities or climate change on riverine fauna over large spatial areas. A comprehensive literature review presented in this study shows that the temperature metrics predicted by the majority of models correspond to yearly aggregates, such as the popular annual maximum weekly mean temperature (MWMT). As a consequence, current models are often unable to predict the annual cycle of stream temperature, nor can the majority of them forecast the inter-annual variation of stream temperature. This study presents a new statistical model to estimate the monthly mean stream temperature of ungauged rivers over multiple years in an Alpine country (Switzerland). Contrary to similar models developed to date, which are mostly based on standard regression approaches, this one attempts to incorporate physical aspects into its structure. It is based on the analytical solution to a simplified version of the energy-balance equation over an entire stream network. Some terms of this solution cannot be readily evaluated at the regional scale due to the lack of appropriate data, and are therefore approximated using classical statistical techniques. This physics-inspired approach presents some advantages: (1) the main model structure is directly obtained from first principles, (2) the spatial extent over which the predictor variables are averaged naturally arises during model development, and (3) most of the regression coefficients can be interpreted from a physical point of view – their values can therefore be constrained to remain within plausible bounds. The evaluation of the model over a new freely available data set shows that the monthly mean stream temperature curve can be reproduced with a rootmean-square error (RMSE) of +/-1.3 °C, which is similar in precision to the predictions obtained with a multi-linear regression model. We illustrate through a simple example how the physical aspects contained in the model structure can be used to gain more insight into the stream temperature dynamics at regional scales.

A New Analytical Model for the Prediction of Stream Temperature in Ungauged Basins

Aurélien Gallice, Wolf Hendrik Huwald, Michael Lehning, Bettina Schaefli

Stream temperature is a hydrological factor which affects the habitat suitability of many aquatic species, and is therefore of great concern in the actual context of climate change. Its prediction in ungauged basins is usually based on statistical approaches, such as multi-linear regression models or machine learning techniques. These models typically predict temperature metrics corresponding to yearly aggregates, such as the popular annual maximum weekly mean temperature (MWMT). As a consequence, they are often unable to predict the annual cycle of stream temperature, nor can the majority of them forecast the inter-annual variation of stream temperature. This study presents a new model to estimate the monthly mean stream temperature of ungauged rivers over multiple years in an Alpine country (Switzerland). Contrary to the current statistical approaches, this model rests upon the analytical solution of a simplified version of the energy-balance equation over an entire stream network. This physically-based approach presents some advantages, among which the possibility to interpret the model coefficients from a physical point of view, hereby enabling the restriction of their calibration range. The evaluation of the model over a new data set shows that the monthly mean stream temperature curve can be reproduced with a root mean square error of 1.3°C, which is similar in precision to the predictions obtained with standard multi-linear regression models. We illustrate through a simple example how the physical basis of the model can be used to gain more insight into the stream temperature dynamics at regional scales.

2015

Comparison of stream temperature modeling approaches: the case of a high Alpine watershed

Francesco Comola, Aurélien Gallice, Wolf Hendrik Huwald, Michael Lehning

Stream temperature controls important aspects of the riverine habitat, such as the rate of spawning or death of many fish species, or the concentration of numerous dissolved substances. In the current context of accelerating climate change, the future evolution of stream temperature is regarded as uncertain, particularly in the Alps. This uncertainty fostered the development of many prediction models, which are usually classified in two categories: mechanistic models and statistical models. Based on the numerical resolution of physical conservation laws, mechanistic models are generally considered to provide more reliable long-term estimates than regression models. However, despite their physical basis, these models are observed to differ quite significantly in some aspects of their implementation, notably (1) the routing of water in the river channel and (2) the estimation of the temperature of groundwater discharging into the stream. For each one of these two aspects, we considered several of the standard modeling approaches reported in the literature and implemented them in a new modular framework. The latter is based on the spatially-distributed snow model Alpine3D, which is essentially used in the framework to compute the amount of water infiltrating in the upper soil layer. Starting from there, different methods can be selected for the computation of the water and energy fluxes in the hillslopes and in the river network. We relied on this framework to compare the various methodologies for river channel routing and groundwater temperature modeling. We notably assessed the impact of each these approaches on the long-term stream temperature predictions of the model under a typical climate change scenario. The case study was conducted over a high Alpine catchment in Switzerland, whose hydrological and thermal regimes are expected to be markedly affected by climate change. The results show that the various modeling approaches lead to significant differences in the model predictions. It is also shown that the temperature of groundwater discharging into the stream has a marked impact on the modeled stream temperature at the catchment outlet. This supports the development of more accurate methodologies to estimate groundwater temperature in current hydrological models.

2015

Statistical Analysis of Mountain Permafrost Temperatures

Evelyn Zenklusen Mutter

The consequences of climate change are clearly visible in the Swiss Alps. In the past decades, increasing air temperatures have induced pronounced glacier retreat and permafrost thawing. Thawing permafrost in steep terrain is a potential natural hazard, as it can become unstable and trigger mass movements such as settlement, debris flows or rock fall. The WSL Institute for Snow and Avalanche Research SLF has been measuring ground temperatures and displacements in permafrost boreholes for more than a decade. This thesis aimed to analyse these ground temperatures with statistical methods, assessing possible changes, trends and physical coherencies. In a first step, temporal changes in daily ground temperatures measured in two adjacent boreholes at Muot da Barba Peider in the Eastern Swiss Alps were analysed. Statistical models, which could for example describe changes in the amplitudes or in the mean, were used to estimate possible trends. The results for the period 1996 - 2008 revealed increasing summer temperature for the upper ground layers, whereas winter temperatures had decreased. For the frozen rock below 10 m however, a general temperature increase was found. Although increasing summer temperatures were consistent with the development of the air temperatures, decreasing winter temperatures could be attributed to a thin early winter snow depth. The general warming trend in the deeper layers was assigned to increased heat transfer through the mountain ridge of Muot da Barba Peider induced by warming air temperatures and lower snow depths. These results confirm that permafrost temperatures in the Alps are influenced by factors such as snow cover, surface properties, hydrology and topography. Increasing air temperatures do not necessarily induce permafrost thawing. Special attention was paid to the so-called "active layer", the topmost ground layer above permafrost, which seasonally thaws in summer. An increase in its thickness implies a potential increase of the material which might be released in a mass movement. Typical active layer characteristics have been analysed and compared for ten different permafrost sites. Whereas over the past decade, the active layer remained rather constant at the individual sites, significant differences due to local terrain properties were visible. The comparison of the daily development of the active layer thickness with that of the thawing degree days revealed that ice-rich ground layers delay the active layer development efficiently and thus isolate the permafrost from warm air temperatures. Two of the ten sites, however, revealed abrupt active layer deepening due to lateral air and/or water flows. Further investigation of the dependence between air and ground temperature was performed. Transfer function models were used to quantify the relation between air and ground temperatures measured at 0.5 m depth at seven different permafrost sites. The results showed that the delay between daily changes in the air and ground temperature ranges from one to six days, depending on the site. The most efficient relation was found for a very coarse-blocky rock glacier site, whereas scree slopes with smaller grain sizes showed a weaker and more prolonged relation. The main heat transfer mechanism in permafrost is conduction, but due to phase change, air or water flows, heat can also be transferred non-conductively. A statistical procedure including spectral analysis, order-restricted inference and a false discovery rate procedure has been developed to detect depths and frequencies at which significant non-conductive heat transfer processes occur. The application of the procedure to two-hourly borehole temperatures measured at Muot da Barba Peider revealed significant non-conductive heat transfer for the period 2005 - 2009 only in an ice-rich layer between 1 and 1.9 m depth. To gain deeper insight into the processes occurring shorter (three-week) periods have been analysed. The results showed non-conductive heat transfer processes that could be attributed to phase changes at the freezing front and at the base of the active layer in autumn, to convective air and vapour flows through the frozen scree in winter, and to phase changes and meltwater infiltration during the thawing period in spring. Analyses of borehole temperatures also revealed special phenomena. A case study for the famous permafrost site at Flüela Pass showed that the permafrost body inside the scree slope, close to the lake has degraded from 7 m to 3.5 m thickness within four years. This rapid permafrost degradation could be attributed to a seasonal ventilation system inside the scree, leading to condensation which melts the permafrost body from below. Increasing lake water temperatures might accelerate the phenomenon. The ground temperatures analysed in this work include about one decade of measurements and therefore are too short for climate-related statements. However, the statistical analyses performed give an interesting insight into the development of permafrost ground temperatures during the past ten years and their interaction with air temperature and local properties. The presented results furthermore emphasize the strong spatial variability of the ground thermal regime in mountain permafrost.

EPFL2012

Statistical Analysis of Mountain Permafrost Temperatures

Evelyn Zenklusen Mutter

EPFL2012

Comparison of stream temperature modeling approaches: the case of a high Alpine watershed

Francesco Comola, Aurélien Gallice, Wolf Hendrik Huwald, Michael Lehning

2015