1. On the suitability of air temperature as a predictive tool for lake surface temperature in a changing climate: A case study for Lake Tahoe, USA
Nathan C. Healey1, Sebastiano Piccolroaz2, Simon J. Hook1, Marco Toffolon2, John D. Lenters3, Geoffrey Schladow4
NASA Jet Propulsion Laboratory, California Institute of Technology, 2. University of Trento, 3.LimnoTech, 4. University of California, Davis
American Geophysical Union Fall Meeting 2015 – Abstract GC53F-1281
Abstract
The ability to predict surface water temperature is essential toward understanding how future climate scenarios will impact inland water bodies such as lakes. Numerous predictive models have been developed to perform this task although many require meteorological inputs whose future prediction is usually associated with large uncertainties, such as e.g., precipitation, cloudiness, wind and radiative fluxes. Conversely, predictions of air temperature from Global Climate Models (GCMs) are usually more reliable and available. The predictive model air2water relies solely on air temperature data to predict lake surface temperature. The objective of this study is to demonstrate that air2water can be used as a predictive tool for climate change scenarios through a case study focused on Lake Tahoe, CA/NV, USA. Lake Tahoe has been selected due to extensive historical in-situ measurements that have been collected at that location since 1967 which we utilize to calibrate and validate air2water, and evaluate its performance. For model runs, we utilize different sources of air temperature data (buoys, land-based weather stations, GCMs) to establish how robustly air2water performs. We employ air temperature data from a combination of global gridded datasets including Climate Research Unit (CRU) TS3.21 (historical), and GCM output from the Coupled Model Intercomparison Project, Phase 5 (CMIP5) Community Climate System Model, version 4 (CCSM4) model (future) with representative concentration pathways of 4.5 and 8.5. Here, we present results from air2water predictions of the relationship between air and water temperature that demonstrate how this model is able to replicate trends on seasonal and interannual timescales. This finding shows promise toward understanding the impacts of future climate change on lakes and to expanding our study to lake surface temperatures globally.
Methodology: air2water
air2water [Piccolroaz et al., 2013] is a simple lumped model that allows for estimating Lake Surface Temperature (LST) using air temperature as the only meteorological forcing. air2water is derived from the volume-integrated heat equation applied to the upper (well-mixed) layer of the lake:
𝜌 𝑐 𝑝 𝑉 𝑠 𝑑 𝑇 𝑤 𝑑𝑡 =𝐴 H 𝑛𝑒𝑡 (1)
Performance in Capturing Long-term Trends
In order to further verify the good performances of the model, and in particular its ability to capture long-term trends, air2water has been tested using 46 years of Ta and Tw measurements (UC Davis, Table 1).
The model has been calibrated during and validated during the two periods: and
Temperature [oC]
Figure 3. Main heat exchange affecting the surface layer.
𝝆 is water density
𝒄 𝒑 is the specific heat capacity
𝑽 𝒔 is the surface volume of water involved in the heat exchange with the atmosphere (time dependent)
𝑻 𝒘 is the LST
𝒕 is time
𝑨 is the surface area of the lake
𝐇 𝒏𝒆𝒕 is the net heat flux into the upper water volume (accounting for the main fluxes entering and exiting V s : short and long wave radiation, sensible and latent heat fluxes).
Figure 6. Comparison between long-term trends of air temperature and lake surface temperature (observed and simulated) within the period Trends are shown for the temperatures averaged over the four seasons: January-March (JFM), April-June (AMJ), July-August (JAS), and October-December (OND). 
Seasonal trends are generally well captured even when substantially different than air temperature: this is possible because, albeit in a simplified form, air2water includes all the major physical processes driving LST dynamics including thermal stratification.  
In order to keep the formulation of the model as simple as possible:
linearization of heat flux terms by Taylor expansion
air temperature as a proxy for the integrated effect of the relevant processes and fluxes (see e.g., Livingstone and Padisák, 2007)
Study Site and Input Data
Prediction under climate change scenarios
Model tested considering two future scenarios: CMIP5-CCSM4 RCP 4.5 and RCP 8.5 to evaluate the effectiveness of air2water as a predictive tool for climate change scenarios.
RCP4.5 and RCP8.5 scenarios have been constructed for each Ta /Tw pair listed in Table 2 (change factor method, or delta method, see e.g. Minville et al., 2008; Diaz-Nieto and Wilby, 2005), for the period
air2water is run in forward mode with the set of parameters calibrated for the historical series (parameters are different for the different sources of air temperature data).
LST prediction is the same irrespective of the source of air temperature data adopted (i.e., notice that the slope of the water temperature/air temperature linear fit is the same in all cases, Figure 7). This results is certainly not trivial, even with models of higher complexity.
Figure 4. Seasonal evolution of the dimensionless thickness 𝛿 of the surface well-mixed layer for the general case of a dimictic lake.
The equations of the model in its full (8-parameters, from a1
to a8) version reads as follows:
𝑑 𝑇 𝑤 𝑑𝑡 = 1 𝛿 𝑎 1 + 𝑎 2 𝑇 𝑎 − 𝑎 3 𝑇 𝑤 + 𝑎 5 𝑐𝑜𝑠 2𝜋 𝑡 𝑡 𝑦 − 𝑎 , (2)
𝛿=exp − 𝑇 𝑤 − 𝑇 ℎ 𝑎 for 𝑇 𝑤 ≥ 𝑇 ℎ 𝛿=exp − 𝑇 ℎ − 𝑇 𝑤 𝑎 7 +exp − 𝑇 𝑤 𝑎 for 𝑇 𝑤 < 𝑇 ℎ (3)
𝑻 𝒂 is air temperature
𝑻 𝒉 is a reference value of the deep water temperature, which is approximately 4°C for deep dimictic lakes
𝜹 is the dimensionless depth of the surface well-mixed layer, i.e., the ratio between the volume 𝑉 𝑠 of the surface layer and a reference volume 𝑉 𝑟 (maximum volume affected by the surface heat flux when the lake experiences the weakest stratification conditions)
The water temperature/air temperature relationship is approximately linear. a
RCP 4.5
Air Temperature [oC]
Water Temperature [oC] b
RCP 8.5
Air Temperature [oC]
Water Temperature [oC]
NASA
UC Davis
SNOTEL
CRU
CMIP5-CCSM4
Air temperature datasets:
Performance in Historical Periods
Figure 1. Map of Lake Tahoe with locations of on-shore weather stations and instrumented buoys (a); example of CRU TS3.21 grid spacing (b); and example of CCSM4 grid spacing (c).
Model calibration is performed by minimizing the Root Mean Square Error (RMSE) between simulations and observations, using water temperature from NASA buoys, and all available datasets of air temperature (see Table 1).
Details about
Lake Tahoe
Elevation: 1897 m A.S.L.
Average Depth: m.
Maximum Depth: m.
Total Surface Area: km2.
Dimensions: 35.4 km long, 19.3 km wide.
Mixing Regime: oligomictic (turnover every ~4 years)
Figure 7. Relationships between reconstructed air temperature and modeled lake surface temperature in the four seasons for two climate change scenarios: (a) RCP 4.5, and (b) RCP 8.5.
Calibration Periods: (UC Davis, CRU, SNOTEL, CMIP5-CCSM4), (NASA buoys)
Validation Period (when available):
Methods: automatic optimization procedure (i.e., Particle Swarm Optimization),
Objective: minimization of the RMSE at monthly resolution
Conclusions
Results: averaged values of RMSE of about 0.54°C and 0.66°C for calibration and validation, respectively (see Table 2).
air2water is a robust tool to predict lake surface temperature when only air temperature is available.
The model shows good performances in capturing historical trends, and roubustness in predicting future trends.
Given different air temperature datasets (even data from GCMs) the outputs in projection are always approximately the same.
Future work will analyze the application of the air2water model for climate change prediction in other lakes for which in-situ data are available. The expected thermal response of lakes will be investigated in details.
calibration
validation
Table 2. Monthly RMSE obtained in calibration and in validation against NASA buoy water temperature considering different sources of observed air temperature.
Figure 2. NASA buoy deployed on Lake Tahoe.
Air Temperature Data Source
RMSE [°C]
Cal
Val
NASA buoy
0.45
0.60
UC Davis
0.53
0.67
SNOTEL
0.56
0.71
CRU TS3.21
n.a.
CMIP5-CCSM4
0.58
Table 1. Details of data utilized in modeling water temperature with air2water
Data set
Data type
Height/Depth and Resolution
Time interval
Frequency
Water temperature
NASA buoy
in situ
water surface/skin - point location
present
5-minute
UC Davis buoy
water surface/~1 m depth - point location
present
Bi-weekly
Air temperature
~3 m height - point location
present
UC Davis meteorological station
Daily
SNOTEL meteorological station
~170 m height - point location
present
Climate Research Group (CRU) TS3.21
Gridded Observations
Equivalent height ~2 m - 0.5o x 0.5o
Monthly
CMIP5-CCSM4
Gridded GCM
Equivalent height ~2 m - 1.0o x 1.0o
References and Acknowledgements
Diaz-Nieto, J., Wilby, R.L. (2005) A comparison of statistical downscaling and climate change factor methods: Impacts on low flows in the River Thames, United Kingdom. Climatic Change, 69, 2,
Livingstone, D.M., Padisak, J. (2007) Large-scale coherence in the response of lake surface-water temperatures to synoptic-scale climate forcing during summer. Limnol. and Oceanog., 52,
Minville, M., Brissette, F., Leconte, R. (2008) Uncertainty of the impact of climate change on the hydrology of a Nordic watershed. Journal of Hydrol., , 70:83.
Piccolroaz, S., Toffolon, M., Majone, B. (2013) A simple lumped model to convert air temperature into surface water temperature in lakes. Hydrol. Earth Syst. Sci., 17, 3323–3338.
We thank Gerardo Rivera, Kendall Holmes, and Linley Kroll from JPL, and Brant Allen and staff from the University of California, Davis Tahoe Environmental Research Center for their assistance in maintaining field data collection and the NASA buoys. The research described on this poster was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. The authors would also like to acknowledge the National Climate Assessment.
Figure 5. Comparison between air temperature and observed and simulated water temperature for the case of UC Davis (Ta) and NASA buoy (Tw)