Number range CHAPTERNWS-HL Cold Season Processes

Research and Development

Victor Koren, Eric Anderson, Michael Smith

Hydrology Laboratory

Office of Hydrologic Development

November 13, 2023

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height="3.7569444444444446in"}

Executive Summary

The National Weather Service Hydrology Laboratory (NWS HL) has a rich
history of modeling cold season processes. The NWS operational snow
model (SNOW-17) is widely recognized as a sound temperature-index model
that well represents the physical processes for which it is calibrated.
It is used around the world in a number of research and operational
settings. A more modest amount of research has been directed to
researching the modifications of the rainfall-runoff transformation due
to the effects of frozen ground.

The infusion of funding from the Advanced Hydrologic Prediction Service
(AHPS) initiative has brought new vigor to HL research and development
in cold season hydrologic processes. Several years ago, collaboration
between the Office of Hydrologic Development and the Environmental
Modeling Center (EMC) of the NWS National Centers for Environmental
Prediction (NCEP) has led to the successful implementation of energy
budget snow models and physically-based frozen ground components in the
land surface component of the NCEP ETA numerical weather prediction
model.

More recently, HL has garnered the experience gained from the
collaborative work with NCEP to renew its efforts into advanced snow
modeling methods for river forecasting. These efforts include
participation in the international Snow Model Intercomparison Project
(SnowMIP) with two models as well as making several modifications to its
current operational temperature index model. A major thrust is planned
to evaluate the utility and quality of new and emerging data sets to
drive operational energy budget snow models for river forecasting. A
pioneering effort to develop an advanced method of computing the effects
of frozen ground on the rainfall-runoff process is nearing completion.
Research to-date shows that this effort can successfully simulate soil
temperature versus depth. Moreover, initial indications are that this
approach produces runoff simulations that are equivalent or superior to
those generated using the existing conceptual approach which requires
seven parameters to calibrate. The beauty of the new approach is that it
is truly physically-based and does not require parameter calibration.

Contents

1.  Introduction 4

2\. Purpose and Scope 4

3\. Relevant web sites 4

4\. Modeling of Snow Accumulation and Melt 4

4.1 Research and Development Strategy4 4

4.1.1 Phase 1 Internal HL research 8

4.1.2 Phase 1 Collaborative Research

4.1.2.a Snow Model Intercomparison Project 8

4.1.2.b NLDAS 9

4.1.3 Phase 2 Evaluation of Data to Support Operational

Energy Budget Model 12

5\. Modeling of Frozen Ground Effects 13

5.1 Research and Development Strategy 13

5.2 Phase 1: Development of physically-based heat transfer component 13

5.3 Phase 2: Implementation of heat transfer component into

water balance model

16

6\. References 18

Appendix 1. Papers and Presentations from Cold Season Process Research

Appendix 2. *Reflections on Future Directions in Snow Modeling for the
Hydrology Program of the National Weather Service*, by Eric Anderson

Appendix 3. HL Comments on Appendix 2.

1\. Introduction

Figure 1 shows that all of the 13 River Forecast Centers (RFCs) of the
NWS have a need to model snow accumulation and melt. Even the RFCs in
the southern tier of the US have areas that experience snow
accumulation, although obviously snow accumulation and melt are dominant
in the intermountain west. Frozen ground effects can also be seen
everywhere, although the upper mid-west experiences the most severe
cases. In this region, a lack of vegetation during the winder, shallow
snow cover, and very cold temperatures produce optimal conditions for
the penetration of frost and subsequent modifications to the
rainfall-runoff process.

2.  Purpose and Scope

The purpose of this document is to provide an overview of the research
and development of snow and frozen ground modeling. While past efforts
will be discussed, the emphasis of this document is on current and
future activities and strategies. This document is not meant to cover
topics such as the effects of ice on river flows.

3\. Relevant web sites

The reader is directed to the following web sites for HL R&D in snow and
frozen ground modeling:

Frozen ground: <http://www.nws.noaa.gov/oh/hrl/frzgrd/index.html>

Snow Modeling: <http://www.nws.noaa.gov/oh/hrl/snow/index.html>

4\. Modeling of Snow Accumulation and Melt

**4.1 Research and Development Strategy**

NWS modeling of snow accumulation and melt for river forecasting began
in the late 1960's with the development of energy budget algorithms
(Anderson, 1968; 1973; 1976). A temperature-index version of this method
(hereafter called Snow-17) was implemented in the National Weather
Service River Forecast System (NWSRFS) in 1973 and is still in use today
at the majority of NWS River Forecast Centers (RFCs). The major reason
this temperature index form of the energy budget model was implemented
is that the data required to force an energy budget model have not been
reliably available and of sufficient quality.

In January, 1996, a major flood occurred in the Northeastern United
States. This event was largely due to the rapid melt of above-average
snow accumulations combined with intense rainfall (Office of Hydrology,
1998; Anderson and Larson, 1997). During the peak of the snowmelt,
extreme conditions prevailed: air temperatures ranged from 13-17^o^ C,
relative humidity was above 90 percent, and the peak sustained winds
were generally over 10 m/s at open sites. Such conditions were well
beyond those for which Snow-17 was calibrated in these regions.

This event and the recommendation from the subsequent disaster survey
report (Office of Hydrology, 1998) underscored the need to re-examine
the utility of energy budget snow models for river forecasting. HL thus
began a dedicated snow research thrust consisting of two phases as shown
in Figure 2. Phase 1 is characterized by analysis of the performance of
the existing Snow-17 in the Snow Model Intercomparion Project (SnowMIP)
as well as exploring several modifications to the algorithm itself. [We
consider that these modifications may improve the operational
performance of Snow-17]{.mark} in cases involving abnormal conditions
for which the model is not calibrated. Phase 2 of the research will
focus on the evaluation of new and emerging data sets that could
potentially drive an operational energy budget snow model for river
forecasting.

![](media/image2.wmf)

Figure 1. Boundaries of NWS River Forecast Center domains. (Note:
Alaska-Pacific RFC domain not shown.

Herein lies one of the major assertions of our snow research strategy:
**the physics of snow accumulation and melt are well understood and that
robust and reliable energy budget models of these processes already
exist**. Indeed, HL's collaboration with NCEP resulted in the successful
inclusion of such a formulation in the land surface component of the Eta
model (Ek et al., 2003; Slater et al, 2001; Koren et al., 1999; Schloser
et al., 2000) and the participation of HL in the recent SnowMIP project
(Koren and Anderson, 2001). Therefore, we believe that Phase 2 should
concentrate on the analysis of new and emerging data sources to drive
advanced snow models and not focus on the development of new algorithms
to model snow accumulation and ablation. Another key component of Phase
2 research is the inclusion of Snow-17 in a distributed model for river
forecasting.

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<td></td>
<td>‘94</td>
<td colspan="2">‘95</td>
<td>‘96</td>
<td colspan="2">‘97</td>
<td colspan="2">‘98</td>
<td colspan="2">‘99</td>
<td colspan="2">‘00</td>
<td colspan="4">‘01</td>
<td>‘02</td>
<td>‘03</td>
<td colspan="2">‘04</td>
<td colspan="3">‘05</td>
<td>‘06</td>
<td>Beyond</td>
</tr>
<tr class="even">
<td></td>
<td></td>
<td></td>
<td colspan="2"></td>
<td></td>
<td colspan="2"></td>
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<td></td>
<td colspan="2"></td>
<td colspan="3"></td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td colspan="20"><strong>SNOW - Phase 1: Analysis &amp; Improvements of
SNOW-17</strong></td>
<td colspan="2"></td>
<td colspan="3"></td>
<td colspan="2"></td>
</tr>
<tr class="even">
<td colspan="4"></td>
<td colspan="5"><p>Jan. ’96 NE snowmelt event</p>
<p>analysis</p></td>
<td colspan="4">SnowMIP participation</td>
<td colspan="9"></td>
<td colspan="3"></td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td></td>
<td colspan="3"></td>
<td colspan="3"></td>
<td colspan="5"><p>Wind function</p>
<p>modification</p></td>
<td colspan="9"></td>
<td colspan="6"></td>
</tr>
<tr class="even">
<td></td>
<td colspan="3"></td>
<td colspan="3"></td>
<td colspan="4"></td>
<td colspan="13">Computation of snow depth</td>
<td colspan="3"></td>
</tr>
<tr class="odd">
<td></td>
<td colspan="16"></td>
<td colspan="6">Analysis of refreezing of liquid water held in
snowpack</td>
<td colspan="4"></td>
</tr>
<tr class="even">
<td></td>
<td colspan="16"></td>
<td colspan="8">Snow-17 in distributed model</td>
<td colspan="2"></td>
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<td colspan="18"><strong>SNOW- Phase 2: Energy Budget Snow
Modeling</strong></td>
</tr>
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<td colspan="13">SnowMIP: analysis of results</td>
<td colspan="5"></td>
</tr>
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<td colspan="11">Analysis of energy forcing data</td>
</tr>
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<td colspan="24"><strong>Physically-based Frozen Ground
Modeling</strong></td>
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<td colspan="11">Devl. of heat transfer component and Implement into ETA
land surface model</td>
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<td colspan="6">Phase 1. Reformulation of SAC-SMA ‘frost index’
component</td>
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<td></td>
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<td colspan="8">Phase 2: Combine water and heat transfer
parameterizations to generate physically-based runoff during cold
seasons</td>
</tr>
</tbody>
</table>

Figure 2. Major plan elements for snow and frozen ground research and
development.

In a parallel thrust, HL is actively developing a physically-based
approach to model the effects of frozen ground on the rainfall-runoff
transformation. Again, this effort is based on the successful
collaboration with NCEP in the development of their land surface
component (e.g., Ek et al., 2003; Koren et al., 1999).

**4.1.1 Phase 1 Snow Modeling: Internal HL R&D**

As shown in Figure 2, this phase contains several efforts to modify the
existing Snow-17 model. These include procedures to aid in real time
manual updating during abnormal events as well as generating new output
fields to aid in calibration and forecasting.

[Wind Function Modification]{.underline}

This effort resulted from Recommendation 1.2 of the disaster survey
report for the large flood event that occurred in the Northeastern
United States in January, 1996 (OHD, 1998). This specific recommendation
called for a run-time modification to be added to the NWSRFS operational
code so that the forecaster can adjust the wind function (Snow-17 UADJ
parameter) during rain-on-snow events. As seem in Figure 3, variations
in the UADJ parameter can have a large effect on the snow pack.

[Computation of Snow Depth]{.underline}

In addition to computing snow water equivalent, Snow-17 has been
modified to produce a time series of computed snow depth. This
modification resulted from the need to have computed temperatures at the
snow-soil interface for frozen ground modeling. This time series is very
helpful in the calibration phase since observed snow depth data are
available in some places. This modification was delivered to the RFCs at
the beginning of FY04.

[Refreezing of liquid water in the snow pack]{.underline}.

[In the course of participating in the SnowMIP project, attention was
given to more fully understanding the snow-pack heat deficit accounting
of Snow-17. While the Snow-17 model behaves exactly as intended by the
developer (Anderson, 1973), there *may* be the possibility to modify the
heat deficit algorithm to achieve results such as those in Figure 4.
Further work is necessary to definitively confirm that any such
modifications to Snow-17 are valid and do not violate the underlying
assumptions of the model.]{.mark}

[Adoption of Snow-17 in a Distributed Model]{.underline}

A cross-cutting effort between snow and distributed modeling will be the
inclusion of Snow-17 into the distributed model within the NWS Hydrology
Lab Research Modeling System. Appendix 2 presents further ideas
connected with implementing Snow-17 in a distributed mode.

**4.1.2 Phase 1 Snow Modeling: Collaborative Research**

**4.2.1.a. Snow Model Intercomparison Project**.

Complementing HL's internal research, a significant emphasis was placed
on collaborating with other research partners. This was primarily
achieved by participating in SnowMIP
(<http://www.cnrm.meteo.fr/snowmip/>). This successful project was
organized by the International Commission on Snow and Ice (ICSI), a
commission of the International Association of Hydrologic Sciences
(IAHS). SnowMIP activities were coordinated through Météo-France:
National Center for Meteorological Research. Participants submitted
uncalibrated simulations from 26 models. The overall goal of SnowMIP was
to meet the need to have a more general comparison of snow models. The
following objectives were identified (Etchevers et al., 2002):

-   To define a common method to compare a large variety of models,

-   To estimate the impact of the different physical parameterizations

-   To identify the key processes for each application.

HL viewed SnowMIP as an accelerated venue through which advances to the
NWS snow modeling capability could be identified. HL participated in
SnowMIP with two models: the Snow-17 temperature-index model and the
energy budget snow model incorporated into the land surface component of
the NCEP numerical weather prediction model (Koren and Anderson, 2001).
This energy budget snow model was developed by Victor Koren of HL (Koren
et al., 1999). Hereafter, this latter model will be referred to as the
NCEP land surface model (LSM). In this way, HL could measure the
strengths of both algorithms against observed data and 24 other models
of various complexity.

Findings from HL's participation in SnowMIP.

HL gained valuable experience from the comparisons resulting from
SnowMIP:

-   Model complexity does not guarantee accuracy. This is clearly seen
    in Figure 5, which shows the wide disparity amongst energy budget
    models in computing snow-water equivalent.

-   Temperature index models provide practical and reasonable results,
    however they are sensitive to weather conditions, specifically wind
    and solar radiation conditions.

-   Energy budget models are sensitive to input data errors,
    specifically wind, solar radiation and albedo treatment.

-   Data quality and uncertainties are a major concern in the effective
    use of an energy budget snow model.

**4.1.2.b North American Land Data Assimilation System**

Additional analysis of Snow-17 and the NOAH LSM snow model was gained
through HL's participation in the North American Land Data Assimilation
System (NLDAS) project (Mitchell et al., 2004). NLDAS was designed to
evaluate four land surface models as candidates for a 4-dimensional data
assimilation system for numerical weather and seasonal climate
prediction models. In the 3-year CONUS executions of the models, the NWS
Snow-17 model performed rather well as stated by Mitchel el al. (2004):

> 'The VIC and (Snow-17) models provided the best simulations of
> snowpack water content compared to SNOTEL observations......The
> (Snow-17) snowpack simulations performed rather well, as its simple
> temperature-index based snow pack model bypasses energy balance and
> albedo and thereby bypasses positive feedback loops that haunt
> snowpack simulations in models with surface energy balance.'

This conclusion further underscores the sensitivity of energy budget
snow models to input forcing and the subsequent need to examine the
quality and robustness of input data as called for in Phase 2 snow R&D.

![](media/image3.wmf){width="6.413888888888889in"
height="4.823611111111111in"}

Figure 3. Snow water equivalent and snow depth for two values of the
Snow-17 wind function parameter UADJ.

![](media/image4.wmf){width="6.499305555555556in" height="4.8875in"}

[Figure 4. Effects of a potential modification to the heat deficit
algorithm in Snow-17. Observed values area shown as white vertical lines
in top pane.]{.mark}

![](media/image5.wmf){width="6.499305555555556in" height="4.8875in"}

Figure 5. Simulation of snow-water equivalent by 23 energy-budget snow
models in SnowMIP.

4.1.3 Phase 2: Evaluation of Data to Support Operational Energy Budget
Model

The experience gained from SnowMIP and the NLDAS projects confirmed that
the major issue for advanced snow modeling for river forecasting is not
a new algorithm for snow accumulation and ablation. Rather, we see as
the major need the extensive analysis of new and emerging sources of
temperature, wind, solar radiation, relative humidity, dew point, etc
that are needed to force an energy budget model. At present, HL is
actively trying to hire a specialist to plan and accomplish this task.
Data sources to be examined include output fields from numerical weather
prediction models, satellite-bases observations, and products from the
National Operational Hydrologic Remote Sensing Center (NOHRSC).

5\. Modeling of Frozen Ground Effects

**5.1 Research and Development Strategy**

NWS modeling of frozen ground effects on the rainfall-runoff process
began in the late 1960's with the development of a conceptual
modification to the Sacramento Soil Moisture Accounting Model (SAC-SMA)
(Anderson and Neuman, 1984). This approach used the concept of a frost
index which modified the runoff generated by the SAC-SMA. As a
conceptual model, this approach requires the calibration of 5
parameters.

As stated earlier, a successful collaboration between the Office of
Hydrologic Development and NCEP resulted in the development of a
heat-transfer component of the NCEP land surface model. As reported by
Koren et al. (1999) and Mitchell et al. (2002), this parameterization
proved to be a valid component that reduced biases in certain computed
values.

Capitalizing on this successful collaboration, HL began to develop an
advanced approach to modifying the SAC-SMA for the effects of frozen
ground. The goal of this research is to develop a physically-based heat
transfer component for the SAC-SMA that requires minimal calibration.
Two requirements are identified for this component:

-   Simple enough to run with sparse and noisy data

-   Matches the complexity of the SAC-SMA

As shown in Figure 2, this work consists of two phases. In Phase 1, a
physically-based heat transfer component is developed, while in Phase 2,
the SAC-SMA model is modified to include the heat-transfer component and
the effects of frozen soil on the generation of runoff.

**5.2 Modeling of Frozen Ground Phase 1: Heat Transfer Component**

Work in this phase was directed at modeling the heat transfer in a
column of soil as shown in Figure 6. Two hurdles were overcome to
develop a scheme suitable for the SAC-S MA First, the SAC-SMA model does
not contain an explicit definition of soil layers, although it defines
upper and lower tension and free water storages that could be
transformed in to a number of soil layers. This hurdle was overcome by
recalculating the SAC-SMA storages in to their representative soil
layers using soil porosity data. As such, the total of the SAC-SMA
tension and free water storages is disaggregated into 4 layers as shown
in Figure 7. The transformation between the SAC-SMA soil layers and the
heat transfer component occurs every time step.

The second hurdle to be overcome is that the heat transfer component in
Figure 6 requires the depth of snow above the soil surface, and the
current version of Snow-17 only computed snow water equivalent. Thus,
Snow-17 was modified to compute this value. A secondary result of this
modification was that the resultant time series of computed snow depth
are valuable for the calibration of Snow-17.

Test results showed that the heat transfer component successfully
computes soil temperature at various depths. Figure 8 shows the computed
and observed soil temperatures for a site in Iowa. Good agreement can be
seen between the computed and observed soil temperatures, validating the
heat transfer parameterization.

The SAC-SMA storages, represented as totals of tension and free water,
plus a water content below wilting point, are recalculated into required
number of soil layers using soil texture data. Three-four layers are
usually used with much higher resolution in the upper zone. At each time
step, SAC-SMA liquid water storage changes due to rainfall/snowmelt are
estimated, and then are transformed into soil moisture states of the
heat transfer model. The heat transfer model splits the total water
content into frozen and liquid water portions based on simulated soil
temperature profile. Estimated new soil moisture states are then
converted back into SAC-SMA model storages. The time step of the frozen
ground component may be a fraction of the SAC-SMA time step.

![](media/image6.wmf){width="6.499305555555556in" height="4.8875in"}

Figure 6. Schematic of the soil layers and heat transfer component.

![](media/image7.wmf){width="6.163888888888889in"
height="4.635416666666667in"}

Figure 7. Schematic of the transfer of SAC-SMA storages to the four soil
layers of the physically-based heat transfer component.

![](media/image8.wmf){width="6.749305555555556in"
height="5.071527777777778in"}

Figure 8. Comparison of computed and observed soil temperatures at
various depths.

**5.3 Phase 2: Implementation of heat transfer component into water
balance model**

In this phase, the SAC-SMA is modified so that the heat transfer
component computes the amount of frozen water in the soil and thus in
the SAC-SMA. The amount of frozen water is then used to adjust the
amount of runoff computed from the SAC-SMA. Very recent results shown in
Figure 9 indicate that the physically-based methodology produces runoff
volumes that are as good or superior to those from the calibrated
conceptual approach of Anderson and Neuman (1984). This is a significant
development because the physically-based approach requires no
calibration while the conceptual formulation specifies seven parameters
to be calibrated.

![](media/image9.wmf){width="6.479166666666667in" height="4.86875in"}

Figure 9. Hydrograph simulation using Sacramento model with three
options: 1. no frozen ground component (purple); 2. original conceptual
frozen ground component (yellow); 3. new physically-based frozen ground
component (red). The physically-based component shows better agreement
with observed discharge (white).

**6. References**

Anderson, E.A., 1976. A point energy and mass balance model of a snow
cover. NOAA Technical Report NWS 19, U.S. Department of Commerce.
February, 150 pp.

Anderson, E.A., 1973. National Weather Service River Forecast System-
Snow Accumulation and Ablation Model. NOAA Technical Memorandum NWS
HYDRO-17, U.S. Department of Commerce, November.

Anderson, E.A., 1968. Development and testing of a snow pack energy
balance equations. Water Resources Research. Vol. 4, No. 1, 19-37.

Anderson, E.A., and Larson, L, 1997. The role of snowmelt in the
January, 1996 floods in the Northeastern Unites States. Internal HL
document.

Anderson, E.A., and Neuman, P.J., 1984. Inclusion of frozen ground
effects in a flood forecasting model. The 5^th^ North. Res. Basins
Symposium and workshop, Vierumaki, Finland, March 19-23.

Ek, M. B., K. E. Mitchell, Y. Lin, E. Rogers, P. Grunmann, **V. Koren**,
G. Gayno, and Tarpley, J.D., 2003. Implementation of Noah land-surface
model advances in the NCEP operational mesoscale Eta model. GCIP3
Special Issue, Journal of Geophysical Research, Vol. 198, No. D22, 8851,
doi:10.1029/2002JD003296.

Etchevers, P. and numerous co-authors, 2002. SnowMIP, an Intercomparison
of snow models: first results. Extended abstract, conference of the
ISSW, August, 8 pp.

**Koren, V**., J. Schaake, K. Mitchell, Q.-Y. Duan, F. Chen, and J.
Baker, 1999. Number range CHAPTERA parameterization of snowpack and
frozen ground intended for NCEP weather and climate models, JGR, Vol.
104, No. D16, 1999, 19569-19586.

Mitchel, K.E., Lohman, D., Houser, P.R., Wood, E.R., **Schaake, J.C**.,
Robock, A., and others including **Victor Koren** and **Qingyun Duan**,
2004. The multi-institution North American Land Data Assimilation System
(NLDAS): Utilizing multiple GCIP products and partners in a continental
distributed hydrological modeling system. GCIP3 Special Issue, Journal
of Geophysical Research-Atmospheres, accepted for publication.

Office of Hydrology, 1998. Northeast Floods of January, 1996. Natural
Disaster Survey Report. U.S. Department of Commerce, March.

Schlosser, et al. (including **V. Koren**), 2000. Simulations of a
Boreal Grassland Hydrology at Valdai, Russia: PILPS 2(d). *Monthly
Weather Review, Vol. 128, No. 2, 301-321, 2000.*

Slater, A.G., and many co-authors including **Koren, V., Schaake, J.,
and Duan**, P.-Y, 2001. The representation of snow in land surface
schemes: Results from PILPS 2(d). Journal of Hydrometerology, Vol. 2,
No. 1, February, 7-25.

**Appendix 1**

**Papers and Publications from Cold Season Process Research**

[Peer-Reviewed Papers in Scientific Journals (HL scientists in
bold)]{.underline}

Ek, M. B., K. E. Mitchell, Y. Lin, E. Rogers, P. Grunmann, **V. Koren**,
G. Gayno, and Tarpley, J.D., 2003. Implementation of Noah land-surface
model advances in the NCEP operational mesoscale Eta model. GCIP3
Special Issue, Journal of Geophysical Research, Vol. 198, No. D22,
8851,doi:10.1029/2002JD003296.

**Koren, V**., J. Schaake, K. Mitchell, Q.-Y. Duan, F. Chen, and J.
Baker, 1999. Number range CHAPTERA parameterization of snowpack and
frozen ground intended for NCEP weather and climate models, JGR, Vol.
104, No. D16, 1999, 19569-19586.

Mitchell, K., M. Ek, D. Lohmann, **V. Koren**, **J. Schaake, Q. Duan**,
P. Grunmann, G. Gayno, Y. Lin, E. Rogers, D. Tarpley, C. Peters-Lidard,
2002. Reducing near-surface cool/moist biases over snowpack and early
spring wet soils in NCEP Eta model forecasts via land surface model
upgrades, *16^th^ Conference on Hydrology, January, 2002, Orlando, FL,
AMS, paper J1.1, pp. J1-j6*.

Mitchel, K.E., Lohman, D., Houser, P.R., Wood, E.R., **Schaake, J.C**.,
Robock, A., and others including **Victor Koren** and **Qingyun Duan**,
2004. The multi-institution North American Land Data Assimilation System
(NLDAS): Utilizing multiple GCIP products and partners in a continental
distributed hydrological modeling system. GCIP3 Special Issue, Journal
of Geophysical Research-Atmospheres, accepted for publication.

Schlosser, et al. (including **V. Koren**), 2000. Simulations of a
Boreal Grassland Hydrology at Valdai, Russia: PILPS 2(d). *Monthly
Weather Review, Vol. 128, No. 2, 301-321, 2000.*

Slater, A.G., and many co-authors including **Koren, V., Schaake, J.,
and Duan**, P.-Y, 2001. The representation of snow in land surface
schemes: Results from PILPS 2(d). Journal of Hydrometerology, Vol. 2,
No. 1, February, 7-25.

[Presentations at conferences]{.underline}

Etchevers, P., et al., (including **V. Koren**), 2002. SnowMIP, an
intercomparison of snow models: first results, *ISSW Meeting*, 2002.

**Koren, V.,** 2004. Physically-based Parameterization of Frozen Ground
Processes in Watershed Runoff Modeling, paper H22B-04, to be presented
at the 2004 Joint Assembly of the AGU, CGU, SEG, and EEGS.

**Koren, V**., 2003. Parameterization of soil moisture-heat transfer
processes for conceptual hydrologic models. AGU-EGS-EUG Assembly, April
9-14, 2003, Nice, France.

**Koren, V., Duan, Q.-Y, and Schaake**, J., 1999. Validation of a
snow-frozen ground parmeterization of the ETA Model. Paper J1.3,
Preprints, 14^th^ Conference on Hydrology, American Meteorological
Society meeting, 10-15 January, Dallas, Texas. 410-413.

**Koren, V. , Qing-Yun Duan, Q.-Y., and Schaake, J.C**., 1995. Modeling
the effect of frozen ground on snowmelt/rainfall-runoff processes.
Proceedings of the International GEWEX Workshop, Banf, Alberta, Canada,
22-26 May, 1995, IGPO Publ. Series No 15, 78-82.

**Koren, V**., 2002. Importance of snow measurements on the river flood
modeling/prediction, WCRP Workshop on Determination of Solid
Precipitation in Cold Climate Regions, Fairbanks, Alaska, June 9-15,
Proceedings of the workshop on a CD-ROM, 2002.

**Koren, V., Q. Duan, J. Schaake**, 1995. A simple frozen ground model
for snowmelt/rainfall-runoff simulation. Abstract on AGU Fall Meeting,
December 11-15, San Francisco, California, Supplement to Eos, No 7,
1995, H41C-3.

**Koren, V., K**. Mitchel, **Q.-Y. Duan, J. Schaake**, and F. Chen,
1998. Snow-Frozen Ground Parameterization in the Mesoscale Eta Model.
Abstract on the GCIP Mississippi River Climate Conference, June 8-12,
1998, St. Louis, Missouri.

**Koren, V., Anderson, E.A., and Smith, M.,** 2000. Conceptualization of
Heat Transfer Processes for Storage-Type Hydrological Models. AGU Fall
Meeting, San-Francisco, California, December 2000, H52E-09, F408.

**Koren, V., and E. Anderson**, 2001. Effect of Weather Conditions on
Snowpack Simulations: Results from Energy Balance and Temperature
Index-Based Models. IAMAS Conference, Innsbruck, Austria, July 2001.

**Koren, V**., 2003. Parameterization of soil moisture-heat transfer
processes for conceptual hydrologic models. AGU-EGS-EUG Assembly, April
9-14, 2003, Nice, France.

Mitchell, K., M. Ek, D. Lohmann, **V. Koren**, **J. Schaake, Q. Duan**,
P. Grunmann, G. Gayno, Y. Lin, E. Rogers, D. Tarpley, C. Peters-Lidard,
2002. Reducing near-surface cool/moist biases over snowpack and early
spring wet soils in NCEP Eta model forecasts via land surface model
upgrades, *16^th^ Conference on Hydrology, January, 2002, Orlando, FL,
AMS, paper J1.1, pp. J1-j6*.

Mitchell, K., **J. Schaake**, D. Tarpley, F. Chen, Y. Lin, M. Baldwin,
E. Rogers, G. Manikin, A. Betts, Z. Janjic, **Q. Duan**, **V. Koren**,
1999. Recent GCIP advancements in coupled land-surface modeling and data
assimilation in the NCEP mesoscale Eta model. *14^th^ Conference on
Hydrology, 10-15 January 1999, Dallas, TX, AMS, 4B.1, 261-264*.

Mitchell, K., Y. Lin, E. Rogers, C. Marshall, M. Ek, D. Lohmann, **J.
Schaake**, D. Tarpley, P. Grunmann, G. Manikin, **Q. Duan**, **V.
Koren**, 2000. Recent GCIP-sponsored advancements in coupled
land-surface modeling and data assimilation in the NCEP Eta mesoscale
model. *15^th^ Conference on Hydrology, 10-15 January 2000, Long Beach,
CA, AMS,* 180-183.

Appendix 2

Reflections on Future Directions in Snow Modeling

for the

Hydrology Program of the National Weather Service

Eric Anderson

November 2003

**Executive Summary**

[Introduction]{.underline}

Presentations and discussions at the recent Snow Hydrology workshop held
at the Northeast RFC made it clear that there are a variety of efforts,
proposals, and thoughts regarding future snow modeling efforts within
the NWS Hydrology Program. It is clear that some consensus is needed so
that the resources of OHD, NOHRSC, and the RFCs can be properly utilized
to provide the greatest benefit and so that there are not duplicated or
wasted efforts. Since I was the developer of the SNOW‑17 model and have
played a major role in the direction of snow modeling within the
Hydrology Program up to this time, I thought it might be helpful to
express my thoughts and insights, for what they are worth, on this
subject.

[Issues]{.underline}

The main snow modeling issues as I see them, are as follows:

>  How to make improvements to the application of the SNOW-17 model to
> overcome existing operational deficiencies,
>
>  How to best utilize energy budget computations, and
>
>  How should distributed modeling be utilized for snow.

[Discussion]{.underline}

There are a number of considerations to take into account before making
decisions about the future direction of snow modeling efforts for the
NWS Hydrology Program.

>  There are 3 main steps that are required in order to successfully
> implement SNOW-17, the temperature index snow model currently used by
> the RFCs, for operational river forecasting:
>
>  The model must be properly calibrated using an extended period of
> consistent historical data \-- calibration expertise has improved
> though there is still room for progress,
>
>  The data used operationally to drive the model must be unbiased as
> compared with the data used for calibration B differences in data
> networks and the algorithms to compute MAT make it likely that a bias
> exists in many cases which limits operational effectiveness, and
>
>  Objective procedures are required that utilize all relevant real
> time observations to adjust model states and computations to reduce
> random errors and overcome model limitations B procedures exist for
> updating water equivalent in the west, but not east of the Rockies,
> and there are no techniques to quantify rate adjustments during
> periods of abnormal melt which often occur during extreme snowmelt
> events.
>
>  It is generally agreed to by most snow hydrologists that the science
> of snow cover energy exchange is quite well understood. Most of this
> science is included in the distributed energy-and-mass-balance snow
> model that is part of the Snow Data Assimilation System (SNODAS) being
> implemented by the NOHRSC.

 The problem in trying to apply an energy budget snow model is not the
science, but obtaining good estimates of all the required data and
modifying those estimates to account for elevation, slope, aspect, and
vegetation cover. Calibration primarily involves adjusting coefficients
and parameters related to the input data.

 An energy budget model will provide improved estimates of snowmelt
over those obtained with a temperature index model if the data used to
drive the model are unbiased and of sufficient quality and an adequate
calibration has been performed.

 The expertise and resources, both human and computational, to apply a
procedure like SNODAS are considerable \-- it is probably unrealistic to
attempt the implementation of such a system at each RFC that utilizes a
snow model.

 It would be difficult to make changes to the algorithms used by
SNOW-17 that would result in improvements over a wide range of
conditions without overly complicating the model.

 Objective updating procedures could be developed to utilize SNODAS
results to not only adjust SNOW-17 estimates of water equivalent, but
also melt rates, areal snow cover, depth, and internal states.

The SNOW-17 model could be applied in a distributed manner. Research is
required to determine how to adequately define the spatial variation of
the input data and how to derive or calibrate the model parameters.
Improved simulations are possible at the beginning and end of the melt
season though overall the gain is likely to be minimal as compared to a
lumped application (utilizing elevation zones in mountainous regions)
when snowmelt is the dominant source of runoff.

[Conclusions]{.underline}

My personal recommendations for future efforts in snow modeling for the
NWS Hydrology Program are:

1\. An energy-and-mass-balance snow model based on the best science
should be utilized,

2\. The energy-and-mass-balance snow model should be developed, applied,
and maintained at a central location rather than being an integral part
of the RFC forecast system \-- the most logical place is the NOHRSC,

3\. The energy-and-mass-balance snow model should be used to provide
objective updates to the states and internal computations of the index
snow model run at the RFCs rather than providing direct input to runoff
models \-- the development of such updating procedures should be a joint
effort between OHD and NOHRSC,

4\. OHD should conduct research on applying the SNOW-17 model in an
distributed manner,

5\. There should be considerably more effort by the RFCs and OHD devoted
to making sure that the data used operationally for the SNOW-17 model is
unbiased as compared to that used for calibration,

6\. Changes should not be made to SNOW-17 unless they are clearly needed
and will improve results over a wide range of climatic conditions \--
the focus should be on developing objective updating procedures and
utilizing the model in a distributed manner, and

7\. Continued training should be provided to the RFCs on all aspects of
snow modeling.

**Introduction**

Presentations and discussions at the recent Snow Hydrology workshop held
at the Northeast RFC made it clear that there are a variety of efforts,
proposals, and thoughts regarding future snow modeling efforts within
the NWS Hydrology Program. From a modeling viewpoint, these range from
modifications to the SNOW‑17 model that is currently used by the RFCs to
the use of a full energy-and-mass-balance model. As far as modeling a
watershed the aim appears to be to move toward a distributed application
of whatever snow model is used. In addition there is the question of
whether a distributed energy budget model could and should be run at the
RFCs as part of their forecast system or whether such a model should be
run centrally with results used to modify the index model used by the
RFCs. It is clear that some consensus is needed regarding the future
direction of the snow modeling efforts so that the resources of OHD,
NOHRSC, and the RFCs can be properly utilized to provide the greatest
benefit and so that there are not duplicated or wasted efforts.

Since I was the developer of the SNOW‑17 model and have played a major
role in snow modeling within the Hydrology Program up to this time, I
thought it might be helpful to express my thoughts and insights, for
what they are worth.

**Background**

Prior to the 1970\'s the forecasting of snowmelt by the RFCs utilized
various index procedures. None of the RFCs used a procedure that did a
full accounting of the precipitation during periods of snow cover nor
did any of the procedures explicitly account for ripening or areal
depletion. Degree‑day methods were used with the melt factor varying
seasonally or based on the portion of the estimated volume of snowmelt
that had already occurred. The seasonal variation in degree day factors
implicitly included ripening of the snow cover and areal depletion. The
potential snowmelt volume was based on either seasonal streamflow volume
regression estimates or snow survey measurements. Coefficients and their
variation over time were generally derived from analyzing past events,
but no formal calibration or verification of the procedures using an
extended period of historical data was conducted. Curves and
coefficients utilized by these early procedures were typically refined
over time based on forecast experience.

In 1973 the Snow Accumulation and Ablation model described in NOAA
Technical Memorandum NWS HYDRO‑17 (Anderson, 1973) became part of the
newly developed National Weather Service River Forecast System (NWSRFS).
This model has commonly been referred to as the SNOW‑17 model. SNOW‑17
is a conceptual model of the snow accumulation and ablation process.
Most of the physical processes that determine the amount of snow that is
accumulated and the energy exchange that takes place within the snow
cover are include, but in a simplified manner. The development of the
SNOW‑17 model relied on various studies of the physics that control snow
accumulation and ablation, including energy budget studies, to determine
the processes to include and the functional form of many of the
equations used in the model even though only air temperature was used to
compute surface energy exchange. Air temperature, certainly at that
point in time, was by far the most easily obtainable data, both
historically and in real time, to use to estimate snow cover energy
exchange and to compute surface melt. It is also relatively straight
forward to extrapolate air temperature from measurement sites to
locations where direct measurements are not available. There was some
effort made to include other indices, such as dew-point, wind, and sky
cover data, in the surface energy exchange computations, however, this
was unsuccessful. The conclusion was that rather than trying to find an
empirical equation involving multiple meteorological variables that
would consistently improve snowmelt computations over an equation
utilizing only air temperature, the next step should be to use the full
energy budget equation to define how all the variables determine snow
cover energy exchange. Of course the use of energy budget equations to
obtain improved results depends on the availability and quality of the
necessary data.

As opposed to prior applications of computing snowmelt based on air
temperature, typically degree day methods, the SNOW-17 model utilizes
separate equations to compute melt depending on whether rain is
occurring. The non-rain melt equation includes a seasonally varying melt
factor. The seasonal variation is primarily needed because of the
variation in the amount of solar radiation available for melt per
increment of temperature above a base value. The rain-on-snow melt
equation relies on several assumptions so that the form of the energy
budget equation can be utilized. The main reason for the two equations
is that melt during rain-on-snow doesn=t exhibit a seasonal variation,
whereas melt during non-rain periods does. The initial version of the
SNOW-17 model, as described in HYDRO-17, was modified somewhat over
several years based on subsequent snowmelt studies, primarily the
development of a detailed energy-and-mass- balance model of a snow cover
(Anderson, 1976). The Anderson (1976) report includes a comparison of
the SNOW-17 model and the energy balance model at a research location
with high quality measurements of the needed variables. The most current
description of the SNOW-17 model is in Section II.2 of the NWSRFS User=s
Manual.

The SNOW-17 model is now used by all RFCs that perform snow
computations. The model has been calibrated at many locations, though
regional parameters are still used in some cases. The model has been
solely applied in a lumped manner, though in mountainous regions
watersheds are generally subdivided into several elevation zones to
account for large differences in the amount of snow and the timing of
melt. In general, the operational results produced by the model have
been a big improvement over past procedures. The use of the SNOW-17
model also allows for the generation of extended probablistic
predictions of a variety of hydrologic variables using ensemble
techniques that was impossible with prior methods of dealing with snow.
The biggest complaints that have been brought to my attention involve
the timing of snowmelt and the computation of melt during extreme or
abnormal meteorological situations. A number of offices have indicated a
tendency for melt to occur too early at the beginning of the snowmelt
season during operation use, but haven=t indicated a similar tendency
when calibrating the model. Several offices also have difficulty in
adjusting model estimates of melt during periods of extreme or abnormal
meteorological conditions, especially periods with high dew-points and
high winds. Situations when the normal relationship between air
temperature and melt breaks down have been documented, however,
currently no objective procedure is available to assist the RFCs in
determining the magnitude of the adjustment factor to apply and how the
modification should vary over time when these situations occur. There
have also been some problems involving the diurnal variation of
streamflow during snowmelt periods. This problem is primarily the result
of determining improper soil moisture model parameters during a
calibration that uses only mean daily flow data to check the model
simulation.

**Issues**

The main snow modeling issues for the future and some of the questions
that arise for each issue, as I see them, are as follows:

1\. [How to make improvements to the application of the SNOW-17 model to
overcome existing operational deficiencies]{.underline}. Is additional
training needed? How to insure that operational data are unbiased
compared to that used for calibration? What improved procedures can be
developed for objectively determining the values of run-time
modifications (MODS) to update water equivalent, areal snow cover, and
snowmelt computations. Are additional MODS needed for use with SNOW-17
(the ability to change the heat deficit or to allow actual wind data to
be used during rain-on-snow events have been mentioned)? Should changes
be made to the SNOW-17 model itself (there has been talk of using
additional indices to compute melt or modify how the refreezing of
liquid water is calculated)?

2\. [How to best utilize energy budget computations]{.underline}. Should
an energy budget snow model be available for use within the RFC=s
forecast system or is it more reasonable to run an energy budget snow
model centrally and use the results to update an index model used by the
RFCs? What is the quality of the data values needed to drive an energy
balance model in order to obtain consistently improved results over an
index model? Are meteorological forecasts of the needed energy variables
sufficiently accurate and if so, for how long into the future can they
be used to provide better melt estimates? How would an energy budget
model be calibrated and how long of a period of record is needed? How
would the data needed for calibration be obtained? Would an extended
period of historical energy budget input data be needed for ensemble
predictions? Do the RFCs have the resources, both human and
computational, to process, quality control, run, monitor, and analyze
the data analysis, modeling, and assimilation procedures required to
properly utilize energy budget snowmelt computations?

3\. [How should distributed modeling be utilized for snow]{.underline}.
Does an energy budget snow model have to be run in a distributed mode?
How would parameter values be determined for the SNOW-17 model if it is
run in a distributed manner (would distributed calibration utilizing an
extended historical period of record be necessary or can parameters for
a distributed application be derived from a lumped calibration, possibly
with a short period of distributed data to fine tuned the results)?
Under what conditions could improved results be anticipated by utilizing
distributed modeling for watersheds with significant snowmelt
contributions? How would a distributed application be utilized for
extended ensemble predictions?

Before addressing many of these issues and offering my opinions, there
is a need to provide some discussion of each of the two main snow
modeling approaches; index methods represented by the SNOW-17 model and
energy budget computations. Some of the future snow modeling issues will
be addressed within this discussion.

**SNOW-17 Model**

There are 3 main steps that are required in order to successfully
implement SNOW-17, or any index snow model, for operational river
forecasting. These are:

1\. [The model must be properly calibrated using an extended period of
consistent historical data]{.underline}. Recommended procedures for
analyzing and processing the historical data and for applying and
calibrating conceptual models, including the SNOW-17 model, are fully
described in chapters 2 through 7 of the Calibration Manual by Anderson
(2002). The main objective of the historical data analysis process is to
generate consistent input time series for the model that have the true
physical scale (i.e. they are as unbiased as possible compared to what
actually occurred in nature) and have minimum random variation given the
available data network. The objectives of the model calibration process
are to produce simulations with a minimum amount of bias given the
limitations of the model and the spatial scale of the computations, to
have each model parameter embody what it was designed to physically
represent, and to have the spatial variation of parameter values be
consistent with physiographic factors.

2\. [The data used operationally to drive the model must be unbiased as
compared with the data used for calibration]{.underline}. Different
station networks and different methods of computing the input variables
used by the model operationally, as compared to the historical network
and data processing procedures, can easily create a bias. Care must be
taken to insure that any bias is minimal. Chapter 8 of the Calibration
Manual discusses some of the ways that bias can occur in the operational
data feed to the models and various steps and techniques that will
minimize the bias. Besides direct comparisons of time series, the
possibility of a bias can often be deduced by comparing the operational
simulations with those obtained during calibration. In general, the
historical simulation should reasonably define the variation that can be
expected in operational results and thus, if the operational simulations
are frequently outside of anything that occurred during calibration, it
is likely that the operational data are biased as compared to that used
historically. For example, the timing of snowmelt is going to vary from
one historical year to another, but if the operational simulation shows
melt occurring much earlier or later than any of the historical years,
it is very likely that there is a bias in the temperature data being
used operationally. This is especially true if the operational
simulation shows the same trend for several years in a row. Insuring
that the data used operationally are unbiased as compared to that used
for calibration is somewhat time consuming and not very glamorous, but
it is absolutely essential to obtaining the full benefits of any model.

3\. [Objective procedures are required that utilize all relevant real
time observations to adjust model states and computations to reduce
random simulation errors and overcome model limitations]{.underline}.
Objective adjustment procedures typically utilize the model simulation
along with predictions generated from additional observations to produce
a more optimal estimate for use by the model. Such procedures are
essential in order to maximize forecast accuracy and minimize
uncertainty. In addition, the proper tools must be available for the
forecasters to subjectively interact with the model and data in order to
resolve differences between simulated and observed values.

From my perspective there has been mixed success within the NWS
Hydrology Program at meeting the objectives of each of these steps.
Because of this, the full benefits of using the SNOW-17 model have not
yet been achieved. There are successes and failures for each of the
steps as discussed below.

[Step 1]{.underline}. The knowledge and expertise needed to properly
generate the historical time series and determine SNOW-17 model
parameter values has increased at the RFCs over time, however, there is
still room for improvement. Mountainous terrain, which is common in many
of the regions where snowmelt runoff is significant, makes the
historical data analysis process more complex. In many mountainous
regions there is a lack of good data at higher elevations where most of
the snow occurs and a majority of the runoff is generated. If one is not
careful, it is easy to produce precipitation and temperature time series
that don=t conform to the physical scale that occurs in nature. Great
care must also be taken to insure that precipitation and evaporation
estimates are spatially consistent and produce a proper water balance.
Chapter 6 of the Calibration Manual provides recommendations for
generating historical time series that are physically realistic and
spatially consistent. This documentation, rather than just notes from
training sessions or workshops, should assist in having more RFC
personnel understand and use the recommended data analysis procedures
when generating historical time series for use in model calibration and
ensemble streamflow predictions (ESP).

I believe that more RFC personnel are becoming adept at SNOW-17 model
calibration. At some offices there wasn=t a good understanding of the
structure of the snow model and how to determine the proper value for
each of the parameters. This resulted in the use of regional parameter
values or unrealistic and spatially inconsistent values when calibration
was attempted. While this situation has improved, my impression is that
it still exists at some level. Hopefully the documentation in chapter 7
of the Calibration Manual will help though there is undoubtedly a need
for continued training on the snow model through workshops and other
methods. The ability to know how to isolate the effect of each of the
model parameters is one skill that particularly needs to be improved. A
good understanding of the structure of a model, its limitations, and how
to determine parameters values are essential to successful operational
application and there is no better way to learn about a model than by
performing calibrations.

[Step 2]{.underline}. The existence of bias between the data used
operationally to run the snow model and the data used for calibration is
a major concern that hasn=t been properly addressed at headquarters or
by most RFCs. In general, biased data are the result of differences in
operational and historical data networks and variations in methods of
generating the values. Differences in the two networks require that the
long term means at all stations are known so that it can be determined
that the long term mean areal estimates produced by each network are the
same. This is not only true in mountainous regions, but also in
non-mountainous areas. It is true for both the precipitation and
temperature data used by the snow model. RFCs in mountainous regions,
especially in the west, have made more of an effort to establish a good
estimate of the long term mean for stations that were not part of the
historical network prior to using the data operationally. This needs to
be done everywhere. Very little effort has been expended at most offices
to make comparisons between operational estimates of precipitation and
temperature and those used during calibration (comparisons have been
made between radar based estimates of precipitation and estimates
derived from historical gage data as part of the distributed modeling
research, but these have largely involved regions where snow is not
important). The checks outlined in chapter 8 of the Calibration Manual
should be followed and frequent comparisons made between the operational
and historical time series.

There is also a potential bias problem in NWSRFS that involves
temperature estimates. Historical MAT time series are generated solely
from maximum and minimum temperature observations, whereas in the
Operational Forecast System (OFS) both instantaneous and max/min data
are utilized. Historically the time of the max and min are based on the
observation time for each station and a fixed diurnal variation is used
to compute 6 hourly MAT values. Operationally the instantaneous data
determines when the max and min occur and the diurnal variation in
temperature (a further discussion of this problem is in Chapter 6-4 of
the Calibration Manual). These differences in data and processing
methods certainly have the potential to create a significant bias. Since
the SNOW-17 model is very sensitive to a temperature bias (see Figure
6-1 in the Calibration Manual), this problem could significantly alter
the timing of snowmelt in an operational simulation as compared to what
was obtained during calibration. Even though the problem has been
identified and requests made by some RFCs to have it fixed, nothing has
been done. Unfortunately, as far as I am aware, no one has quantified
the magnitude of this potential difference between historical and
operational MAT time series and the factors that may determine how the
bias may be affected by region and historical data observation times. If
the magnitude of the bias were known, there might be a greater chance of
having someone work on a solution. Even though it should be clear that a
significant temperature bias could exist operationally and would affect
the timing of melt, there has been a tendency when the timing of
snowmelt is off (typically too early as mentioned previously) to call
for changes to the model structure or request that a MOD be added to OFS
that would allow the user to change the heat deficit in SNOW-17
(generally to increase the heat deficit to delay runoff from the snow
cover). In many of these cases I=m sure that the heat deficit would have
to be set to a value well outside the range of anything that was
encountered during calibration and that the MOD would have to be used
multiple times to delay snowmelt by a sufficient amount. While a MOD to
change the heat deficit may be a good idea, it is very likely that bias
temperature data are the primary cause of the operational snowmelt
timing problems. This problem needs to be resolved.

[Step 3]{.underline}. The primary focus to date regarding objective
updating procedures for use with the SNOW-17 model has been water
equivalent. First, some western RFCs developed regression equations for
updating water equivalent using relationships between historical
simulated water equivalent and one or more snow course sites. This
concept was taken further with the development of the Snow Updating and
Estimation System (SEUS) \[Day(1990)\]. The National Operational
Hydrologic Remote Sensing Center (NOHRSC) was given the responsibility
to support the operational implementation of SEUS. However, after a
couple years the key personnel working with SEUS left the NOHRSC and
this implementation effort stalled. More recently Riverside Technology
Inc. (RTi) developed a snow updating system for the Bonneville Power
Administration (BPA), referred to as **snowupdate**. This system is now
used by the Northwest RFC (NWRFC) and I believe some other western RFCs.
**Snowupdate** is sort of a simplified versus of SEUS. All of these
procedures to objectively update model estimates of water equivalent are
based on having a long record of measurements at snow course sites at
regular intervals and thus are restricted to use in the western states
and Alaska.

In the east and upper midwest such water equivalent measurements are
generally not available. Most measurements of water equivalent in these
regions are made at irregular intervals and typically only during years
with significant snow cover. Within the past few years the NOHRSC has
developed the Snow Data Assimilation System (SNODAS) \[Carroll et. al.
(2001)\]. SNODAS is a distributed, energy-and-mass-balance snow model
and data assimilation system. One of the aims of SNODAS is to assimilate
all available measurements of the amount of snow (point water equivalent
and depth observations as well as aerial gamma flight line derived
values) with model estimates to derive an improved estimate of the
spatial variation in water equivalent. The intention is to give RFCs,
especially those in the east and midwest, a mean areal value that can be
used to update the SNOW-17 model estimate. In order to make such a
update objective, several years of overlapping areal estimates from both
SNOW-17 and a stable SNODAS configuration must be available. Currently
the SNODAS estimates have only been used in a subjective manner to
replace SNOW-17 computed values in eastern basins where the SNOW-17
values are highly suspect.

Other than water equivalent, no objective updating procedures exist for
SNOW-17. MODs are available in the OFS to update the areal extent of
snow cover, the non-rain melt rate, and the wind function during
rain-on-snow events, however, there aren=t any objective methods for
determining the values to use. These MODs are currently used in a
subjective manner by comparing simulated and observed hydrograph
response and looking at satellite snow cover observations. It is
especially important to develop objective means of adjusting the melt
rate since it is clearly known that there are meteorological situations
when the relationship between air temperature and melt varies
considerably from the average relationship determined via calibration.
In many cases these situations are associated with extreme snowmelt
events. It is difficult during such events to decide on the proper melt
adjustments based primarily on a hydrograph comparison since other
problems, such as errors in precipitation amount, antecedent conditions,
or ice jams, are typically also occurring and the melt rate adjustments
vary over time as meteorological conditions change.

Besides the currently available MODs in the OFS for the SNOW-17 model,
there may be a need for a MOD that would adjust the heat deficit.
Several RFCs have requested such a MOD though in many cases the
perceived need is likely the result of a temperature bias between the
operational input and that used for calibration as discussed previously.

**Energy Budget Snow Models**

It is generally agreed to by most snow hydrologists and others involved
in studying the physics of snow that the science of snow cover energy
exchange is quite well understood. Most of this science is included in
the snow model that is used by SNODAS. SNODAS is based on the SNTHERM.89
model developed by Jordan (1991). The early development of SNTHERM drew
extensively from the energy-and-mass-balance model developed by Anderson
(1976). These energy-and-mass-balance snow models are one-dimensional
models that represent the energy exchange and mass changes in a snow
cover at a point. In order to apply such models to watersheds they must
be applied in a distributed mode. This is not only because snow
conditions vary considerably spatially, but because of large spatial
variations in the input variables and how they are affected by
vegetation and terrain. It is physically unrealistic to apply an energy
budget snow model on a lumped basis to a watershed.

The problem with trying to use an energy-and-mass-balance model is not
the science, but is how to obtain the data needed to run such a model.
An energy budget snow model requires estimates of air temperature, dew
point, wind speed, incoming solar radiation, albedo, incoming
atmospheric longwave radiation, and precipitation. At research sites
high quality measurements of all these variables are generally
available, however, the situation is much different when an energy
budget model is being applied over a large region. At each point where
the model is run estimates of these variables must be generated by
interpolating and extrapolating available measurements. In addition,
adjustments must be applied for the effect of the terrain (slope,
aspect, elevation) and vegetative cover on each variable. Also, direct
measurements of some of the variables (e.g. albedo and incoming
longwave, and perhaps even incoming solar, radiation) are generally not
available and thus the values must be estimated from other data. SNODAS
is run hourly using 1 km, gridded, meteorological input data downscaled
from mesoscale numerical weather prediction (NWP) model analyses with
the snow cover divided into three layers. Digital elevation data are
used to assign the elevation and derive the slope and aspect of each
grid cell. Each grid cell is also assigned forest cover and type
information, derived from remotely sensed data, and soils information.
Updating of the SNODAS model is done periodically (based on comparisons
by the NOHRSC staff between computed and observed snow cover amounts and
available resources) using all available measurements of water
equivalent and depth . My understanding is that satellite areal extent
of snow observations are not currently used directly in the updating
process, but a manual comparison is made between model and observed snow
cover. The assimilation of the observations into the model is an
interactive process.

Some comments on energy budget snow models in general and the SNODAS
application in particular are relevant at this point. The comments on
SNODAS are based on knowledge of the algorithms and on infrequent
comparisons of simulated values with SNOTEL data and personal
observations primarily for an area in the central Colorado mountains
(Summit County and surrounding area).

> 1\. All models require some calibration even if they include detail
> representations of all the relevant physical processes (often referred
> to as deterministic models) and are being driven by high quality
> measurements of all input variables. In general, people think of
> calibration as being associated with conceptual or black-box type
> models, but even point applications of deterministic models require
> some calibration since no model contains a totally complete
> reproduction of what occurs in nature. However, the more physically
> complete a model, the easier it should be to at least know what each
> parameter or coefficient represents and thus have a better
> understanding of the range of realistic values. The wind function is
> the main element of an energy budget snow model that typically
> requires some calibration even at a research site. The wind function
> varies with the roughness of the snow surface, the stability of the
> atmosphere, and other factors affecting the air flow at a particular
> location. Even a theoretically based wind function that accounts for
> stability requires some calibration since the changing properties of
> the snow surface are not being modeled nor are other unique aspects of
> the wind flow at a given site. SNODAS uses a bulk transfer
> representation of the wind function which accounts for stability and
> fixed values from the literature for the parameters and coefficients
> involved. Figures 5.12 through 5.17 in Anderson (1976) illustrate how
> different, yet reasonable, values of the wind function parameters and
> coefficients can affect model results.
>
> 2\. While some limited calibration is required for an energy budget
> snow model at a point with very high quality data, considerably more
> calibration is needed when applying such a model to an area. Partly
> this is due to assumptions and simplifications that must be made to
> account for the spatial variability in physiographic factors when
> running the model in a distributed mode, but mostly it is caused by
> uncertainties in determining the input variables for the model,
> especially when there are few, if any, direct measurements of these
> quantities.

In this situation calibration primarily involves parameters that control
the derivation of the input variables used by the model and not those of
the model itself. Without some kind of calibration it is impossible to
know whether the results are unbiased. For an energy budget snow model
the main difficulties are in getting the proper wind speed and radiation
components. The wind speed supplied to the model typically has to be
derived for some level in the atmosphere from available measurements,
adjusted to the elevation of the area being modeled, modified for
terrain effects based on wind direction, aspect, and slope, and altered
to account for the effect of the vegetation. Radiation incoming from the
atmosphere in many cases is computed based on sky conditions rather than
direct measurements. Adjustments to these radiation estimates for
terrain effects are fairly straight forward, but the modification of the
radiation terms for the effect of vegetation contain more uncertainty.
In addition, for areal applications, the albedo of the snow is not
measured but estimated. Albedo can be estimated from surface grain size
or density (which also must be computed since they are not measured) or
in some cases a constant albedo is assumed. The current SNODAS
configuration uses universal coefficients based on logical assumptions
to estimate and adjust the data being used to drive the energy budget
model at each grid point. A constant albedo of 0.70 is currently used
though algorithms to vary the albedo based on snow surface conditions
are being considered. While such coefficients and assumptions may result
in a somewhat realistic build up and ablation of a snow cover, it is
highly likely that the results at most specific locations contain a bias
and could be significantly improved by some level of calibration.

3\. The largest source of error in the current SNODAS application
appears to be the precipitation field used by the model. This is
especially true in mountainous regions. In the part of Colorado that I
have examined, the estimated storm amounts are generally very low and
there are problems with the orographic distribution. Updating the
modeled amount of snow through assimilation with observations (only done
once in Colorado) can partially correct the problem for the point in
time when the data are assimilated, however, errors in the overall
pattern of snow distribution cannot be totally removed by updating with
the existing snow data network. Large errors in the amount and
distribution of the snow cover make it very difficult to determine the
reasonableness of the computations during ablation periods. A better
estimate of the precipitation field is needed. In order to obtain a
reasonably accurate, dynamic estimate of the amount and spatial
distribution of precipitation in mountainous regions for use with any
distributed model a procedure involving orographic modeling at the
proper scale, along with the assimilation of gage measurements and other
relevant observations, is likely needed.

4\. An energy budget model will definitely provide improved estimates of
snowmelt and snow cover outflow over those that can be obtained with a
temperature index model, however, this is only true when the data used
to drive the energy model are unbiased and of sufficient quality and
model coefficients have been calibrated to remove any bias in the
results. The differences between the two models should be greatest for
locations where there is a large variability in the meteorological
conditions during melt periods. Differences should be greatest at open
sites where the relative magnitude of the terms in the surface energy
balance equation can vary considerably from one period to another (e.g.
solar radiation may dominate for several clear days which are followed
by a warm, cloudy, windy, humid period where most melt is the result of
latent and sensible heat transfer). Differences should be smallest for a
very dense, conifer forest where there is little penetration of solar
radiation and wind movement is minimal and thus most of the energy is
due to longwave exchange between the forest and the snow which is nearly
linear with temperature. The SNOW-17 model produced results that were
quite similar to an energy budget model at a open, research site in
Vermont \[Anderson(1976)\]. Differences occurred during periods with
high winds and high dew points and during a cool, clear period when the
snow surface was well aged (melt undercomputed by SNOW-17) and during a
period with little wind but abnormally warm temperatures (melt
overcomputed by SNOW-17). Of course, all the SNOW-17 parameters had to
be calibrated to the location, whereas only the wind function
coefficient needed calibration for the energy budget model.

5\. In order to use an energy-and-mass-balance snow model as an integral
part of an RFC forecast system (i.e. provide direct rain plus melt input
to a rainfall-runoff model) would require a detailed calibration. To
perform such a calibration over a large region would be a major effort
and undoubtedly require the development of some new strategies. The
calibration should involve comparisons between model results and point
or flight line measurements of the amount of snow, satellite
observations of areal cover, and any other available measurements of
snow properties, in addition to performing streamflow simulations in
conjunction with the RFC=s rainfall-runoff and channel system models. As
previously mentioned, the calibration of an energy budget snow model
would primarily involve making changes to parameters that control the
gridded data values being feed to the model. In order to perform such a
calibration a sufficiently long historical period of record would be
required. I would guess that 3-5 years with a significant snow cover
might be sufficient for the snow component though a longer record would
likely be needed to properly calibrate the full suite of models. This is
a shorter period than generally needed to calibrate a temperature index
procedure due to the physical nature of the model, but involves
generating historical estimates of many more types of data. The period
should ideally contain snow covers of different magnitudes and a variety
of melt scenarios. It would also be critically important that the
methods for determining the model input variables and their spatial
variation be consistent throughout the period. Calibrations could be
performed for individual watersheds, but to make sure that the
parameters were spatially consistent, it is most likely that a strategy
would have to be devised that covered a large area involving many
watersheds. Obviously the operational use of a calibrated energy budget
snow model would require that the real time data estimates be generated
in a manner that was consistent with those used during calibration.
Changes in how the real time data were determined would lead to the need
to recalibrate the model.

A comparison of SNODAS computed water equivalents and observed values at
SNOTEL sites was possible in Colorado for the 2003 melt season after the
April 1^st^ assimilation produced a reasonable magnitude for the snow
cover. SNODAS uses coefficients and parameters based on literature to
adjust input data fields and perform energy exchange computations. There
is currently no calibration. Almost all of the SNOTEL sites that I
examined showed the computed ablation of the snow cover to be anywhere
from 5 to 15 days later than the measurements indicated. This indicates
to me that some level of calibration is needed. SNODAS could likely
produce more realistic overall simulations of snow cover accumulation
and ablation by making improvements such as providing better estimates
of some input data fields (e.g. precipitation), adding a method to vary
albedo with snow surface conditions, and tweaking some of the
coefficients that control how the NWP data are downscaled and modified
for terrain and vegetation. Such improvements hopefully will occur over
time as SNODAS evolves into a stable configuration. However, if one is
going to use the results from an energy-and-mass-balance snow model like
SNODAS to directly provide unbiased input (i.e. rain+melt) for
operational streamflow simulations, a full calibration is required.
Without a full calibration the alternative would be to use the results
from a stable (i.e. changes not being made to the data or model
algorithms) energy budget model as input to objective procedures that
would provide updates to a calibrated temperature index model.

6\. It is my understanding that the resources required to run SNODAS are
considerable. This is both the computer resources to process the needed
data, run the model, and archive results and the human resources needed
to interact with and monitor the input data, model results, and
assimilation of snow observations. SNODAS currently only simulates with
observed data. Ideally an expansion can be made at some time to produce
snow cover simulations involving forecasts of meteorological data fields
at least for a few days into the future.

**Discussion of Issues**

The two preceding sections discussed the two basic types of snow models
and expressed opinions regarding some of issues affecting the future of
snow modeling within the NWS Hydrology Program. This section will
provide a further discussion of these issues.

[How to Improve the Operational Application of SNOW-17]{.underline}

1\. An attempt to add other variables, such as dew point and wind speed,
as indices to computing snowmelt is a waste of time in my opinion. It
would be quite difficult to determine how to combine such variables with
air temperature to produce an improved estimate of snowmelt on a
consistent basis. Granted during certain extreme events high dew points
and high wind speeds combine to produce abnormally large amounts of
melt, however, it would be difficult to come up with an empirical
formulation that would not only improve the results during such
situations but work well during all other periods. Based on my
experience, improvements to the computation of snowmelt beyond using air
temperature requires the use of an energy budget approach in some
manner. This could be done by the direct computation of snowmelt using
an energy budget model or the adjustment of SNOW-17 estimates based on
energy balance computations.

2\. Air temperature has been shown in many studies to be a good estimate
of daily snowmelt, however, as far as the diurnal variation in melt, the
estimates are not as good. In general, more melt is generated per
increment of temperature above a base value during daylight hours than
at night. Thus typically a temperature index model will produce a more
damped diurnal melt pattern than actually exists though this depends on
the density of the forest cover and the meteorological situation. Six
hourly computations of melt, even if not showing the full daily
amplitude of the melt pattern, definitely have more value than
calculating melt on a daily basis, however, hourly melt computations
with a temperature index model would likely produce only marginal
improvements over 6-hour estimates. In some fast responding watersheds
hourly runoff estimates are needed during high intensity rainfall events
in order to properly simulate streamflow. The SNOW-17 code has been
designed to be able to use hourly precipitation time series with
6-hourly temperature data. This allows the variation in rainfall
intensity to be preserved on an hourly basis without having to generate
hourly temperature estimates.

During active melt periods significant surface melt is occurring during
the day while in many cases there is heat loss at night resulting in the
refreezing of liquid water and lowering of the temperature near the
surface of the snow cover. At an open site with calm winds and clear
skies the heat loss is undoubtedly greater than the air temperature
would indicate. Under such conditions there would be a heat loss even
when the air temperature was above freezing at night due to a negative
longwave radiation exchange. However, if the site is forested or the sky
is overcast or it is windy, the energy balance is much different and
heat exchange computed by a temperature index model should be much more
reasonable. There have been suggestions that the SNOW-17 algorithms that
control the refreezing of liquid water need to be modified. The evidence
for this is based on comparisons with observed data at open sites that
frequently have calm, clear nights during active melt. Changes could
undoubtedly be made that would improve results at these sites, but most
likely negatively affect the results at other locations. It is my
opinion that one has to recognize that there are limitations to a
temperature index model and not overly complicate the model or go beyond
the information contained in the data by trying to figure out how
meteorological conditions and thus the energy balance are varying based
solely on air temperature. If straightforward changes can be made that
apply universally without adding additional parameters, that is fine,
but the complexity of the SNOW-17 model is very close to the limit of
what is reasonable when solely using air temperature to compute surface
energy exchange.

3\. MODs are currently available to make the majority of the adjustments
that are needed when using the SNOW-17 model operationally for river
forecasting. The changes that need to be made most frequently to the
model are to update the amount of water equivalent (.WECHNG MOD) and to
varying the surface melt computations (.MFC and .UADJ MODs). A MOD is
also available to change the areal extent of the snow cover (.AESCCHNG).
As mentioned earlier, there are objective procedures for updating water
equivalent at least in regions with snow course records taken at regular
intervals, however, there aren=t any objective techniques for updating
water equivalent in regions with only depth data or infrequent water
equivalent observations nor are there objective procedures for
determining appropriate values for updating melt computations or areal
snow cover. Possible approaches are discussed under the next section on
How to Utilize of Energy Budget Computations. As far as other run time
adjustments, it was previously indicated that there are requests for a
MOD to update the heat deficit. Considerations for updating the heat
deficit based on SNODAS output are discussed in the next section

There has also been a suggestion that .UADJ MOD values could be computed
based on actual wind observations during rain-on-snow events. The idea
is to compute the average wind speed during such events based on the
calibrated value of the UADJ parameter and the wind function used to
obtain initial estimates of the parameter (see Section 7-4 of the
Calibration Manual) and then use the ratio of observed wind speed to
this average speed to get values for the .UADJ MOD. While the wind
function given in Section 7-4 is likely not universal and in many
watersheds there is a fair amount of uncertainty in the calibrated value
of the UADJ parameter, the most difficult part of this approach would be
deriving the actual areal average wind speed at 1 meter over the snow
surface for a complex watershed based on measurements of wind speed at
point locations which may not even be within the watershed. An
alternative approach to determining an appropriate value for the .UADJ
MOD is given in the next section.

[How to Utilize Energy Budget Computations]{.underline}

1\. The application of an energy balance snow model to a large region
seems to be a major undertaking requiring a considerable amount of
knowledge and expertise. A number of tasks are involved. First, the
input data fields must be monitored. There may be a need to
interactively adjust some of the input such as the form of the
precipitation. If an energy budget model were run at an RFC, the
monitoring and adjusting of the input data would most likely be part of
the HAS function. Second, there is a need to calibrate the model or at
least make some changes to coefficients and parameters so that the model
reasonably mimics what actually is occurring. A full calibration would
be needed if the model were being used to provide direct input to
rainfall-runoff computations. Any level of calibration requires a
detailed knowledge of the data analysis and modeling procedures. Third,
the model must periodically be updated by assimilating the model results
with all available snow observations. From my understanding this
involves various interactions with the observed data that requires a
certain amount of knowledge and experience. The question becomes can an
energy balance snow model be run effectively at each RFC where snow is
important or should such a model be run at a central location such as
the NOHRSC as is currently the case with SNODAS?

If an energy balance snow model is run at each RFC there are two
alternatives as I see it for how the model is utilized. The first would
be to actually use the energy balance model as a direct step in the
streamflow simulation process just like SNOW-17 is currently used.
Computations would be done on a watershed basis within each forecast
component segment. In this case the output from the model would directly
be passed to a soil moisture accounting model and used to compute
runoff. In this situation the model must be properly calibrated using
not only snow observations but also streamflow data. The model would be
rerun for each watershed every time the RFC forecast system is rerun.
Some MODs would likely be needed so that the forecaster could make
changes when computed values differ from observed in addition to the
assimilation of snow observations to update the total amount of snow.
While results would be generated segment by segment, a method of viewing
the results over the entire RFC area would be needed to maintain spatial
consistency and perform the assimilation step. The model would be used
for both short term and extended forecasts. It may be that some kind of
scale or modeling transition would need to be made as you go further out
into the future when the quality of the energy input becomes very
uncertain to keep computational requirements at a reasonable level.

The second alternative for using an energy budget snow model at an RFC
would be to run the model outside of the regular forecast system
similarly to how SNODAS is currently run at the NOHRSC. In this case the
model would likely only be run for the current time and for a few days
into the future. Results from the model would be used to update the
states and computations for SNOW-17 as discussed later in this section.
A full calibration wouldn=t be required though adjustments would be
needed to insure that the model was realistically reproducing nature.
Either alternative would require that the staff of each RFC using the
model have a very good understanding of the data analysis, modeling, and
assimilation procedures involved so that the model could be used
effectively across the country. If such a snow model was run at the
RFCs, it would be essential that energy budget snow modeling expertise
be available at the national level, probably at the Office of Hydrologic
Development (OHD), to provide assistance and training to the RFCs.

If a energy balance snow model is run centrally the most logical place
is the NOHRSC. The NOHRSC has considerable expertise and experience with
all types of snow data analysis and modeling procedures though currently
one person has most of the energy balance modeling expertise. It would
be imperative in this case that a sufficiently knowledgeable staff is
maintained so that the whole energy budget modeling effort wouldn=t be
in jeopardy if one or two people left as in the case of the SEUS
project. The same can also be said for OHD and the RFCs if the energy
budget snow model were run as an integral part of each RFC=s forecast
system. If an energy budget snow model is run at the NOHRSC, it would
most logically be used to provide updates to the SNOW-17 model at the
RFCs as discussed later in this section rather than having the snow
cover outflow be used directly to compute runoff. It is critical that
the RFCs be able to run their forecast models whenever needed and not be
dependant on direct modeling results from an external office.

2\. As mentioned above, an energy balance snow model could be run as an
integral component of the RFC forecast system to generate both short
term and extended forecasts. This would likely create a considerable
computational burden for the forecast system if hourly energy
computations were performed at a fine grid for all time steps. If this
were the case, it would also mean that input data fields for all the
variables would need to be provided for each ensemble when probabilistic
predictions were being generated. Since the benefits of an energy
balance model are highly dependent on having high quality estimates of
the needed data, it is likely that as one goes out into the future and
the ability to forecast wind and radiation fields rapidly diminish there
is no longer a need to utilize the same temporal and spatial scale nor
even to continue with energy budget computations. Thus the scale and
modeling approach could change after the first few days of the forecast
period, as long as the results were consistent.

3\. As an alternative to running an energy-and-mass-balance snow model
as an integral part of an RFC forecast system, the model could be run
externally and the results used to update an index snow model like
SNOW-17. This is the basic idea behind the SNODAS effort at the NOHRSC.
SNODAS was developed in response to recommendations from the report on
the 1996 snowmelt flood in the northeastern U.S. \[Office of
Hydrology(1998)\]. That report indicated a method was needed to utilize
all available snow observations to determine a best estimate of the
amount of snow available for melt. In the eastern and central portions
of the U.S. there are few regular measurements of water equivalent and
the quality of many of these are questionable. Especially during large
snow years there are additional water equivalent measurements at points
and over flight lines, but even these lack the necessary spatial
coverage in most areas to produce good areal estimates. However, there
are a large number of depth observations that are routinely collected.
The idea behind SNODAS was to run a distributed energy-and-mass-balance
snow model utilizing the latest science to simulate the states of the
snow cover including depth, density, water equivalent, liquid water
content, and temperature. It would then be possible to assimilate both
depth and water equivalent observations with the model results to
produce an improved estimate of the total amount of snow and its spatial
distribution. Thus, the initial primary focus of SNODAS was to provide
improved estimates of mean areal water equivalent to the RFCs for each
of their watersheds in order to update the values being generated by
SNOW-17.

Besides water equivalent, a stable, properly adjusted
energy-and-mass-balance snow model with quality input should be able to
be used to update various other states, plus internal computations of an
index model like SNOW-17. In order to derive an objective procedure, in
most cases, there must be several years of stable, overlapping results
from both models since there is no way to guarantee a one-to-one
correspondence between the estimates from both models. The SNOW-17
values that could be updated with information obtained from an energy
budget model like SNODAS, possible updating techniques, and factors to
consider are discussed below.

> a\. Water Equivalent - As indicated, SNODAS was developed to provide
> improved estimates of water equivalent for RFCs in the eastern and
> north central regions of the U.S.. SNOW-17 was updated at some RFCs
> this past winter using SNODAS estimates. The SNODAS values merely
> replaced the SNOW-17 estimates. To avoid a possible bias and insure
> that the updating is near optimal, several years of overlapping data
> from both models are needed to develop an objective procedure. Western
> RFCs adjust SNOW-17 water equivalent estimates with updating
> procedures that utilize snow course data. One problem with these
> procedures is that the relationship between the model and the snow
> courses can vary throughout the snow season. The equations that are
> used for updating are typically fairly stable when the snow cover is
> accumulating, but break down during the melt season since the point to
> area relationship is constantly changing during the ablation period.
> Since SNODAS is modeling the entire accumulation and melt process, it
> is likely that there would be a consistent relationship throughout the
> entire snow season between SNOW-17 and SNODAS water equivalent
> estimates, thus offering the possibility of an improvement over
> current updating procedures.

b\. Melt Rates - One of the major problems when using SNOW-17
operationally is the lack of a method of determining exactly when and by
how much to adjust melt rates. It is known that a temperature index
model cannot accurately calculate the amount of melt during certain
meteorological situations. By knowing current conditions a forecaster
can guess at whether a melt adjustment is required, but has no real idea
of the magnitude of the correction. An energy budget snow model that has
been adjusted to produce a realistic representation of the ablation
period should be able to provide reasonable values for the .MFC and
.UADJ MODs. The non-rain melt factors (divide the surface melt computed
by the energy budget by the air temperature minus the base temperature)
and wind functions (solve the SNOW-17 rain-on-snow melt equation for the
wind function with the melt set to the value computed by the energy
budget model) that would be needed to generate the melt produced by the
energy balance equations could be calculated for a multiple year period
for the areas being modeled with SNOW-17 (generally either watersheds or
elevation zones). These quantities could then be compared to the
calibrated values used by SNOW-17 to derive an objective procedure for
adjusting the temperature index melt estimates. Since there are
uncertainties even in the energy budget melt estimates, derived
adjustments would likely only be used when the value clearly indicates
abnormal conditions. Melt adjustments could be determined for the
observed data periods and also out into the future using forecast values
of the energy budget input variables. Adjustments in the future could
vary from one ensemble to another when making probabilistic predictions
to reflect the uncertainty of the forecasted value of the input
variables. Besides adjusting melt rates during abnormal conditions, such
a procedure might modify diurnal variations in melt when air temperature
doesn=t produce the correct pattern. When using such a procedure
operationally, interactive capabilities may be warranted to insure
spatial consistency in the adjustments and to allow for forecaster
input.

c\. Areal Snow Cover - Objective procedures could currently be derived
using overlapping periods of satellite based areal cover estimates and
model generated values to update SNOW-17. In the future, areal cover
estimates from SNODAS that have been verified to be realistic based on
comparisons or updates with satellite based values could be used to
derive an objective procedure to update the areal extent of snow cover
in SNOW-17. In either case, the updating procedure would have to account
for the fact that the areal cover needed by the model is not typically
the same as what would be observed in nature. This is due to the fact
that the relationship between the melt rate over the snow covered
portion of the area being modeled and the melt rate when the entire area
is snow covered is implicitly incorporated into the SNOW-17 areal
depletion curve.

d\. Heat Deficit - The heat deficit in SNOW-17 is defined as the amount
of energy that must be supplied to the snow cover in order to return it
to the combined thermal and liquid water state as when the heat deficit
was last equal to zero. The accumulation of a heat deficit doesn=t
differentiate between liquid water that may be refrozen within the snow
and the lowering of the snow temperature. The SNOW-17 heat deficit only
indicates the amount of energy that must be supplied to return the snow
cover to its original combined temperature and liquid water state. As an
example, a snow cover could have been isothermal at 0C with 5 mm of
liquid water in storage when the heat deficit began to accumulate. When
the heat deficit returned to zero, the temperature and liquid water
content could be back to their original values or there could still be
parts of the snow profile where the temperature was below freezing, but
the overall amount of liquid water in storage is now greater than the
original 5 mm. It is not possible to compute the heat deficit directly
based on the temperature and liquid water profile of the snow cover,
either measured or modeled, at a given point in time. This is because
the temperature and liquid water states when a heat deficit began to
accumulate in SNOW-17 are unknown. An energy budget model, like SNODAS,
could be modified to calculate the heat deficit so that an objective
updating procedure could be developed for use with SNOW-17.

e\. Since SNOW-17 can now calculate snow depth as well as water
equivalent an objective procedure could be developed to update the snow
depth based on SNODAS estimates.

[How to Utilize Distributed Modeling]{.underline}

1\. It is quite clear that an energy budget snow model should be run in
a distributed mode; certainly for any watershed with varied terrain and
forest cover. It doesn=t make a lot of sense to use a physically based
model and then apply it in a lumped manner unless possibly conditions
are very uniform across the drainage. If an energy budget model were
applied in a lumped manner (would require some kind of depletion curve
to account for the areal snow coverage) there might be some improvement
in the computation of melt during events with very abnormal
meteorological conditions, but the combination of the dampening of the
spatial variations and uncertainty in the values of the input variables
would cause the results during most days to be no better and more likely
worse than could be obtained with a temperature index model.

2\. The SNOW-17 model could be applied in a distributed manner though
some research would be required to determine whether the spatial
variability of the input variables can be adequately defined, how to
derive or calibrate the parameters, how to update the model
operationally, and when it is advantageous to apply the model in a
distributed mode. Some thoughts on these questions follow.

a\. In order to really benefit by a distributed application of any model
it is essential to have good estimates of the spatial distribution of
the primary input variables. For SNOW-17 air temperature and
precipitation are the two driving variables. Air temperature primarily
is a function of elevation though temperature can also vary with aspect,
forest cover, and other factors. Though seasonally varying average lapse
rates can be readily estimated, there are deviations in the relationship
between temperature and elevation depending on meteorological
conditions. An approach similar to that currently used by SNODAS
involving the downscaling of NWP model estimates could be used for a
distributed application of SNOW-17 though it seems like at least all
available surface observations ought to be assimilated to produce the
final gridded fields.

Good spatial estimates of precipitation in regions with significant
snowfall and especially in mountainous terrain would likely require
further procedure development and testing. Reasonable estimates of
spatial variations in rainfall can frequently be obtained in flat
terrain by combining radar information with gage measurements and other
observations. In mountainous terrain and especially when snow is
occurring, the accuracy of radar based estimates deteriorates. In
regions with significant relief, precipitation could be allocated
spatially for distributed applications of the snow model based on long
term isohyetal patterns. However, a more dynamic approach, perhaps
including the use of a orographic precipitation model, would be a big
improvement not only for distributed applications of the snow model but
even when the model is used in a lumped mode with multiple elevation
zones For both temperature and precipitation it is essential that
however the spatial estimates are derived for operational use that they
are unbiased compared to the data used to calibrate the model.

b\. A distributed application of the SNOW-17 model could be attempted by
using the parameters from a lumped calibration for every grid cell. This
would probably only be realistic where the spatial variability during
rainfall events is the major reason for running models in a distributed
manner. This would most likely be for a region that is non-mountainous
with little variation in forest cover or one where snowmelt runoff is
generally insignificant. In mountainous regions where there is a
substantial amount of runoff from snow, it seems like if there is any
advantage in running the SNOW-17 model in a distributed mode it is to
try to simulate the variation in the accumulation and ablation pattern
over the area. The parameters for a distributed application of the
SNOW-17 model could be obtained by running the model in a distributed
mode for a sufficiently long historical period and adjusting parameter
values in some logical manner or the parameters from a lumped
calibration could possibly be modified, maybe involving a few years of
distributed input, to reflect their spatial variation. It would likely
be quite difficult to obtain the historical data that would be required
by new procedures for generating spatial temperature and precipitation
patterns to provide an adequately long historical record for calibrating
the model by running it in a distributed mode. This calibration approach
is likely more feasible after a sufficiently long, stable, historical
record has been obtained by archiving gridded input estimates. In the
short term, at least, it seems that trying to utilize the results from a
lumped calibration is the most realistic alternative.

One possible approach for deriving the spatial variation in SNOW-17
energy exchange rate parameters (MFMAX, MFMIN, UADJ, and maybe NMF) is
to utilize an energy budget model like SNODAS. SNODAS could be run and
melt factors computed using a year or two of archived data. The ratio of
the average parameter estimate for each grid cell to the average for the
area being modeled (either a watershed or elevation zone) could be
calculated and used to assign values for these parameters for a
distributed application of SNOW-17. Even if the average areal parameter
estimates calculated from the energy budget were different than those
for the SNOW-17 calibration, the ratio of the estimates for each grid
cell to the area average should provide a reasonable approach of
accounting for spatial variations in these energy exchange rate
parameters due to elevation, slope, aspect, and forest cover. The
pattern for distributing some of the minor SNOW-17 model parameters
could be based on guidelines for how these parameters vary with climatic
and physiographic factors given in the Calibration Manual. The spatial
and temporal scale of the application shouldn=t have a significant
effect, as it does in the case of the Sacramento Model, since SNOW-17 is
basically a linear model. The biggest potential problem for deriving
distributed SNOW-17 parameter values based on a lumped calibration
revolves around the depletion curve. For a distributed application of
the model each grid cell should either be snow covered or bare. The
areal snow cover pattern and overall extent of the snow cover for the
area is then computed based on which grid cells are snow covered at any
given time. The areal cover in a distributed application would be based
on the assumed spatial distribution of temperature, precipitation, and
the model parameters, especially those controlling melt rates, in an
explicit manner. In a lumped application of SNOW-17 all the factors that
control the typical accumulation and melt patterns over the area being
modeled are included in the area depletion algorithm. This includes
spatial variations caused by typical temperature, precipitation, and
melt rate patterns, as well as implicit variability due to such things
as how the ratio of the actual melt rate over the snow covered area to
the total area melt rate varies as the snow cover is depleted and how
snow is redistributed by wind after it reaches the ground. A distributed
application of SNOW-17 wouldn=t directly account for all these factors
and thus, would likely produce biased results as compared to the lumped
application. Some adjustment to the distributed parameters derived from
a lumped calibration would likely be necessary. A few years of
distributed input would probably be needed to make these modifications

c\. A distributed application of the SNOW-17 model could be updated
operationally based on information derived from an
energy-and-mass-balance model in a similar manner to that described
previously in this section for a lumped application of SNOW-17 under
item 3 of AHow to Utilize Energy Budget Computations.@ Updates would be
applied grid cell by grid cell rather than a lumped basis.

d\. There is undoubtedly a benefit to be gained by running
rainfall-runoff and channel system models in a distributed manner for
watersheds where it has been shown that rainfall variability has a
significant effect on hydrograph response. Whether it is essential from
a modeling perspective and whether improved results can be obtained by
running the snow model in a distributed mode for such watersheds needs
to be verified. It might be possible to run the snow model in a lumped
manner, as long as convective events with spatially varying rainfall
patterns are unlikely during periods when snow exists. Many watersheds
that fall into this category are in the central and northern Great
Plains region of the U.S.. In these cases there should not be much
spatial variability in air temperature and model parameters. In order to
benefit by applying the snow model in a distributed manner in this
region one would have to deal with problems in obtaining good spatial
estimates of precipitation during snow events and the redistribution of
the snow cover by wind (frequently in this region much of the snow ends
up in drifts, ditches, hedgerows, etc.).

In mountainous regions with large amounts of snow there are some
potential advantages to running the snow model in a distributed manner.
The possible benefits occur primarily at the beginning and end of the
snowmelt season. Benefits could also occur during rain-on-snow events.
Early in the melt season the snow can be melting in some parts of a
watershed while not in other parts (primarily due to elevation and
aspect differences). Later in the melt season when significant bare
ground exists, a lumped application can provide enough melt water to
keep the soil saturated, whereas in reality the soil in those areas that
have been free of snow for some time may be quite dry. A distributed
application has the potential to improve simulations when rain occurs on
an area partially covered by snow. The use of elevation zones allows
lumped applications to partly simulate these situations, but a
distributed version of the model could likely provide further
improvements. During rain-on-snow events a distributed application has
the potential to better reproduce the watershed response by knowing more
about where the rain is occurring. The biggest question with running the
snow model in a distributed manner in mountainous regions is whether all
the factors that are included in the areal depletion curve can be
adequately incorporated into the distributed version. Overall, for most
of the mountainous regions of the U.S., while there is the potential to
improve snowmelt runoff simulations by applying SNOW-17 in a distributed
manner, it is my guess that substantial improvements are unlikely.

3\. One item that needs to be taken into account when considering
whether to run hydrologic models in a distributed mode for river
forecasting is the requirement for and the impact on extended
probabilistic predictions. In some regions there is little memory in the
current state of the hydrologic system or the impact of current
conditions are only relevant for a fairly short period into the future.
In these cases the ensemble of potential future scenarios can likely be
generated in a distributed manner from meteorological predictions and
limited historical data in order to produce short term probabilistic
flood forecasts. Also the computational requirements are probably
manageable. However, in most regions where runoff from snow is
significant the current state of the snow cover has a major impact on
the streamflow that can result for a considerable period into the
future. In these regions ESP products, in many cases extending months
into the future, are very important to the RFC=s clients. Possible
streamflow ensembles are produced by utilizing historical estimates of
the model input variables with possible modifications based on
meteorological predictions. Many potential input scenarios are needed to
adequately define the probability distribution of the future streamflow.
With a lumped model, the historical traces that were generated in
conjunction with the calibration process are used for ESP runs. In the
case of a distributed application, it is unlikely that gridded
historical data estimates could be reasonably generated for a
sufficiently long period due to data availability and resource
limitations. This would certainly be the case for an energy budget snow
model, however, for a distributed application of SNOW-17 it would depend
on whether gridded data fields could be derived from historical lumped
MAP and MAT time series or whether new methods involving additional data
are being used to produce gridded precipitation and temperature values.
It will take many years to accumulate a sufficiently long record for ESP
applications by archiving real time gridded data fields. Also, in order
to use such archived records for ESP runs the underlying input and the
algorithms used to produce the gridded fields must be consistent over
time. There appears to be two options in this case. One is to somehow
statistically generate the gridded ensembles of the input variables and
the other is to switch from a distributed to a lumped mode when making
extended ESP runs. The switch could occur for the entire length of the
ESP run or could occur a few days into the future when the skill level
in producing gridded forecasts greatly deteriorates. In the case of the
Sacramento Model this would require that parameter values be altered
when the switch occurs to reflect changes in the temporal and spatial
scale of the application. In the case of SNOW-17 it would require
utilizing the areal depletion curve to account for the effects partial
snow cover. Either the rules for changing parameter values or two sets
of parameters would need to be available in order to switch from a
distributed to a lumped mode when making an extended ESP runs.

**Conclusions**

My personal recommendations for future efforts in snow modeling for the
NWS Hydrology Program, based on the preceding discussion, are as
follows.

1\. [An energy-and-mass-balance snow model based on the best available
science should be utilized]{.underline}. Such a model will increase the
understanding of the current state of the snow cover and the changes
that will occur based on meteorological forecasts. It will readily allow
for the assimilation of all available snow observations to be used to
update model states. The model should not only be run for observed data
periods, but also for as long into the future as warranted based on the
skill level of forecasting the variables needed for energy budget
computations. In order for such a model to provide maximum benefits high
quality, unbiased estimates of the input data must be available. This
likely means that improvements be made to some of the data fields,
especially precipitation, that are currently used by SNODAS. The model
parameters and coefficients, including those used to downscale
meteorological data and account for vegetation effects, need to be
adjusted so that the model realistically simulates snow accumulation and
ablation over its entire area of application. Even a limited calibration
should involve not only snow observations, but also some streamflow
data.

2\. [The energy-and-mass-balance snow model should be developed,
applied, and maintained at a central location rather than being an
integral part of the RFC forecast system]{.underline}. The expertise
needed to properly apply such a model and the resources, both human and
computational, required to run the model, monitor the input data, and
assimilate observations is more than can be realistically expected at
each RFC where snow computations are important. Also the benefits that
can be obtained by utilizing an energy budget model can fully be
attained by running the model at a central site. The most logical place
for the model is the NOHRSC. It is critical that the NOHRSC be provided
with the resources, again both human and computational, to perform this
function. This effort cannot be dependent on one or two people.
Sufficient human resources are needed so that if key people leave the
NOHRSC the modeling effort will continue to be properly supported.

3\. [The energy-and-mass-balance snow model should be used to provide
objective updates to the states and internal computations of the index
snow model run at the RFCs rather than providing direct input to RFC
runoff models]{.underline}. The most critical updates are for the total
amount of snow, primarily water equivalent, and adjustments to the melt
rates when abnormal meteorological conditions exist. Adjustments to the
melt rates of the RFC model, plus estimates of the uncertainty of these
updates, should be provided for both the observed and future data
periods. All of the updating procedures should recognize that there is
likely not a one-to-one correspondence between the results from each
model. The development of these objective updating procedures should be
a joint effort between NOHRSC and OHD with the NOHRSC having the primary
expertise on the energy-and-mass-balance model and OHD on the RFC snow
model. The RFCs should be frequently consulted and informed regarding
how the procedures might operate and the impacts on RFC operations.

4\. [OHD should conduct research on applying the SNOW-17 model in an
distributed manner]{.underline}. This research should determine how such
an application could be utilized to provide the full range of forecasts,
from short term deterministic to long term probabilistic, required at
the RFCs. The effort should include methods of providing gridded input,
calibration techniques, updating procedures, and how to generate
extended probabilistic predictions. Recommendations for how and when to
use the model in a distributed mode should be developed. It is likely
that there are still many cases in regions with significant snowmelt
runoff where a properly applied lumped version of the snow model
(includes use of elevation zones in mountainous areas) will provide
results that are at least as good as a distributed application.

5\. [There should be considerably more effort devoted to making sure
that the data used operationally for the SNOW-17 model are unbiased as
compared to that used for calibration]{.underline}. A number of problems
that the RFCs are experiencing when using the model in real time are
likely not due to model deficiencies, but are the result of using bias
data. The RFCs need to follow appropriate procedures to make sure that
mean areal data estimates from their historical and operational networks
produce the same long term averages. OHD needs to correct the problem
caused by having different temperature data and algorithms used to
compute historical MAT values than are used to generate MAT estimates
with OFS.

6\. [Changes should not be made to the existing RFC index snow model,
SNOW-17, unless they are clearly needed and will improve model
performance when tested over a wide range of climatic
conditions]{.underline}. The recent addition of depth computations is an
example of a worthwhile enhancement. The focus in the future should be
on how to best update the SNOW-17 model based on energy-and-mass-balance
model information and how to utilize SNOW-17 in a distributed manner.
Considerable time and resources could be expended trying to add
additional variables, such as dew point and wind, to the index
computations or utilizing a dynamic wind function. These resources would
be better spent on developing objective procedures for updating SNOW-17
based on energy budget model computations.

7\. [Continued training should be provided to the RFCs on all aspects of
snow modeling]{.underline}. There is a need to improve the ability of
RFC personnel to properly calibrate and apply the SNOW-17 model. There
is also a need for RFC personnel to understand the basics of the
energy-and-mass-balance model and especially how information obtained
from that model can be used to improve RFC operations.

**References**

Anderson, Eric A (1973) National Weather Service River Forecast System -
Snow Accumulation and Ablation Model, *NOAA Technical Memorandum NWS
HYDRO-17,* U.S. Dept. of Commerce, National Weather Service, Silver
Spring, MD, 217 pp.

Anderson, Eric A (1976) A Point Energy and Mass Balance Model of a Snow
Cover, *NOAA Technical Report NWS 19,* Dept. of Commerce, National
Weather Service, Silver Spring,

150 pp.

Anderson, Eric (2002) Calibration of Conceptual Hydrologic Models for
Use in River Forecasting (available online at
www.nws.noaa.gov/oh/hrl/calb/calibration1102/main.htm).

Carroll, Tom, Don Cline, Greg Fall, Anders Nilsson, Long Li, and Andy
Rost (2001) NOHRSC Operations and the Simulation of Snow Cover
Properties for the Coterminous U.S., *Proceedings of the 69^th^ Annual
Western Snow Conference,* Sun Valley, ID, pp 1-10.

Day, Gerald N. (1990) A Methodology for Updating a Conceptual Snow Model
With Snow Measurements, *NOAA Technical Report NWS 43,* Dept. of
Commerce, National Weather Service, Silver Spring, MD, 133 pp.

Jordan, Rachel (1991) A One-Dimensional Temperature Model for a Snow
Cover - Technical Documentation for SNTHERM.89, *Special Report 91-16,*
U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, NH,
49 pp.

Office of Hydrology (1998), Northeast Floods of January 1996, *NOAA
Natural Disaster Survey Report,* Office of Hydrology, National Weather
Service, Silver Spring, MD, 99 pp.

Appendix 3

HL Comments on

'Reflections on Future Directions in Snow Modeling for the

Hydrology Program of the National Weather Service'

by Eric Anderson

HL agrees the ideas presented in Appendix 2 and sees them as an ideal
starting point for more detailed planning. As stated in section 4.1, the
primary emphasis of our R&D strategy for advanced snow modeling is to
examine the data quality issues. As this work progresses, we will
re-evaluate the ideas of modifying Snow-17 to add other variables such
as wind speed and dew point. For example, if the data analyses show that
operational energy budget modeling appears feasible, then there is less
reason to investigate potential Snow-17 modifications. On the other
hand, the consideration of possible modifications to Snow-17 may be more
appropriate if the data analyses show that operational energy budget
snow modeling is infeasible for the near future. [Any ideas for
significant changes to Snow-17 will be accompanied by a clear, precise
explanation of why the change is needed. If a solution is proposed, a
detailed description of what might be done and how it will be verified
will be presented for comment.]{.mark}